%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW390+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:26:06 EDT 2023

% Result   : Theorem 1.76s 2.48s
% Output   : Proof 1.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW390+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 22:39:20 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 1.76/2.48  
% 1.76/2.48  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.76/2.48  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.76/2.48  %-----------------------------------------------------
% 1.76/2.48  ncf(matrix, plain, [(52490 ^ _780205) ^ [] : [-(v_P(52487 ^ [], 52488 ^ []))], (52492 ^ _780205) ^ [_2083162, _2083164] : [c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), _2083164), v_c), _2083162)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))], (2 ^ _780205) ^ [_780235] : [-(_780235 = _780235)], (4 ^ _780205) ^ [_780258, _780260] : [_780260 = _780258, -(_780258 = _780260)], (10 ^ _780205) ^ [_780331, _780333, _780335] : [-(_780335 = _780331), _780335 = _780333, _780333 = _780331], (20 ^ _780205) ^ [_780468, _780470, _780472, _780474, _780476, _780478, _780480, _780482, _780484, _780486, _780488, _780490] : [-(c_Finite__Set_Ofolding__image__simple__idem(_780488, _780484, _780480, _780476, _780472, _780468)), c_Finite__Set_Ofolding__image__simple__idem(_780490, _780486, _780482, _780478, _780474, _780470), _780490 = _780488, _780486 = _780484, _780482 = _780480, _780478 = _780476, _780474 = _780472, _780470 = _780468], (50 ^ _780205) ^ [_781013, _781015, _781017, _781019, _781021, _781023] : [-(c_Big__Operators_Osemilattice__big(_781021, _781017, _781013)), c_Big__Operators_Osemilattice__big(_781023, _781019, _781015), _781023 = _781021, _781019 = _781017, _781015 = _781013], (68 ^ _780205) ^ [_781282, _781284, _781286, _781288, _781290, _781292] : [-(c_Finite__Set_Ofolding__one(_781290, _781286, _781282)), c_Finite__Set_Ofolding__one(_781292, _781288, _781284), _781292 = _781290, _781288 = _781286, _781284 = _781282], (86 ^ _780205) ^ [_781551, _781553, _781555, _781557, _781559, _781561, _781563, _781565, _781567, _781569, _781571, _781573] : [-(c_Nitpick_Ofold__graph_H(_781571, _781567, _781563, _781559, _781555, _781551)), c_Nitpick_Ofold__graph_H(_781573, _781569, _781565, _781561, _781557, _781553), _781573 = _781571, _781569 = _781567, _781565 = _781563, _781561 = _781559, _781557 = _781555, _781553 = _781551], (116 ^ _780205) ^ [_782096, _782098, _782100, _782102, _782104, _782106, _782108, _782110, _782112, _782114, _782116, _782118] : [-(c_Finite__Set_Ofolding__image__simple(_782116, _782112, _782108, _782104, _782100, _782096)), c_Finite__Set_Ofolding__image__simple(_782118, _782114, _782110, _782106, _782102, _782098), _782118 = _782116, _782114 = _782112, _782110 = _782108, _782106 = _782104, _782102 = _782100, _782098 = _782096], (146 ^ _780205) ^ [_782641, _782643, _782645, _782647, _782649, _782651, _782653, _782655, _782657, _782659] : [-(c_Big__Operators_Ocomm__monoid__big(_782657, _782653, _782649, _782645, _782641)), c_Big__Operators_Ocomm__monoid__big(_782659, _782655, _782651, _782647, _782643), _782659 = _782657, _782655 = _782653, _782651 = _782649, _782647 = _782645, _782643 = _782641], (172 ^ _780205) ^ [_783086, _783088] : [-(class_Rings_Odivision__ring__inverse__zero(_783086)), _783088 = _783086, class_Rings_Odivision__ring__inverse__zero(_783088)], (182 ^ _780205) ^ [_783211, _783213] : [-(class_Rings_Odivision__ring(_783211)), _783213 = _783211, class_Rings_Odivision__ring(_783213)], (192 ^ _780205) ^ [_783336, _783338] : [-(class_Fields_Olinordered__field__inverse__zero(_783336)), _783338 = _783336, class_Fields_Olinordered__field__inverse__zero(_783338)], (202 ^ _780205) ^ [_783461, _783463, _783465, _783467] : [-(c_Int_Oiszero(_783465, _783461)), c_Int_Oiszero(_783467, _783463), _783467 = _783465, _783463 = _783461], (216 ^ _780205) ^ [_783654, _783656, _783658, _783660] : [-(c_Nitpick_Orefl_H(_783658, _783654)), c_Nitpick_Orefl_H(_783660, _783656), _783660 = _783658, _783656 = _783654], (230 ^ _780205) ^ [_783847, _783849] : [-(class_Fields_Ofield__inverse__zero(_783847)), _783849 = _783847, class_Fields_Ofield__inverse__zero(_783849)], (240 ^ _780205) ^ [_783972, _783974] : [-(class_Fields_Olinordered__field(_783972)), _783974 = _783972, class_Fields_Olinordered__field(_783974)], (250 ^ _780205) ^ [_784097, _784099] : [-(class_Fields_Ofield(_784097)), _784099 = _784097, class_Fields_Ofield(_784099)], (260 ^ _780205) ^ [_784222, _784224] : [-(c_Nat__Transfer_Ois__nat(_784222)), _784224 = _784222, c_Nat__Transfer_Ois__nat(_784224)], (270 ^ _780205) ^ [_784347, _784349, _784351, _784353, _784355, _784357] : [-(c_Finite__Set_Ofolding__one__idem(_784355, _784351, _784347)), c_Finite__Set_Ofolding__one__idem(_784357, _784353, _784349), _784357 = _784355, _784353 = _784351, _784349 = _784347], (288 ^ _780205) ^ [_784616, _784618, _784620, _784622] : [-(c_FunDef_Oreduction__pair(_784620, _784616)), c_FunDef_Oreduction__pair(_784622, _784618), _784622 = _784620, _784618 = _784616], (302 ^ _780205) ^ [_784809, _784811, _784813, _784815] : [-(c_Nitpick_Owf_H(_784813, _784809)), c_Nitpick_Owf_H(_784815, _784811), _784815 = _784813, _784811 = _784809], (316 ^ _780205) ^ [_785002, _785004] : [-(c_Nitpick_Ounknown(_785002)), _785004 = _785002, c_Nitpick_Ounknown(_785004)], (326 ^ _780205) ^ [_785127, _785129, _785131, _785133] : [-(c_Wellfounded_OwfP(_785131, _785127)), c_Wellfounded_OwfP(_785133, _785129), _785133 = _785131, _785129 = _785127], (340 ^ _780205) ^ [_785320, _785322, _785324, _785326, _785328, _785330, _785332, _785334] : [-(c_Finite__Set_Ofolding(_785332, _785328, _785324, _785320)), c_Finite__Set_Ofolding(_785334, _785330, _785326, _785322), _785334 = _785332, _785330 = _785328, _785326 = _785324, _785322 = _785320], (362 ^ _780205) ^ [_785673, _785675, _785677, _785679, _785681, _785683] : [-(c_Hoare__Mirabelle_Ohoare__valids(_785681, _785677, _785673)), c_Hoare__Mirabelle_Ohoare__valids(_785683, _785679, _785675), _785683 = _785681, _785679 = _785677, _785675 = _785673], (380 ^ _780205) ^ [_785942, _785944, _785946, _785948, _785950, _785952, _785954, _785956] : [-(c_Finite__Set_Ofolding__idem(_785954, _785950, _785946, _785942)), c_Finite__Set_Ofolding__idem(_785956, _785952, _785948, _785944), _785956 = _785954, _785952 = _785950, _785948 = _785946, _785944 = _785942], (402 ^ _780205) ^ [_786295, _786297, _786299, _786301] : [-(c_Relation_Oirrefl(_786299, _786295)), c_Relation_Oirrefl(_786301, _786297), _786301 = _786299, _786297 = _786295], (416 ^ _780205) ^ [_786488, _786490, _786492, _786494, _786496, _786498] : [-(c_Relation_Ototal__on(_786496, _786492, _786488)), c_Relation_Ototal__on(_786498, _786494, _786490), _786498 = _786496, _786494 = _786492, _786490 = _786488], (434 ^ _780205) ^ [_786757, _786759, _786761, _786763, _786765, _786767] : [-(c_Relation_Osingle__valued(_786765, _786761, _786757)), c_Relation_Osingle__valued(_786767, _786763, _786759), _786767 = _786765, _786763 = _786761, _786759 = _786757], (452 ^ _780205) ^ [_787026, _787028] : [-(class_Rings_Oinverse(_787026)), _787028 = _787026, class_Rings_Oinverse(_787028)], (462 ^ _780205) ^ [_787151, _787153, _787155, _787157, _787159, _787161] : [-(c_Nitpick_Oless__frac(_787159, _787155, _787151)), c_Nitpick_Oless__frac(_787161, _787157, _787153), _787161 = _787159, _787157 = _787155, _787153 = _787151], (480 ^ _780205) ^ [_787420, _787422, _787424, _787426, _787428, _787430] : [-(c_Nitpick_Oless__eq__frac(_787428, _787424, _787420)), c_Nitpick_Oless__eq__frac(_787430, _787426, _787422), _787430 = _787428, _787426 = _787424, _787422 = _787420], (498 ^ _780205) ^ [_787689, _787691] : [-(c_Nat__Transfer_Onat__set(_787689)), _787691 = _787689, c_Nat__Transfer_Onat__set(_787691)], (508 ^ _780205) ^ [_787814, _787816, _787818, _787820, _787822, _787824, _787826, _787828] : [-(c_List_Olistrelp(_787826, _787822, _787818, _787814)), c_List_Olistrelp(_787828, _787824, _787820, _787816), _787828 = _787826, _787824 = _787822, _787820 = _787818, _787816 = _787814], (530 ^ _780205) ^ [_788167, _788169] : [-(class_Lattices_Oab__semigroup__idem__mult(_788167)), _788169 = _788167, class_Lattices_Oab__semigroup__idem__mult(_788169)], (540 ^ _780205) ^ [_788292, _788294, _788296, _788298, _788300, _788302] : [-(c_Finite__Set_Ofun__left__comm__idem(_788300, _788296, _788292)), c_Finite__Set_Ofun__left__comm__idem(_788302, _788298, _788294), _788302 = _788300, _788298 = _788296, _788294 = _788292], (558 ^ _780205) ^ [_788561, _788563, _788565, _788567, _788569, _788571, _788573, _788575, _788577, _788579] : [-(c_Typedef_Otype__definition(_788577, _788573, _788569, _788565, _788561)), c_Typedef_Otype__definition(_788579, _788575, _788571, _788567, _788563), _788579 = _788577, _788575 = _788573, _788571 = _788569, _788567 = _788565, _788563 = _788561], (584 ^ _780205) ^ [_789006, _789008, _789010, _789012, _789014, _789016] : [-(c_Finite__Set_Ofun__left__comm(_789014, _789010, _789006)), c_Finite__Set_Ofun__left__comm(_789016, _789012, _789008), _789016 = _789014, _789012 = _789010, _789008 = _789006], (602 ^ _780205) ^ [_789275, _789277] : [-(c_List_Onat__list(_789275)), _789277 = _789275, c_List_Onat__list(_789277)], (612 ^ _780205) ^ [_789400, _789402, _789404, _789406, _789408, _789410, _789412, _789414, _789416, _789418] : [-(c_List_Olist__all2(_789416, _789412, _789408, _789404, _789400)), c_List_Olist__all2(_789418, _789414, _789410, _789406, _789402), _789418 = _789416, _789414 = _789412, _789410 = _789408, _789406 = _789404, _789402 = _789400], (638 ^ _780205) ^ [_789845, _789847, _789849, _789851] : [-(c_List_Olinorder__class_Osorted(_789849, _789845)), c_List_Olinorder__class_Osorted(_789851, _789847), _789851 = _789849, _789847 = _789845], (652 ^ _780205) ^ [_790038, _790040, _790042, _790044] : [-(c_FunDef_Ois__measure(_790042, _790038)), c_FunDef_Ois__measure(_790044, _790040), _790044 = _790042, _790040 = _790038], (666 ^ _780205) ^ [_790231, _790233, _790235, _790237, _790239, _790241, _790243, _790245] : [-(c_Nat__Transfer_Otransfer__morphism(_790243, _790239, _790235, _790231)), c_Nat__Transfer_Otransfer__morphism(_790245, _790241, _790237, _790233), _790245 = _790243, _790241 = _790239, _790237 = _790235, _790233 = _790231], (688 ^ _780205) ^ [_790584, _790586, _790588, _790590, _790592, _790594] : [-(c_List_Olist__ex1(_790592, _790588, _790584)), c_List_Olist__ex1(_790594, _790590, _790586), _790594 = _790592, _790590 = _790588, _790586 = _790584], (706 ^ _780205) ^ [_790853, _790855, _790857, _790859, _790861, _790863] : [-(c_List_Oall__interval__int(_790861, _790857, _790853)), c_List_Oall__interval__int(_790863, _790859, _790855), _790863 = _790861, _790859 = _790857, _790855 = _790853], (724 ^ _780205) ^ [_791122, _791124, _791126, _791128] : [-(c_Predicate_Oreflp(_791126, _791122)), c_Predicate_Oreflp(_791128, _791124), _791128 = _791126, _791124 = _791122], (738 ^ _780205) ^ [_791315, _791317, _791319, _791321, _791323, _791325, _791327, _791329] : [-(c_Wellfounded_Omax__extp(_791327, _791323, _791319, _791315)), c_Wellfounded_Omax__extp(_791329, _791325, _791321, _791317), _791329 = _791327, _791325 = _791323, _791321 = _791319, _791317 = _791315], (760 ^ _780205) ^ [_791668, _791670, _791672, _791674] : [-(c_Wellfounded_Oacyclic(_791672, _791668)), c_Wellfounded_Oacyclic(_791674, _791670), _791674 = _791672, _791670 = _791668], (774 ^ _780205) ^ [_791861, _791863, _791865, _791867] : [-(c_Relation_Oantisym(_791865, _791861)), c_Relation_Oantisym(_791867, _791863), _791867 = _791865, _791863 = _791861], (788 ^ _780205) ^ [_792054, _792056, _792058, _792060, _792062, _792064] : [-(c_Equiv__Relations_Oequiv(_792062, _792058, _792054)), c_Equiv__Relations_Oequiv(_792064, _792060, _792056), _792064 = _792062, _792060 = _792058, _792056 = _792054], (806 ^ _780205) ^ [_792323, _792325, _792327, _792329] : [-(c_Relation_Otrans(_792327, _792323)), c_Relation_Otrans(_792329, _792325), _792329 = _792327, _792325 = _792323], (820 ^ _780205) ^ [_792516, _792518, _792520, _792522] : [-(c_Relation_Osym(_792520, _792516)), c_Relation_Osym(_792522, _792518), _792522 = _792520, _792518 = _792516], (834 ^ _780205) ^ [_792709, _792711, _792713, _792715] : [-(c_Predicate_Osymp(_792713, _792709)), c_Predicate_Osymp(_792715, _792711), _792715 = _792713, _792711 = _792709], (848 ^ _780205) ^ [_792902, _792904, _792906, _792908] : [-(c_Predicate_Otransp(_792906, _792902)), c_Predicate_Otransp(_792908, _792904), _792908 = _792906, _792904 = _792902], (862 ^ _780205) ^ [_793095, _793097, _793099, _793101] : [-(c_Equiv__Relations_Opart__equivp(_793099, _793095)), c_Equiv__Relations_Opart__equivp(_793101, _793097), _793101 = _793099, _793097 = _793095], (876 ^ _780205) ^ [_793288, _793290, _793292, _793294, _793296, _793298, _793300, _793302] : [-(c_Fun_Oinj__on(_793300, _793296, _793292, _793288)), c_Fun_Oinj__on(_793302, _793298, _793294, _793290), _793302 = _793300, _793298 = _793296, _793294 = _793292, _793290 = _793288], (898 ^ _780205) ^ [_793641, _793643, _793645, _793647, _793649, _793651, _793653, _793655, _793657, _793659] : [-(c_Fun_Obij__betw(_793657, _793653, _793649, _793645, _793641)), c_Fun_Obij__betw(_793659, _793655, _793651, _793647, _793643), _793659 = _793657, _793655 = _793653, _793651 = _793649, _793647 = _793645, _793643 = _793641], (924 ^ _780205) ^ [_794086, _794088, _794090, _794092, _794094, _794096] : [-(c_Relation_Orefl__on(_794094, _794090, _794086)), c_Relation_Orefl__on(_794096, _794092, _794088), _794096 = _794094, _794092 = _794090, _794088 = _794086], (942 ^ _780205) ^ [_794355, _794357, _794359, _794361] : [-(c_Equiv__Relations_Oequivp(_794359, _794355)), c_Equiv__Relations_Oequivp(_794361, _794357), _794361 = _794359, _794357 = _794355], (956 ^ _780205) ^ [_794548, _794550, _794552, _794554] : [-(c_Wellfounded_Owf(_794552, _794548)), c_Wellfounded_Owf(_794554, _794550), _794554 = _794552, _794550 = _794548], (970 ^ _780205) ^ [_794741, _794743, _794745, _794747, _794749, _794751, _794753, _794755, _794757, _794759, _794761, _794763] : [-(c_Equiv__Relations_Ocongruent2(_794761, _794757, _794753, _794749, _794745, _794741)), c_Equiv__Relations_Ocongruent2(_794763, _794759, _794755, _794751, _794747, _794743), _794763 = _794761, _794759 = _794757, _794755 = _794753, _794751 = _794749, _794747 = _794745, _794743 = _794741], (1000 ^ _780205) ^ [_795286, _795288, _795290, _795292, _795294, _795296, _795298, _795300] : [-(c_Equiv__Relations_Ocongruent(_795298, _795294, _795290, _795286)), c_Equiv__Relations_Ocongruent(_795300, _795296, _795292, _795288), _795300 = _795298, _795296 = _795294, _795292 = _795290, _795288 = _795286], (1022 ^ _780205) ^ [_795639, _795641, _795643, _795645, _795647, _795649] : [-(c_List_Olist__all(_795647, _795643, _795639)), c_List_Olist__all(_795649, _795645, _795641), _795649 = _795647, _795645 = _795643, _795641 = _795639], (1040 ^ _780205) ^ [_795908, _795910, _795912, _795914, _795916, _795918] : [-(c_List_Olist__ex(_795916, _795912, _795908)), c_List_Olist__ex(_795918, _795914, _795910), _795918 = _795916, _795914 = _795912, _795910 = _795908], (1058 ^ _780205) ^ [_796177, _796179, _796181, _796183, _796185, _796187] : [-(c_List_Oall__interval__nat(_796185, _796181, _796177)), c_List_Oall__interval__nat(_796187, _796183, _796179), _796187 = _796185, _796183 = _796181, _796179 = _796177], (1076 ^ _780205) ^ [_796446, _796448, _796450, _796452, _796454, _796456, _796458, _796460, _796462, _796464] : [-(c_Finite__Set_Ofolding__image(_796462, _796458, _796454, _796450, _796446)), c_Finite__Set_Ofolding__image(_796464, _796460, _796456, _796452, _796448), _796464 = _796462, _796460 = _796458, _796456 = _796454, _796452 = _796450, _796448 = _796446], (1102 ^ _780205) ^ [_796891, _796893] : [-(class_Lattices_Obounded__lattice(_796891)), _796893 = _796891, class_Lattices_Obounded__lattice(_796893)], (1112 ^ _780205) ^ [_797016, _797018] : [-(class_Rings_Olinordered__semiring__1__strict(_797016)), _797018 = _797016, class_Rings_Olinordered__semiring__1__strict(_797018)], (1122 ^ _780205) ^ [_797141, _797143] : [-(class_Groups_Oordered__ab__group__add__abs(_797141)), _797143 = _797141, class_Groups_Oordered__ab__group__add__abs(_797143)], (1132 ^ _780205) ^ [_797266, _797268] : [-(class_Groups_Olinordered__ab__group__add(_797266)), _797268 = _797266, class_Groups_Olinordered__ab__group__add(_797268)], (1142 ^ _780205) ^ [_797391, _797393] : [-(class_Rings_Oring__1__no__zero__divisors(_797391)), _797393 = _797391, class_Rings_Oring__1__no__zero__divisors(_797393)], (1152 ^ _780205) ^ [_797516, _797518] : [-(class_Rings_Olinordered__ring__strict(_797516)), _797518 = _797516, class_Rings_Olinordered__ring__strict(_797518)], (1162 ^ _780205) ^ [_797641, _797643] : [-(class_Rings_Oring__no__zero__divisors(_797641)), _797643 = _797641, class_Rings_Oring__no__zero__divisors(_797643)], (1172 ^ _780205) ^ [_797766, _797768] : [-(class_Rings_Olinordered__semiring__1(_797766)), _797768 = _797766, class_Rings_Olinordered__semiring__1(_797768)], (1182 ^ _780205) ^ [_797891, _797893] : [-(class_Groups_Oordered__ab__group__add(_797891)), _797893 = _797891, class_Groups_Oordered__ab__group__add(_797893)], (1192 ^ _780205) ^ [_798016, _798018] : [-(class_Rings_Oordered__ring__abs(_798016)), _798018 = _798016, class_Rings_Oordered__ring__abs(_798018)], (1202 ^ _780205) ^ [_798141, _798143] : [-(class_Rings_Olinordered__ring(_798141)), _798143 = _798141, class_Rings_Olinordered__ring(_798143)], (1212 ^ _780205) ^ [_798266, _798268] : [-(class_Rings_Olinordered__idom(_798266)), _798268 = _798266, class_Rings_Olinordered__idom(_798268)], (1222 ^ _780205) ^ [_798391, _798393] : [-(class_Groups_Oab__group__add(_798391)), _798393 = _798391, class_Groups_Oab__group__add(_798393)], (1232 ^ _780205) ^ [_798516, _798518] : [-(class_Rings_Oordered__ring(_798516)), _798518 = _798516, class_Rings_Oordered__ring(_798518)], (1242 ^ _780205) ^ [_798641, _798643] : [-(class_Rings_Ocomm__ring__1(_798641)), _798643 = _798641, class_Rings_Ocomm__ring__1(_798643)], (1252 ^ _780205) ^ [_798766, _798768] : [-(class_Groups_Ogroup__add(_798766)), _798768 = _798766, class_Groups_Ogroup__add(_798768)], (1262 ^ _780205) ^ [_798891, _798893] : [-(class_Divides_Oring__div(_798891)), _798893 = _798891, class_Divides_Oring__div(_798893)], (1272 ^ _780205) ^ [_799016, _799018] : [-(class_Rings_Ocomm__ring(_799016)), _799018 = _799016, class_Rings_Ocomm__ring(_799018)], (1282 ^ _780205) ^ [_799141, _799143] : [-(class_Int_Oring__char__0(_799141)), _799143 = _799141, class_Int_Oring__char__0(_799143)], (1292 ^ _780205) ^ [_799266, _799268] : [-(class_Int_Onumber__ring(_799266)), _799268 = _799266, class_Int_Onumber__ring(_799268)], (1302 ^ _780205) ^ [_799391, _799393] : [-(class_Groups_Osgn__if(_799391)), _799393 = _799391, class_Groups_Osgn__if(_799393)], (1312 ^ _780205) ^ [_799516, _799518] : [-(class_Groups_Oabs__if(_799516)), _799518 = _799516, class_Groups_Oabs__if(_799518)], (1322 ^ _780205) ^ [_799641, _799643] : [-(class_Rings_Oring__1(_799641)), _799643 = _799641, class_Rings_Oring__1(_799643)], (1332 ^ _780205) ^ [_799766, _799768] : [-(class_Rings_Oring(_799766)), _799768 = _799766, class_Rings_Oring(_799768)], (1342 ^ _780205) ^ [_799891, _799893] : [-(class_Rings_Oidom(_799891)), _799893 = _799891, class_Rings_Oidom(_799893)], (1352 ^ _780205) ^ [_800016, _800018] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_800016)), _800018 = _800016, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_800018)], (1362 ^ _780205) ^ [_800141, _800143] : [-(class_Orderings_Owellorder(_800141)), _800143 = _800141, class_Orderings_Owellorder(_800143)], (1372 ^ _780205) ^ [_800266, _800268] : [-(class_Complete__Lattice_Ocomplete__lattice(_800266)), _800268 = _800266, class_Complete__Lattice_Ocomplete__lattice(_800268)], (1382 ^ _780205) ^ [_800391, _800393] : [-(class_Lattices_Obounded__lattice__top(_800391)), _800393 = _800391, class_Lattices_Obounded__lattice__top(_800393)], (1392 ^ _780205) ^ [_800516, _800518] : [-(class_Lattices_Obounded__lattice__bot(_800516)), _800518 = _800516, class_Lattices_Obounded__lattice__bot(_800518)], (1402 ^ _780205) ^ [_800641, _800643] : [-(class_Lattices_Osemilattice__sup(_800641)), _800643 = _800641, class_Lattices_Osemilattice__sup(_800643)], (1412 ^ _780205) ^ [_800766, _800768] : [-(class_Lattices_Osemilattice__inf(_800766)), _800768 = _800766, class_Lattices_Osemilattice__inf(_800768)], (1422 ^ _780205) ^ [_800891, _800893] : [-(class_Lattices_Odistrib__lattice(_800891)), _800893 = _800891, class_Lattices_Odistrib__lattice(_800893)], (1432 ^ _780205) ^ [_801016, _801018] : [-(class_Lattices_Oboolean__algebra(_801016)), _801018 = _801016, class_Lattices_Oboolean__algebra(_801018)], (1442 ^ _780205) ^ [_801141, _801143] : [-(class_Lattices_Olattice(_801141)), _801143 = _801141, class_Lattices_Olattice(_801143)], (1452 ^ _780205) ^ [_801266, _801268] : [-(class_Orderings_Otop(_801266)), _801268 = _801266, class_Orderings_Otop(_801268)], (1462 ^ _780205) ^ [_801391, _801393] : [-(class_Orderings_Obot(_801391)), _801393 = _801391, class_Orderings_Obot(_801393)], (1472 ^ _780205) ^ [_801516, _801518] : [-(class_Groups_Ouminus(_801516)), _801518 = _801516, class_Groups_Ouminus(_801518)], (1482 ^ _780205) ^ [_801641, _801643] : [-(class_Lazy__Sequence_Osmall__lazy(_801641)), _801643 = _801641, class_Lazy__Sequence_Osmall__lazy(_801643)], (1492 ^ _780205) ^ [_801766, _801768] : [-(class_Finite__Set_Ofinite(_801766)), _801768 = _801766, class_Finite__Set_Ofinite(_801768)], (1502 ^ _780205) ^ [_801891, _801893] : [-(class_Enum_Oenum(_801891)), _801893 = _801891, class_Enum_Oenum(_801893)], (1512 ^ _780205) ^ [_802016, _802018] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_802016)), _802018 = _802016, class_Groups_Oordered__cancel__ab__semigroup__add(_802018)], (1522 ^ _780205) ^ [_802141, _802143] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_802141)), _802143 = _802141, class_Groups_Oordered__ab__semigroup__add__imp__le(_802143)], (1532 ^ _780205) ^ [_802266, _802268] : [-(class_Rings_Olinordered__comm__semiring__strict(_802266)), _802268 = _802266, class_Rings_Olinordered__comm__semiring__strict(_802268)], (1542 ^ _780205) ^ [_802391, _802393] : [-(class_Groups_Olinordered__ab__semigroup__add(_802391)), _802393 = _802391, class_Groups_Olinordered__ab__semigroup__add(_802393)], (1552 ^ _780205) ^ [_802516, _802518] : [-(class_Rings_Olinordered__semiring__strict(_802516)), _802518 = _802516, class_Rings_Olinordered__semiring__strict(_802518)], (1562 ^ _780205) ^ [_802641, _802643] : [-(class_Groups_Oordered__ab__semigroup__add(_802641)), _802643 = _802641, class_Groups_Oordered__ab__semigroup__add(_802643)], (1572 ^ _780205) ^ [_802766, _802768] : [-(class_Groups_Oordered__comm__monoid__add(_802766)), _802768 = _802766, class_Groups_Oordered__comm__monoid__add(_802768)], (1582 ^ _780205) ^ [_802891, _802893] : [-(class_Groups_Ocancel__ab__semigroup__add(_802891)), _802893 = _802891, class_Groups_Ocancel__ab__semigroup__add(_802893)], (1592 ^ _780205) ^ [_803016, _803018] : [-(class_Rings_Oordered__cancel__semiring(_803016)), _803018 = _803016, class_Rings_Oordered__cancel__semiring(_803018)], (1602 ^ _780205) ^ [_803141, _803143] : [-(class_Rings_Oordered__comm__semiring(_803141)), _803143 = _803141, class_Rings_Oordered__comm__semiring(_803143)], (1612 ^ _780205) ^ [_803266, _803268] : [-(class_Groups_Ocancel__semigroup__add(_803266)), _803268 = _803266, class_Groups_Ocancel__semigroup__add(_803268)], (1622 ^ _780205) ^ [_803391, _803393] : [-(class_Rings_Olinordered__semiring(_803391)), _803393 = _803391, class_Rings_Olinordered__semiring(_803393)], (1632 ^ _780205) ^ [_803516, _803518] : [-(class_Rings_Olinordered__semidom(_803516)), _803518 = _803516, class_Rings_Olinordered__semidom(_803518)], (1642 ^ _780205) ^ [_803641, _803643] : [-(class_Groups_Oab__semigroup__mult(_803641)), _803643 = _803641, class_Groups_Oab__semigroup__mult(_803643)], (1652 ^ _780205) ^ [_803766, _803768] : [-(class_Groups_Ocomm__monoid__mult(_803766)), _803768 = _803766, class_Groups_Ocomm__monoid__mult(_803768)], (1662 ^ _780205) ^ [_803891, _803893] : [-(class_Groups_Oab__semigroup__add(_803891)), _803893 = _803891, class_Groups_Oab__semigroup__add(_803893)], (1672 ^ _780205) ^ [_804016, _804018] : [-(class_Rings_Oordered__semiring(_804016)), _804018 = _804016, class_Rings_Oordered__semiring(_804018)], (1682 ^ _780205) ^ [_804141, _804143] : [-(class_Rings_Ono__zero__divisors(_804141)), _804143 = _804141, class_Rings_Ono__zero__divisors(_804143)], (1692 ^ _780205) ^ [_804266, _804268] : [-(class_Groups_Ocomm__monoid__add(_804266)), _804268 = _804266, class_Groups_Ocomm__monoid__add(_804268)], (1702 ^ _780205) ^ [_804391, _804393] : [-(class_Rings_Ocomm__semiring__1(_804391)), _804393 = _804391, class_Rings_Ocomm__semiring__1(_804393)], (1712 ^ _780205) ^ [_804516, _804518] : [-(class_Groups_Osemigroup__add(_804516)), _804518 = _804516, class_Groups_Osemigroup__add(_804518)], (1722 ^ _780205) ^ [_804641, _804643] : [-(class_Divides_Osemiring__div(_804641)), _804643 = _804641, class_Divides_Osemiring__div(_804643)], (1732 ^ _780205) ^ [_804766, _804768] : [-(class_Rings_Ocomm__semiring(_804766)), _804768 = _804766, class_Rings_Ocomm__semiring(_804768)], (1742 ^ _780205) ^ [_804891, _804893] : [-(class_Nat_Osemiring__char__0(_804891)), _804893 = _804891, class_Nat_Osemiring__char__0(_804893)], (1752 ^ _780205) ^ [_805016, _805018] : [-(class_Rings_Ozero__neq__one(_805016)), _805018 = _805016, class_Rings_Ozero__neq__one(_805018)], (1762 ^ _780205) ^ [_805141, _805143] : [-(class_Orderings_Opreorder(_805141)), _805143 = _805141, class_Orderings_Opreorder(_805143)], (1772 ^ _780205) ^ [_805266, _805268] : [-(class_Orderings_Olinorder(_805266)), _805268 = _805266, class_Orderings_Olinorder(_805268)], (1782 ^ _780205) ^ [_805391, _805393] : [-(class_Groups_Omonoid__mult(_805391)), _805393 = _805391, class_Groups_Omonoid__mult(_805393)], (1792 ^ _780205) ^ [_805516, _805518] : [-(class_Groups_Omonoid__add(_805516)), _805518 = _805516, class_Groups_Omonoid__add(_805518)], (1802 ^ _780205) ^ [_805641, _805643] : [-(class_Rings_Osemiring__1(_805641)), _805643 = _805641, class_Rings_Osemiring__1(_805643)], (1812 ^ _780205) ^ [_805766, _805768] : [-(class_Rings_Osemiring__0(_805766)), _805768 = _805766, class_Rings_Osemiring__0(_805768)], (1822 ^ _780205) ^ [_805891, _805893] : [-(class_Rings_Omult__zero(_805891)), _805893 = _805891, class_Rings_Omult__zero(_805893)], (1832 ^ _780205) ^ [_806016, _806018] : [-(class_Orderings_Oorder(_806016)), _806018 = _806016, class_Orderings_Oorder(_806018)], (1842 ^ _780205) ^ [_806141, _806143] : [-(class_Rings_Osemiring(_806141)), _806143 = _806141, class_Rings_Osemiring(_806143)], (1852 ^ _780205) ^ [_806266, _806268] : [-(class_Orderings_Oord(_806266)), _806268 = _806266, class_Orderings_Oord(_806268)], (1862 ^ _780205) ^ [_806391, _806393] : [-(class_Groups_Ominus(_806391)), _806393 = _806391, class_Groups_Ominus(_806393)], (1872 ^ _780205) ^ [_806516, _806518] : [-(class_Power_Opower(_806516)), _806518 = _806516, class_Power_Opower(_806518)], (1882 ^ _780205) ^ [_806641, _806643] : [-(class_Groups_Ozero(_806641)), _806643 = _806641, class_Groups_Ozero(_806643)], (1892 ^ _780205) ^ [_806766, _806768] : [-(class_Int_Onumber(_806766)), _806768 = _806766, class_Int_Onumber(_806768)], (1902 ^ _780205) ^ [_806891, _806893] : [-(class_Groups_Oone(_806891)), _806893 = _806891, class_Groups_Oone(_806893)], (1912 ^ _780205) ^ [_807016, _807018] : [-(class_Rings_Odvd(_807016)), _807018 = _807016, class_Rings_Odvd(_807018)], (1922 ^ _780205) ^ [_807141, _807143] : [-(class_Nat_Osize(_807141)), _807143 = _807141, class_Nat_Osize(_807143)], (1932 ^ _780205) ^ [_807266, _807268] : [-(hBOOL(_807266)), _807268 = _807266, hBOOL(_807268)], (1942 ^ _780205) ^ [_807391, _807393, _807395, _807397] : [-(v_P(_807395, _807391)), v_P(_807397, _807393), _807397 = _807395, _807393 = _807391], (1956 ^ _780205) ^ [_807580, _807582, _807584, _807586, _807588, _807590] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_807588, _807584, _807580)), c_Hoare__Mirabelle_Ohoare__derivs(_807590, _807586, _807582), _807590 = _807588, _807586 = _807584, _807582 = _807580], (1974 ^ _780205) ^ [_808649, _808651, _808653, _808655, _808657, _808659, _808661, _808663] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_808663, _808659, _808655, _808651) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_808661, _808657, _808653, _808649)), _808663 = _808661, _808659 = _808657, _808655 = _808653, _808651 = _808649], (1992 ^ _780205) ^ [_808950, _808952, _808954, _808956, _808958, _808960, _808962, _808964] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_808964, _808960, _808956, _808952) = c_Hoare__Mirabelle_Otriple_Otriple__case(_808962, _808958, _808954, _808950)), _808964 = _808962, _808960 = _808958, _808956 = _808954, _808952 = _808950], (2010 ^ _780205) ^ [_809251, _809253, _809255, _809257, _809259, _809261] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_809261, _809257, _809253) = c_Hoare__Mirabelle_Otriple_Otriple__size(_809259, _809255, _809251)), _809261 = _809259, _809257 = _809255, _809253 = _809251], (2024 ^ _780205) ^ [_809472, _809474] : [_809474 = _809472, -(c_Nat_Osemiring__1__class_ONats(_809474) = c_Nat_Osemiring__1__class_ONats(_809472))], (2030 ^ _780205) ^ [_809557, _809559] : [_809559 = _809557, -(c_Int_Osucc(_809559) = c_Int_Osucc(_809557))], (2036 ^ _780205) ^ [_809642, _809644, _809646, _809648] : [-(c_SMT_Oz3mod(_809648, _809644) = c_SMT_Oz3mod(_809646, _809642)), _809648 = _809646, _809644 = _809642], (2046 ^ _780205) ^ [_809791, _809793, _809795, _809797] : [-(c_SMT_Oz3div(_809797, _809793) = c_SMT_Oz3div(_809795, _809791)), _809797 = _809795, _809793 = _809791], (2056 ^ _780205) ^ [_809940, _809942, _809944, _809946] : [-(c_Int_Onat__aux(_809946, _809942) = c_Int_Onat__aux(_809944, _809940)), _809946 = _809944, _809942 = _809940], (2066 ^ _780205) ^ [_810089, _810091] : [_810091 = _810089, -(c_Int_Oring__1__class_OInts(_810091) = c_Int_Oring__1__class_OInts(_810089))], (2072 ^ _780205) ^ [_810174, _810176, _810178, _810180, _810182, _810184] : [-(c_Power_Opower_Opower(_810184, _810180, _810176) = c_Power_Opower_Opower(_810182, _810178, _810174)), _810184 = _810182, _810180 = _810178, _810176 = _810174], (2086 ^ _780205) ^ [_810395, _810397, _810399, _810401] : [-(c_Nitpick_Onat__lcm(_810401, _810397) = c_Nitpick_Onat__lcm(_810399, _810395)), _810401 = _810399, _810397 = _810395], (2096 ^ _780205) ^ [_810544, _810546] : [_810546 = _810544, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_810546) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_810544))], (2102 ^ _780205) ^ [_810629, _810631, _810633, _810635, _810637, _810639, _810641, _810643] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_810643, _810639, _810635, _810631) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_810641, _810637, _810633, _810629)), _810643 = _810641, _810639 = _810637, _810635 = _810633, _810631 = _810629], (2120 ^ _780205) ^ [_810930, _810932, _810934, _810936, _810938, _810940, _810942, _810944] : [-(c_Sum__Type_OPlus(_810944, _810940, _810936, _810932) = c_Sum__Type_OPlus(_810942, _810938, _810934, _810930)), _810944 = _810942, _810940 = _810938, _810936 = _810934, _810932 = _810930], (2138 ^ _780205) ^ [_811231, _811233, _811235, _811237] : [-(c_Nat__Transfer_Otsub(_811237, _811233) = c_Nat__Transfer_Otsub(_811235, _811231)), _811237 = _811235, _811233 = _811231], (2148 ^ _780205) ^ [_811380, _811382, _811384, _811386] : [-(c_Random_Olog(_811386, _811382) = c_Random_Olog(_811384, _811380)), _811386 = _811384, _811382 = _811380], (2158 ^ _780205) ^ [_811529, _811531, _811533, _811535, _811537, _811539] : [-(c_Random_Ominus__shift(_811539, _811535, _811531) = c_Random_Ominus__shift(_811537, _811533, _811529)), _811539 = _811537, _811535 = _811533, _811531 = _811529], (2172 ^ _780205) ^ [_811750, _811752, _811754, _811756] : [-(c_Random_Oinc__shift(_811756, _811752) = c_Random_Oinc__shift(_811754, _811750)), _811756 = _811754, _811752 = _811750], (2182 ^ _780205) ^ [_811899, _811901] : [_811901 = _811899, -(c_Com_Ocom_Ocom__size(_811901) = c_Com_Ocom_Ocom__size(_811899))], (2188 ^ _780205) ^ [_811984, _811986, _811988, _811990] : [-(c_Com_Ocom_OSemi(_811990, _811986) = c_Com_Ocom_OSemi(_811988, _811984)), _811990 = _811988, _811986 = _811984], (2198 ^ _780205) ^ [_812133, _812135, _812137, _812139, _812141, _812143] : [-(c_Com_Ocom_OLocal(_812143, _812139, _812135) = c_Com_Ocom_OLocal(_812141, _812137, _812133)), _812143 = _812141, _812139 = _812137, _812135 = _812133], (2212 ^ _780205) ^ [_812354, _812356, _812358, _812360, _812362, _812364, _812366, _812368, _812370, _812372] : [-(c_Nitpick_Opair__box_Opair__box__size(_812372, _812368, _812364, _812360, _812356) = c_Nitpick_Opair__box_Opair__box__size(_812370, _812366, _812362, _812358, _812354)), _812372 = _812370, _812368 = _812366, _812364 = _812362, _812360 = _812358, _812356 = _812354], (2234 ^ _780205) ^ [_812743, _812745, _812747, _812749] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_812749, _812745) = c_Code__Numeral_Odiv__mod__code__numeral(_812747, _812743)), _812749 = _812747, _812745 = _812743], (2244 ^ _780205) ^ [_812892, _812894, _812896, _812898, _812900, _812902, _812904, _812906, _812908, _812910] : [-(c_Nitpick_Opair__box_Opair__box__rec(_812910, _812906, _812902, _812898, _812894) = c_Nitpick_Opair__box_Opair__box__rec(_812908, _812904, _812900, _812896, _812892)), _812910 = _812908, _812906 = _812904, _812902 = _812900, _812898 = _812896, _812894 = _812892], (2266 ^ _780205) ^ [_813281, _813283, _813285, _813287, _813289, _813291, _813293, _813295, _813297, _813299] : [-(c_Nitpick_Opair__box_Opair__box__case(_813299, _813295, _813291, _813287, _813283) = c_Nitpick_Opair__box_Opair__box__case(_813297, _813293, _813289, _813285, _813281)), _813299 = _813297, _813295 = _813293, _813291 = _813289, _813287 = _813285, _813283 = _813281], (2288 ^ _780205) ^ [_813670, _813672, _813674, _813676, _813678, _813680, _813682, _813684] : [-(c_Nitpick_Opair__box_OPairBox(_813684, _813680, _813676, _813672) = c_Nitpick_Opair__box_OPairBox(_813682, _813678, _813674, _813670)), _813684 = _813682, _813680 = _813678, _813676 = _813674, _813672 = _813670], (2306 ^ _780205) ^ [_813971, _813973, _813975, _813977] : [-(c_Nitpick_Onat__gcd(_813977, _813973) = c_Nitpick_Onat__gcd(_813975, _813971)), _813977 = _813975, _813973 = _813971], (2316 ^ _780205) ^ [_814120, _814122] : [_814122 = _814120, -(c_Nat_Onat_Onat__size(_814122) = c_Nat_Onat_Onat__size(_814120))], (2322 ^ _780205) ^ [_814205, _814207, _814209, _814211] : [-(c_Divides_OposDivAlg(_814211, _814207) = c_Divides_OposDivAlg(_814209, _814205)), _814211 = _814209, _814207 = _814205], (2332 ^ _780205) ^ [_814354, _814356, _814358, _814360] : [-(c_Divides_OnegDivAlg(_814360, _814356) = c_Divides_OnegDivAlg(_814358, _814354)), _814360 = _814358, _814356 = _814354], (2342 ^ _780205) ^ [_814503, _814505, _814507, _814509, _814511, _814513, _814515, _814517, _814519, _814521] : [-(c_Product__Type_Oprod_Oprod__size(_814521, _814517, _814513, _814509, _814505) = c_Product__Type_Oprod_Oprod__size(_814519, _814515, _814511, _814507, _814503)), _814521 = _814519, _814517 = _814515, _814513 = _814511, _814509 = _814507, _814505 = _814503], (2364 ^ _780205) ^ [_814892, _814894, _814896, _814898, _814900, _814902, _814904, _814906, _814908, _814910] : [-(c_Product__Type_Oprod_Oprod__rec(_814910, _814906, _814902, _814898, _814894) = c_Product__Type_Oprod_Oprod__rec(_814908, _814904, _814900, _814896, _814892)), _814910 = _814908, _814906 = _814904, _814902 = _814900, _814898 = _814896, _814894 = _814892], (2386 ^ _780205) ^ [_815281, _815283] : [_815283 = _815281, -(c_Nitpick_Ozero__frac(_815283) = c_Nitpick_Ozero__frac(_815281))], (2392 ^ _780205) ^ [_815366, _815368] : [_815368 = _815366, -(c_Nitpick_Oone__frac(_815368) = c_Nitpick_Oone__frac(_815366))], (2398 ^ _780205) ^ [_815451, _815453, _815455, _815457] : [-(c_Nitpick_Onumber__of__frac(_815457, _815453) = c_Nitpick_Onumber__of__frac(_815455, _815451)), _815457 = _815455, _815453 = _815451], (2408 ^ _780205) ^ [_815600, _815602, _815604, _815606] : [-(c_Divides_Odivmod__int__rel(_815606, _815602) = c_Divides_Odivmod__int__rel(_815604, _815600)), _815606 = _815604, _815602 = _815600], (2418 ^ _780205) ^ [_815749, _815751] : [_815751 = _815749, -(c_Divides_Oadjust(_815751) = c_Divides_Oadjust(_815749))], (2424 ^ _780205) ^ [_815834, _815836, _815838, _815840] : [-(c_Divides_Odivmod__int(_815840, _815836) = c_Divides_Odivmod__int(_815838, _815834)), _815840 = _815838, _815836 = _815834], (2434 ^ _780205) ^ [_815983, _815985, _815987, _815989] : [-(c_Groups_Osgn__class_Osgn(_815989, _815985) = c_Groups_Osgn__class_Osgn(_815987, _815983)), _815989 = _815987, _815985 = _815983], (2444 ^ _780205) ^ [_816132, _816134, _816136, _816138] : [-(c_Divides_Opdivmod(_816138, _816134) = c_Divides_Opdivmod(_816136, _816132)), _816138 = _816136, _816134 = _816132], (2454 ^ _780205) ^ [_816281, _816283, _816285, _816287] : [-(c_FunDef_Orp__inv__image(_816287, _816283) = c_FunDef_Orp__inv__image(_816285, _816281)), _816287 = _816285, _816283 = _816281], (2464 ^ _780205) ^ [_816430, _816432, _816434, _816436, _816438, _816440] : [-(c_Nat_Onat_Onat__rec(_816440, _816436, _816432) = c_Nat_Onat_Onat__rec(_816438, _816434, _816430)), _816440 = _816438, _816436 = _816434, _816432 = _816430], (2478 ^ _780205) ^ [_816651, _816653, _816655, _816657, _816659, _816661, _816663, _816665] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_816665, _816661, _816657, _816653) = c_Nat_Osemiring__1__class_Oof__nat__aux(_816663, _816659, _816655, _816651)), _816665 = _816663, _816661 = _816659, _816657 = _816655, _816653 = _816651], (2496 ^ _780205) ^ [_816952, _816954, _816956, _816958] : [-(c_Nitpick_Onorm__frac(_816958, _816954) = c_Nitpick_Onorm__frac(_816956, _816952)), _816958 = _816956, _816954 = _816952], (2506 ^ _780205) ^ [_817101, _817103] : [_817103 = _817101, -(c_Int_OBit0(_817103) = c_Int_OBit0(_817101))], (2512 ^ _780205) ^ [_817186, _817188, _817190, _817192, _817194, _817196] : [-(c_SetInterval_Oord_OatMost(_817196, _817192, _817188) = c_SetInterval_Oord_OatMost(_817194, _817190, _817186)), _817196 = _817194, _817192 = _817190, _817188 = _817186], (2526 ^ _780205) ^ [_817407, _817409, _817411, _817413, _817415, _817417] : [-(c_SetInterval_Oord_OatLeast(_817417, _817413, _817409) = c_SetInterval_Oord_OatLeast(_817415, _817411, _817407)), _817417 = _817415, _817413 = _817411, _817409 = _817407], (2540 ^ _780205) ^ [_817628, _817630, _817632, _817634, _817636, _817638] : [-(c_SetInterval_Oord_OlessThan(_817638, _817634, _817630) = c_SetInterval_Oord_OlessThan(_817636, _817632, _817628)), _817638 = _817636, _817634 = _817632, _817630 = _817628], (2554 ^ _780205) ^ [_817849, _817851, _817853, _817855, _817857, _817859] : [-(c_SetInterval_Oord_OgreaterThan(_817859, _817855, _817851) = c_SetInterval_Oord_OgreaterThan(_817857, _817853, _817849)), _817859 = _817857, _817855 = _817853, _817851 = _817849], (2568 ^ _780205) ^ [_818070, _818072] : [_818072 = _818070, -(c_Int_Opred(_818072) = c_Int_Opred(_818070))], (2574 ^ _780205) ^ [_818155, _818157, _818159, _818161] : [-(c_Orderings_Oord_Omax(_818161, _818157) = c_Orderings_Oord_Omax(_818159, _818155)), _818161 = _818159, _818157 = _818155], (2584 ^ _780205) ^ [_818304, _818306, _818308, _818310] : [-(c_Orderings_Oord_Omin(_818310, _818306) = c_Orderings_Oord_Omin(_818308, _818304)), _818310 = _818308, _818306 = _818304], (2594 ^ _780205) ^ [_818453, _818455, _818457, _818459, _818461, _818463, _818465, _818467, _818469, _818471] : [-(c_Finite__Set_Ofold__graph(_818471, _818467, _818463, _818459, _818455) = c_Finite__Set_Ofold__graph(_818469, _818465, _818461, _818457, _818453)), _818471 = _818469, _818467 = _818465, _818463 = _818461, _818459 = _818457, _818455 = _818453], (2616 ^ _780205) ^ [_818842, _818844, _818846, _818848] : [-(c_Divides_Odivmod__nat(_818848, _818844) = c_Divides_Odivmod__nat(_818846, _818842)), _818848 = _818846, _818844 = _818842], (2626 ^ _780205) ^ [_818991, _818993, _818995, _818997] : [-(c_Divides_Odivmod__nat__rel(_818997, _818993) = c_Divides_Odivmod__nat__rel(_818995, _818991)), _818997 = _818995, _818993 = _818991], (2636 ^ _780205) ^ [_819140, _819142, _819144, _819146, _819148, _819150] : [-(c_Finite__Set_Ofold1Set(_819150, _819146, _819142) = c_Finite__Set_Ofold1Set(_819148, _819144, _819140)), _819150 = _819148, _819146 = _819144, _819142 = _819140], (2650 ^ _780205) ^ [_819361, _819363, _819365, _819367] : [-(c_Set_Othe__elem(_819367, _819363) = c_Set_Othe__elem(_819365, _819361)), _819367 = _819365, _819363 = _819361], (2660 ^ _780205) ^ [_819510, _819512, _819514, _819516, _819518, _819520] : [-(c_Partial__Function_Oflat__lub(_819520, _819516, _819512) = c_Partial__Function_Oflat__lub(_819518, _819514, _819510)), _819520 = _819518, _819516 = _819514, _819512 = _819510], (2674 ^ _780205) ^ [_819731, _819733] : [_819733 = _819731, -(c_SetInterval_Oord__class_OgreaterThan(_819733) = c_SetInterval_Oord__class_OgreaterThan(_819731))], (2680 ^ _780205) ^ [_819816, _819818] : [_819818 = _819816, -(c_SetInterval_Oord__class_OatLeast(_819818) = c_SetInterval_Oord__class_OatLeast(_819816))], (2686 ^ _780205) ^ [_819901, _819903] : [_819903 = _819901, -(c_Equiv__Relations_Oquotient(_819903) = c_Equiv__Relations_Oquotient(_819901))], (2692 ^ _780205) ^ [_819986, _819988, _819990, _819992, _819994, _819996, _819998, _820000] : [-(c_Nitpick_Oprod(_820000, _819996, _819992, _819988) = c_Nitpick_Oprod(_819998, _819994, _819990, _819986)), _820000 = _819998, _819996 = _819994, _819992 = _819990, _819988 = _819986], (2710 ^ _780205) ^ [_820287, _820289] : [_820289 = _820287, -(c_Wellfounded_Omeasure(_820289) = c_Wellfounded_Omeasure(_820287))], (2716 ^ _780205) ^ [_820372, _820374, _820376, _820378] : [-(c_Wellfounded_Omin__ext(_820378, _820374) = c_Wellfounded_Omin__ext(_820376, _820372)), _820378 = _820376, _820374 = _820372], (2726 ^ _780205) ^ [_820521, _820523, _820525, _820527, _820529, _820531] : [-(c_Wellfounded_Omlex__prod(_820531, _820527, _820523) = c_Wellfounded_Omlex__prod(_820529, _820525, _820521)), _820531 = _820529, _820527 = _820525, _820523 = _820521], (2740 ^ _780205) ^ [_820742, _820744] : [_820744 = _820742, -(c_Int_Oint__ge__less__than2(_820744) = c_Int_Oint__ge__less__than2(_820742))], (2746 ^ _780205) ^ [_820827, _820829] : [_820829 = _820827, -(c_Int_Oint__ge__less__than(_820829) = c_Int_Oint__ge__less__than(_820827))], (2752 ^ _780205) ^ [_820912, _820914, _820916, _820918, _820920, _820922, _820924, _820926] : [-(c_Recdef_Osame__fst(_820926, _820922, _820918, _820914) = c_Recdef_Osame__fst(_820924, _820920, _820916, _820912)), _820926 = _820924, _820922 = _820920, _820918 = _820916, _820914 = _820912], (2770 ^ _780205) ^ [_821213, _821215, _821217, _821219, _821221, _821223] : [-(c_FunDef_Oin__rel(_821223, _821219, _821215) = c_FunDef_Oin__rel(_821221, _821217, _821213)), _821223 = _821221, _821219 = _821217, _821215 = _821213], (2784 ^ _780205) ^ [_821434, _821436, _821438, _821440] : [-(c_Predicate_OPowp(_821440, _821436) = c_Predicate_OPowp(_821438, _821434)), _821440 = _821438, _821436 = _821434], (2794 ^ _780205) ^ [_821583, _821585] : [_821585 = _821583, -(c_Set_OBall(_821585) = c_Set_OBall(_821583))], (2800 ^ _780205) ^ [_821668, _821670] : [_821670 = _821668, -(c_HOL_OAll(_821670) = c_HOL_OAll(_821668))], (2806 ^ _780205) ^ [_821753, _821755, _821757, _821759, _821761, _821763] : [-(c_Predicate_ODomainP(_821763, _821759, _821755) = c_Predicate_ODomainP(_821761, _821757, _821753)), _821763 = _821761, _821759 = _821757, _821755 = _821753], (2820 ^ _780205) ^ [_821974, _821976, _821978, _821980, _821982, _821984] : [-(c_Predicate_ORangeP(_821984, _821980, _821976) = c_Predicate_ORangeP(_821982, _821978, _821974)), _821984 = _821982, _821980 = _821978, _821976 = _821974], (2834 ^ _780205) ^ [_822195, _822197, _822199, _822201, _822203, _822205, _822207, _822209] : [-(c_Product__Type_Oapsnd(_822209, _822205, _822201, _822197) = c_Product__Type_Oapsnd(_822207, _822203, _822199, _822195)), _822209 = _822207, _822205 = _822203, _822201 = _822199, _822197 = _822195], (2852 ^ _780205) ^ [_822496, _822498, _822500, _822502, _822504, _822506, _822508, _822510] : [-(c_Product__Type_Oapfst(_822510, _822506, _822502, _822498) = c_Product__Type_Oapfst(_822508, _822504, _822500, _822496)), _822510 = _822508, _822506 = _822504, _822502 = _822500, _822498 = _822496], (2870 ^ _780205) ^ [_822797, _822799, _822801, _822803, _822805, _822807] : [-(c_Com_Ocom_OCond(_822807, _822803, _822799) = c_Com_Ocom_OCond(_822805, _822801, _822797)), _822807 = _822805, _822803 = _822801, _822799 = _822797], (2884 ^ _780205) ^ [_823018, _823020, _823022, _823024] : [-(c_Com_Ocom_OWhile(_823024, _823020) = c_Com_Ocom_OWhile(_823022, _823018)), _823024 = _823022, _823020 = _823018], (2894 ^ _780205) ^ [_823167, _823169, _823171, _823173, _823175, _823177] : [-(c_Hoare__Mirabelle_Opeek__and(_823177, _823173, _823169) = c_Hoare__Mirabelle_Opeek__and(_823175, _823171, _823167)), _823177 = _823175, _823173 = _823171, _823169 = _823167], (2908 ^ _780205) ^ [_823388, _823390, _823392, _823394] : [-(c_Wellfounded_Omax__ext(_823394, _823390) = c_Wellfounded_Omax__ext(_823392, _823388)), _823394 = _823392, _823390 = _823388], (2918 ^ _780205) ^ [_823537, _823539, _823541, _823543, _823545, _823547, _823549, _823551] : [-(c_Random_Oiterate(_823551, _823547, _823543, _823539) = c_Random_Oiterate(_823549, _823545, _823541, _823537)), _823551 = _823549, _823547 = _823545, _823543 = _823541, _823539 = _823537], (2936 ^ _780205) ^ [_823838, _823840] : [_823840 = _823838, -(c_Relation_OField(_823840) = c_Relation_OField(_823838))], (2942 ^ _780205) ^ [_823923, _823925, _823927, _823929] : [-(c_Relation_ORange(_823929, _823925) = c_Relation_ORange(_823927, _823923)), _823929 = _823927, _823925 = _823923], (2952 ^ _780205) ^ [_824072, _824074, _824076, _824078] : [-(c_Relation_ODomain(_824078, _824074) = c_Relation_ODomain(_824076, _824072)), _824078 = _824076, _824074 = _824072], (2962 ^ _780205) ^ [_824221, _824223] : [_824223 = _824221, -(c_Nat_Ofunpow(_824223) = c_Nat_Ofunpow(_824221))], (2968 ^ _780205) ^ [_824306, _824308, _824310, _824312] : [-(c_Nitpick_Oint__lcm(_824312, _824308) = c_Nitpick_Oint__lcm(_824310, _824306)), _824312 = _824310, _824308 = _824306], (2978 ^ _780205) ^ [_824455, _824457, _824459, _824461, _824463, _824465] : [-(c_Product__Type_Ointernal__split(_824465, _824461, _824457) = c_Product__Type_Ointernal__split(_824463, _824459, _824455)), _824465 = _824463, _824461 = _824459, _824457 = _824455], (2992 ^ _780205) ^ [_824676, _824678, _824680, _824682, _824684, _824686] : [-(c_Nitpick_Otimes__frac(_824686, _824682, _824678) = c_Nitpick_Otimes__frac(_824684, _824680, _824676)), _824686 = _824684, _824682 = _824680, _824678 = _824676], (3006 ^ _780205) ^ [_824897, _824899, _824901, _824903, _824905, _824907] : [-(c_Nitpick_Oof__frac(_824907, _824903, _824899) = c_Nitpick_Oof__frac(_824905, _824901, _824897)), _824907 = _824905, _824903 = _824901, _824899 = _824897], (3020 ^ _780205) ^ [_825118, _825120] : [_825120 = _825118, -(c_Rings_Oinverse__class_Odivide(_825120) = c_Rings_Oinverse__class_Odivide(_825118))], (3026 ^ _780205) ^ [_825203, _825205] : [_825205 = _825203, -(c_Int_Oring__1__class_Oof__int(_825205) = c_Int_Oring__1__class_Oof__int(_825203))], (3032 ^ _780205) ^ [_825288, _825290, _825292, _825294] : [-(c_Nitpick_Oinverse__frac(_825294, _825290) = c_Nitpick_Oinverse__frac(_825292, _825288)), _825294 = _825292, _825290 = _825288], (3042 ^ _780205) ^ [_825437, _825439] : [_825439 = _825437, -(c_Nitpick_Ofrac(_825439) = c_Nitpick_Ofrac(_825437))], (3048 ^ _780205) ^ [_825522, _825524, _825526, _825528] : [-(c_Nitpick_OAbs__Frac(_825528, _825524) = c_Nitpick_OAbs__Frac(_825526, _825522)), _825528 = _825526, _825524 = _825522], (3058 ^ _780205) ^ [_825671, _825673, _825675, _825677, _825679, _825681] : [-(c_Nitpick_Oplus__frac(_825681, _825677, _825673) = c_Nitpick_Oplus__frac(_825679, _825675, _825671)), _825681 = _825679, _825677 = _825675, _825673 = _825671], (3072 ^ _780205) ^ [_825892, _825894, _825896, _825898] : [-(c_Nitpick_Ouminus__frac(_825898, _825894) = c_Nitpick_Ouminus__frac(_825896, _825892)), _825898 = _825896, _825894 = _825892], (3082 ^ _780205) ^ [_826041, _826043] : [_826043 = _826041, -(c_Nitpick_Odenom(_826043) = c_Nitpick_Odenom(_826041))], (3088 ^ _780205) ^ [_826126, _826128] : [_826128 = _826126, -(c_Nitpick_Onum(_826128) = c_Nitpick_Onum(_826126))], (3094 ^ _780205) ^ [_826211, _826213] : [_826213 = _826211, -(c_Nitpick_ORep__Frac(_826213) = c_Nitpick_ORep__Frac(_826211))], (3100 ^ _780205) ^ [_826296, _826298] : [_826298 = _826296, -(c_HOL_Obool_Obool__size(_826298) = c_HOL_Obool_Obool__size(_826296))], (3106 ^ _780205) ^ [_826381, _826383, _826385, _826387] : [-(c_List_Olenlex(_826387, _826383) = c_List_Olenlex(_826385, _826381)), _826387 = _826385, _826383 = _826381], (3116 ^ _780205) ^ [_826530, _826532, _826534, _826536, _826538, _826540, _826542, _826544, _826546, _826548, _826550, _826552] : [-(c_Product__Type_Omap__pair(_826552, _826548, _826544, _826540, _826536, _826532) = c_Product__Type_Omap__pair(_826550, _826546, _826542, _826538, _826534, _826530)), _826552 = _826550, _826548 = _826546, _826544 = _826542, _826540 = _826538, _826536 = _826534, _826532 = _826530], (3142 ^ _780205) ^ [_827015, _827017, _827019, _827021] : [-(c_List_Olexn(_827021, _827017) = c_List_Olexn(_827019, _827015)), _827021 = _827019, _827017 = _827015], (3152 ^ _780205) ^ [_827164, _827166, _827168, _827170] : [-(c_Wellfounded_Oacc(_827170, _827166) = c_Wellfounded_Oacc(_827168, _827164)), _827170 = _827168, _827166 = _827164], (3162 ^ _780205) ^ [_827313, _827315, _827317, _827319] : [-(c_Nitpick_Ocard_H(_827319, _827315) = c_Nitpick_Ocard_H(_827317, _827313)), _827319 = _827317, _827315 = _827313], (3172 ^ _780205) ^ [_827462, _827464, _827466, _827468, _827470, _827472] : [-(c_List_Oset__Cons(_827472, _827468, _827464) = c_List_Oset__Cons(_827470, _827466, _827462)), _827472 = _827470, _827468 = _827466, _827464 = _827462], (3186 ^ _780205) ^ [_827683, _827685, _827687, _827689] : [-(c_List_Olistset(_827689, _827685) = c_List_Olistset(_827687, _827683)), _827689 = _827687, _827685 = _827683], (3196 ^ _780205) ^ [_827832, _827834, _827836, _827838] : [-(c_List_Olistrel1(_827838, _827834) = c_List_Olistrel1(_827836, _827832)), _827838 = _827836, _827834 = _827832], (3206 ^ _780205) ^ [_827981, _827983, _827985, _827987, _827989, _827991, _827993, _827995] : [-(c_Nat_Onat_Onat__case(_827995, _827991, _827987, _827983) = c_Nat_Onat_Onat__case(_827993, _827989, _827985, _827981)), _827995 = _827993, _827991 = _827989, _827987 = _827985, _827983 = _827981], (3224 ^ _780205) ^ [_828282, _828284, _828286, _828288] : [-(c_Nat_Ocompow(_828288, _828284) = c_Nat_Ocompow(_828286, _828282)), _828288 = _828286, _828284 = _828282], (3234 ^ _780205) ^ [_828431, _828433] : [_828433 = _828431, -(c_List_Orotate1(_828433) = c_List_Orotate1(_828431))], (3240 ^ _780205) ^ [_828516, _828518, _828520, _828522] : [-(c_Finite__Set_Ofold1(_828522, _828518) = c_Finite__Set_Ofold1(_828520, _828516)), _828522 = _828520, _828518 = _828516], (3250 ^ _780205) ^ [_828665, _828667, _828669, _828671] : [-(c_Big__Operators_Olattice__class_OSup__fin(_828671, _828667) = c_Big__Operators_Olattice__class_OSup__fin(_828669, _828665)), _828671 = _828669, _828667 = _828665], (3260 ^ _780205) ^ [_828814, _828816, _828818, _828820] : [-(c_Big__Operators_Olattice__class_OInf__fin(_828820, _828816) = c_Big__Operators_Olattice__class_OInf__fin(_828818, _828814)), _828820 = _828818, _828816 = _828814], (3270 ^ _780205) ^ [_828963, _828965, _828967, _828969] : [-(c_Big__Operators_Olinorder__class_OMin(_828969, _828965) = c_Big__Operators_Olinorder__class_OMin(_828967, _828963)), _828969 = _828967, _828965 = _828963], (3280 ^ _780205) ^ [_829112, _829114, _829116, _829118] : [-(c_Big__Operators_Olinorder__class_OMax(_829118, _829114) = c_Big__Operators_Olinorder__class_OMax(_829116, _829112)), _829118 = _829116, _829114 = _829112], (3290 ^ _780205) ^ [_829261, _829263, _829265, _829267, _829269, _829271] : [-(c_Big__Operators_Olattice_OInf__fin(_829271, _829267, _829263) = c_Big__Operators_Olattice_OInf__fin(_829269, _829265, _829261)), _829271 = _829269, _829267 = _829265, _829263 = _829261], (3304 ^ _780205) ^ [_829482, _829484, _829486, _829488, _829490, _829492] : [-(c_Big__Operators_Olattice_OSup__fin(_829492, _829488, _829484) = c_Big__Operators_Olattice_OSup__fin(_829490, _829486, _829482)), _829492 = _829490, _829488 = _829486, _829484 = _829482], (3318 ^ _780205) ^ [_829703, _829705, _829707, _829709, _829711, _829713, _829715, _829717, _829719, _829721] : [-(c_Fun_Ofun__upd(_829721, _829717, _829713, _829709, _829705) = c_Fun_Ofun__upd(_829719, _829715, _829711, _829707, _829703)), _829721 = _829719, _829717 = _829715, _829713 = _829711, _829709 = _829707, _829705 = _829703], (3340 ^ _780205) ^ [_830092, _830094, _830096, _830098, _830100, _830102, _830104, _830106] : [-(c_Nitpick_Osetsum_H(_830106, _830102, _830098, _830094) = c_Nitpick_Osetsum_H(_830104, _830100, _830096, _830092)), _830106 = _830104, _830102 = _830100, _830098 = _830096, _830094 = _830092], (3358 ^ _780205) ^ [_830393, _830395, _830397, _830399, _830401, _830403] : [-(c_List_Olist_Olist__size(_830403, _830399, _830395) = c_List_Olist_Olist__size(_830401, _830397, _830393)), _830403 = _830401, _830399 = _830397, _830395 = _830393], (3372 ^ _780205) ^ [_830614, _830616, _830618, _830620] : [-(c_Random_Oselect(_830620, _830616) = c_Random_Oselect(_830618, _830614)), _830620 = _830618, _830616 = _830614], (3382 ^ _780205) ^ [_830763, _830765] : [_830765 = _830763, -(c_Random_Orange(_830765) = c_Random_Orange(_830763))], (3388 ^ _780205) ^ [_830848, _830850, _830852, _830854] : [-(c_Code__Numeral_Onat__of__aux(_830854, _830850) = c_Code__Numeral_Onat__of__aux(_830852, _830848)), _830854 = _830852, _830850 = _830848], (3398 ^ _780205) ^ [_830997, _830999] : [_830999 = _830997, -(c_Lazy__Sequence_Ohb__not__seq(_830999) = c_Lazy__Sequence_Ohb__not__seq(_830997))], (3404 ^ _780205) ^ [_831082, _831084] : [_831084 = _831082, -(c_Int_OBit1(_831084) = c_Int_OBit1(_831082))], (3410 ^ _780205) ^ [_831167, _831169, _831171, _831173] : [-(c_List_Olistsp(_831173, _831169) = c_List_Olistsp(_831171, _831167)), _831173 = _831171, _831169 = _831167], (3420 ^ _780205) ^ [_831316, _831318, _831320, _831322] : [-(c_List_Olists(_831322, _831318) = c_List_Olists(_831320, _831316)), _831322 = _831320, _831318 = _831316], (3430 ^ _780205) ^ [_831465, _831467, _831469, _831471, _831473, _831475, _831477, _831479] : [-(c_Enum_Oproduct(_831479, _831475, _831471, _831467) = c_Enum_Oproduct(_831477, _831473, _831469, _831465)), _831479 = _831477, _831475 = _831473, _831471 = _831469, _831467 = _831465], (3448 ^ _780205) ^ [_831766, _831768, _831770, _831772] : [-(c_Product__Type_OSigma(_831772, _831768) = c_Product__Type_OSigma(_831770, _831766)), _831772 = _831770, _831768 = _831766], (3458 ^ _780205) ^ [_831915, _831917] : [_831917 = _831915, -(c_Set_OPow(_831917) = c_Set_OPow(_831915))], (3464 ^ _780205) ^ [_832000, _832002, _832004, _832006] : [-(c_HOL_OLet(_832006, _832002) = c_HOL_OLet(_832004, _832000)), _832006 = _832004, _832002 = _832000], (3474 ^ _780205) ^ [_832149, _832151, _832153, _832155] : [-(c_Enum_Osublists(_832155, _832151) = c_Enum_Osublists(_832153, _832149)), _832155 = _832153, _832151 = _832149], (3484 ^ _780205) ^ [_832298, _832300, _832302, _832304] : [-(c_Enum_Oenum__the(_832304, _832300) = c_Enum_Oenum__the(_832302, _832298)), _832304 = _832302, _832300 = _832298], (3494 ^ _780205) ^ [_832447, _832449, _832451, _832453, _832455, _832457] : [-(c_Finite__Set_Ofold(_832457, _832453, _832449) = c_Finite__Set_Ofold(_832455, _832451, _832447)), _832457 = _832455, _832453 = _832451, _832449 = _832447], (3508 ^ _780205) ^ [_832668, _832670, _832672, _832674, _832676, _832678] : [-(c_Enum_On__lists(_832678, _832674, _832670) = c_Enum_On__lists(_832676, _832672, _832668)), _832678 = _832676, _832674 = _832672, _832670 = _832668], (3522 ^ _780205) ^ [_832889, _832891, _832893, _832895] : [-(c_List_OremoveAll(_832895, _832891) = c_List_OremoveAll(_832893, _832889)), _832895 = _832893, _832891 = _832889], (3532 ^ _780205) ^ [_833038, _833040, _833042, _833044, _833046, _833048] : [-(c_List_Opartition(_833048, _833044, _833040) = c_List_Opartition(_833046, _833042, _833038)), _833048 = _833046, _833044 = _833042, _833040 = _833038], (3546 ^ _780205) ^ [_833259, _833261, _833263, _833265, _833267, _833269, _833271, _833273] : [-(c_List_Olist_Olist__case(_833273, _833269, _833265, _833261) = c_List_Olist_Olist__case(_833271, _833267, _833263, _833259)), _833273 = _833271, _833269 = _833267, _833265 = _833263, _833261 = _833259], (3564 ^ _780205) ^ [_833560, _833562, _833564, _833566] : [-(c_Random_Oselect__weight(_833566, _833562) = c_Random_Oselect__weight(_833564, _833560)), _833566 = _833564, _833562 = _833560], (3574 ^ _780205) ^ [_833709, _833711, _833713, _833715] : [-(c_Random_Opick(_833715, _833711) = c_Random_Opick(_833713, _833709)), _833715 = _833713, _833711 = _833709], (3584 ^ _780205) ^ [_833858, _833860] : [_833860 = _833858, -(c_List_Otranspose__rel(_833860) = c_List_Otranspose__rel(_833858))], (3590 ^ _780205) ^ [_833943, _833945, _833947, _833949, _833951, _833953] : [-(c_List_Osublist(_833953, _833949, _833945) = c_List_Osublist(_833951, _833947, _833943)), _833953 = _833951, _833949 = _833947, _833945 = _833943], (3604 ^ _780205) ^ [_834164, _834166] : [_834166 = _834164, -(c_Int_Onumber__class_Onumber__of(_834166) = c_Int_Onumber__class_Onumber__of(_834164))], (3610 ^ _780205) ^ [_834249, _834251] : [_834251 = _834249, -(c_SetInterval_Oord__class_OlessThan(_834251) = c_SetInterval_Oord__class_OlessThan(_834249))], (3616 ^ _780205) ^ [_834334, _834336, _834338, _834340, _834342, _834344] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_834344, _834340, _834336) = c_SetInterval_Oord__class_OgreaterThanAtMost(_834342, _834338, _834334)), _834344 = _834342, _834340 = _834338, _834336 = _834334], (3630 ^ _780205) ^ [_834555, _834557, _834559, _834561, _834563, _834565] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_834565, _834561, _834557) = c_SetInterval_Oord__class_OgreaterThanLessThan(_834563, _834559, _834555)), _834565 = _834563, _834561 = _834559, _834557 = _834555], (3644 ^ _780205) ^ [_834776, _834778] : [_834778 = _834776, -(c_SetInterval_Oord__class_OatMost(_834778) = c_SetInterval_Oord__class_OatMost(_834776))], (3650 ^ _780205) ^ [_834861, _834863, _834865, _834867, _834869, _834871, _834873, _834875] : [-(c_List_Olinorder__class_Osort__key(_834875, _834871, _834867, _834863) = c_List_Olinorder__class_Osort__key(_834873, _834869, _834865, _834861)), _834875 = _834873, _834871 = _834869, _834867 = _834865, _834863 = _834861], (3668 ^ _780205) ^ [_835162, _835164, _835166, _835168, _835170, _835172, _835174, _835176, _835178, _835180] : [-(c_List_Olinorder__class_Oinsort__insert__key(_835180, _835176, _835172, _835168, _835164) = c_List_Olinorder__class_Oinsort__insert__key(_835178, _835174, _835170, _835166, _835162)), _835180 = _835178, _835176 = _835174, _835172 = _835170, _835168 = _835166, _835164 = _835162], (3690 ^ _780205) ^ [_835551, _835553, _835555, _835557] : [-(c_List_Olinorder__class_Osorted__list__of__set(_835557, _835553) = c_List_Olinorder__class_Osorted__list__of__set(_835555, _835551)), _835557 = _835555, _835553 = _835551], (3700 ^ _780205) ^ [_835700, _835702, _835704, _835706, _835708, _835710] : [-(c_List_Oremove1(_835710, _835706, _835702) = c_List_Oremove1(_835708, _835704, _835700)), _835710 = _835708, _835706 = _835704, _835702 = _835700], (3714 ^ _780205) ^ [_835921, _835923, _835925, _835927] : [-(c_List_Orotate(_835927, _835923) = c_List_Orotate(_835925, _835921)), _835927 = _835925, _835923 = _835921], (3724 ^ _780205) ^ [_836070, _836072, _836074, _836076] : [-(c_List_Olist__update(_836076, _836072) = c_List_Olist__update(_836074, _836070)), _836076 = _836074, _836072 = _836070], (3734 ^ _780205) ^ [_836219, _836221, _836223, _836225, _836227, _836229, _836231, _836233, _836235, _836237] : [-(c_List_Ofoldr(_836237, _836233, _836229, _836225, _836221) = c_List_Ofoldr(_836235, _836231, _836227, _836223, _836219)), _836237 = _836235, _836233 = _836231, _836229 = _836227, _836225 = _836223, _836221 = _836219], (3756 ^ _780205) ^ [_836608, _836610] : [_836610 = _836608, -(c_Orderings_Oord__class_Omax(_836610) = c_Orderings_Oord__class_Omax(_836608))], (3762 ^ _780205) ^ [_836693, _836695, _836697, _836699] : [-(c_List_Otranspose(_836699, _836695) = c_List_Otranspose(_836697, _836693)), _836699 = _836697, _836695 = _836693], (3772 ^ _780205) ^ [_836842, _836844, _836846, _836848] : [-(c_List_Obutlast(_836848, _836844) = c_List_Obutlast(_836846, _836842)), _836848 = _836846, _836844 = _836842], (3782 ^ _780205) ^ [_836991, _836993] : [_836993 = _836991, -(c_List_Oreturn__list(_836993) = c_List_Oreturn__list(_836991))], (3788 ^ _780205) ^ [_837076, _837078] : [_837078 = _837076, -(c_List_Oembed__list(_837078) = c_List_Oembed__list(_837076))], (3794 ^ _780205) ^ [_837161, _837163] : [_837163 = _837161, -(c_List_Omonoid__add__class_Olistsum(_837163) = c_List_Omonoid__add__class_Olistsum(_837161))], (3800 ^ _780205) ^ [_837246, _837248, _837250, _837252] : [-(c_List_Oremdups(_837252, _837248) = c_List_Oremdups(_837250, _837246)), _837252 = _837250, _837248 = _837246], (3810 ^ _780205) ^ [_837395, _837397, _837399, _837401, _837403, _837405] : [-(c_List_Oinsert(_837405, _837401, _837397) = c_List_Oinsert(_837403, _837399, _837395)), _837405 = _837403, _837401 = _837399, _837397 = _837395], (3824 ^ _780205) ^ [_837616, _837618, _837620, _837622, _837624, _837626, _837628, _837630] : [-(c_List_Omaps(_837630, _837626, _837622, _837618) = c_List_Omaps(_837628, _837624, _837620, _837616)), _837630 = _837628, _837626 = _837624, _837622 = _837620, _837618 = _837616], (3842 ^ _780205) ^ [_837917, _837919, _837921, _837923] : [-(c_List_Olex(_837923, _837919) = c_List_Olex(_837921, _837917)), _837923 = _837921, _837919 = _837917], (3852 ^ _780205) ^ [_838066, _838068, _838070, _838072] : [-(c_List_Omeasures(_838072, _838068) = c_List_Omeasures(_838070, _838066)), _838072 = _838070, _838068 = _838066], (3862 ^ _780205) ^ [_838215, _838217, _838219, _838221, _838223, _838225, _838227, _838229] : [-(c_List_Ofoldl(_838229, _838225, _838221, _838217) = c_List_Ofoldl(_838227, _838223, _838219, _838215)), _838229 = _838227, _838225 = _838223, _838221 = _838219, _838217 = _838215], (3880 ^ _780205) ^ [_838516, _838518] : [_838518 = _838516, -(c_Enum_Oenum__class_Oenum__ex(_838518) = c_Enum_Oenum__class_Oenum__ex(_838516))], (3886 ^ _780205) ^ [_838601, _838603, _838605, _838607, _838609, _838611, _838613, _838615] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_838615, _838611, _838607, _838603) = c_New__Random__Sequence_Opos__not__random__dseq(_838613, _838609, _838605, _838601)), _838615 = _838613, _838611 = _838609, _838607 = _838605, _838603 = _838601], (3904 ^ _780205) ^ [_838902, _838904] : [_838904 = _838902, -(c_New__DSequence_Opos__not__seq(_838904) = c_New__DSequence_Opos__not__seq(_838902))], (3910 ^ _780205) ^ [_838987, _838989, _838991, _838993, _838995, _838997] : [-(c_List_OdropWhile(_838997, _838993, _838989) = c_List_OdropWhile(_838995, _838991, _838987)), _838997 = _838995, _838993 = _838991, _838989 = _838987], (3924 ^ _780205) ^ [_839208, _839210] : [_839210 = _839208, -(c_List_Odistinct(_839210) = c_List_Odistinct(_839208))], (3930 ^ _780205) ^ [_839293, _839295, _839297, _839299, _839301, _839303] : [-(c_List_OtakeWhile(_839303, _839299, _839295) = c_List_OtakeWhile(_839301, _839297, _839293)), _839303 = _839301, _839299 = _839297, _839295 = _839293], (3944 ^ _780205) ^ [_839514, _839516, _839518, _839520, _839522, _839524] : [-(c_List_Olinorder__class_Oinsort__key(_839524, _839520, _839516) = c_List_Olinorder__class_Oinsort__key(_839522, _839518, _839514)), _839524 = _839522, _839520 = _839518, _839516 = _839514], (3958 ^ _780205) ^ [_839735, _839737] : [_839737 = _839735, -(c_Enum_Oenum__class_Oenum__all(_839737) = c_Enum_Oenum__class_Oenum__all(_839735))], (3964 ^ _780205) ^ [_839820, _839822] : [_839822 = _839820, -(c_Nat_Osemiring__1__class_Oof__nat(_839822) = c_Nat_Osemiring__1__class_Oof__nat(_839820))], (3970 ^ _780205) ^ [_839905, _839907] : [_839907 = _839905, -(c_Lazy__Sequence_Ohit__bound(_839907) = c_Lazy__Sequence_Ohit__bound(_839905))], (3976 ^ _780205) ^ [_839990, _839992, _839994, _839996, _839998, _840000, _840002, _840004, _840006, _840008, _840010, _840012, _840014, _840016] : [-(c_New__Random__Sequence_Opos__decr__bind(_840016, _840012, _840008, _840004, _840000, _839996, _839992) = c_New__Random__Sequence_Opos__decr__bind(_840014, _840010, _840006, _840002, _839998, _839994, _839990)), _840016 = _840014, _840012 = _840010, _840008 = _840006, _840004 = _840002, _840000 = _839998, _839996 = _839994, _839992 = _839990], (4006 ^ _780205) ^ [_840579, _840581, _840583, _840585, _840587, _840589, _840591, _840593] : [-(c_New__DSequence_Opos__decr__bind(_840593, _840589, _840585, _840581) = c_New__DSequence_Opos__decr__bind(_840591, _840587, _840583, _840579)), _840593 = _840591, _840589 = _840587, _840585 = _840583, _840581 = _840579], (4024 ^ _780205) ^ [_840880, _840882, _840884, _840886, _840888, _840890, _840892, _840894, _840896, _840898, _840900, _840902, _840904, _840906] : [-(c_New__Random__Sequence_Oneg__decr__bind(_840906, _840902, _840898, _840894, _840890, _840886, _840882) = c_New__Random__Sequence_Oneg__decr__bind(_840904, _840900, _840896, _840892, _840888, _840884, _840880)), _840906 = _840904, _840902 = _840900, _840898 = _840896, _840894 = _840892, _840890 = _840888, _840886 = _840884, _840882 = _840880], (4054 ^ _780205) ^ [_841469, _841471, _841473, _841475, _841477, _841479, _841481, _841483] : [-(c_New__DSequence_Oneg__decr__bind(_841483, _841479, _841475, _841471) = c_New__DSequence_Oneg__decr__bind(_841481, _841477, _841473, _841469)), _841483 = _841481, _841479 = _841477, _841475 = _841473, _841471 = _841469], (4072 ^ _780205) ^ [_841770, _841772, _841774, _841776, _841778, _841780, _841782, _841784] : [-(c_Lazy__Sequence_Ohb__bind(_841784, _841780, _841776, _841772) = c_Lazy__Sequence_Ohb__bind(_841782, _841778, _841774, _841770)), _841784 = _841782, _841780 = _841778, _841776 = _841774, _841772 = _841770], (4090 ^ _780205) ^ [_842071, _842073, _842075, _842077, _842079, _842081, _842083, _842085] : [-(c_New__Random__Sequence_Opos__empty(_842085, _842081, _842077, _842073) = c_New__Random__Sequence_Opos__empty(_842083, _842079, _842075, _842071)), _842085 = _842083, _842081 = _842079, _842077 = _842075, _842073 = _842071], (4108 ^ _780205) ^ [_842372, _842374] : [_842374 = _842372, -(c_New__DSequence_Opos__empty(_842374) = c_New__DSequence_Opos__empty(_842372))], (4114 ^ _780205) ^ [_842457, _842459, _842461, _842463, _842465, _842467, _842469, _842471] : [-(c_New__DSequence_Oneg__bind(_842471, _842467, _842463, _842459) = c_New__DSequence_Oneg__bind(_842469, _842465, _842461, _842457)), _842471 = _842469, _842467 = _842465, _842463 = _842461, _842459 = _842457], (4132 ^ _780205) ^ [_842758, _842760, _842762, _842764, _842766, _842768, _842770, _842772] : [-(c_New__Random__Sequence_Oneg__map(_842772, _842768, _842764, _842760) = c_New__Random__Sequence_Oneg__map(_842770, _842766, _842762, _842758)), _842772 = _842770, _842768 = _842766, _842764 = _842762, _842760 = _842758], (4150 ^ _780205) ^ [_843059, _843061, _843063, _843065, _843067, _843069, _843071, _843073] : [-(c_New__Random__Sequence_Oneg__bind(_843073, _843069, _843065, _843061) = c_New__Random__Sequence_Oneg__bind(_843071, _843067, _843063, _843059)), _843073 = _843071, _843069 = _843067, _843065 = _843063, _843061 = _843059], (4168 ^ _780205) ^ [_843360, _843362] : [_843362 = _843360, -(c_New__Random__Sequence_Oneg__single(_843362) = c_New__Random__Sequence_Oneg__single(_843360))], (4174 ^ _780205) ^ [_843445, _843447, _843449, _843451, _843453, _843455, _843457, _843459] : [-(c_New__DSequence_Opos__bind(_843459, _843455, _843451, _843447) = c_New__DSequence_Opos__bind(_843457, _843453, _843449, _843445)), _843459 = _843457, _843455 = _843453, _843451 = _843449, _843447 = _843445], (4192 ^ _780205) ^ [_843746, _843748, _843750, _843752] : [-(c_New__DSequence_Oneg__single(_843752, _843748) = c_New__DSequence_Oneg__single(_843750, _843746)), _843752 = _843750, _843748 = _843746], (4202 ^ _780205) ^ [_843895, _843897, _843899, _843901] : [-(c_Lazy__Sequence_Ohb__single(_843901, _843897) = c_Lazy__Sequence_Ohb__single(_843899, _843895)), _843901 = _843899, _843897 = _843895], (4212 ^ _780205) ^ [_844044, _844046, _844048, _844050, _844052, _844054, _844056, _844058] : [-(c_New__Random__Sequence_Opos__map(_844058, _844054, _844050, _844046) = c_New__Random__Sequence_Opos__map(_844056, _844052, _844048, _844044)), _844058 = _844056, _844054 = _844052, _844050 = _844048, _844046 = _844044], (4230 ^ _780205) ^ [_844345, _844347, _844349, _844351, _844353, _844355, _844357, _844359] : [-(c_New__Random__Sequence_Opos__bind(_844359, _844355, _844351, _844347) = c_New__Random__Sequence_Opos__bind(_844357, _844353, _844349, _844345)), _844359 = _844357, _844355 = _844353, _844351 = _844349, _844347 = _844345], (4248 ^ _780205) ^ [_844646, _844648] : [_844648 = _844646, -(c_New__Random__Sequence_Opos__single(_844648) = c_New__Random__Sequence_Opos__single(_844646))], (4254 ^ _780205) ^ [_844731, _844733, _844735, _844737, _844739, _844741] : [-(c_List_Osplice(_844741, _844737, _844733) = c_List_Osplice(_844739, _844735, _844731)), _844741 = _844739, _844737 = _844735, _844733 = _844731], (4268 ^ _780205) ^ [_844952, _844954, _844956, _844958] : [-(c_New__DSequence_Opos__single(_844958, _844954) = c_New__DSequence_Opos__single(_844956, _844952)), _844958 = _844956, _844954 = _844952], (4278 ^ _780205) ^ [_845101, _845103, _845105, _845107, _845109, _845111] : [-(c_Predicate_Oconversep(_845111, _845107, _845103) = c_Predicate_Oconversep(_845109, _845105, _845101)), _845111 = _845109, _845107 = _845105, _845103 = _845101], (4292 ^ _780205) ^ [_845322, _845324] : [_845324 = _845322, -(c_List_Otl(_845324) = c_List_Otl(_845322))], (4298 ^ _780205) ^ [_845407, _845409] : [_845409 = _845407, -(c_List_Orev(_845409) = c_List_Orev(_845407))], (4304 ^ _780205) ^ [_845492, _845494] : [_845494 = _845492, -(c_List_Otake(_845494) = c_List_Otake(_845492))], (4310 ^ _780205) ^ [_845577, _845579] : [_845579 = _845577, -(c_List_Odrop(_845579) = c_List_Odrop(_845577))], (4316 ^ _780205) ^ [_845662, _845664] : [_845664 = _845662, -(c_List_Ohd(_845664) = c_List_Ohd(_845662))], (4322 ^ _780205) ^ [_845747, _845749, _845751, _845753] : [-(c_List_Olast(_845753, _845749) = c_List_Olast(_845751, _845747)), _845753 = _845751, _845749 = _845747], (4332 ^ _780205) ^ [_845896, _845898, _845900, _845902] : [-(c_List_Ozip(_845902, _845898) = c_List_Ozip(_845900, _845896)), _845902 = _845900, _845898 = _845896], (4342 ^ _780205) ^ [_846045, _846047] : [_846047 = _846045, -(c_Orderings_Oord__class_Omin(_846047) = c_Orderings_Oord__class_Omin(_846045))], (4348 ^ _780205) ^ [_846130, _846132] : [_846132 = _846130, -(c_List_Onth(_846132) = c_List_Onth(_846130))], (4354 ^ _780205) ^ [_846215, _846217, _846219, _846221] : [-(c_List_Ofilter(_846221, _846217) = c_List_Ofilter(_846219, _846215)), _846221 = _846219, _846217 = _846215], (4364 ^ _780205) ^ [_846364, _846366, _846368, _846370] : [-(c_List_Oconcat(_846370, _846366) = c_List_Oconcat(_846368, _846364)), _846370 = _846368, _846366 = _846364], (4374 ^ _780205) ^ [_846513, _846515] : [_846515 = _846513, -(c_List_Oappend(_846515) = c_List_Oappend(_846513))], (4380 ^ _780205) ^ [_846598, _846600, _846602, _846604] : [-(c_List_Omap(_846604, _846600) = c_List_Omap(_846602, _846598)), _846604 = _846602, _846600 = _846598], (4390 ^ _780205) ^ [_846747, _846749, _846751, _846753, _846755, _846757] : [-(c_List_Oreplicate(_846757, _846753, _846749) = c_List_Oreplicate(_846755, _846751, _846747)), _846757 = _846755, _846753 = _846751, _846749 = _846747], (4404 ^ _780205) ^ [_846968, _846970] : [_846970 = _846968, -(c_If(_846970) = c_If(_846968))], (4410 ^ _780205) ^ [_847053, _847055, _847057, _847059, _847061, _847063, _847065, _847067, _847069, _847071] : [-(c_Predicate_Opred__comp(_847071, _847067, _847063, _847059, _847055) = c_Predicate_Opred__comp(_847069, _847065, _847061, _847057, _847053)), _847071 = _847069, _847067 = _847065, _847063 = _847061, _847059 = _847057, _847055 = _847053], (4432 ^ _780205) ^ [_847442, _847444, _847446, _847448, _847450, _847452, _847454, _847456] : [-(c_Lazy__Sequence_Oproduct(_847456, _847452, _847448, _847444) = c_Lazy__Sequence_Oproduct(_847454, _847450, _847446, _847442)), _847456 = _847454, _847452 = _847450, _847448 = _847446, _847444 = _847442], (4450 ^ _780205) ^ [_847743, _847745, _847747, _847749, _847751, _847753, _847755, _847757, _847759, _847761, _847763, _847765] : [-(c_New__Random__Sequence_Opos__union(_847765, _847761, _847757, _847753, _847749, _847745) = c_New__Random__Sequence_Opos__union(_847763, _847759, _847755, _847751, _847747, _847743)), _847765 = _847763, _847761 = _847759, _847757 = _847755, _847753 = _847751, _847749 = _847747, _847745 = _847743], (4476 ^ _780205) ^ [_848228, _848230, _848232, _848234, _848236, _848238] : [-(c_New__DSequence_Opos__union(_848238, _848234, _848230) = c_New__DSequence_Opos__union(_848236, _848232, _848228)), _848238 = _848236, _848234 = _848232, _848230 = _848228], (4490 ^ _780205) ^ [_848449, _848451] : [_848451 = _848449, -(c_Lazy__Sequence_Oempty(_848451) = c_Lazy__Sequence_Oempty(_848449))], (4496 ^ _780205) ^ [_848534, _848536] : [_848536 = _848534, -(c_Lazy__Sequence_Osingle(_848536) = c_Lazy__Sequence_Osingle(_848534))], (4502 ^ _780205) ^ [_848619, _848621, _848623, _848625] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_848625, _848621) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_848623, _848619)), _848625 = _848623, _848621 = _848619], (4512 ^ _780205) ^ [_848768, _848770, _848772, _848774] : [-(c_Lazy__Sequence_Osmall__lazy_H(_848774, _848770) = c_Lazy__Sequence_Osmall__lazy_H(_848772, _848768)), _848774 = _848772, _848770 = _848768], (4522 ^ _780205) ^ [_848917, _848919, _848921, _848923] : [-(c_Wellfounded_Oaccp(_848923, _848919) = c_Wellfounded_Oaccp(_848921, _848917)), _848923 = _848921, _848919 = _848917], (4532 ^ _780205) ^ [_849066, _849068, _849070, _849072, _849074, _849076, _849078, _849080, _849082, _849084] : [-(c_Option_Ooption_Ooption__case(_849084, _849080, _849076, _849072, _849068) = c_Option_Ooption_Ooption__case(_849082, _849078, _849074, _849070, _849066)), _849084 = _849082, _849080 = _849078, _849076 = _849074, _849072 = _849070, _849068 = _849066], (4554 ^ _780205) ^ [_849455, _849457] : [_849457 = _849455, -(c_Lazy__Sequence_Oyieldn(_849457) = c_Lazy__Sequence_Oyieldn(_849455))], (4560 ^ _780205) ^ [_849540, _849542, _849544, _849546, _849548, _849550] : [-(c_Lazy__Sequence_Oanamorph(_849550, _849546, _849542) = c_Lazy__Sequence_Oanamorph(_849548, _849544, _849540)), _849550 = _849548, _849546 = _849544, _849542 = _849540], (4574 ^ _780205) ^ [_849761, _849763] : [_849763 = _849761, -(c_Lazy__Sequence_Oyield(_849763) = c_Lazy__Sequence_Oyield(_849761))], (4580 ^ _780205) ^ [_849846, _849848] : [_849848 = _849846, -(c_List_Olist_ONil(_849848) = c_List_Olist_ONil(_849846))], (4586 ^ _780205) ^ [_849931, _849933] : [_849933 = _849931, -(c_List_Olist_OCons(_849933) = c_List_Olist_OCons(_849931))], (4592 ^ _780205) ^ [_850016, _850018] : [_850018 = _850016, -(c_List_Omember(_850018) = c_List_Omember(_850016))], (4598 ^ _780205) ^ [_850101, _850103, _850105, _850107] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850107, _850103) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850105, _850101)), _850107 = _850105, _850103 = _850101], (4608 ^ _780205) ^ [_850250, _850252, _850254, _850256] : [-(c_HOL_OThe(_850256, _850252) = c_HOL_OThe(_850254, _850250)), _850256 = _850254, _850252 = _850250], (4618 ^ _780205) ^ [_850399, _850401, _850403, _850405, _850407, _850409] : [-(c_FunDef_OTHE__default(_850409, _850405, _850401) = c_FunDef_OTHE__default(_850407, _850403, _850399)), _850409 = _850407, _850405 = _850403, _850401 = _850399], (4632 ^ _780205) ^ [_850620, _850622] : [_850622 = _850620, -(c_Nat_Osize__class_Osize(_850622) = c_Nat_Osize__class_Osize(_850620))], (4638 ^ _780205) ^ [_850705, _850707, _850709, _850711] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_850711, _850707) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_850709, _850705)), _850711 = _850709, _850707 = _850705], (4648 ^ _780205) ^ [_850854, _850856, _850858, _850860, _850862, _850864, _850866, _850868, _850870, _850872] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_850872, _850868, _850864, _850860, _850856) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_850870, _850866, _850862, _850858, _850854)), _850872 = _850870, _850868 = _850866, _850864 = _850862, _850860 = _850858, _850856 = _850854], (4670 ^ _780205) ^ [_851243, _851245, _851247, _851249] : [-(c_List_Oupto(_851249, _851245) = c_List_Oupto(_851247, _851243)), _851249 = _851247, _851245 = _851243], (4680 ^ _780205) ^ [_851392, _851394] : [_851394 = _851392, -(c_Code__Numeral_OSuc__code__numeral(_851394) = c_Code__Numeral_OSuc__code__numeral(_851392))], (4686 ^ _780205) ^ [_851477, _851479, _851481, _851483, _851485, _851487, _851489, _851491] : [-(c_Product__Type_Oscomp(_851491, _851487, _851483, _851479) = c_Product__Type_Oscomp(_851489, _851485, _851481, _851477)), _851491 = _851489, _851487 = _851485, _851483 = _851481, _851479 = _851477], (4704 ^ _780205) ^ [_851778, _851780, _851782, _851784, _851786, _851788, _851790, _851792] : [-(c_Random__Sequence_ORandom(_851792, _851788, _851784, _851780) = c_Random__Sequence_ORandom(_851790, _851786, _851782, _851778)), _851792 = _851790, _851788 = _851786, _851784 = _851782, _851780 = _851778], (4722 ^ _780205) ^ [_852079, _852081] : [_852081 = _852079, -(c_DSequence_Ounion(_852081) = c_DSequence_Ounion(_852079))], (4728 ^ _780205) ^ [_852164, _852166, _852168, _852170, _852172, _852174, _852176, _852178] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_852178, _852174, _852170, _852166) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_852176, _852172, _852168, _852164)), _852178 = _852176, _852174 = _852172, _852170 = _852168, _852166 = _852164], (4746 ^ _780205) ^ [_852465, _852467, _852469, _852471, _852473, _852475] : [-(c_Random__Sequence_Oempty(_852475, _852471, _852467) = c_Random__Sequence_Oempty(_852473, _852469, _852465)), _852475 = _852473, _852471 = _852469, _852467 = _852465], (4760 ^ _780205) ^ [_852686, _852688] : [_852688 = _852686, -(c_DSequence_Oempty(_852688) = c_DSequence_Oempty(_852686))], (4766 ^ _780205) ^ [_852771, _852773] : [_852773 = _852771, -(c_DSequence_Osingle(_852773) = c_DSequence_Osingle(_852771))], (4772 ^ _780205) ^ [_852856, _852858, _852860, _852862, _852864, _852866, _852868, _852870] : [-(c_Random__Sequence_Omap(_852870, _852866, _852862, _852858) = c_Random__Sequence_Omap(_852868, _852864, _852860, _852856)), _852870 = _852868, _852866 = _852864, _852862 = _852860, _852858 = _852856], (4790 ^ _780205) ^ [_853157, _853159, _853161, _853163, _853165, _853167, _853169, _853171] : [-(c_Random__Sequence_Obind(_853171, _853167, _853163, _853159) = c_Random__Sequence_Obind(_853169, _853165, _853161, _853157)), _853171 = _853169, _853167 = _853165, _853163 = _853161, _853159 = _853157], (4808 ^ _780205) ^ [_853458, _853460] : [_853460 = _853458, -(c_Random__Sequence_Osingle(_853460) = c_Random__Sequence_Osingle(_853458))], (4814 ^ _780205) ^ [_853543, _853545, _853547, _853549] : [-(c_Product__Type_Osnd(_853549, _853545) = c_Product__Type_Osnd(_853547, _853543)), _853549 = _853547, _853545 = _853543], (4824 ^ _780205) ^ [_853692, _853694, _853696, _853698] : [-(c_Product__Type_Ofst(_853698, _853694) = c_Product__Type_Ofst(_853696, _853692)), _853698 = _853696, _853694 = _853692], (4834 ^ _780205) ^ [_853841, _853843, _853845, _853847, _853849, _853851] : [-(c_Relation_OImage(_853851, _853847, _853843) = c_Relation_OImage(_853849, _853845, _853841)), _853851 = _853849, _853847 = _853845, _853843 = _853841], (4848 ^ _780205) ^ [_854062, _854064, _854066, _854068, _854070, _854072, _854074, _854076] : [-(c_Wellfounded_Olex__prod(_854076, _854072, _854068, _854064) = c_Wellfounded_Olex__prod(_854074, _854070, _854066, _854062)), _854076 = _854074, _854072 = _854070, _854068 = _854066, _854064 = _854062], (4866 ^ _780205) ^ [_854363, _854365] : [_854365 = _854363, -(c_Wellfounded_Ofinite__psubset(_854365) = c_Wellfounded_Ofinite__psubset(_854363))], (4872 ^ _780205) ^ [_854448, _854450, _854452, _854454] : [-(c_List_Olexord(_854454, _854450) = c_List_Olexord(_854452, _854448)), _854454 = _854452, _854450 = _854448], (4882 ^ _780205) ^ [_854597, _854599] : [_854599 = _854597, -(c_Set_OBex(_854599) = c_Set_OBex(_854597))], (4888 ^ _780205) ^ [_854682, _854684] : [_854684 = _854682, -(c_List_Oset(_854684) = c_List_Oset(_854682))], (4894 ^ _780205) ^ [_854767, _854769, _854771, _854773] : [-(c_Complete__Lattice_OSup__class_OSup(_854773, _854769) = c_Complete__Lattice_OSup__class_OSup(_854771, _854767)), _854773 = _854771, _854769 = _854767], (4904 ^ _780205) ^ [_854916, _854918, _854920, _854922] : [-(c_Complete__Lattice_OInf__class_OInf(_854922, _854918) = c_Complete__Lattice_OInf__class_OInf(_854920, _854916)), _854922 = _854920, _854918 = _854916], (4914 ^ _780205) ^ [_855065, _855067, _855069, _855071, _855073, _855075, _855077, _855079, _855081, _855083, _855085, _855087] : [-(c_Partial__Function_Ofun__lub(_855087, _855083, _855079, _855075, _855071, _855067) = c_Partial__Function_Ofun__lub(_855085, _855081, _855077, _855073, _855069, _855065)), _855087 = _855085, _855083 = _855081, _855079 = _855077, _855075 = _855073, _855071 = _855069, _855067 = _855065], (4940 ^ _780205) ^ [_855550, _855552, _855554, _855556, _855558, _855560] : [-(c_Relation_Orel__comp(_855560, _855556, _855552) = c_Relation_Orel__comp(_855558, _855554, _855550)), _855560 = _855558, _855556 = _855554, _855552 = _855550], (4954 ^ _780205) ^ [_855771, _855773, _855775, _855777] : [-(c_Relation_OId__on(_855777, _855773) = c_Relation_OId__on(_855775, _855771)), _855777 = _855775, _855773 = _855771], (4964 ^ _780205) ^ [_855920, _855922] : [_855922 = _855920, -(c_Relation_OId(_855922) = c_Relation_OId(_855920))], (4970 ^ _780205) ^ [_856005, _856007, _856009, _856011] : [-(c_List_Olistrel(_856011, _856007) = c_List_Olistrel(_856009, _856005)), _856011 = _856009, _856007 = _856005], (4980 ^ _780205) ^ [_856154, _856156, _856158, _856160] : [-(c_Relation_Oinv__image(_856160, _856156) = c_Relation_Oinv__image(_856158, _856154)), _856160 = _856158, _856156 = _856154], (4990 ^ _780205) ^ [_856303, _856305, _856307, _856309] : [-(c_Relation_Oconverse(_856309, _856305) = c_Relation_Oconverse(_856307, _856303)), _856309 = _856307, _856305 = _856303], (5000 ^ _780205) ^ [_856452, _856454] : [_856454 = _856452, -(c_HOL_OEx(_856454) = c_HOL_OEx(_856452))], (5006 ^ _780205) ^ [_856537, _856539, _856541, _856543] : [-(c_Hilbert__Choice_OEps(_856543, _856539) = c_Hilbert__Choice_OEps(_856541, _856537)), _856543 = _856541, _856539 = _856537], (5016 ^ _780205) ^ [_856686, _856688, _856690, _856692, _856694, _856696] : [-(c_Finite__Set_Ofold__image(_856696, _856692, _856688) = c_Finite__Set_Ofold__image(_856694, _856690, _856686)), _856696 = _856694, _856692 = _856690, _856688 = _856686], (5030 ^ _780205) ^ [_856907, _856909, _856911, _856913] : [-(c_Quickcheck_Obeyond(_856913, _856909) = c_Quickcheck_Obeyond(_856911, _856907)), _856913 = _856911, _856909 = _856907], (5040 ^ _780205) ^ [_857056, _857058, _857060, _857062, _857064, _857066, _857068, _857070, _857072, _857074] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_857074, _857070, _857066, _857062, _857058) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_857072, _857068, _857064, _857060, _857056)), _857074 = _857072, _857070 = _857068, _857066 = _857064, _857062 = _857060, _857058 = _857056], (5062 ^ _780205) ^ [_857445, _857447] : [_857447 = _857445, -(c_Set_OCollect(_857447) = c_Set_OCollect(_857445))], (5068 ^ _780205) ^ [_857530, _857532] : [_857532 = _857530, -(c_Lattices_Osemilattice__inf__class_Oinf(_857532) = c_Lattices_Osemilattice__inf__class_Oinf(_857530))], (5074 ^ _780205) ^ [_857615, _857617] : [_857617 = _857615, -(c_Lattices_Osemilattice__sup__class_Osup(_857617) = c_Lattices_Osemilattice__sup__class_Osup(_857615))], (5080 ^ _780205) ^ [_857700, _857702, _857704, _857706, _857708, _857710, _857712, _857714] : [-(c_Fun_Othe__inv__into(_857714, _857710, _857706, _857702) = c_Fun_Othe__inv__into(_857712, _857708, _857704, _857700)), _857714 = _857712, _857710 = _857708, _857706 = _857704, _857702 = _857700], (5098 ^ _780205) ^ [_858001, _858003] : [_858003 = _858001, -(c_Fun_Oid(_858003) = c_Fun_Oid(_858001))], (5104 ^ _780205) ^ [_858086, _858088, _858090, _858092, _858094, _858096, _858098, _858100] : [-(c_Product__Type_Ocurry(_858100, _858096, _858092, _858088) = c_Product__Type_Ocurry(_858098, _858094, _858090, _858086)), _858100 = _858098, _858096 = _858094, _858092 = _858090, _858088 = _858086], (5122 ^ _780205) ^ [_858387, _858389, _858391, _858393, _858395, _858397] : [-(c_Product__Type_Oprod_Oprod__case(_858397, _858393, _858389) = c_Product__Type_Oprod_Oprod__case(_858395, _858391, _858387)), _858397 = _858395, _858393 = _858391, _858389 = _858387], (5136 ^ _780205) ^ [_858608, _858610, _858612, _858614, _858616, _858618] : [-(c_Set_Ovimage(_858618, _858614, _858610) = c_Set_Ovimage(_858616, _858612, _858608)), _858618 = _858616, _858614 = _858612, _858610 = _858608], (5150 ^ _780205) ^ [_858829, _858831, _858833, _858835, _858837, _858839, _858841, _858843] : [-(c_Hilbert__Choice_Oinv__into(_858843, _858839, _858835, _858831) = c_Hilbert__Choice_Oinv__into(_858841, _858837, _858833, _858829)), _858843 = _858841, _858839 = _858837, _858835 = _858833, _858831 = _858829], (5168 ^ _780205) ^ [_859130, _859132] : [_859132 = _859130, -(c_Orderings_Otop__class_Otop(_859132) = c_Orderings_Otop__class_Otop(_859130))], (5174 ^ _780205) ^ [_859215, _859217, _859219, _859221, _859223, _859225] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_859225, _859221, _859217) = c_SetInterval_Oord__class_OatLeastAtMost(_859223, _859219, _859215)), _859225 = _859223, _859221 = _859219, _859217 = _859215], (5188 ^ _780205) ^ [_859436, _859438, _859440, _859442, _859444, _859446] : [-(c_Set_Oimage(_859446, _859442, _859438) = c_Set_Oimage(_859444, _859440, _859436)), _859446 = _859444, _859442 = _859440, _859438 = _859436], (5202 ^ _780205) ^ [_859657, _859659] : [_859659 = _859657, -(c_Finite__Set_Ocard(_859659) = c_Finite__Set_Ocard(_859657))], (5208 ^ _780205) ^ [_859742, _859744, _859746, _859748] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_859748, _859744) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_859746, _859742)), _859748 = _859746, _859744 = _859742], (5218 ^ _780205) ^ [_859891, _859893, _859895, _859897] : [-(c_Quotient_ORespects(_859897, _859893) = c_Quotient_ORespects(_859895, _859891)), _859897 = _859895, _859893 = _859891], (5228 ^ _780205) ^ [_860040, _860042, _860044, _860046, _860048, _860050, _860052, _860054] : [-(c_Quotient_OBabs(_860054, _860050, _860046, _860042) = c_Quotient_OBabs(_860052, _860048, _860044, _860040)), _860054 = _860052, _860050 = _860048, _860046 = _860044, _860042 = _860040], (5246 ^ _780205) ^ [_860341, _860343, _860345, _860347] : [-(c_Transitive__Closure_Otrancl(_860347, _860343) = c_Transitive__Closure_Otrancl(_860345, _860341)), _860347 = _860345, _860343 = _860341], (5256 ^ _780205) ^ [_860490, _860492, _860494, _860496] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_860496, _860492) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_860494, _860490)), _860496 = _860494, _860492 = _860490], (5266 ^ _780205) ^ [_860639, _860641, _860643, _860645] : [-(c_Transitive__Closure_Ortrancl(_860645, _860641) = c_Transitive__Closure_Ortrancl(_860643, _860639)), _860645 = _860643, _860641 = _860639], (5276 ^ _780205) ^ [_860788, _860790, _860792, _860794] : [-(c_Product__Type_OPair(_860794, _860790) = c_Product__Type_OPair(_860792, _860788)), _860794 = _860792, _860790 = _860788], (5286 ^ _780205) ^ [_860937, _860939, _860941, _860943, _860945, _860947] : [-(c_Lazy__Sequence_Oappend(_860947, _860943, _860939) = c_Lazy__Sequence_Oappend(_860945, _860941, _860937)), _860947 = _860945, _860943 = _860941, _860939 = _860937], (5300 ^ _780205) ^ [_861158, _861160, _861162, _861164] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_861164, _861160) = c_SetInterval_Oord__class_OatLeastLessThan(_861162, _861158)), _861164 = _861162, _861160 = _861158], (5310 ^ _780205) ^ [_861307, _861309, _861311, _861313] : [-(c_List_Oupt(_861313, _861309) = c_List_Oupt(_861311, _861307)), _861313 = _861311, _861309 = _861307], (5320 ^ _780205) ^ [_861456, _861458, _861460, _861462, _861464, _861466, _861468, _861470] : [-(c_Fun_Ocomp(_861470, _861466, _861462, _861458) = c_Fun_Ocomp(_861468, _861464, _861460, _861456)), _861470 = _861468, _861466 = _861464, _861462 = _861460, _861458 = _861456], (5338 ^ _780205) ^ [_861757, _861759, _861761, _861763, _861765, _861767] : [-(c_Lazy__Sequence_Obind(_861767, _861763, _861759) = c_Lazy__Sequence_Obind(_861765, _861761, _861757)), _861767 = _861765, _861763 = _861761, _861759 = _861757], (5352 ^ _780205) ^ [_861978, _861980, _861982, _861984] : [-(c_Lazy__Sequence_Oflat(_861984, _861980) = c_Lazy__Sequence_Oflat(_861982, _861978)), _861984 = _861982, _861980 = _861978], (5362 ^ _780205) ^ [_862127, _862129, _862131, _862133, _862135, _862137] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_862137, _862133, _862129) = c_Lazy__Sequence_Olazy__sequence_OInsert(_862135, _862131, _862127)), _862137 = _862135, _862133 = _862131, _862129 = _862127], (5376 ^ _780205) ^ [_862348, _862350] : [_862350 = _862348, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_862350) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_862348))], (5382 ^ _780205) ^ [_862433, _862435, _862437, _862439, _862441, _862443, _862445, _862447, _862449, _862451] : [-(c_New__DSequence_Opos__map(_862451, _862447, _862443, _862439, _862435) = c_New__DSequence_Opos__map(_862449, _862445, _862441, _862437, _862433)), _862451 = _862449, _862447 = _862445, _862443 = _862441, _862439 = _862437, _862435 = _862433], (5404 ^ _780205) ^ [_862822, _862824, _862826, _862828, _862830, _862832, _862834, _862836] : [-(c_Lazy__Sequence_Omap(_862836, _862832, _862828, _862824) = c_Lazy__Sequence_Omap(_862834, _862830, _862826, _862822)), _862836 = _862834, _862832 = _862830, _862828 = _862826, _862824 = _862822], (5422 ^ _780205) ^ [_863123, _863125] : [_863125 = _863123, -(c_Power_Opower__class_Opower(_863125) = c_Power_Opower__class_Opower(_863123))], (5428 ^ _780205) ^ [_863208, _863210] : [_863210 = _863208, -(c_Groups_Oone__class_Oone(_863210) = c_Groups_Oone__class_Oone(_863208))], (5434 ^ _780205) ^ [_863293, _863295] : [_863295 = _863293, -(c_Orderings_Oord__class_Oless__eq(_863295) = c_Orderings_Oord__class_Oless__eq(_863293))], (5440 ^ _780205) ^ [_863378, _863380] : [_863380 = _863378, -(c_Groups_Oplus__class_Oplus(_863380) = c_Groups_Oplus__class_Oplus(_863378))], (5446 ^ _780205) ^ [_863463, _863465] : [_863465 = _863463, -(c_Groups_Otimes__class_Otimes(_863465) = c_Groups_Otimes__class_Otimes(_863463))], (5452 ^ _780205) ^ [_863548, _863550] : [_863550 = _863548, -(c_Finite__Set_Ofinite(_863550) = c_Finite__Set_Ofinite(_863548))], (5458 ^ _780205) ^ [_863633, _863635] : [_863635 = _863633, -(c_member(_863635) = c_member(_863633))], (5464 ^ _780205) ^ [_863718, _863720, _863722, _863724] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_863724, _863720) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_863722, _863718)), _863724 = _863722, _863720 = _863718], (5474 ^ _780205) ^ [_863867, _863869, _863871, _863873, _863875, _863877, _863879, _863881] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_863881, _863877, _863873, _863869) = c_SetInterval_Oord_OgreaterThanLessThan(_863879, _863875, _863871, _863867)), _863881 = _863879, _863877 = _863875, _863873 = _863871, _863869 = _863867], (5492 ^ _780205) ^ [_864168, _864170, _864172, _864174, _864176, _864178, _864180, _864182, _864184, _864186] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_864186, _864182, _864178, _864174, _864170) = c_SetInterval_Oord_OgreaterThanAtMost(_864184, _864180, _864176, _864172, _864168)), _864186 = _864184, _864182 = _864180, _864178 = _864176, _864174 = _864172, _864170 = _864168], (5514 ^ _780205) ^ [_864557, _864559, _864561, _864563, _864565, _864567, _864569, _864571, _864573, _864575] : [-(c_SetInterval_Oord_OatLeastLessThan(_864575, _864571, _864567, _864563, _864559) = c_SetInterval_Oord_OatLeastLessThan(_864573, _864569, _864565, _864561, _864557)), _864575 = _864573, _864571 = _864569, _864567 = _864565, _864563 = _864561, _864559 = _864557], (5536 ^ _780205) ^ [_864946, _864948] : [_864948 = _864946, -(c_Groups_Ominus__class_Ominus(_864948) = c_Groups_Ominus__class_Ominus(_864946))], (5542 ^ _780205) ^ [_865031, _865033] : [_865033 = _865031, -(c_Groups_Ouminus__class_Ouminus(_865033) = c_Groups_Ouminus__class_Ouminus(_865031))], (5548 ^ _780205) ^ [_865116, _865118] : [_865118 = _865116, -(c_Divides_Odiv__class_Odiv(_865118) = c_Divides_Odiv__class_Odiv(_865116))], (5554 ^ _780205) ^ [_865201, _865203, _865205, _865207, _865209, _865211] : [-(c_Divides_Odiv__class_Omod(_865211, _865207, _865203) = c_Divides_Odiv__class_Omod(_865209, _865205, _865201)), _865211 = _865209, _865207 = _865205, _865203 = _865201], (5568 ^ _780205) ^ [_865422, _865424] : [_865424 = _865422, -(c_Groups_Ozero__class_Ozero(_865424) = c_Groups_Ozero__class_Ozero(_865422))], (5574 ^ _780205) ^ [_865507, _865509] : [_865509 = _865507, -(c_Orderings_Oord__class_Oless(_865509) = c_Orderings_Oord__class_Oless(_865507))], (5580 ^ _780205) ^ [_865592, _865594, _865596, _865598, _865600, _865602, _865604, _865606] : [-(c_SetInterval_Oord_OatLeastAtMost(_865606, _865602, _865598, _865594) = c_SetInterval_Oord_OatLeastAtMost(_865604, _865600, _865596, _865592)), _865606 = _865604, _865602 = _865600, _865598 = _865596, _865594 = _865592], (5598 ^ _780205) ^ [_865893, _865895] : [_865895 = _865893, -(c_Groups_Oabs__class_Oabs(_865895) = c_Groups_Oabs__class_Oabs(_865893))], (5604 ^ _780205) ^ [_865978, _865980] : [_865980 = _865978, -(c_Rings_Odvd__class_Odvd(_865980) = c_Rings_Odvd__class_Odvd(_865978))], (5610 ^ _780205) ^ [_866063, _866065] : [_866065 = _866063, -(tc_List_Olist(_866065) = tc_List_Olist(_866063))], (5616 ^ _780205) ^ [_866148, _866150, _866152, _866154] : [-(tc_sum(_866154, _866150) = tc_sum(_866152, _866148)), _866154 = _866152, _866150 = _866148], (5626 ^ _780205) ^ [_866297, _866299] : [_866299 = _866297, -(tc_Option_Ooption(_866299) = tc_Option_Ooption(_866297))], (5632 ^ _780205) ^ [_866382, _866384, _866386, _866388] : [-(tc_Nitpick_Opair__box(_866388, _866384) = tc_Nitpick_Opair__box(_866386, _866382)), _866388 = _866386, _866384 = _866382], (5642 ^ _780205) ^ [_866531, _866533, _866535, _866537] : [-(tc_prod(_866537, _866533) = tc_prod(_866535, _866531)), _866537 = _866535, _866533 = _866531], (5652 ^ _780205) ^ [_866680, _866682] : [_866682 = _866680, -(tc_Lazy__Sequence_Olazy__sequence(_866682) = tc_Lazy__Sequence_Olazy__sequence(_866680))], (5658 ^ _780205) ^ [_866765, _866767] : [_866767 = _866765, -(c_COMBI(_866767) = c_COMBI(_866765))], (5664 ^ _780205) ^ [_866850, _866852, _866854, _866856] : [-(c_COMBK(_866856, _866852) = c_COMBK(_866854, _866850)), _866856 = _866854, _866852 = _866850], (5674 ^ _780205) ^ [_866999, _867001, _867003, _867005, _867007, _867009] : [-(c_COMBB(_867009, _867005, _867001) = c_COMBB(_867007, _867003, _866999)), _867009 = _867007, _867005 = _867003, _867001 = _866999], (5688 ^ _780205) ^ [_867220, _867222, _867224, _867226, _867228, _867230] : [-(c_COMBC(_867230, _867226, _867222) = c_COMBC(_867228, _867224, _867220)), _867230 = _867228, _867226 = _867224, _867222 = _867220], (5702 ^ _780205) ^ [_867441, _867443, _867445, _867447, _867449, _867451] : [-(c_COMBS(_867451, _867447, _867443) = c_COMBS(_867449, _867445, _867441)), _867451 = _867449, _867447 = _867445, _867443 = _867441], (5716 ^ _780205) ^ [_867662, _867664] : [_867664 = _867662, -(c_Set_Oinsert(_867664) = c_Set_Oinsert(_867662))], (5722 ^ _780205) ^ [_867747, _867749, _867751, _867753] : [-(hAPP(_867753, _867749) = hAPP(_867751, _867747)), _867753 = _867751, _867749 = _867747], (5732 ^ _780205) ^ [_867896, _867898] : [_867898 = _867896, -(c_Hoare__Mirabelle_Otriple_Otriple(_867898) = c_Hoare__Mirabelle_Otriple_Otriple(_867896))], (5738 ^ _780205) ^ [_867981, _867983] : [_867983 = _867981, -(c_Orderings_Obot__class_Obot(_867983) = c_Orderings_Obot__class_Obot(_867981))], (5754 ^ _780205) ^ [_868211, _868213] : [_868213 = _868211, -(tc_Hoare__Mirabelle_Otriple(_868213) = tc_Hoare__Mirabelle_Otriple(_868211))], (5744 ^ _780205) ^ [_868066, _868068, _868070, _868072] : [-(tc_fun(_868072, _868068) = tc_fun(_868070, _868066)), _868072 = _868070, _868068 = _868066], (5760 ^ _780205) ^ [_871162, _871164] : [hAPP(_871162, 5761 ^ [_871162, _871164]) = hAPP(_871164, 5761 ^ [_871162, _871164]), -(_871162 = _871164)], (5767 ^ _780205) ^ [_871288, _871290] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871288, _871290, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871288), tc_HOL_Obool))))], (5769 ^ _780205) ^ [_871321, _871323] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871321, _871323, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871321), tc_HOL_Obool))))], (5771 ^ _780205) ^ [_871384, _871386, _871388, _871390, _871392, _871394, _871396] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871384), _871386), _871388), _871390) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871384), _871392), _871394), _871396), 5774 ^ _780205 : [(5775 ^ _780205) ^ [] : [-(_871386 = _871392)], (5777 ^ _780205) ^ [] : [-(_871388 = _871394)], (5779 ^ _780205) ^ [] : [-(_871390 = _871396)]]], (5781 ^ _780205) ^ [_871561, _871563, _871565, _871567, _871569, _871571, _871573] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871561), _871563), _871565), _871567) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871561), _871569), _871571), _871573)), _871563 = _871569, _871565 = _871571, _871567 = _871573], (5795 ^ _780205) ^ [_871818, _871820, _871822, _871824] : [c_Hoare__Mirabelle_Ohoare__derivs(_871818, _871820, _871822), c_Hoare__Mirabelle_Ohoare__derivs(_871818, _871824, _871820), -(c_Hoare__Mirabelle_Ohoare__derivs(_871818, _871824, _871822))], (5805 ^ _780205) ^ [_871961, _871963, _871965, _871967] : [c_Hoare__Mirabelle_Ohoare__derivs(_871961, _871963, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871961)), _871965), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871961), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_871961, _871963, _871967), -(c_Hoare__Mirabelle_Ohoare__derivs(_871961, _871963, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871961)), _871965), _871967)))], (5815 ^ _780205) ^ [_872158, _872160, _872162, _872164] : [c_Hoare__Mirabelle_Ohoare__derivs(_872158, _872160, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872158)), _872162), _872164)), 5818 ^ _780205 : [(5819 ^ _780205) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_872158, _872160, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872158)), _872162), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872158), tc_HOL_Obool)))))], (5821 ^ _780205) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_872158, _872160, _872164))]]], (5823 ^ _780205) ^ [_872325, _872327, _872329, _872331, _872333, _872335] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_872325, _872327, _872329, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872325), _872331), _872333), _872335)) = hAPP(hAPP(hAPP(_872329, _872331), _872333), _872335))], (5825 ^ _780205) ^ [_872383, _872385, _872387, _872389, _872391, _872393] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_872383, _872385, _872387, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_872383), _872389), _872391), _872393)) = hAPP(hAPP(hAPP(_872387, _872389), _872391), _872393))], (5827 ^ _780205) ^ [_872456, _872458, _872460] : [c_Orderings_Obot__class_Obot(tc_fun(_872456, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_872456), _872458), _872460)], (5829 ^ _780205) ^ [_872511, _872513, _872515] : [hAPP(hAPP(c_Set_Oinsert(_872511), _872513), _872515) = c_Orderings_Obot__class_Obot(tc_fun(_872511, tc_HOL_Obool))], (5831 ^ _780205) ^ [_872575, _872577, _872579, _872581, _872583] : [hAPP(hAPP(c_Set_Oinsert(_872575), _872577), hAPP(hAPP(c_Set_Oinsert(_872575), _872579), c_Orderings_Obot__class_Obot(tc_fun(_872575, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_872575), _872581), hAPP(hAPP(c_Set_Oinsert(_872575), _872583), c_Orderings_Obot__class_Obot(tc_fun(_872575, tc_HOL_Obool)))), 5836 ^ _780205 : [(5837 ^ _780205) ^ [] : [-(_872577 = _872581)], (5839 ^ _780205) ^ [] : [-(_872579 = _872583)]], 5840 ^ _780205 : [(5841 ^ _780205) ^ [] : [-(_872577 = _872583)], (5843 ^ _780205) ^ [] : [-(_872579 = _872581)]]], (5845 ^ _780205) ^ [_872837, _872839, _872841, _872843, _872845] : [-(hAPP(hAPP(c_Set_Oinsert(_872837), _872839), hAPP(hAPP(c_Set_Oinsert(_872837), _872841), c_Orderings_Obot__class_Obot(tc_fun(_872837, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_872837), _872843), hAPP(hAPP(c_Set_Oinsert(_872837), _872845), c_Orderings_Obot__class_Obot(tc_fun(_872837, tc_HOL_Obool))))), 5846 ^ _780205 : [(5847 ^ _780205) ^ [] : [_872839 = _872843, _872841 = _872845], (5853 ^ _780205) ^ [] : [_872839 = _872845, _872841 = _872843]]], (5861 ^ _780205) ^ [_873153, _873155, _873157] : [hAPP(hAPP(c_Set_Oinsert(_873153), _873155), c_Orderings_Obot__class_Obot(tc_fun(_873153, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_873153), _873157), c_Orderings_Obot__class_Obot(tc_fun(_873153, tc_HOL_Obool))), -(_873155 = _873157)], (5867 ^ _780205) ^ [_873284, _873286, _873288] : [class_Orderings_Obot(_873284), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_873286, _873284)), _873288) = c_Orderings_Obot__class_Obot(_873284))], (5873 ^ _780205) ^ [_873381, _873383, _873385] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_873381, _873383, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873381)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873381), _873385), c_Com_Ocom_OSKIP), _873385)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873381), tc_HOL_Obool)))))], (5875 ^ _780205) ^ [_873437, _873439, _873441] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_873437, _873439, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873437)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873437), _873441), c_Com_Ocom_OSKIP), _873441)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873437), tc_HOL_Obool)))))], (5877 ^ _780205) ^ [_873493, _873495, _873497, _873499, _873501, _873503] : [c_Hoare__Mirabelle_Ohoare__derivs(_873493, _873495, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873493)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873493), _873497), _873499), _873501)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873493), tc_HOL_Obool)))), 5884 ^ _780205 : [(5885 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_873501, 5882 ^ [_873493, _873495, _873497, _873499, _873501, _873503]), 5883 ^ [_873493, _873495, _873497, _873499, _873501, _873503])))], (5887 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_873503, 5882 ^ [_873493, _873495, _873497, _873499, _873501, _873503]), 5883 ^ [_873493, _873495, _873497, _873499, _873501, _873503]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_873493, _873495, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873493)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873493), _873497), _873499), _873503)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873493), tc_HOL_Obool)))))], (5891 ^ _780205) ^ [_873922, _873924, _873926, _873928, _873930, _873932] : [c_Hoare__Mirabelle_Ohoare__derivs(_873922, _873924, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873922)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873922), _873926), _873928), _873930)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873922), tc_HOL_Obool)))), 5898 ^ _780205 : [(5899 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_873932, 5896 ^ [_873922, _873924, _873926, _873928, _873930, _873932]), 5897 ^ [_873922, _873924, _873926, _873928, _873930, _873932])))], (5901 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_873926, 5896 ^ [_873922, _873924, _873926, _873928, _873930, _873932]), 5897 ^ [_873922, _873924, _873926, _873928, _873930, _873932]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_873922, _873924, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_873922)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873922), _873932), _873928), _873930)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_873922), tc_HOL_Obool)))))], (5905 ^ _780205) ^ [_874351, _874353, _874355, _874357, _874359, _874361, _874363] : [c_Hoare__Mirabelle_Ohoare__derivs(_874351, _874353, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_874351)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874351), _874355), _874357), _874359)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_874351), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_874351, _874353, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_874351)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874351), _874359), _874361), _874363)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_874351), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_874351, _874353, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_874351)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874351), _874355), c_Com_Ocom_OSemi(_874357, _874361)), _874363)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_874351), tc_HOL_Obool)))))], (5925 ^ _780205) ^ [_874815, _874817, _874819, _874821] : [5926 ^ _780205 : [(5927 ^ _780205) ^ [] : [_874817 = _874821], (5929 ^ _780205) ^ [] : [hBOOL(hAPP(_874819, _874821))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_874815), _874817), _874819), _874821)))], (5915 ^ _780205) ^ [_874701, _874703, _874705, _874707] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_874701), _874703), _874705), _874707)), -(_874703 = _874707), -(hBOOL(hAPP(_874705, _874707)))], (5933 ^ _780205) ^ [_874960, _874962, _874964, _874966] : [-(hAPP(hAPP(c_Set_Oinsert(_874960), _874962), hAPP(hAPP(c_Set_Oinsert(_874960), _874964), _874966)) = hAPP(hAPP(c_Set_Oinsert(_874960), _874964), hAPP(hAPP(c_Set_Oinsert(_874960), _874962), _874966)))], (5935 ^ _780205) ^ [_875021, _875023, _875025] : [-(hAPP(hAPP(c_Set_Oinsert(_875021), _875023), hAPP(hAPP(c_Set_Oinsert(_875021), _875023), _875025)) = hAPP(hAPP(c_Set_Oinsert(_875021), _875023), _875025))], (5937 ^ _780205) ^ [_875072, _875074] : [-(c_Set_Othe__elem(_875072, hAPP(hAPP(c_Set_Oinsert(_875072), _875074), c_Orderings_Obot__class_Obot(tc_fun(_875072, tc_HOL_Obool)))) = _875074)], (5939 ^ _780205) ^ [_875125, _875127] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_875125, _875127)], (5941 ^ _780205) ^ [_875165, _875167] : [c_Com_Ocom_OSemi(_875165, _875167) = c_Com_Ocom_OSKIP], (5943 ^ _780205) ^ [_875214, _875216, _875218, _875220] : [c_Com_Ocom_OSemi(_875214, _875216) = c_Com_Ocom_OSemi(_875218, _875220), 5946 ^ _780205 : [(5947 ^ _780205) ^ [] : [-(_875214 = _875218)], (5949 ^ _780205) ^ [] : [-(_875216 = _875220)]]], (5951 ^ _780205) ^ [_875329, _875331, _875333, _875335] : [-(c_Com_Ocom_OSemi(_875329, _875331) = c_Com_Ocom_OSemi(_875333, _875335)), _875329 = _875333, _875331 = _875335], (5961 ^ _780205) ^ [_875480, _875482, _875484] : [c_Hoare__Mirabelle_Ohoare__derivs(_875480, _875482, _875484), -(c_Hoare__Mirabelle_Ohoare__valids(_875480, _875482, _875484))], (5967 ^ _780205) ^ [_875563, _875565, _875567, _875569, _875571, _875573, _875575] : [c_Hoare__Mirabelle_Ohoare__derivs(_875563, _875565, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_875563)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_875563), _875567), _875569), _875571)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_875563), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_875563, _875565, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_875563)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_875563), _875573), _875569), _875575)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_875563), tc_HOL_Obool))))), 5974 ^ _780205 : [(5975 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_875573, 5972 ^ [_875563, _875565, _875567, _875569, _875571, _875573, _875575]), 5973 ^ [_875563, _875565, _875567, _875569, _875571, _875573, _875575])))], (5984 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_875575, 5972 ^ [_875563, _875565, _875567, _875569, _875571, _875573, _875575]), 5976 ^ [_875563, _875565, _875567, _875569, _875571, _875573, _875575]))], (5978 ^ _780205) ^ [_876037] : [hBOOL(hAPP(hAPP(_875567, _876037), 5973 ^ [_875563, _875565, _875567, _875569, _875571, _875573, _875575])), -(hBOOL(hAPP(hAPP(_875571, _876037), 5976 ^ [_875563, _875565, _875567, _875569, _875571, _875573, _875575])))]]], (5988 ^ _780205) ^ [_876334, _876336, _876338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876334, tc_HOL_Obool)), _876336), hAPP(hAPP(c_Set_Oinsert(_876334), _876338), c_Orderings_Obot__class_Obot(tc_fun(_876334, tc_HOL_Obool))))), -(_876336 = c_Orderings_Obot__class_Obot(tc_fun(_876334, tc_HOL_Obool))), -(_876336 = hAPP(hAPP(c_Set_Oinsert(_876334), _876338), c_Orderings_Obot__class_Obot(tc_fun(_876334, tc_HOL_Obool))))], (5998 ^ _780205) ^ [_876508, _876510, _876512] : [hBOOL(hAPP(hAPP(c_member(_876508), _876510), hAPP(hAPP(c_Set_Oinsert(_876508), _876512), c_Orderings_Obot__class_Obot(tc_fun(_876508, tc_HOL_Obool))))), -(_876510 = _876512)], (6004 ^ _780205) ^ [_876645, _876647, _876649] : [hBOOL(hAPP(hAPP(c_member(_876645), _876647), hAPP(hAPP(c_Set_Oinsert(_876645), _876649), c_Orderings_Obot__class_Obot(tc_fun(_876645, tc_HOL_Obool))))), -(_876647 = _876649)], (6010 ^ _780205) ^ [_876760, _876762, _876764] : [_876762 = _876764, -(hBOOL(hAPP(hAPP(c_member(_876760), _876762), hAPP(hAPP(c_Set_Oinsert(_876760), _876764), c_Orderings_Obot__class_Obot(tc_fun(_876760, tc_HOL_Obool))))))], (6016 ^ _780205) ^ [_876881, _876883, _876885, _876887] : [c_Finite__Set_Ofolding__one(_876881, _876883, _876885), -(hAPP(_876885, hAPP(hAPP(c_Set_Oinsert(_876881), _876887), c_Orderings_Obot__class_Obot(tc_fun(_876881, tc_HOL_Obool)))) = _876887)], (6022 ^ _780205) ^ [_877017, _877019, _877021, _877023] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_877017, _877019, hAPP(hAPP(c_Set_Oinsert(_877017), _877021), c_Orderings_Obot__class_Obot(tc_fun(_877017, tc_HOL_Obool)))), _877023)), -(_877021 = _877023)], (6028 ^ _780205) ^ [_877132, _877134, _877136, _877138] : [_877136 = _877138, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_877132, _877134, hAPP(hAPP(c_Set_Oinsert(_877132), _877136), c_Orderings_Obot__class_Obot(tc_fun(_877132, tc_HOL_Obool)))), _877138)))], (6034 ^ _780205) ^ [_877253, _877255, _877257] : [-(hAPP(hAPP(c_Set_Oinsert(_877253), _877255), _877257) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_877253, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_877253), _877255), c_Orderings_Obot__class_Obot(tc_fun(_877253, tc_HOL_Obool)))), _877257))], (6036 ^ _780205) ^ [_877312, _877314] : [class_Orderings_Opreorder(_877312), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877312), _877314), _877314)))], (6042 ^ _780205) ^ [_877401, _877403, _877405, _877407] : [_877401 = _877403, 6047 ^ _780205 : [(6048 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877405), _877407), _877401)))], (6050 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877405), _877407), _877403)))]], 6051 ^ _780205 : [(6052 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_877405), _877407), _877401))], (6054 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_877405), _877407), _877403))]]], (6056 ^ _780205) ^ [_877664, _877666, _877668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877664, tc_HOL_Obool)), _877666), _877668)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877664, tc_HOL_Obool)), _877668), _877666)), -(_877666 = _877668)], (6066 ^ _780205) ^ [_877849, _877851] : [hBOOL(hAPP(hAPP(c_member(_877849), _877851), c_Orderings_Obot__class_Obot(tc_fun(_877849, tc_HOL_Obool))))], (6068 ^ _780205) ^ [_877886, _877888, _877890, _877892] : [hBOOL(hAPP(hAPP(c_member(_877886), _877888), hAPP(hAPP(c_Set_Oinsert(_877886), _877890), _877892))), -(_877888 = _877890), -(hBOOL(hAPP(hAPP(c_member(_877886), _877888), _877892)))], (6078 ^ _780205) ^ [_878026, _878028, _878030, _878032] : [6079 ^ _780205 : [(6080 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_878026), _878028), _878030))], (6082 ^ _780205) ^ [] : [_878028 = _878032]], -(hBOOL(hAPP(hAPP(c_member(_878026), _878028), hAPP(hAPP(c_Set_Oinsert(_878026), _878032), _878030))))], (6086 ^ _780205) ^ [_878191, _878193, _878195, _878197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878191, tc_HOL_Obool)), _878193), _878195)), hBOOL(hAPP(hAPP(c_member(_878191), _878197), _878193)), -(hBOOL(hAPP(hAPP(c_member(_878191), _878197), _878195)))], (6096 ^ _780205) ^ [_878376, _878378, _878380, _878382] : [hBOOL(hAPP(hAPP(c_member(_878376), _878378), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_878376, tc_HOL_Obool)), _878380), _878382))), -(hBOOL(hAPP(hAPP(c_member(_878376), _878378), _878380))), -(hBOOL(hAPP(hAPP(c_member(_878376), _878378), _878382)))], (6106 ^ _780205) ^ [_878536, _878538, _878540, _878542] : [6107 ^ _780205 : [(6108 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_878536), _878538), _878540))], (6110 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_878536), _878538), _878542))]], -(hBOOL(hAPP(hAPP(c_member(_878536), _878538), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_878536, tc_HOL_Obool)), _878542), _878540))))], (6114 ^ _780205) ^ [_878721, _878723] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878721, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_878721, tc_HOL_Obool))), _878723)))], (6116 ^ _780205) ^ [_878761, _878763] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878761, tc_HOL_Obool)), _878763), _878763)))], (6118 ^ _780205) ^ [_878796, _878798, _878800] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878796, tc_HOL_Obool)), _878798), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_878796, tc_HOL_Obool)), _878798), _878800))))], (6120 ^ _780205) ^ [_878844, _878846, _878848] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878844, tc_HOL_Obool)), _878846), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_878844, tc_HOL_Obool)), _878848), _878846))))], (6122 ^ _780205) ^ [_878892, _878894] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_878892, tc_HOL_Obool)), _878894), _878894) = _878894)], (6124 ^ _780205) ^ [_878928, _878930, _878932, _878934] : [class_Orderings_Oord(_878928), 6127 ^ _780205 : [(6128 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878930, _878928)), _878932), _878934)), 6131 ^ _780205 : [(6132 ^ _780205) ^ [_879085] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878928), hAPP(_878932, _879085)), hAPP(_878934, _879085))))]]], (6134 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878928), hAPP(_878932, 6135 ^ [_878928, _878930, _878932, _878934])), hAPP(_878934, 6135 ^ [_878928, _878930, _878932, _878934]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878930, _878928)), _878932), _878934)))]]], (6141 ^ _780205) ^ [_879292, _879294, _879296] : [hBOOL(hAPP(hAPP(c_member(_879292), _879294), _879296)), -(hBOOL(hAPP(_879296, _879294)))], (6147 ^ _780205) ^ [_879385, _879387, _879389] : [hBOOL(hAPP(_879389, _879387)), -(hBOOL(hAPP(hAPP(c_member(_879385), _879387), _879389)))], (6153 ^ _780205) ^ [_879484, _879486, _879488] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879484, tc_HOL_Obool)), _879486), _879488) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879484, tc_HOL_Obool)), _879488), _879486))], (6155 ^ _780205) ^ [_879533, _879535, _879537] : [class_Orderings_Olinorder(_879533), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879533), _879535), _879537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879533), _879537), _879535)))], (6165 ^ _780205) ^ [_879669, _879671, _879673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879669, tc_HOL_Obool)), _879671), _879673)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879669, tc_HOL_Obool)), _879671), _879673) = _879673)], (6171 ^ _780205) ^ [_879786, _879788, _879790] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879786, tc_HOL_Obool)), _879788), _879790) = _879790, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879786, tc_HOL_Obool)), _879788), _879790)))], (6177 ^ _780205) ^ [_879927, _879929, _879931] : [_879927 = _879929, 6180 ^ _780205 : [(6181 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879931, tc_HOL_Obool)), _879927), _879929)))], (6183 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879931, tc_HOL_Obool)), _879929), _879927)))]]], (6185 ^ _780205) ^ [_880068, _880070, _880072] : [-(_880068 = _880070), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880072, tc_HOL_Obool)), _880068), _880070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880072, tc_HOL_Obool)), _880070), _880068))], (6195 ^ _780205) ^ [_880243, _880245, _880247] : [class_Orderings_Oorder(_880243), 6198 ^ _780205 : [(6199 ^ _780205) ^ [] : [_880245 = _880247, 6202 ^ _780205 : [(6203 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880243), _880245), _880247)))], (6205 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880243), _880247), _880245)))]]], (6207 ^ _780205) ^ [] : [-(_880245 = _880247), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880243), _880245), _880247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880243), _880247), _880245))]]], (6217 ^ _780205) ^ [_880570, _880572, _880574] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880570, tc_HOL_Obool)), _880572), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880570, tc_HOL_Obool)), _880572), _880574)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880570, tc_HOL_Obool)), _880572), _880574))], (6219 ^ _780205) ^ [_880630, _880632, _880634, _880636] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880630, tc_HOL_Obool)), _880632), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880630, tc_HOL_Obool)), _880634), _880636)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880630, tc_HOL_Obool)), _880634), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880630, tc_HOL_Obool)), _880632), _880636)))], (6231 ^ _780205) ^ [_880878, _880880, _880882, _880884] : [6232 ^ _780205 : [(6233 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_880878), _880880), _880882))], (6235 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_880878), _880880), _880884))]], -(hBOOL(hAPP(hAPP(c_member(_880878), _880880), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880878, tc_HOL_Obool)), _880882), _880884))))], (6221 ^ _780205) ^ [_880724, _880726, _880728, _880730] : [hBOOL(hAPP(hAPP(c_member(_880724), _880726), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_880724, tc_HOL_Obool)), _880728), _880730))), -(hBOOL(hAPP(hAPP(c_member(_880724), _880726), _880728))), -(hBOOL(hAPP(hAPP(c_member(_880724), _880726), _880730)))], (6239 ^ _780205) ^ [_881063, _881065, _881067, _881069] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881063, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881063, tc_HOL_Obool)), _881065), _881067)), _881069) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881063, tc_HOL_Obool)), _881065), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881063, tc_HOL_Obool)), _881067), _881069)))], (6241 ^ _780205) ^ [_881157, _881159, _881161, _881163] : [6242 ^ _780205 : [(6243 ^ _780205) ^ [_881267] : [hBOOL(hAPP(hAPP(c_member(_881157), _881267), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881157, tc_HOL_Obool)), _881159), _881161))), hBOOL(hAPP(_881163, _881267))]], 6251 ^ _780205 : [(6252 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_881157), 6250 ^ [_881157, _881159, _881161, _881163]), _881159)))], (6254 ^ _780205) ^ [] : [-(hBOOL(hAPP(_881163, 6250 ^ [_881157, _881159, _881161, _881163])))]], 6256 ^ _780205 : [(6257 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_881157), 6255 ^ [_881157, _881159, _881161, _881163]), _881161)))], (6259 ^ _780205) ^ [] : [-(hBOOL(hAPP(_881163, 6255 ^ [_881157, _881159, _881161, _881163])))]]], (6261 ^ _780205) ^ [_881556, _881558, _881560, _881562] : [6275 ^ _780205 : [(6276 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_881556), 6274 ^ [_881556, _881558, _881560, _881562]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881556, tc_HOL_Obool)), _881558), _881560))))], (6278 ^ _780205) ^ [] : [-(hBOOL(hAPP(_881562, 6274 ^ [_881556, _881558, _881560, _881562])))]], 6262 ^ _780205 : [(6263 ^ _780205) ^ [_881669] : [hBOOL(hAPP(hAPP(c_member(_881556), _881669), _881558)), hBOOL(hAPP(_881562, _881669))], (6269 ^ _780205) ^ [_881765] : [hBOOL(hAPP(hAPP(c_member(_881556), _881765), _881560)), hBOOL(hAPP(_881562, _881765))]]], (6299 ^ _780205) ^ [_882402, _882404, _882406, _882408] : [6303 ^ _780205 : [(6304 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_882402), 6302 ^ [_882402, _882404, _882406, _882408]), _882404)))], (6306 ^ _780205) ^ [] : [hBOOL(hAPP(_882408, 6302 ^ [_882402, _882404, _882406, _882408]))]], 6308 ^ _780205 : [(6309 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_882402), 6307 ^ [_882402, _882404, _882406, _882408]), _882406)))], (6311 ^ _780205) ^ [] : [hBOOL(hAPP(_882408, 6307 ^ [_882402, _882404, _882406, _882408]))]], 6312 ^ _780205 : [(6313 ^ _780205) ^ [_882735] : [hBOOL(hAPP(hAPP(c_member(_882402), _882735), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_882402, tc_HOL_Obool)), _882404), _882406))), -(hBOOL(hAPP(_882408, _882735)))]]], (6280 ^ _780205) ^ [_881980, _881982, _881984, _881986] : [6282 ^ _780205 : [(6283 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_881980), 6281 ^ [_881980, _881982, _881984, _881986]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_881980, tc_HOL_Obool)), _881982), _881984))))], (6285 ^ _780205) ^ [] : [hBOOL(hAPP(_881986, 6281 ^ [_881980, _881982, _881984, _881986]))]], 6286 ^ _780205 : [(6287 ^ _780205) ^ [_882200] : [hBOOL(hAPP(hAPP(c_member(_881980), _882200), _881982)), -(hBOOL(hAPP(_881986, _882200)))], (6293 ^ _780205) ^ [_882297] : [hBOOL(hAPP(hAPP(c_member(_881980), _882297), _881984)), -(hBOOL(hAPP(_881986, _882297)))]]], (6319 ^ _780205) ^ [_882866, _882868, _882870] : [_882866 = _882868, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882870, tc_HOL_Obool)), _882866), _882868)))], (6325 ^ _780205) ^ [_882965, _882967, _882969] : [_882965 = _882967, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882969, tc_HOL_Obool)), _882967), _882965)))], (6331 ^ _780205) ^ [_883064, _883066, _883068] : [class_Orderings_Opreorder(_883064), _883066 = _883068, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883064), _883066), _883068)))], (6341 ^ _780205) ^ [_883209, _883211, _883213, _883215] : [hBOOL(hAPP(hAPP(c_member(_883209), _883211), _883213)), -(hBOOL(hAPP(hAPP(c_member(_883209), _883211), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_883209, tc_HOL_Obool)), _883213), _883215))))], (6347 ^ _780205) ^ [_883340, _883342, _883344, _883346] : [hBOOL(hAPP(hAPP(c_member(_883340), _883342), _883344)), -(hBOOL(hAPP(hAPP(c_member(_883340), _883342), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_883340, tc_HOL_Obool)), _883346), _883344))))], (6353 ^ _780205) ^ [_883471, _883473, _883475, _883477, _883479] : [class_Orderings_Oord(_883471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883473, _883471)), _883475), _883477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883471), hAPP(_883475, _883479)), hAPP(_883477, _883479))))], (6363 ^ _780205) ^ [_883656, _883658, _883660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883656, tc_HOL_Obool)), _883658), _883660)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_883656, tc_HOL_Obool)), _883658), _883660) = _883660)], (6369 ^ _780205) ^ [_883777, _883779, _883781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883777, tc_HOL_Obool)), _883779), _883781)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_883777, tc_HOL_Obool)), _883781), _883779) = _883781)], (6375 ^ _780205) ^ [_883898, _883900, _883902, _883904] : [_883898 = _883900, 6378 ^ _780205 : [(6379 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_883902), _883904), _883898)), -(hBOOL(hAPP(hAPP(c_member(_883902), _883904), _883900)))], (6385 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_883902), _883904), _883900)), -(hBOOL(hAPP(hAPP(c_member(_883902), _883904), _883898)))]]], (6391 ^ _780205) ^ [_884159, _884161, _884163, _884165] : [_884159 = _884161, 6394 ^ _780205 : [(6395 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_884163), _884159), _884165)), -(hBOOL(hAPP(hAPP(c_member(_884163), _884161), _884165)))], (6401 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_884163), _884161), _884165)), -(hBOOL(hAPP(hAPP(c_member(_884163), _884159), _884165)))]]], (6407 ^ _780205) ^ [_884420, _884422, _884424, _884426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884420, tc_HOL_Obool)), _884422), _884424)), hBOOL(hAPP(hAPP(c_member(_884420), _884426), _884422)), -(hBOOL(hAPP(hAPP(c_member(_884420), _884426), _884424)))], (6417 ^ _780205) ^ [_884605, _884607, _884609] : [class_Orderings_Oorder(_884605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884605), _884607), _884609)), 6424 ^ _780205 : [(6425 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884605), _884609), _884607)), -(_884609 = _884607)], (6431 ^ _780205) ^ [] : [_884609 = _884607, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884605), _884609), _884607)))]]], (6437 ^ _780205) ^ [_884905, _884907, _884909, _884911] : [_884905 = _884907, hBOOL(hAPP(hAPP(c_member(_884909), _884907), _884911)), -(hBOOL(hAPP(hAPP(c_member(_884909), _884905), _884911)))], (6447 ^ _780205) ^ [_885070, _885072, _885074, _885076] : [class_Orderings_Oord(_885070), _885072 = _885074, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885070), _885074), _885076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885070), _885072), _885076)))], (6461 ^ _780205) ^ [_885289, _885291, _885293, _885295] : [class_Orderings_Oorder(_885289), _885291 = _885293, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885289), _885295), _885293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885289), _885295), _885291)))], (6475 ^ _780205) ^ [_885508, _885510, _885512, _885514] : [hBOOL(hAPP(hAPP(c_member(_885508), _885510), _885512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885508, tc_HOL_Obool)), _885512), _885514)), -(hBOOL(hAPP(hAPP(c_member(_885508), _885510), _885514)))], (6485 ^ _780205) ^ [_885693, _885695, _885697, _885699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885693, tc_HOL_Obool)), _885695), _885697)), hBOOL(hAPP(hAPP(c_member(_885693), _885699), _885695)), -(hBOOL(hAPP(hAPP(c_member(_885693), _885699), _885697)))], (6495 ^ _780205) ^ [_885878, _885880, _885882, _885884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885878, tc_HOL_Obool)), _885880), _885882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885878, tc_HOL_Obool)), _885882), _885884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885878, tc_HOL_Obool)), _885880), _885884)))], (6505 ^ _780205) ^ [_886075, _886077, _886079, _886081] : [class_Orderings_Oord(_886075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886075), _886077), _886079)), _886079 = _886081, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886075), _886077), _886081)))], (6519 ^ _780205) ^ [_886294, _886296, _886298, _886300] : [class_Orderings_Oorder(_886294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886294), _886296), _886298)), _886296 = _886300, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886294), _886300), _886298)))], (6533 ^ _780205) ^ [_886513, _886515, _886517] : [class_Orderings_Oorder(_886513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886513), _886515), _886517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886513), _886517), _886515)), -(_886515 = _886517)], (6547 ^ _780205) ^ [_886726, _886728, _886730, _886732] : [class_Orderings_Opreorder(_886726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886726), _886728), _886730)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886726), _886730), _886732)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886726), _886728), _886732)))], (6561 ^ _780205) ^ [_886959, _886961, _886963] : [class_Orderings_Oorder(_886959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886959), _886961), _886963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886959), _886963), _886961)), -(_886963 = _886961)], (6575 ^ _780205) ^ [_887172, _887174, _887176, _887178] : [class_Orderings_Oorder(_887172), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887172), _887174), _887176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887172), _887178), _887174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887172), _887178), _887176)))], (6589 ^ _780205) ^ [_887405, _887407, _887409, _887411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887405, tc_HOL_Obool)), _887407), _887409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887405, tc_HOL_Obool)), _887411), _887409)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887405, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887405, tc_HOL_Obool)), _887407), _887411)), _887409)))], (6599 ^ _780205) ^ [_887624, _887626, _887628, _887630, _887632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887624, tc_HOL_Obool)), _887626), _887628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887624, tc_HOL_Obool)), _887630), _887632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887624, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887624, tc_HOL_Obool)), _887626), _887630)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887624, tc_HOL_Obool)), _887628), _887632))))], (6609 ^ _780205) ^ [_887869, _887871, _887873] : [_887869 = _887871, 6612 ^ _780205 : [(6613 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887873, tc_HOL_Obool)), _887869), _887871)))], (6615 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887873, tc_HOL_Obool)), _887871), _887869)))]]], (6617 ^ _780205) ^ [_888018, _888020, _888022, _888024, _888026] : [class_Orderings_Oord(_888018), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888020, _888018)), _888022), _888024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888018), hAPP(_888022, _888026)), hAPP(_888024, _888026))))], (6627 ^ _780205) ^ [_888203, _888205, _888207] : [class_Orderings_Olinorder(_888203), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888203), _888205), _888207))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888203), _888207), _888205)))], (6637 ^ _780205) ^ [_888322, _888324, _888326, _888328] : [-(hBOOL(hAPP(hAPP(c_member(_888322), _888324), _888326))), 6640 ^ _780205 : [(6641 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888322, tc_HOL_Obool)), _888326), hAPP(hAPP(c_Set_Oinsert(_888322), _888324), _888328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888322, tc_HOL_Obool)), _888326), _888328)))], (6647 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888322, tc_HOL_Obool)), _888326), _888328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888322, tc_HOL_Obool)), _888326), hAPP(hAPP(c_Set_Oinsert(_888322), _888324), _888328))))]]], (6653 ^ _780205) ^ [_888651, _888653, _888655, _888657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888651, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_888651), _888653), _888655)), _888657)), 6656 ^ _780205 : [(6657 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_888651), _888653), _888657)))], (6659 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888651, tc_HOL_Obool)), _888655), _888657)))]]], (6661 ^ _780205) ^ [_888824, _888826, _888828, _888830] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888824, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_888824), _888826), _888828)), _888830))), hBOOL(hAPP(hAPP(c_member(_888824), _888826), _888830)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888824, tc_HOL_Obool)), _888828), _888830))], (6671 ^ _780205) ^ [_889048, _889050, _889052] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_889048, _889050, c_Orderings_Obot__class_Obot(tc_fun(_889048, tc_HOL_Obool))), _889052))], (6673 ^ _780205) ^ [_889086, _889088, _889090, _889092] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_889086, _889088, _889090), _889092)), _889090 = c_Orderings_Obot__class_Obot(tc_fun(_889086, tc_HOL_Obool))], (6679 ^ _780205) ^ [_889190, _889192] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889190, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_889190, tc_HOL_Obool))), _889192) = _889192)], (6681 ^ _780205) ^ [_889231, _889233] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889231, tc_HOL_Obool)), _889233), c_Orderings_Obot__class_Obot(tc_fun(_889231, tc_HOL_Obool))) = _889233)], (6683 ^ _780205) ^ [_889290, _889292, _889294] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889290, tc_HOL_Obool)), _889292), _889294) = c_Orderings_Obot__class_Obot(tc_fun(_889290, tc_HOL_Obool)), 6686 ^ _780205 : [(6687 ^ _780205) ^ [] : [-(_889292 = c_Orderings_Obot__class_Obot(tc_fun(_889290, tc_HOL_Obool)))], (6689 ^ _780205) ^ [] : [-(_889294 = c_Orderings_Obot__class_Obot(tc_fun(_889290, tc_HOL_Obool)))]]], (6691 ^ _780205) ^ [_889443, _889445, _889447] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889443, tc_HOL_Obool)), _889445), _889447) = c_Orderings_Obot__class_Obot(tc_fun(_889443, tc_HOL_Obool))), _889445 = c_Orderings_Obot__class_Obot(tc_fun(_889443, tc_HOL_Obool)), _889447 = c_Orderings_Obot__class_Obot(tc_fun(_889443, tc_HOL_Obool))], (6701 ^ _780205) ^ [_889630, _889632, _889634, _889636] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889630, tc_HOL_Obool)), _889632), hAPP(hAPP(c_Set_Oinsert(_889630), _889634), _889636)) = hAPP(hAPP(c_Set_Oinsert(_889630), _889634), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889630, tc_HOL_Obool)), _889632), _889636)))], (6703 ^ _780205) ^ [_889697, _889699, _889701, _889703] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889697, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_889697), _889699), _889701)), _889703) = hAPP(hAPP(c_Set_Oinsert(_889697), _889699), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889697, tc_HOL_Obool)), _889701), _889703)))], (6705 ^ _780205) ^ [_889764, _889766] : [class_Orderings_Obot(_889764), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889764), c_Orderings_Obot__class_Obot(_889764)), _889766)))], (6711 ^ _780205) ^ [_889866, _889868] : [-(hBOOL(hAPP(hAPP(c_member(_889866), 6712 ^ [_889866, _889868]), _889868))), -(_889868 = c_Orderings_Obot__class_Obot(tc_fun(_889866, tc_HOL_Obool)))], (6718 ^ _780205) ^ [_889917, _889919] : [_889919 = c_Orderings_Obot__class_Obot(tc_fun(_889917, tc_HOL_Obool)), 6721 ^ _780205 : [(6722 ^ _780205) ^ [_889997] : [hBOOL(hAPP(hAPP(c_member(_889917), _889997), _889919))]]], (6724 ^ _780205) ^ [_890048, _890050] : [6725 ^ _780205 : [(6726 ^ _780205) ^ [_890101] : [hBOOL(hAPP(hAPP(c_member(_890048), _890101), _890050))]], _890050 = c_Orderings_Obot__class_Obot(tc_fun(_890048, tc_HOL_Obool))], (6730 ^ _780205) ^ [_890157, _890159] : [-(_890159 = c_Orderings_Obot__class_Obot(tc_fun(_890157, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_890157), 6733 ^ [_890157, _890159]), _890159)))], (6737 ^ _780205) ^ [_890226, _890228] : [hBOOL(hAPP(hAPP(c_member(_890226), _890228), c_Orderings_Obot__class_Obot(tc_fun(_890226, tc_HOL_Obool))))], (6739 ^ _780205) ^ [_890263, _890265, _890267] : [_890263 = c_Orderings_Obot__class_Obot(tc_fun(_890265, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_890265), _890267), _890263))], (6745 ^ _780205) ^ [_890382, _890384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890382, tc_HOL_Obool)), _890384), c_Orderings_Obot__class_Obot(tc_fun(_890382, tc_HOL_Obool)))), -(_890384 = c_Orderings_Obot__class_Obot(tc_fun(_890382, tc_HOL_Obool)))], (6751 ^ _780205) ^ [_890495, _890497] : [_890497 = c_Orderings_Obot__class_Obot(tc_fun(_890495, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890495, tc_HOL_Obool)), _890497), c_Orderings_Obot__class_Obot(tc_fun(_890495, tc_HOL_Obool)))))], (6757 ^ _780205) ^ [_890614, _890616, _890618] : [-(hBOOL(hAPP(hAPP(c_member(_890614), _890616), hAPP(hAPP(c_Set_Oinsert(_890614), _890616), _890618))))], (6769 ^ _780205) ^ [_890811, _890813, _890815, _890817] : [6770 ^ _780205 : [(6771 ^ _780205) ^ [] : [_890813 = _890815], (6773 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890811), _890813), _890817))]], -(hBOOL(hAPP(hAPP(c_member(_890811), _890813), hAPP(hAPP(c_Set_Oinsert(_890811), _890815), _890817))))], (6759 ^ _780205) ^ [_890677, _890679, _890681, _890683] : [hBOOL(hAPP(hAPP(c_member(_890677), _890679), hAPP(hAPP(c_Set_Oinsert(_890677), _890681), _890683))), -(_890679 = _890681), -(hBOOL(hAPP(hAPP(c_member(_890677), _890679), _890683)))], (6777 ^ _780205) ^ [_890975, _890977, _890979, _890981] : [-(hBOOL(hAPP(hAPP(c_member(_890975), _890977), _890979))), -(hBOOL(hAPP(hAPP(c_member(_890975), _890977), _890981))), 6784 ^ _780205 : [(6785 ^ _780205) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_890975), _890977), _890979) = hAPP(hAPP(c_Set_Oinsert(_890975), _890977), _890981), -(_890979 = _890981)], (6791 ^ _780205) ^ [] : [_890979 = _890981, -(hAPP(hAPP(c_Set_Oinsert(_890975), _890977), _890979) = hAPP(hAPP(c_Set_Oinsert(_890975), _890977), _890981))]]], (6797 ^ _780205) ^ [_891320, _891322, _891324, _891326] : [hBOOL(hAPP(hAPP(c_member(_891320), _891322), _891324)), -(hBOOL(hAPP(hAPP(c_member(_891320), _891322), hAPP(hAPP(c_Set_Oinsert(_891320), _891326), _891324))))], (6803 ^ _780205) ^ [_891445, _891447, _891449] : [hBOOL(hAPP(hAPP(c_member(_891445), _891447), _891449)), -(hAPP(hAPP(c_Set_Oinsert(_891445), _891447), _891449) = _891449)], (6809 ^ _780205) ^ [_891554, _891556, _891558] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891554, tc_HOL_Obool)), _891556), hAPP(hAPP(c_Set_Oinsert(_891554), _891558), _891556))))], (6811 ^ _780205) ^ [_891599, _891601, _891603, _891605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891599, tc_HOL_Obool)), _891601), _891603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891599, tc_HOL_Obool)), _891601), hAPP(hAPP(c_Set_Oinsert(_891599), _891605), _891603))))], (6817 ^ _780205) ^ [_891736, _891738, _891740, _891742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891736, tc_HOL_Obool)), _891738), _891740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891736, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_891736), _891742), _891738)), hAPP(hAPP(c_Set_Oinsert(_891736), _891742), _891740))))], (6823 ^ _780205) ^ [_891889, _891891, _891893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_891889), tc_HOL_Obool)), _891891), _891893)), -(c_Hoare__Mirabelle_Ohoare__derivs(_891889, _891893, _891891))], (6829 ^ _780205) ^ [_891994, _891996, _891998, _892000] : [c_Hoare__Mirabelle_Ohoare__derivs(_891994, _891996, _891998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_891994), tc_HOL_Obool)), _892000), _891998)), -(c_Hoare__Mirabelle_Ohoare__derivs(_891994, _891996, _892000))], (6839 ^ _780205) ^ [_892159, _892161, _892163, _892165] : [c_Hoare__Mirabelle_Ohoare__derivs(_892159, _892161, _892163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_892159), tc_HOL_Obool)), _892161), _892165)), -(c_Hoare__Mirabelle_Ohoare__derivs(_892159, _892165, _892163))], (6849 ^ _780205) ^ [_892324, _892326, _892328, _892330] : [6850 ^ _780205 : [(6851 ^ _780205) ^ [] : [hBOOL(hAPP(_892324, _892326))], (6853 ^ _780205) ^ [] : [hBOOL(hAPP(_892328, _892326))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892330, tc_HOL_Obool)), _892328), _892324), _892326)))], (6857 ^ _780205) ^ [_892479, _892481, _892483, _892485] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892479, tc_HOL_Obool)), _892481), _892483), _892485)), -(hBOOL(hAPP(_892481, _892485))), -(hBOOL(hAPP(_892483, _892485)))], (6867 ^ _780205) ^ [_892609, _892611, _892613, _892615, _892617] : [class_Lattices_Olattice(_892609), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892611, _892609)), _892613), _892615), _892617) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892609), hAPP(_892613, _892617)), hAPP(_892615, _892617)))], (6873 ^ _780205) ^ [_892746, _892748] : [class_Lattices_Obounded__lattice__bot(_892746), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892746), c_Orderings_Obot__class_Obot(_892746)), _892748) = _892748)], (6879 ^ _780205) ^ [_892841, _892843] : [class_Lattices_Obounded__lattice__bot(_892841), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892841), _892843), c_Orderings_Obot__class_Obot(_892841)) = _892843)], (6885 ^ _780205) ^ [_892936, _892938, _892940] : [class_Lattices_Obounded__lattice__bot(_892936), 6888 ^ _780205 : [(6889 ^ _780205) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892936), _892938), _892940) = c_Orderings_Obot__class_Obot(_892936), 6892 ^ _780205 : [(6893 ^ _780205) ^ [] : [-(_892938 = c_Orderings_Obot__class_Obot(_892936))], (6895 ^ _780205) ^ [] : [-(_892940 = c_Orderings_Obot__class_Obot(_892936))]]], (6897 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892936), _892938), _892940) = c_Orderings_Obot__class_Obot(_892936)), _892938 = c_Orderings_Obot__class_Obot(_892936), _892940 = c_Orderings_Obot__class_Obot(_892936)]]], (6907 ^ _780205) ^ [_893263, _893265, _893267, _893269] : [class_Lattices_Osemilattice__sup(_893263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893263), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893263), _893265), _893267)), _893269)), 6914 ^ _780205 : [(6915 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893263), _893265), _893269)))], (6917 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893263), _893267), _893269)))]]], (6919 ^ _780205) ^ [_893486, _893488, _893490, _893492, _893494] : [class_Lattices_Osemilattice__sup(_893486), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893486), _893488), _893490)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893486), _893492), _893494)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893486), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893486), _893488), _893492)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893486), _893490), _893494))))], (6933 ^ _780205) ^ [_893757, _893759, _893761, _893763] : [class_Lattices_Osemilattice__sup(_893757), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893757), _893759), _893761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893757), _893763), _893761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893757), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893757), _893759), _893763)), _893761)))], (6947 ^ _780205) ^ [_894006, _894008, _894010, _894012] : [class_Lattices_Osemilattice__sup(_894006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894006), _894008), _894010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894006), _894012), _894010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894006), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894006), _894008), _894012)), _894010)))], (6961 ^ _780205) ^ [_894255, _894257, _894259] : [class_Lattices_Osemilattice__sup(_894255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894255), _894257), _894259)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894255), _894259), _894257) = _894259)], (6971 ^ _780205) ^ [_894416, _894418, _894420] : [class_Lattices_Osemilattice__sup(_894416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894416), _894418), _894420)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894416), _894418), _894420) = _894420)], (6981 ^ _780205) ^ [_894595, _894597, _894599] : [hBOOL(hAPP(hAPP(c_member(_894595), _894597), hAPP(c_fequal, _894599))), -(_894597 = _894599)], (6987 ^ _780205) ^ [_894690, _894692, _894694] : [_894692 = _894694, -(hBOOL(hAPP(hAPP(c_member(_894690), _894692), hAPP(c_fequal, _894694))))], (6993 ^ _780205) ^ [_894791, _894793] : [class_Lattices_Osemilattice__sup(_894791), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894791), _894793), _894793) = _894793)], (6999 ^ _780205) ^ [_894882, _894884] : [class_Lattices_Osemilattice__sup(_894882), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894882), _894884), _894884) = _894884)], (7005 ^ _780205) ^ [_894973, _894975, _894977] : [class_Lattices_Osemilattice__sup(_894973), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894973), _894975), _894977) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894973), _894977), _894975))], (7011 ^ _780205) ^ [_895082, _895084, _895086] : [class_Lattices_Olattice(_895082), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895082), _895084), _895086) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895082), _895086), _895084))], (7017 ^ _780205) ^ [_895191, _895193, _895195] : [class_Lattices_Osemilattice__sup(_895191), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895191), _895193), _895195) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895191), _895195), _895193))], (7023 ^ _780205) ^ [_895300, _895302, _895304] : [class_Lattices_Osemilattice__sup(_895300), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895300), _895302), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895300), _895302), _895304)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895300), _895302), _895304))], (7029 ^ _780205) ^ [_895425, _895427, _895429] : [class_Lattices_Olattice(_895425), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895425), _895427), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895425), _895427), _895429)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895425), _895427), _895429))], (7035 ^ _780205) ^ [_895550, _895552, _895554] : [class_Lattices_Osemilattice__sup(_895550), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895550), _895552), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895550), _895552), _895554)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895550), _895552), _895554))], (7041 ^ _780205) ^ [_895675, _895677, _895679, _895681] : [class_Lattices_Osemilattice__sup(_895675), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895675), _895677), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895675), _895679), _895681)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895675), _895679), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895675), _895677), _895681)))], (7047 ^ _780205) ^ [_895818, _895820, _895822, _895824] : [class_Lattices_Olattice(_895818), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895818), _895820), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895818), _895822), _895824)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895818), _895822), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895818), _895820), _895824)))], (7053 ^ _780205) ^ [_895961, _895963, _895965, _895967] : [class_Lattices_Osemilattice__sup(_895961), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895961), _895963), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895961), _895965), _895967)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895961), _895965), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895961), _895963), _895967)))], (7059 ^ _780205) ^ [_896104, _896106, _896108, _896110] : [class_Lattices_Osemilattice__sup(_896104), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896104), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896104), _896106), _896108)), _896110) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896104), _896106), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896104), _896108), _896110)))], (7065 ^ _780205) ^ [_896247, _896249, _896251, _896253] : [class_Lattices_Olattice(_896247), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896247), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896247), _896249), _896251)), _896253) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896247), _896249), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896247), _896251), _896253)))], (7071 ^ _780205) ^ [_896390, _896392, _896394, _896396] : [class_Lattices_Osemilattice__sup(_896390), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896390), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896390), _896392), _896394)), _896396) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896390), _896392), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896390), _896394), _896396)))], (7077 ^ _780205) ^ [_896533, _896535, _896537, _896539] : [hBOOL(hAPP(_896533, _896535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896537, tc_HOL_Obool)), _896533), _896539)), -(hBOOL(hAPP(_896539, _896535)))], (7087 ^ _780205) ^ [_896698, _896700, _896702, _896704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896698, tc_HOL_Obool)), _896700), _896702)), hBOOL(hAPP(_896700, _896704)), -(hBOOL(hAPP(_896702, _896704)))], (7097 ^ _780205) ^ [_896863, _896865, _896867, _896869] : [hBOOL(hAPP(_896863, _896865)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896867, tc_HOL_Obool)), _896863), _896869), _896865)))], (7103 ^ _780205) ^ [_896974, _896976, _896978, _896980] : [hBOOL(hAPP(_896974, _896976)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896978, tc_HOL_Obool)), _896980), _896974), _896976)))], (7109 ^ _780205) ^ [_897085, _897087, _897089] : [class_Lattices_Olattice(_897085), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897085), _897087), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897085), _897087), _897089))))], (7115 ^ _780205) ^ [_897192, _897194, _897196] : [class_Lattices_Osemilattice__sup(_897192), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897192), _897194), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897192), _897194), _897196))))], (7121 ^ _780205) ^ [_897299, _897301, _897303] : [class_Lattices_Olattice(_897299), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897299), _897301), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897299), _897303), _897301))))], (7127 ^ _780205) ^ [_897406, _897408, _897410] : [class_Lattices_Osemilattice__sup(_897406), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897406), _897408), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897406), _897410), _897408))))], (7133 ^ _780205) ^ [_897513, _897515, _897517] : [class_Lattices_Osemilattice__sup(_897513), 7136 ^ _780205 : [(7137 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897513), _897515), _897517)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897513), _897515), _897517) = _897517)], (7143 ^ _780205) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897513), _897515), _897517) = _897517, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897513), _897515), _897517)))]]], (7149 ^ _780205) ^ [_897769, _897771, _897773, _897775] : [class_Lattices_Osemilattice__sup(_897769), 7152 ^ _780205 : [(7153 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897769), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897769), _897771), _897773)), _897775)), 7156 ^ _780205 : [(7157 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897769), _897771), _897775)))], (7159 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897769), _897773), _897775)))]]], (7161 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897769), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897769), _897771), _897773)), _897775))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897769), _897771), _897775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897769), _897773), _897775))]]], (7171 ^ _780205) ^ [_898149, _898151, _898153, _898155] : [class_Lattices_Osemilattice__sup(_898149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898149), _898151), _898153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898149), _898151), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898149), _898153), _898155))))], (7181 ^ _780205) ^ [_898328, _898330, _898332, _898334] : [class_Lattices_Osemilattice__sup(_898328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898328), _898330), _898332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898328), _898330), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898328), _898334), _898332))))], (7191 ^ _780205) ^ [_898507, _898509, _898511, _898513, _898515] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_898507, _898507, _898509, _898511, _898513), _898515)), -(hBOOL(hAPP(hAPP(c_member(_898507), _898511), _898513))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_898507, _898509, hAPP(hAPP(c_Set_Oinsert(_898507), _898511), _898513)), _898515)))], (7201 ^ _780205) ^ [_898663, _898665, _898667, _898669, _898671] : [c_Finite__Set_Ofolding__one(_898663, _898665, _898667), hBOOL(hAPP(c_Finite__Set_Ofinite(_898663), _898669)), -(hBOOL(hAPP(hAPP(c_member(_898663), _898671), _898669))), -(_898669 = c_Orderings_Obot__class_Obot(tc_fun(_898663, tc_HOL_Obool))), -(hAPP(_898667, hAPP(hAPP(c_Set_Oinsert(_898663), _898671), _898669)) = hAPP(hAPP(_898665, _898671), hAPP(_898667, _898669)))], (7219 ^ _780205) ^ [_898908, _898910, _898912, _898914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898908, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898908, tc_HOL_Obool)), _898910), hAPP(hAPP(c_Set_Oinsert(_898908), _898912), c_Orderings_Obot__class_Obot(tc_fun(_898908, tc_HOL_Obool))))), _898914)), hBOOL(hAPP(hAPP(c_member(_898908), _898912), _898910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898908, tc_HOL_Obool)), _898910), hAPP(hAPP(c_Set_Oinsert(_898908), _898912), _898914))))], (7245 ^ _780205) ^ [_899516, _899518, _899520, _899522] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899516, tc_HOL_Obool)), _899518), hAPP(hAPP(c_Set_Oinsert(_899516), _899520), _899522)))), 7248 ^ _780205 : [(7249 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899516), _899520), _899518)))], (7251 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899516, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899516, tc_HOL_Obool)), _899518), hAPP(hAPP(c_Set_Oinsert(_899516), _899520), c_Orderings_Obot__class_Obot(tc_fun(_899516, tc_HOL_Obool))))), _899522))]], 7252 ^ _780205 : [(7253 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899516), _899520), _899518))], (7255 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899516, tc_HOL_Obool)), _899518), _899522))]]], (7229 ^ _780205) ^ [_899184, _899186, _899188, _899190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899184, tc_HOL_Obool)), _899186), hAPP(hAPP(c_Set_Oinsert(_899184), _899188), _899190))), 7232 ^ _780205 : [(7233 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899184), _899188), _899186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899184, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899184, tc_HOL_Obool)), _899186), hAPP(hAPP(c_Set_Oinsert(_899184), _899188), c_Orderings_Obot__class_Obot(tc_fun(_899184, tc_HOL_Obool))))), _899190)))], (7239 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899184), _899188), _899186))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899184, tc_HOL_Obool)), _899186), _899190)))]]], (7259 ^ _780205) ^ [_899894, _899896] : [-(_899894 = c_Orderings_Obot__class_Obot(tc_fun(_899896, tc_HOL_Obool))), 7264 ^ _780205 : [(7265 ^ _780205) ^ [] : [-(_899894 = hAPP(hAPP(c_Set_Oinsert(_899896), 7262 ^ [_899894, _899896]), 7263 ^ [_899894, _899896]))], (7267 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899896), 7262 ^ [_899894, _899896]), 7263 ^ [_899894, _899896]))]]], (7269 ^ _780205) ^ [_900101, _900103] : [_900101 = c_Orderings_Obot__class_Obot(tc_fun(_900103, tc_HOL_Obool)), 7270 ^ _780205 : [(7271 ^ _780205) ^ [_900170, _900172] : [_900101 = hAPP(hAPP(c_Set_Oinsert(_900103), _900172), _900170), -(hBOOL(hAPP(hAPP(c_member(_900103), _900172), _900170)))]]], (7279 ^ _780205) ^ [_900317, _900319] : [class_Lattices_Olattice(_900317), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_900317), _900319), _900319) = _900319)], (7285 ^ _780205) ^ [_900408, _900410, _900412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900408, tc_HOL_Obool)), _900410), _900412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_900408, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_900408, _900410)), c_Predicate_OPowp(_900408, _900412))))], (7291 ^ _780205) ^ [_900545, _900547, _900549] : [7293 ^ _780205 : [(7294 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900545), 7292 ^ [_900545, _900547, _900549]), _900547)))], (7296 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_900545), 7292 ^ [_900545, _900547, _900549]), _900549))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900545, tc_HOL_Obool)), _900547), _900549)))], (7300 ^ _780205) ^ [_900749, _900751, _900753, _900755, _900757] : [-(hAPP(c_Set_Ovimage(_900749, _900751, _900753), hAPP(hAPP(c_Set_Oinsert(_900751), _900755), _900757)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900749, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_900749, _900751, _900753), hAPP(hAPP(c_Set_Oinsert(_900751), _900755), c_Orderings_Obot__class_Obot(tc_fun(_900751, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_900749, _900751, _900753), _900757)))], (7302 ^ _780205) ^ [_900857, _900859, _900861, _900863, _900865] : [hBOOL(hAPP(hAPP(c_member(_900857), _900859), hAPP(c_Set_Ovimage(_900857, _900861, _900863), hAPP(hAPP(c_Set_Oinsert(_900861), _900865), c_Orderings_Obot__class_Obot(tc_fun(_900861, tc_HOL_Obool)))))), -(hAPP(_900863, _900859) = _900865)], (7308 ^ _780205) ^ [_900996, _900998, _901000, _901002, _901004] : [hAPP(_901002, _900998) = _901004, -(hBOOL(hAPP(hAPP(c_member(_900996), _900998), hAPP(c_Set_Ovimage(_900996, _901000, _901002), hAPP(hAPP(c_Set_Oinsert(_901000), _901004), c_Orderings_Obot__class_Obot(tc_fun(_901000, tc_HOL_Obool)))))))], (7314 ^ _780205) ^ [_901141, _901143, _901145] : [hBOOL(hAPP(hAPP(c_member(_901141), _901143), _901145)), -(hAPP(hAPP(c_Set_Oinsert(_901141), _901143), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901141, tc_HOL_Obool)), _901145), hAPP(hAPP(c_Set_Oinsert(_901141), _901143), c_Orderings_Obot__class_Obot(tc_fun(_901141, tc_HOL_Obool))))) = _901145)], (7320 ^ _780205) ^ [_901298] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_901298), c_Orderings_Obot__class_Obot(tc_fun(_901298, tc_HOL_Obool)))))], (7322 ^ _780205) ^ [_901330, _901332, _901334] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_901330), _901332)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_901330), hAPP(hAPP(c_Set_Oinsert(_901330), _901334), _901332))))], (7328 ^ _780205) ^ [_901441, _901443, _901445, _901447] : [hBOOL(hAPP(hAPP(c_member(_901441), _901443), _901445)), -(hBOOL(hAPP(hAPP(c_member(_901441), _901443), _901447))), -(hBOOL(hAPP(hAPP(c_member(_901441), _901443), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901441, tc_HOL_Obool)), _901445), _901447))))], (7338 ^ _780205) ^ [_901601, _901603, _901605, _901607] : [hBOOL(hAPP(hAPP(c_member(_901601), _901603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901601, tc_HOL_Obool)), _901605), _901607))), 7341 ^ _780205 : [(7342 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_901601), _901603), _901605)))], (7344 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_901601), _901603), _901607))]]], (7346 ^ _780205) ^ [_901780, _901782, _901784] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_901780), _901782)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_901780), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901780, tc_HOL_Obool)), _901782), _901784))))], (7352 ^ _780205) ^ [_901897, _901899, _901901, _901903, _901905, _901907] : [hAPP(_901897, _901899) = _901901, hBOOL(hAPP(hAPP(c_member(_901903), _901901), _901905)), -(hBOOL(hAPP(hAPP(c_member(_901907), _901899), hAPP(c_Set_Ovimage(_901907, _901903, _901897), _901905))))], (7362 ^ _780205) ^ [_902090, _902092, _902094, _902096, _902098] : [class_Groups_Ominus(_902090), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902092, _902090)), _902094), _902096), _902098) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_902090), hAPP(_902094, _902098)), hAPP(_902096, _902098)))], (7368 ^ _780205) ^ [_902227, _902229, _902231, _902233, _902235] : [-(hAPP(c_Set_Ovimage(_902227, _902229, _902231), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902229, tc_HOL_Obool)), _902233), _902235)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902227, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_902227, _902229, _902231), _902233)), hAPP(c_Set_Ovimage(_902227, _902229, _902231), _902235)))], (7370 ^ _780205) ^ [_902301, _902303, _902305] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902301, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902301, tc_HOL_Obool)), _902303), _902305)), _902305) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902301, tc_HOL_Obool)), _902303), _902305))], (7372 ^ _780205) ^ [_902385, _902387, _902389, _902391, _902393] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_902385, _902387, _902389), _902391), _902393)), -(hBOOL(hAPP(_902391, hAPP(_902389, _902393))))], (7378 ^ _780205) ^ [_902492, _902494, _902496, _902498, _902500] : [hBOOL(hAPP(_902498, hAPP(_902496, _902500))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_902492, _902494, _902496), _902498), _902500)))], (7384 ^ _780205) ^ [_902605, _902607] : [class_Finite__Set_Ofinite(_902605), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_902605), _902607)))], (7390 ^ _780205) ^ [_902688, _902690] : [class_Finite__Set_Ofinite(_902688), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_902688), _902690)))], (7396 ^ _780205) ^ [_902771, _902773, _902775] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902771), _902773)), 7399 ^ _780205 : [(7400 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902771), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902771, tc_HOL_Obool)), _902775), _902773))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_902771), _902775)))], (7406 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902771), _902775)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_902771), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902771, tc_HOL_Obool)), _902775), _902773))))]]], (7412 ^ _780205) ^ [_903049, _903051, _903053, _903055, _903057, _903059] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_903049, _903051, _903053, _903055, _903057), _903059)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_903049), _903057)))], (7418 ^ _780205) ^ [_903179, _903181, _903183, _903185] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903179), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903179, tc_HOL_Obool)), _903181), hAPP(hAPP(c_Set_Oinsert(_903179), _903183), _903185)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_903179), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903179, tc_HOL_Obool)), _903181), _903185))))], (7424 ^ _780205) ^ [_903332, _903334, _903336, _903338] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903332), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903332, tc_HOL_Obool)), _903334), _903338))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_903332), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903332, tc_HOL_Obool)), _903334), hAPP(hAPP(c_Set_Oinsert(_903332), _903336), _903338)))))], (7430 ^ _780205) ^ [_903512, _903514, _903516, _903518] : [hBOOL(hAPP(hAPP(c_member(_903512), _903514), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903512, tc_HOL_Obool)), _903516), _903518))), 7433 ^ _780205 : [(7434 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_903512), _903514), _903516)))], (7436 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_903512), _903514), _903518))]]], (7438 ^ _780205) ^ [_903687, _903689, _903691, _903693] : [-(hBOOL(hAPP(hAPP(c_member(_903687), _903689), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903687, tc_HOL_Obool)), _903691), _903693)))), hBOOL(hAPP(hAPP(c_member(_903687), _903689), _903691)), -(hBOOL(hAPP(hAPP(c_member(_903687), _903689), _903693)))], (7448 ^ _780205) ^ [_903893, _903895, _903897, _903899] : [hBOOL(hAPP(hAPP(c_member(_903893), _903895), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903893, tc_HOL_Obool)), _903897), _903899))), -(hBOOL(hAPP(hAPP(c_member(_903893), _903895), _903897)))], (7454 ^ _780205) ^ [_904024, _904026, _904028, _904030] : [hBOOL(hAPP(hAPP(c_member(_904024), _904026), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904024, tc_HOL_Obool)), _904028), _904030))), hBOOL(hAPP(hAPP(c_member(_904024), _904026), _904030))], (7460 ^ _780205) ^ [_904180, _904182, _904184, _904186, _904188] : [hBOOL(hAPP(hAPP(c_member(_904180), _904182), hAPP(c_Set_Ovimage(_904180, _904184, _904186), _904188))), -(hBOOL(hAPP(hAPP(c_member(_904184), hAPP(_904186, _904182)), _904188)))], (7466 ^ _780205) ^ [_904307, _904309, _904311, _904313, _904315] : [hBOOL(hAPP(hAPP(c_member(_904311), hAPP(_904313, _904309)), _904315)), -(hBOOL(hAPP(hAPP(c_member(_904307), _904309), hAPP(c_Set_Ovimage(_904307, _904311, _904313), _904315))))], (7472 ^ _780205) ^ [_904440, _904442, _904444, _904446, _904448] : [hBOOL(hAPP(hAPP(c_member(_904440), _904442), hAPP(c_Set_Ovimage(_904440, _904444, _904446), _904448))), -(hBOOL(hAPP(hAPP(c_member(_904444), hAPP(_904446, _904442)), _904448)))], (7478 ^ _780205) ^ [_904571, _904573, _904575, _904577, _904579] : [hBOOL(hAPP(hAPP(c_member(_904571), hAPP(_904573, _904575)), _904577)), -(hBOOL(hAPP(hAPP(c_member(_904579), _904575), hAPP(c_Set_Ovimage(_904579, _904571, _904573), _904577))))], (7484 ^ _780205) ^ [_904702, _904704] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904702, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_904702, tc_HOL_Obool))), _904704) = c_Orderings_Obot__class_Obot(tc_fun(_904702, tc_HOL_Obool)))], (7486 ^ _780205) ^ [_904748, _904750] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904748, tc_HOL_Obool)), _904750), c_Orderings_Obot__class_Obot(tc_fun(_904748, tc_HOL_Obool))) = _904750)], (7488 ^ _780205) ^ [_904789, _904791] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904789, tc_HOL_Obool)), _904791), _904791) = c_Orderings_Obot__class_Obot(tc_fun(_904789, tc_HOL_Obool)))], (7490 ^ _780205) ^ [_904830, _904832, _904834] : [-(hAPP(c_Set_Ovimage(_904830, _904832, _904834), c_Orderings_Obot__class_Obot(tc_fun(_904832, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_904830, tc_HOL_Obool)))], (7492 ^ _780205) ^ [_904874, _904876, _904878] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904874, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904874, tc_HOL_Obool)), _904876), _904878)), _904876)))], (7494 ^ _780205) ^ [_904922, _904924, _904926, _904928, _904930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904922, tc_HOL_Obool)), _904924), _904926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904922, tc_HOL_Obool)), _904928), _904930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904922, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904922, tc_HOL_Obool)), _904924), _904930)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904922, tc_HOL_Obool)), _904926), _904928))))], (7504 ^ _780205) ^ [_905167, _905169, _905171, _905173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905167, tc_HOL_Obool)), _905169), _905171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905167, tc_HOL_Obool)), _905171), _905173)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905167, tc_HOL_Obool)), _905171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905167, tc_HOL_Obool)), _905173), _905169)) = _905169)], (7514 ^ _780205) ^ [_905388, _905390, _905392, _905394, _905396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905388, tc_HOL_Obool)), _905390), _905392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905394, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_905394, _905388, _905396), _905390)), hAPP(c_Set_Ovimage(_905394, _905388, _905396), _905392))))], (7520 ^ _780205) ^ [_905539, _905541, _905543] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905539, tc_HOL_Obool)), _905541), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905539, tc_HOL_Obool)), _905543), _905541)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905539, tc_HOL_Obool)), _905541), _905543))], (7522 ^ _780205) ^ [_905599, _905601, _905603] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905599, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905599, tc_HOL_Obool)), _905601), _905603)), _905603) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905599, tc_HOL_Obool)), _905601), _905603))], (7524 ^ _780205) ^ [_905659, _905661, _905663, _905665] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905659, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905659, tc_HOL_Obool)), _905661), _905663)), _905665) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905659, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905659, tc_HOL_Obool)), _905661), _905665)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905659, tc_HOL_Obool)), _905663), _905665)))], (7526 ^ _780205) ^ [_905743, _905745, _905747, _905749, _905751] : [-(hAPP(c_Set_Ovimage(_905743, _905745, _905747), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905745, tc_HOL_Obool)), _905749), _905751)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905743, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_905743, _905745, _905747), _905749)), hAPP(c_Set_Ovimage(_905743, _905745, _905747), _905751)))], (7528 ^ _780205) ^ [_905817] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_905817), c_Orderings_Obot__class_Obot(tc_fun(_905817, tc_HOL_Obool)))))], (7530 ^ _780205) ^ [_905867, _905869, _905871] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_905867), hAPP(hAPP(c_Set_Oinsert(_905867), _905869), _905871))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_905867), _905871)))], (7536 ^ _780205) ^ [_905974, _905976, _905978] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_905974), _905978)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_905974), hAPP(hAPP(c_Set_Oinsert(_905974), _905976), _905978))))], (7542 ^ _780205) ^ [_906087, _906089, _906091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906087, tc_HOL_Obool)), _906089), _906091)), hBOOL(hAPP(c_Finite__Set_Ofinite(_906087), _906091)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_906087), _906089)))], (7552 ^ _780205) ^ [_906256, _906258, _906260] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_906256), _906258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906256, tc_HOL_Obool)), _906260), _906258)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_906256), _906260)))], (7562 ^ _780205) ^ [_906425, _906427, _906429] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_906425), _906427)), hBOOL(hAPP(c_Finite__Set_Ofinite(_906425), _906429)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_906425), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906425, tc_HOL_Obool)), _906427), _906429))))], (7572 ^ _780205) ^ [_906622, _906624, _906626] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_906622), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906622, tc_HOL_Obool)), _906624), _906626))), 7575 ^ _780205 : [(7576 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_906622), _906624)))], (7578 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_906622), _906626)))]]], (7580 ^ _780205) ^ [_906769, _906771, _906773] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_906769), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906769, tc_HOL_Obool)), _906771), _906773)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_906769), _906771)), hBOOL(hAPP(c_Finite__Set_Ofinite(_906769), _906773))], (7590 ^ _780205) ^ [_906950, _906952, _906954, _906956] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_906950, _906952, _906954, _906956, c_Orderings_Obot__class_Obot(tc_fun(_906950, tc_HOL_Obool))), _906956)))], (7592 ^ _780205) ^ [_906992, _906994, _906996, _906998] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_906992, _906994, _906996, _906998, c_Orderings_Obot__class_Obot(tc_fun(_906992, tc_HOL_Obool))), _906998)))], (7594 ^ _780205) ^ [_907034, _907036, _907038, _907040, _907042] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_907034, _907036, _907038, _907040, c_Orderings_Obot__class_Obot(tc_fun(_907034, tc_HOL_Obool))), _907042)), -(_907042 = _907040)], (7600 ^ _780205) ^ [_907143, _907145, _907147, _907149, _907151, _907153, _907155] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_907143, _907145, _907147, _907149, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907143, tc_HOL_Obool)), _907151), hAPP(hAPP(c_Set_Oinsert(_907143), _907153), c_Orderings_Obot__class_Obot(tc_fun(_907143, tc_HOL_Obool))))), _907155)), hBOOL(hAPP(hAPP(c_member(_907143), _907153), _907151)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_907143, _907145, _907147, _907149, _907151), hAPP(hAPP(_907147, _907153), _907155))))], (7610 ^ _780205) ^ [_907398, _907400, _907402, _907404, _907406] : [c_Finite__Set_Ofolding__one(_907398, _907400, _907402), hBOOL(hAPP(c_Finite__Set_Ofinite(_907398), _907404)), 7617 ^ _780205 : [(7618 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907398, tc_HOL_Obool)), _907404), hAPP(hAPP(c_Set_Oinsert(_907398), _907406), c_Orderings_Obot__class_Obot(tc_fun(_907398, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_907398, tc_HOL_Obool)), -(hAPP(_907402, hAPP(hAPP(c_Set_Oinsert(_907398), _907406), _907404)) = _907406)], (7624 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907398, tc_HOL_Obool)), _907404), hAPP(hAPP(c_Set_Oinsert(_907398), _907406), c_Orderings_Obot__class_Obot(tc_fun(_907398, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_907398, tc_HOL_Obool))), -(hAPP(_907402, hAPP(hAPP(c_Set_Oinsert(_907398), _907406), _907404)) = hAPP(hAPP(_907400, _907406), hAPP(_907402, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907398, tc_HOL_Obool)), _907404), hAPP(hAPP(c_Set_Oinsert(_907398), _907406), c_Orderings_Obot__class_Obot(tc_fun(_907398, tc_HOL_Obool)))))))]]], (7630 ^ _780205) ^ [_907880, _907882, _907884, _907886] : [hBOOL(hAPP(hAPP(c_member(_907880), _907882), _907884)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907880, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_907880), _907882), _907886)), _907884) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907880, tc_HOL_Obool)), _907886), _907884))], (7636 ^ _780205) ^ [_908050, _908052, _908054, _908056] : [hBOOL(hAPP(hAPP(c_member(_908050), _908052), _908054)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908050, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_908050), _908052), _908056)), _908054) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908050, tc_HOL_Obool)), _908056), _908054))], (7642 ^ _780205) ^ [_908199, _908201, _908203, _908205] : [-(hBOOL(hAPP(hAPP(c_member(_908199), _908201), _908203))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908199, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_908199), _908201), _908205)), _908203) = hAPP(hAPP(c_Set_Oinsert(_908199), _908201), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908199, tc_HOL_Obool)), _908205), _908203)))], (7648 ^ _780205) ^ [_908286, _908288, _908290, _908292] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908286, tc_HOL_Obool)), _908288), hAPP(hAPP(c_Set_Oinsert(_908286), _908290), _908292)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908286, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908286, tc_HOL_Obool)), _908288), _908292)), hAPP(hAPP(c_Set_Oinsert(_908286), _908290), c_Orderings_Obot__class_Obot(tc_fun(_908286, tc_HOL_Obool)))))], (7650 ^ _780205) ^ [_908369, _908371, _908373, _908375] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908369, tc_HOL_Obool)), _908371), hAPP(hAPP(c_Set_Oinsert(_908369), _908373), _908375)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908369, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908369, tc_HOL_Obool)), _908371), hAPP(hAPP(c_Set_Oinsert(_908369), _908373), c_Orderings_Obot__class_Obot(tc_fun(_908369, tc_HOL_Obool))))), _908375))], (7652 ^ _780205) ^ [_908452, _908454, _908456] : [-(hAPP(hAPP(c_Set_Oinsert(_908452), _908454), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908452, tc_HOL_Obool)), _908456), hAPP(hAPP(c_Set_Oinsert(_908452), _908454), c_Orderings_Obot__class_Obot(tc_fun(_908452, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_908452), _908454), _908456))], (7654 ^ _780205) ^ [_908540, _908542, _908544, _908546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908540, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908540, tc_HOL_Obool)), _908542), _908544)), _908546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908540, tc_HOL_Obool)), _908542), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908540, tc_HOL_Obool)), _908544), _908546))))], (7660 ^ _780205) ^ [_908701, _908703, _908705, _908707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908701, tc_HOL_Obool)), _908703), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908701, tc_HOL_Obool)), _908705), _908707))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908701, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908701, tc_HOL_Obool)), _908703), _908705)), _908707)))], (7666 ^ _780205) ^ [_908868, _908870, _908872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908868, tc_HOL_Obool)), _908870), _908872)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908868, tc_HOL_Obool)), _908870), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908868, tc_HOL_Obool)), _908872), _908870)) = _908872)], (7672 ^ _780205) ^ [_909011, _909013, _909015, _909017, _909019] : [c_Finite__Set_Ofolding__one(_909011, _909013, _909015), hBOOL(hAPP(c_Finite__Set_Ofinite(_909011), _909017)), hBOOL(hAPP(hAPP(c_member(_909011), _909019), _909017)), 7683 ^ _780205 : [(7684 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909011, tc_HOL_Obool)), _909017), hAPP(hAPP(c_Set_Oinsert(_909011), _909019), c_Orderings_Obot__class_Obot(tc_fun(_909011, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_909011, tc_HOL_Obool)), -(hAPP(_909015, _909017) = _909019)], (7690 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909011, tc_HOL_Obool)), _909017), hAPP(hAPP(c_Set_Oinsert(_909011), _909019), c_Orderings_Obot__class_Obot(tc_fun(_909011, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_909011, tc_HOL_Obool))), -(hAPP(_909015, _909017) = hAPP(hAPP(_909013, _909019), hAPP(_909015, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909011, tc_HOL_Obool)), _909017), hAPP(hAPP(c_Set_Oinsert(_909011), _909019), c_Orderings_Obot__class_Obot(tc_fun(_909011, tc_HOL_Obool)))))))]]], (7696 ^ _780205) ^ [_909532, _909534, _909536, _909538, _909540, _909542, _909544] : [-(hBOOL(hAPP(hAPP(c_member(_909532), _909534), _909536))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_909532, _909538, _909540, _909542, _909536), _909544)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_909532, _909538, _909540, _909542, hAPP(hAPP(c_Set_Oinsert(_909532), _909534), _909536)), hAPP(hAPP(_909540, _909534), _909544))))], (7706 ^ _780205) ^ [_909742, _909744, _909746] : [-(hBOOL(hAPP(hAPP(c_member(_909742), _909744), _909746))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909742, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_909742), _909744), _909746)), hAPP(hAPP(c_Set_Oinsert(_909742), _909744), c_Orderings_Obot__class_Obot(tc_fun(_909742, tc_HOL_Obool)))) = _909746)], (7712 ^ _780205) ^ [_909819, _909821, _909823, _909825, _909827, _909829, _909831, _909833] : [c_Finite__Set_Ofolding__image__simple(_909819, _909821, _909823, _909825, _909827, _909829), hBOOL(hAPP(c_Finite__Set_Ofinite(_909821), _909831)), hBOOL(hAPP(hAPP(c_member(_909821), _909833), _909831)), -(hAPP(_909829, _909831) = hAPP(hAPP(_909823, hAPP(_909827, _909833)), hAPP(_909829, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909821, tc_HOL_Obool)), _909831), hAPP(hAPP(c_Set_Oinsert(_909821), _909833), c_Orderings_Obot__class_Obot(tc_fun(_909821, tc_HOL_Obool)))))))], (7726 ^ _780205) ^ [_910144, _910146, _910148, _910150, _910152, _910154, _910156, _910158] : [c_Finite__Set_Ofolding__image__simple(_910144, _910146, _910148, _910150, _910152, _910154), hBOOL(hAPP(c_Finite__Set_Ofinite(_910146), _910156)), -(hAPP(_910154, hAPP(hAPP(c_Set_Oinsert(_910146), _910158), _910156)) = hAPP(hAPP(_910148, hAPP(_910152, _910158)), hAPP(_910154, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910146, tc_HOL_Obool)), _910156), hAPP(hAPP(c_Set_Oinsert(_910146), _910158), c_Orderings_Obot__class_Obot(tc_fun(_910146, tc_HOL_Obool)))))))], (7736 ^ _780205) ^ [_910407, _910409, _910411] : [class_Lattices_Olattice(_910407), hBOOL(hAPP(c_Finite__Set_Ofinite(_910407), _910409)), hBOOL(hAPP(hAPP(c_member(_910407), _910411), _910409)), 7747 ^ _780205 : [(7748 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910407, tc_HOL_Obool)), _910409), hAPP(hAPP(c_Set_Oinsert(_910407), _910411), c_Orderings_Obot__class_Obot(tc_fun(_910407, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_910407, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_910407, _910409) = _910411)], (7754 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910407, tc_HOL_Obool)), _910409), hAPP(hAPP(c_Set_Oinsert(_910407), _910411), c_Orderings_Obot__class_Obot(tc_fun(_910407, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_910407, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_910407, _910409) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910407), _910411), c_Big__Operators_Olattice__class_OSup__fin(_910407, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910407, tc_HOL_Obool)), _910409), hAPP(hAPP(c_Set_Oinsert(_910407), _910411), c_Orderings_Obot__class_Obot(tc_fun(_910407, tc_HOL_Obool)))))))]]], (7760 ^ _780205) ^ [_910913, _910915, _910917, _910919, _910921] : [class_Groups_Oordered__ab__group__add(_910913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_910913), _910915), _910917) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_910913), _910919), _910921), 7767 ^ _780205 : [(7768 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910913), _910915), _910917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910913), _910919), _910921)))], (7774 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910913), _910919), _910921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910913), _910915), _910917)))]]], (7780 ^ _780205) ^ [_911268, _911270, _911272, _911274] : [c_Finite__Set_Ofolding__one(_911268, _911270, _911272), hBOOL(hAPP(c_Finite__Set_Ofinite(_911268), _911274)), -(_911274 = c_Orderings_Obot__class_Obot(tc_fun(_911268, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_911268), hAPP(hAPP(_911270, 7793 ^ [_911268, _911270, _911272, _911274]), 7794 ^ [_911268, _911270, _911272, _911274])), hAPP(hAPP(c_Set_Oinsert(_911268), 7793 ^ [_911268, _911270, _911272, _911274]), hAPP(hAPP(c_Set_Oinsert(_911268), 7794 ^ [_911268, _911270, _911272, _911274]), c_Orderings_Obot__class_Obot(tc_fun(_911268, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_911268), hAPP(_911272, _911274)), _911274)))], (7800 ^ _780205) ^ [_911754, _911756, _911758] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_911754), _911756)), hBOOL(hAPP(_911758, _911756)), 7811 ^ _780205 : [(7812 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_911754), 7810 ^ [_911754, _911756, _911758])))], (7814 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911754), 7809 ^ [_911754, _911756, _911758]), 7810 ^ [_911754, _911756, _911758])))], (7816 ^ _780205) ^ [] : [-(hBOOL(hAPP(_911758, 7810 ^ [_911754, _911756, _911758])))], (7818 ^ _780205) ^ [] : [hBOOL(hAPP(_911758, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911754, tc_HOL_Obool)), 7810 ^ [_911754, _911756, _911758]), hAPP(hAPP(c_Set_Oinsert(_911754), 7809 ^ [_911754, _911756, _911758]), c_Orderings_Obot__class_Obot(tc_fun(_911754, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_911758, c_Orderings_Obot__class_Obot(tc_fun(_911754, tc_HOL_Obool)))))], (7822 ^ _780205) ^ [_912279, _912281, _912283, _912285, _912287] : [c_Finite__Set_Ofolding__one__idem(_912279, _912281, _912283), hBOOL(hAPP(c_Finite__Set_Ofinite(_912279), _912285)), -(_912285 = c_Orderings_Obot__class_Obot(tc_fun(_912279, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_912279), _912287)), -(_912287 = c_Orderings_Obot__class_Obot(tc_fun(_912279, tc_HOL_Obool))), -(hAPP(_912283, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912279, tc_HOL_Obool)), _912285), _912287)) = hAPP(hAPP(_912281, hAPP(_912283, _912285)), hAPP(_912283, _912287)))], (7844 ^ _780205) ^ [_912644, _912646, _912648, _912650, _912652] : [c_Finite__Set_Ofolding__one__idem(_912644, _912646, _912648), hBOOL(hAPP(c_Finite__Set_Ofinite(_912644), _912650)), -(_912652 = c_Orderings_Obot__class_Obot(tc_fun(_912644, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912644, tc_HOL_Obool)), _912652), _912650)), -(hAPP(hAPP(_912646, hAPP(_912648, _912652)), hAPP(_912648, _912650)) = hAPP(_912648, _912650))], (7862 ^ _780205) ^ [_912974, _912976, _912978, _912980] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_912974), _912976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912974, tc_HOL_Obool)), _912976), _912978)), hBOOL(hAPP(_912980, c_Orderings_Obot__class_Obot(tc_fun(_912974, tc_HOL_Obool)))), 7877 ^ _780205 : [(7878 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_912974), 7876 ^ [_912974, _912976, _912978, _912980])))], (7880 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912974), 7875 ^ [_912974, _912976, _912978, _912980]), _912978)))], (7882 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_912974), 7875 ^ [_912974, _912976, _912978, _912980]), 7876 ^ [_912974, _912976, _912978, _912980]))], (7884 ^ _780205) ^ [] : [-(hBOOL(hAPP(_912980, 7876 ^ [_912974, _912976, _912978, _912980])))], (7886 ^ _780205) ^ [] : [hBOOL(hAPP(_912980, hAPP(hAPP(c_Set_Oinsert(_912974), 7875 ^ [_912974, _912976, _912978, _912980]), 7876 ^ [_912974, _912976, _912978, _912980])))]], -(hBOOL(hAPP(_912980, _912976)))], (7890 ^ _780205) ^ [_913639, _913641, _913643, _913645, _913647] : [c_Finite__Set_Ofolding__one__idem(_913639, _913641, _913643), hBOOL(hAPP(c_Finite__Set_Ofinite(_913639), _913645)), -(_913645 = c_Orderings_Obot__class_Obot(tc_fun(_913639, tc_HOL_Obool))), -(hAPP(_913643, hAPP(hAPP(c_Set_Oinsert(_913639), _913647), _913645)) = hAPP(hAPP(_913641, _913647), hAPP(_913643, _913645)))], (7904 ^ _780205) ^ [_913855, _913857, _913859] : [class_Lattices_Olattice(_913855), hBOOL(hAPP(c_Finite__Set_Ofinite(_913855), _913857)), 7911 ^ _780205 : [(7912 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913855, tc_HOL_Obool)), _913857), hAPP(hAPP(c_Set_Oinsert(_913855), _913859), c_Orderings_Obot__class_Obot(tc_fun(_913855, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_913855, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_913855, hAPP(hAPP(c_Set_Oinsert(_913855), _913859), _913857)) = _913859)], (7918 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913855, tc_HOL_Obool)), _913857), hAPP(hAPP(c_Set_Oinsert(_913855), _913859), c_Orderings_Obot__class_Obot(tc_fun(_913855, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_913855, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_913855, hAPP(hAPP(c_Set_Oinsert(_913855), _913859), _913857)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913855), _913859), c_Big__Operators_Olattice__class_OSup__fin(_913855, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913855, tc_HOL_Obool)), _913857), hAPP(hAPP(c_Set_Oinsert(_913855), _913859), c_Orderings_Obot__class_Obot(tc_fun(_913855, tc_HOL_Obool)))))))]]], (7924 ^ _780205) ^ [_914325, _914327, _914329, _914331] : [c_Finite__Set_Ofolding__one__idem(_914325, _914327, _914329), -(hAPP(hAPP(_914327, _914331), _914331) = _914331)], (7930 ^ _780205) ^ [_914420, _914422, _914424, _914426, _914428, _914430] : [c_Finite__Set_Ofolding__image__simple(_914420, _914422, _914424, _914426, _914428, _914430), -(hAPP(_914430, c_Orderings_Obot__class_Obot(tc_fun(_914422, tc_HOL_Obool))) = _914426)], (7936 ^ _780205) ^ [_914529, _914531] : [class_Lattices_Olattice(_914529), -(c_Big__Operators_Olattice__class_OSup__fin(_914529, hAPP(hAPP(c_Set_Oinsert(_914529), _914531), c_Orderings_Obot__class_Obot(tc_fun(_914529, tc_HOL_Obool)))) = _914531)], (7942 ^ _780205) ^ [_914636, _914638, _914640, _914642, _914644] : [class_Groups_Oab__group__add(_914636), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_914636), _914638), _914640) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_914636), _914642), _914644), 7949 ^ _780205 : [(7950 ^ _780205) ^ [] : [_914638 = _914640, -(_914642 = _914644)], (7956 ^ _780205) ^ [] : [_914642 = _914644, -(_914638 = _914640)]]], (7962 ^ _780205) ^ [_914949, _914951, _914953] : [class_Lattices_Olattice(_914949), hBOOL(hAPP(c_Finite__Set_Ofinite(_914949), _914951)), hBOOL(hAPP(hAPP(c_member(_914949), _914953), _914951)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914949), _914953), c_Big__Operators_Olattice__class_OSup__fin(_914949, _914951)) = c_Big__Operators_Olattice__class_OSup__fin(_914949, _914951))], (7976 ^ _780205) ^ [_915184, _915186, _915188, _915190, _915192] : [c_Finite__Set_Ofolding__one__idem(_915184, _915186, _915188), hBOOL(hAPP(c_Finite__Set_Ofinite(_915184), _915190)), hBOOL(hAPP(hAPP(c_member(_915184), _915192), _915190)), -(hAPP(hAPP(_915186, _915192), hAPP(_915188, _915190)) = hAPP(_915188, _915190))], (7990 ^ _780205) ^ [_915431, _915433, _915435] : [class_Lattices_Olattice(_915431), hBOOL(hAPP(c_Finite__Set_Ofinite(_915431), _915433)), -(_915433 = c_Orderings_Obot__class_Obot(tc_fun(_915431, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_915431, hAPP(hAPP(c_Set_Oinsert(_915431), _915435), _915433)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915431), _915435), c_Big__Operators_Olattice__class_OSup__fin(_915431, _915433)))], (8004 ^ _780205) ^ [_915639, _915641, _915643] : [class_Lattices_Olattice(_915639), hBOOL(hAPP(c_Finite__Set_Ofinite(_915639), _915641)), -(_915643 = c_Orderings_Obot__class_Obot(tc_fun(_915639, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915639, tc_HOL_Obool)), _915643), _915641)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915639), c_Big__Operators_Olattice__class_OSup__fin(_915639, _915643)), c_Big__Operators_Olattice__class_OSup__fin(_915639, _915641)) = c_Big__Operators_Olattice__class_OSup__fin(_915639, _915641))], (8022 ^ _780205) ^ [_915953, _915955, _915957] : [class_Lattices_Olattice(_915953), hBOOL(hAPP(c_Finite__Set_Ofinite(_915953), _915955)), -(_915955 = c_Orderings_Obot__class_Obot(tc_fun(_915953, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_915953), _915957)), -(_915957 = c_Orderings_Obot__class_Obot(tc_fun(_915953, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_915953, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915953, tc_HOL_Obool)), _915955), _915957)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915953), c_Big__Operators_Olattice__class_OSup__fin(_915953, _915955)), c_Big__Operators_Olattice__class_OSup__fin(_915953, _915957)))], (8044 ^ _780205) ^ [_916302, _916304, _916306, _916308, _916310, _916312, _916314, _916316] : [c_Finite__Set_Ofolding__image__simple(_916302, _916304, _916306, _916308, _916310, _916312), hBOOL(hAPP(c_Finite__Set_Ofinite(_916304), _916314)), -(hBOOL(hAPP(hAPP(c_member(_916304), _916316), _916314))), -(hAPP(_916312, hAPP(hAPP(c_Set_Oinsert(_916304), _916316), _916314)) = hAPP(hAPP(_916306, hAPP(_916310, _916316)), hAPP(_916312, _916314)))], (8058 ^ _780205) ^ [_916546, _916548, _916550] : [class_Lattices_Olattice(_916546), hBOOL(hAPP(c_Finite__Set_Ofinite(_916546), _916548)), -(hBOOL(hAPP(hAPP(c_member(_916546), _916550), _916548))), -(_916548 = c_Orderings_Obot__class_Obot(tc_fun(_916546, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_916546, hAPP(hAPP(c_Set_Oinsert(_916546), _916550), _916548)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916546), _916550), c_Big__Operators_Olattice__class_OSup__fin(_916546, _916548)))], (8076 ^ _780205) ^ [_916783, _916785] : [class_Lattices_Olattice(_916783), hBOOL(hAPP(c_Finite__Set_Ofinite(_916783), _916785)), -(_916785 = c_Orderings_Obot__class_Obot(tc_fun(_916783, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_916783), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916783), 8089 ^ [_916783, _916785]), 8090 ^ [_916783, _916785])), hAPP(hAPP(c_Set_Oinsert(_916783), 8089 ^ [_916783, _916785]), hAPP(hAPP(c_Set_Oinsert(_916783), 8090 ^ [_916783, _916785]), c_Orderings_Obot__class_Obot(tc_fun(_916783, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_916783), c_Big__Operators_Olattice__class_OSup__fin(_916783, _916785)), _916785)))], (8096 ^ _780205) ^ [_917227, _917229, _917231, _917233, _917235] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_917227, _917229, hAPP(hAPP(c_Set_Oinsert(_917227), _917231), _917233)), _917235)), 8101 ^ _780205 : [(8102 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_917227), _917231), _917233) = hAPP(hAPP(c_Set_Oinsert(_917227), 8099 ^ [_917227, _917229, _917231, _917233, _917235]), 8100 ^ [_917227, _917229, _917231, _917233, _917235]))], (8104 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_917227, _917227, _917229, 8099 ^ [_917227, _917229, _917231, _917233, _917235], 8100 ^ [_917227, _917229, _917231, _917233, _917235]), _917235)))], (8106 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_917227), 8099 ^ [_917227, _917229, _917231, _917233, _917235]), 8100 ^ [_917227, _917229, _917231, _917233, _917235]))]]], (8108 ^ _780205) ^ [_917644, _917646, _917648, _917650, _917652] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_917644, _917646, hAPP(hAPP(c_Set_Oinsert(_917644), _917648), _917650)), _917652)), 8113 ^ _780205 : [(8114 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_917644), _917648), _917650) = hAPP(hAPP(c_Set_Oinsert(_917644), 8111 ^ [_917644, _917646, _917648, _917650, _917652]), 8112 ^ [_917644, _917646, _917648, _917650, _917652]))], (8116 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_917644, _917644, _917646, 8111 ^ [_917644, _917646, _917648, _917650, _917652], 8112 ^ [_917644, _917646, _917648, _917650, _917652]), _917652)))], (8118 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_917644), 8111 ^ [_917644, _917646, _917648, _917650, _917652]), 8112 ^ [_917644, _917646, _917648, _917650, _917652]))]]], (8120 ^ _780205) ^ [_918035, _918037, _918039, _918041, _918043] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_918035, _918037, hAPP(hAPP(c_Set_Oinsert(_918035), _918039), _918041)), _918043))), 8121 ^ _780205 : [(8122 ^ _780205) ^ [_918139, _918141] : [hAPP(hAPP(c_Set_Oinsert(_918035), _918039), _918041) = hAPP(hAPP(c_Set_Oinsert(_918035), _918141), _918139), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_918035, _918035, _918037, _918141, _918139), _918043)), -(hBOOL(hAPP(hAPP(c_member(_918035), _918141), _918139)))]]], (8134 ^ _780205) ^ [_918396, _918398, _918400, _918402, _918404] : [class_Rings_Oring(_918396), hBOOL(hAPP(c_Finite__Set_Ofinite(_918398), _918400)), hBOOL(hAPP(hAPP(c_member(_918398), _918402), _918400)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918398, _918396), _918404), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918398, tc_HOL_Obool)), _918400), hAPP(hAPP(c_Set_Oinsert(_918398), _918402), c_Orderings_Obot__class_Obot(tc_fun(_918398, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918396), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918398, _918396), _918404), _918400)), hAPP(_918404, _918402)))], (8148 ^ _780205) ^ [_918721, _918723, _918725, _918727, _918729] : [class_Groups_Oab__group__add(_918721), hBOOL(hAPP(c_Finite__Set_Ofinite(_918723), _918725)), 8155 ^ _780205 : [(8156 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_918723), _918727), _918725)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918723, _918721), _918729), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918723, tc_HOL_Obool)), _918725), hAPP(hAPP(c_Set_Oinsert(_918723), _918727), c_Orderings_Obot__class_Obot(tc_fun(_918723, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918721), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918723, _918721), _918729), _918725)), hAPP(_918729, _918727)))], (8162 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_918723), _918727), _918725))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918723, _918721), _918729), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918723, tc_HOL_Obool)), _918725), hAPP(hAPP(c_Set_Oinsert(_918723), _918727), c_Orderings_Obot__class_Obot(tc_fun(_918723, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918723, _918721), _918729), _918725))]]], (8168 ^ _780205) ^ [_919191, _919193, _919195, _919197, _919199] : [class_Groups_Oab__semigroup__mult(_919191), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_919191, _919191, c_Groups_Otimes__class_Otimes(_919191), _919193, _919195), _919197)), hBOOL(hAPP(hAPP(c_member(_919191), _919199), _919195)), -(hBOOL(hAPP(hAPP(c_member(_919191), _919193), _919195))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_919191, _919191, c_Groups_Otimes__class_Otimes(_919191), _919199, hAPP(hAPP(c_Set_Oinsert(_919191), _919193), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919191, tc_HOL_Obool)), _919195), hAPP(hAPP(c_Set_Oinsert(_919191), _919199), c_Orderings_Obot__class_Obot(tc_fun(_919191, tc_HOL_Obool)))))), _919197)))], (8186 ^ _780205) ^ [_919535, _919537, _919539] : [class_Lattices_Olattice(_919535), hBOOL(hAPP(c_Finite__Set_Ofinite(_919535), _919537)), -(_919537 = c_Orderings_Obot__class_Obot(tc_fun(_919535, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_919535), _919539)), -(_919539 = c_Orderings_Obot__class_Obot(tc_fun(_919535, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919535, tc_HOL_Obool)), _919537), _919539) = c_Orderings_Obot__class_Obot(tc_fun(_919535, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_919535, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_919535, tc_HOL_Obool)), _919537), _919539)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919535), c_Big__Operators_Olattice__class_OSup__fin(_919535, _919537)), c_Big__Operators_Olattice__class_OSup__fin(_919535, _919539)))], (8212 ^ _780205) ^ [_920012, _920014, _920016] : [class_Lattices_Olattice(_920012), hBOOL(hAPP(c_Finite__Set_Ofinite(_920012), _920014)), hBOOL(hAPP(c_Finite__Set_Ofinite(_920012), _920016)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_920012, tc_HOL_Obool)), _920014), _920016) = c_Orderings_Obot__class_Obot(tc_fun(_920012, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920012), c_Big__Operators_Olattice__class_OSup__fin(_920012, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920012, tc_HOL_Obool)), _920014), _920016))), c_Big__Operators_Olattice__class_OSup__fin(_920012, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_920012, tc_HOL_Obool)), _920014), _920016))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920012), c_Big__Operators_Olattice__class_OSup__fin(_920012, _920014)), c_Big__Operators_Olattice__class_OSup__fin(_920012, _920016)))], (8256 ^ _780205) ^ [_920908, _920910, _920912, _920914] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_920908, tc_HOL_Obool)), _920910), hAPP(hAPP(c_Set_Oinsert(_920908), _920912), _920914)))), 8259 ^ _780205 : [(8260 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_920908), _920912), _920914)))], (8262 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_920908, tc_HOL_Obool)), _920910), _920914))]], 8263 ^ _780205 : [(8264 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_920908), _920912), _920914))], (8266 ^ _780205) ^ [] : [8267 ^ _780205 : [(8268 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_920908), _920912), _920910)))], (8270 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_920908, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920908, tc_HOL_Obool)), _920910), hAPP(hAPP(c_Set_Oinsert(_920908), _920912), c_Orderings_Obot__class_Obot(tc_fun(_920908, tc_HOL_Obool))))), _920914))]], 8271 ^ _780205 : [(8272 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_920908), _920912), _920910))], (8274 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920908, tc_HOL_Obool)), _920910), _920914))]]]]], (8230 ^ _780205) ^ [_920381, _920383, _920385, _920387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_920381, tc_HOL_Obool)), _920383), hAPP(hAPP(c_Set_Oinsert(_920381), _920385), _920387))), 8233 ^ _780205 : [(8234 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_920381), _920385), _920387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_920381, tc_HOL_Obool)), _920383), _920387)))], (8240 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_920381), _920385), _920387))), 8243 ^ _780205 : [(8244 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_920381), _920385), _920383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_920381, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920381, tc_HOL_Obool)), _920383), hAPP(hAPP(c_Set_Oinsert(_920381), _920385), c_Orderings_Obot__class_Obot(tc_fun(_920381, tc_HOL_Obool))))), _920387)))], (8250 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_920381), _920385), _920383))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920381, tc_HOL_Obool)), _920383), _920387)))]]]]], (8278 ^ _780205) ^ [_921447, _921449, _921451, _921453, _921455, _921457, _921459, _921461] : [c_Finite__Set_Ofolding__image__simple__idem(_921447, _921449, _921451, _921453, _921455, _921457), hBOOL(hAPP(c_Finite__Set_Ofinite(_921449), _921459)), hBOOL(hAPP(c_Finite__Set_Ofinite(_921449), _921461)), -(hAPP(_921457, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921449, tc_HOL_Obool)), _921459), _921461)) = hAPP(hAPP(_921451, hAPP(_921457, _921459)), hAPP(_921457, _921461)))], (8292 ^ _780205) ^ [_921740, _921742, _921744, _921746, _921748, _921750, _921752, _921754] : [c_Finite__Set_Ofolding__image__simple__idem(_921740, _921742, _921744, _921746, _921748, _921750), hBOOL(hAPP(c_Finite__Set_Ofinite(_921742), _921752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921742, tc_HOL_Obool)), _921754), _921752)), -(hAPP(hAPP(_921744, hAPP(_921750, _921754)), hAPP(_921750, _921752)) = hAPP(_921750, _921752))], (8306 ^ _780205) ^ [_922023, _922025, _922027, _922029] : [hBOOL(hAPP(_922023, _922025)), hBOOL(hAPP(_922027, _922025)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922029, tc_HOL_Obool)), _922023), _922027), _922025)))], (8316 ^ _780205) ^ [_922194, _922196, _922198, _922200] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922194, tc_HOL_Obool)), _922196), _922198), _922200)), 8319 ^ _780205 : [(8320 ^ _780205) ^ [] : [-(hBOOL(hAPP(_922196, _922200)))], (8322 ^ _780205) ^ [] : [-(hBOOL(hAPP(_922198, _922200)))]]], (8324 ^ _780205) ^ [_922339, _922341, _922343, _922345] : [hBOOL(hAPP(hAPP(c_member(_922339), _922341), _922343)), hBOOL(hAPP(hAPP(c_member(_922339), _922341), _922345)), -(hBOOL(hAPP(hAPP(c_member(_922339), _922341), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922339, tc_HOL_Obool)), _922343), _922345))))], (8334 ^ _780205) ^ [_922540, _922542, _922544, _922546] : [hBOOL(hAPP(hAPP(c_member(_922540), _922542), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922540, tc_HOL_Obool)), _922544), _922546))), 8337 ^ _780205 : [(8338 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_922540), _922542), _922544)))], (8340 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_922540), _922542), _922546)))]]], (8342 ^ _780205) ^ [_922715, _922717, _922719] : [8343 ^ _780205 : [(8344 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_922715), _922717))], (8346 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_922715), _922719))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_922715), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922715, tc_HOL_Obool)), _922717), _922719))))], (8350 ^ _780205) ^ [_922878, _922880, _922882, _922884] : [class_Groups_Oab__semigroup__mult(_922878), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922878), _922880), _922882)), _922884) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922878), _922880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922878), _922882), _922884)))], (8356 ^ _780205) ^ [_923021, _923023] : [class_Lattices_Oab__semigroup__idem__mult(_923021), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923021), _923023), _923023) = _923023)], (8362 ^ _780205) ^ [_923112, _923114] : [class_Lattices_Oab__semigroup__idem__mult(_923112), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923112), _923114), _923114) = _923114)], (8368 ^ _780205) ^ [_923203, _923205] : [class_Lattices_Osemilattice__inf(_923203), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923203), _923205), _923205) = _923205)], (8374 ^ _780205) ^ [_923294, _923296] : [class_Lattices_Osemilattice__inf(_923294), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923294), _923296), _923296) = _923296)], (8380 ^ _780205) ^ [_923385, _923387, _923389] : [class_Lattices_Osemilattice__inf(_923385), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923385), _923387), _923389) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923385), _923389), _923387))], (8386 ^ _780205) ^ [_923494, _923496, _923498] : [class_Lattices_Olattice(_923494), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923494), _923496), _923498) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923494), _923498), _923496))], (8392 ^ _780205) ^ [_923603, _923605, _923607] : [class_Lattices_Osemilattice__inf(_923603), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923603), _923605), _923607) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923603), _923607), _923605))], (8398 ^ _780205) ^ [_923712, _923714, _923716] : [class_Lattices_Oab__semigroup__idem__mult(_923712), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923712), _923714), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923712), _923714), _923716)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923712), _923714), _923716))], (8404 ^ _780205) ^ [_923837, _923839, _923841] : [class_Lattices_Osemilattice__inf(_923837), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923837), _923839), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923837), _923839), _923841)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923837), _923839), _923841))], (8410 ^ _780205) ^ [_923962, _923964, _923966] : [class_Lattices_Olattice(_923962), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923962), _923964), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923962), _923964), _923966)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923962), _923964), _923966))], (8416 ^ _780205) ^ [_924087, _924089, _924091] : [class_Lattices_Osemilattice__inf(_924087), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924087), _924089), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924087), _924089), _924091)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924087), _924089), _924091))], (8422 ^ _780205) ^ [_924212, _924214, _924216, _924218] : [class_Lattices_Osemilattice__inf(_924212), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924212), _924214), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924212), _924216), _924218)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924212), _924216), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924212), _924214), _924218)))], (8428 ^ _780205) ^ [_924355, _924357, _924359, _924361] : [class_Lattices_Olattice(_924355), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924355), _924357), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924355), _924359), _924361)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924355), _924359), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924355), _924357), _924361)))], (8434 ^ _780205) ^ [_924498, _924500, _924502, _924504] : [class_Lattices_Osemilattice__inf(_924498), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924498), _924500), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924498), _924502), _924504)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924498), _924502), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924498), _924500), _924504)))], (8440 ^ _780205) ^ [_924641, _924643, _924645, _924647] : [class_Lattices_Osemilattice__inf(_924641), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924641), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924641), _924643), _924645)), _924647) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924641), _924643), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924641), _924645), _924647)))], (8446 ^ _780205) ^ [_924784, _924786, _924788, _924790] : [class_Lattices_Olattice(_924784), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924784), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924784), _924786), _924788)), _924790) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924784), _924786), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924784), _924788), _924790)))], (8452 ^ _780205) ^ [_924927, _924929, _924931, _924933] : [class_Lattices_Osemilattice__inf(_924927), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924927), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924927), _924929), _924931)), _924933) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924927), _924929), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924927), _924931), _924933)))], (8458 ^ _780205) ^ [_925070, _925072, _925074, _925076, _925078] : [class_Lattices_Olattice(_925070), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_925072, _925070)), _925074), _925076), _925078) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925070), hAPP(_925074, _925078)), hAPP(_925076, _925078)))], (8464 ^ _780205) ^ [_925207, _925209, _925211, _925213] : [class_Lattices_Osemilattice__inf(_925207), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925207), _925209), _925211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925207), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925207), _925209), _925213)), _925211)))], (8474 ^ _780205) ^ [_925386, _925388, _925390, _925392] : [class_Lattices_Osemilattice__inf(_925386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925386), _925388), _925390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925386), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925386), _925392), _925388)), _925390)))], (8484 ^ _780205) ^ [_925565, _925567, _925569, _925571] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_925565, tc_HOL_Obool)), _925567), _925569), _925571)), -(hBOOL(hAPP(_925567, _925571)))], (8490 ^ _780205) ^ [_925676, _925678, _925680, _925682] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_925676, tc_HOL_Obool)), _925678), _925680), _925682)), -(hBOOL(hAPP(_925680, _925682)))], (8496 ^ _780205) ^ [_925787, _925789] : [class_Orderings_Opreorder(_925787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925787), _925789), _925789))], (8502 ^ _780205) ^ [_925877, _925879, _925881] : [class_Orderings_Olinorder(_925877), 8505 ^ _780205 : [(8516 ^ _780205) ^ [] : [8517 ^ _780205 : [(8518 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925877), _925879), _925881))], (8520 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925877), _925881), _925879))]], _925879 = _925881], (8506 ^ _780205) ^ [] : [-(_925879 = _925881), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925877), _925879), _925881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925877), _925881), _925879)))]]], (8524 ^ _780205) ^ [_926131, _926133, _926135] : [class_Orderings_Olinorder(_926131), 8527 ^ _780205 : [(8538 ^ _780205) ^ [] : [8539 ^ _780205 : [(8540 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926131), _926135), _926133))], (8542 ^ _780205) ^ [] : [_926133 = _926135]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926131), _926133), _926135))], (8528 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926131), _926133), _926135))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926131), _926135), _926133))), -(_926133 = _926135)]]], (8546 ^ _780205) ^ [_926385, _926387] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926385, tc_HOL_Obool)), _926387), _926387) = _926387)], (8548 ^ _780205) ^ [_926421, _926423, _926425] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926421, tc_HOL_Obool)), _926423), _926425) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926421, tc_HOL_Obool)), _926425), _926423))], (8550 ^ _780205) ^ [_926470, _926472, _926474] : [class_Orderings_Olinorder(_926470), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926470), _926472), _926474))), -(_926472 = _926474), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926470), _926474), _926472)))], (8564 ^ _780205) ^ [_926601, _926603, _926605] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926601, tc_HOL_Obool)), _926603), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926601, tc_HOL_Obool)), _926603), _926605)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926601, tc_HOL_Obool)), _926603), _926605))], (8566 ^ _780205) ^ [_926661, _926663, _926665, _926667] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926661, tc_HOL_Obool)), _926663), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926661, tc_HOL_Obool)), _926665), _926667)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926661, tc_HOL_Obool)), _926665), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926661, tc_HOL_Obool)), _926663), _926667)))], (8568 ^ _780205) ^ [_926734, _926736, _926738, _926740] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926734, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926734, tc_HOL_Obool)), _926736), _926738)), _926740) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926734, tc_HOL_Obool)), _926736), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926734, tc_HOL_Obool)), _926738), _926740)))], (8570 ^ _780205) ^ [_926807, _926809, _926811] : [class_Orderings_Olinorder(_926807), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926807), _926809), _926811))), 8577 ^ _780205 : [(8578 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926807), _926811), _926809))), -(_926811 = _926809)], (8584 ^ _780205) ^ [] : [_926811 = _926809, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926807), _926811), _926809))]]], (8590 ^ _780205) ^ [_927066, _927068, _927070] : [class_Orderings_Olinorder(_927066), -(_927068 = _927070), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927066), _927068), _927070))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927066), _927070), _927068)))], (8604 ^ _780205) ^ [_927201, _927203, _927205] : [class_Orderings_Oorder(_927201), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927201), _927203), _927205)), _927203 = _927205], (8614 ^ _780205) ^ [_927347, _927349, _927351] : [class_Orderings_Opreorder(_927347), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927347), _927349), _927351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927347), _927351), _927349))], (8624 ^ _780205) ^ [_927507, _927509, _927511] : [class_Orderings_Opreorder(_927507), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927507), _927509), _927511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927507), _927511), _927509))], (8634 ^ _780205) ^ [_927667, _927669, _927671] : [class_Orderings_Oorder(_927667), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927667), _927669), _927671)), _927669 = _927671], (8644 ^ _780205) ^ [_927813, _927815, _927817] : [class_Orderings_Oorder(_927813), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927813), _927815), _927817)), _927817 = _927815], (8654 ^ _780205) ^ [_927959, _927961, _927963] : [class_Orderings_Opreorder(_927959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927959), _927961), _927963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927959), _927963), _927961))], (8664 ^ _780205) ^ [_928119, _928121, _928123] : [class_Orderings_Oorder(_928119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928119), _928121), _928123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928119), _928123), _928121))], (8674 ^ _780205) ^ [_928279, _928281, _928283, _928285] : [class_Orderings_Oord(_928279), _928281 = _928283, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928279), _928283), _928285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928279), _928281), _928285)))], (8688 ^ _780205) ^ [_928498, _928500, _928502, _928504] : [class_Orderings_Oorder(_928498), _928500 = _928502, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928498), _928504), _928502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928498), _928504), _928500)))], (8702 ^ _780205) ^ [_928717, _928719, _928721, _928723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928717, tc_HOL_Obool)), _928719), _928721)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928717, tc_HOL_Obool)), _928721), _928723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928717, tc_HOL_Obool)), _928719), _928723)))], (8712 ^ _780205) ^ [_928914, _928916, _928918, _928920] : [class_Orderings_Oord(_928914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928914), _928916), _928918)), _928918 = _928920, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928914), _928916), _928920)))], (8726 ^ _780205) ^ [_929133, _929135, _929137, _929139] : [class_Orderings_Oorder(_929133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929133), _929135), _929137)), _929135 = _929139, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929133), _929139), _929137)))], (8740 ^ _780205) ^ [_929352, _929354, _929356, _929358] : [class_Orderings_Opreorder(_929352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929352), _929354), _929356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929352), _929356), _929358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929352), _929354), _929358)))], (8754 ^ _780205) ^ [_929585, _929587, _929589, _929591] : [class_Orderings_Oorder(_929585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929585), _929587), _929589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929585), _929591), _929587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929585), _929591), _929589)))], (8768 ^ _780205) ^ [_929818, _929820, _929822] : [class_Orderings_Opreorder(_929818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929818), _929820), _929822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929818), _929822), _929820))], (8778 ^ _780205) ^ [_929978, _929980, _929982] : [class_Orderings_Olinorder(_929978), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929978), _929980), _929982))), -(_929980 = _929982), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929978), _929982), _929980)))], (8792 ^ _780205) ^ [_930113, _930115] : [class_Lattices_Olattice(_930113), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930113), _930115), _930115) = _930115)], (8798 ^ _780205) ^ [_930204, _930206, _930208, _930210, _930212, _930214, _930216] : [c_Finite__Set_Ofolding__image__simple__idem(_930204, _930206, _930208, _930210, _930212, _930214), -(hAPP(hAPP(_930208, _930216), _930216) = _930216)], (8804 ^ _780205) ^ [_930311, _930313, _930315, _930317] : [class_Lattices_Osemilattice__inf(_930311), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930311), _930313), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930311), _930315), _930317))), 8811 ^ _780205 : [(8812 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930311), _930313), _930315)))], (8814 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930311), _930313), _930317)))]]], (8816 ^ _780205) ^ [_930534, _930536, _930538, _930540, _930542] : [class_Lattices_Osemilattice__inf(_930534), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930534), _930536), _930538)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930534), _930540), _930542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930534), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930534), _930536), _930540)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930534), _930538), _930542))))], (8830 ^ _780205) ^ [_930805, _930807, _930809, _930811] : [class_Lattices_Osemilattice__inf(_930805), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930805), _930807), _930809)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930805), _930807), _930811)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930805), _930807), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930805), _930809), _930811))))], (8844 ^ _780205) ^ [_931054, _931056, _931058, _931060] : [class_Lattices_Osemilattice__inf(_931054), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931054), _931056), _931058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931054), _931056), _931060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931054), _931056), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931054), _931058), _931060))))], (8858 ^ _780205) ^ [_931303, _931305, _931307] : [class_Lattices_Osemilattice__inf(_931303), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931303), _931305), _931307)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931303), _931307), _931305) = _931305)], (8868 ^ _780205) ^ [_931464, _931466, _931468] : [class_Lattices_Osemilattice__inf(_931464), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931464), _931466), _931468)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931464), _931466), _931468) = _931466)], (8878 ^ _780205) ^ [_931625, _931627, _931629, _931631] : [class_Lattices_Osemilattice__inf(_931625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931625), _931627), _931629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931625), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931625), _931631), _931627)), _931629)))], (8888 ^ _780205) ^ [_931804, _931806, _931808, _931810] : [class_Lattices_Osemilattice__inf(_931804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931804), _931806), _931808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931804), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931804), _931806), _931810)), _931808)))], (8898 ^ _780205) ^ [_931983, _931985, _931987, _931989] : [class_Lattices_Osemilattice__inf(_931983), 8901 ^ _780205 : [(8902 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931983), _931985), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931983), _931987), _931989))), 8905 ^ _780205 : [(8906 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931983), _931985), _931987)))], (8908 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931983), _931985), _931989)))]]], (8910 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931983), _931985), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931983), _931987), _931989)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931983), _931985), _931987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931983), _931985), _931989))]]], (8920 ^ _780205) ^ [_932363, _932365, _932367] : [class_Lattices_Osemilattice__inf(_932363), 8923 ^ _780205 : [(8924 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932363), _932365), _932367)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932363), _932365), _932367) = _932365)], (8930 ^ _780205) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932363), _932365), _932367) = _932365, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932363), _932365), _932367)))]]], (8936 ^ _780205) ^ [_932619, _932621, _932623] : [class_Lattices_Osemilattice__inf(_932619), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932619), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932619), _932621), _932623)), _932623)))], (8942 ^ _780205) ^ [_932726, _932728, _932730] : [class_Lattices_Olattice(_932726), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932726), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932726), _932728), _932730)), _932730)))], (8948 ^ _780205) ^ [_932833, _932835, _932837] : [class_Lattices_Osemilattice__inf(_932833), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932833), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932833), _932835), _932837)), _932835)))], (8954 ^ _780205) ^ [_932940, _932942, _932944] : [class_Lattices_Olattice(_932940), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932940), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932940), _932942), _932944)), _932942)))], (8960 ^ _780205) ^ [_933047, _933049] : [class_Lattices_Obounded__lattice__bot(_933047), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933047), c_Orderings_Obot__class_Obot(_933047)), _933049) = c_Orderings_Obot__class_Obot(_933047))], (8966 ^ _780205) ^ [_933146, _933148] : [class_Lattices_Obounded__lattice__bot(_933146), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933146), _933148), c_Orderings_Obot__class_Obot(_933146)) = c_Orderings_Obot__class_Obot(_933146))], (8972 ^ _780205) ^ [_933245, _933247, _933249, _933251] : [class_Lattices_Odistrib__lattice(_933245), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933245), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933245), _933247), _933249)), _933251) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933245), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933245), _933247), _933251)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933245), _933249), _933251)))], (8978 ^ _780205) ^ [_933404, _933406, _933408, _933410] : [class_Lattices_Odistrib__lattice(_933404), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933404), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933404), _933406), _933408)), _933410) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933404), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933404), _933406), _933410)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933404), _933408), _933410)))], (8984 ^ _780205) ^ [_933563, _933565, _933567, _933569] : [class_Lattices_Odistrib__lattice(_933563), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933563), _933565), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933563), _933567), _933569)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933563), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933563), _933565), _933567)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933563), _933565), _933569)))], (8990 ^ _780205) ^ [_933722, _933724, _933726, _933728] : [class_Lattices_Odistrib__lattice(_933722), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933722), _933724), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933722), _933726), _933728)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933722), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933722), _933724), _933726)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933722), _933724), _933728)))], (8996 ^ _780205) ^ [_933881, _933883, _933885] : [class_Lattices_Olattice(_933881), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933881), _933883), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933881), _933883), _933885)) = _933883)], (9002 ^ _780205) ^ [_933990, _933992, _933994] : [class_Lattices_Olattice(_933990), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933990), _933992), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_933990), _933992), _933994)) = _933992)], (9008 ^ _780205) ^ [_934120, _934122, _934124, _934126] : [hBOOL(hAPP(hAPP(c_member(_934120), _934122), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934120, tc_HOL_Obool)), _934124), _934126))), 9011 ^ _780205 : [(9012 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_934120), _934122), _934124)))], (9014 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_934120), _934122), _934126)))]]], (9016 ^ _780205) ^ [_934287, _934289, _934291, _934293] : [-(hBOOL(hAPP(hAPP(c_member(_934287), _934289), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934287, tc_HOL_Obool)), _934291), _934293)))), hBOOL(hAPP(hAPP(c_member(_934287), _934289), _934291)), hBOOL(hAPP(hAPP(c_member(_934287), _934289), _934293))], (9026 ^ _780205) ^ [_934490, _934492, _934494, _934496] : [hBOOL(hAPP(hAPP(c_member(_934490), _934492), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934490, tc_HOL_Obool)), _934494), _934496))), -(hBOOL(hAPP(hAPP(c_member(_934490), _934492), _934494)))], (9032 ^ _780205) ^ [_934621, _934623, _934625, _934627] : [hBOOL(hAPP(hAPP(c_member(_934621), _934623), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934621, tc_HOL_Obool)), _934625), _934627))), -(hBOOL(hAPP(hAPP(c_member(_934621), _934623), _934627)))], (9038 ^ _780205) ^ [_934752, _934754, _934756, _934758] : [class_Orderings_Oord(_934752), 9041 ^ _780205 : [(9042 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934754, _934752)), _934756), _934758)), 9045 ^ _780205 : [(9046 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934754, _934752)), _934756), _934758)))], (9048 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934754, _934752)), _934758), _934756))]]], (9050 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934754, _934752)), _934756), _934758))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934754, _934752)), _934756), _934758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934754, _934752)), _934758), _934756)))]]], (9060 ^ _780205) ^ [_935144, _935146, _935148] : [class_Orderings_Olinorder(_935144), 9063 ^ _780205 : [(9064 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935144), _935146), _935148))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935144), _935148), _935146)))], (9070 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935144), _935148), _935146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935144), _935146), _935148))]]], (9076 ^ _780205) ^ [_935353, _935355, _935357] : [class_Orderings_Olinorder(_935353), 9079 ^ _780205 : [(9080 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935353), _935355), _935357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935353), _935357), _935355)))], (9086 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935353), _935357), _935355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935353), _935355), _935357))]]], (9092 ^ _780205) ^ [_935562, _935564, _935566] : [class_Orderings_Olinorder(_935562), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935562), _935564), _935566))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935562), _935566), _935564)))], (9102 ^ _780205) ^ [_935680, _935682, _935684] : [class_Orderings_Oorder(_935680), 9105 ^ _780205 : [(9106 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935680), _935682), _935684)), 9109 ^ _780205 : [(9110 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935680), _935682), _935684)))], (9112 ^ _780205) ^ [] : [_935682 = _935684]]], (9114 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935680), _935682), _935684))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935680), _935682), _935684)), -(_935682 = _935684)]]], (9124 ^ _780205) ^ [_936016, _936018, _936020] : [class_Orderings_Opreorder(_936016), 9127 ^ _780205 : [(9128 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936016), _936018), _936020)), 9131 ^ _780205 : [(9132 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936016), _936018), _936020)))], (9134 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936016), _936020), _936018))]]], (9136 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936016), _936018), _936020))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936016), _936018), _936020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936016), _936020), _936018)))]]], (9146 ^ _780205) ^ [_936373, _936375, _936377] : [class_Orderings_Oorder(_936373), 9149 ^ _780205 : [(9160 ^ _780205) ^ [] : [9161 ^ _780205 : [(9162 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936373), _936375), _936377))], (9164 ^ _780205) ^ [] : [_936375 = _936377]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936373), _936375), _936377)))], (9150 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936373), _936375), _936377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936373), _936375), _936377))), -(_936375 = _936377)]]], (9168 ^ _780205) ^ [_936671, _936673, _936675] : [class_Orderings_Olinorder(_936671), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936671), _936673), _936675))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936671), _936675), _936673)))], (9178 ^ _780205) ^ [_936791, _936793, _936795] : [class_Orderings_Olinorder(_936791), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936791), _936793), _936795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936791), _936795), _936793)))], (9188 ^ _780205) ^ [_936911, _936913, _936915] : [class_Orderings_Olinorder(_936911), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936911), _936913), _936915))), 9195 ^ _780205 : [(9196 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936911), _936913), _936915)), -(_936913 = _936915)], (9202 ^ _780205) ^ [] : [_936913 = _936915, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936911), _936913), _936915)))]]], (9208 ^ _780205) ^ [_937214, _937216, _937218] : [class_Orderings_Oorder(_937214), -(_937216 = _937218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937214), _937216), _937218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937214), _937216), _937218)))], (9222 ^ _780205) ^ [_937430, _937432, _937434] : [class_Orderings_Oorder(_937430), -(_937432 = _937434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937430), _937434), _937432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937430), _937434), _937432)))], (9236 ^ _780205) ^ [_937646, _937648, _937650] : [class_Orderings_Olinorder(_937646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937646), _937648), _937650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937646), _937650), _937648))], (9246 ^ _780205) ^ [_937806, _937808, _937810] : [class_Orderings_Opreorder(_937806), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937806), _937808), _937810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937806), _937808), _937810)))], (9256 ^ _780205) ^ [_937965, _937967, _937969] : [class_Orderings_Olinorder(_937965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937965), _937967), _937969)), 9263 ^ _780205 : [(9264 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937965), _937967), _937969))), -(_937967 = _937969)], (9270 ^ _780205) ^ [] : [_937967 = _937969, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937965), _937967), _937969))]]], (9276 ^ _780205) ^ [_938221, _938223, _938225] : [class_Orderings_Oorder(_938221), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938221), _938223), _938225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938221), _938223), _938225))), -(_938223 = _938225)], (9290 ^ _780205) ^ [_938393, _938395, _938397] : [class_Orderings_Oorder(_938393), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938393), _938395), _938397)), -(_938395 = _938397), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938393), _938395), _938397)))], (9304 ^ _780205) ^ [_938567, _938569, _938571] : [class_Orderings_Oorder(_938567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938567), _938569), _938571)), -(_938571 = _938569), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938567), _938569), _938571)))], (9318 ^ _780205) ^ [_938741, _938743, _938745, _938747] : [class_Orderings_Opreorder(_938741), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938741), _938743), _938745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938741), _938745), _938747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938741), _938743), _938747)))], (9332 ^ _780205) ^ [_938974, _938976, _938978, _938980] : [class_Orderings_Oorder(_938974), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938974), _938976), _938978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938974), _938980), _938976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938974), _938980), _938978)))], (9346 ^ _780205) ^ [_939207, _939209, _939211, _939213] : [class_Orderings_Opreorder(_939207), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939207), _939209), _939211)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939207), _939211), _939213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939207), _939209), _939213)))], (9360 ^ _780205) ^ [_939440, _939442, _939444, _939446] : [class_Orderings_Oorder(_939440), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939440), _939442), _939444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939440), _939446), _939442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939440), _939446), _939444)))], (9374 ^ _780205) ^ [_939673, _939675, _939677, _939679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_939673, tc_HOL_Obool)), _939675), _939677)), hBOOL(hAPP(hAPP(c_member(_939673), _939679), _939675)), -(hBOOL(hAPP(hAPP(c_member(_939673), _939679), _939677)))], (9384 ^ _780205) ^ [_939858, _939860] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939858, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_939858, tc_HOL_Obool))), _939860) = c_Orderings_Obot__class_Obot(tc_fun(_939858, tc_HOL_Obool)))], (9386 ^ _780205) ^ [_939904, _939906] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939904, tc_HOL_Obool)), _939906), c_Orderings_Obot__class_Obot(tc_fun(_939904, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_939904, tc_HOL_Obool)))], (9402 ^ _780205) ^ [_940282, _940284, _940286] : [9404 ^ _780205 : [(9405 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_940282), 9403 ^ [_940282, _940284, _940286]), _940284)))], (9408 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_940282), 9406 ^ [_940282, _940284, _940286]), _940286)))], (9410 ^ _780205) ^ [] : [-(9403 ^ [_940282, _940284, _940286] = 9406 ^ [_940282, _940284, _940286])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940282, tc_HOL_Obool)), _940284), _940286) = c_Orderings_Obot__class_Obot(tc_fun(_940282, tc_HOL_Obool)))], (9388 ^ _780205) ^ [_939968, _939970, _939972] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939968, tc_HOL_Obool)), _939970), _939972) = c_Orderings_Obot__class_Obot(tc_fun(_939968, tc_HOL_Obool)), 9391 ^ _780205 : [(9392 ^ _780205) ^ [_940092] : [hBOOL(hAPP(hAPP(c_member(_939968), _940092), _939970)), 9395 ^ _780205 : [(9396 ^ _780205) ^ [_940182] : [hBOOL(hAPP(hAPP(c_member(_939968), _940182), _939972)), _940092 = _940182]]]]], (9414 ^ _780205) ^ [_940443, _940445, _940447, _940449] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940443, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_940443), _940445), _940447)), hAPP(hAPP(c_Set_Oinsert(_940443), _940445), _940449)) = hAPP(hAPP(c_Set_Oinsert(_940443), _940445), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940443, tc_HOL_Obool)), _940447), _940449)))], (9416 ^ _780205) ^ [_940530, _940532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940530, tc_HOL_Obool)), _940532), c_Orderings_Obot__class_Obot(tc_fun(_940530, tc_HOL_Obool))))], (9418 ^ _780205) ^ [_940570, _940572, _940574] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940570, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940570, tc_HOL_Obool)), _940572), _940574)), _940572)))], (9420 ^ _780205) ^ [_940618, _940620, _940622] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940618, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940618, tc_HOL_Obool)), _940620), _940622)), _940622)))], (9422 ^ _780205) ^ [_940666, _940668, _940670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940666, tc_HOL_Obool)), _940668), _940670)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940666, tc_HOL_Obool)), _940668), _940670) = _940668)], (9428 ^ _780205) ^ [_940787, _940789, _940791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940787, tc_HOL_Obool)), _940789), _940791)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940787, tc_HOL_Obool)), _940791), _940789) = _940789)], (9434 ^ _780205) ^ [_940908, _940910, _940912, _940914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940908, tc_HOL_Obool)), _940910), _940912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940908, tc_HOL_Obool)), _940910), _940914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940908, tc_HOL_Obool)), _940910), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940908, tc_HOL_Obool)), _940912), _940914))))], (9444 ^ _780205) ^ [_941127, _941129, _941131, _941133, _941135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941127, tc_HOL_Obool)), _941129), _941131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941127, tc_HOL_Obool)), _941133), _941135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941127, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941127, tc_HOL_Obool)), _941129), _941133)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941127, tc_HOL_Obool)), _941131), _941135))))], (9454 ^ _780205) ^ [_941372, _941374, _941376, _941378, _941380] : [class_Groups_Oordered__ab__group__add(_941372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_941372), _941374), _941376) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_941372), _941378), _941380), 9461 ^ _780205 : [(9462 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941372), _941374), _941376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941372), _941378), _941380)))], (9468 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941372), _941378), _941380)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941372), _941374), _941376)))]]], (9474 ^ _780205) ^ [_941727, _941729, _941731, _941733] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941727, tc_HOL_Obool)), _941729), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941727, tc_HOL_Obool)), _941731), _941733)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941727, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941727, tc_HOL_Obool)), _941729), _941731)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941727, tc_HOL_Obool)), _941729), _941733)))], (9476 ^ _780205) ^ [_941811, _941813, _941815, _941817] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941811, tc_HOL_Obool)), _941813), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941811, tc_HOL_Obool)), _941815), _941817)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941811, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941811, tc_HOL_Obool)), _941813), _941815)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941811, tc_HOL_Obool)), _941813), _941817)))], (9478 ^ _780205) ^ [_941895, _941897, _941899, _941901] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941895, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941895, tc_HOL_Obool)), _941897), _941899)), _941901) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941895, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941895, tc_HOL_Obool)), _941897), _941901)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941895, tc_HOL_Obool)), _941899), _941901)))], (9480 ^ _780205) ^ [_941979, _941981, _941983, _941985] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941979, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941979, tc_HOL_Obool)), _941981), _941983)), _941985) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941979, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941979, tc_HOL_Obool)), _941981), _941985)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941979, tc_HOL_Obool)), _941983), _941985)))], (9482 ^ _780205) ^ [_942063, _942065, _942067, _942069] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942063, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942063, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942063, tc_HOL_Obool)), _942065), _942067)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942063, tc_HOL_Obool)), _942067), _942069))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942063, tc_HOL_Obool)), _942069), _942065)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942063, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942063, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942063, tc_HOL_Obool)), _942065), _942067)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942063, tc_HOL_Obool)), _942067), _942069))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942063, tc_HOL_Obool)), _942069), _942065)))], (9484 ^ _780205) ^ [_942202, _942204, _942206, _942208] : [class_Lattices_Osemilattice__sup(_942202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942202), _942204), _942206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942202), _942204), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_942202), _942208), _942206))))], (9494 ^ _780205) ^ [_942381, _942383, _942385, _942387] : [class_Lattices_Osemilattice__sup(_942381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942381), _942383), _942385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942381), _942383), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_942381), _942385), _942387))))], (9504 ^ _780205) ^ [_942578, _942580, _942582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942578, tc_HOL_Obool)), _942580), _942582)), 9507 ^ _780205 : [(9508 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942578, tc_HOL_Obool)), _942580), _942582)))], (9510 ^ _780205) ^ [] : [_942580 = _942582]]], (9512 ^ _780205) ^ [_942727, _942729, _942731] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942727, tc_HOL_Obool)), _942729), _942731))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942727, tc_HOL_Obool)), _942729), _942731)), -(_942729 = _942731)], (9532 ^ _780205) ^ [_943051, _943053, _943055] : [9533 ^ _780205 : [(9534 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943051, tc_HOL_Obool)), _943053), _943055))], (9536 ^ _780205) ^ [] : [_943053 = _943055]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943051, tc_HOL_Obool)), _943053), _943055)))], (9522 ^ _780205) ^ [_942923, _942925, _942927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942923, tc_HOL_Obool)), _942925), _942927)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942923, tc_HOL_Obool)), _942925), _942927))), -(_942925 = _942927)], (9540 ^ _780205) ^ [_943210, _943212, _943214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943210, tc_HOL_Obool)), _943212), _943214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943210, tc_HOL_Obool)), _943212), _943214)))], (9546 ^ _780205) ^ [_943329, _943331, _943333, _943335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943329, tc_HOL_Obool)), _943331), _943333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943329, tc_HOL_Obool)), _943333), _943335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943329, tc_HOL_Obool)), _943331), _943335)))], (9556 ^ _780205) ^ [_943526, _943528, _943530, _943532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943526, tc_HOL_Obool)), _943528), _943530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943526, tc_HOL_Obool)), _943530), _943532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943526, tc_HOL_Obool)), _943528), _943532)))], (9566 ^ _780205) ^ [_943723, _943725, _943727, _943729] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943723, tc_HOL_Obool)), _943725), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943723, tc_HOL_Obool)), _943727), _943729)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943723, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943723, tc_HOL_Obool)), _943725), _943727)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943723, tc_HOL_Obool)), _943725), _943729)))], (9568 ^ _780205) ^ [_943807, _943809, _943811, _943813] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943807, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943807, tc_HOL_Obool)), _943809), _943811)), _943813) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943807, tc_HOL_Obool)), _943809), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943807, tc_HOL_Obool)), _943811), _943813)))], (9570 ^ _780205) ^ [_943880, _943882, _943884, _943886] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943880, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943880, tc_HOL_Obool)), _943882), _943884)), _943886) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943880, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943880, tc_HOL_Obool)), _943882), _943886)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943880, tc_HOL_Obool)), _943884), _943886)))], (9572 ^ _780205) ^ [_943964, _943966, _943968, _943970] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943964, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943964, tc_HOL_Obool)), _943966), _943968)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943964, tc_HOL_Obool)), _943970), _943968)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943964, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943964, tc_HOL_Obool)), _943966), _943968)), _943970))], (9574 ^ _780205) ^ [_944048, _944050, _944052, _944054, _944056] : [-(hAPP(c_Set_Ovimage(_944048, _944050, _944052), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944050, tc_HOL_Obool)), _944054), _944056)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944048, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_944048, _944050, _944052), _944054)), hAPP(c_Set_Ovimage(_944048, _944050, _944052), _944056)))], (9576 ^ _780205) ^ [_944122, _944124, _944126, _944128] : [class_Lattices_Olattice(_944122), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944122), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944122), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944122), _944124), _944126)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944122), _944124), _944128))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944122), _944124), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944122), _944126), _944128)))))], (9582 ^ _780205) ^ [_944295, _944297, _944299, _944301] : [class_Lattices_Olattice(_944295), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944295), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944295), _944297), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944295), _944299), _944301))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944295), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944295), _944297), _944299)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944295), _944297), _944301)))))], (9588 ^ _780205) ^ [_944468, _944470, _944472, _944474] : [hBOOL(hAPP(hAPP(c_member(_944468), _944470), _944472)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944468, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_944468), _944470), _944474)), _944472) = hAPP(hAPP(c_Set_Oinsert(_944468), _944470), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944468, tc_HOL_Obool)), _944474), _944472)))], (9594 ^ _780205) ^ [_944639, _944641, _944643, _944645] : [hBOOL(hAPP(hAPP(c_member(_944639), _944641), _944643)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944639, tc_HOL_Obool)), _944643), hAPP(hAPP(c_Set_Oinsert(_944639), _944641), _944645)) = hAPP(hAPP(c_Set_Oinsert(_944639), _944641), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944639, tc_HOL_Obool)), _944643), _944645)))], (9600 ^ _780205) ^ [_944806, _944808, _944810, _944812] : [-(hBOOL(hAPP(hAPP(c_member(_944806), _944808), _944810))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944806, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_944806), _944808), _944812)), _944810) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944806, tc_HOL_Obool)), _944812), _944810))], (9606 ^ _780205) ^ [_944879, _944881, _944883, _944885] : [-(hBOOL(hAPP(hAPP(c_member(_944879), _944881), _944883))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944879, tc_HOL_Obool)), _944883), hAPP(hAPP(c_Set_Oinsert(_944879), _944881), _944885)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944879, tc_HOL_Obool)), _944883), _944885))], (9612 ^ _780205) ^ [_944971, _944973, _944975, _944977] : [hBOOL(hAPP(hAPP(c_member(_944971), _944973), _944975)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944971, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_944971), _944973), _944977)), _944975) = hAPP(hAPP(c_Set_Oinsert(_944971), _944973), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944971, tc_HOL_Obool)), _944977), _944975)))], (9618 ^ _780205) ^ [_945136, _945138, _945140, _945142] : [-(hBOOL(hAPP(hAPP(c_member(_945136), _945138), _945140))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945136, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_945136), _945138), _945142)), _945140) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945136, tc_HOL_Obool)), _945142), _945140))], (9624 ^ _780205) ^ [_945230, _945232, _945234, _945236] : [hBOOL(hAPP(hAPP(c_member(_945230), _945232), _945234)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945230, tc_HOL_Obool)), _945234), hAPP(hAPP(c_Set_Oinsert(_945230), _945232), _945236)) = hAPP(hAPP(c_Set_Oinsert(_945230), _945232), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945230, tc_HOL_Obool)), _945234), _945236)))], (9630 ^ _780205) ^ [_945395, _945397, _945399, _945401] : [-(hBOOL(hAPP(hAPP(c_member(_945395), _945397), _945399))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945395, tc_HOL_Obool)), _945399), hAPP(hAPP(c_Set_Oinsert(_945395), _945397), _945401)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945395, tc_HOL_Obool)), _945399), _945401))], (9636 ^ _780205) ^ [_945474, _945476, _945478] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945474, tc_HOL_Obool)), _945476), _945478) = c_Orderings_Obot__class_Obot(tc_fun(_945474, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_945474, tc_HOL_Obool)), _945476), _945478) = _945476)], (9642 ^ _780205) ^ [_945607, _945609, _945611] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945607, tc_HOL_Obool)), _945609), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_945607, tc_HOL_Obool)), _945611), _945609)) = c_Orderings_Obot__class_Obot(tc_fun(_945607, tc_HOL_Obool)))], (9644 ^ _780205) ^ [_945682, _945684, _945686, _945688] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945682, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945682, tc_HOL_Obool)), _945684), _945686)), _945688) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945682, tc_HOL_Obool)), _945684), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945682, tc_HOL_Obool)), _945686), _945688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945682, tc_HOL_Obool)), _945688), _945684)))], (9650 ^ _780205) ^ [_945867, _945869, _945871, _945873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945867, tc_HOL_Obool)), _945873), _945869)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945867, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945867, tc_HOL_Obool)), _945869), _945871)), _945873) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945867, tc_HOL_Obool)), _945869), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945867, tc_HOL_Obool)), _945871), _945873)))], (9656 ^ _780205) ^ [_946058, _946060, _946062, _946064] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946058, tc_HOL_Obool)), _946060), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946058, tc_HOL_Obool)), _946062), _946064)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946058, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946058, tc_HOL_Obool)), _946060), _946062)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946058, tc_HOL_Obool)), _946060), _946064)))], (9658 ^ _780205) ^ [_946142, _946144, _946146, _946148] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946142, tc_HOL_Obool)), _946144), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946142, tc_HOL_Obool)), _946146), _946148)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946142, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946142, tc_HOL_Obool)), _946144), _946146)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946142, tc_HOL_Obool)), _946144), _946148)))], (9660 ^ _780205) ^ [_946226, _946228, _946230] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946226, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946226, tc_HOL_Obool)), _946228), _946230)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946226, tc_HOL_Obool)), _946228), _946230)) = _946228)], (9662 ^ _780205) ^ [_946286, _946288, _946290, _946292] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_946286), _946288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_946286, tc_HOL_Obool)), _946288), _946290)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_946286, tc_Nat_Onat), _946292), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946286, tc_HOL_Obool)), _946290), _946288)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_946286, tc_Nat_Onat), _946292), _946290)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_946286, tc_Nat_Onat), _946292), _946288)))], (9672 ^ _780205) ^ [_946539, _946541, _946543] : [class_Lattices_Olattice(_946539), hBOOL(hAPP(c_Finite__Set_Ofinite(_946539), _946541)), hBOOL(hAPP(hAPP(c_member(_946539), _946543), _946541)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946539), _946543), c_Big__Operators_Olattice__class_OSup__fin(_946539, _946541)) = _946543)], (9686 ^ _780205) ^ [_946768, _946770, _946772, _946774, _946776] : [class_Groups_Oab__semigroup__mult(_946768), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_946768, _946768, c_Groups_Otimes__class_Otimes(_946768), _946770, _946772), _946774)), -(hBOOL(hAPP(hAPP(c_member(_946768), _946770), _946772))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_946768, _946768, c_Groups_Otimes__class_Otimes(_946768), _946776, hAPP(hAPP(c_Set_Oinsert(_946768), _946770), _946772)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946768), _946776), _946774))))], (9700 ^ _780205) ^ [_947008, _947010, _947012, _947014, _947016, _947018, _947020, _947022] : [c_Finite__Set_Ofolding__image__simple(_947008, _947010, _947012, _947014, _947016, _947018), hBOOL(hAPP(c_Finite__Set_Ofinite(_947010), _947020)), hBOOL(hAPP(c_Finite__Set_Ofinite(_947010), _947022)), -(hAPP(hAPP(_947012, hAPP(_947018, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_947010, tc_HOL_Obool)), _947020), _947022))), hAPP(_947018, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947010, tc_HOL_Obool)), _947020), _947022))) = hAPP(hAPP(_947012, hAPP(_947018, _947020)), hAPP(_947018, _947022)))], (9714 ^ _780205) ^ [_947356, _947358, _947360, _947362] : [hBOOL(hAPP(hAPP(c_member(_947356), _947358), _947360)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947356, tc_Nat_Onat), _947362), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947356, tc_HOL_Obool)), _947360), hAPP(hAPP(c_Set_Oinsert(_947356), _947358), c_Orderings_Obot__class_Obot(tc_fun(_947356, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947356, tc_Nat_Onat), _947362), _947360)), hAPP(_947362, _947358)))], (9720 ^ _780205) ^ [_947547, _947549, _947551, _947553] : [-(hBOOL(hAPP(hAPP(c_member(_947547), _947549), _947551))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947547, tc_Nat_Onat), _947553), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947547, tc_HOL_Obool)), _947551), hAPP(hAPP(c_Set_Oinsert(_947547), _947549), c_Orderings_Obot__class_Obot(tc_fun(_947547, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947547, tc_Nat_Onat), _947553), _947551))], (9726 ^ _780205) ^ [_947638, _947640, _947642, _947644, _947646] : [class_Groups_Oab__group__add(_947638), hBOOL(hAPP(c_Finite__Set_Ofinite(_947640), _947642)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947640, tc_HOL_Obool)), _947644), _947642)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947640, _947638), _947646), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947640, tc_HOL_Obool)), _947642), _947644)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947638), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947640, _947638), _947646), _947642)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947640, _947638), _947646), _947644)))], (9740 ^ _780205) ^ [_947955, _947957, _947959, _947961, _947963] : [c_Finite__Set_Ofolding__one(_947955, _947957, _947959), hBOOL(hAPP(c_Finite__Set_Ofinite(_947955), _947961)), hBOOL(hAPP(c_Finite__Set_Ofinite(_947955), _947963)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947955, tc_HOL_Obool)), _947961), _947963) = c_Orderings_Obot__class_Obot(tc_fun(_947955, tc_HOL_Obool))), -(hAPP(hAPP(_947957, hAPP(_947959, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_947955, tc_HOL_Obool)), _947961), _947963))), hAPP(_947959, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947955, tc_HOL_Obool)), _947961), _947963))) = hAPP(hAPP(_947957, hAPP(_947959, _947961)), hAPP(_947959, _947963)))], (9758 ^ _780205) ^ [_948311, _948313, _948315, _948317, _948319] : [c_Finite__Set_Ofolding__one(_948311, _948313, _948315), hBOOL(hAPP(c_Finite__Set_Ofinite(_948311), _948317)), -(_948317 = c_Orderings_Obot__class_Obot(tc_fun(_948311, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_948311), _948319)), -(_948319 = c_Orderings_Obot__class_Obot(tc_fun(_948311, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_948311, tc_HOL_Obool)), _948317), _948319) = c_Orderings_Obot__class_Obot(tc_fun(_948311, tc_HOL_Obool)), -(hAPP(_948315, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948311, tc_HOL_Obool)), _948317), _948319)) = hAPP(hAPP(_948313, hAPP(_948315, _948317)), hAPP(_948315, _948319)))], (9784 ^ _780205) ^ [_948812, _948814, _948816, _948818, _948820, _948822, _948824, _948826] : [c_Finite__Set_Ofolding__image__simple(_948812, _948814, _948816, _948818, _948820, _948822), hBOOL(hAPP(c_Finite__Set_Ofinite(_948814), _948824)), hBOOL(hAPP(c_Finite__Set_Ofinite(_948814), _948826)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_948814, tc_HOL_Obool)), _948824), _948826) = c_Orderings_Obot__class_Obot(tc_fun(_948814, tc_HOL_Obool)), -(hAPP(_948822, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948814, tc_HOL_Obool)), _948824), _948826)) = hAPP(hAPP(_948816, hAPP(_948822, _948824)), hAPP(_948822, _948826)))], (9802 ^ _780205) ^ [_949201, _949203, _949205, _949207, _949209, _949211, _949213, _949215] : [c_Finite__Set_Ofolding__image__simple__idem(_949201, _949203, _949205, _949207, _949209, _949211), hBOOL(hAPP(c_Finite__Set_Ofinite(_949203), _949213)), hBOOL(hAPP(hAPP(c_member(_949203), _949215), _949213)), -(hAPP(hAPP(_949205, hAPP(_949209, _949215)), hAPP(_949211, _949213)) = hAPP(_949211, _949213))], (9816 ^ _780205) ^ [_949478, _949480, _949482, _949484, _949486, _949488, _949490, _949492] : [c_Finite__Set_Ofolding__image__simple__idem(_949478, _949480, _949482, _949484, _949486, _949488), hBOOL(hAPP(c_Finite__Set_Ofinite(_949480), _949490)), -(hAPP(_949488, hAPP(hAPP(c_Set_Oinsert(_949480), _949492), _949490)) = hAPP(hAPP(_949482, hAPP(_949486, _949492)), hAPP(_949488, _949490)))], (9826 ^ _780205) ^ [_949693, _949695, _949697] : [class_Lattices_Olattice(_949693), hBOOL(hAPP(c_Finite__Set_Ofinite(_949693), _949695)), hBOOL(hAPP(hAPP(c_member(_949693), _949697), _949695)), 9837 ^ _780205 : [(9838 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949693, tc_HOL_Obool)), _949695), hAPP(hAPP(c_Set_Oinsert(_949693), _949697), c_Orderings_Obot__class_Obot(tc_fun(_949693, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_949693, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_949693, _949695) = _949697)], (9844 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949693, tc_HOL_Obool)), _949695), hAPP(hAPP(c_Set_Oinsert(_949693), _949697), c_Orderings_Obot__class_Obot(tc_fun(_949693, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_949693, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_949693, _949695) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949693), _949697), c_Big__Operators_Olattice__class_OInf__fin(_949693, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949693, tc_HOL_Obool)), _949695), hAPP(hAPP(c_Set_Oinsert(_949693), _949697), c_Orderings_Obot__class_Obot(tc_fun(_949693, tc_HOL_Obool)))))))]]], (9850 ^ _780205) ^ [_950199, _950201, _950203, _950205, _950207] : [class_Groups_Ocomm__monoid__add(_950199), class_Groups_Oordered__cancel__ab__semigroup__add(_950199), hBOOL(hAPP(c_Finite__Set_Ofinite(_950201), _950203)), -(_950203 = c_Orderings_Obot__class_Obot(tc_fun(_950201, tc_HOL_Obool))), 9868 ^ _780205 : [(9869 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_950201), 9867 ^ [_950199, _950201, _950203, _950205, _950207]), _950203)))], (9871 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950199), hAPP(_950205, 9867 ^ [_950199, _950201, _950203, _950205, _950207])), hAPP(_950207, 9867 ^ [_950199, _950201, _950203, _950205, _950207])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950199), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_950201, _950199), _950205), _950203)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_950201, _950199), _950207), _950203))))], (9875 ^ _780205) ^ [_950730, _950732, _950734, _950736, _950738] : [class_Groups_Ocomm__monoid__add(_950730), hBOOL(hAPP(c_Finite__Set_Ofinite(_950732), _950734)), hBOOL(hAPP(hAPP(c_member(_950732), _950736), _950734)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_950732, _950730), _950738), _950734) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950730), hAPP(_950738, _950736)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_950732, _950730), _950738), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950732, tc_HOL_Obool)), _950734), hAPP(hAPP(c_Set_Oinsert(_950732), _950736), c_Orderings_Obot__class_Obot(tc_fun(_950732, tc_HOL_Obool)))))))], (9889 ^ _780205) ^ [_951055, _951057, _951059, _951061, _951063] : [class_Groups_Ocomm__monoid__add(_951055), hBOOL(hAPP(c_Finite__Set_Ofinite(_951057), _951059)), hBOOL(hAPP(hAPP(c_member(_951057), _951061), _951059)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_951057, _951055), _951063), _951059) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951055), hAPP(_951063, _951061)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_951057, _951055), _951063), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_951057, tc_HOL_Obool)), _951059), hAPP(hAPP(c_Set_Oinsert(_951057), _951061), c_Orderings_Obot__class_Obot(tc_fun(_951057, tc_HOL_Obool)))))))], (9903 ^ _780205) ^ [_951380, _951382, _951384] : [class_Lattices_Olattice(_951380), hBOOL(hAPP(c_Finite__Set_Ofinite(_951380), _951382)), hBOOL(hAPP(c_Finite__Set_Ofinite(_951380), _951384)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_951380, tc_HOL_Obool)), _951382), _951384) = c_Orderings_Obot__class_Obot(tc_fun(_951380, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951380), c_Big__Operators_Olattice__class_OInf__fin(_951380, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951380, tc_HOL_Obool)), _951382), _951384))), c_Big__Operators_Olattice__class_OInf__fin(_951380, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_951380, tc_HOL_Obool)), _951382), _951384))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951380), c_Big__Operators_Olattice__class_OInf__fin(_951380, _951382)), c_Big__Operators_Olattice__class_OInf__fin(_951380, _951384)))], (9921 ^ _780205) ^ [_951728, _951730, _951732] : [class_Lattices_Olattice(_951728), hBOOL(hAPP(c_Finite__Set_Ofinite(_951728), _951730)), -(_951730 = c_Orderings_Obot__class_Obot(tc_fun(_951728, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_951728), _951732)), -(_951732 = c_Orderings_Obot__class_Obot(tc_fun(_951728, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_951728, tc_HOL_Obool)), _951730), _951732) = c_Orderings_Obot__class_Obot(tc_fun(_951728, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_951728, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951728, tc_HOL_Obool)), _951730), _951732)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951728), c_Big__Operators_Olattice__class_OInf__fin(_951728, _951730)), c_Big__Operators_Olattice__class_OInf__fin(_951728, _951732)))], (9947 ^ _780205) ^ [_952205, _952207, _952209] : [class_Lattices_Olattice(_952205), hBOOL(hAPP(c_Finite__Set_Ofinite(_952205), _952207)), 9954 ^ _780205 : [(9955 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952205, tc_HOL_Obool)), _952207), hAPP(hAPP(c_Set_Oinsert(_952205), _952209), c_Orderings_Obot__class_Obot(tc_fun(_952205, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_952205, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_952205, hAPP(hAPP(c_Set_Oinsert(_952205), _952209), _952207)) = _952209)], (9961 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952205, tc_HOL_Obool)), _952207), hAPP(hAPP(c_Set_Oinsert(_952205), _952209), c_Orderings_Obot__class_Obot(tc_fun(_952205, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_952205, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_952205, hAPP(hAPP(c_Set_Oinsert(_952205), _952209), _952207)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952205), _952209), c_Big__Operators_Olattice__class_OInf__fin(_952205, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952205, tc_HOL_Obool)), _952207), hAPP(hAPP(c_Set_Oinsert(_952205), _952209), c_Orderings_Obot__class_Obot(tc_fun(_952205, tc_HOL_Obool)))))))]]], (9967 ^ _780205) ^ [_952675, _952677, _952679] : [class_Lattices_Olattice(_952675), hBOOL(hAPP(c_Finite__Set_Ofinite(_952675), _952677)), -(hBOOL(hAPP(hAPP(c_member(_952675), _952679), _952677))), -(_952677 = c_Orderings_Obot__class_Obot(tc_fun(_952675, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_952675, hAPP(hAPP(c_Set_Oinsert(_952675), _952679), _952677)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952675), _952679), c_Big__Operators_Olattice__class_OInf__fin(_952675, _952677)))], (9985 ^ _780205) ^ [_952912, _952914, _952916] : [class_Groups_Oab__semigroup__mult(_952912), hBOOL(hAPP(c_Finite__Set_Ofinite(_952912), _952914)), -(_952914 = c_Orderings_Obot__class_Obot(tc_fun(_952912, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_952912), _952916)), -(_952916 = c_Orderings_Obot__class_Obot(tc_fun(_952912, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952912, tc_HOL_Obool)), _952914), _952916) = c_Orderings_Obot__class_Obot(tc_fun(_952912, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_952912, c_Groups_Otimes__class_Otimes(_952912)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952912, tc_HOL_Obool)), _952914), _952916)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952912), hAPP(c_Finite__Set_Ofold1(_952912, c_Groups_Otimes__class_Otimes(_952912)), _952914)), hAPP(c_Finite__Set_Ofold1(_952912, c_Groups_Otimes__class_Otimes(_952912)), _952916)))], (10011 ^ _780205) ^ [_953419, _953421, _953423, _953425, _953427, _953429, _953431, _953433] : [c_Finite__Set_Ofolding__image__simple(_953419, _953421, _953423, _953425, _953427, _953429), hBOOL(hAPP(c_Finite__Set_Ofinite(_953421), _953431)), hBOOL(hAPP(c_Finite__Set_Ofinite(_953421), _953433)), 10025 ^ _780205 : [(10026 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_953421), 10024 ^ [_953419, _953421, _953423, _953425, _953427, _953429, _953431, _953433]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953421, tc_HOL_Obool)), _953431), _953433))))], (10028 ^ _780205) ^ [] : [hAPP(_953427, 10024 ^ [_953419, _953421, _953423, _953425, _953427, _953429, _953431, _953433]) = _953425]], -(hAPP(_953429, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_953421, tc_HOL_Obool)), _953431), _953433)) = hAPP(hAPP(_953423, hAPP(_953429, _953431)), hAPP(_953429, _953433)))], (10032 ^ _780205) ^ [_953920, _953922, _953924] : [class_Groups_Oab__semigroup__mult(_953920), -(_953922 = c_Orderings_Obot__class_Obot(tc_fun(_953920, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_953920), _953922)), -(hBOOL(hAPP(hAPP(c_member(_953920), _953924), _953922))), -(hAPP(c_Finite__Set_Ofold1(_953920, c_Groups_Otimes__class_Otimes(_953920)), hAPP(hAPP(c_Set_Oinsert(_953920), _953924), _953922)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953920), _953924), hAPP(c_Finite__Set_Ofold1(_953920, c_Groups_Otimes__class_Otimes(_953920)), _953922)))], (10050 ^ _780205) ^ [_954219, _954221, _954223, _954225] : [class_Groups_Ocancel__semigroup__add(_954219), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954219), _954221), _954223) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954219), _954225), _954223), -(_954221 = _954225)], (10060 ^ _780205) ^ [_954386, _954388, _954390, _954392] : [class_Groups_Ocancel__ab__semigroup__add(_954386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954386), _954388), _954390) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954386), _954388), _954392), -(_954390 = _954392)], (10070 ^ _780205) ^ [_954553, _954555, _954557, _954559] : [class_Groups_Ocancel__semigroup__add(_954553), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954553), _954555), _954557) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954553), _954555), _954559), -(_954557 = _954559)], (10080 ^ _780205) ^ [_954720, _954722, _954724, _954726] : [class_Groups_Ocancel__semigroup__add(_954720), 10083 ^ _780205 : [(10084 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954720), _954722), _954724) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954720), _954726), _954724), -(_954722 = _954726)], (10090 ^ _780205) ^ [] : [_954722 = _954726, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954720), _954722), _954724) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954720), _954726), _954724))]]], (10096 ^ _780205) ^ [_954985, _954987, _954989, _954991] : [class_Groups_Ocancel__semigroup__add(_954985), 10099 ^ _780205 : [(10100 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954985), _954987), _954989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954985), _954987), _954991), -(_954989 = _954991)], (10106 ^ _780205) ^ [] : [_954989 = _954991, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954985), _954987), _954989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954985), _954987), _954991))]]], (10112 ^ _780205) ^ [_955250, _955252, _955254, _955256] : [class_Groups_Oab__semigroup__add(_955250), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955250), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955250), _955252), _955254)), _955256) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955250), _955252), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955250), _955254), _955256)))], (10118 ^ _780205) ^ [_955393, _955395, _955397, _955399] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_955393), 10121 ^ _780205 : [(10122 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955393), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955393), _955395), _955397)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955393), _955399), _955397))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955393), _955395), _955399)))], (10128 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955393), _955395), _955399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955393), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955393), _955395), _955397)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955393), _955399), _955397))))]]], (10134 ^ _780205) ^ [_955700, _955702, _955704, _955706] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_955700), 10137 ^ _780205 : [(10138 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955700), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955700), _955702), _955704)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955700), _955702), _955706))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955700), _955704), _955706)))], (10144 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955700), _955704), _955706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955700), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955700), _955702), _955704)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955700), _955702), _955706))))]]], (10150 ^ _780205) ^ [_956007, _956009, _956011, _956013] : [class_Groups_Oordered__ab__semigroup__add(_956007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956007), _956009), _956011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956007), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956007), _956009), _956013)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956007), _956011), _956013))))], (10160 ^ _780205) ^ [_956202, _956204, _956206, _956208] : [class_Groups_Oordered__ab__semigroup__add(_956202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956202), _956204), _956206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956202), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956202), _956208), _956204)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956202), _956208), _956206))))], (10170 ^ _780205) ^ [_956397, _956399, _956401, _956403, _956405] : [class_Groups_Oordered__ab__semigroup__add(_956397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956397), _956399), _956401)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956397), _956403), _956405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956397), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956397), _956399), _956403)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956397), _956401), _956405))))], (10184 ^ _780205) ^ [_956668, _956670, _956672, _956674] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_956668), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956668), _956670), _956672)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956668), _956674), _956672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956668), _956670), _956674)))], (10194 ^ _780205) ^ [_956863, _956865, _956867, _956869] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_956863), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956863), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956863), _956865), _956867)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956863), _956865), _956869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956863), _956867), _956869)))], (10204 ^ _780205) ^ [_957058, _957060, _957062, _957064] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_957058), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957058), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957058), _957060), _957062)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957058), _957060), _957064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957058), _957062), _957064)))], (10214 ^ _780205) ^ [_957253, _957255, _957257, _957259] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_957253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957253), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957253), _957255), _957257)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957253), _957259), _957257))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957253), _957255), _957259)))], (10224 ^ _780205) ^ [_957448, _957450, _957452, _957454, _957456] : [class_Groups_Oordered__cancel__ab__semigroup__add(_957448), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957448), _957450), _957452)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957448), _957454), _957456)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957448), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957448), _957450), _957454)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957448), _957452), _957456))))], (10238 ^ _780205) ^ [_957719, _957721, _957723, _957725] : [class_Groups_Oordered__cancel__ab__semigroup__add(_957719), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957719), _957721), _957723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957719), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957719), _957725), _957721)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957719), _957725), _957723))))], (10248 ^ _780205) ^ [_957914, _957916, _957918, _957920] : [class_Groups_Oordered__cancel__ab__semigroup__add(_957914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957914), _957916), _957918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957914), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957914), _957916), _957920)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957914), _957918), _957920))))], (10258 ^ _780205) ^ [_958109, _958111, _958113, _958115] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_958109), 10261 ^ _780205 : [(10262 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958109), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958109), _958111), _958113)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958109), _958111), _958115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958109), _958113), _958115)))], (10268 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958109), _958113), _958115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958109), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958109), _958111), _958113)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958109), _958111), _958115))))]]], (10274 ^ _780205) ^ [_958416, _958418, _958420, _958422] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_958416), 10277 ^ _780205 : [(10278 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958416), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958416), _958418), _958420)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958416), _958422), _958420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958416), _958418), _958422)))], (10284 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958416), _958418), _958422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958416), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958416), _958418), _958420)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958416), _958422), _958420))))]]], (10290 ^ _780205) ^ [_958723, _958725] : [class_Lattices_Olattice(_958723), hBOOL(hAPP(c_Finite__Set_Ofinite(_958723), _958725)), -(c_Big__Operators_Olattice__class_OInf__fin(_958723, _958725) = hAPP(c_Finite__Set_Ofold1(_958723, c_Lattices_Osemilattice__inf__class_Oinf(_958723)), _958725))], (10300 ^ _780205) ^ [_958880, _958882, _958884] : [class_Groups_Ogroup__add(_958880), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958880), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_958880), _958882), _958884)), _958884) = _958882)], (10306 ^ _780205) ^ [_958989, _958991, _958993] : [class_Groups_Ogroup__add(_958989), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_958989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958989), _958991), _958993)), _958993) = _958991)], (10312 ^ _780205) ^ [_959098, _959100, _959102, _959104, _959106] : [class_Groups_Oordered__cancel__ab__semigroup__add(_959098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959098), _959100), _959102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959098), _959104), _959106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959098), _959100), _959104)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959098), _959102), _959106))))], (10326 ^ _780205) ^ [_959369, _959371, _959373, _959375, _959377] : [class_Groups_Oordered__cancel__ab__semigroup__add(_959369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959369), _959371), _959373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959369), _959375), _959377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959369), _959371), _959375)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959369), _959373), _959377))))], (10340 ^ _780205) ^ [_959640, _959642, _959644, _959646] : [_959640 = c_Finite__Set_Ofold1(_959642, _959644), -(hAPP(_959640, hAPP(hAPP(c_Set_Oinsert(_959642), _959646), c_Orderings_Obot__class_Obot(tc_fun(_959642, tc_HOL_Obool)))) = _959646)], (10346 ^ _780205) ^ [_959759, _959761, _959763] : [-(hAPP(c_Finite__Set_Ofold1(_959759, _959761), hAPP(hAPP(c_Set_Oinsert(_959759), _959763), c_Orderings_Obot__class_Obot(tc_fun(_959759, tc_HOL_Obool)))) = _959763)], (10348 ^ _780205) ^ [_959805, _959807] : [class_Lattices_Olattice(_959805), -(c_Big__Operators_Olattice__class_OInf__fin(_959805, hAPP(hAPP(c_Set_Oinsert(_959805), _959807), c_Orderings_Obot__class_Obot(tc_fun(_959805, tc_HOL_Obool)))) = _959807)], (10354 ^ _780205) ^ [_959912, _959914, _959916, _959918] : [c_Finite__Set_Ofolding__one(_959912, _959914, _959916), hBOOL(hAPP(c_Finite__Set_Ofinite(_959912), _959918)), -(hAPP(_959916, _959918) = hAPP(c_Finite__Set_Ofold1(_959912, _959914), _959918))], (10364 ^ _780205) ^ [_960077, _960079, _960081, _960083] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_960077), _960079)), hBOOL(hAPP(c_Finite__Set_Ofinite(_960077), _960081)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_960077, tc_Nat_Onat), _960083), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960077, tc_HOL_Obool)), _960079), _960081)) = 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(_960077, tc_Nat_Onat), _960083), _960079)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_960077, tc_Nat_Onat), _960083), _960081))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_960077, tc_Nat_Onat), _960083), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960077, tc_HOL_Obool)), _960079), _960081))))], (10374 ^ _780205) ^ [_960370, _960372, _960374] : [class_Lattices_Olattice(_960370), hBOOL(hAPP(c_Finite__Set_Ofinite(_960370), _960372)), hBOOL(hAPP(hAPP(c_member(_960370), _960374), _960372)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_960370), _960374), c_Big__Operators_Olattice__class_OInf__fin(_960370, _960372)) = _960374)], (10388 ^ _780205) ^ [_960599, _960601, _960603] : [class_Lattices_Olattice(_960599), hBOOL(hAPP(c_Finite__Set_Ofinite(_960599), _960601)), hBOOL(hAPP(hAPP(c_member(_960599), _960603), _960601)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_960599), _960603), c_Big__Operators_Olattice__class_OInf__fin(_960599, _960601)) = c_Big__Operators_Olattice__class_OInf__fin(_960599, _960601))], (10402 ^ _780205) ^ [_960834, _960836] : [class_Lattices_Olattice(_960834), hBOOL(hAPP(c_Finite__Set_Ofinite(_960834), _960836)), -(c_Big__Operators_Olattice__class_OSup__fin(_960834, _960836) = hAPP(c_Finite__Set_Ofold1(_960834, c_Lattices_Osemilattice__sup__class_Osup(_960834)), _960836))], (10412 ^ _780205) ^ [_960991, _960993, _960995, _960997, _960999] : [class_Groups_Ocomm__monoid__add(_960991), hBOOL(hAPP(c_Finite__Set_Ofinite(_960993), _960995)), -(hBOOL(hAPP(hAPP(c_member(_960993), _960997), _960995))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_960993, _960991), _960999), hAPP(hAPP(c_Set_Oinsert(_960993), _960997), _960995)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960991), hAPP(_960999, _960997)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_960993, _960991), _960999), _960995)))], (10426 ^ _780205) ^ [_961241, _961243, _961245, _961247, _961249] : [class_Groups_Ocomm__monoid__add(_961241), hBOOL(hAPP(c_Finite__Set_Ofinite(_961243), _961245)), -(hBOOL(hAPP(hAPP(c_member(_961243), _961247), _961245))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_961243, _961241), _961249), hAPP(hAPP(c_Set_Oinsert(_961243), _961247), _961245)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961241), hAPP(_961249, _961247)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_961243, _961241), _961249), _961245)))], (10440 ^ _780205) ^ [_961491, _961493, _961495, _961497, _961499] : [class_Groups_Ocomm__monoid__add(_961491), hBOOL(hAPP(c_Finite__Set_Ofinite(_961493), _961495)), hBOOL(hAPP(c_Finite__Set_Ofinite(_961493), _961497)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961491), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_961493, _961491), _961499), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_961493, tc_HOL_Obool)), _961495), _961497))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_961493, _961491), _961499), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961493, tc_HOL_Obool)), _961495), _961497))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961491), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_961493, _961491), _961499), _961495)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_961493, _961491), _961499), _961497)))], (10454 ^ _780205) ^ [_961852, _961854, _961856] : [class_Lattices_Osemilattice__inf(_961852), hBOOL(hAPP(c_Finite__Set_Ofinite(_961852), _961854)), hBOOL(hAPP(hAPP(c_member(_961852), _961856), _961854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961852), hAPP(c_Finite__Set_Ofold1(_961852, c_Lattices_Osemilattice__inf__class_Oinf(_961852)), _961854)), _961856)))], (10468 ^ _780205) ^ [_962089, _962091, _962093] : [class_Lattices_Osemilattice__inf(_962089), hBOOL(hAPP(c_Finite__Set_Ofinite(_962089), _962091)), -(_962091 = c_Orderings_Obot__class_Obot(tc_fun(_962089, tc_HOL_Obool))), 10479 ^ _780205 : [(10490 ^ _780205) ^ [] : [10492 ^ _780205 : [(10493 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_962089), 10491 ^ [_962089, _962091, _962093]), _962091)))], (10495 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962089), _962093), 10491 ^ [_962089, _962091, _962093]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962089), _962093), hAPP(c_Finite__Set_Ofold1(_962089, c_Lattices_Osemilattice__inf__class_Oinf(_962089)), _962091))))], (10480 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962089), _962093), hAPP(c_Finite__Set_Ofold1(_962089, c_Lattices_Osemilattice__inf__class_Oinf(_962089)), _962091))), 10483 ^ _780205 : [(10484 ^ _780205) ^ [_962382] : [hBOOL(hAPP(hAPP(c_member(_962089), _962382), _962091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962089), _962093), _962382)))]]]]], (10499 ^ _780205) ^ [_962667, _962669, _962671] : [class_Lattices_Oab__semigroup__idem__mult(_962667), -(_962669 = c_Orderings_Obot__class_Obot(tc_fun(_962667, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_962667), _962669)), -(hAPP(c_Finite__Set_Ofold1(_962667, c_Groups_Otimes__class_Otimes(_962667)), hAPP(hAPP(c_Set_Oinsert(_962667), _962671), _962669)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962667), _962671), hAPP(c_Finite__Set_Ofold1(_962667, c_Groups_Otimes__class_Otimes(_962667)), _962669)))], (10513 ^ _780205) ^ [_962937, _962939, _962941] : [class_Lattices_Oab__semigroup__idem__mult(_962937), hBOOL(hAPP(c_Finite__Set_Ofinite(_962937), _962939)), -(_962939 = c_Orderings_Obot__class_Obot(tc_fun(_962937, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_962937), _962941)), -(_962941 = c_Orderings_Obot__class_Obot(tc_fun(_962937, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_962937, c_Groups_Otimes__class_Otimes(_962937)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962937, tc_HOL_Obool)), _962939), _962941)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962937), hAPP(c_Finite__Set_Ofold1(_962937, c_Groups_Otimes__class_Otimes(_962937)), _962939)), hAPP(c_Finite__Set_Ofold1(_962937, c_Groups_Otimes__class_Otimes(_962937)), _962941)))], (10535 ^ _780205) ^ [_963316, _963318, _963320] : [class_Lattices_Olattice(_963316), hBOOL(hAPP(c_Finite__Set_Ofinite(_963316), _963318)), -(_963318 = c_Orderings_Obot__class_Obot(tc_fun(_963316, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_963316, hAPP(hAPP(c_Set_Oinsert(_963316), _963320), _963318)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963316), _963320), c_Big__Operators_Olattice__class_OInf__fin(_963316, _963318)))], (10549 ^ _780205) ^ [_963524, _963526, _963528] : [class_Lattices_Olattice(_963524), hBOOL(hAPP(c_Finite__Set_Ofinite(_963524), _963526)), -(_963528 = c_Orderings_Obot__class_Obot(tc_fun(_963524, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963524, tc_HOL_Obool)), _963528), _963526)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963524), c_Big__Operators_Olattice__class_OInf__fin(_963524, _963528)), c_Big__Operators_Olattice__class_OInf__fin(_963524, _963526)) = c_Big__Operators_Olattice__class_OInf__fin(_963524, _963526))], (10567 ^ _780205) ^ [_963838, _963840, _963842] : [class_Lattices_Olattice(_963838), hBOOL(hAPP(c_Finite__Set_Ofinite(_963838), _963840)), -(_963840 = c_Orderings_Obot__class_Obot(tc_fun(_963838, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_963838), _963842)), -(_963842 = c_Orderings_Obot__class_Obot(tc_fun(_963838, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_963838, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963838, tc_HOL_Obool)), _963840), _963842)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_963838), c_Big__Operators_Olattice__class_OInf__fin(_963838, _963840)), c_Big__Operators_Olattice__class_OInf__fin(_963838, _963842)))], (10589 ^ _780205) ^ [_964187, _964189] : [class_Lattices_Olattice(_964187), hBOOL(hAPP(c_Finite__Set_Ofinite(_964187), _964189)), -(_964189 = c_Orderings_Obot__class_Obot(tc_fun(_964187, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964187), c_Big__Operators_Olattice__class_OInf__fin(_964187, _964189)), c_Big__Operators_Olattice__class_OSup__fin(_964187, _964189))))], (10603 ^ _780205) ^ [_964373, _964375, _964377, _964379, _964381] : [class_Groups_Ocomm__monoid__add(_964373), hBOOL(hAPP(c_Finite__Set_Ofinite(_964375), _964377)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964375, _964373), _964379), hAPP(hAPP(c_Set_Oinsert(_964375), _964381), _964377)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964373), hAPP(_964379, _964381)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964375, _964373), _964379), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964375, tc_HOL_Obool)), _964377), hAPP(hAPP(c_Set_Oinsert(_964375), _964381), c_Orderings_Obot__class_Obot(tc_fun(_964375, tc_HOL_Obool)))))))], (10613 ^ _780205) ^ [_964642, _964644, _964646, _964648, _964650] : [class_Groups_Ocomm__monoid__add(_964642), hBOOL(hAPP(c_Finite__Set_Ofinite(_964644), _964646)), hBOOL(hAPP(c_Finite__Set_Ofinite(_964644), _964648)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964644, tc_HOL_Obool)), _964646), _964648) = c_Orderings_Obot__class_Obot(tc_fun(_964644, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964644, _964642), _964650), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964644, tc_HOL_Obool)), _964646), _964648)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964642), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964644, _964642), _964650), _964646)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_964644, _964642), _964650), _964648)))], (10631 ^ _780205) ^ [_965037, _965039, _965041, _965043, _965045] : [class_Groups_Oab__group__add(_965037), hBOOL(hAPP(c_Finite__Set_Ofinite(_965039), _965041)), hBOOL(hAPP(c_Finite__Set_Ofinite(_965039), _965043)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_965039, _965037), _965045), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_965039, tc_HOL_Obool)), _965041), _965043)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_965037), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965037), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_965039, _965037), _965045), _965041)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_965039, _965037), _965045), _965043))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_965039, _965037), _965045), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965039, tc_HOL_Obool)), _965041), _965043))))], (10645 ^ _780205) ^ [_965398, _965400, _965402, _965404] : [c_Big__Operators_Osemilattice__big(_965398, _965400, _965402), hBOOL(hAPP(c_Finite__Set_Ofinite(_965398), _965404)), -(hAPP(_965402, _965404) = hAPP(c_Finite__Set_Ofold1(_965398, _965400), _965404))], (10655 ^ _780205) ^ [_965563, _965565, _965567, _965569, _965571, _965573] : [class_Rings_Oordered__ring(_965563), 10658 ^ _780205 : [(10659 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965563), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965563), _965565), _965567)), _965569)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965563), _965571), _965567)), _965573))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965563), _965569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965563), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_965563), _965571), _965565)), _965567)), _965573))))], (10665 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965563), _965569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965563), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_965563), _965571), _965565)), _965567)), _965573))), 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hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966002), _966004), _966010)), _966006)), _966008)), _966012)))], (10681 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966002), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966002), _966004), _966010)), _966006)), _966008)), _966012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966002), _966004), _966006)), _966008)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966002), _966010), _966006)), _966012))))]]], (10687 ^ _780205) ^ [_966441, _966443, _966445, _966447, _966449, _966451] : [class_Rings_Oordered__ring(_966441), 10690 ^ _780205 : [(10691 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966441), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966441), 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hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966441), _966449), _966445)), _966451))))]]], (10703 ^ _780205) ^ [_966880, _966882, _966884, _966886, _966888, _966890] : [class_Rings_Oordered__ring(_966880), 10706 ^ _780205 : [(10707 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966880), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966880), _966882), _966884)), _966886)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966880), _966888), _966884)), _966890))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966880), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966880), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966880), _966882), _966888)), _966884)), _966886)), _966890)))], (10713 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966880), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966880), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966880), _966882), _966888)), _966884)), _966886)), _966890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966880), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966880), _966882), _966884)), _966886)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966880), _966888), _966884)), _966890))))]]], (10719 ^ _780205) ^ [_967319, _967321, _967323, _967325, _967327, _967329] : [class_Rings_Oring(_967319), 10722 ^ _780205 : [(10723 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967319), _967321), _967323)), _967325) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967319), _967327), _967323)), _967329), -(_967325 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967319), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967319), _967327), _967321)), _967323)), _967329))], (10729 ^ _780205) ^ [] : [_967325 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967319), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967319), _967327), _967321)), _967323)), _967329), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967319), _967321), _967323)), _967325) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967319), _967327), _967323)), _967329))]]], (10735 ^ _780205) ^ [_967716, _967718, _967720, _967722, _967724, _967726] : [class_Rings_Oring(_967716), 10738 ^ _780205 : [(10739 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967716), _967718), _967720)), _967722) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967716), _967724), _967720)), _967726), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967716), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967716), _967718), _967724)), _967720)), _967722) = _967726)], (10745 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967716), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967716), _967718), _967724)), _967720)), _967722) = _967726, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967716), _967718), _967720)), _967722) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967716), _967724), _967720)), _967726))]]], (10751 ^ _780205) ^ [_968113, _968115] : [class_Lattices_Olattice(_968113), hBOOL(hAPP(c_Finite__Set_Ofinite(_968113), _968115)), -(_968115 = c_Orderings_Obot__class_Obot(tc_fun(_968113, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_968113), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_968113), 10764 ^ [_968113, _968115]), 10765 ^ [_968113, _968115])), hAPP(hAPP(c_Set_Oinsert(_968113), 10764 ^ [_968113, _968115]), hAPP(hAPP(c_Set_Oinsert(_968113), 10765 ^ [_968113, _968115]), c_Orderings_Obot__class_Obot(tc_fun(_968113, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_968113), c_Big__Operators_Olattice__class_OInf__fin(_968113, _968115)), _968115)))], (10771 ^ _780205) ^ [_968557, _968559] : [class_Groups_Oab__semigroup__mult(_968557), hBOOL(hAPP(c_Finite__Set_Ofinite(_968557), _968559)), -(_968559 = c_Orderings_Obot__class_Obot(tc_fun(_968557, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_968557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968557), 10784 ^ [_968557, _968559]), 10785 ^ [_968557, _968559])), hAPP(hAPP(c_Set_Oinsert(_968557), 10784 ^ [_968557, _968559]), hAPP(hAPP(c_Set_Oinsert(_968557), 10785 ^ [_968557, _968559]), c_Orderings_Obot__class_Obot(tc_fun(_968557, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_968557), hAPP(c_Finite__Set_Ofold1(_968557, c_Groups_Otimes__class_Otimes(_968557)), _968559)), _968559)))], (10791 ^ _780205) ^ [_969011, _969013, _969015, _969017] : [class_Rings_Ocomm__semiring__1(_969011), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969011), _969013), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969011), _969015), _969017)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969011), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969011), _969013), _969015)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969011), _969013), _969017)))], (10797 ^ _780205) ^ [_969170, _969172, _969174] : [class_Rings_Olinordered__idom(_969170), -(_969172 = _969174), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969170), _969172), _969174))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969170), _969174), _969172)))], (10811 ^ _780205) ^ [_969305, _969307, _969309, _969311, _969313] : [class_Rings_Ocomm__semiring__1(_969305), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969305), _969307), _969309)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969305), _969311), _969313)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969305), _969307), _969311)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969305), _969309), _969313)))], (10817 ^ _780205) ^ [_969482, _969484, _969486, _969488] : [class_Rings_Ocomm__semiring__1(_969482), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969482), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969482), _969484), _969486)), _969488) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969482), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969482), _969484), _969488)), _969486))], (10823 ^ _780205) ^ [_969625, _969627, _969629, _969631] : [class_Rings_Ocomm__semiring__1(_969625), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969625), _969627), _969629)), _969631) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969625), _969627), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969625), _969629), _969631)))], (10829 ^ _780205) ^ [_969768, _969770, _969772, _969774] : [class_Rings_Ocomm__semiring__1(_969768), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969768), _969770), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969768), _969772), _969774)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969768), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969768), _969770), _969772)), _969774))], (10835 ^ _780205) ^ [_969911, _969913, _969915, _969917] : [class_Rings_Ocomm__semiring__1(_969911), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969911), _969913), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969911), _969915), _969917)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969911), _969915), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969911), _969913), _969917)))], (10841 ^ _780205) ^ [_970054, _970056, _970058] : [class_Rings_Ocomm__semiring__1(_970054), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970054), _970056), 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970340), _970342), _970344)), _970348)))], (10859 ^ _780205) ^ [_970517, _970519, _970521, _970523, _970525] : [class_Rings_Ocomm__semiring__1(_970517), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970517), _970519), _970521)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970517), _970523), _970525)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970517), _970519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970517), _970521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970517), _970523), _970525))))], (10865 ^ _780205) ^ [_970694, _970696, _970698, _970700] : [class_Rings_Ocomm__semiring__1(_970694), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970694), _970696), _970698)), _970700) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970694), _970696), _970700)), _970698))], (10871 ^ _780205) ^ [_970837, _970839, _970841, _970843] : [class_Rings_Ocomm__semiring__1(_970837), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970837), _970839), _970841)), _970843) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970837), _970839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970837), _970841), _970843)))], (10877 ^ _780205) ^ [_970980, _970982, _970984, _970986] : [class_Rings_Ocomm__semiring__1(_970980), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970980), _970982), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970980), _970984), _970986)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970980), _970982), _970984)), _970986))], (10883 ^ _780205) ^ [_971123, _971125, _971127, _971129] : [class_Rings_Ocomm__semiring__1(_971123), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971123), _971125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971123), _971127), _971129)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971123), _971127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971123), _971125), _971129)))], (10889 ^ _780205) ^ [_971266, _971268, _971270] : [class_Rings_Ocomm__semiring__1(_971266), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971266), _971268), _971270) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971266), _971270), _971268))], (10895 ^ _780205) ^ [_971375, _971377, _971379, _971381, _971383] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_971375), 10898 ^ _780205 : [(10909 ^ _780205) ^ [] : [10910 ^ _780205 : [(10911 ^ _780205) ^ [] : [_971377 = _971381], (10913 ^ _780205) ^ [] : [_971379 = _971383]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971375), _971377), _971379)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971375), _971381), _971383)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971375), _971377), _971383)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971375), _971381), _971379)))], (10899 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971375), _971377), _971379)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971375), _971381), _971383)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971375), _971377), _971383)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971375), _971381), _971379)), -(_971377 = _971381), -(_971379 = _971383)]]], (10917 ^ _780205) ^ [_971787, _971789, _971791, _971793, _971795] : [class_Rings_Osemiring(_971787), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971787), _971789), _971791)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971787), _971793), _971791)), _971795)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971787), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971787), _971789), _971793)), _971791)), _971795))], (10923 ^ _780205) ^ [_971980, _971982, _971984, _971986] : [class_Rings_Ocomm__semiring__1(_971980), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971980), _971982), _971984)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971980), _971986), _971984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971980), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971980), _971982), _971986)), _971984))], (10929 ^ _780205) ^ [_972139, _972141, _972143, _972145] : [class_Rings_Ocomm__semiring__1(_972139), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972139), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972139), _972141), _972143)), _972145) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972139), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972139), _972141), _972145)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972139), _972143), _972145)))], (10935 ^ _780205) ^ [_972298, _972300, _972302, _972304] : [class_Rings_Ocomm__semiring(_972298), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972298), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972298), _972300), _972302)), _972304) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972298), _972300), _972304)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972298), _972302), _972304)))], (10941 ^ _780205) ^ [_972457, _972459, _972461, _972463, _972465] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_972457), 10944 ^ _780205 : [(10955 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972457), _972459), _972463)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972457), _972461), _972465)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972457), _972459), _972465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972457), _972461), _972463))), 10958 ^ _780205 : [(10959 ^ _780205) ^ [] : [_972459 = _972461], (10961 ^ _780205) ^ [] : [_972463 = _972465]]], (10945 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972457), _972459), _972463)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972457), _972461), _972465)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972457), _972459), _972465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972457), _972461), _972463)), -(_972459 = _972461), -(_972463 = _972465)]]], (10963 ^ _780205) ^ [_972875, _972877, _972879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _972875), _972877)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _972877), _972879)), _972875) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _972877), _972875)), _972879))], (10969 ^ _780205) ^ [_973012, _973014, _973016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973012), _973014)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _973014), _973012)), _973016) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973014), _973016)), _973012))], (10975 ^ _780205) ^ [_973149, _973151, _973153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973149), _973151)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973153), _973151)), _973149) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973153), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _973151), _973149)))], (10981 ^ _780205) ^ [_973286, _973288, _973290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973286), _973288)), 10984 ^ _780205 : [(10985 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _973288), _973286) = _973290, -(_973288 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973290), _973286))], (10991 ^ _780205) ^ [] : [_973288 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973290), _973286), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _973288), _973286) = _973290)]]], (10997 ^ _780205) ^ [_973545, _973547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973545), _973547)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _973547), _973545)), _973545) = _973547)], (11003 ^ _780205) ^ [_973656, _973658, _973660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973656), _973658)), 11006 ^ _780205 : [(11007 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973660), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _973658), _973656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973660), _973656)), _973658)))], (11013 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973660), _973656)), _973658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973660), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _973658), _973656))))]]], (11019 ^ _780205) ^ [_973945, _973947, _973949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _973945), _973947)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973949), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _973947), _973945)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _973949), _973947)), _973945))], (11025 ^ _780205) ^ [_974082, _974084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974082), _974084)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _974082), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _974084), _974082)) = _974084)], (11031 ^ _780205) ^ [_974193, _974195, _974197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974193), _974195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974197), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _974195), _974197)), _974193))))], (11037 ^ _780205) ^ [_974334, _974336, _974338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _974334), _974336)), _974338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974334), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _974338), _974336))))], (11043 ^ _780205) ^ [_974453, _974455, _974457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974453), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _974457), _974455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _974453), _974455)), _974457)))], (11049 ^ _780205) ^ [_974578] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974578), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974578), _974578))))], (11051 ^ _780205) ^ [_974612] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974612), _974612)))))], (11053 ^ _780205) ^ [_974652, _974654, _974656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974652), _974654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974652), _974656)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974654), _974656))))], (11059 ^ _780205) ^ [_974775, _974777, _974779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974775), _974777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974779), _974775)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974779), _974777))))], (11065 ^ _780205) ^ [_974898, _974900, _974902, _974904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974898), _974900)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974902), _974904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974898), _974902)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974900), _974904))))], (11075 ^ _780205) ^ [_975089, _975091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975089), _975091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975091), _975089)), -(_975089 = _975091)], (11085 ^ _780205) ^ [_975238, _975240, _975242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975238), _975240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975240), _975242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975238), _975242)))], (11095 ^ _780205) ^ [_975401, _975403] : [_975401 = _975403, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975401), _975403)))], (11101 ^ _780205) ^ [_975484, _975486] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975484), _975486))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975486), _975484)))], (11107 ^ _780205) ^ [_975530] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975530), _975530)))], (11109 ^ _780205) ^ [_975558, _975560] : [11110 ^ _780205 : [(11111 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _975558), _975560))], (11113 ^ _780205) ^ [] : [_975558 = _975560]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975558), _975560)))], (11117 ^ _780205) ^ [_975693, _975695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975693), _975695)), -(_975693 = _975695), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _975693), _975695)))], (11127 ^ _780205) ^ [_975805, _975807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _975805), _975807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975805), _975807)))], (11143 ^ _780205) ^ [_976023, _976025] : [11144 ^ _780205 : [(11145 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _976023), _976025))], (11147 ^ _780205) ^ [] : [_976023 = _976025]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _976023), _976025)))], (11133 ^ _780205) ^ [_975917, _975919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975917), _975919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _975917), _975919))), -(_975917 = _975919)], (11151 ^ _780205) ^ [_976175, _976177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _976175), _976177)), 11154 ^ _780205 : [(11155 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _976175), _976177)))], (11157 ^ _780205) ^ [] : [_976175 = _976177]]], (11159 ^ _780205) ^ [_976302, _976304] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _976302), _976304))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _976302), _976304)), -(_976302 = _976304)], (11169 ^ _780205) ^ [_976474, _976476, _976478] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976474), _976476) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976478), _976476), -(_976474 = _976478)], (11175 ^ _780205) ^ [_976573, _976575, _976577] : [_976573 = _976577, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976573), _976575) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976577), _976575))], (11181 ^ _780205) ^ [_976696, _976698, _976700] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976696), _976698) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976696), _976700), -(_976698 = _976700)], (11187 ^ _780205) ^ [_976795, _976797, _976799] : [_976797 = _976799, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976795), _976797) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976795), _976799))], (11193 ^ _780205) ^ [_976900, _976902, _976904] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976900), _976902)), _976904) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976902), _976904)))], (11195 ^ _780205) ^ [_976951, _976953, _976955] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976951), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976953), _976955)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976953), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _976951), _976955)))], (11197 ^ _780205) ^ [_977002, _977004] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977002), _977004) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977004), _977002))], (11199 ^ _780205) ^ [_977039, _977041] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977039), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977041), _977039))))], (11201 ^ _780205) ^ [_977075, _977077] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977075), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977075), _977077))))], (11203 ^ _780205) ^ [_977126, _977128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977126), _977128)), -(_977128 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977126), 11206 ^ [_977126, _977128]))], (11210 ^ _780205) ^ [_977233, _977235] : [11211 ^ _780205 : [(11212 ^ _780205) ^ [_977283] : [_977235 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977233), _977283)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977233), _977235)))], (11216 ^ _780205) ^ [_977365, _977367, _977369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977365), _977367)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977365), _977369))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977367), _977369)))], (11222 ^ _780205) ^ [_977484, _977486, _977488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977486), _977488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977484), _977486)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977484), _977488))))], (11228 ^ _780205) ^ [_977609, _977611, _977613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977609), _977611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977609), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977611), _977613))))], (11234 ^ _780205) ^ [_977720, _977722, _977724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977720), _977722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977720), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977724), _977722))))], (11240 ^ _780205) ^ [_977831, _977833, _977835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977831), _977833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977831), _977835)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977833), _977835))))], (11246 ^ _780205) ^ [_977954, _977956, _977958, _977960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977954), _977956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _977958), _977960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977954), _977958)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _977956), _977960))))], (11256 ^ _780205) ^ [_978145, _978147, _978149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978145), _978147)), _978149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _978147), _978149)))], (11262 ^ _780205) ^ [_978256, _978258, _978260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978256), _978258)), _978260)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _978256), _978260)))], (11268 ^ _780205) ^ [_978367, _978369, _978371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978367), _978369)), _978371)), 11271 ^ _780205 : [(11272 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _978367), _978371)))], (11274 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _978369), _978371)))]]], (11276 ^ _780205) ^ [_978530, _978532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978530), _978532)), _978530))], (11278 ^ _780205) ^ [_978578, _978580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978578), _978580)), _978580))], (11280 ^ _780205) ^ [_978614, _978616, _978618] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978614), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978616), _978618)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978614), _978616)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978614), _978618)))], (11282 ^ _780205) ^ [_978671, _978673, _978675] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978671), _978673)), _978675) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978671), _978675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978673), _978675)))], (11284 ^ _780205) ^ [_978746, _978748, _978750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978746), _978748)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978746), _978750))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _978748), _978750)))], (11290 ^ _780205) ^ [_978865, _978867, _978869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _978867), _978869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978865), _978867)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978865), _978869))))], (11296 ^ _780205) ^ [_978990, _978992, _978994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _978990), _978992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _978990), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978992), _978994))))], (11302 ^ _780205) ^ [_979101, _979103, _979105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979101), _979103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _979105), _979103))))], (11308 ^ _780205) ^ [_979212, _979214, _979216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979212), _979214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _979212), _979216)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _979214), _979216))))], (11314 ^ _780205) ^ [_979335, _979337, _979339, _979341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979335), _979337)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979339), _979341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _979335), _979339)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _979337), _979341))))], (11324 ^ _780205) ^ [_979526, _979528, _979530, _979532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979526), _979528)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _979530), _979528) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _979526), _979532), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979530), _979532)))], (11334 ^ _780205) ^ [_979707, _979709, _979711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _979707), _979709)), _979711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979707), _979711)))], (11340 ^ _780205) ^ [_979818, _979820, _979822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979818), _979820)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979818), _979822)), 11347 ^ _780205 : [(11348 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _979820), _979818)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _979822), _979818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979820), _979822)))], (11354 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979820), _979822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _979820), _979818)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _979822), _979818))))]]], (11360 ^ _780205) ^ [_980171, _980173, _980175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _980171), _980173)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _980175), _980171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980171), _980175)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980173), _980175))))], (11370 ^ _780205) ^ [_980358, _980360, _980362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _980358), _980360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _980358), _980362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980362), _980360)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980362), _980358))))], (11380 ^ _780205) ^ [_980545, _980547, _980549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _980545), _980547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980545), _980549)), _980547)))], (11386 ^ _780205) ^ [_980656, _980658, _980660] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980656), _980658)), _980660) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980656), _980660)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980658), _980660)))], (11388 ^ _780205) ^ [_980713, _980715, _980717] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980713), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980715), _980717)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980713), _980715)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _980713), _980717)))], (11390 ^ _780205) ^ [_980770, _980772, _980774] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980770), _980772)), _980774) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980770), _980774)), _980772))], (11392 ^ _780205) ^ [_980821, _980823] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980821), _980823)), _980821)))], (11394 ^ _780205) ^ [_980857, _980859, _980861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _980857), _980859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980861), _980859)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980861), _980857))))], (11400 ^ _780205) ^ [_980980, _980982, _980984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _980980), _980982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980980), _980984)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980982), _980984))))], (11406 ^ _780205) ^ [_981103, _981105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _981103), _981105)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981105), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981105), _981103)) = _981103)], (11412 ^ _780205) ^ [_981214, _981216, _981218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _981214), _981216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _981214), _981218)), 11419 ^ _780205 : [(11420 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981216), _981214) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981218), _981214), -(_981216 = _981218)], (11426 ^ _780205) ^ [] : [_981216 = _981218, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981216), _981214) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981218), _981214))]]], (11432 ^ _780205) ^ [_981537, _981539, _981541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _981537), _981539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _981537), _981541)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981539), _981537)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981541), _981537)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981539), _981541))], (11442 ^ _780205) ^ [_981738, _981740, _981742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _981738), _981740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _981738), _981742)), 11449 ^ _780205 : [(11450 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981740), _981738)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981742), _981738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _981740), _981742)))], (11456 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _981740), _981742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981740), _981738)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _981742), _981738))))]]], (11462 ^ _780205) ^ [_982087, _982089] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982087), _982089))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982089), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982087), _982089)) = _982087)], (11468 ^ _780205) ^ [_982158, _982160, _982162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982158), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982160), _982162))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982158), _982162)), _982160)))], (11474 ^ _780205) ^ [_982277, _982279, _982281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982277), _982281)), _982279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982277), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982279), _982281))))], (11480 ^ _780205) ^ [_982402, _982404] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982402), _982404)), _982404) = _982402)], (11482 ^ _780205) ^ [_982439, _982441] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982439), _982441)), _982439) = _982441)], (11484 ^ _780205) ^ [_982476, _982478, _982480] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982476), _982478)), _982480) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982478), _982480)))], (11486 ^ _780205) ^ [_982527, _982529, _982531] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982527), _982529)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982527), _982531)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982529), _982531))], (11488 ^ _780205) ^ [_982578, _982580, _982582] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982578), _982580)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982582), _982580)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982578), _982582))], (11490 ^ _780205) ^ [_982629, _982631, _982633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _982629), _982631)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982633), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982631), _982629)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _982633), _982629)), _982631))], (11496 ^ _780205) ^ [_982766, _982768, _982770, _982772, _982774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _982766), _982768)), 11499 ^ _780205 : [(11500 ^ _780205) ^ [] : [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), _982768), _982770)), _982772)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982766), _982770)), _982774))), -(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), _982768), _982766)), _982770)), _982772)), _982774)))], (11506 ^ _780205) ^ [] : [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), _982768), _982766)), _982770)), _982772)), _982774)), -(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), _982768), _982770)), _982772)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982766), _982770)), _982774))))]]], (11512 ^ _780205) ^ [_983157, _983159, _983161, _983163, _983165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983157), _983159)), 11515 ^ _780205 : [(11516 ^ _780205) ^ [] : [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), _983159), _983161)), _983163)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983157), _983161)), _983165))), -(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), _983159), _983157)), _983161)), _983163)), _983165)))], (11522 ^ _780205) ^ [] : [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), _983159), _983157)), _983161)), _983163)), _983165)), -(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), _983159), _983161)), _983163)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983157), _983161)), _983165))))]]], (11528 ^ _780205) ^ [_983548, _983550, _983552, _983554, _983556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983548), _983550)), -(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), _983550), _983552)), _983554)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983548), _983552)), _983556)) = 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), _983550), _983548)), _983552)), _983554)), _983556))], (11534 ^ _780205) ^ [_983749, _983751, _983753, _983755, _983757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983749), _983751)), 11537 ^ _780205 : [(11538 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983751), _983753)), _983755) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983749), _983753)), _983757), -(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), _983751), _983749)), _983753)), _983755) = _983757)], (11544 ^ _780205) ^ [] : [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), _983751), _983749)), _983753)), _983755) = _983757, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983751), _983753)), _983755) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _983749), _983753)), _983757))]]], (11550 ^ _780205) ^ [_984110, _984112, _984114, _984116, _984118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984110), _984112)), 11553 ^ _780205 : [(11554 ^ _780205) ^ [] : [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), _984110), _984114)), _984116)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984112), _984114)), _984118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984116), 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), _984112), _984110)), _984114)), _984118))))], (11560 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984116), 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), _984112), _984110)), _984114)), _984118))), -(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), _984110), _984114)), _984116)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984112), _984114)), _984118))))]]], (11566 ^ _780205) ^ [_984501, _984503, _984505, _984507, _984509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984501), _984503)), 11569 ^ _780205 : [(11570 ^ _780205) ^ [] : [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), _984501), _984505)), _984507)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984503), _984505)), _984509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984507), 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), _984503), _984501)), _984505)), _984509))))], (11576 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984507), 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), _984503), _984501)), _984505)), _984509))), -(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), _984501), _984505)), _984507)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984503), _984505)), _984509))))]]], (11582 ^ _780205) ^ [_984892, _984894, _984896, _984898, _984900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984892), _984894)), -(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), _984892), _984896)), _984898)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984894), _984896)), _984900)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984898), 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), _984894), _984892)), _984896)), _984900)))], (11588 ^ _780205) ^ [_985093, _985095, _985097, _985099, _985101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985093), _985095)), 11591 ^ _780205 : [(11592 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985093), _985097)), _985099) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985095), _985097)), _985101), -(_985099 = 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), _985095), _985093)), _985097)), _985101))], (11598 ^ _780205) ^ [] : [_985099 = 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), _985095), _985093)), _985097)), _985101), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985093), _985097)), _985099) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985095), _985097)), _985101))]]], (11604 ^ _780205) ^ [_985454, _985456, _985458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985454), _985456)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985454), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985456), _985458))))], (11610 ^ _780205) ^ [_985565, _985567, _985569] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985565), _985567)), _985569) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985567), _985569)))], (11612 ^ _780205) ^ [_985616, _985618] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985616), _985618) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985618), _985616))], (11614 ^ _780205) ^ [_985662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985662), _985662))], (11626 ^ _780205) ^ [_985748, _985750] : [11627 ^ _780205 : [(11628 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985748), _985750))], (11630 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985750), _985748))]], _985748 = _985750], (11616 ^ _780205) ^ [_985699, _985701] : [-(_985699 = _985701), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985699), _985701))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985701), _985699)))], (11634 ^ _780205) ^ [_985882, _985884] : [-(_985882 = _985884), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985882), _985884))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985884), _985882)))], (11644 ^ _780205) ^ [_985944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985944), _985944))], (11646 ^ _780205) ^ [_985972, _985974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _985972), _985974)), _985974 = _985972], (11652 ^ _780205) ^ [_986060, _986062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986060), _986062)), _986060 = _986062], (11658 ^ _780205) ^ [_986148, _986150, _986152] : [11659 ^ _780205 : [(11660 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986148), _986150)))], (11662 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_986152, _986150), _986148))]], 11665 ^ _780205 : [(11666 ^ _780205) ^ [] : [-(_986148 = _986150)], (11668 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_986152, _986150), _986148))]], 11671 ^ _780205 : [(11672 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986150), _986148)))], (11674 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_986152, _986150), _986148))]], -(hBOOL(hAPP(hAPP(_986152, _986150), _986148)))], (11678 ^ _780205) ^ [_986494, _986496, _986498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986494), _986496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986498), _986496))))], (11684 ^ _780205) ^ [_986605, _986607, _986609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986605), _986607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986605), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986607), _986609))))], (11690 ^ _780205) ^ [_986716, _986718, _986720, _986722] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986716), _986718)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986720), _986718)), _986722)) = 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), _986716), _986720)), _986718)), _986722))], (11692 ^ _780205) ^ [_986787, _986789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986787), _986789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986787), _986789)))], (11698 ^ _780205) ^ [_986884, _986886, _986888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986884), _986886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986884), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986888), _986886))))], (11704 ^ _780205) ^ [_986995, _986997, _986999] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_986995), _986997)), hBOOL(hAPP(hAPP(c_member(_986995), _986999), _986997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_986995), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_986995, tc_HOL_Obool)), _986997), hAPP(hAPP(c_Set_Oinsert(_986995), _986999), c_Orderings_Obot__class_Obot(tc_fun(_986995, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_986995), _986997))))], (11714 ^ _780205) ^ [_987228, _987230, _987232, _987234] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_987228), _987230)), hBOOL(hAPP(hAPP(c_member(_987228), _987232), _987230)), hBOOL(hAPP(hAPP(c_member(_987228), _987234), _987230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_987228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987228, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987228, tc_HOL_Obool)), _987230), hAPP(hAPP(c_Set_Oinsert(_987228), _987232), c_Orderings_Obot__class_Obot(tc_fun(_987228, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_987228), _987234), c_Orderings_Obot__class_Obot(tc_fun(_987228, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_987228), _987230))))], (11728 ^ _780205) ^ [_987583, _987585, _987587, _987589, _987591] : [class_Groups_Ocomm__monoid__mult(_987583), hBOOL(hAPP(c_Finite__Set_Ofinite(_987585), _987587)), hBOOL(hAPP(hAPP(c_member(_987585), _987589), _987587)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_987585, _987583), _987591), _987587) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987583), hAPP(_987591, _987589)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_987585, _987583), _987591), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987585, tc_HOL_Obool)), _987587), hAPP(hAPP(c_Set_Oinsert(_987585), _987589), c_Orderings_Obot__class_Obot(tc_fun(_987585, tc_HOL_Obool)))))))], (11742 ^ _780205) ^ [_987908, _987910, _987912] : [class_Lattices_Olattice(_987908), hBOOL(hAPP(c_Finite__Set_Ofinite(_987908), _987910)), -(hBOOL(hAPP(hAPP(c_member(_987908), _987912), _987910))), -(c_Big__Operators_Olattice__class_OInf__fin(_987908, hAPP(hAPP(c_Set_Oinsert(_987908), _987912), _987910)) = hAPP(hAPP(c_Finite__Set_Ofold(_987908, _987908, c_Lattices_Osemilattice__inf__class_Oinf(_987908)), _987912), _987910))], (11756 ^ _780205) ^ [_988122, _988124, _988126] : [class_Lattices_Olattice(_988122), hBOOL(hAPP(c_Finite__Set_Ofinite(_988122), _988124)), -(hBOOL(hAPP(hAPP(c_member(_988122), _988126), _988124))), -(c_Big__Operators_Olattice__class_OSup__fin(_988122, hAPP(hAPP(c_Set_Oinsert(_988122), _988126), _988124)) = hAPP(hAPP(c_Finite__Set_Ofold(_988122, _988122, c_Lattices_Osemilattice__sup__class_Osup(_988122)), _988126), _988124))], (11770 ^ _780205) ^ [_988336, _988338, _988340] : [class_Groups_Oab__semigroup__mult(_988336), hBOOL(hAPP(c_Finite__Set_Ofinite(_988336), _988338)), -(hBOOL(hAPP(hAPP(c_member(_988336), _988340), _988338))), -(hAPP(c_Finite__Set_Ofold1(_988336, c_Groups_Otimes__class_Otimes(_988336)), hAPP(hAPP(c_Set_Oinsert(_988336), _988340), _988338)) = hAPP(hAPP(c_Finite__Set_Ofold(_988336, _988336, c_Groups_Otimes__class_Otimes(_988336)), _988340), _988338))], (11784 ^ _780205) ^ [_988560, _988562, _988564] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_988560), _988562)), hBOOL(hAPP(_988564, c_Orderings_Obot__class_Obot(tc_fun(_988560, tc_HOL_Obool)))), 11795 ^ _780205 : [(11796 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_988560), 11794 ^ [_988560, _988562, _988564])))], (11798 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_988560), 11793 ^ [_988560, _988562, _988564]), 11794 ^ [_988560, _988562, _988564]))], (11800 ^ _780205) ^ [] : [-(hBOOL(hAPP(_988564, 11794 ^ [_988560, _988562, _988564])))], (11802 ^ _780205) ^ [] : [hBOOL(hAPP(_988564, hAPP(hAPP(c_Set_Oinsert(_988560), 11793 ^ [_988560, _988562, _988564]), 11794 ^ [_988560, _988562, _988564])))]], -(hBOOL(hAPP(_988564, _988562)))], (11806 ^ _780205) ^ [_989047, _989049, _989051, _989053, _989055, _989057, _989059] : [hBOOL(hAPP(hAPP(c_member(_989047), _989049), _989051)), c_Nitpick_Ofold__graph_H(_989047, _989053, _989055, _989057, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_989047, tc_HOL_Obool)), _989051), hAPP(hAPP(c_Set_Oinsert(_989047), _989049), c_Orderings_Obot__class_Obot(tc_fun(_989047, tc_HOL_Obool)))), _989059), -(c_Nitpick_Ofold__graph_H(_989047, _989053, _989055, _989057, _989051, hAPP(hAPP(_989055, _989049), _989059)))], (11816 ^ _780205) ^ [_989286, _989288, _989290] : [class_Orderings_Olinorder(_989286), -(_989288 = c_Orderings_Obot__class_Obot(tc_fun(_989286, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989286, tc_HOL_Obool)), _989288), _989290)), hBOOL(hAPP(c_Finite__Set_Ofinite(_989286), _989290)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989286), hAPP(c_Finite__Set_Ofold1(_989286, c_Orderings_Oord__class_Omin(_989286)), _989290)), hAPP(c_Finite__Set_Ofold1(_989286, c_Orderings_Oord__class_Omin(_989286)), _989288))))], (11834 ^ _780205) ^ [_989612, _989614] : [class_Orderings_Olinorder(_989612), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_989612), _989614), _989614) = _989614)], (11840 ^ _780205) ^ [_989703, _989705, _989707, _989709] : [class_Orderings_Olinorder(_989703), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_989703), hAPP(hAPP(c_Orderings_Oord__class_Omin(_989703), _989705), _989707)), _989709) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_989703), _989705), hAPP(hAPP(c_Orderings_Oord__class_Omin(_989703), _989707), _989709)))], (11846 ^ _780205) ^ [_989846, _989848, _989850, _989852] : [class_Orderings_Olinorder(_989846), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_989846), hAPP(hAPP(c_Orderings_Oord__class_Omin(_989846), _989848), _989850)), _989852) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_989846), _989848), hAPP(hAPP(c_Orderings_Oord__class_Omin(_989846), _989850), _989852)))], (11852 ^ _780205) ^ [_989989, _989991, _989993, _989995] : [class_Orderings_Olinorder(_989989), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_989989), _989991), hAPP(hAPP(c_Orderings_Oord__class_Omin(_989989), _989993), _989995)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_989989), _989993), hAPP(hAPP(c_Orderings_Oord__class_Omin(_989989), _989991), _989995)))], (11858 ^ _780205) ^ [_990132, _990134, _990136, _990138] : [class_Orderings_Olinorder(_990132), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_990132), _990134), hAPP(hAPP(c_Orderings_Oord__class_Omin(_990132), _990136), _990138)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_990132), _990136), hAPP(hAPP(c_Orderings_Oord__class_Omin(_990132), _990134), _990138)))], (11864 ^ _780205) ^ [_990275, _990277, _990279] : [class_Orderings_Olinorder(_990275), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_990275), _990277), hAPP(hAPP(c_Orderings_Oord__class_Omin(_990275), _990277), _990279)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_990275), _990277), _990279))], (11870 ^ _780205) ^ [_990400, _990402, _990404] : [class_Orderings_Olinorder(_990400), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_990400), _990402), hAPP(hAPP(c_Orderings_Oord__class_Omin(_990400), _990402), _990404)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_990400), _990402), _990404))], (11876 ^ _780205) ^ [_990525, _990527, _990529] : [class_Orderings_Olinorder(_990525), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_990525), _990527), _990529) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_990525), _990529), _990527))], (11882 ^ _780205) ^ [_990634, _990636, _990638] : [class_Orderings_Olinorder(_990634), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_990634), _990636), _990638) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_990634), _990638), _990636))], (11888 ^ _780205) ^ [_990743, _990745] : [class_Orderings_Olinorder(_990743), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_990743), _990745), _990745) = _990745)], (11894 ^ _780205) ^ [_990834, _990836, _990838, _990840] : [class_Orderings_Olinorder(_990834), hBOOL(hAPP(c_Finite__Set_Ofinite(_990834), _990836)), -(hAPP(hAPP(c_Finite__Set_Ofold(_990834, _990834, c_Orderings_Oord__class_Omin(_990834)), _990838), hAPP(hAPP(c_Set_Oinsert(_990834), _990840), _990836)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_990834), _990840), hAPP(hAPP(c_Finite__Set_Ofold(_990834, _990834, c_Orderings_Oord__class_Omin(_990834)), _990838), _990836)))], (11904 ^ _780205) ^ [_991057, _991059, _991061] : [class_Orderings_Olinorder(_991057), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991057), hAPP(hAPP(c_Orderings_Oord__class_Omin(_991057), _991059), _991061)), _991059)))], (11910 ^ _780205) ^ [_991164, _991166, _991168] : [class_Orderings_Olinorder(_991164), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991164), hAPP(hAPP(c_Orderings_Oord__class_Omin(_991164), _991166), _991168)), _991168)))], (11916 ^ _780205) ^ [_991271, _991273, _991275] : [class_Orderings_Olinorder(_991271), 11919 ^ _780205 : [(11920 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991271), _991273), _991275)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_991271), _991273), _991275) = _991273)], (11926 ^ _780205) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_991271), _991273), _991275) = _991273, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991271), _991273), _991275)))]]], (11932 ^ _780205) ^ [_991527, _991529, _991531, _991533] : [class_Orderings_Olinorder(_991527), 11935 ^ _780205 : [(11936 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991527), _991529), hAPP(hAPP(c_Orderings_Oord__class_Omin(_991527), _991531), _991533))), 11939 ^ _780205 : [(11940 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991527), _991529), _991531)))], (11942 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991527), _991529), _991533)))]]], (11944 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991527), _991529), hAPP(hAPP(c_Orderings_Oord__class_Omin(_991527), _991531), _991533)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991527), _991529), _991531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991527), _991529), _991533))]]], (11954 ^ _780205) ^ [_991907, _991909, _991911, _991913] : [class_Orderings_Olinorder(_991907), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991907), _991909), _991911)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991907), hAPP(hAPP(c_Orderings_Oord__class_Omin(_991907), _991909), _991913)), _991911)))], (11964 ^ _780205) ^ [_992086, _992088, _992090, _992092] : [class_Orderings_Olinorder(_992086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992086), _992088), _992090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992086), hAPP(hAPP(c_Orderings_Oord__class_Omin(_992086), _992092), _992088)), _992090)))], (11974 ^ _780205) ^ [_992265, _992267, _992269] : [class_Orderings_Olinorder(_992265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992265), _992267), _992269)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_992265), _992267), _992269) = _992267)], (11984 ^ _780205) ^ [_992426, _992428, _992430] : [class_Orderings_Olinorder(_992426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992426), _992428), _992430)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_992426), _992430), _992428) = _992428)], (11994 ^ _780205) ^ [_992587, _992589, _992591, _992593] : [class_Orderings_Olinorder(_992587), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992587), _992589), _992591)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992587), _992589), _992593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992587), _992589), hAPP(hAPP(c_Orderings_Oord__class_Omin(_992587), _992591), _992593))))], (12008 ^ _780205) ^ [_992836, _992838, _992840, _992842] : [class_Orderings_Olinorder(_992836), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992836), _992838), _992840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992836), _992838), _992842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992836), _992838), hAPP(hAPP(c_Orderings_Oord__class_Omin(_992836), _992840), _992842))))], (12022 ^ _780205) ^ [_993085, _993087, _993089, _993091, _993093] : [class_Orderings_Olinorder(_993085), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993085), _993087), _993089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993085), _993091), _993093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993085), hAPP(hAPP(c_Orderings_Oord__class_Omin(_993085), _993087), _993091)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_993085), _993089), _993093))))], (12036 ^ _780205) ^ [_993356, _993358, _993360, _993362] : [class_Orderings_Olinorder(_993356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993356), _993358), hAPP(hAPP(c_Orderings_Oord__class_Omin(_993356), _993360), _993362))), 12043 ^ _780205 : [(12044 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993356), _993358), _993360)))], (12046 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993356), _993358), _993362)))]]], (12048 ^ _780205) ^ [_993579, _993581, _993583, _993585] : [class_Orderings_Olinorder(_993579), 12051 ^ _780205 : [(12062 ^ _780205) ^ [] : [12063 ^ _780205 : [(12064 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993579), _993581), _993585))], (12066 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993579), _993583), _993585))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993579), hAPP(hAPP(c_Orderings_Oord__class_Omin(_993579), _993581), _993583)), _993585)))], (12052 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993579), hAPP(hAPP(c_Orderings_Oord__class_Omin(_993579), _993581), _993583)), _993585)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993579), _993581), _993585))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993579), _993583), _993585)))]]], (12070 ^ _780205) ^ [_993928, _993930, _993932, _993934] : [class_Orderings_Olinorder(_993928), 12073 ^ _780205 : [(12084 ^ _780205) ^ [] : [12085 ^ _780205 : [(12086 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993928), _993930), _993934))], (12088 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993928), _993932), _993934))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993928), hAPP(hAPP(c_Orderings_Oord__class_Omin(_993928), _993930), _993932)), _993934)))], (12074 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993928), hAPP(hAPP(c_Orderings_Oord__class_Omin(_993928), _993930), _993932)), _993934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993928), _993930), _993934))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993928), _993932), _993934)))]]], (12092 ^ _780205) ^ [_994277, _994279, _994281, _994283] : [class_Orderings_Olinorder(_994277), 12095 ^ _780205 : [(12096 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994277), _994279), hAPP(hAPP(c_Orderings_Oord__class_Omin(_994277), _994281), _994283))), 12099 ^ _780205 : [(12100 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994277), _994279), _994281)))], (12102 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994277), _994279), _994283)))]]], (12104 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994277), _994279), hAPP(hAPP(c_Orderings_Oord__class_Omin(_994277), _994281), _994283)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994277), _994279), _994281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994277), _994279), _994283))]]], (12114 ^ _780205) ^ [_994657, _994659, _994661, _994663] : [class_Orderings_Olinorder(_994657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994657), _994659), _994661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994657), hAPP(hAPP(c_Orderings_Oord__class_Omin(_994657), _994663), _994659)), _994661)))], (12124 ^ _780205) ^ [_994836, _994838, _994840, _994842] : [class_Orderings_Olinorder(_994836), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994836), _994838), _994840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994836), hAPP(hAPP(c_Orderings_Oord__class_Omin(_994836), _994838), _994842)), _994840)))], (12134 ^ _780205) ^ [_995015, _995017, _995019, _995021] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_995015), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995015), hAPP(hAPP(c_Orderings_Oord__class_Omin(_995015), _995017), _995019)), _995021) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_995015), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995015), _995017), _995021)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995015), _995019), _995021)))], (12140 ^ _780205) ^ [_995174, _995176, _995178, _995180] : [class_Groups_Oordered__ab__group__add(_995174), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_995174), hAPP(hAPP(c_Orderings_Oord__class_Omin(_995174), _995176), _995178)), _995180) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_995174), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_995174), _995176), _995180)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_995174), _995178), _995180)))], (12146 ^ _780205) ^ [_995333, _995335, _995337, _995339] : [-(c_Nitpick_Ofold__graph_H(_995333, _995335, _995337, _995339, c_Orderings_Obot__class_Obot(tc_fun(_995333, tc_HOL_Obool)), _995339))], (12148 ^ _780205) ^ [_995371, _995373, _995375, _995377] : [-(c_Nitpick_Ofold__graph_H(_995371, _995373, _995375, _995377, c_Orderings_Obot__class_Obot(tc_fun(_995371, tc_HOL_Obool)), _995377))], (12150 ^ _780205) ^ [_995409] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_995409) = c_Orderings_Oord__class_Omin(_995409)), class_Lattices_Osemilattice__inf(_995409), class_Orderings_Olinorder(_995409)], (12160 ^ _780205) ^ [_995538, _995540, _995542, _995544] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_995538, _995540, _995542), _995544), c_Orderings_Obot__class_Obot(tc_fun(_995538, tc_HOL_Obool))) = _995544)], (12162 ^ _780205) ^ [_995582, _995584, _995586] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _995582), _995584)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _995586), _995584)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _995582), _995586)), _995584))], (12164 ^ _780205) ^ [_995639, _995641, _995643, _995645] : [class_Orderings_Olinorder(_995639), hBOOL(hAPP(c_Finite__Set_Ofinite(_995639), _995641)), hBOOL(hAPP(hAPP(c_member(_995639), _995643), _995641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995639), hAPP(hAPP(c_Finite__Set_Ofold(_995639, _995639, c_Orderings_Oord__class_Omin(_995639)), _995645), _995641)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_995639), _995643), _995645))))], (12178 ^ _780205) ^ [_995906, _995908, _995910] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_995906), _995908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_995906), _995908)), hAPP(c_Finite__Set_Ocard(_995906), hAPP(hAPP(c_Set_Oinsert(_995906), _995910), _995908)))))], (12184 ^ _780205) ^ [_996039, _996041, _996043] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_996039), _996041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_996039, tc_HOL_Obool)), _996043), _996041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_996039), _996041)), hAPP(c_Finite__Set_Ocard(_996039), _996043))), -(_996043 = _996041)], (12198 ^ _780205) ^ [_996284, _996286, _996288] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_996284), _996286)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_996284, tc_HOL_Obool)), _996288), _996286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_996284), _996288)), hAPP(c_Finite__Set_Ocard(_996284), _996286))))], (12208 ^ _780205) ^ [_996475, _996477, _996479] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_996475), _996477)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_996475, tc_HOL_Obool)), _996477), _996479) = hAPP(hAPP(c_Finite__Set_Ofold(_996475, tc_fun(_996475, tc_HOL_Obool), c_Set_Oinsert(_996475)), _996479), _996477))], (12214 ^ _780205) ^ [_996614, _996616, _996618, _996620] : [class_Lattices_Osemilattice__sup(_996614), hBOOL(hAPP(c_Finite__Set_Ofinite(_996614), _996616)), -(hAPP(hAPP(c_Finite__Set_Ofold(_996614, _996614, c_Lattices_Osemilattice__sup__class_Osup(_996614)), _996618), hAPP(hAPP(c_Set_Oinsert(_996614), _996620), _996616)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_996614), _996620), hAPP(hAPP(c_Finite__Set_Ofold(_996614, _996614, c_Lattices_Osemilattice__sup__class_Osup(_996614)), _996618), _996616)))], (12224 ^ _780205) ^ [_996837, _996839, _996841, _996843] : [class_Lattices_Osemilattice__inf(_996837), hBOOL(hAPP(c_Finite__Set_Ofinite(_996837), _996839)), -(hAPP(hAPP(c_Finite__Set_Ofold(_996837, _996837, c_Lattices_Osemilattice__inf__class_Oinf(_996837)), _996841), hAPP(hAPP(c_Set_Oinsert(_996837), _996843), _996839)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_996837), _996843), hAPP(hAPP(c_Finite__Set_Ofold(_996837, _996837, c_Lattices_Osemilattice__inf__class_Oinf(_996837)), _996841), _996839)))], (12234 ^ _780205) ^ [_997060, _997062, _997064] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_997060), _997062)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_997060, tc_HOL_Obool)), _997064), _997062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_997060), _997064)), hAPP(c_Finite__Set_Ocard(_997060), _997062))))], (12244 ^ _780205) ^ [_997251, _997253, _997255, _997257, _997259] : [c_Finite__Set_Ofolding__one__idem(_997251, _997253, _997255), hBOOL(hAPP(c_Finite__Set_Ofinite(_997251), _997257)), -(hAPP(_997255, hAPP(hAPP(c_Set_Oinsert(_997251), _997259), _997257)) = hAPP(hAPP(c_Finite__Set_Ofold(_997251, _997251, _997253), _997259), _997257))], (12254 ^ _780205) ^ [_997444, _997446, _997448, _997450, _997452] : [class_Groups_Ocomm__monoid__mult(_997444), hBOOL(hAPP(c_Finite__Set_Ofinite(_997446), _997448)), -(hBOOL(hAPP(hAPP(c_member(_997446), _997450), _997448))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_997446, _997444), _997452), hAPP(hAPP(c_Set_Oinsert(_997446), _997450), _997448)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997444), hAPP(_997452, _997450)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_997446, _997444), _997452), _997448)))], (12268 ^ _780205) ^ [_997694, _997696, _997698, _997700, _997702] : [class_Groups_Ocomm__monoid__mult(_997694), hBOOL(hAPP(c_Finite__Set_Ofinite(_997696), _997698)), -(hBOOL(hAPP(hAPP(c_member(_997696), _997700), _997698))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_997696, _997694), _997702), hAPP(hAPP(c_Set_Oinsert(_997696), _997700), _997698)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997694), hAPP(_997702, _997700)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_997696, _997694), _997702), _997698)))], (12282 ^ _780205) ^ [_997944, _997946, _997948, _997950, _997952] : [class_Groups_Ocomm__monoid__mult(_997944), hBOOL(hAPP(c_Finite__Set_Ofinite(_997946), _997948)), hBOOL(hAPP(c_Finite__Set_Ofinite(_997946), _997950)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997944), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_997946, _997944), _997952), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_997946, tc_HOL_Obool)), _997948), _997950))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_997946, _997944), _997952), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_997946, tc_HOL_Obool)), _997948), _997950))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997944), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_997946, _997944), _997952), _997948)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_997946, _997944), _997952), _997950)))], (12296 ^ _780205) ^ [_998305, _998307, _998309, _998311, _998313] : [class_Groups_Ocomm__monoid__mult(_998305), hBOOL(hAPP(c_Finite__Set_Ofinite(_998307), _998309)), hBOOL(hAPP(c_Finite__Set_Ofinite(_998307), _998311)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998305), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_998307, _998305), _998313), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998307, tc_HOL_Obool)), _998309), _998311))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_998307, _998305), _998313), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998307, tc_HOL_Obool)), _998309), _998311))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998305), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_998307, _998305), _998313), _998309)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_998307, _998305), _998313), _998311)))], (12310 ^ _780205) ^ [_998666, _998668, _998670] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_998666), _998668)), hBOOL(hAPP(c_Finite__Set_Ofinite(_998666), _998670)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_998666), _998668)), hAPP(c_Finite__Set_Ocard(_998666), _998670)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_998666), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998666, tc_HOL_Obool)), _998668), _998670))), hAPP(c_Finite__Set_Ocard(_998666), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998666, tc_HOL_Obool)), _998668), _998670))))], (12320 ^ _780205) ^ [_998923, _998925, _998927] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_998923), _998925)), hBOOL(hAPP(c_Finite__Set_Ofinite(_998923), _998927)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_998923), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998923, tc_HOL_Obool)), _998925), _998927))), hAPP(c_Finite__Set_Ocard(_998923), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998923, tc_HOL_Obool)), _998925), _998927))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_998923), _998925)), hAPP(c_Finite__Set_Ocard(_998923), _998927)))], (12330 ^ _780205) ^ [_999180, _999182, _999184, _999186] : [class_Lattices_Osemilattice__sup(_999180), hBOOL(hAPP(c_Finite__Set_Ofinite(_999180), _999182)), hBOOL(hAPP(hAPP(c_member(_999180), _999184), _999182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999180), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_999180), _999184), _999186)), hAPP(hAPP(c_Finite__Set_Ofold(_999180, _999180, c_Lattices_Osemilattice__sup__class_Osup(_999180)), _999186), _999182))))], (12344 ^ _780205) ^ [_999447, _999449, _999451, _999453] : [class_Lattices_Osemilattice__inf(_999447), hBOOL(hAPP(c_Finite__Set_Ofinite(_999447), _999449)), hBOOL(hAPP(hAPP(c_member(_999447), _999451), _999449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999447), hAPP(hAPP(c_Finite__Set_Ofold(_999447, _999447, c_Lattices_Osemilattice__inf__class_Oinf(_999447)), _999453), _999449)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_999447), _999451), _999453))))], (12358 ^ _780205) ^ [_999714, _999716, _999718] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_999714), _999716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999714, tc_HOL_Obool)), _999716), _999718)), -(hAPP(c_Finite__Set_Ocard(_999714), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_999714, tc_HOL_Obool)), _999718), _999716)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_999714), _999718)), hAPP(c_Finite__Set_Ocard(_999714), _999716)))], (12368 ^ _780205) ^ [_999939, _999941, _999943] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_999939), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_999939, tc_HOL_Obool)), _999941), _999943))), -(hAPP(c_Finite__Set_Ocard(_999939), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_999939, tc_HOL_Obool)), _999941), _999943)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_999939), _999941)), hAPP(c_Finite__Set_Ocard(_999939), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_999939, tc_HOL_Obool)), _999941), _999943))))], (12374 ^ _780205) ^ [_1000134, _1000136, _1000138] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1000134), _1000136)), -(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(_1000134), _1000138)), hAPP(c_Finite__Set_Ocard(_1000134), _1000136))), hAPP(c_Finite__Set_Ocard(_1000134), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1000134, tc_HOL_Obool)), _1000138), _1000136)))))], (12380 ^ _780205) ^ [_1000295, _1000297, _1000299] : [class_Orderings_Olinorder(_1000295), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000295), _1000297)), hBOOL(hAPP(hAPP(c_member(_1000295), _1000299), _1000297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000295), hAPP(c_Finite__Set_Ofold1(_1000295, c_Orderings_Oord__class_Omin(_1000295)), _1000297)), _1000299)))], (12394 ^ _780205) ^ [_1000532, _1000534, _1000536] : [class_Orderings_Olinorder(_1000532), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000532), _1000534)), -(_1000534 = c_Orderings_Obot__class_Obot(tc_fun(_1000532, tc_HOL_Obool))), 12405 ^ _780205 : [(12406 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000532), hAPP(c_Finite__Set_Ofold1(_1000532, c_Orderings_Oord__class_Omin(_1000532)), _1000534)), _1000536)), 12410 ^ _780205 : [(12411 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1000532), 12409 ^ [_1000532, _1000534, _1000536]), _1000534)))], (12413 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000532), 12409 ^ [_1000532, _1000534, _1000536]), _1000536)))]]], (12415 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000532), hAPP(c_Finite__Set_Ofold1(_1000532, c_Orderings_Oord__class_Omin(_1000532)), _1000534)), _1000536))), 12416 ^ _780205 : [(12417 ^ _780205) ^ [_1000921] : [hBOOL(hAPP(hAPP(c_member(_1000532), _1000921), _1000534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000532), _1000921), _1000536))]]]]], (12425 ^ _780205) ^ [_1001082, _1001084, _1001086] : [class_Orderings_Olinorder(_1001082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001082), _1001084)), -(_1001084 = c_Orderings_Obot__class_Obot(tc_fun(_1001082, tc_HOL_Obool))), 12436 ^ _780205 : [(12447 ^ _780205) ^ [] : [12449 ^ _780205 : [(12450 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001082), 12448 ^ [_1001082, _1001084, _1001086]), _1001084)))], (12452 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001082), _1001086), 12448 ^ [_1001082, _1001084, _1001086]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001082), _1001086), hAPP(c_Finite__Set_Ofold1(_1001082, c_Orderings_Oord__class_Omin(_1001082)), _1001084))))], (12437 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001082), _1001086), hAPP(c_Finite__Set_Ofold1(_1001082, c_Orderings_Oord__class_Omin(_1001082)), _1001084))), 12440 ^ _780205 : [(12441 ^ _780205) ^ [_1001375] : [hBOOL(hAPP(hAPP(c_member(_1001082), _1001375), _1001084)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001082), _1001086), _1001375)))]]]]], (12456 ^ _780205) ^ [_1001660, _1001662, _1001664] : [class_Orderings_Olinorder(_1001660), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001660), _1001662)), -(_1001662 = c_Orderings_Obot__class_Obot(tc_fun(_1001660, tc_HOL_Obool))), 12467 ^ _780205 : [(12468 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001660), hAPP(c_Finite__Set_Ofold1(_1001660, c_Orderings_Oord__class_Omin(_1001660)), _1001662)), _1001664)), 12472 ^ _780205 : [(12473 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001660), 12471 ^ [_1001660, _1001662, _1001664]), _1001662)))], (12475 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001660), 12471 ^ [_1001660, _1001662, _1001664]), _1001664)))]]], (12477 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001660), hAPP(c_Finite__Set_Ofold1(_1001660, c_Orderings_Oord__class_Omin(_1001660)), _1001662)), _1001664))), 12478 ^ _780205 : [(12479 ^ _780205) ^ [_1002049] : [hBOOL(hAPP(hAPP(c_member(_1001660), _1002049), _1001662)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001660), _1002049), _1001664))]]]]], (12487 ^ _780205) ^ [_1002210, _1002212, _1002214] : [class_Orderings_Olinorder(_1002210), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002210), _1002212)), -(_1002212 = c_Orderings_Obot__class_Obot(tc_fun(_1002210, tc_HOL_Obool))), 12498 ^ _780205 : [(12509 ^ _780205) ^ [] : [12511 ^ _780205 : [(12512 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1002210), 12510 ^ [_1002210, _1002212, _1002214]), _1002212)))], (12514 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002210), _1002214), 12510 ^ [_1002210, _1002212, _1002214]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002210), _1002214), hAPP(c_Finite__Set_Ofold1(_1002210, c_Orderings_Oord__class_Omin(_1002210)), _1002212))))], (12499 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002210), _1002214), hAPP(c_Finite__Set_Ofold1(_1002210, c_Orderings_Oord__class_Omin(_1002210)), _1002212))), 12502 ^ _780205 : [(12503 ^ _780205) ^ [_1002503] : [hBOOL(hAPP(hAPP(c_member(_1002210), _1002503), _1002212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002210), _1002214), _1002503)))]]]]], (12518 ^ _780205) ^ [_1002788, _1002790, _1002792] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002788), _1002790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002788, tc_HOL_Obool)), _1002792), _1002790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1002788), _1002792)), hAPP(c_Finite__Set_Ocard(_1002788), _1002790))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1002788, tc_HOL_Obool)), _1002792), _1002790)))], (12532 ^ _780205) ^ [_1003053, _1003055, _1003057] : [class_Lattices_Oab__semigroup__idem__mult(_1003053), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003053), _1003055)), -(hAPP(c_Finite__Set_Ofold1(_1003053, c_Groups_Otimes__class_Otimes(_1003053)), hAPP(hAPP(c_Set_Oinsert(_1003053), _1003057), _1003055)) = hAPP(hAPP(c_Finite__Set_Ofold(_1003053, _1003053, c_Groups_Otimes__class_Otimes(_1003053)), _1003057), _1003055))], (12542 ^ _780205) ^ [_1003248, _1003250, _1003252] : [class_Lattices_Olattice(_1003248), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003248), _1003250)), -(c_Big__Operators_Olattice__class_OSup__fin(_1003248, hAPP(hAPP(c_Set_Oinsert(_1003248), _1003252), _1003250)) = hAPP(hAPP(c_Finite__Set_Ofold(_1003248, _1003248, c_Lattices_Osemilattice__sup__class_Osup(_1003248)), _1003252), _1003250))], (12552 ^ _780205) ^ [_1003433, _1003435, _1003437] : [class_Lattices_Olattice(_1003433), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003433), _1003435)), -(c_Big__Operators_Olattice__class_OInf__fin(_1003433, hAPP(hAPP(c_Set_Oinsert(_1003433), _1003437), _1003435)) = hAPP(hAPP(c_Finite__Set_Ofold(_1003433, _1003433, c_Lattices_Osemilattice__inf__class_Oinf(_1003433)), _1003437), _1003435))], (12562 ^ _780205) ^ [_1003618, _1003620, _1003622, _1003624, _1003626] : [c_Finite__Set_Ofolding__one(_1003618, _1003620, _1003622), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003618), _1003624)), -(hBOOL(hAPP(hAPP(c_member(_1003618), _1003626), _1003624))), -(hAPP(_1003622, hAPP(hAPP(c_Set_Oinsert(_1003618), _1003626), _1003624)) = hAPP(hAPP(c_Finite__Set_Ofold(_1003618, _1003618, _1003620), _1003626), _1003624))], (12576 ^ _780205) ^ [_1003840, _1003842, _1003844, _1003846, _1003848] : [class_Groups_Ocomm__monoid__mult(_1003840), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003842), _1003844)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1003842, _1003840), _1003846), hAPP(hAPP(c_Set_Oinsert(_1003842), _1003848), _1003844)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003840), hAPP(_1003846, _1003848)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1003842, _1003840), _1003846), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1003842, tc_HOL_Obool)), _1003844), hAPP(hAPP(c_Set_Oinsert(_1003842), _1003848), c_Orderings_Obot__class_Obot(tc_fun(_1003842, tc_HOL_Obool)))))))], (12586 ^ _780205) ^ [_1004109, _1004111, _1004113, _1004115, _1004117] : [class_Groups_Ocomm__monoid__mult(_1004109), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004111), _1004113)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004111), _1004115)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1004111, tc_HOL_Obool)), _1004113), _1004115) = c_Orderings_Obot__class_Obot(tc_fun(_1004111, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1004111, _1004109), _1004117), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004111, tc_HOL_Obool)), _1004113), _1004115)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004109), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1004111, _1004109), _1004117), _1004113)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1004111, _1004109), _1004117), _1004115)))], (12604 ^ _780205) ^ [_1004504, _1004506, _1004508, _1004510, _1004512] : [class_Groups_Ocomm__monoid__mult(_1004504), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004506), _1004508)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004506), _1004510)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1004506, tc_HOL_Obool)), _1004508), _1004510) = c_Orderings_Obot__class_Obot(tc_fun(_1004506, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1004506, _1004504), _1004512), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004506, tc_HOL_Obool)), _1004508), _1004510)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004504), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1004506, _1004504), _1004512), _1004508)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1004506, _1004504), _1004512), _1004510)))], (12622 ^ _780205) ^ [_1004899, _1004901, _1004903] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1004899), _1004901)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004899), _1004903)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1004899, tc_HOL_Obool)), _1004901), _1004903) = c_Orderings_Obot__class_Obot(tc_fun(_1004899, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1004899), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004899, tc_HOL_Obool)), _1004901), _1004903)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1004899), _1004901)), hAPP(c_Finite__Set_Ocard(_1004899), _1004903)))], (12636 ^ _780205) ^ [_1005198, _1005200, _1005202] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1005198), _1005200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1005198), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005198, tc_HOL_Obool)), _1005200), hAPP(hAPP(c_Set_Oinsert(_1005198), _1005202), c_Orderings_Obot__class_Obot(tc_fun(_1005198, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1005198), _1005200))))], (12642 ^ _780205) ^ [_1005363, _1005365, _1005367, _1005369, _1005371, _1005373] : [c_Finite__Set_Ofun__left__comm(_1005363, _1005365, _1005367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005363), _1005369)), hBOOL(hAPP(hAPP(c_member(_1005363), _1005371), _1005369)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1005363, _1005365, _1005367), _1005373), _1005369) = hAPP(hAPP(_1005367, _1005371), hAPP(hAPP(c_Finite__Set_Ofold(_1005363, _1005365, _1005367), _1005373), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005363, tc_HOL_Obool)), _1005369), hAPP(hAPP(c_Set_Oinsert(_1005363), _1005371), c_Orderings_Obot__class_Obot(tc_fun(_1005363, tc_HOL_Obool)))))))], (12656 ^ _780205) ^ [_1005692] : [class_Orderings_Oord(_1005692), -(c_Orderings_Oord__class_Omin(_1005692) = c_Orderings_Oord_Omin(_1005692, c_Orderings_Oord__class_Oless__eq(_1005692)))], (12662 ^ _780205) ^ [_1005779, _1005781, _1005783, _1005785, _1005787, _1005789] : [c_Finite__Set_Ofun__left__comm(_1005779, _1005781, _1005783), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005779), _1005785)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1005779, _1005781, _1005783), _1005787), hAPP(hAPP(c_Set_Oinsert(_1005779), _1005789), _1005785)) = hAPP(hAPP(_1005783, _1005789), hAPP(hAPP(c_Finite__Set_Ofold(_1005779, _1005781, _1005783), _1005787), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1005779, tc_HOL_Obool)), _1005785), hAPP(hAPP(c_Set_Oinsert(_1005779), _1005789), c_Orderings_Obot__class_Obot(tc_fun(_1005779, tc_HOL_Obool)))))))], (12672 ^ _780205) ^ [_1006050, _1006052, _1006054] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1006050), _1006052)), hBOOL(hAPP(hAPP(c_member(_1006050), _1006054), _1006052)), -(hAPP(c_Finite__Set_Ocard(_1006050), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006050, tc_HOL_Obool)), _1006052), hAPP(hAPP(c_Set_Oinsert(_1006050), _1006054), c_Orderings_Obot__class_Obot(tc_fun(_1006050, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1006050), _1006052)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12682 ^ _780205) ^ [_1006285, _1006287, _1006289] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1006285), _1006287)), 12685 ^ _780205 : [(12686 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1006285), _1006289), _1006287)), -(hAPP(c_Finite__Set_Ocard(_1006285), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006285, tc_HOL_Obool)), _1006287), hAPP(hAPP(c_Set_Oinsert(_1006285), _1006289), c_Orderings_Obot__class_Obot(tc_fun(_1006285, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1006285), _1006287)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12692 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1006285), _1006289), _1006287))), -(hAPP(c_Finite__Set_Ocard(_1006285), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006285, tc_HOL_Obool)), _1006287), hAPP(hAPP(c_Set_Oinsert(_1006285), _1006289), c_Orderings_Obot__class_Obot(tc_fun(_1006285, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1006285), _1006287))]]], (12698 ^ _780205) ^ [_1006649, _1006651, _1006653] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1006649), _1006651)), hBOOL(hAPP(hAPP(c_member(_1006649), _1006653), _1006651)), -(hAPP(c_Finite__Set_Ocard(_1006649), _1006651) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1006649), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006649, tc_HOL_Obool)), _1006651), hAPP(hAPP(c_Set_Oinsert(_1006649), _1006653), c_Orderings_Obot__class_Obot(tc_fun(_1006649, tc_HOL_Obool)))))))], (12708 ^ _780205) ^ [_1006878, _1006880, _1006882] : [class_Orderings_Olinorder(_1006878), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006878), _1006880)), hBOOL(hAPP(hAPP(c_member(_1006878), _1006882), _1006880)), 12719 ^ _780205 : [(12720 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006878, tc_HOL_Obool)), _1006880), hAPP(hAPP(c_Set_Oinsert(_1006878), _1006882), c_Orderings_Obot__class_Obot(tc_fun(_1006878, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1006878, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1006878, _1006880) = _1006882)], (12726 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006878, tc_HOL_Obool)), _1006880), hAPP(hAPP(c_Set_Oinsert(_1006878), _1006882), c_Orderings_Obot__class_Obot(tc_fun(_1006878, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1006878, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1006878, _1006880) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1006878), _1006882), c_Big__Operators_Olinorder__class_OMin(_1006878, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006878, tc_HOL_Obool)), _1006880), hAPP(hAPP(c_Set_Oinsert(_1006878), _1006882), c_Orderings_Obot__class_Obot(tc_fun(_1006878, tc_HOL_Obool)))))))]]], (12732 ^ _780205) ^ [_1007414, _1007416, _1007418, _1007420, _1007422, _1007424, _1007426] : [c_Nitpick_Ofold__graph_H(_1007414, _1007416, _1007418, _1007420, _1007422, hAPP(hAPP(_1007418, _1007424), _1007426)), 12737 ^ _780205 : [(12738 ^ _780205) ^ [] : [-(_1007422 = c_Orderings_Obot__class_Obot(tc_fun(_1007414, tc_HOL_Obool)))], (12740 ^ _780205) ^ [] : [-(hAPP(hAPP(_1007418, _1007424), _1007426) = _1007420)]], 12743 ^ _780205 : [(12744 ^ _780205) ^ [] : [-(hAPP(hAPP(_1007418, _1007424), _1007426) = hAPP(hAPP(_1007418, 12741 ^ [_1007414, _1007416, _1007418, _1007420, _1007422, _1007424, _1007426]), 12742 ^ [_1007414, _1007416, _1007418, _1007420, _1007422, _1007424, _1007426]))], (12746 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1007414), 12741 ^ [_1007414, _1007416, _1007418, _1007420, _1007422, _1007424, _1007426]), _1007422)))], (12748 ^ _780205) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1007414, _1007416, _1007418, _1007420, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007414, tc_HOL_Obool)), _1007422), hAPP(hAPP(c_Set_Oinsert(_1007414), 12741 ^ [_1007414, _1007416, _1007418, _1007420, _1007422, _1007424, _1007426]), c_Orderings_Obot__class_Obot(tc_fun(_1007414, tc_HOL_Obool)))), 12742 ^ [_1007414, _1007416, _1007418, _1007420, _1007422, _1007424, _1007426]))]]], (12750 ^ _780205) ^ [_1007851, _1007853, _1007855, _1007857, _1007859, _1007861, _1007863] : [-(c_Nitpick_Ofold__graph_H(_1007851, _1007853, _1007855, _1007857, _1007859, hAPP(hAPP(_1007855, _1007861), _1007863))), 12751 ^ _780205 : [(12752 ^ _780205) ^ [] : [_1007859 = c_Orderings_Obot__class_Obot(tc_fun(_1007851, tc_HOL_Obool)), hAPP(hAPP(_1007855, _1007861), _1007863) = _1007857], (12758 ^ _780205) ^ [_1008080, _1008082] : [hAPP(hAPP(_1007855, _1007861), _1007863) = hAPP(hAPP(_1007855, _1008082), _1008080), hBOOL(hAPP(hAPP(c_member(_1007851), _1008082), _1007859)), c_Nitpick_Ofold__graph_H(_1007851, _1007853, _1007855, _1007857, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007851, tc_HOL_Obool)), _1007859), hAPP(hAPP(c_Set_Oinsert(_1007851), _1008082), c_Orderings_Obot__class_Obot(tc_fun(_1007851, tc_HOL_Obool)))), _1008080)]]], (12770 ^ _780205) ^ [_1008372, _1008374, _1008376] : [class_Orderings_Olinorder(_1008372), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008372), _1008374)), hBOOL(hAPP(hAPP(c_member(_1008372), _1008376), _1008374)), 12781 ^ _780205 : [(12782 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008372, tc_HOL_Obool)), _1008374), hAPP(hAPP(c_Set_Oinsert(_1008372), _1008376), c_Orderings_Obot__class_Obot(tc_fun(_1008372, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1008372, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1008372, c_Orderings_Oord__class_Omin(_1008372), _1008374) = _1008376)], (12788 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008372, tc_HOL_Obool)), _1008374), hAPP(hAPP(c_Set_Oinsert(_1008372), _1008376), c_Orderings_Obot__class_Obot(tc_fun(_1008372, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1008372, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1008372, c_Orderings_Oord__class_Omin(_1008372), _1008374) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1008372), _1008376), c_Big__Operators_Olattice_OInf__fin(_1008372, c_Orderings_Oord__class_Omin(_1008372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008372, tc_HOL_Obool)), _1008374), hAPP(hAPP(c_Set_Oinsert(_1008372), _1008376), c_Orderings_Obot__class_Obot(tc_fun(_1008372, tc_HOL_Obool)))))))]]], (12794 ^ _780205) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (12796 ^ _780205) ^ [_1008914, _1008916] : [class_Groups_Oone(_1008914), 12799 ^ _780205 : [(12800 ^ _780205) ^ [] : [c_Groups_Oone__class_Oone(_1008914) = _1008916, -(_1008916 = c_Groups_Oone__class_Oone(_1008914))], (12806 ^ _780205) ^ [] : [_1008916 = c_Groups_Oone__class_Oone(_1008914), -(c_Groups_Oone__class_Oone(_1008914) = _1008916)]]], (12812 ^ _780205) ^ [_1009131, _1009133, _1009135, _1009137, _1009139, _1009141] : [c_Finite__Set_Ofun__left__comm(_1009131, _1009133, _1009135), -(hAPP(hAPP(_1009135, _1009137), hAPP(hAPP(_1009135, _1009139), _1009141)) = hAPP(hAPP(_1009135, _1009139), hAPP(hAPP(_1009135, _1009137), _1009141)))], (12818 ^ _780205) ^ [_1009266, _1009268] : [class_Rings_Ocomm__semiring__1(_1009266), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009266), _1009268), c_Groups_Oone__class_Oone(_1009266)) = _1009268)], (12824 ^ _780205) ^ [_1009361, _1009363] : [class_Rings_Ocomm__semiring__1(_1009361), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009361), c_Groups_Oone__class_Oone(_1009361)), _1009363) = _1009363)], (12830 ^ _780205) ^ [_1009456, _1009458] : [class_Groups_Omonoid__mult(_1009456), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009456), c_Groups_Oone__class_Oone(_1009456)), _1009458) = _1009458)], (12836 ^ _780205) ^ [_1009551, _1009553] : [class_Groups_Ocomm__monoid__mult(_1009551), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009551), c_Groups_Oone__class_Oone(_1009551)), _1009553) = _1009553)], (12842 ^ _780205) ^ [_1009646, _1009648] : [class_Groups_Omonoid__mult(_1009646), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009646), _1009648), c_Groups_Oone__class_Oone(_1009646)) = _1009648)], (12848 ^ _780205) ^ [_1009741, _1009743] : [class_Groups_Ocomm__monoid__mult(_1009741), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009741), _1009743), c_Groups_Oone__class_Oone(_1009741)) = _1009743)], (12854 ^ _780205) ^ [_1009836, _1009838, _1009840] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1009836), _1009838)), 12857 ^ _780205 : [(12868 ^ _780205) ^ [] : [12870 ^ _780205 : [(12871 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1009836), 12869 ^ [_1009836, _1009838, _1009840]), _1009838)))], (12873 ^ _780205) ^ [] : [hAPP(_1009840, 12869 ^ [_1009836, _1009838, _1009840]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1009836, tc_Nat_Onat), _1009840), _1009838) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12858 ^ _780205) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1009836, tc_Nat_Onat), _1009840), _1009838) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 12861 ^ _780205 : [(12862 ^ _780205) ^ [_1009998] : [hBOOL(hAPP(hAPP(c_member(_1009836), _1009998), _1009838)), -(hAPP(_1009840, _1009998) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (12877 ^ _780205) ^ [_1010271, _1010273] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010271), _1010273) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 12880 ^ _780205 : [(12881 ^ _780205) ^ [] : [-(_1010271 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12883 ^ _780205) ^ [] : [-(_1010273 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12885 ^ _780205) ^ [_1010382, _1010384] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010382), _1010384) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1010382 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1010384 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12895 ^ _780205) ^ [_1010525] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010525), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1010525)], (12897 ^ _780205) ^ [_1010569, _1010571] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010569), _1010571), 12900 ^ _780205 : [(12901 ^ _780205) ^ [] : [-(_1010569 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12903 ^ _780205) ^ [] : [-(_1010571 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12905 ^ _780205) ^ [_1010680, _1010682] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010680), _1010682)), _1010680 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1010682 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12915 ^ _780205) ^ [_1010823] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1010823) = _1010823)], (12917 ^ _780205) ^ [_1010849] : [class_Groups_Oab__semigroup__mult(_1010849), -(c_Finite__Set_Ofun__left__comm(_1010849, _1010849, c_Groups_Otimes__class_Otimes(_1010849)))], (12923 ^ _780205) ^ [_1010928, _1010930] : [class_Rings_Olinordered__semidom(_1010928), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010928), _1010930), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010928), _1010930), c_Groups_Oone__class_Oone(_1010928)))))], (12929 ^ _780205) ^ [_1011037, _1011039, _1011041] : [class_Rings_Olinordered__semidom(_1011037), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011037), c_Groups_Oone__class_Oone(_1011037)), _1011039)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011037), c_Groups_Oone__class_Oone(_1011037)), _1011041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011037), c_Groups_Oone__class_Oone(_1011037)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011037), _1011039), _1011041))))], (12943 ^ _780205) ^ [_1011292, _1011294] : [class_Rings_Ocomm__semiring__1(_1011292), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011292), _1011294), _1011294) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011292), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011292), c_Groups_Oone__class_Oone(_1011292)), c_Groups_Oone__class_Oone(_1011292))), _1011294))], (12949 ^ _780205) ^ [_1011423, _1011425, _1011427] : [class_Rings_Ocomm__semiring__1(_1011423), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011423), _1011425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011423), _1011427), _1011425)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011423), _1011427), c_Groups_Oone__class_Oone(_1011423))), _1011425))], (12955 ^ _780205) ^ [_1011568, _1011570, _1011572] : [class_Rings_Ocomm__semiring__1(_1011568), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011568), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011568), _1011570), _1011572)), _1011572) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011568), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011568), _1011570), c_Groups_Oone__class_Oone(_1011568))), _1011572))], (12961 ^ _780205) ^ [_1011713, _1011715, _1011717, _1011719, _1011721, _1011723, _1011725] : [c_Finite__Set_Ofun__left__comm(_1011713, _1011715, _1011717), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1011713, _1011715, _1011717, _1011719, _1011721), _1011723)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1011713, _1011715, _1011717, _1011719, _1011721), _1011725)), -(_1011725 = _1011723)], (12975 ^ _780205) ^ [_1011958, _1011960, _1011962] : [class_Groups_Ocomm__monoid__mult(_1011958), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011960, _1011958), _1011962), c_Orderings_Obot__class_Obot(tc_fun(_1011960, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1011958))], (12981 ^ _780205) ^ [_1012067, _1012069, _1012071] : [class_Groups_Ocomm__monoid__mult(_1012067), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012069, _1012067), _1012071), c_Orderings_Obot__class_Obot(tc_fun(_1012069, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1012067))], (12987 ^ _780205) ^ [_1012176, _1012178, _1012180, _1012182] : [class_Groups_Ocomm__monoid__mult(_1012176), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012178), _1012180))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012178, _1012176), _1012182), _1012180) = c_Groups_Oone__class_Oone(_1012176))], (12997 ^ _780205) ^ [_1012300, _1012302, _1012304, _1012306] : [class_Groups_Ocomm__monoid__mult(_1012300), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012302), _1012304))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012302, _1012300), _1012306), _1012304) = c_Groups_Oone__class_Oone(_1012300))], (13007 ^ _780205) ^ [_1012424, _1012426] : [class_Orderings_Olinorder(_1012424), -(c_Big__Operators_Olinorder__class_OMin(_1012424, hAPP(hAPP(c_Set_Oinsert(_1012424), _1012426), c_Orderings_Obot__class_Obot(tc_fun(_1012424, tc_HOL_Obool)))) = _1012426)], (13013 ^ _780205) ^ [_1012531, _1012533, _1012535] : [class_Orderings_Olinorder(_1012531), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012531), _1012533)), hBOOL(hAPP(hAPP(c_member(_1012531), _1012535), _1012533)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1012531), _1012535), c_Big__Operators_Olattice_OInf__fin(_1012531, c_Orderings_Oord__class_Omin(_1012531), _1012533)) = c_Big__Operators_Olattice_OInf__fin(_1012531, c_Orderings_Oord__class_Omin(_1012531), _1012533))], (13027 ^ _780205) ^ [_1012778, _1012780, _1012782, _1012784, _1012786, _1012788] : [c_Finite__Set_Ofun__left__comm(_1012778, _1012780, _1012782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012778), _1012784)), -(hAPP(hAPP(_1012782, _1012786), hAPP(hAPP(c_Finite__Set_Ofold(_1012778, _1012780, _1012782), _1012788), _1012784)) = hAPP(hAPP(c_Finite__Set_Ofold(_1012778, _1012780, _1012782), hAPP(hAPP(_1012782, _1012786), _1012788)), _1012784))], (13037 ^ _780205) ^ [_1012997, _1012999] : [class_Orderings_Olinorder(_1012997), -(c_Big__Operators_Olattice_OInf__fin(_1012997, c_Orderings_Oord__class_Omin(_1012997), hAPP(hAPP(c_Set_Oinsert(_1012997), _1012999), c_Orderings_Obot__class_Obot(tc_fun(_1012997, tc_HOL_Obool)))) = _1012999)], (13043 ^ _780205) ^ [_1013110, _1013112, _1013114] : [class_Orderings_Olinorder(_1013110), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013110), _1013112)), hBOOL(hAPP(hAPP(c_member(_1013110), _1013114), _1013112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013110), c_Big__Operators_Olinorder__class_OMin(_1013110, _1013112)), _1013114)))], (13057 ^ _780205) ^ [_1013337, _1013339] : [class_Orderings_Olinorder(_1013337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013337), _1013339)), -(_1013339 = c_Orderings_Obot__class_Obot(tc_fun(_1013337, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1013337), c_Big__Operators_Olinorder__class_OMin(_1013337, _1013339)), _1013339)))], (13071 ^ _780205) ^ [_1013517, _1013519, _1013521] : [class_Orderings_Olinorder(_1013517), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013517), _1013519)), hBOOL(hAPP(hAPP(c_member(_1013517), _1013521), _1013519)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1013517), _1013521), c_Big__Operators_Olinorder__class_OMin(_1013517, _1013519)) = c_Big__Operators_Olinorder__class_OMin(_1013517, _1013519))], (13085 ^ _780205) ^ [_1013752, _1013754] : [class_Orderings_Olinorder(_1013752), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013752), _1013754)), -(c_Big__Operators_Olattice_OInf__fin(_1013752, c_Orderings_Oord__class_Omin(_1013752), _1013754) = hAPP(c_Finite__Set_Ofold1(_1013752, c_Orderings_Oord__class_Omin(_1013752)), _1013754))], (13095 ^ _780205) ^ [_1013915, _1013917, _1013919, _1013921, _1013923, _1013925] : [c_Finite__Set_Ofun__left__comm(_1013915, _1013917, _1013919), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1013915, _1013917, _1013919, _1013921, _1013923), _1013925)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1013915, _1013917, _1013919), _1013921), _1013923) = _1013925)], (13105 ^ _780205) ^ [_1014098, _1014100] : [class_Orderings_Olinorder(_1014098), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014098), _1014100)), -(c_Big__Operators_Olinorder__class_OMin(_1014098, _1014100) = hAPP(c_Finite__Set_Ofold1(_1014098, c_Orderings_Oord__class_Omin(_1014098)), _1014100))], (13115 ^ _780205) ^ [_1014255, _1014257, _1014259] : [class_Orderings_Olinorder(_1014255), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014255), _1014257)), -(_1014257 = c_Orderings_Obot__class_Obot(tc_fun(_1014255, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1014255, c_Orderings_Oord__class_Omin(_1014255), hAPP(hAPP(c_Set_Oinsert(_1014255), _1014259), _1014257)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1014255), _1014259), c_Big__Operators_Olattice_OInf__fin(_1014255, c_Orderings_Oord__class_Omin(_1014255), _1014257)))], (13129 ^ _780205) ^ [_1014475, _1014477, _1014479] : [class_Orderings_Olinorder(_1014475), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014475), _1014477)), -(_1014479 = c_Orderings_Obot__class_Obot(tc_fun(_1014475, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1014475, tc_HOL_Obool)), _1014479), _1014477)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1014475), c_Big__Operators_Olattice_OInf__fin(_1014475, c_Orderings_Oord__class_Omin(_1014475), _1014479)), c_Big__Operators_Olattice_OInf__fin(_1014475, c_Orderings_Oord__class_Omin(_1014475), _1014477)) = c_Big__Operators_Olattice_OInf__fin(_1014475, c_Orderings_Oord__class_Omin(_1014475), _1014477))], (13147 ^ _780205) ^ [_1014807, _1014809, _1014811] : [class_Orderings_Olinorder(_1014807), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014807), _1014809)), -(_1014809 = c_Orderings_Obot__class_Obot(tc_fun(_1014807, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014807), _1014811)), -(_1014811 = c_Orderings_Obot__class_Obot(tc_fun(_1014807, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1014807, c_Orderings_Oord__class_Omin(_1014807), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014807, tc_HOL_Obool)), _1014809), _1014811)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1014807), c_Big__Operators_Olattice_OInf__fin(_1014807, c_Orderings_Oord__class_Omin(_1014807), _1014809)), c_Big__Operators_Olattice_OInf__fin(_1014807, c_Orderings_Oord__class_Omin(_1014807), _1014811)))], (13169 ^ _780205) ^ [_1015174, _1015176, _1015178] : [class_Orderings_Olinorder(_1015174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015174, tc_HOL_Obool)), _1015176), _1015178)), -(_1015176 = c_Orderings_Obot__class_Obot(tc_fun(_1015174, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015174), _1015178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015174), c_Big__Operators_Olinorder__class_OMin(_1015174, _1015178)), c_Big__Operators_Olinorder__class_OMin(_1015174, _1015176))))], (13187 ^ _780205) ^ [_1015480, _1015482, _1015484] : [class_Orderings_Olinorder(_1015480), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015480), _1015482)), -(c_Big__Operators_Olattice_OInf__fin(_1015480, c_Orderings_Oord__class_Omin(_1015480), hAPP(hAPP(c_Set_Oinsert(_1015480), _1015484), _1015482)) = hAPP(hAPP(c_Finite__Set_Ofold(_1015480, _1015480, c_Orderings_Oord__class_Omin(_1015480)), _1015484), _1015482))], (13197 ^ _780205) ^ [_1015671, _1015673, _1015675] : [class_Orderings_Olinorder(_1015671), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015671), _1015673)), -(_1015673 = c_Orderings_Obot__class_Obot(tc_fun(_1015671, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1015671, hAPP(hAPP(c_Set_Oinsert(_1015671), _1015675), _1015673)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1015671), _1015675), c_Big__Operators_Olinorder__class_OMin(_1015671, _1015673)))], (13211 ^ _780205) ^ [_1015879, _1015881, _1015883] : [class_Orderings_Olinorder(_1015879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015879), _1015881)), -(_1015883 = c_Orderings_Obot__class_Obot(tc_fun(_1015879, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015879, tc_HOL_Obool)), _1015883), _1015881)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1015879), c_Big__Operators_Olinorder__class_OMin(_1015879, _1015883)), c_Big__Operators_Olinorder__class_OMin(_1015879, _1015881)) = c_Big__Operators_Olinorder__class_OMin(_1015879, _1015881))], (13229 ^ _780205) ^ [_1016193, _1016195, _1016197] : [class_Orderings_Olinorder(_1016193), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016193), _1016195)), -(_1016195 = c_Orderings_Obot__class_Obot(tc_fun(_1016193, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016193), _1016197)), -(_1016197 = c_Orderings_Obot__class_Obot(tc_fun(_1016193, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1016193, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016193, tc_HOL_Obool)), _1016195), _1016197)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1016193), c_Big__Operators_Olinorder__class_OMin(_1016193, _1016195)), c_Big__Operators_Olinorder__class_OMin(_1016193, _1016197)))], (13251 ^ _780205) ^ [_1016542, _1016544, _1016546] : [class_Orderings_Olinorder(_1016542), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016542), _1016544)), -(c_Big__Operators_Olinorder__class_OMin(_1016542, hAPP(hAPP(c_Set_Oinsert(_1016542), _1016546), _1016544)) = hAPP(hAPP(c_Finite__Set_Ofold(_1016542, _1016542, c_Orderings_Oord__class_Omin(_1016542)), _1016546), _1016544))], (13261 ^ _780205) ^ [_1016727, _1016729, _1016731, _1016733, _1016735] : [c_Finite__Set_Ofun__left__comm(_1016727, _1016729, _1016731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016727), _1016733)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1016727, _1016729, _1016731, _1016735, _1016733), hAPP(hAPP(c_Finite__Set_Ofold(_1016727, _1016729, _1016731), _1016735), _1016733))))], (13271 ^ _780205) ^ [_1016914, _1016916, _1016918] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1016914), _1016916)), -(hBOOL(hAPP(hAPP(c_member(_1016914), _1016918), _1016916))), -(hAPP(c_Finite__Set_Ocard(_1016914), hAPP(hAPP(c_Set_Oinsert(_1016914), _1016918), _1016916)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1016914), _1016916)))], (13281 ^ _780205) ^ [_1017072, _1017074, _1017076] : [class_Orderings_Olinorder(_1017072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017072), _1017074)), -(hBOOL(hAPP(hAPP(c_member(_1017072), _1017076), _1017074))), -(_1017074 = c_Orderings_Obot__class_Obot(tc_fun(_1017072, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1017072, c_Orderings_Oord__class_Omin(_1017072), hAPP(hAPP(c_Set_Oinsert(_1017072), _1017076), _1017074)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1017072), _1017076), c_Big__Operators_Olattice_OInf__fin(_1017072, c_Orderings_Oord__class_Omin(_1017072), _1017074)))], (13299 ^ _780205) ^ [_1017321, _1017323, _1017325] : [class_Orderings_Olinorder(_1017321), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017321), _1017323)), 13306 ^ _780205 : [(13307 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017321, tc_HOL_Obool)), _1017323), hAPP(hAPP(c_Set_Oinsert(_1017321), _1017325), c_Orderings_Obot__class_Obot(tc_fun(_1017321, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1017321, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1017321, c_Orderings_Oord__class_Omin(_1017321), hAPP(hAPP(c_Set_Oinsert(_1017321), _1017325), _1017323)) = _1017325)], (13313 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017321, tc_HOL_Obool)), _1017323), hAPP(hAPP(c_Set_Oinsert(_1017321), _1017325), c_Orderings_Obot__class_Obot(tc_fun(_1017321, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1017321, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1017321, c_Orderings_Oord__class_Omin(_1017321), hAPP(hAPP(c_Set_Oinsert(_1017321), _1017325), _1017323)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1017321), _1017325), c_Big__Operators_Olattice_OInf__fin(_1017321, c_Orderings_Oord__class_Omin(_1017321), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017321, tc_HOL_Obool)), _1017323), hAPP(hAPP(c_Set_Oinsert(_1017321), _1017325), c_Orderings_Obot__class_Obot(tc_fun(_1017321, tc_HOL_Obool)))))))]]], (13319 ^ _780205) ^ [_1017809, _1017811, _1017813] : [class_Orderings_Olinorder(_1017809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017809), _1017811)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017809), _1017813)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1017809, tc_HOL_Obool)), _1017811), _1017813) = c_Orderings_Obot__class_Obot(tc_fun(_1017809, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1017809), c_Big__Operators_Olattice_OInf__fin(_1017809, c_Orderings_Oord__class_Omin(_1017809), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017809, tc_HOL_Obool)), _1017811), _1017813))), c_Big__Operators_Olattice_OInf__fin(_1017809, c_Orderings_Oord__class_Omin(_1017809), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1017809, tc_HOL_Obool)), _1017811), _1017813))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1017809), c_Big__Operators_Olattice_OInf__fin(_1017809, c_Orderings_Oord__class_Omin(_1017809), _1017811)), c_Big__Operators_Olattice_OInf__fin(_1017809, c_Orderings_Oord__class_Omin(_1017809), _1017813)))], (13337 ^ _780205) ^ [_1018181, _1018183, _1018185] : [class_Orderings_Olinorder(_1018181), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018181), _1018183)), -(_1018183 = c_Orderings_Obot__class_Obot(tc_fun(_1018181, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018181), _1018185)), -(_1018185 = c_Orderings_Obot__class_Obot(tc_fun(_1018181, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1018181, tc_HOL_Obool)), _1018183), _1018185) = c_Orderings_Obot__class_Obot(tc_fun(_1018181, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1018181, c_Orderings_Oord__class_Omin(_1018181), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1018181, tc_HOL_Obool)), _1018183), _1018185)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1018181), c_Big__Operators_Olattice_OInf__fin(_1018181, c_Orderings_Oord__class_Omin(_1018181), _1018183)), c_Big__Operators_Olattice_OInf__fin(_1018181, c_Orderings_Oord__class_Omin(_1018181), _1018185)))], (13363 ^ _780205) ^ [_1018676, _1018678, _1018680] : [class_Orderings_Olinorder(_1018676), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018676), _1018678)), -(hBOOL(hAPP(hAPP(c_member(_1018676), _1018680), _1018678))), -(c_Big__Operators_Olattice_OInf__fin(_1018676, c_Orderings_Oord__class_Omin(_1018676), hAPP(hAPP(c_Set_Oinsert(_1018676), _1018680), _1018678)) = hAPP(hAPP(c_Finite__Set_Ofold(_1018676, _1018676, c_Orderings_Oord__class_Omin(_1018676)), _1018680), _1018678))], (13377 ^ _780205) ^ [_1018896, _1018898, _1018900] : [class_Orderings_Olinorder(_1018896), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018896), _1018898)), -(hBOOL(hAPP(hAPP(c_member(_1018896), _1018900), _1018898))), -(_1018898 = c_Orderings_Obot__class_Obot(tc_fun(_1018896, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1018896, hAPP(hAPP(c_Set_Oinsert(_1018896), _1018900), _1018898)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1018896), _1018900), c_Big__Operators_Olinorder__class_OMin(_1018896, _1018898)))], (13395 ^ _780205) ^ [_1019133, _1019135, _1019137] : [class_Orderings_Olinorder(_1019133), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019133), _1019135)), 13402 ^ _780205 : [(13403 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1019133, tc_HOL_Obool)), _1019135), hAPP(hAPP(c_Set_Oinsert(_1019133), _1019137), c_Orderings_Obot__class_Obot(tc_fun(_1019133, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1019133, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1019133, hAPP(hAPP(c_Set_Oinsert(_1019133), _1019137), _1019135)) = _1019137)], (13409 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1019133, tc_HOL_Obool)), _1019135), hAPP(hAPP(c_Set_Oinsert(_1019133), _1019137), c_Orderings_Obot__class_Obot(tc_fun(_1019133, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1019133, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1019133, hAPP(hAPP(c_Set_Oinsert(_1019133), _1019137), _1019135)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1019133), _1019137), c_Big__Operators_Olinorder__class_OMin(_1019133, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1019133, tc_HOL_Obool)), _1019135), hAPP(hAPP(c_Set_Oinsert(_1019133), _1019137), c_Orderings_Obot__class_Obot(tc_fun(_1019133, tc_HOL_Obool)))))))]]], (13415 ^ _780205) ^ [_1019603, _1019605, _1019607] : [class_Orderings_Olinorder(_1019603), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019603), _1019605)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019603), _1019607)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019603, tc_HOL_Obool)), _1019605), _1019607) = c_Orderings_Obot__class_Obot(tc_fun(_1019603, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1019603), c_Big__Operators_Olinorder__class_OMin(_1019603, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1019603, tc_HOL_Obool)), _1019605), _1019607))), c_Big__Operators_Olinorder__class_OMin(_1019603, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019603, tc_HOL_Obool)), _1019605), _1019607))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1019603), c_Big__Operators_Olinorder__class_OMin(_1019603, _1019605)), c_Big__Operators_Olinorder__class_OMin(_1019603, _1019607)))], (13433 ^ _780205) ^ [_1019951, _1019953, _1019955] : [class_Orderings_Olinorder(_1019951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019951), _1019953)), -(_1019953 = c_Orderings_Obot__class_Obot(tc_fun(_1019951, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019951), _1019955)), -(_1019955 = c_Orderings_Obot__class_Obot(tc_fun(_1019951, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019951, tc_HOL_Obool)), _1019953), _1019955) = c_Orderings_Obot__class_Obot(tc_fun(_1019951, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1019951, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1019951, tc_HOL_Obool)), _1019953), _1019955)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1019951), c_Big__Operators_Olinorder__class_OMin(_1019951, _1019953)), c_Big__Operators_Olinorder__class_OMin(_1019951, _1019955)))], (13459 ^ _780205) ^ [_1020428, _1020430, _1020432] : [class_Orderings_Olinorder(_1020428), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020428), _1020430)), -(hBOOL(hAPP(hAPP(c_member(_1020428), _1020432), _1020430))), -(c_Big__Operators_Olinorder__class_OMin(_1020428, hAPP(hAPP(c_Set_Oinsert(_1020428), _1020432), _1020430)) = hAPP(hAPP(c_Finite__Set_Ofold(_1020428, _1020428, c_Orderings_Oord__class_Omin(_1020428)), _1020432), _1020430))], (13473 ^ _780205) ^ [_1020642, _1020644, _1020646, _1020648] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1020642), _1020644)), hBOOL(hAPP(hAPP(c_member(_1020642), _1020646), _1020644)), -(hBOOL(hAPP(hAPP(c_member(_1020642), _1020646), _1020648))), -(hAPP(c_Finite__Set_Ocard(_1020642), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020642, tc_HOL_Obool)), _1020644), hAPP(hAPP(c_Set_Oinsert(_1020642), _1020646), _1020648))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1020642), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020642, tc_HOL_Obool)), _1020644), _1020648))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13487 ^ _780205) ^ [_1020922, _1020924, _1020926] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1020922), _1020924)), -(hAPP(c_Finite__Set_Ocard(_1020922), hAPP(hAPP(c_Set_Oinsert(_1020922), _1020926), _1020924)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1020922), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020922, tc_HOL_Obool)), _1020924), hAPP(hAPP(c_Set_Oinsert(_1020922), _1020926), c_Orderings_Obot__class_Obot(tc_fun(_1020922, tc_HOL_Obool)))))))], (13493 ^ _780205) ^ [_1021099, _1021101, _1021103, _1021105, _1021107, _1021109] : [c_Finite__Set_Ofun__left__comm(_1021099, _1021101, _1021103), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021099), _1021105)), -(hBOOL(hAPP(hAPP(c_member(_1021099), _1021107), _1021105))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1021099, _1021101, _1021103), _1021109), hAPP(hAPP(c_Set_Oinsert(_1021099), _1021107), _1021105)) = hAPP(hAPP(_1021103, _1021107), hAPP(hAPP(c_Finite__Set_Ofold(_1021099, _1021101, _1021103), _1021109), _1021105)))], (13507 ^ _780205) ^ [_1021351, _1021353, _1021355, _1021357, _1021359, _1021361] : [c_Finite__Set_Ofun__left__comm(_1021351, _1021353, _1021355), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021351), _1021357)), -(hBOOL(hAPP(hAPP(c_member(_1021351), _1021359), _1021357))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1021351, _1021353, _1021355), _1021361), hAPP(hAPP(c_Set_Oinsert(_1021351), _1021359), _1021357)) = hAPP(hAPP(c_Finite__Set_Ofold(_1021351, _1021353, _1021355), hAPP(hAPP(_1021355, _1021359), _1021361)), _1021357))], (13521 ^ _780205) ^ [_1021603, _1021605, _1021607, _1021609, _1021611, _1021613, _1021615] : [c_Finite__Set_Ofun__left__comm(_1021603, _1021605, _1021607), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1021603, _1021605, _1021607, _1021609, _1021611), _1021613)), hBOOL(hAPP(hAPP(c_member(_1021603), _1021615), _1021611)), 13533 ^ _780205 : [(13534 ^ _780205) ^ [] : [-(_1021613 = hAPP(hAPP(_1021607, _1021615), 13532 ^ [_1021603, _1021605, _1021607, _1021609, _1021611, _1021613, _1021615]))], (13536 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1021603, _1021605, _1021607, _1021609, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1021603, tc_HOL_Obool)), _1021611), hAPP(hAPP(c_Set_Oinsert(_1021603), _1021615), c_Orderings_Obot__class_Obot(tc_fun(_1021603, tc_HOL_Obool))))), 13532 ^ [_1021603, _1021605, _1021607, _1021609, _1021611, _1021613, _1021615])))]]], (13538 ^ _780205) ^ [_1021987, _1021989] : [class_Orderings_Olinorder(_1021987), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021987), _1021989)), -(_1021989 = c_Orderings_Obot__class_Obot(tc_fun(_1021987, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1021987), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1021987), 13551 ^ [_1021987, _1021989]), 13552 ^ [_1021987, _1021989])), hAPP(hAPP(c_Set_Oinsert(_1021987), 13551 ^ [_1021987, _1021989]), hAPP(hAPP(c_Set_Oinsert(_1021987), 13552 ^ [_1021987, _1021989]), c_Orderings_Obot__class_Obot(tc_fun(_1021987, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1021987), c_Big__Operators_Olattice_OInf__fin(_1021987, c_Orderings_Oord__class_Omin(_1021987), _1021989)), _1021989)))], (13558 ^ _780205) ^ [_1022437, _1022439] : [class_Orderings_Olinorder(_1022437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022437), _1022439)), -(_1022439 = c_Orderings_Obot__class_Obot(tc_fun(_1022437, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1022437), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1022437), 13571 ^ [_1022437, _1022439]), 13572 ^ [_1022437, _1022439])), hAPP(hAPP(c_Set_Oinsert(_1022437), 13571 ^ [_1022437, _1022439]), hAPP(hAPP(c_Set_Oinsert(_1022437), 13572 ^ [_1022437, _1022439]), c_Orderings_Obot__class_Obot(tc_fun(_1022437, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1022437), c_Big__Operators_Olinorder__class_OMin(_1022437, _1022439)), _1022439)))], (13578 ^ _780205) ^ [_1022881, _1022883, _1022885, _1022887, _1022889] : [class_Groups_Ocomm__monoid__mult(_1022881), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022883), _1022885)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022883), _1022887)), 13592 ^ _780205 : [(13593 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1022883), 13591 ^ [_1022881, _1022883, _1022885, _1022887, _1022889]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1022883, tc_HOL_Obool)), _1022885), _1022887))))], (13595 ^ _780205) ^ [] : [hAPP(_1022889, 13591 ^ [_1022881, _1022883, _1022885, _1022887, _1022889]) = c_Groups_Oone__class_Oone(_1022881)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1022883, _1022881), _1022889), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1022883, tc_HOL_Obool)), _1022885), _1022887)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022881), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1022883, _1022881), _1022889), _1022885)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1022883, _1022881), _1022889), _1022887)))], (13599 ^ _780205) ^ [_1023376, _1023378, _1023380, _1023382, _1023384] : [class_Groups_Ocomm__monoid__mult(_1023376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023378), _1023380)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023378), _1023382)), 13613 ^ _780205 : [(13614 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1023378), 13612 ^ [_1023376, _1023378, _1023380, _1023382, _1023384]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1023378, tc_HOL_Obool)), _1023380), _1023382))))], (13616 ^ _780205) ^ [] : [hAPP(_1023384, 13612 ^ [_1023376, _1023378, _1023380, _1023382, _1023384]) = c_Groups_Oone__class_Oone(_1023376)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1023378, _1023376), _1023384), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1023378, tc_HOL_Obool)), _1023380), _1023382)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023376), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1023378, _1023376), _1023384), _1023380)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1023378, _1023376), _1023384), _1023382)))], (13620 ^ _780205) ^ [_1023871, _1023873, _1023875, _1023877, _1023879] : [class_Groups_Ocomm__monoid__mult(_1023871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023873), _1023875)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023873), _1023877)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1023873, tc_HOL_Obool)), _1023875), _1023877) = c_Orderings_Obot__class_Obot(tc_fun(_1023873, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1023871, _1023873, c_Groups_Otimes__class_Otimes(_1023871)), _1023879), c_Groups_Oone__class_Oone(_1023871)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1023873, tc_HOL_Obool)), _1023875), _1023877)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023871), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1023871, _1023873, c_Groups_Otimes__class_Otimes(_1023871)), _1023879), c_Groups_Oone__class_Oone(_1023871)), _1023875)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1023871, _1023873, c_Groups_Otimes__class_Otimes(_1023871)), _1023879), c_Groups_Oone__class_Oone(_1023871)), _1023877)))], (13638 ^ _780205) ^ [_1024314, _1024316, _1024318, _1024320, _1024322] : [class_Groups_Ocomm__monoid__mult(_1024314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024316), _1024318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024316, tc_HOL_Obool)), _1024320), _1024318)), 13652 ^ _780205 : [(13653 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1024316), 13651 ^ [_1024314, _1024316, _1024318, _1024320, _1024322]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1024316, tc_HOL_Obool)), _1024318), _1024320))))], (13655 ^ _780205) ^ [] : [hAPP(_1024322, 13651 ^ [_1024314, _1024316, _1024318, _1024320, _1024322]) = c_Groups_Oone__class_Oone(_1024314)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1024316, _1024314), _1024322), _1024318) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1024316, _1024314), _1024322), _1024320))], (13659 ^ _780205) ^ [_1024765, _1024767, _1024769, _1024771, _1024773] : [class_Groups_Ocomm__monoid__mult(_1024765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024767), _1024769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024767, tc_HOL_Obool)), _1024771), _1024769)), 13673 ^ _780205 : [(13674 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1024767), 13672 ^ [_1024765, _1024767, _1024769, _1024771, _1024773]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1024767, tc_HOL_Obool)), _1024769), _1024771))))], (13676 ^ _780205) ^ [] : [hAPP(_1024773, 13672 ^ [_1024765, _1024767, _1024769, _1024771, _1024773]) = c_Groups_Oone__class_Oone(_1024765)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1024767, _1024765), _1024773), _1024771) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1024767, _1024765), _1024773), _1024769))], (13680 ^ _780205) ^ [_1025216, _1025218, _1025220] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1025216), _1025218)), hBOOL(hAPP(hAPP(c_member(_1025216), _1025220), _1025218)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1025216), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025216, tc_HOL_Obool)), _1025218), hAPP(hAPP(c_Set_Oinsert(_1025216), _1025220), c_Orderings_Obot__class_Obot(tc_fun(_1025216, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1025216), _1025218))], (13690 ^ _780205) ^ [_1025445, _1025447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025445), _1025447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1025445)), hAPP(c_Nat_OSuc, _1025447))))], (13696 ^ _780205) ^ [_1025554] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025554), hAPP(c_Nat_OSuc, _1025554))))], (13698 ^ _780205) ^ [_1025585, _1025587] : [hAPP(c_Nat_OSuc, _1025585) = hAPP(c_Nat_OSuc, _1025587), -(_1025585 = _1025587)], (13704 ^ _780205) ^ [_1025689, _1025691] : [hAPP(c_Nat_OSuc, _1025689) = hAPP(c_Nat_OSuc, _1025691), -(_1025689 = _1025691)], (13710 ^ _780205) ^ [_1025774, _1025776] : [_1025774 = _1025776, -(hAPP(c_Nat_OSuc, _1025774) = hAPP(c_Nat_OSuc, _1025776))], (13716 ^ _780205) ^ [_1025874] : [hAPP(c_Nat_OSuc, _1025874) = _1025874], (13718 ^ _780205) ^ [_1025909] : [_1025909 = hAPP(c_Nat_OSuc, _1025909)], (13720 ^ _780205) ^ [_1025935, _1025937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1025935)), hAPP(c_Nat_OSuc, _1025937))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025935), _1025937)))], (13726 ^ _780205) ^ [_1026044, _1026046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1026044)), _1026046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026044), _1026046)))], (13732 ^ _780205) ^ [_1026147, _1026149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026147), hAPP(c_Nat_OSuc, _1026149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026147), _1026149))), -(_1026147 = _1026149)], (13742 ^ _780205) ^ [_1026265, _1026267, _1026269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026265), _1026267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026267), _1026269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1026265)), _1026269)))], (13752 ^ _780205) ^ [_1026434, _1026436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026434), _1026436)), -(hAPP(c_Nat_OSuc, _1026434) = _1026436), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1026434)), _1026436)))], (13762 ^ _780205) ^ [_1026558, _1026560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026558), _1026560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026558), hAPP(c_Nat_OSuc, _1026560))))], (13768 ^ _780205) ^ [_1026660, _1026662] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026660), _1026662))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026660), hAPP(c_Nat_OSuc, _1026662))), -(_1026662 = _1026660)], (13778 ^ _780205) ^ [_1026807, _1026809] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026807), _1026809))), 13781 ^ _780205 : [(13782 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026807), hAPP(c_Nat_OSuc, _1026809))), -(_1026807 = _1026809)], (13788 ^ _780205) ^ [] : [_1026807 = _1026809, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026807), hAPP(c_Nat_OSuc, _1026809))))]]], (13794 ^ _780205) ^ [_1027056, _1027058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027056)), hAPP(c_Nat_OSuc, _1027058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027056), _1027058)))], (13800 ^ _780205) ^ [_1027161, _1027163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027161), _1027163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027161)), hAPP(c_Nat_OSuc, _1027163))))], (13816 ^ _780205) ^ [_1027399, _1027401] : [13817 ^ _780205 : [(13818 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027399), _1027401))], (13820 ^ _780205) ^ [] : [_1027399 = _1027401]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027399), hAPP(c_Nat_OSuc, _1027401))))], (13806 ^ _780205) ^ [_1027287, _1027289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027287), hAPP(c_Nat_OSuc, _1027289))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027287), _1027289))), -(_1027287 = _1027289)], (13824 ^ _780205) ^ [_1027551, _1027553] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027551), _1027553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027553), hAPP(c_Nat_OSuc, _1027551))))], (13830 ^ _780205) ^ [_1027596, _1027598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027598), hAPP(c_Nat_OSuc, _1027596))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027596), _1027598))], (13836 ^ _780205) ^ [_1027702, _1027704] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027702)), _1027704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027702), hAPP(c_Nat_OSuc, _1027704)))], (13838 ^ _780205) ^ [_1027745, _1027747] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027745)), _1027747) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027745), _1027747)))], (13840 ^ _780205) ^ [_1027788, _1027790] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027788), hAPP(c_Nat_OSuc, _1027790)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027788), _1027790)))], (13842 ^ _780205) ^ [_1027831, _1027833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027831)), _1027833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027831), _1027833)))], (13848 ^ _780205) ^ [_1027934, _1027936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027934), hAPP(c_Nat_OSuc, _1027936))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027934), _1027936))), -(_1027934 = hAPP(c_Nat_OSuc, _1027936))], (13858 ^ _780205) ^ [_1028058, _1028060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028058), _1028060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028058), hAPP(c_Nat_OSuc, _1028060))))], (13864 ^ _780205) ^ [_1028176, _1028178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028176)), hAPP(c_Nat_OSuc, _1028178))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028176), _1028178)))], (13870 ^ _780205) ^ [_1028281, _1028283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028281), _1028283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028281)), hAPP(c_Nat_OSuc, _1028283))))], (13886 ^ _780205) ^ [_1028525, _1028527] : [13887 ^ _780205 : [(13888 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028525), _1028527))], (13890 ^ _780205) ^ [] : [_1028525 = hAPP(c_Nat_OSuc, _1028527)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028525), hAPP(c_Nat_OSuc, _1028527))))], (13876 ^ _780205) ^ [_1028407, _1028409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028407), hAPP(c_Nat_OSuc, _1028409))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028407), _1028409))), -(_1028407 = hAPP(c_Nat_OSuc, _1028409))], (13894 ^ _780205) ^ [_1028683, _1028685] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028683), _1028685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028685)), _1028683)))], (13900 ^ _780205) ^ [_1028728, _1028730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028730)), _1028728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028728), _1028730))], (13906 ^ _780205) ^ [_1028843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028843)), _1028843))], (13908 ^ _780205) ^ [_1028874, _1028876] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028874)), hAPP(c_Nat_OSuc, _1028876)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028874), _1028876))], (13910 ^ _780205) ^ [_1028917, _1028919, _1028921] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028917)), _1028919)), hAPP(c_Nat_OSuc, _1028921)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028917), _1028919)), _1028921))], (13912 ^ _780205) ^ [_1028992, _1028994, _1028996] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028992)), _1028994) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1028992)), _1028996), -(_1028994 = _1028996)], (13918 ^ _780205) ^ [_1029103, _1029105, _1029107] : [_1029105 = _1029107, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029103)), _1029105) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029103)), _1029107))], (13924 ^ _780205) ^ [_1029220, _1029222, _1029224, _1029226, _1029228] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1029220, _1029222, _1029224), _1029226), _1029228), c_Orderings_Obot__class_Obot(tc_fun(_1029222, tc_HOL_Obool))) = _1029228)], (13926 ^ _780205) ^ [_1029269, _1029271] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029269)), hAPP(c_Nat_OSuc, _1029271)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1029269), _1029271)))], (13928 ^ _780205) ^ [_1029315, _1029317] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029315), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029315), _1029317)))))], (13930 ^ _780205) ^ [_1029354, _1029356] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029354), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029356), _1029354)))))], (13932 ^ _780205) ^ [_1029408, _1029410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029408), _1029410)), -(_1029410 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029408), 13935 ^ [_1029408, _1029410])))], (13939 ^ _780205) ^ [_1029521, _1029523] : [13940 ^ _780205 : [(13941 ^ _780205) ^ [_1029574] : [_1029523 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029521), _1029574))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029521), _1029523)))], (13945 ^ _780205) ^ [_1029641, _1029643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029641)), _1029643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029641), _1029643)))], (13951 ^ _780205) ^ [_1029744, _1029746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029744), _1029746)), 13954 ^ _780205 : [(13955 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029746), hAPP(c_Nat_OSuc, _1029744))), -(_1029746 = _1029744)], (13961 ^ _780205) ^ [] : [_1029746 = _1029744, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029746), hAPP(c_Nat_OSuc, _1029744))))]]], (13967 ^ _780205) ^ [_1029985, _1029987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029985), _1029987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1029985)), _1029987)))], (13973 ^ _780205) ^ [_1030088, _1030090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030088), _1030090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030088), hAPP(c_Nat_OSuc, _1030090))))], (13979 ^ _780205) ^ [_1030206, _1030208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1030206)), _1030208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030206), _1030208)))], (13985 ^ _780205) ^ [_1030305, _1030307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030305), _1030307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1030305)), _1030307)))], (13991 ^ _780205) ^ [_1030425, _1030427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030425), hAPP(c_Nat_OSuc, _1030427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030425), _1030427)))], (13997 ^ _780205) ^ [_1030524, _1030526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030524), _1030526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030524), hAPP(c_Nat_OSuc, _1030526))))], (14003 ^ _780205) ^ [_1030644, _1030646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030644), _1030646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1030644)), _1030646)))], (14009 ^ _780205) ^ [_1030743, _1030745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1030743)), _1030745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030743), _1030745)))], (14015 ^ _780205) ^ [_1030848, _1030850] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030848), _1030850)), hAPP(c_Nat_OSuc, _1030848))))], (14017 ^ _780205) ^ [_1030905, _1030907, _1030909] : [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, _1030905)), _1030907)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1030905)), _1030909))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030907), _1030909)))], (14023 ^ _780205) ^ [_1031036, _1031038, _1031040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1031038), _1031040)), -(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, _1031036)), _1031038)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1031036)), _1031040))))], (14029 ^ _780205) ^ [_1031173, _1031175] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031173), hAPP(c_Nat_OSuc, _1031175)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031173), _1031175)))], (14031 ^ _780205) ^ [_1031219, _1031221] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1031219)), _1031221) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031219), _1031221)))], (14033 ^ _780205) ^ [_1031265, _1031267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031265), _1031267)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1031267)), _1031265) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031267), _1031265)))], (14039 ^ _780205) ^ [_1031406, _1031408, _1031410] : [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, _1031406)), _1031408)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1031406)), _1031410))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031408), _1031410)))], (14045 ^ _780205) ^ [_1031537, _1031539, _1031541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031539), _1031541)), -(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, _1031537)), _1031539)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1031537)), _1031541))))], (14051 ^ _780205) ^ [_1031674] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1031674)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1031674)], (14053 ^ _780205) ^ [_1031706, _1031708, _1031710, _1031712, _1031714, _1031716, _1031718] : [c_Finite__Set_Ofolding__image__simple(_1031706, _1031708, _1031710, _1031712, _1031714, _1031716), hBOOL(hAPP(c_Finite__Set_Ofinite(_1031708), _1031718)), -(hAPP(_1031716, _1031718) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1031706, _1031708, _1031710), _1031714), _1031712), _1031718))], (14063 ^ _780205) ^ [_1031903, _1031905, _1031907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031903), _1031905)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031907), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031905), _1031903))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031907), _1031903)), hAPP(c_Nat_OSuc, _1031905)))], (14069 ^ _780205) ^ [_1032052, _1032054, _1032056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032052), _1032054)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1032054), _1032052))), _1032056) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1032054)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1032052), _1032056)))], (14075 ^ _780205) ^ [_1032201, _1032203, _1032205] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1032201), _1032203)), -(hBOOL(hAPP(hAPP(c_member(_1032201), _1032205), _1032203))), -(hAPP(c_Finite__Set_Ocard(_1032201), hAPP(hAPP(c_Set_Oinsert(_1032201), _1032205), _1032203)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1032201), _1032203)))], (14085 ^ _780205) ^ [_1032359, _1032361, _1032363] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1032359), _1032361)), 14088 ^ _780205 : [(14089 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1032359), _1032363), _1032361)), -(hAPP(c_Finite__Set_Ocard(_1032359), hAPP(hAPP(c_Set_Oinsert(_1032359), _1032363), _1032361)) = hAPP(c_Finite__Set_Ocard(_1032359), _1032361))], (14095 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1032359), _1032363), _1032361))), -(hAPP(c_Finite__Set_Ocard(_1032359), hAPP(hAPP(c_Set_Oinsert(_1032359), _1032363), _1032361)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1032359), _1032361)))]]], (14101 ^ _780205) ^ [_1032653, _1032655, _1032657, _1032659, _1032661, _1032663] : [class_Groups_Oab__semigroup__mult(_1032653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032655), _1032657)), -(hBOOL(hAPP(hAPP(c_member(_1032655), _1032659), _1032657))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1032653, _1032655, c_Groups_Otimes__class_Otimes(_1032653)), _1032661), _1032663), hAPP(hAPP(c_Set_Oinsert(_1032655), _1032659), _1032657)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032653), hAPP(_1032661, _1032659)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1032653, _1032655, c_Groups_Otimes__class_Otimes(_1032653)), _1032661), _1032663), _1032657)))], (14115 ^ _780205) ^ [_1032931, _1032933, _1032935, _1032937] : [class_Groups_Ocomm__monoid__mult(_1032931), 14118 ^ _780205 : [(14119 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1032933), _1032935)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1032933, _1032931), _1032937), _1032935) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1032931, _1032933, c_Groups_Otimes__class_Otimes(_1032931)), _1032937), c_Groups_Oone__class_Oone(_1032931)), _1032935))], (14125 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1032933), _1032935))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1032933, _1032931), _1032937), _1032935) = c_Groups_Oone__class_Oone(_1032931))]]], (14131 ^ _780205) ^ [_1033203, _1033205, _1033207, _1033209] : [class_Groups_Ocomm__monoid__mult(_1033203), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033205), _1033207)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1033205, _1033203), _1033209), _1033207) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1033203, _1033205, c_Groups_Otimes__class_Otimes(_1033203)), _1033209), c_Groups_Oone__class_Oone(_1033203)), _1033207))], (14141 ^ _780205) ^ [_1033398, _1033400, _1033402] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1033398), _1033400)), -(hAPP(c_Finite__Set_Ocard(_1033398), hAPP(hAPP(c_Set_Oinsert(_1033398), _1033402), _1033400)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1033398), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1033398, tc_HOL_Obool)), _1033400), hAPP(hAPP(c_Set_Oinsert(_1033398), _1033402), c_Orderings_Obot__class_Obot(tc_fun(_1033398, tc_HOL_Obool)))))))], (14147 ^ _780205) ^ [_1033575, _1033577, _1033579, _1033581, _1033583] : [class_Groups_Ocomm__monoid__mult(_1033575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033577), _1033579)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033577), _1033581)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033575), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1033575, _1033577, c_Groups_Otimes__class_Otimes(_1033575)), _1033583), c_Groups_Oone__class_Oone(_1033575)), _1033579)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1033575, _1033577, c_Groups_Otimes__class_Otimes(_1033575)), _1033583), c_Groups_Oone__class_Oone(_1033575)), _1033581)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033575), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1033575, _1033577, c_Groups_Otimes__class_Otimes(_1033575)), _1033583), c_Groups_Oone__class_Oone(_1033575)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1033577, tc_HOL_Obool)), _1033579), _1033581))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1033575, _1033577, c_Groups_Otimes__class_Otimes(_1033575)), _1033583), c_Groups_Oone__class_Oone(_1033575)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1033577, tc_HOL_Obool)), _1033579), _1033581))))], (14161 ^ _780205) ^ [_1034000, _1034002] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034000), hAPP(c_Nat_OSuc, _1034002)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034000), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1034002))], (14163 ^ _780205) ^ [_1034046] : [-(hAPP(c_Nat_OSuc, _1034046) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1034046))], (14165 ^ _780205) ^ [_1034075] : [-(hAPP(c_Nat_OSuc, _1034075) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1034075), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (14167 ^ _780205) ^ [_1034107, _1034109, _1034111, _1034113, _1034115, _1034117, _1034119] : [c_Big__Operators_Ocomm__monoid__big(_1034107, _1034109, _1034111, _1034113, _1034115), 14170 ^ _780205 : [(14171 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1034109), _1034117)), -(hAPP(hAPP(_1034115, _1034119), _1034117) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1034107, _1034109, _1034111), _1034119), _1034113), _1034117))], (14177 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1034109), _1034117))), -(hAPP(hAPP(_1034115, _1034119), _1034117) = _1034113)]]], (14183 ^ _780205) ^ [_1034375, _1034377, _1034379, _1034381, _1034383] : [class_Groups_Ocomm__monoid__mult(_1034375), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034377), _1034379)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034377), _1034381)), 14197 ^ _780205 : [(14198 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1034377), 14196 ^ [_1034375, _1034377, _1034379, _1034381, _1034383]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1034377, tc_HOL_Obool)), _1034379), _1034381))))], (14200 ^ _780205) ^ [] : [hAPP(_1034383, 14196 ^ [_1034375, _1034377, _1034379, _1034381, _1034383]) = c_Groups_Oone__class_Oone(_1034375)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1034375, _1034377, c_Groups_Otimes__class_Otimes(_1034375)), _1034383), c_Groups_Oone__class_Oone(_1034375)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1034377, tc_HOL_Obool)), _1034379), _1034381)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034375), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1034375, _1034377, c_Groups_Otimes__class_Otimes(_1034375)), _1034383), c_Groups_Oone__class_Oone(_1034375)), _1034379)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1034375, _1034377, c_Groups_Otimes__class_Otimes(_1034375)), _1034383), c_Groups_Oone__class_Oone(_1034375)), _1034381)))], (14204 ^ _780205) ^ [_1034918, _1034920] : [class_Complete__Lattice_Ocomplete__lattice(_1034918), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034918), _1034920)), -(c_Complete__Lattice_OSup__class_OSup(_1034918, _1034920) = hAPP(hAPP(c_Finite__Set_Ofold(_1034918, _1034918, c_Lattices_Osemilattice__sup__class_Osup(_1034918)), c_Orderings_Obot__class_Obot(_1034918)), _1034920))], (14214 ^ _780205) ^ [_1035087, _1035089, _1035091, _1035093, _1035095, _1035097, _1035099] : [c_Finite__Set_Ofun__left__comm(_1035087, _1035089, _1035091), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1035087, _1035089, _1035091, _1035093, hAPP(hAPP(c_Set_Oinsert(_1035087), _1035095), _1035097)), _1035099)), -(hBOOL(hAPP(hAPP(c_member(_1035087), _1035095), _1035097))), 14226 ^ _780205 : [(14227 ^ _780205) ^ [] : [-(_1035099 = hAPP(hAPP(_1035091, _1035095), 14225 ^ [_1035087, _1035089, _1035091, _1035093, _1035095, _1035097, _1035099]))], (14229 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1035087, _1035089, _1035091, _1035093, _1035097), 14225 ^ [_1035087, _1035089, _1035091, _1035093, _1035095, _1035097, _1035099])))]]], (14231 ^ _780205) ^ [_1035413, _1035415] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1035413), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1035413, tc_HOL_Obool), _1035415))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1035413, tc_HOL_Obool)), _1035415)))], (14237 ^ _780205) ^ [_1035524, _1035526, _1035528] : [class_Complete__Lattice_Ocomplete__lattice(_1035524), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035524), _1035526)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1035524), _1035528), c_Complete__Lattice_OSup__class_OSup(_1035524, _1035526)) = hAPP(hAPP(c_Finite__Set_Ofold(_1035524, _1035524, c_Lattices_Osemilattice__sup__class_Osup(_1035524)), _1035528), _1035526))], (14247 ^ _780205) ^ [_1035709, _1035711] : [class_Complete__Lattice_Ocomplete__lattice(_1035709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035709), _1035711)), -(_1035711 = c_Orderings_Obot__class_Obot(tc_fun(_1035709, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1035709, _1035711) = c_Complete__Lattice_OSup__class_OSup(_1035709, _1035711))], (14261 ^ _780205) ^ [_1035881, _1035883, _1035885, _1035887, _1035889, _1035891, _1035893] : [c_Big__Operators_Ocomm__monoid__big(_1035881, _1035883, _1035885, _1035887, _1035889), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035883), _1035891))), -(hAPP(hAPP(_1035889, _1035893), _1035891) = _1035887)], (14271 ^ _780205) ^ [_1036009, _1036011, _1036013] : [class_Complete__Lattice_Ocomplete__lattice(_1036009), -(c_Complete__Lattice_OSup__class_OSup(_1036009, hAPP(hAPP(c_Set_Oinsert(_1036009), _1036011), hAPP(hAPP(c_Set_Oinsert(_1036009), _1036013), c_Orderings_Obot__class_Obot(tc_fun(_1036009, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1036009), _1036011), _1036013))], (14277 ^ _780205) ^ [_1036150, _1036152, _1036154] : [class_Complete__Lattice_Ocomplete__lattice(_1036150), -(c_Complete__Lattice_OSup__class_OSup(_1036150, hAPP(hAPP(c_Set_Oinsert(_1036150), _1036152), _1036154)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1036150), _1036152), c_Complete__Lattice_OSup__class_OSup(_1036150, _1036154)))], (14283 ^ _780205) ^ [_1036271, _1036273] : [class_Complete__Lattice_Ocomplete__lattice(_1036271), -(c_Complete__Lattice_OSup__class_OSup(_1036271, hAPP(hAPP(c_Set_Oinsert(_1036271), _1036273), c_Orderings_Obot__class_Obot(tc_fun(_1036271, tc_HOL_Obool)))) = _1036273)], (14289 ^ _780205) ^ [_1036378] : [class_Complete__Lattice_Ocomplete__lattice(_1036378), -(c_Complete__Lattice_OSup__class_OSup(_1036378, c_Orderings_Obot__class_Obot(tc_fun(_1036378, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1036378))], (14295 ^ _780205) ^ [_1036471, _1036473, _1036475] : [class_Complete__Lattice_Ocomplete__lattice(_1036471), hBOOL(hAPP(hAPP(c_member(_1036471), _1036473), _1036475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036471), _1036473), c_Complete__Lattice_OSup__class_OSup(_1036471, _1036475))))], (14305 ^ _780205) ^ [_1036636, _1036638, _1036640, _1036642] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1036636, tc_HOL_Obool)), _1036638), _1036640)), hBOOL(hAPP(hAPP(c_member(_1036636), _1036642), _1036638)), -(hBOOL(hAPP(hAPP(c_member(_1036636), _1036642), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1036636, tc_HOL_Obool), _1036640))))], (14315 ^ _780205) ^ [_1036833, _1036835, _1036837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1036833, tc_HOL_Obool), tc_HOL_Obool)), _1036835), _1036837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1036833, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1036833, tc_HOL_Obool), _1036835)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1036833, tc_HOL_Obool), _1036837))))], (14321 ^ _780205) ^ [_1036982, _1036984, _1036986] : [class_Complete__Lattice_Ocomplete__lattice(_1036982), class_Orderings_Olinorder(_1036982), 14328 ^ _780205 : [(14329 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036982), _1036984), c_Complete__Lattice_OSup__class_OSup(_1036982, _1036986))), 14333 ^ _780205 : [(14334 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1036982), 14332 ^ [_1036982, _1036984, _1036986]), _1036986)))], (14336 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036982), _1036984), 14332 ^ [_1036982, _1036984, _1036986])))]]], (14338 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036982), _1036984), c_Complete__Lattice_OSup__class_OSup(_1036982, _1036986)))), 14339 ^ _780205 : [(14340 ^ _780205) ^ [_1037288] : [hBOOL(hAPP(hAPP(c_member(_1036982), _1037288), _1036986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036982), _1036984), _1037288))]]]]], (14348 ^ _780205) ^ [_1037442] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1037442, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1037442, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1037442, tc_HOL_Obool)))], (14350 ^ _780205) ^ [_1037484, _1037486, _1037488] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1037484, tc_HOL_Obool)), _1037486), _1037488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1037484, tc_HOL_Obool)), _1037486), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1037484, tc_HOL_Obool), _1037488))))], (14356 ^ _780205) ^ [_1037615, _1037617, _1037619] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1037615, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1037615, tc_HOL_Obool)), _1037617), _1037619)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1037615, tc_HOL_Obool)), _1037617), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1037615, tc_HOL_Obool), _1037619)))], (14358 ^ _780205) ^ [_1037676, _1037678, _1037680] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1037676, tc_HOL_Obool)), _1037678), _1037680) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1037676, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1037676, tc_HOL_Obool)), _1037678), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1037676, tc_HOL_Obool)), _1037680), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1037676, tc_HOL_Obool), tc_HOL_Obool))))))], (14360 ^ _780205) ^ [_1037750, _1037752, _1037754] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1037750, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1037750, tc_HOL_Obool), tc_HOL_Obool)), _1037752), _1037754)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1037750, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1037750, tc_HOL_Obool), _1037752)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1037750, tc_HOL_Obool), _1037754)))], (14372 ^ _780205) ^ [_1038106, _1038108, _1038110] : [14374 ^ _780205 : [(14375 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1038106, tc_HOL_Obool)), 14373 ^ [_1038106, _1038108, _1038110]), _1038108)))], (14377 ^ _780205) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1038106, tc_HOL_Obool)), 14373 ^ [_1038106, _1038108, _1038110]), _1038110) = c_Orderings_Obot__class_Obot(tc_fun(_1038106, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1038106, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1038106, tc_HOL_Obool), _1038108)), _1038110) = c_Orderings_Obot__class_Obot(tc_fun(_1038106, tc_HOL_Obool)))], (14362 ^ _780205) ^ [_1037838, _1037840, _1037842] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1037838, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1037838, tc_HOL_Obool), _1037840)), _1037842) = c_Orderings_Obot__class_Obot(tc_fun(_1037838, tc_HOL_Obool)), 14365 ^ _780205 : [(14366 ^ _780205) ^ [_1037973] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1037838, tc_HOL_Obool)), _1037973), _1037840)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1037838, tc_HOL_Obool)), _1037973), _1037842) = c_Orderings_Obot__class_Obot(tc_fun(_1037838, tc_HOL_Obool)))]]], (14381 ^ _780205) ^ [_1038369, _1038371, _1038373] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038369, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1038369, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1038369, tc_HOL_Obool), tc_HOL_Obool)), _1038371), _1038373))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1038369, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1038369, tc_HOL_Obool), _1038371)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1038369, tc_HOL_Obool), _1038373)))))], (14383 ^ _780205) ^ [_1038449, _1038451, _1038453] : [class_Complete__Lattice_Ocomplete__lattice(_1038449), 14386 ^ _780205 : [(14397 ^ _780205) ^ [] : [14399 ^ _780205 : [(14400 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1038449), 14398 ^ [_1038449, _1038451, _1038453]), _1038451)))], (14402 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038449), 14398 ^ [_1038449, _1038451, _1038453]), _1038453))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038449), c_Complete__Lattice_OSup__class_OSup(_1038449, _1038451)), _1038453)))], (14387 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038449), c_Complete__Lattice_OSup__class_OSup(_1038449, _1038451)), _1038453)), 14390 ^ _780205 : [(14391 ^ _780205) ^ [_1038607] : [hBOOL(hAPP(hAPP(c_member(_1038449), _1038607), _1038451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038449), _1038607), _1038453)))]]]]], (14406 ^ _780205) ^ [_1038883, _1038885] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1038883, tc_HOL_Obool)), _1038885)), 14412 ^ _780205 : [(14413 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1038883, tc_HOL_Obool)), 14411 ^ [_1038883, _1038885]), _1038885)))], (14415 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1038883), 14411 ^ [_1038883, _1038885]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038883), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1038883, tc_HOL_Obool), _1038885))))], (14419 ^ _780205) ^ [_1039142, _1039144, _1039146, _1039148, _1039150, _1039152] : [c_Finite__Set_Ofun__left__comm__idem(_1039142, _1039144, _1039146), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039142), _1039148)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1039142, _1039144, _1039146), _1039150), hAPP(hAPP(c_Set_Oinsert(_1039142), _1039152), _1039148)) = hAPP(hAPP(_1039146, _1039152), hAPP(hAPP(c_Finite__Set_Ofold(_1039142, _1039144, _1039146), _1039150), _1039148)))], (14429 ^ _780205) ^ [_1039365, _1039367, _1039369, _1039371, _1039373, _1039375] : [c_Finite__Set_Ofun__left__comm__idem(_1039365, _1039367, _1039369), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039365), _1039371)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1039365, _1039367, _1039369), _1039373), hAPP(hAPP(c_Set_Oinsert(_1039365), _1039375), _1039371)) = hAPP(hAPP(c_Finite__Set_Ofold(_1039365, _1039367, _1039369), hAPP(hAPP(_1039369, _1039375), _1039373)), _1039371))], (14439 ^ _780205) ^ [_1039587, _1039589, _1039591] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1039587, tc_HOL_Obool)), _1039589), _1039591))), 14445 ^ _780205 : [(14446 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1039587, tc_HOL_Obool)), 14444 ^ [_1039587, _1039589, _1039591]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1039587, tc_HOL_Obool)), _1039589), _1039591))))], (14449 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1039587, tc_HOL_Obool)), 14447 ^ [_1039587, _1039589, _1039591]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1039587, tc_HOL_Obool)), _1039589), _1039591))))], (14451 ^ _780205) ^ [] : [14444 ^ [_1039587, _1039589, _1039591] = 14447 ^ [_1039587, _1039589, _1039591]], (14453 ^ _780205) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1039587, tc_HOL_Obool)), 14444 ^ [_1039587, _1039589, _1039591]), 14447 ^ [_1039587, _1039589, _1039591]) = c_Orderings_Obot__class_Obot(tc_fun(_1039587, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1039587, tc_HOL_Obool)), _1039589), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1039587, tc_HOL_Obool), _1039591)) = c_Orderings_Obot__class_Obot(tc_fun(_1039587, tc_HOL_Obool)))], (14457 ^ _780205) ^ [_1040181, _1040183, _1040185, _1040187, _1040189, _1040191] : [class_Rings_Olinordered__semiring__1__strict(_1040181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040181), _1040183), _1040185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040181), _1040187), _1040185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040181), c_Groups_Ozero__class_Ozero(_1040181)), _1040189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040181), c_Groups_Ozero__class_Ozero(_1040181)), _1040191)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040181), _1040189), _1040191) = c_Groups_Oone__class_Oone(_1040181), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040181), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040181), _1040189), _1040183)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040181), _1040191), _1040187))), _1040185)))], (14483 ^ _780205) ^ [_1040710, _1040712, _1040714] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1040710, tc_HOL_Obool)), _1040712)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040710), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1040710, tc_HOL_Obool), _1040712))), 14493 ^ _780205 : [(14494 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1040710, tc_HOL_Obool)), 14492 ^ [_1040710, _1040712, _1040714]), _1040712)))], (14496 ^ _780205) ^ [] : [hAPP(c_Finite__Set_Ocard(_1040710), 14492 ^ [_1040710, _1040712, _1040714]) = _1040714]], 14500 ^ _780205 : [(14501 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1040710, tc_HOL_Obool)), 14499 ^ [_1040710, _1040712, _1040714]), _1040712)))], (14504 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1040710, tc_HOL_Obool)), 14502 ^ [_1040710, _1040712, _1040714]), _1040712)))], (14506 ^ _780205) ^ [] : [14499 ^ [_1040710, _1040712, _1040714] = 14502 ^ [_1040710, _1040712, _1040714]], (14508 ^ _780205) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040710, tc_HOL_Obool)), 14499 ^ [_1040710, _1040712, _1040714]), 14502 ^ [_1040710, _1040712, _1040714]) = c_Orderings_Obot__class_Obot(tc_fun(_1040710, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040714), hAPP(c_Finite__Set_Ocard(tc_fun(_1040710, tc_HOL_Obool)), _1040712)) = hAPP(c_Finite__Set_Ocard(_1040710), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1040710, tc_HOL_Obool), _1040712)))], (14512 ^ _780205) ^ [_1041492, _1041494, _1041496, _1041498] : [class_Groups_Ocomm__monoid__mult(_1041492), hBOOL(hAPP(c_Finite__Set_Ofinite(_1041494), _1041496)), 14522 ^ _780205 : [(14523 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1041494), 14521 ^ [_1041492, _1041494, _1041496, _1041498]), _1041496)))], (14525 ^ _780205) ^ [] : [hAPP(_1041498, 14521 ^ [_1041492, _1041494, _1041496, _1041498]) = c_Groups_Oone__class_Oone(_1041492)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1041492, _1041494, c_Groups_Otimes__class_Otimes(_1041492)), _1041498), c_Groups_Oone__class_Oone(_1041492)), _1041496) = c_Groups_Oone__class_Oone(_1041492))], (14529 ^ _780205) ^ [_1041833, _1041835, _1041837, _1041839] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041833), _1041835)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1041837), _1041839)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1041833, _1041837)), c_Sum__Type_OPlus(_1041833, _1041837, _1041835, _1041839)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1041833), _1041835)), hAPP(c_Finite__Set_Ocard(_1041837), _1041839)))], (14539 ^ _780205) ^ [_1042053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042053), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14541 ^ _780205) ^ [_1042081] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1042081)))], (14543 ^ _780205) ^ [_1042106] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1042106))))], (14545 ^ _780205) ^ [_1042134, _1042136] : [class_Groups_Ozero(_1042134), 14548 ^ _780205 : [(14549 ^ _780205) ^ [] : [c_Groups_Ozero__class_Ozero(_1042134) = _1042136, -(_1042136 = c_Groups_Ozero__class_Ozero(_1042134))], (14555 ^ _780205) ^ [] : [_1042136 = c_Groups_Ozero__class_Ozero(_1042134), -(c_Groups_Ozero__class_Ozero(_1042134) = _1042136)]]], (14561 ^ _780205) ^ [_1042351, _1042353, _1042355, _1042357, _1042359] : [c_Finite__Set_Ofun__left__comm__idem(_1042351, _1042353, _1042355), -(hAPP(hAPP(_1042355, _1042357), hAPP(hAPP(_1042355, _1042357), _1042359)) = hAPP(hAPP(_1042355, _1042357), _1042359))], (14567 ^ _780205) ^ [_1042472, _1042474, _1042476] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1042472), 14570 ^ _780205 : [(14571 ^ _780205) ^ [] : [_1042474 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042472), _1042474), _1042476), -(_1042476 = c_Groups_Ozero__class_Ozero(_1042472))], (14577 ^ _780205) ^ [] : [_1042476 = c_Groups_Ozero__class_Ozero(_1042472), -(_1042474 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042472), _1042474), _1042476))]]], (14583 ^ _780205) ^ [_1042713, _1042715] : [class_Rings_Ocomm__semiring__1(_1042713), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042713), _1042715), c_Groups_Ozero__class_Ozero(_1042713)) = _1042715)], (14589 ^ _780205) ^ [_1042808, _1042810] : [class_Rings_Ocomm__semiring__1(_1042808), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042808), c_Groups_Ozero__class_Ozero(_1042808)), _1042810) = _1042810)], (14595 ^ _780205) ^ [_1042903, _1042905] : [class_Groups_Omonoid__add(_1042903), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042903), c_Groups_Ozero__class_Ozero(_1042903)), _1042905) = _1042905)], (14601 ^ _780205) ^ [_1042998, _1043000] : [class_Groups_Ocomm__monoid__add(_1042998), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042998), c_Groups_Ozero__class_Ozero(_1042998)), _1043000) = _1043000)], (14607 ^ _780205) ^ [_1043093, _1043095] : [class_Groups_Olinordered__ab__group__add(_1043093), 14610 ^ _780205 : [(14611 ^ _780205) ^ [] : [c_Groups_Ozero__class_Ozero(_1043093) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043093), _1043095), _1043095), -(_1043095 = c_Groups_Ozero__class_Ozero(_1043093))], (14617 ^ _780205) ^ [] : [_1043095 = c_Groups_Ozero__class_Ozero(_1043093), -(c_Groups_Ozero__class_Ozero(_1043093) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043093), _1043095), _1043095))]]], (14623 ^ _780205) ^ [_1043334, _1043336] : [class_Groups_Omonoid__add(_1043334), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043334), _1043336), c_Groups_Ozero__class_Ozero(_1043334)) = _1043336)], (14629 ^ _780205) ^ [_1043429, _1043431] : [class_Groups_Ocomm__monoid__add(_1043429), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043429), _1043431), c_Groups_Ozero__class_Ozero(_1043429)) = _1043431)], (14635 ^ _780205) ^ [_1043524, _1043526, _1043528] : [class_Rings_Ono__zero__divisors(_1043524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043524), _1043526), _1043528) = c_Groups_Ozero__class_Ozero(_1043524), -(_1043526 = c_Groups_Ozero__class_Ozero(_1043524)), -(_1043528 = c_Groups_Ozero__class_Ozero(_1043524))], (14649 ^ _780205) ^ [_1043696, _1043698, _1043700] : [class_Rings_Ono__zero__divisors(_1043696), -(_1043698 = c_Groups_Ozero__class_Ozero(_1043696)), -(_1043700 = c_Groups_Ozero__class_Ozero(_1043696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043696), _1043698), _1043700) = c_Groups_Ozero__class_Ozero(_1043696)], (14663 ^ _780205) ^ [_1043916, _1043918, _1043920] : [class_Rings_Oring__no__zero__divisors(_1043916), 14666 ^ _780205 : [(14677 ^ _780205) ^ [] : [14678 ^ _780205 : [(14679 ^ _780205) ^ [] : [_1043918 = c_Groups_Ozero__class_Ozero(_1043916)], (14681 ^ _780205) ^ [] : [_1043920 = c_Groups_Ozero__class_Ozero(_1043916)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043916), _1043918), _1043920) = c_Groups_Ozero__class_Ozero(_1043916))], (14667 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043916), _1043918), _1043920) = c_Groups_Ozero__class_Ozero(_1043916), -(_1043918 = c_Groups_Ozero__class_Ozero(_1043916)), -(_1043920 = c_Groups_Ozero__class_Ozero(_1043916))]]], (14685 ^ _780205) ^ [_1044214, _1044216] : [class_Rings_Ocomm__semiring__1(_1044214), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044214), _1044216), c_Groups_Ozero__class_Ozero(_1044214)) = c_Groups_Ozero__class_Ozero(_1044214))], (14691 ^ _780205) ^ [_1044313, _1044315] : [class_Rings_Omult__zero(_1044313), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044313), _1044315), c_Groups_Ozero__class_Ozero(_1044313)) = c_Groups_Ozero__class_Ozero(_1044313))], (14697 ^ _780205) ^ [_1044412, _1044414] : [class_Rings_Ocomm__semiring__1(_1044412), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044412), c_Groups_Ozero__class_Ozero(_1044412)), _1044414) = c_Groups_Ozero__class_Ozero(_1044412))], (14703 ^ _780205) ^ [_1044511, _1044513] : [class_Rings_Omult__zero(_1044511), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044511), c_Groups_Ozero__class_Ozero(_1044511)), _1044513) = c_Groups_Ozero__class_Ozero(_1044511))], (14709 ^ _780205) ^ [_1044610, _1044612, _1044614] : [class_Groups_Ogroup__add(_1044610), 14712 ^ _780205 : [(14713 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044610), _1044612), _1044614) = c_Groups_Ozero__class_Ozero(_1044610), -(_1044612 = _1044614)], (14719 ^ _780205) ^ [] : [_1044612 = _1044614, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044610), _1044612), _1044614) = c_Groups_Ozero__class_Ozero(_1044610))]]], (14725 ^ _780205) ^ [_1044851, _1044853, _1044855] : [class_Groups_Oab__group__add(_1044851), 14728 ^ _780205 : [(14729 ^ _780205) ^ [] : [_1044853 = _1044855, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044851), _1044853), _1044855) = c_Groups_Ozero__class_Ozero(_1044851))], (14735 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044851), _1044853), _1044855) = c_Groups_Ozero__class_Ozero(_1044851), -(_1044853 = _1044855)]]], (14741 ^ _780205) ^ [_1045092, _1045094] : [class_Groups_Ogroup__add(_1045092), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045092), _1045094), _1045094) = c_Groups_Ozero__class_Ozero(_1045092))], (14747 ^ _780205) ^ [_1045187, _1045189] : [class_Groups_Ogroup__add(_1045187), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045187), _1045189), c_Groups_Ozero__class_Ozero(_1045187)) = _1045189)], (14753 ^ _780205) ^ [_1045282] : [class_Rings_Ozero__neq__one(_1045282), c_Groups_Oone__class_Oone(_1045282) = c_Groups_Ozero__class_Ozero(_1045282)], (14759 ^ _780205) ^ [_1045364] : [class_Rings_Ozero__neq__one(_1045364), c_Groups_Ozero__class_Ozero(_1045364) = c_Groups_Oone__class_Oone(_1045364)], (14765 ^ _780205) ^ [_1045455] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1045455)], (14767 ^ _780205) ^ [_1045490] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1045490)], (14769 ^ _780205) ^ [_1045525] : [hAPP(c_Nat_OSuc, _1045525) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14771 ^ _780205) ^ [_1045560] : [hAPP(c_Nat_OSuc, _1045560) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14773 ^ _780205) ^ [_1045595] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1045595)], (14775 ^ _780205) ^ [_1045630] : [hAPP(c_Nat_OSuc, _1045630) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14777 ^ _780205) ^ [_1045665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045665), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14779 ^ _780205) ^ [_1045699] : [-(_1045699 = 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)), _1045699)))], (14785 ^ _780205) ^ [_1045731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1045731)), _1045731 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14791 ^ _780205) ^ [_1045822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045822), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14793 ^ _780205) ^ [_1045850, _1045852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045850), _1045852)), _1045852 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14799 ^ _780205) ^ [_1045934] : [-(_1045934 = 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)), _1045934)))], (14805 ^ _780205) ^ [_1045970] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1045970) = _1045970)], (14807 ^ _780205) ^ [_1045996] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045996), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1045996)], (14809 ^ _780205) ^ [_1046040, _1046042] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046040), _1046042) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 14812 ^ _780205 : [(14813 ^ _780205) ^ [] : [-(_1046040 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14815 ^ _780205) ^ [] : [-(_1046042 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (14817 ^ _780205) ^ [_1046151, _1046153] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046151), _1046153) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1046153 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14827 ^ _780205) ^ [_1046294, _1046296] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046294), _1046296) = _1046294, -(_1046296 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14833 ^ _780205) ^ [_1046383] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046383)))], (14835 ^ _780205) ^ [_1046420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046420), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1046420 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14841 ^ _780205) ^ [_1046501] : [_1046501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046501), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14847 ^ _780205) ^ [_1046588, _1046590] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046588), _1046590) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046590), _1046588) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1046588 = _1046590)], (14857 ^ _780205) ^ [_1046741] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046741), _1046741) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14859 ^ _780205) ^ [_1046770] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046770), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1046770)], (14861 ^ _780205) ^ [_1046799] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046799) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14873 ^ _780205) ^ [_1046955, _1046957, _1046959] : [14874 ^ _780205 : [(14875 ^ _780205) ^ [] : [_1046955 = _1046959], (14877 ^ _780205) ^ [] : [_1046957 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046955), _1046957) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046959), _1046957))], (14863 ^ _780205) ^ [_1046843, _1046845, _1046847] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046843), _1046845) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046847), _1046845), -(_1046843 = _1046847), -(_1046845 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14891 ^ _780205) ^ [_1047228, _1047230, _1047232] : [14892 ^ _780205 : [(14893 ^ _780205) ^ [] : [_1047230 = _1047232], (14895 ^ _780205) ^ [] : [_1047228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047228), _1047230) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047228), _1047232))], (14881 ^ _780205) ^ [_1047116, _1047118, _1047120] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047116), _1047118) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047116), _1047120), -(_1047118 = _1047120), -(_1047116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14909 ^ _780205) ^ [_1047484, _1047486] : [14910 ^ _780205 : [(14911 ^ _780205) ^ [] : [_1047484 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14913 ^ _780205) ^ [] : [_1047486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047484), _1047486) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14899 ^ _780205) ^ [_1047386, _1047388] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047386), _1047388) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1047386 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1047388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14917 ^ _780205) ^ [_1047613] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047613), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14919 ^ _780205) ^ [_1047642] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1047642) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14931 ^ _780205) ^ [_1047798, _1047800, _1047802] : [14932 ^ _780205 : [(14933 ^ _780205) ^ [] : [_1047798 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14935 ^ _780205) ^ [] : [_1047800 = _1047802]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047798), _1047800) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047798), _1047802))], (14921 ^ _780205) ^ [_1047686, _1047688, _1047690] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047686), _1047688) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047686), _1047690), -(_1047686 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1047688 = _1047690)], (14939 ^ _780205) ^ [_1047941] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1047941), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14941 ^ _780205) ^ [_1047970] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1047970) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14943 ^ _780205) ^ [_1047996] : [-(c_Finite__Set_Ofun__left__comm__idem(_1047996, tc_fun(_1047996, tc_HOL_Obool), c_Set_Oinsert(_1047996)))], (14945 ^ _780205) ^ [_1048046, _1048048, _1048050, _1048052] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1048046, _1048048)), c_Sum__Type_OPlus(_1048046, _1048048, _1048050, _1048052))), 14948 ^ _780205 : [(14949 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048046), _1048050)))], (14951 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048048), _1048052)))]]], (14953 ^ _780205) ^ [_1048189, _1048191, _1048193, _1048195] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1048189, _1048191)), c_Sum__Type_OPlus(_1048189, _1048191, _1048193, _1048195)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048189), _1048193)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048191), _1048195))], (14963 ^ _780205) ^ [_1048368, _1048370, _1048372, _1048374] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048368), _1048370)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048372), _1048374)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1048368, _1048372)), c_Sum__Type_OPlus(_1048368, _1048372, _1048370, _1048374))))], (14973 ^ _780205) ^ [_1048545, _1048547, _1048549, _1048551] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1048545, _1048547)), c_Sum__Type_OPlus(_1048545, _1048547, _1048549, _1048551))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048545), _1048549)))], (14979 ^ _780205) ^ [_1048658, _1048660, _1048662, _1048664] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1048658, _1048660)), c_Sum__Type_OPlus(_1048658, _1048660, _1048662, _1048664))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048660), _1048664)))], (14995 ^ _780205) ^ [_1048991, _1048993, _1048995, _1048997] : [14996 ^ _780205 : [(14997 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048991), _1048993)))], (14999 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048995), _1048997)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1048991, _1048995)), c_Sum__Type_OPlus(_1048991, _1048995, _1048993, _1048997)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14985 ^ _780205) ^ [_1048786, _1048788, _1048790, _1048792] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1048786, _1048790)), c_Sum__Type_OPlus(_1048786, _1048790, _1048788, _1048792)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1048786), _1048788)), hAPP(c_Finite__Set_Ocard(_1048790), _1048792))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048786), _1048788)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048790), _1048792))], (15003 ^ _780205) ^ [_1049091] : [class_Lattices_Oab__semigroup__idem__mult(_1049091), -(c_Finite__Set_Ofun__left__comm__idem(_1049091, _1049091, c_Groups_Otimes__class_Otimes(_1049091)))], (15009 ^ _780205) ^ [_1049170] : [class_Lattices_Osemilattice__sup(_1049170), -(c_Finite__Set_Ofun__left__comm__idem(_1049170, _1049170, c_Lattices_Osemilattice__sup__class_Osup(_1049170)))], (15015 ^ _780205) ^ [_1049249] : [class_Lattices_Osemilattice__inf(_1049249), -(c_Finite__Set_Ofun__left__comm__idem(_1049249, _1049249, c_Lattices_Osemilattice__inf__class_Oinf(_1049249)))], (15021 ^ _780205) ^ [_1049328] : [class_Orderings_Olinorder(_1049328), -(c_Finite__Set_Ofun__left__comm__idem(_1049328, _1049328, c_Orderings_Oord__class_Omin(_1049328)))], (15027 ^ _780205) ^ [_1049407, _1049409] : [class_Groups_Olinordered__ab__group__add(_1049407), 15030 ^ _780205 : [(15031 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049407), c_Groups_Ozero__class_Ozero(_1049407)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049407), _1049409), _1049409))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049407), c_Groups_Ozero__class_Ozero(_1049407)), _1049409)))], (15037 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049407), c_Groups_Ozero__class_Ozero(_1049407)), _1049409)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049407), c_Groups_Ozero__class_Ozero(_1049407)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049407), _1049409), _1049409))))]]], (15043 ^ _780205) ^ [_1049690, _1049692] : [class_Groups_Olinordered__ab__group__add(_1049690), 15046 ^ _780205 : [(15047 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049690), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049690), _1049692), _1049692)), c_Groups_Ozero__class_Ozero(_1049690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049690), _1049692), c_Groups_Ozero__class_Ozero(_1049690))))], (15053 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049690), _1049692), c_Groups_Ozero__class_Ozero(_1049690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049690), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049690), _1049692), _1049692)), c_Groups_Ozero__class_Ozero(_1049690))))]]], (15059 ^ _780205) ^ [_1049973, _1049975, _1049977] : [class_Groups_Oordered__comm__monoid__add(_1049973), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049973), c_Groups_Ozero__class_Ozero(_1049973)), _1049975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049973), c_Groups_Ozero__class_Ozero(_1049973)), _1049977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049973), c_Groups_Ozero__class_Ozero(_1049973)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049973), _1049975), _1049977))))], (15073 ^ _780205) ^ [_1050228, _1050230, _1050232] : [class_Groups_Oordered__comm__monoid__add(_1050228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050228), c_Groups_Ozero__class_Ozero(_1050228)), _1050230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050228), c_Groups_Ozero__class_Ozero(_1050228)), _1050232)), 15084 ^ _780205 : [(15085 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050228), _1050230), _1050232) = c_Groups_Ozero__class_Ozero(_1050228), 15088 ^ _780205 : [(15089 ^ _780205) ^ [] : [-(_1050230 = c_Groups_Ozero__class_Ozero(_1050228))], (15091 ^ _780205) ^ [] : [-(_1050232 = c_Groups_Ozero__class_Ozero(_1050228))]]], (15093 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050228), _1050230), _1050232) = c_Groups_Ozero__class_Ozero(_1050228)), _1050230 = c_Groups_Ozero__class_Ozero(_1050228), _1050232 = c_Groups_Ozero__class_Ozero(_1050228)]]], (15103 ^ _780205) ^ [_1050699, _1050701, _1050703, _1050705] : [class_Groups_Oordered__comm__monoid__add(_1050699), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050699), c_Groups_Ozero__class_Ozero(_1050699)), _1050701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050699), _1050703), _1050705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050699), _1050703), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050699), _1050701), _1050705))))], (15117 ^ _780205) ^ [_1050952, _1050954, _1050956, _1050958] : [class_Groups_Oordered__comm__monoid__add(_1050952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050952), c_Groups_Ozero__class_Ozero(_1050952)), _1050954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050952), _1050956), _1050958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050952), _1050956), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050952), _1050958), _1050954))))], (15131 ^ _780205) ^ [_1051205, _1051207, _1051209] : [class_Groups_Oordered__comm__monoid__add(_1051205), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051205), _1051207), c_Groups_Ozero__class_Ozero(_1051205))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051205), _1051209), c_Groups_Ozero__class_Ozero(_1051205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051205), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051205), _1051207), _1051209)), c_Groups_Ozero__class_Ozero(_1051205))))], (15145 ^ _780205) ^ [_1051460, _1051462] : [class_Rings_Olinordered__ring(_1051460), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051460), c_Groups_Ozero__class_Ozero(_1051460)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051460), _1051462), _1051462))))], (15151 ^ _780205) ^ [_1051569, _1051571, _1051573] : [class_Rings_Olinordered__ring__strict(_1051569), 15154 ^ _780205 : [(15155 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051569), c_Groups_Ozero__class_Ozero(_1051569)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051569), _1051571), _1051573))), 15160 ^ _780205 : [(15161 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051569), c_Groups_Ozero__class_Ozero(_1051569)), _1051571)))], (15163 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051569), c_Groups_Ozero__class_Ozero(_1051569)), _1051573)))]], 15164 ^ _780205 : [(15165 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051569), _1051571), c_Groups_Ozero__class_Ozero(_1051569))))], (15167 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051569), _1051573), c_Groups_Ozero__class_Ozero(_1051569))))]]], (15169 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051569), c_Groups_Ozero__class_Ozero(_1051569)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051569), _1051571), _1051573)))), 15170 ^ _780205 : [(15171 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051569), c_Groups_Ozero__class_Ozero(_1051569)), _1051571)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051569), c_Groups_Ozero__class_Ozero(_1051569)), _1051573))], (15177 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051569), _1051571), c_Groups_Ozero__class_Ozero(_1051569))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051569), _1051573), c_Groups_Ozero__class_Ozero(_1051569)))]]]]], (15185 ^ _780205) ^ [_1052159, _1052161, _1052163] : [class_Rings_Olinordered__ring__strict(_1052159), 15188 ^ _780205 : [(15189 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052159), _1052161), _1052163)), c_Groups_Ozero__class_Ozero(_1052159))), 15194 ^ _780205 : [(15195 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052159), c_Groups_Ozero__class_Ozero(_1052159)), _1052161)))], (15197 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052159), _1052163), c_Groups_Ozero__class_Ozero(_1052159))))]], 15198 ^ _780205 : [(15199 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052159), _1052161), c_Groups_Ozero__class_Ozero(_1052159))))], (15201 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052159), c_Groups_Ozero__class_Ozero(_1052159)), _1052163)))]]], (15203 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052159), _1052161), _1052163)), c_Groups_Ozero__class_Ozero(_1052159)))), 15204 ^ _780205 : [(15205 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052159), c_Groups_Ozero__class_Ozero(_1052159)), _1052161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052159), _1052163), c_Groups_Ozero__class_Ozero(_1052159)))], (15211 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052159), _1052161), c_Groups_Ozero__class_Ozero(_1052159))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052159), c_Groups_Ozero__class_Ozero(_1052159)), _1052163))]]]]], (15219 ^ _780205) ^ [_1052749, _1052751, _1052753] : [class_Rings_Oordered__cancel__semiring(_1052749), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052749), c_Groups_Ozero__class_Ozero(_1052749)), _1052751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052749), c_Groups_Ozero__class_Ozero(_1052749)), _1052753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052749), c_Groups_Ozero__class_Ozero(_1052749)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052749), _1052751), _1052753))))], (15233 ^ _780205) ^ [_1053004, _1053006, _1053008] : [class_Rings_Oordered__cancel__semiring(_1053004), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053004), c_Groups_Ozero__class_Ozero(_1053004)), _1053006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053004), _1053008), c_Groups_Ozero__class_Ozero(_1053004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053004), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053004), _1053006), _1053008)), c_Groups_Ozero__class_Ozero(_1053004))))], (15247 ^ _780205) ^ [_1053259, _1053261, _1053263] : [class_Rings_Oordered__cancel__semiring(_1053259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053259), c_Groups_Ozero__class_Ozero(_1053259)), _1053261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053259), _1053263), c_Groups_Ozero__class_Ozero(_1053259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053259), _1053263), _1053261)), c_Groups_Ozero__class_Ozero(_1053259))))], (15261 ^ _780205) ^ [_1053514, _1053516, _1053518] : [class_Rings_Oordered__cancel__semiring(_1053514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053514), _1053516), c_Groups_Ozero__class_Ozero(_1053514))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053514), c_Groups_Ozero__class_Ozero(_1053514)), _1053518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053514), _1053516), _1053518)), c_Groups_Ozero__class_Ozero(_1053514))))], (15275 ^ _780205) ^ [_1053769, _1053771, _1053773] : [class_Rings_Oordered__ring(_1053769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053769), _1053771), c_Groups_Ozero__class_Ozero(_1053769))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053769), _1053773), c_Groups_Ozero__class_Ozero(_1053769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053769), c_Groups_Ozero__class_Ozero(_1053769)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053769), _1053771), _1053773))))], (15289 ^ _780205) ^ [_1054024, _1054026, _1054028, _1054030] : [class_Rings_Oordered__semiring(_1054024), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054024), _1054026), _1054028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054024), c_Groups_Ozero__class_Ozero(_1054024)), _1054030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054024), _1054026), _1054030)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054024), _1054028), _1054030))))], (15303 ^ _780205) ^ [_1054293, _1054295, _1054297, _1054299] : [class_Rings_Oordered__semiring(_1054293), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054293), _1054295), _1054297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054293), c_Groups_Ozero__class_Ozero(_1054293)), _1054299)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054293), _1054299), _1054295)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054293), _1054299), _1054297))))], (15317 ^ _780205) ^ [_1054562, _1054564, _1054566, _1054568] : [class_Rings_Oordered__comm__semiring(_1054562), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054562), _1054564), _1054566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054562), c_Groups_Ozero__class_Ozero(_1054562)), _1054568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054562), _1054568), _1054564)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054562), _1054568), _1054566))))], (15331 ^ _780205) ^ [_1054831, _1054833, _1054835, _1054837] : [class_Rings_Oordered__ring(_1054831), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054831), _1054833), _1054835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054831), _1054837), c_Groups_Ozero__class_Ozero(_1054831))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054831), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054831), _1054835), _1054837)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054831), _1054833), _1054837))))], (15345 ^ _780205) ^ [_1055100, _1055102, _1055104, _1055106] : [class_Rings_Oordered__ring(_1055100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055100), _1055102), _1055104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055100), _1055106), c_Groups_Ozero__class_Ozero(_1055100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055100), _1055106), _1055104)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055100), _1055106), _1055102))))], (15359 ^ _780205) ^ [_1055369, _1055371, _1055373, _1055375, _1055377] : [class_Rings_Oordered__semiring(_1055369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055369), _1055371), _1055373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055369), _1055375), _1055377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055369), c_Groups_Ozero__class_Ozero(_1055369)), _1055371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055369), c_Groups_Ozero__class_Ozero(_1055369)), _1055375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055369), _1055371), _1055375)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055369), _1055373), _1055377))))], (15381 ^ _780205) ^ [_1055792, _1055794, _1055796, _1055798, _1055800] : [class_Rings_Oordered__semiring(_1055792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055792), _1055794), _1055796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055792), _1055798), _1055800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055792), c_Groups_Ozero__class_Ozero(_1055792)), _1055796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055792), c_Groups_Ozero__class_Ozero(_1055792)), _1055798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055792), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055792), _1055794), _1055798)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055792), _1055796), _1055800))))], (15403 ^ _780205) ^ [_1056215, _1056217, _1056219] : [class_Rings_Oordered__ring(_1056215), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056215), c_Groups_Ozero__class_Ozero(_1056215)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056215), _1056217), _1056219)))), 15408 ^ _780205 : [(15409 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056215), c_Groups_Ozero__class_Ozero(_1056215)), _1056217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056215), c_Groups_Ozero__class_Ozero(_1056215)), _1056219))], (15415 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056215), _1056217), c_Groups_Ozero__class_Ozero(_1056215))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056215), _1056219), c_Groups_Ozero__class_Ozero(_1056215)))]]], (15423 ^ _780205) ^ [_1056591, _1056593, _1056595] : [class_Rings_Oordered__cancel__semiring(_1056591), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056591), _1056593), _1056595)), c_Groups_Ozero__class_Ozero(_1056591)))), 15428 ^ _780205 : [(15429 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056591), c_Groups_Ozero__class_Ozero(_1056591)), _1056593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056591), _1056595), c_Groups_Ozero__class_Ozero(_1056591)))], (15435 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056591), _1056593), c_Groups_Ozero__class_Ozero(_1056591))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056591), c_Groups_Ozero__class_Ozero(_1056591)), _1056595))]]], (15443 ^ _780205) ^ [_1056967, _1056969, _1056971, _1056973] : [class_Rings_Olinordered__semidom(_1056967), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056967), c_Groups_Ozero__class_Ozero(_1056967)), _1056969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056967), _1056971), _1056973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056967), _1056971), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056967), _1056969), _1056973))))], (15457 ^ _780205) ^ [_1057220, _1057222] : [class_Groups_Olinordered__ab__group__add(_1057220), 15460 ^ _780205 : [(15461 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057220), c_Groups_Ozero__class_Ozero(_1057220)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057220), _1057222), _1057222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057220), c_Groups_Ozero__class_Ozero(_1057220)), _1057222)))], (15467 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057220), c_Groups_Ozero__class_Ozero(_1057220)), _1057222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057220), c_Groups_Ozero__class_Ozero(_1057220)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057220), _1057222), _1057222))))]]], (15473 ^ _780205) ^ [_1057503, _1057505] : [class_Groups_Olinordered__ab__group__add(_1057503), 15476 ^ _780205 : [(15477 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057503), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057503), _1057505), _1057505)), c_Groups_Ozero__class_Ozero(_1057503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057503), _1057505), c_Groups_Ozero__class_Ozero(_1057503))))], (15483 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057503), _1057505), c_Groups_Ozero__class_Ozero(_1057503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057503), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057503), _1057505), _1057505)), c_Groups_Ozero__class_Ozero(_1057503))))]]], (15489 ^ _780205) ^ [_1057786, _1057788, _1057790] : [class_Groups_Oordered__comm__monoid__add(_1057786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057786), c_Groups_Ozero__class_Ozero(_1057786)), _1057788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057786), c_Groups_Ozero__class_Ozero(_1057786)), _1057790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057786), c_Groups_Ozero__class_Ozero(_1057786)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057786), _1057788), _1057790))))], (15503 ^ _780205) ^ [_1058041, _1058043, _1058045] : [class_Groups_Oordered__comm__monoid__add(_1058041), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058041), _1058043), c_Groups_Ozero__class_Ozero(_1058041))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058041), _1058045), c_Groups_Ozero__class_Ozero(_1058041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058041), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058041), _1058043), _1058045)), c_Groups_Ozero__class_Ozero(_1058041))))], (15517 ^ _780205) ^ [_1058296, _1058298, _1058300, _1058302] : [class_Rings_Olinordered__ring__strict(_1058296), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058296), _1058298), _1058300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058296), _1058302), c_Groups_Ozero__class_Ozero(_1058296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058296), _1058302), _1058300)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058296), _1058302), _1058298))))], (15531 ^ _780205) ^ [_1058565, _1058567, _1058569, _1058571] : [class_Rings_Olinordered__ring__strict(_1058565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058565), _1058567), _1058569)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058565), _1058571), c_Groups_Ozero__class_Ozero(_1058565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058565), _1058569), _1058571)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058565), _1058567), _1058571))))], (15545 ^ _780205) ^ [_1058834, _1058836, _1058838, _1058840] : [class_Rings_Olinordered__comm__semiring__strict(_1058834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058834), _1058836), _1058838)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058834), c_Groups_Ozero__class_Ozero(_1058834)), _1058840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058834), _1058840), _1058836)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058834), _1058840), _1058838))))], (15559 ^ _780205) ^ [_1059103, _1059105, _1059107, _1059109] : [class_Rings_Olinordered__semiring__strict(_1059103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059103), _1059105), _1059107)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059103), c_Groups_Ozero__class_Ozero(_1059103)), _1059109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059103), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059103), _1059109), _1059105)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059103), _1059109), _1059107))))], (15573 ^ _780205) ^ [_1059372, _1059374, _1059376, _1059378] : [class_Rings_Olinordered__semiring__strict(_1059372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059372), _1059374), _1059376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059372), c_Groups_Ozero__class_Ozero(_1059372)), _1059378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059372), _1059374), _1059378)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059372), _1059376), _1059378))))], (15587 ^ _780205) ^ [_1059641, _1059643, _1059645] : [class_Rings_Olinordered__ring__strict(_1059641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059641), _1059643), c_Groups_Ozero__class_Ozero(_1059641))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059641), _1059645), c_Groups_Ozero__class_Ozero(_1059641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059641), c_Groups_Ozero__class_Ozero(_1059641)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059641), _1059643), _1059645))))], (15601 ^ _780205) ^ [_1059896, _1059898, _1059900] : [class_Rings_Olinordered__semiring__strict(_1059896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059896), _1059898), c_Groups_Ozero__class_Ozero(_1059896))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059896), c_Groups_Ozero__class_Ozero(_1059896)), _1059900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059896), _1059898), _1059900)), c_Groups_Ozero__class_Ozero(_1059896))))], (15615 ^ _780205) ^ [_1060151, _1060153, _1060155, _1060157] : [class_Rings_Olinordered__ring__strict(_1060151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060151), _1060153), c_Groups_Ozero__class_Ozero(_1060151))), 15622 ^ _780205 : [(15623 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060151), _1060153), _1060155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060151), _1060153), _1060157))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060151), _1060157), _1060155)))], (15629 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060151), _1060157), _1060155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060151), _1060153), _1060155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060151), _1060153), _1060157))))]]], (15635 ^ _780205) ^ [_1060532, _1060534, _1060536] : [class_Rings_Olinordered__semiring__strict(_1060532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060532), c_Groups_Ozero__class_Ozero(_1060532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060532), _1060534), _1060536))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060532), c_Groups_Ozero__class_Ozero(_1060532)), _1060536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060532), c_Groups_Ozero__class_Ozero(_1060532)), _1060534)))], (15649 ^ _780205) ^ [_1060787, _1060789, _1060791] : [class_Rings_Olinordered__semiring__strict(_1060787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060787), c_Groups_Ozero__class_Ozero(_1060787)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060787), _1060789), _1060791))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060787), c_Groups_Ozero__class_Ozero(_1060787)), _1060789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060787), c_Groups_Ozero__class_Ozero(_1060787)), _1060791)))], (15663 ^ _780205) ^ [_1061042, _1061044, _1061046] : [class_Rings_Olinordered__semiring__strict(_1061042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061042), c_Groups_Ozero__class_Ozero(_1061042)), _1061044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061042), _1061046), c_Groups_Ozero__class_Ozero(_1061042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061042), _1061046), _1061044)), c_Groups_Ozero__class_Ozero(_1061042))))], (15677 ^ _780205) ^ [_1061297, _1061299, _1061301] : [class_Rings_Olinordered__semiring__strict(_1061297), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061297), c_Groups_Ozero__class_Ozero(_1061297)), _1061299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061297), _1061301), c_Groups_Ozero__class_Ozero(_1061297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061297), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061297), _1061299), _1061301)), c_Groups_Ozero__class_Ozero(_1061297))))], (15691 ^ _780205) ^ [_1061552, _1061554, _1061556] : [class_Rings_Olinordered__semiring__strict(_1061552), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061552), c_Groups_Ozero__class_Ozero(_1061552)), _1061554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061552), c_Groups_Ozero__class_Ozero(_1061552)), _1061556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061552), c_Groups_Ozero__class_Ozero(_1061552)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061552), _1061554), _1061556))))], (15705 ^ _780205) ^ [_1061807, _1061809, _1061811, _1061813] : [class_Rings_Olinordered__ring__strict(_1061807), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061807), c_Groups_Ozero__class_Ozero(_1061807)), _1061809)), 15712 ^ _780205 : [(15713 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061807), _1061809), _1061811)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061807), _1061809), _1061813))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061807), _1061811), _1061813)))], (15719 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061807), _1061811), _1061813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061807), _1061809), _1061811)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061807), _1061809), _1061813))))]]], (15725 ^ _780205) ^ [_1062188, _1062190, _1062192, _1062194] : [class_Rings_Olinordered__ring__strict(_1062188), 15728 ^ _780205 : [(15729 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062188), _1062190), _1062192)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062188), _1062190), _1062194))), 15734 ^ _780205 : [(15735 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062188), c_Groups_Ozero__class_Ozero(_1062188)), _1062190)))], (15737 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062188), _1062192), _1062194)))]], 15738 ^ _780205 : [(15739 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062188), _1062190), c_Groups_Ozero__class_Ozero(_1062188))))], (15741 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062188), _1062194), _1062192)))]]], (15743 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062188), _1062190), _1062192)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062188), _1062190), _1062194)))), 15744 ^ _780205 : [(15745 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062188), c_Groups_Ozero__class_Ozero(_1062188)), _1062190)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062188), _1062192), _1062194))], (15751 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062188), _1062190), c_Groups_Ozero__class_Ozero(_1062188))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062188), _1062194), _1062192))]]]]], (15759 ^ _780205) ^ [_1062794, _1062796, _1062798, _1062800] : [class_Rings_Olinordered__ring__strict(_1062794), 15762 ^ _780205 : [(15763 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062794), _1062796), _1062798)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062794), _1062800), _1062798))), 15768 ^ _780205 : [(15769 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062794), c_Groups_Ozero__class_Ozero(_1062794)), _1062798)))], (15771 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062794), _1062796), _1062800)))]], 15772 ^ _780205 : [(15773 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062794), _1062798), c_Groups_Ozero__class_Ozero(_1062794))))], (15775 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062794), _1062800), _1062796)))]]], (15777 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062794), _1062796), _1062798)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062794), _1062800), _1062798)))), 15778 ^ _780205 : [(15779 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062794), c_Groups_Ozero__class_Ozero(_1062794)), _1062798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062794), _1062796), _1062800))], (15785 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062794), _1062798), c_Groups_Ozero__class_Ozero(_1062794))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1062794), _1062800), _1062796))]]]]], (15793 ^ _780205) ^ [_1063400, _1063402] : [class_Rings_Olinordered__ring(_1063400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063400), _1063402), _1063402)), c_Groups_Ozero__class_Ozero(_1063400)))], (15799 ^ _780205) ^ [_1063510, _1063512, _1063514] : [class_Groups_Oordered__ab__group__add(_1063510), 15802 ^ _780205 : [(15803 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063510), _1063512), _1063514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063510), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1063510), _1063512), _1063514)), c_Groups_Ozero__class_Ozero(_1063510))))], (15809 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063510), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1063510), _1063512), _1063514)), c_Groups_Ozero__class_Ozero(_1063510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1063510), _1063512), _1063514)))]]], (15815 ^ _780205) ^ [_1063793, _1063795, _1063797] : [class_Groups_Oordered__ab__group__add(_1063793), 15818 ^ _780205 : [(15819 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063793), _1063795), _1063797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063793), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1063793), _1063795), _1063797)), c_Groups_Ozero__class_Ozero(_1063793))))], (15825 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063793), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1063793), _1063795), _1063797)), c_Groups_Ozero__class_Ozero(_1063793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063793), _1063795), _1063797)))]]], (15831 ^ _780205) ^ [_1064076, _1064078, _1064080] : [class_Rings_Olinordered__ring__strict(_1064076), 15834 ^ _780205 : [(15835 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064076), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064076), _1064078), _1064078)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064076), _1064080), _1064080)) = c_Groups_Ozero__class_Ozero(_1064076), 15838 ^ _780205 : [(15839 ^ _780205) ^ [] : [-(_1064078 = c_Groups_Ozero__class_Ozero(_1064076))], (15841 ^ _780205) ^ [] : [-(_1064080 = c_Groups_Ozero__class_Ozero(_1064076))]]], (15843 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064076), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064076), _1064078), _1064078)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064076), _1064080), _1064080)) = c_Groups_Ozero__class_Ozero(_1064076)), _1064078 = c_Groups_Ozero__class_Ozero(_1064076), _1064080 = c_Groups_Ozero__class_Ozero(_1064076)]]], (15853 ^ _780205) ^ [_1064451, _1064453, _1064455, _1064457, _1064459, _1064461] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1064451), -(_1064453 = c_Groups_Ozero__class_Ozero(_1064451)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064451), _1064455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064451), _1064453), _1064459)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064451), _1064457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064451), _1064453), _1064461)), _1064455 = _1064457, -(_1064459 = _1064461)], (15871 ^ _780205) ^ [_1064789] : [class_Rings_Olinordered__semidom(_1064789), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064789), c_Groups_Oone__class_Oone(_1064789)), c_Groups_Ozero__class_Ozero(_1064789)))], (15877 ^ _780205) ^ [_1064885] : [class_Rings_Olinordered__semidom(_1064885), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064885), c_Groups_Ozero__class_Ozero(_1064885)), c_Groups_Oone__class_Oone(_1064885))))], (15883 ^ _780205) ^ [_1064980] : [class_Rings_Olinordered__semidom(_1064980), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064980), c_Groups_Ozero__class_Ozero(_1064980)), c_Groups_Oone__class_Oone(_1064980))))], (15889 ^ _780205) ^ [_1065075] : [class_Rings_Olinordered__semidom(_1065075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065075), c_Groups_Oone__class_Oone(_1065075)), c_Groups_Ozero__class_Ozero(_1065075)))], (15895 ^ _780205) ^ [_1065171, _1065173, _1065175] : [class_Groups_Ocomm__monoid__add(_1065171), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1065173, _1065171), _1065175), c_Orderings_Obot__class_Obot(tc_fun(_1065173, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1065171))], (15901 ^ _780205) ^ [_1065280, _1065282, _1065284] : [class_Groups_Ocomm__monoid__add(_1065280), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1065282, _1065280), _1065284), c_Orderings_Obot__class_Obot(tc_fun(_1065282, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1065280))], (15907 ^ _780205) ^ [_1065389, _1065391, _1065393, _1065395] : [class_Groups_Ocomm__monoid__add(_1065389), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1065391), _1065393))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1065391, _1065389), _1065395), _1065393) = c_Groups_Ozero__class_Ozero(_1065389))], (15917 ^ _780205) ^ [_1065513, _1065515, _1065517, _1065519] : [class_Groups_Ocomm__monoid__add(_1065513), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1065515), _1065517))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1065515, _1065513), _1065519), _1065517) = c_Groups_Ozero__class_Ozero(_1065513))], (15927 ^ _780205) ^ [_1065637, _1065639, _1065641, _1065643] : [class_Rings_Ocomm__semiring__1(_1065637), class_Rings_Ono__zero__divisors(_1065637), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065639), _1065641)), 15938 ^ _780205 : [(15939 ^ _780205) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1065639, _1065637), _1065643), _1065641) = c_Groups_Ozero__class_Ozero(_1065637), 15943 ^ _780205 : [(15944 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1065639), 15942 ^ [_1065637, _1065639, _1065641, _1065643]), _1065641)))], (15946 ^ _780205) ^ [] : [-(hAPP(_1065643, 15942 ^ [_1065637, _1065639, _1065641, _1065643]) = c_Groups_Ozero__class_Ozero(_1065637))]]], (15948 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1065639, _1065637), _1065643), _1065641) = c_Groups_Ozero__class_Ozero(_1065637)), 15949 ^ _780205 : [(15950 ^ _780205) ^ [_1066015] : [hBOOL(hAPP(hAPP(c_member(_1065639), _1066015), _1065641)), hAPP(_1065643, _1066015) = c_Groups_Ozero__class_Ozero(_1065637)]]]]], (15958 ^ _780205) ^ [_1066170, _1066172, _1066174, _1066176] : [class_Rings_Ocomm__semiring__1(_1066170), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066172), _1066174)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1066172, _1066170), _1066176), _1066174) = c_Groups_Ozero__class_Ozero(_1066170)), 15967 ^ _780205 : [(15968 ^ _780205) ^ [_1066351] : [hBOOL(hAPP(hAPP(c_member(_1066172), _1066351), _1066174)), hAPP(_1066176, _1066351) = c_Groups_Ozero__class_Ozero(_1066170)]]], (15976 ^ _780205) ^ [_1066515, _1066517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066515), hAPP(c_Nat_OSuc, _1066517))), -(_1066515 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15984 ^ _780205 : [(15985 ^ _780205) ^ [] : [-(_1066515 = hAPP(c_Nat_OSuc, 15983 ^ [_1066515, _1066517]))], (15987 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15983 ^ [_1066515, _1066517]), _1066517)))]]], (15989 ^ _780205) ^ [_1066695, _1066697] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066695), hAPP(c_Nat_OSuc, _1066697)))), 15990 ^ _780205 : [(15991 ^ _780205) ^ [] : [_1066695 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15993 ^ _780205) ^ [_1066783] : [_1066695 = hAPP(c_Nat_OSuc, _1066783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066783), _1066697))]]], (16001 ^ _780205) ^ [_1066929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066929), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1066929 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16007 ^ _780205) ^ [_1067010] : [_1067010 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1067010), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (16013 ^ _780205) ^ [_1067109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1067109)), -(_1067109 = hAPP(c_Nat_OSuc, 16016 ^ [_1067109]))], (16020 ^ _780205) ^ [_1067200] : [16021 ^ _780205 : [(16022 ^ _780205) ^ [_1067242] : [_1067200 = hAPP(c_Nat_OSuc, _1067242)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1067200)))], (16026 ^ _780205) ^ [_1067315, _1067317] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067315), _1067317), 16031 ^ _780205 : [(16032 ^ _780205) ^ [] : [-(_1067315 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16034 ^ _780205) ^ [] : [-(_1067317 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 16035 ^ _780205 : [(16036 ^ _780205) ^ [] : [-(_1067315 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16038 ^ _780205) ^ [] : [-(_1067317 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (16040 ^ _780205) ^ [_1067499, _1067501] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067499), _1067501)), 16041 ^ _780205 : [(16042 ^ _780205) ^ [] : [_1067499 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1067501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16048 ^ _780205) ^ [] : [_1067499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1067501 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (16056 ^ _780205) ^ [_1067740, _1067742] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067740), _1067742) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 16061 ^ _780205 : [(16062 ^ _780205) ^ [] : [-(_1067740 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16064 ^ _780205) ^ [] : [-(_1067742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 16065 ^ _780205 : [(16066 ^ _780205) ^ [] : [-(_1067740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16068 ^ _780205) ^ [] : [-(_1067742 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (16070 ^ _780205) ^ [_1067924, _1067926] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067924), _1067926) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 16071 ^ _780205 : [(16072 ^ _780205) ^ [] : [_1067924 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1067926 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16078 ^ _780205) ^ [] : [_1067924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1067926 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (16096 ^ _780205) ^ [_1068275, _1068277] : [16097 ^ _780205 : [(16098 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068275))], (16100 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068277))]], -(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), _1068275), _1068277))))], (16086 ^ _780205) ^ [_1068165, _1068167] : [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), _1068165), _1068167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068167)))], (16104 ^ _780205) ^ [_1068416] : [-(hAPP(c_Finite__Set_Ocard(_1068416), c_Orderings_Obot__class_Obot(tc_fun(_1068416, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16106 ^ _780205) ^ [_1068445, _1068447] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1068445), _1068447))), -(hAPP(c_Finite__Set_Ocard(_1068445), _1068447) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16112 ^ _780205) ^ [_1068505, _1068507] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1068505), _1068507) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 16115 ^ _780205 : [(16116 ^ _780205) ^ [] : [-(_1068505 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16118 ^ _780205) ^ [] : [-(_1068507 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (16120 ^ _780205) ^ [_1068616, _1068618] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1068616), _1068618) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1068616 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068618 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16130 ^ _780205) ^ [_1068774, _1068776] : [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), _1068774), _1068776))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068776), _1068774)))], (16136 ^ _780205) ^ [_1068873, _1068875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068875), _1068873)), -(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), _1068873), _1068875))))], (16142 ^ _780205) ^ [_1068978, _1068980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1068980), _1068978)), _1068980)))], (16152 ^ _780205) ^ [_1069152, _1069154] : [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), _1069152), _1069154))), 16155 ^ _780205 : [(16156 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069152)))], (16158 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069154)))]]], (16160 ^ _780205) ^ [_1069275, _1069277] : [-(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), _1069275), _1069277)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069277))], (16170 ^ _780205) ^ [_1069448, _1069450, _1069452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069448), _1069450)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069448), _1069452))), 16173 ^ _780205 : [(16174 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069448)))], (16176 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069450), _1069452)))]]], (16178 ^ _780205) ^ [_1069597, _1069599, _1069601] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069597), _1069599)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069597), _1069601)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069597)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069599), _1069601))], (16188 ^ _780205) ^ [_1069798, _1069800, _1069802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069798), _1069800)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069802), _1069800))), 16191 ^ _780205 : [(16192 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069800)))], (16194 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069798), _1069802)))]]], (16196 ^ _780205) ^ [_1069947, _1069949, _1069951] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069947), _1069949)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069951), _1069949)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069949)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069947), _1069951))], (16206 ^ _780205) ^ [_1070130, _1070132, _1070134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070130), _1070132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1070134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070130), _1070134)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070132), _1070134))))], (16216 ^ _780205) ^ [_1070311, _1070313, _1070315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070311), _1070313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1070315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070315), _1070311)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070315), _1070313))))], (16226 ^ _780205) ^ [_1070492, _1070494, _1070496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1070492)), 16229 ^ _780205 : [(16230 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070492), _1070494)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070492), _1070496))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070494), _1070496)))], (16236 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070494), _1070496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070492), _1070494)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070492), _1070496))))]]], (16242 ^ _780205) ^ [_1070775, _1070777, _1070779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1070775)), 16245 ^ _780205 : [(16246 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070775), _1070777) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070775), _1070779), -(_1070777 = _1070779)], (16252 ^ _780205) ^ [] : [_1070777 = _1070779, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070775), _1070777) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070775), _1070779))]]], (16258 ^ _780205) ^ [_1071028, _1071030] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071028), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1071028), _1071030)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16260 ^ _780205) ^ [_1071065, _1071067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071065), _1071067)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071065), _1071067) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16266 ^ _780205) ^ [_1071179, _1071181] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071179), _1071181) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071179), _1071181)))], (16272 ^ _780205) ^ [_1071274, _1071276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071274), _1071276)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071274), _1071276) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16278 ^ _780205) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16280 ^ _780205) ^ [_1071393, _1071395] : [_1071393 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1071393), _1071395), -(_1071395 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1071393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16290 ^ _780205) ^ [_1071495, _1071497, _1071499] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1071495), _1071497)), 16293 ^ _780205 : [(16304 ^ _780205) ^ [] : [16306 ^ _780205 : [(16307 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071495), 16305 ^ [_1071495, _1071497, _1071499]), _1071497)))], (16309 ^ _780205) ^ [] : [hAPP(_1071499, 16305 ^ [_1071495, _1071497, _1071499]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1071495, tc_Nat_Onat), _1071499), _1071497) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16294 ^ _780205) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1071495, tc_Nat_Onat), _1071499), _1071497) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 16297 ^ _780205 : [(16298 ^ _780205) ^ [_1071657] : [hBOOL(hAPP(hAPP(c_member(_1071495), _1071657), _1071497)), -(hAPP(_1071499, _1071657) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (16313 ^ _780205) ^ [_1071915, _1071917, _1071919] : [class_Groups_Oordered__comm__monoid__add(_1071915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071915), _1071917), c_Groups_Ozero__class_Ozero(_1071915))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071915), _1071919), c_Groups_Ozero__class_Ozero(_1071915))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071915), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1071915), _1071917), _1071919)), c_Groups_Ozero__class_Ozero(_1071915))))], (16327 ^ _780205) ^ [_1072170, _1072172, _1072174] : [class_Groups_Oordered__comm__monoid__add(_1072170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072170), _1072172), c_Groups_Ozero__class_Ozero(_1072170))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072170), _1072174), c_Groups_Ozero__class_Ozero(_1072170))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072170), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072170), _1072172), _1072174)), c_Groups_Ozero__class_Ozero(_1072170))))], (16341 ^ _780205) ^ [_1072425, _1072427, _1072429, _1072431] : [class_Groups_Oordered__comm__monoid__add(_1072425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072425), c_Groups_Ozero__class_Ozero(_1072425)), _1072427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072425), _1072429), _1072431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072425), _1072429), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072425), _1072427), _1072431))))], (16355 ^ _780205) ^ [_1072678, _1072680, _1072682, _1072684] : [class_Groups_Oordered__comm__monoid__add(_1072678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072678), c_Groups_Ozero__class_Ozero(_1072678)), _1072680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072678), _1072682), _1072684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072678), _1072682), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072678), _1072680), _1072684))))], (16369 ^ _780205) ^ [_1072931, _1072933, _1072935] : [class_Groups_Oordered__comm__monoid__add(_1072931), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072931), c_Groups_Ozero__class_Ozero(_1072931)), _1072933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072931), c_Groups_Ozero__class_Ozero(_1072931)), _1072935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072931), c_Groups_Ozero__class_Ozero(_1072931)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072931), _1072933), _1072935))))], (16383 ^ _780205) ^ [_1073186, _1073188, _1073190] : [class_Groups_Oordered__comm__monoid__add(_1073186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073186), c_Groups_Ozero__class_Ozero(_1073186)), _1073188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073186), c_Groups_Ozero__class_Ozero(_1073186)), _1073190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073186), c_Groups_Ozero__class_Ozero(_1073186)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073186), _1073188), _1073190))))], (16397 ^ _780205) ^ [_1073441, _1073443, _1073445, _1073447] : [class_Rings_Olinordered__ring__strict(_1073441), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073441), c_Groups_Ozero__class_Ozero(_1073441)), _1073443)), 16404 ^ _780205 : [(16405 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073441), _1073443), _1073445)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073441), _1073443), _1073447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073441), _1073445), _1073447)))], (16411 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073441), _1073445), _1073447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073441), _1073443), _1073445)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073441), _1073443), _1073447))))]]], (16417 ^ _780205) ^ [_1073822, _1073824, _1073826, _1073828] : [class_Rings_Olinordered__ring__strict(_1073822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073822), _1073824), c_Groups_Ozero__class_Ozero(_1073822))), 16424 ^ _780205 : [(16425 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073822), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073822), _1073824), _1073826)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073822), _1073824), _1073828))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073822), _1073828), _1073826)))], (16431 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073822), _1073828), _1073826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073822), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073822), _1073824), _1073826)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073822), _1073824), _1073828))))]]], (16437 ^ _780205) ^ [_1074203, _1074205, _1074207, _1074209, _1074211] : [class_Rings_Olinordered__semiring__strict(_1074203), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074203), _1074205), _1074207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074203), _1074209), _1074211)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074203), c_Groups_Ozero__class_Ozero(_1074203)), _1074207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074203), c_Groups_Ozero__class_Ozero(_1074203)), _1074209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074203), _1074205), _1074209)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074203), _1074207), _1074211))))], (16459 ^ _780205) ^ [_1074626, _1074628, _1074630, _1074632, _1074634] : [class_Rings_Olinordered__semiring__strict(_1074626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074626), _1074628), _1074630)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074626), _1074632), _1074634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074626), c_Groups_Ozero__class_Ozero(_1074626)), _1074628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074626), c_Groups_Ozero__class_Ozero(_1074626)), _1074632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074626), _1074628), _1074632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074626), _1074630), _1074634))))], (16481 ^ _780205) ^ [_1075049, _1075051, _1075053, _1075055, _1075057] : [class_Rings_Olinordered__semiring__strict(_1075049), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075049), _1075051), _1075053)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075049), _1075055), _1075057)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075049), c_Groups_Ozero__class_Ozero(_1075049)), _1075051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075049), c_Groups_Ozero__class_Ozero(_1075049)), _1075055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075049), _1075051), _1075055)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075049), _1075053), _1075057))))], (16503 ^ _780205) ^ [_1075472, _1075474, _1075476, _1075478, _1075480] : [class_Rings_Olinordered__semiring__strict(_1075472), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075472), _1075474), 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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))), _1081625)))]]], (16843 ^ _780205) ^ [_1081746, _1081748] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1081746), _1081748)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1081746)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1081748))], (16853 ^ _780205) ^ [_1081901, _1081903, _1081905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1081901)), 16856 ^ _780205 : [(16857 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), 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_1082381)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082379), _1082383))))], (16869 ^ _780205) ^ [_1082202, _1082204, _1082206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082202), _1082204)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082202), _1082206))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1082204), _1082206)))], (16897 ^ _780205) ^ [_1082736, _1082738, _1082740] : [16898 ^ _780205 : [(16899 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082738)))], (16901 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1082736), _1082740))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082736), _1082738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082740), _1082738))))], (16887 ^ _780205) ^ [_1082559, _1082561, _1082563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082559), _1082561)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1082563), _1082561))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1082559), _1082563)))], (16905 ^ _780205) ^ [_1082898, _1082900, _1082902] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1082898), _1082900)), 16908 ^ _780205 : [(16909 ^ _780205) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082898, tc_Nat_Onat), _1082902), _1082900) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 16913 ^ _780205 : [(16914 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1082898), 16912 ^ [_1082898, _1082900, _1082902]), _1082900)))], (16916 ^ _780205) ^ [] : [-(hAPP(_1082902, 16912 ^ [_1082898, _1082900, _1082902]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16918 ^ _780205) ^ [_1083218] : [hBOOL(hAPP(hAPP(c_member(_1082898), _1083218), _1082900)), -(16912 ^ [_1082898, _1082900, _1082902] = _1083218), -(hAPP(_1082902, _1083218) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (16928 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082898, tc_Nat_Onat), _1082902), _1082900) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 16929 ^ _780205 : [(16930 ^ _780205) ^ [_1083379] : [hBOOL(hAPP(hAPP(c_member(_1082898), _1083379), _1082900)), hAPP(_1082902, _1083379) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 16938 ^ _780205 : [(16939 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1082898), 16937 ^ [_1082898, _1082900, _1082902, _1083379]), _1082900)))], (16941 ^ _780205) ^ [] : [_1083379 = 16937 ^ [_1082898, _1082900, _1082902, _1083379]], (16943 ^ _780205) ^ [] : [hAPP(_1082902, 16937 ^ [_1082898, _1082900, _1082902, _1083379]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (16947 ^ _780205) ^ [_1083732, _1083734, _1083736] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1083732), _1083734)), 16950 ^ _780205 : [(16951 ^ _780205) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083732, tc_Nat_Onat), _1083736), _1083734) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 16955 ^ _780205 : [(16956 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1083732), 16954 ^ [_1083732, _1083734, _1083736]), _1083734)))], (16958 ^ _780205) ^ [] : [-(hAPP(_1083736, 16954 ^ [_1083732, _1083734, _1083736]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (16960 ^ _780205) ^ [_1084052] : [hBOOL(hAPP(hAPP(c_member(_1083732), _1084052), _1083734)), -(16954 ^ [_1083732, _1083734, _1083736] = _1084052), -(hAPP(_1083736, _1084052) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (16970 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083732, tc_Nat_Onat), _1083736), _1083734) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 16971 ^ _780205 : [(16972 ^ _780205) ^ [_1084213] : [hBOOL(hAPP(hAPP(c_member(_1083732), _1084213), _1083734)), hAPP(_1083736, _1084213) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 16980 ^ _780205 : [(16981 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1083732), 16979 ^ [_1083732, _1083734, _1083736, _1084213]), _1083734)))], (16983 ^ _780205) ^ [] : [_1084213 = 16979 ^ [_1083732, _1083734, _1083736, _1084213]], (16985 ^ _780205) ^ [] : [hAPP(_1083736, 16979 ^ [_1083732, _1083734, _1083736, _1084213]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (16989 ^ _780205) ^ [_1084566, _1084568, _1084570] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1084566), _1084568)), 16992 ^ _780205 : [(17003 ^ _780205) ^ [] : [17005 ^ _780205 : [(17006 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1084566), 17004 ^ [_1084566, _1084568, _1084570]), _1084568)))], (17008 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1084570, 17004 ^ [_1084566, _1084568, _1084570])))]], -(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(_1084566, tc_Nat_Onat), _1084570), _1084568))))], (16993 ^ _780205) ^ [] : [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(_1084566, tc_Nat_Onat), _1084570), _1084568))), 16996 ^ _780205 : [(16997 ^ _780205) ^ [_1084734] : [hBOOL(hAPP(hAPP(c_member(_1084566), _1084734), _1084568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1084570, _1084734))))]]]]], (17012 ^ _780205) ^ [_1085002, _1085004, _1085006, _1085008, _1085010, _1085012] : [class_Rings_Olinordered__semiring__1(_1085002), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085002), _1085004), _1085006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085002), _1085008), _1085006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085002), c_Groups_Ozero__class_Ozero(_1085002)), _1085010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085002), c_Groups_Ozero__class_Ozero(_1085002)), _1085012)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085002), _1085010), _1085012) = c_Groups_Oone__class_Oone(_1085002), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085002), _1085010), _1085004)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085002), _1085012), _1085008))), _1085006)))], (17038 ^ _780205) ^ [_1085546, _1085548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1085546), _1085548))), 17041 ^ _780205 : [(17042 ^ _780205) ^ [] : [_1085548 = c_Orderings_Obot__class_Obot(tc_fun(_1085546, tc_HOL_Obool))], (17044 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1085546), _1085548)))]]], (17046 ^ _780205) ^ [_1085687, _1085689] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1085687), _1085689)))), -(_1085689 = c_Orderings_Obot__class_Obot(tc_fun(_1085687, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085687), _1085689))], (17056 ^ _780205) ^ [_1085853, _1085855, _1085857, _1085859] : [class_Groups_Ocomm__monoid__add(_1085853), 17059 ^ _780205 : [(17060 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1085855), _1085857)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085855, _1085853), _1085859), _1085857) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1085853, _1085855, c_Groups_Oplus__class_Oplus(_1085853)), _1085859), c_Groups_Ozero__class_Ozero(_1085853)), _1085857))], (17066 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1085855), _1085857))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085855, _1085853), _1085859), _1085857) = c_Groups_Ozero__class_Ozero(_1085853))]]], (17072 ^ _780205) ^ [_1086125, _1086127, _1086129, _1086131] : [class_Groups_Ocomm__monoid__add(_1086125), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086127), _1086129)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1086127, _1086125), _1086131), _1086129) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086125, _1086127, c_Groups_Oplus__class_Oplus(_1086125)), _1086131), c_Groups_Ozero__class_Ozero(_1086125)), _1086129))], (17082 ^ _780205) ^ [_1086320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1086320)), -(_1086320 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1086320), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (17088 ^ _780205) ^ [_1086417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1086417)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1086417), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1086417)], (17094 ^ _780205) ^ [_1086523, _1086525] : [_1086523 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086523), _1086525) = _1086525)], (17100 ^ _780205) ^ [_1086606, _1086608] : [-(_1086606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086606), _1086608) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1086606), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1086608)))], (17106 ^ _780205) ^ [_1086674, _1086676] : [_1086674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086674), _1086676) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17112 ^ _780205) ^ [_1086757, _1086759] : [-(_1086757 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086757), _1086759) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1086757), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1086759)))], (17118 ^ _780205) ^ [_1086819, _1086821] : [class_Rings_Olinordered__idom(_1086819), 17121 ^ _780205 : [(17122 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086819), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1086819), _1086821), _1086821)), c_Groups_Ozero__class_Ozero(_1086819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086819), _1086821), c_Groups_Ozero__class_Ozero(_1086819))))], (17128 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086819), _1086821), c_Groups_Ozero__class_Ozero(_1086819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086819), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1086819), _1086821), _1086821)), c_Groups_Ozero__class_Ozero(_1086819))))]]], (17134 ^ _780205) ^ [_1087102, _1087104, _1087106, _1087108, _1087110] : [class_Groups_Oordered__comm__monoid__add(_1087102), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087104), _1087106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1087104, tc_HOL_Obool)), _1087108), _1087106)), 17148 ^ _780205 : [(17149 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1087104), 17147 ^ [_1087102, _1087104, _1087106, _1087108, _1087110]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1087104, tc_HOL_Obool)), _1087106), _1087108))))], (17151 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087102), c_Groups_Ozero__class_Ozero(_1087102)), hAPP(_1087110, 17147 ^ [_1087102, _1087104, _1087106, _1087108, _1087110])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087102), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087104, _1087102), _1087110), _1087108)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087104, _1087102), _1087110), _1087106))))], (17155 ^ _780205) ^ [_1087588, _1087590, _1087592, _1087594, _1087596] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_1087588, _1087590, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1087588), _1087592), _1087594), _1087596)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17157 ^ _780205) ^ [_1087655, _1087657, _1087659, _1087661] : [c_Sum__Type_OPlus(_1087655, _1087657, _1087659, _1087661) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1087655, _1087657), tc_HOL_Obool)), 17160 ^ _780205 : [(17161 ^ _780205) ^ [] : [-(_1087659 = c_Orderings_Obot__class_Obot(tc_fun(_1087655, tc_HOL_Obool)))], (17163 ^ _780205) ^ [] : [-(_1087661 = c_Orderings_Obot__class_Obot(tc_fun(_1087657, tc_HOL_Obool)))]]], (17165 ^ _780205) ^ [_1087804, _1087806, _1087808, _1087810] : [-(c_Sum__Type_OPlus(_1087804, _1087806, _1087808, _1087810) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1087804, _1087806), tc_HOL_Obool))), _1087808 = c_Orderings_Obot__class_Obot(tc_fun(_1087804, tc_HOL_Obool)), _1087810 = c_Orderings_Obot__class_Obot(tc_fun(_1087806, tc_HOL_Obool))], (17175 ^ _780205) ^ [_1087989, _1087991, _1087993] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1087989), _1087991)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087989), _1087993)), 17185 ^ _780205 : [(17186 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1087989), 17184 ^ [_1087989, _1087991, _1087993]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1087989, tc_HOL_Obool)), _1087991), _1087993))))], (17188 ^ _780205) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1087989), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1087989, tc_HOL_Obool)), _1087991), _1087993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1087989), _1087991)), hAPP(c_Finite__Set_Ocard(_1087989), _1087993)))], (17192 ^ _780205) ^ [_1088333, _1088335, _1088337, _1088339, _1088341] : [class_Groups_Ocomm__monoid__add(_1088333), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088335), _1088337)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088335), _1088339)), 17206 ^ _780205 : [(17207 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1088335), 17205 ^ [_1088333, _1088335, _1088337, _1088339, _1088341]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088335, tc_HOL_Obool)), _1088337), _1088339))))], (17209 ^ _780205) ^ [] : [hAPP(_1088341, 17205 ^ [_1088333, _1088335, _1088337, _1088339, _1088341]) = c_Groups_Ozero__class_Ozero(_1088333)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088335, _1088333), _1088341), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088335, tc_HOL_Obool)), _1088337), _1088339)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088333), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088335, _1088333), _1088341), _1088337)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088335, _1088333), _1088341), _1088339)))], (17213 ^ _780205) ^ [_1088828, _1088830, _1088832, _1088834, _1088836] : [class_Groups_Ocomm__monoid__add(_1088828), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088830), _1088832)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088830), _1088834)), 17227 ^ _780205 : [(17228 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1088830), 17226 ^ [_1088828, _1088830, _1088832, _1088834, _1088836]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088830, tc_HOL_Obool)), _1088832), _1088834))))], (17230 ^ _780205) ^ [] : [hAPP(_1088836, 17226 ^ [_1088828, _1088830, _1088832, _1088834, _1088836]) = c_Groups_Ozero__class_Ozero(_1088828)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088830, _1088828), _1088836), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088830, tc_HOL_Obool)), _1088832), _1088834)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088828), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088830, _1088828), _1088836), _1088832)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088830, _1088828), _1088836), _1088834)))], (17234 ^ _780205) ^ [_1089323, _1089325, _1089327, _1089329, _1089331] : [class_Groups_Ocomm__monoid__add(_1089323), class_Groups_Oordered__ab__semigroup__add(_1089323), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089325), _1089327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1089325, tc_HOL_Obool)), _1089329), _1089327)), 17252 ^ _780205 : [(17253 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1089325), 17251 ^ [_1089323, _1089325, _1089327, _1089329, _1089331]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1089325, tc_HOL_Obool)), _1089327), _1089329))))], (17255 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089323), c_Groups_Ozero__class_Ozero(_1089323)), hAPP(_1089331, 17251 ^ [_1089323, _1089325, _1089327, _1089329, _1089331])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089323), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1089325, _1089323), _1089331), _1089329)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1089325, _1089323), _1089331), _1089327))))], (17259 ^ _780205) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17261 ^ _780205) ^ [_1089885, _1089887] : [class_Groups_Olinordered__ab__group__add(_1089885), 17264 ^ _780205 : [(17265 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089885), _1089887), _1089887) = c_Groups_Ozero__class_Ozero(_1089885), -(_1089887 = c_Groups_Ozero__class_Ozero(_1089885))], (17271 ^ _780205) ^ [] : [_1089887 = c_Groups_Ozero__class_Ozero(_1089885), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089885), _1089887), _1089887) = c_Groups_Ozero__class_Ozero(_1089885))]]], (17277 ^ _780205) ^ [_1090126, _1090128, _1090130, _1090132] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_1090126)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1090126), _1090128), _1090130), _1090132)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17279 ^ _780205) ^ [_1090191, _1090193, _1090195] : [hAPP(c_Finite__Set_Ocard(_1090191), _1090193) = hAPP(c_Nat_OSuc, _1090195), 17284 ^ _780205 : [(17285 ^ _780205) ^ [] : [-(_1090193 = hAPP(hAPP(c_Set_Oinsert(_1090191), 17282 ^ [_1090191, _1090193, _1090195]), 17283 ^ [_1090191, _1090193, _1090195]))], (17287 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1090191), 17282 ^ [_1090191, _1090193, _1090195]), 17283 ^ [_1090191, _1090193, _1090195]))], (17289 ^ _780205) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1090191), 17283 ^ [_1090191, _1090193, _1090195]) = _1090195)], (17291 ^ _780205) ^ [] : [_1090195 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(17283 ^ [_1090191, _1090193, _1090195] = c_Orderings_Obot__class_Obot(tc_fun(_1090191, tc_HOL_Obool)))]]], (17297 ^ _780205) ^ [_1090609, _1090611, _1090613] : [-(hAPP(c_Finite__Set_Ocard(_1090609), _1090611) = hAPP(c_Nat_OSuc, _1090613)), 17298 ^ _780205 : [(17299 ^ _780205) ^ [_1090709, _1090711] : [_1090611 = hAPP(hAPP(c_Set_Oinsert(_1090609), _1090711), _1090709), -(hBOOL(hAPP(hAPP(c_member(_1090609), _1090711), _1090709))), hAPP(c_Finite__Set_Ocard(_1090609), _1090709) = _1090613, 17310 ^ _780205 : [(17311 ^ _780205) ^ [] : [-(_1090613 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17313 ^ _780205) ^ [] : [_1090709 = c_Orderings_Obot__class_Obot(tc_fun(_1090609, tc_HOL_Obool))]]]]], (17317 ^ _780205) ^ [_1091031, _1091033] : [class_Rings_Olinordered__idom(_1091031), hBOOL(hAPP(hAPP(c_member(_1091031), _1091033), c_Int_Oring__1__class_OInts(_1091031))), 17324 ^ _780205 : [(17325 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091031), c_Groups_Oone__class_Oone(_1091031)), _1091033)), _1091033)), c_Groups_Ozero__class_Ozero(_1091031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091031), _1091033), c_Groups_Ozero__class_Ozero(_1091031))))], (17331 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091031), _1091033), c_Groups_Ozero__class_Ozero(_1091031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091031), c_Groups_Oone__class_Oone(_1091031)), _1091033)), _1091033)), c_Groups_Ozero__class_Ozero(_1091031))))]]], (17337 ^ _780205) ^ [_1091414, _1091416] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_1091414, _1091416)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1091414)), c_Com_Ocom_Ocom__size(_1091416))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17339 ^ _780205) ^ [_1091460, _1091462] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_1091460, _1091462)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1091460)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1091462))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (17341 ^ _780205) ^ [_1091509, _1091511, _1091513, _1091515, _1091517] : [class_Fields_Ofield(_1091509), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091511), _1091513)), -(hAPP(_1091515, _1091517) = c_Groups_Ozero__class_Ozero(_1091509)), 17352 ^ _780205 : [(17353 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1091511), _1091517), _1091513)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1091511, _1091509), _1091515), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1091511, tc_HOL_Obool)), _1091513), hAPP(hAPP(c_Set_Oinsert(_1091511), _1091517), c_Orderings_Obot__class_Obot(tc_fun(_1091511, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1091509), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1091511, _1091509), _1091515), _1091513)), hAPP(_1091515, _1091517)))], (17359 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1091511), _1091517), _1091513))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1091511, _1091509), _1091515), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1091511, tc_HOL_Obool)), _1091513), hAPP(hAPP(c_Set_Oinsert(_1091511), _1091517), c_Orderings_Obot__class_Obot(tc_fun(_1091511, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1091511, _1091509), _1091515), _1091513))]]], (17365 ^ _780205) ^ [_1092049, _1092051] : [-(hBOOL(hAPP(_1092049, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1092049, _1092051)), 17373 ^ _780205 : [(17374 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17372 ^ [_1092049, _1092051]), _1092051)))], (17382 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1092049, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 17372 ^ [_1092049, _1092051]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (17376 ^ _780205) ^ [_1092287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1092287), 17372 ^ [_1092049, _1092051])), hBOOL(hAPP(_1092049, _1092287))]]], (17384 ^ _780205) ^ [_1092439, _1092441] : [class_Rings_Odivision__ring(_1092439), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1092439), c_Groups_Ozero__class_Ozero(_1092439)), _1092441) = c_Groups_Ozero__class_Ozero(_1092439))], (17390 ^ _780205) ^ [_1092538, _1092540] : [class_Rings_Odivision__ring__inverse__zero(_1092538), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1092538), _1092540), c_Groups_Ozero__class_Ozero(_1092538)) = c_Groups_Ozero__class_Ozero(_1092538))], (17396 ^ _780205) ^ [_1092637, _1092639, _1092641, _1092643] : [class_Rings_Odivision__ring(_1092637), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1092637), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092637), _1092639), _1092641)), _1092643) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092637), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1092637), _1092639), _1092643)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1092637), _1092641), _1092643)))], (17402 ^ _780205) ^ [_1092796, _1092798, _1092800, _1092802] : [class_Rings_Odivision__ring(_1092796), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092796), _1092798), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1092796), _1092800), _1092802)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1092796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092796), _1092798), _1092800)), _1092802))], (17408 ^ _780205) ^ [_1092939, _1092941, _1092943, _1092945] : [class_Rings_Odivision__ring(_1092939), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1092939), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092939), _1092941), _1092943)), _1092945) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092939), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1092939), _1092941), _1092945)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1092939), _1092943), _1092945)))], (17414 ^ _780205) ^ [_1093098, _1093100] : [class_Rings_Odivision__ring(_1093098), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1093098), _1093100), c_Groups_Oone__class_Oone(_1093098)) = _1093100)], (17420 ^ _780205) ^ [_1093193, _1093195, _1093197, _1093199] : [class_Rings_Odivision__ring(_1093193), -(_1093195 = c_Groups_Ozero__class_Ozero(_1093193)), 17427 ^ _780205 : [(17428 ^ _780205) ^ [] : [_1093197 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1093193), _1093199), _1093195), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093193), _1093197), _1093195) = _1093199)], (17434 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093193), _1093197), _1093195) = _1093199, -(_1093197 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1093193), _1093199), _1093195))]]], (17440 ^ _780205) ^ [_1093521, _1093523, _1093525, _1093527] : [class_Rings_Odivision__ring(_1093521), -(_1093523 = c_Groups_Ozero__class_Ozero(_1093521)), 17447 ^ _780205 : [(17448 ^ _780205) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1093521), _1093525), _1093523) = _1093527, -(_1093525 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093521), _1093527), _1093523))], (17454 ^ _780205) ^ [] : [_1093525 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093521), _1093527), _1093523), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1093521), _1093525), _1093523) = _1093527)]]], (17460 ^ _780205) ^ [_1093849, _1093851, _1093853, _1093855] : [class_Rings_Odivision__ring(_1093849), -(_1093851 = c_Groups_Ozero__class_Ozero(_1093849)), _1093853 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093849), _1093855), _1093851), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1093849), _1093853), _1093851) = _1093855)], (17474 ^ _780205) ^ [_1094079, _1094081, _1094083, _1094085] : [class_Rings_Odivision__ring(_1094079), -(_1094081 = c_Groups_Ozero__class_Ozero(_1094079)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094079), _1094083), _1094081) = _1094085, -(_1094083 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1094079), _1094085), _1094081))], (17488 ^ _780205) ^ [_1094309, _1094311] : [class_Rings_Odivision__ring__inverse__zero(_1094309), 17491 ^ _780205 : [(17492 ^ _780205) ^ [] : [_1094311 = c_Groups_Ozero__class_Ozero(_1094309), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1094309), _1094311), _1094311) = c_Groups_Ozero__class_Ozero(_1094309))], (17498 ^ _780205) ^ [] : [-(_1094311 = c_Groups_Ozero__class_Ozero(_1094309)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1094309), _1094311), _1094311) = c_Groups_Oone__class_Oone(_1094309))]]], (17504 ^ _780205) ^ [_1094531, _1094533] : [class_Rings_Odivision__ring(_1094531), -(_1094533 = c_Groups_Ozero__class_Ozero(_1094531)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1094531), _1094533), _1094533) = c_Groups_Oone__class_Oone(_1094531))], (17514 ^ _780205) ^ [_1094645, _1094647, _1094649] : [class_Rings_Odivision__ring(_1094645), -(_1094647 = c_Groups_Ozero__class_Ozero(_1094645)), 17521 ^ _780205 : [(17522 ^ _780205) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1094645), _1094649), _1094647) = c_Groups_Oone__class_Oone(_1094645), -(_1094649 = _1094647)], (17528 ^ _780205) ^ [] : [_1094649 = _1094647, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1094645), _1094649), _1094647) = c_Groups_Oone__class_Oone(_1094645))]]], (17534 ^ _780205) ^ [_1094947] : [class_Rings_Oring__1(_1094947), -(hBOOL(hAPP(hAPP(c_member(_1094947), c_Groups_Ozero__class_Ozero(_1094947)), c_Int_Oring__1__class_OInts(_1094947))))], (17540 ^ _780205) ^ [_1095042, _1095044, _1095046] : [class_Rings_Oring__1(_1095042), hBOOL(hAPP(hAPP(c_member(_1095042), _1095044), c_Int_Oring__1__class_OInts(_1095042))), hBOOL(hAPP(hAPP(c_member(_1095042), _1095046), c_Int_Oring__1__class_OInts(_1095042))), -(hBOOL(hAPP(hAPP(c_member(_1095042), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095042), _1095044), _1095046)), c_Int_Oring__1__class_OInts(_1095042))))], (17554 ^ _780205) ^ [_1095297, _1095299, _1095301] : [class_Rings_Oring__1(_1095297), hBOOL(hAPP(hAPP(c_member(_1095297), _1095299), c_Int_Oring__1__class_OInts(_1095297))), hBOOL(hAPP(hAPP(c_member(_1095297), _1095301), c_Int_Oring__1__class_OInts(_1095297))), -(hBOOL(hAPP(hAPP(c_member(_1095297), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095297), _1095299), _1095301)), c_Int_Oring__1__class_OInts(_1095297))))], (17568 ^ _780205) ^ [_1095552, _1095554, _1095556] : [class_Rings_Oring__1(_1095552), hBOOL(hAPP(hAPP(c_member(_1095552), _1095554), c_Int_Oring__1__class_OInts(_1095552))), hBOOL(hAPP(hAPP(c_member(_1095552), _1095556), c_Int_Oring__1__class_OInts(_1095552))), -(hBOOL(hAPP(hAPP(c_member(_1095552), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1095552), _1095554), _1095556)), c_Int_Oring__1__class_OInts(_1095552))))], (17582 ^ _780205) ^ [_1095807] : [class_Rings_Oring__1(_1095807), -(hBOOL(hAPP(hAPP(c_member(_1095807), c_Groups_Oone__class_Oone(_1095807)), c_Int_Oring__1__class_OInts(_1095807))))], (17588 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17590 ^ _780205) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17592 ^ _780205) ^ [_1095938, _1095940] : [class_Int_Oring__char__0(_1095938), hBOOL(hAPP(hAPP(c_member(_1095938), _1095940), c_Int_Oring__1__class_OInts(_1095938))), 17599 ^ _780205 : [(17600 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095938), _1095940), _1095940) = c_Groups_Ozero__class_Ozero(_1095938), -(_1095940 = c_Groups_Ozero__class_Ozero(_1095938))], (17606 ^ _780205) ^ [] : [_1095940 = c_Groups_Ozero__class_Ozero(_1095938), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095938), _1095940), _1095940) = c_Groups_Ozero__class_Ozero(_1095938))]]], (17612 ^ _780205) ^ [_1096249, _1096251] : [class_Int_Oring__char__0(_1096249), hBOOL(hAPP(hAPP(c_member(_1096249), _1096251), c_Int_Oring__1__class_OInts(_1096249))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096249), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096249), c_Groups_Oone__class_Oone(_1096249)), _1096251)), _1096251) = c_Groups_Ozero__class_Ozero(_1096249)], (17622 ^ _780205) ^ [_1096435, _1096437, _1096439, _1096441] : [class_Fields_Olinordered__field__inverse__zero(_1096435), 17625 ^ _780205 : [(17652 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096435), _1096437), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1096435), _1096439), _1096441)))), 17655 ^ _780205 : [(17656 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096435), c_Groups_Ozero__class_Ozero(_1096435)), _1096441)))], (17658 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096435), _1096437), _1096441)), _1096439))]], 17659 ^ _780205 : [(17660 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096435), c_Groups_Ozero__class_Ozero(_1096435)), _1096441))], (17662 ^ _780205) ^ [] : [17663 ^ _780205 : [(17664 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096435), _1096441), c_Groups_Ozero__class_Ozero(_1096435))))], (17666 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096435), _1096439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096435), _1096437), _1096441)))]], 17667 ^ _780205 : [(17668 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096435), _1096441), c_Groups_Ozero__class_Ozero(_1096435)))], (17670 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096435), _1096437), c_Groups_Ozero__class_Ozero(_1096435)))]]]]], (17626 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096435), _1096437), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1096435), _1096439), _1096441))), 17629 ^ _780205 : [(17630 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096435), c_Groups_Ozero__class_Ozero(_1096435)), _1096441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096435), _1096437), _1096441)), _1096439)))], (17636 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096435), c_Groups_Ozero__class_Ozero(_1096435)), _1096441))), 17639 ^ _780205 : [(17640 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096435), _1096441), c_Groups_Ozero__class_Ozero(_1096435))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096435), _1096439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096435), _1096437), _1096441))))], (17646 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096435), _1096441), c_Groups_Ozero__class_Ozero(_1096435)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096435), _1096437), c_Groups_Ozero__class_Ozero(_1096435))))]]]]]]], (17674 ^ _780205) ^ [_1097388, _1097390, _1097392, _1097394] : [class_Fields_Olinordered__field__inverse__zero(_1097388), 17677 ^ _780205 : [(17704 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097388), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1097388), _1097390), _1097392)), _1097394))), 17707 ^ _780205 : [(17708 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097388), c_Groups_Ozero__class_Ozero(_1097388)), _1097392)))], (17710 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097388), _1097390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097388), _1097394), _1097392)))]], 17711 ^ _780205 : [(17712 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097388), c_Groups_Ozero__class_Ozero(_1097388)), _1097392))], (17714 ^ _780205) ^ [] : [17715 ^ _780205 : [(17716 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097388), _1097392), c_Groups_Ozero__class_Ozero(_1097388))))], (17718 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097388), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097388), _1097394), _1097392)), _1097390))]], 17719 ^ _780205 : [(17720 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097388), _1097392), c_Groups_Ozero__class_Ozero(_1097388)))], (17722 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097388), c_Groups_Ozero__class_Ozero(_1097388)), _1097394))]]]]], (17678 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097388), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1097388), _1097390), _1097392)), _1097394)), 17681 ^ _780205 : [(17682 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097388), c_Groups_Ozero__class_Ozero(_1097388)), _1097392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097388), _1097390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097388), _1097394), _1097392))))], (17688 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097388), c_Groups_Ozero__class_Ozero(_1097388)), _1097392))), 17691 ^ _780205 : [(17692 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097388), _1097392), c_Groups_Ozero__class_Ozero(_1097388))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097388), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097388), _1097394), _1097392)), _1097390)))], (17698 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097388), _1097392), c_Groups_Ozero__class_Ozero(_1097388)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097388), c_Groups_Ozero__class_Ozero(_1097388)), _1097394)))]]]]]]], (17726 ^ _780205) ^ [_1098341, _1098343, _1098345, _1098347] : [class_Fields_Olinordered__field(_1098341), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098341), c_Groups_Ozero__class_Ozero(_1098341)), _1098343)), 17733 ^ _780205 : [(17734 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098341), _1098345), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1098341), _1098347), _1098343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098341), _1098345), _1098343)), _1098347)))], (17740 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098341), _1098345), _1098343)), _1098347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098341), _1098345), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1098341), _1098347), _1098343))))]]], (17746 ^ _780205) ^ [_1098722, _1098724, _1098726, _1098728] : [class_Fields_Olinordered__field(_1098722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098722), c_Groups_Ozero__class_Ozero(_1098722)), _1098724)), 17753 ^ _780205 : [(17754 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098722), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1098722), _1098726), _1098724)), _1098728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098722), _1098726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098722), _1098728), _1098724))))], (17760 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098722), _1098726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098722), _1098728), _1098724))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098722), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1098722), _1098726), _1098724)), _1098728)))]]], (17766 ^ _780205) ^ [_1099103, _1099105, _1099107, _1099109] : [class_Fields_Olinordered__field(_1099103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099103), c_Groups_Ozero__class_Ozero(_1099103)), _1099105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099103), _1099107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099103), _1099109), _1099105))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099103), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099103), _1099107), _1099105)), _1099109)))], (17780 ^ _780205) ^ [_1099372, _1099374, _1099376, _1099378] : [class_Fields_Olinordered__field(_1099372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099372), c_Groups_Ozero__class_Ozero(_1099372)), _1099374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099372), _1099376), _1099374)), _1099378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099372), _1099376), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099372), _1099378), _1099374))))], (17794 ^ _780205) ^ [_1099641, _1099643, _1099645, _1099647] : [class_Fields_Olinordered__field(_1099641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099641), _1099643), c_Groups_Ozero__class_Ozero(_1099641))), 17801 ^ _780205 : [(17802 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099641), _1099645), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099641), _1099647), _1099643))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099641), _1099647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099641), _1099645), _1099643))))], (17808 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099641), _1099647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099641), _1099645), _1099643))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099641), _1099645), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099641), _1099647), _1099643))))]]], (17814 ^ _780205) ^ [_1100022, _1100024, _1100026, _1100028, _1100030] : [class_Fields_Ofield__inverse__zero(_1100022), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100022), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100022), _1100024), _1100026)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100022), _1100028), _1100030)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100022), _1100024), _1100028)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100022), _1100026), _1100030)))], (17820 ^ _780205) ^ [_1100199, _1100201, _1100203] : [class_Fields_Olinordered__field__inverse__zero(_1100199), 17823 ^ _780205 : [(17824 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100199), c_Groups_Ozero__class_Ozero(_1100199)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100199), _1100201), _1100203))), 17829 ^ _780205 : [(17830 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100199), c_Groups_Ozero__class_Ozero(_1100199)), _1100201)))], (17832 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100199), c_Groups_Ozero__class_Ozero(_1100199)), _1100203)))]], 17833 ^ _780205 : [(17834 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100199), _1100201), c_Groups_Ozero__class_Ozero(_1100199))))], (17836 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100199), _1100203), c_Groups_Ozero__class_Ozero(_1100199))))]]], (17838 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100199), c_Groups_Ozero__class_Ozero(_1100199)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100199), _1100201), _1100203)))), 17839 ^ _780205 : [(17840 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100199), c_Groups_Ozero__class_Ozero(_1100199)), _1100201)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100199), c_Groups_Ozero__class_Ozero(_1100199)), _1100203))], (17846 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100199), _1100201), c_Groups_Ozero__class_Ozero(_1100199))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100199), _1100203), c_Groups_Ozero__class_Ozero(_1100199)))]]]]], (17854 ^ _780205) ^ [_1100789, _1100791, _1100793] : [class_Fields_Olinordered__field__inverse__zero(_1100789), 17857 ^ _780205 : [(17858 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100789), _1100791), _1100793)), c_Groups_Ozero__class_Ozero(_1100789))), 17863 ^ _780205 : [(17864 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), c_Groups_Ozero__class_Ozero(_1100789)), _1100791)))], (17866 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), _1100793), c_Groups_Ozero__class_Ozero(_1100789))))]], 17867 ^ _780205 : [(17868 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), _1100791), c_Groups_Ozero__class_Ozero(_1100789))))], (17870 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), c_Groups_Ozero__class_Ozero(_1100789)), _1100793)))]]], (17872 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100789), _1100791), _1100793)), c_Groups_Ozero__class_Ozero(_1100789)))), 17873 ^ _780205 : [(17874 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), c_Groups_Ozero__class_Ozero(_1100789)), _1100791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), _1100793), c_Groups_Ozero__class_Ozero(_1100789)))], (17880 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), _1100791), c_Groups_Ozero__class_Ozero(_1100789))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), c_Groups_Ozero__class_Ozero(_1100789)), _1100793))]]]]], (17888 ^ _780205) ^ [_1101379, _1101381, _1101383, _1101385] : [class_Fields_Olinordered__field__inverse__zero(_1101379), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101379), _1101381), _1101383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101379), c_Groups_Ozero__class_Ozero(_1101379)), _1101385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101379), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101379), _1101381), _1101385)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101379), _1101383), _1101385))))], (17902 ^ _780205) ^ [_1101648, _1101650, _1101652, _1101654] : [class_Fields_Olinordered__field__inverse__zero(_1101648), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101648), _1101650), _1101652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101648), _1101654), c_Groups_Ozero__class_Ozero(_1101648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101648), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101648), _1101652), _1101654)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101648), _1101650), _1101654))))], (17916 ^ _780205) ^ [_1101917, _1101919, _1101921, _1101923] : [class_Fields_Olinordered__field(_1101917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101917), _1101919), _1101921)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101917), _1101923), c_Groups_Ozero__class_Ozero(_1101917))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101917), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101917), _1101921), _1101923)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101917), _1101919), _1101923))))], (17930 ^ _780205) ^ [_1102186, _1102188, _1102190, _1102192] : [class_Fields_Olinordered__field(_1102186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102186), _1102188), _1102190)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102186), c_Groups_Ozero__class_Ozero(_1102186)), _1102192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102186), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102186), _1102188), _1102192)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102186), _1102190), _1102192))))], (17944 ^ _780205) ^ [_1102455, _1102457, _1102459] : [class_Fields_Olinordered__field(_1102455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102455), _1102457), c_Groups_Ozero__class_Ozero(_1102455))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102455), _1102459), c_Groups_Ozero__class_Ozero(_1102455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102455), c_Groups_Ozero__class_Ozero(_1102455)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102455), _1102457), _1102459))))], (17958 ^ _780205) ^ [_1102710, _1102712, _1102714] : [class_Fields_Olinordered__field(_1102710), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102710), _1102712), c_Groups_Ozero__class_Ozero(_1102710))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102710), c_Groups_Ozero__class_Ozero(_1102710)), _1102714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102710), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102710), _1102712), _1102714)), c_Groups_Ozero__class_Ozero(_1102710))))], (17972 ^ _780205) ^ [_1102965, _1102967, _1102969] : [class_Fields_Olinordered__field(_1102965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102965), c_Groups_Ozero__class_Ozero(_1102965)), _1102967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102965), _1102969), c_Groups_Ozero__class_Ozero(_1102965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102965), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102965), _1102967), _1102969)), c_Groups_Ozero__class_Ozero(_1102965))))], (17986 ^ _780205) ^ [_1103220, _1103222, _1103224] : [class_Fields_Olinordered__field(_1103220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103220), c_Groups_Ozero__class_Ozero(_1103220)), _1103222)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103220), c_Groups_Ozero__class_Ozero(_1103220)), _1103224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103220), c_Groups_Ozero__class_Ozero(_1103220)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1103220), _1103222), _1103224))))], (18000 ^ _780205) ^ [_1103475, _1103477, _1103479] : [class_Fields_Olinordered__field__inverse__zero(_1103475), 18003 ^ _780205 : [(18004 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103475), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1103475), _1103477), _1103479)), c_Groups_Ozero__class_Ozero(_1103475))), 18009 ^ _780205 : [(18010 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103475), c_Groups_Ozero__class_Ozero(_1103475)), _1103477)))], (18012 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103475), _1103479), c_Groups_Ozero__class_Ozero(_1103475))))]], 18013 ^ _780205 : [(18014 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103475), _1103477), c_Groups_Ozero__class_Ozero(_1103475))))], (18016 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103475), c_Groups_Ozero__class_Ozero(_1103475)), _1103479)))]]], (18018 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103475), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1103475), _1103477), _1103479)), c_Groups_Ozero__class_Ozero(_1103475)))), 18019 ^ _780205 : [(18020 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103475), c_Groups_Ozero__class_Ozero(_1103475)), _1103477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103475), _1103479), c_Groups_Ozero__class_Ozero(_1103475)))], (18026 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103475), _1103477), c_Groups_Ozero__class_Ozero(_1103475))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103475), c_Groups_Ozero__class_Ozero(_1103475)), _1103479))]]]]], (18034 ^ _780205) ^ [_1104065, _1104067, _1104069] : [class_Fields_Olinordered__field__inverse__zero(_1104065), 18037 ^ _780205 : [(18038 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104065), c_Groups_Ozero__class_Ozero(_1104065)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104065), _1104067), _1104069))), 18043 ^ _780205 : [(18044 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104065), c_Groups_Ozero__class_Ozero(_1104065)), _1104067)))], (18046 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104065), c_Groups_Ozero__class_Ozero(_1104065)), _1104069)))]], 18047 ^ _780205 : [(18048 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104065), _1104067), c_Groups_Ozero__class_Ozero(_1104065))))], (18050 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104065), _1104069), c_Groups_Ozero__class_Ozero(_1104065))))]]], (18052 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104065), c_Groups_Ozero__class_Ozero(_1104065)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104065), _1104067), _1104069)))), 18053 ^ _780205 : [(18054 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104065), c_Groups_Ozero__class_Ozero(_1104065)), _1104067)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104065), c_Groups_Ozero__class_Ozero(_1104065)), _1104069))], (18060 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104065), _1104067), c_Groups_Ozero__class_Ozero(_1104065))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104065), _1104069), c_Groups_Ozero__class_Ozero(_1104065)))]]]]], (18068 ^ _780205) ^ [_1104655, _1104657, _1104659, _1104661] : [class_Fields_Ofield__inverse__zero(_1104655), 18071 ^ _780205 : [(18088 ^ _780205) ^ [] : [-(_1104657 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104655), _1104659), _1104661)), 18091 ^ _780205 : [(18092 ^ _780205) ^ [] : [_1104661 = c_Groups_Ozero__class_Ozero(_1104655)], (18094 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104655), _1104657), _1104661) = _1104659]], 18095 ^ _780205 : [(18096 ^ _780205) ^ [] : [-(_1104661 = c_Groups_Ozero__class_Ozero(_1104655))], (18098 ^ _780205) ^ [] : [_1104657 = c_Groups_Ozero__class_Ozero(_1104655)]]], (18072 ^ _780205) ^ [] : [_1104657 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104655), _1104659), _1104661), 18075 ^ _780205 : [(18076 ^ _780205) ^ [] : [-(_1104661 = c_Groups_Ozero__class_Ozero(_1104655)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104655), _1104657), _1104661) = _1104659)], (18082 ^ _780205) ^ [] : [_1104661 = c_Groups_Ozero__class_Ozero(_1104655), -(_1104657 = c_Groups_Ozero__class_Ozero(_1104655))]]]]], (18102 ^ _780205) ^ [_1105149, _1105151, _1105153, _1105155] : [class_Fields_Ofield__inverse__zero(_1105149), 18105 ^ _780205 : [(18122 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105149), _1105151), _1105153) = _1105155), 18125 ^ _780205 : [(18126 ^ _780205) ^ [] : [_1105153 = c_Groups_Ozero__class_Ozero(_1105149)], (18128 ^ _780205) ^ [] : [_1105151 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105149), _1105155), _1105153)]], 18129 ^ _780205 : [(18130 ^ _780205) ^ [] : [-(_1105153 = c_Groups_Ozero__class_Ozero(_1105149))], (18132 ^ _780205) ^ [] : [_1105155 = c_Groups_Ozero__class_Ozero(_1105149)]]], (18106 ^ _780205) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105149), _1105151), _1105153) = _1105155, 18109 ^ _780205 : [(18110 ^ _780205) ^ [] : [-(_1105153 = c_Groups_Ozero__class_Ozero(_1105149)), -(_1105151 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105149), _1105155), _1105153))], (18116 ^ _780205) ^ [] : [_1105153 = c_Groups_Ozero__class_Ozero(_1105149), -(_1105155 = c_Groups_Ozero__class_Ozero(_1105149))]]]]], (18136 ^ _780205) ^ [_1105643, _1105645, _1105647, _1105649] : [class_Fields_Ofield__inverse__zero(_1105643), -(_1105645 = c_Groups_Ozero__class_Ozero(_1105643)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105643), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105643), _1105647), _1105645)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105643), _1105649), _1105645)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105643), _1105647), _1105649))], (18146 ^ _780205) ^ [_1105805, _1105807, _1105809, _1105811] : [class_Fields_Ofield__inverse__zero(_1105805), -(_1105807 = c_Groups_Ozero__class_Ozero(_1105805)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105805), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105805), _1105807), _1105809)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105805), _1105807), _1105811)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105805), _1105809), _1105811))], (18156 ^ _780205) ^ [_1105967, _1105969, _1105971, _1105973, _1105975] : [class_Fields_Ofield(_1105967), -(_1105969 = c_Groups_Ozero__class_Ozero(_1105967)), -(_1105971 = c_Groups_Ozero__class_Ozero(_1105967)), 18167 ^ _780205 : [(18168 ^ _780205) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105967), _1105973), _1105969) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105967), _1105975), _1105971), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105967), _1105973), _1105971) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105967), _1105975), _1105969))], (18174 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105967), _1105973), _1105971) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105967), _1105975), _1105969), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105967), _1105973), _1105969) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105967), _1105975), _1105971))]]], (18180 ^ _780205) ^ [_1106416, _1106418, _1106420] : [class_Fields_Olinordered__field(_1106416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106416), c_Groups_Ozero__class_Ozero(_1106416)), _1106418)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106416), c_Groups_Ozero__class_Ozero(_1106416)), _1106420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106416), c_Groups_Ozero__class_Ozero(_1106416)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106416), _1106418), _1106420))))], (18194 ^ _780205) ^ [_1106671, _1106673, _1106675] : [class_Fields_Olinordered__field(_1106671), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106671), c_Groups_Ozero__class_Ozero(_1106671)), _1106673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106671), _1106675), c_Groups_Ozero__class_Ozero(_1106671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106671), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106671), _1106673), _1106675)), c_Groups_Ozero__class_Ozero(_1106671))))], (18208 ^ _780205) ^ [_1106926, _1106928, _1106930, _1106932, _1106934] : [class_Fields_Olinordered__field(_1106926), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106926), c_Groups_Ozero__class_Ozero(_1106926)), _1106928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106926), _1106928), _1106930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106926), c_Groups_Ozero__class_Ozero(_1106926)), _1106932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106926), _1106932), _1106934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106926), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106926), _1106928), _1106934)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106926), _1106930), _1106932))))], (18230 ^ _780205) ^ [_1107349, _1107351, _1107353, _1107355, _1107357] : [class_Fields_Olinordered__field(_1107349), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107349), c_Groups_Ozero__class_Ozero(_1107349)), _1107351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107349), _1107351), _1107353)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107349), c_Groups_Ozero__class_Ozero(_1107349)), _1107355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107349), _1107355), _1107357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107349), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107349), _1107351), _1107357)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107349), _1107353), _1107355))))], (18252 ^ _780205) ^ [_1107772, _1107774, _1107776, _1107778, _1107780] : [class_Fields_Olinordered__field(_1107772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107772), c_Groups_Ozero__class_Ozero(_1107772)), _1107774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107772), _1107774), _1107776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107772), c_Groups_Ozero__class_Ozero(_1107772)), _1107778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107772), _1107778), _1107780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107772), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107772), _1107774), _1107780)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107772), _1107776), _1107778))))], (18274 ^ _780205) ^ [_1108195, _1108197, _1108199] : [class_Fields_Olinordered__field(_1108195), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108195), _1108197), c_Groups_Ozero__class_Ozero(_1108195))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108195), c_Groups_Ozero__class_Ozero(_1108195)), _1108199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108195), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108195), _1108197), _1108199)), c_Groups_Ozero__class_Ozero(_1108195))))], (18288 ^ _780205) ^ [_1108450, _1108452, _1108454] : [class_Fields_Olinordered__field(_1108450), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108450), _1108452), c_Groups_Ozero__class_Ozero(_1108450))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108450), _1108454), c_Groups_Ozero__class_Ozero(_1108450))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108450), c_Groups_Ozero__class_Ozero(_1108450)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108450), _1108452), _1108454))))], (18302 ^ _780205) ^ [_1108705, _1108707, _1108709, _1108711] : [class_Fields_Olinordered__field(_1108705), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108705), _1108707), _1108709)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108705), _1108711), c_Groups_Ozero__class_Ozero(_1108705))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108705), c_Groups_Ozero__class_Ozero(_1108705)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108705), _1108707), _1108709))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108705), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108705), _1108711), _1108707)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108705), _1108711), _1108709))))], (18320 ^ _780205) ^ [_1109064, _1109066, _1109068, _1109070] : [class_Fields_Olinordered__field(_1109064), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109064), _1109066), _1109068)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109064), c_Groups_Ozero__class_Ozero(_1109064)), _1109070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109064), c_Groups_Ozero__class_Ozero(_1109064)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109064), _1109068), _1109066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109064), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109064), _1109070), _1109068)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109064), _1109070), _1109066))))], (18338 ^ _780205) ^ [_1109423, _1109425, _1109427, _1109429] : [class_Fields_Olinordered__field(_1109423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109423), _1109425), c_Groups_Ozero__class_Ozero(_1109423))), 18345 ^ _780205 : [(18346 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109423), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109423), _1109427), _1109425)), _1109429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109423), _1109429), _1109425)), _1109427)))], (18352 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109423), _1109429), _1109425)), _1109427)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109423), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109423), _1109427), _1109425)), _1109429)))]]], (18358 ^ _780205) ^ [_1109804, _1109806, _1109808, _1109810] : [class_Fields_Olinordered__field(_1109804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109804), _1109806), c_Groups_Ozero__class_Ozero(_1109804))), 18365 ^ _780205 : [(18366 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109804), _1109808), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109804), _1109810), _1109806))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109804), _1109810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109804), _1109808), _1109806))))], (18372 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109804), _1109810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109804), _1109808), _1109806))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109804), _1109808), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109804), _1109810), _1109806))))]]], (18378 ^ _780205) ^ [_1110185, _1110187, _1110189, _1110191] : [class_Fields_Olinordered__field(_1110185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110185), c_Groups_Ozero__class_Ozero(_1110185)), _1110187)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110185), _1110189), _1110187)), _1110191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110185), _1110189), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110185), _1110191), _1110187))))], (18392 ^ _780205) ^ [_1110454, _1110456, _1110458, _1110460] : [class_Fields_Olinordered__field(_1110454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110454), c_Groups_Ozero__class_Ozero(_1110454)), _1110456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110454), _1110458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110454), _1110460), _1110456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110454), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110454), _1110458), _1110456)), _1110460)))], (18406 ^ _780205) ^ [_1110723, _1110725, _1110727, _1110729] : [class_Fields_Olinordered__field(_1110723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110723), c_Groups_Ozero__class_Ozero(_1110723)), _1110725)), 18413 ^ _780205 : [(18414 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110723), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110723), _1110727), _1110725)), _1110729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110723), _1110727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110723), _1110729), _1110725))))], (18420 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110723), _1110727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110723), _1110729), _1110725))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110723), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110723), _1110727), _1110725)), _1110729)))]]], (18426 ^ _780205) ^ [_1111104, _1111106, _1111108, _1111110] : [class_Fields_Olinordered__field(_1111104), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111104), c_Groups_Ozero__class_Ozero(_1111104)), _1111106)), 18433 ^ _780205 : [(18434 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111104), _1111108), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111104), _1111110), _1111106))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1111104), _1111108), _1111106)), _1111110)))], (18440 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1111104), _1111108), _1111106)), _1111110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111104), _1111108), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111104), _1111110), _1111106))))]]], (18446 ^ _780205) ^ [_1111485, _1111487, _1111489, _1111491] : [class_Fields_Olinordered__field__inverse__zero(_1111485), 18449 ^ _780205 : [(18476 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111485), _1111487), _1111489)), _1111491))), 18479 ^ _780205 : [(18480 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), c_Groups_Ozero__class_Ozero(_1111485)), _1111489)))], (18482 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), _1111487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1111485), _1111491), _1111489)))]], 18483 ^ _780205 : [(18484 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), c_Groups_Ozero__class_Ozero(_1111485)), _1111489))], (18486 ^ _780205) ^ [] : [18487 ^ _780205 : [(18488 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), _1111489), c_Groups_Ozero__class_Ozero(_1111485))))], (18490 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1111485), _1111491), _1111489)), _1111487))]], 18491 ^ _780205 : [(18492 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), _1111489), c_Groups_Ozero__class_Ozero(_1111485)))], (18494 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), c_Groups_Ozero__class_Ozero(_1111485)), _1111491))]]]]], (18450 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111485), _1111487), _1111489)), _1111491)), 18453 ^ _780205 : [(18454 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), c_Groups_Ozero__class_Ozero(_1111485)), _1111489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), _1111487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1111485), _1111491), _1111489))))], (18460 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), c_Groups_Ozero__class_Ozero(_1111485)), _1111489))), 18463 ^ _780205 : [(18464 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), _1111489), c_Groups_Ozero__class_Ozero(_1111485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1111485), _1111491), _1111489)), _1111487)))], (18470 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), _1111489), c_Groups_Ozero__class_Ozero(_1111485)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111485), c_Groups_Ozero__class_Ozero(_1111485)), _1111491)))]]]]]]], (18498 ^ _780205) ^ [_1112438, _1112440, _1112442, _1112444] : [class_Fields_Olinordered__field__inverse__zero(_1112438), 18501 ^ _780205 : [(18528 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112440), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112438), _1112442), _1112444)))), 18531 ^ _780205 : [(18532 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), c_Groups_Ozero__class_Ozero(_1112438)), _1112444)))], (18534 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112438), _1112440), _1112444)), _1112442))]], 18535 ^ _780205 : [(18536 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), c_Groups_Ozero__class_Ozero(_1112438)), _1112444))], (18538 ^ _780205) ^ [] : [18539 ^ _780205 : [(18540 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112444), c_Groups_Ozero__class_Ozero(_1112438))))], (18542 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112438), _1112440), _1112444)))]], 18543 ^ _780205 : [(18544 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112444), c_Groups_Ozero__class_Ozero(_1112438)))], (18546 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112440), c_Groups_Ozero__class_Ozero(_1112438)))]]]]], (18502 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112440), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112438), _1112442), _1112444))), 18505 ^ _780205 : [(18506 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), c_Groups_Ozero__class_Ozero(_1112438)), _1112444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112438), _1112440), _1112444)), _1112442)))], (18512 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), c_Groups_Ozero__class_Ozero(_1112438)), _1112444))), 18515 ^ _780205 : [(18516 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112444), c_Groups_Ozero__class_Ozero(_1112438))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112438), _1112440), _1112444))))], (18522 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112444), c_Groups_Ozero__class_Ozero(_1112438)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112440), c_Groups_Ozero__class_Ozero(_1112438))))]]]]]]], (18550 ^ _780205) ^ [_1113391, _1113393, _1113395, _1113397] : [class_Fields_Ofield__inverse__zero(_1113391), -(_1113393 = c_Groups_Ozero__class_Ozero(_1113391)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113391), _1113395), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113391), _1113397), _1113393)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113391), _1113397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113391), _1113395), _1113393))), _1113393))], (18560 ^ _780205) ^ [_1113569, _1113571, _1113573, _1113575] : [class_Fields_Ofield(_1113569), -(_1113571 = c_Groups_Ozero__class_Ozero(_1113569)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113569), _1113573), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113569), _1113575), _1113571)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113569), _1113571), _1113573)), _1113575)), _1113571))], (18570 ^ _780205) ^ [_1113747, _1113749, _1113751, _1113753] : [class_Fields_Ofield__inverse__zero(_1113747), -(_1113749 = c_Groups_Ozero__class_Ozero(_1113747)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113747), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113747), _1113751), _1113749)), _1113753) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113747), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113747), _1113751), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113747), _1113753), _1113749))), _1113749))], (18580 ^ _780205) ^ [_1113925, _1113927, _1113929, _1113931] : [class_Fields_Ofield(_1113925), -(_1113927 = c_Groups_Ozero__class_Ozero(_1113925)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113925), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113925), _1113929), _1113927)), _1113931) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113925), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113925), _1113929), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113925), _1113927), _1113931))), _1113927))], (18590 ^ _780205) ^ [_1114103, _1114105, _1114107, _1114109, _1114111] : [class_Fields_Ofield(_1114103), -(_1114105 = c_Groups_Ozero__class_Ozero(_1114103)), -(_1114107 = c_Groups_Ozero__class_Ozero(_1114103)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114103), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114103), _1114109), _1114105)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114103), _1114111), _1114107)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114103), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114103), _1114109), _1114107)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114103), _1114111), _1114105))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114103), _1114105), _1114107)))], (18604 ^ _780205) ^ [_1114350, _1114352, _1114354, _1114356, _1114358] : [class_Fields_Ofield(_1114350), -(_1114352 = c_Groups_Ozero__class_Ozero(_1114350)), -(_1114354 = c_Groups_Ozero__class_Ozero(_1114350)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1114350), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114350), _1114356), _1114352)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114350), _1114358), _1114354)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114350), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1114350), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114350), _1114356), _1114354)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114350), _1114358), _1114352))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114350), _1114352), _1114354)))], (18618 ^ _780205) ^ [_1114597, _1114599, _1114601, _1114603] : [class_Fields_Ofield(_1114597), -(_1114599 = c_Groups_Ozero__class_Ozero(_1114597)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1114597), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114597), _1114601), _1114599)), _1114603) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114597), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1114597), _1114601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114597), _1114599), _1114603))), _1114599))], (18628 ^ _780205) ^ [_1114775, _1114777, _1114779, _1114781] : [class_Fields_Ofield(_1114775), -(_1114777 = c_Groups_Ozero__class_Ozero(_1114775)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1114775), _1114779), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114775), _1114781), _1114777)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114775), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1114775), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114775), _1114777), _1114779)), _1114781)), _1114777))], (18638 ^ _780205) ^ [_1114953, _1114955, _1114957] : [class_Fields_Olinordered__field(_1114953), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114953), _1114955), _1114957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114953), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114953), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114953), _1114955), _1114957)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114953), c_Groups_Oone__class_Oone(_1114953)), c_Groups_Oone__class_Oone(_1114953)))), _1114957)))], (18648 ^ _780205) ^ [_1115168, _1115170, _1115172] : [class_Fields_Olinordered__field(_1115168), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115168), _1115170), _1115172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115168), _1115170), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115168), _1115170), _1115172)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115168), c_Groups_Oone__class_Oone(_1115168)), c_Groups_Oone__class_Oone(_1115168))))))], (18658 ^ _780205) ^ [_1115383, _1115385, _1115387, _1115389] : [class_Fields_Olinordered__field__inverse__zero(_1115383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115383), _1115385), _1115387)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115383), _1115389), c_Groups_Ozero__class_Ozero(_1115383))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115383), c_Groups_Ozero__class_Ozero(_1115383)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115383), _1115385), _1115387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115383), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115383), _1115389), _1115385)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115383), _1115389), _1115387))))], (18676 ^ _780205) ^ [_1115742, _1115744, _1115746, _1115748] : [class_Fields_Olinordered__field(_1115742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115742), _1115744), _1115746)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115742), c_Groups_Ozero__class_Ozero(_1115742)), _1115748)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115742), c_Groups_Ozero__class_Ozero(_1115742)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115742), _1115746), _1115744))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115742), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115742), _1115748), _1115746)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115742), _1115748), _1115744))))], (18694 ^ _780205) ^ [_1116101, _1116103, _1116105, _1116107] : [class_Fields_Olinordered__field(_1116101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116101), _1116103), c_Groups_Ozero__class_Ozero(_1116101))), 18701 ^ _780205 : [(18702 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116101), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116101), _1116105), _1116103)), _1116107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116101), _1116107), _1116103)), _1116105)))], (18708 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116101), _1116107), _1116103)), _1116105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116101), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116101), _1116105), _1116103)), _1116107)))]]], (18714 ^ _780205) ^ [_1116482, _1116484, _1116486, _1116488, _1116490] : [class_Fields_Ofield(_1116482), hBOOL(hAPP(c_Finite__Set_Ofinite(_1116484), _1116486)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1116484), _1116488)), 18728 ^ _780205 : [(18729 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1116484), 18727 ^ [_1116482, _1116484, _1116486, _1116488, _1116490]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1116484, tc_HOL_Obool)), _1116486), _1116488))))], (18731 ^ _780205) ^ [] : [-(hAPP(_1116490, 18727 ^ [_1116482, _1116484, _1116486, _1116488, _1116490]) = c_Groups_Ozero__class_Ozero(_1116482))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1116484, _1116482), _1116490), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1116484, tc_HOL_Obool)), _1116486), _1116488)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116482), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116482), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1116484, _1116482), _1116490), _1116486)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1116484, _1116482), _1116490), _1116488))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1116484, _1116482), _1116490), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1116484, tc_HOL_Obool)), _1116486), _1116488))))], (18735 ^ _780205) ^ [_1116978, _1116980, _1116982, _1116984, _1116986] : [class_Groups_Ocomm__monoid__add(_1116978), hBOOL(hAPP(c_Finite__Set_Ofinite(_1116980), _1116982)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1116980, tc_HOL_Obool)), _1116984), _1116982)), 18749 ^ _780205 : [(18750 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1116980), 18748 ^ [_1116978, _1116980, _1116982, _1116984, _1116986]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1116980, tc_HOL_Obool)), _1116982), _1116984))))], (18752 ^ _780205) ^ [] : [hAPP(_1116986, 18748 ^ [_1116978, _1116980, _1116982, _1116984, _1116986]) = c_Groups_Ozero__class_Ozero(_1116978)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1116980, _1116978), _1116986), _1116984) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1116980, _1116978), _1116986), _1116982))], (18756 ^ _780205) ^ [_1117429, _1117431, _1117433, _1117435, _1117437] : [class_Groups_Ocomm__monoid__add(_1117429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1117431), _1117433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1117431, tc_HOL_Obool)), _1117435), _1117433)), 18770 ^ _780205 : [(18771 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1117431), 18769 ^ [_1117429, _1117431, _1117433, _1117435, _1117437]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1117431, tc_HOL_Obool)), _1117433), _1117435))))], (18773 ^ _780205) ^ [] : [hAPP(_1117437, 18769 ^ [_1117429, _1117431, _1117433, _1117435, _1117437]) = c_Groups_Ozero__class_Ozero(_1117429)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1117431, _1117429), _1117437), _1117433) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1117431, _1117429), _1117437), _1117435))], (18777 ^ _780205) ^ [_1117880, _1117882, _1117884] : [class_Fields_Olinordered__field__inverse__zero(_1117880), 18783 ^ _780205 : [(18784 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117880), c_Groups_Ozero__class_Ozero(_1117880)), 18782 ^ [_1117880, _1117882, _1117884])))], (18786 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117880), 18782 ^ [_1117880, _1117882, _1117884]), c_Groups_Oone__class_Oone(_1117880))))], (18788 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117880), 18782 ^ [_1117880, _1117882, _1117884]), _1117882)), _1117884))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117880), _1117882), _1117884)))], (18792 ^ _780205) ^ [_1118229, _1118231, _1118233] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1118229), _1118231)), 18798 ^ _780205 : [(18799 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1118229), 18797 ^ [_1118229, _1118231, _1118233]), _1118231)))], (18801 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1118233, 18797 ^ [_1118229, _1118231, _1118233])))]], -(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(_1118229, tc_Nat_Onat), _1118233), _1118231))))], (18805 ^ _780205) ^ [_1118490, _1118492, _1118494, _1118496] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1118490, tc_Nat_Onat), _1118492), _1118494) = hAPP(c_Nat_OSuc, _1118496), 18809 ^ _780205 : [(18810 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1118490), 18808 ^ [_1118490, _1118492, _1118494, _1118496]), _1118494)))], (18812 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1118492, 18808 ^ [_1118490, _1118492, _1118494, _1118496]))))]]], (18814 ^ _780205) ^ [_1118672, _1118674, _1118676] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_1118672, _1118674, _1118676)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1118674)), c_Com_Ocom_Ocom__size(_1118676))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18816 ^ _780205) ^ [_1118748, _1118750, _1118752, _1118754, _1118756, _1118758] : [c_Com_Ocom_OCond(_1118748, _1118750, _1118752) = c_Com_Ocom_OCond(_1118754, _1118756, _1118758), 18819 ^ _780205 : [(18820 ^ _780205) ^ [] : [-(_1118748 = _1118754)], (18822 ^ _780205) ^ [] : [-(_1118750 = _1118756)], (18824 ^ _780205) ^ [] : [-(_1118752 = _1118758)]]], (18826 ^ _780205) ^ [_1118895, _1118897, _1118899, _1118901, _1118903, _1118905] : [-(c_Com_Ocom_OCond(_1118895, _1118897, _1118899) = c_Com_Ocom_OCond(_1118901, _1118903, _1118905)), _1118895 = _1118901, _1118897 = _1118903, _1118899 = _1118905], (18840 ^ _780205) ^ [_1119139, _1119141, _1119143, _1119145, _1119147] : [c_Com_Ocom_OCond(_1119139, _1119141, _1119143) = c_Com_Ocom_OSemi(_1119145, _1119147)], (18842 ^ _780205) ^ [_1119198, _1119200, _1119202, _1119204, _1119206] : [c_Com_Ocom_OSemi(_1119198, _1119200) = c_Com_Ocom_OCond(_1119202, _1119204, _1119206)], (18844 ^ _780205) ^ [_1119251, _1119253, _1119255] : [c_Com_Ocom_OCond(_1119251, _1119253, _1119255) = c_Com_Ocom_OSKIP], (18846 ^ _780205) ^ [_1119297, _1119299, _1119301] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_1119297, _1119299, _1119301)], (18848 ^ _780205) ^ [_1119328, _1119330, _1119332] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_1119328, _1119330, _1119332)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1119330)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1119332))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18850 ^ _780205) ^ [_1119380, _1119382] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1119380), _1119382)), 18856 ^ _780205 : [(18857 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1119380), 18855 ^ [_1119380, _1119382]), _1119382)))], (18859 ^ _780205) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1119380), _1119382) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18863 ^ _780205) ^ [_1119580, _1119582, _1119584, _1119586] : [class_Orderings_Olinorder(_1119580), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119580), _1119582)), 18873 ^ _780205 : [(18874 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1119580), 18872 ^ [_1119580, _1119582, _1119584, _1119586]), _1119582)))], (18876 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119580), _1119584), 18872 ^ [_1119580, _1119582, _1119584, _1119586]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119580), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1119580), _1119584), _1119586)), hAPP(hAPP(c_Finite__Set_Ofold(_1119580, _1119580, c_Orderings_Oord__class_Omin(_1119580)), _1119586), _1119582))))], (18880 ^ _780205) ^ [_1119944, _1119946, _1119948, _1119950, _1119952, _1119954] : [class_Groups_Oab__semigroup__mult(_1119944), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119946), _1119948)), 18890 ^ _780205 : [(18891 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1119946), 18889 ^ [_1119944, _1119946, _1119948, _1119950, _1119952, _1119954]), _1119948)))], (18893 ^ _780205) ^ [] : [hAPP(_1119950, 18889 ^ [_1119944, _1119946, _1119948, _1119950, _1119952, _1119954]) = hAPP(_1119952, 18889 ^ [_1119944, _1119946, _1119948, _1119950, _1119952, _1119954])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1119944, _1119946, c_Groups_Otimes__class_Otimes(_1119944)), _1119950), _1119954), _1119948) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1119944, _1119946, c_Groups_Otimes__class_Otimes(_1119944)), _1119952), _1119954), _1119948))], (18897 ^ _780205) ^ [_1120349, _1120351, _1120353] : [class_Orderings_Olinorder(_1120349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1120349), _1120351)), 18907 ^ _780205 : [(18908 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1120349), 18906 ^ [_1120349, _1120351, _1120353]), _1120351)))], (18910 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120349), _1120353), 18906 ^ [_1120349, _1120351, _1120353]))]], hBOOL(hAPP(hAPP(c_member(_1120349), _1120353), _1120351)), -(c_Big__Operators_Olinorder__class_OMin(_1120349, _1120351) = _1120353)], (18918 ^ _780205) ^ [_1120721, _1120723, _1120725, _1120727] : [class_Lattices_Osemilattice__inf(_1120721), hBOOL(hAPP(c_Finite__Set_Ofinite(_1120721), _1120723)), 18928 ^ _780205 : [(18929 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1120721), 18927 ^ [_1120721, _1120723, _1120725, _1120727]), _1120723)))], (18931 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120721), _1120725), 18927 ^ [_1120721, _1120723, _1120725, _1120727]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120721), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1120721), _1120725), _1120727)), hAPP(hAPP(c_Finite__Set_Ofold(_1120721, _1120721, c_Lattices_Osemilattice__inf__class_Oinf(_1120721)), _1120727), _1120723))))], (18935 ^ _780205) ^ [_1121085, _1121087, _1121089, _1121091] : [class_Lattices_Osemilattice__sup(_1121085), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121085), _1121087)), 18945 ^ _780205 : [(18946 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1121085), 18944 ^ [_1121085, _1121087, _1121089, _1121091]), _1121087)))], (18948 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121085), 18944 ^ [_1121085, _1121087, _1121089, _1121091]), _1121089))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121085), hAPP(hAPP(c_Finite__Set_Ofold(_1121085, _1121085, c_Lattices_Osemilattice__sup__class_Osup(_1121085)), _1121091), _1121087)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1121085), _1121089), _1121091))))], (18952 ^ _780205) ^ [_1121449] : [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), _1121449))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1121449) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1121449)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (18958 ^ _780205) ^ [_1121564, _1121566, _1121568] : [class_Int_Onumber__ring(_1121564), class_Int_Oring__char__0(_1121564), 18965 ^ _780205 : [(18966 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1121564), _1121566) = hAPP(c_Int_Onumber__class_Onumber__of(_1121564), _1121568), -(_1121566 = _1121568)], (18972 ^ _780205) ^ [] : [_1121566 = _1121568, -(hAPP(c_Int_Onumber__class_Onumber__of(_1121564), _1121566) = hAPP(c_Int_Onumber__class_Onumber__of(_1121564), _1121568))]]], (18978 ^ _780205) ^ [_1121859, _1121861, _1121863] : [class_Int_Onumber(_1121859), 18981 ^ _780205 : [(18982 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1121859), _1121861) = _1121863, -(_1121863 = hAPP(c_Int_Onumber__class_Onumber__of(_1121859), _1121861))], (18988 ^ _780205) ^ [] : [_1121863 = hAPP(c_Int_Onumber__class_Onumber__of(_1121859), _1121861), -(hAPP(c_Int_Onumber__class_Onumber__of(_1121859), _1121861) = _1121863)]]], (18994 ^ _780205) ^ [_1122100, _1122102, _1122104] : [class_Int_Onumber__ring(_1122100), class_Rings_Olinordered__idom(_1122100), 19001 ^ _780205 : [(19002 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122100), hAPP(c_Int_Onumber__class_Onumber__of(_1122100), _1122102)), hAPP(c_Int_Onumber__class_Onumber__of(_1122100), _1122104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1122102), _1122104)))], (19008 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1122102), _1122104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122100), hAPP(c_Int_Onumber__class_Onumber__of(_1122100), _1122102)), hAPP(c_Int_Onumber__class_Onumber__of(_1122100), _1122104))))]]], (19014 ^ _780205) ^ [_1122431, _1122433, _1122435] : [class_Int_Onumber__ring(_1122431), class_Rings_Olinordered__idom(_1122431), 19021 ^ _780205 : [(19022 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122431), hAPP(c_Int_Onumber__class_Onumber__of(_1122431), _1122433)), hAPP(c_Int_Onumber__class_Onumber__of(_1122431), _1122435))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122433), _1122435)))], (19028 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122433), _1122435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122431), hAPP(c_Int_Onumber__class_Onumber__of(_1122431), _1122433)), hAPP(c_Int_Onumber__class_Onumber__of(_1122431), _1122435))))]]], (19034 ^ _780205) ^ [_1122762, _1122764, _1122766, _1122768] : [class_Int_Onumber__ring(_1122762), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122762), hAPP(c_Int_Onumber__class_Onumber__of(_1122762), _1122764)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122762), hAPP(c_Int_Onumber__class_Onumber__of(_1122762), _1122766)), _1122768)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122762), hAPP(c_Int_Onumber__class_Onumber__of(_1122762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122764), _1122766))), _1122768))], (19040 ^ _780205) ^ [_1122931, _1122933, _1122935] : [class_Int_Onumber__ring(_1122931), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122931), hAPP(c_Int_Onumber__class_Onumber__of(_1122931), _1122933)), hAPP(c_Int_Onumber__class_Onumber__of(_1122931), _1122935)) = hAPP(c_Int_Onumber__class_Onumber__of(_1122931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122933), _1122935)))], (19046 ^ _780205) ^ [_1123066, _1123068, _1123070] : [class_Int_Onumber__ring(_1123066), -(hAPP(c_Int_Onumber__class_Onumber__of(_1123066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123068), _1123070)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123066), hAPP(c_Int_Onumber__class_Onumber__of(_1123066), _1123068)), hAPP(c_Int_Onumber__class_Onumber__of(_1123066), _1123070)))], (19052 ^ _780205) ^ [_1123201, _1123203, _1123205] : [class_Int_Onumber__ring(_1123201), -(hAPP(c_Int_Onumber__class_Onumber__of(_1123201), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123203), _1123205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123201), hAPP(c_Int_Onumber__class_Onumber__of(_1123201), _1123203)), hAPP(c_Int_Onumber__class_Onumber__of(_1123201), _1123205)))], (19058 ^ _780205) ^ [_1123336, _1123338, _1123340] : [class_Int_Onumber__ring(_1123336), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123336), hAPP(c_Int_Onumber__class_Onumber__of(_1123336), _1123338)), hAPP(c_Int_Onumber__class_Onumber__of(_1123336), _1123340)) = hAPP(c_Int_Onumber__class_Onumber__of(_1123336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123338), _1123340)))], (19064 ^ _780205) ^ [_1123471, _1123473, _1123475, _1123477] : [class_Int_Onumber__ring(_1123471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123471), hAPP(c_Int_Onumber__class_Onumber__of(_1123471), _1123473)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123471), hAPP(c_Int_Onumber__class_Onumber__of(_1123471), _1123475)), _1123477)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123471), hAPP(c_Int_Onumber__class_Onumber__of(_1123471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123473), _1123475))), _1123477))], (19070 ^ _780205) ^ [_1123640, _1123642, _1123644] : [class_Int_Onumber__ring(_1123640), -(hAPP(c_Int_Onumber__class_Onumber__of(_1123640), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1123642), _1123644)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1123640), hAPP(c_Int_Onumber__class_Onumber__of(_1123640), _1123642)), hAPP(c_Int_Onumber__class_Onumber__of(_1123640), _1123644)))], (19076 ^ _780205) ^ [_1123775, _1123777, _1123779] : [class_Int_Onumber(_1123775), class_Orderings_Olinorder(_1123775), 19083 ^ _780205 : [(19084 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123775), hAPP(c_Int_Onumber__class_Onumber__of(_1123775), _1123777)), hAPP(c_Int_Onumber__class_Onumber__of(_1123775), _1123779))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123775), hAPP(c_Int_Onumber__class_Onumber__of(_1123775), _1123779)), hAPP(c_Int_Onumber__class_Onumber__of(_1123775), _1123777)))], (19090 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123775), hAPP(c_Int_Onumber__class_Onumber__of(_1123775), _1123779)), hAPP(c_Int_Onumber__class_Onumber__of(_1123775), _1123777)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123775), hAPP(c_Int_Onumber__class_Onumber__of(_1123775), _1123777)), hAPP(c_Int_Onumber__class_Onumber__of(_1123775), _1123779))))]]], (19096 ^ _780205) ^ [_1124102, _1124104, _1124106, _1124108] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124102), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124102), _1124104), _1124106)), hAPP(c_Int_Onumber__class_Onumber__of(_1124102), _1124108)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124102), _1124104), hAPP(c_Int_Onumber__class_Onumber__of(_1124102), _1124108))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124102), _1124106), hAPP(c_Int_Onumber__class_Onumber__of(_1124102), _1124108)))), class_Int_Onumber(_1124102), class_Rings_Osemiring(_1124102)], (19106 ^ _780205) ^ [_1124345, _1124347, _1124349, _1124351] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124345), hAPP(c_Int_Onumber__class_Onumber__of(_1124345), _1124347)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124345), _1124349), _1124351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124345), hAPP(c_Int_Onumber__class_Onumber__of(_1124345), _1124347)), _1124349)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124345), hAPP(c_Int_Onumber__class_Onumber__of(_1124345), _1124347)), _1124351))), class_Int_Onumber(_1124345), class_Rings_Osemiring(_1124345)], (19116 ^ _780205) ^ [_1124588, _1124590, _1124592, _1124594] : [class_Int_Onumber__ring(_1124588), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124588), hAPP(c_Int_Onumber__class_Onumber__of(_1124588), _1124590)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124588), hAPP(c_Int_Onumber__class_Onumber__of(_1124588), _1124592)), _1124594)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124588), hAPP(c_Int_Onumber__class_Onumber__of(_1124588), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124590), _1124592))), _1124594))], (19122 ^ _780205) ^ [_1124757, _1124759, _1124761, _1124763] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124757), hAPP(c_Int_Onumber__class_Onumber__of(_1124757), _1124759)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124757), _1124761), _1124763)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124757), hAPP(c_Int_Onumber__class_Onumber__of(_1124757), _1124759)), _1124761)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124757), hAPP(c_Int_Onumber__class_Onumber__of(_1124757), _1124759)), _1124763))), class_Int_Onumber(_1124757), class_Rings_Oring(_1124757)], (19132 ^ _780205) ^ [_1125000, _1125002, _1125004, _1125006] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125000), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125000), _1125002), _1125004)), hAPP(c_Int_Onumber__class_Onumber__of(_1125000), _1125006)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125000), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125000), _1125002), hAPP(c_Int_Onumber__class_Onumber__of(_1125000), _1125006))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125000), _1125004), hAPP(c_Int_Onumber__class_Onumber__of(_1125000), _1125006)))), class_Int_Onumber(_1125000), class_Rings_Oring(_1125000)], (19142 ^ _780205) ^ [_1125243, _1125245, _1125247] : [class_Int_Onumber(_1125243), class_Orderings_Oord(_1125243), 19149 ^ _780205 : [(19150 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125243), hAPP(c_Int_Onumber__class_Onumber__of(_1125243), _1125245)), hAPP(c_Int_Onumber__class_Onumber__of(_1125243), _1125247))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1125243), hAPP(c_Int_Onumber__class_Onumber__of(_1125243), _1125245)), hAPP(c_Int_Onumber__class_Onumber__of(_1125243), _1125247)) = hAPP(c_Int_Onumber__class_Onumber__of(_1125243), _1125245))], (19156 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125243), hAPP(c_Int_Onumber__class_Onumber__of(_1125243), _1125245)), hAPP(c_Int_Onumber__class_Onumber__of(_1125243), _1125247)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1125243), hAPP(c_Int_Onumber__class_Onumber__of(_1125243), _1125245)), hAPP(c_Int_Onumber__class_Onumber__of(_1125243), _1125247)) = hAPP(c_Int_Onumber__class_Onumber__of(_1125243), _1125247))]]], (19162 ^ _780205) ^ [_1125635, _1125637] : [class_Int_Onumber__ring(_1125635), -(hBOOL(hAPP(hAPP(c_member(_1125635), hAPP(c_Int_Onumber__class_Onumber__of(_1125635), _1125637)), c_Int_Oring__1__class_OInts(_1125635))))], (19168 ^ _780205) ^ [_1125738, _1125740, _1125742, _1125744] : [class_Fields_Ofield__inverse__zero(_1125738), class_Int_Onumber(_1125738), 19175 ^ _780205 : [(19192 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125738), _1125740), hAPP(c_Int_Onumber__class_Onumber__of(_1125738), _1125742)) = _1125744), 19195 ^ _780205 : [(19196 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1125738), _1125742) = c_Groups_Ozero__class_Ozero(_1125738)], (19198 ^ _780205) ^ [] : [_1125740 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125738), _1125744), hAPP(c_Int_Onumber__class_Onumber__of(_1125738), _1125742))]], 19199 ^ _780205 : [(19200 ^ _780205) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1125738), _1125742) = c_Groups_Ozero__class_Ozero(_1125738))], (19202 ^ _780205) ^ [] : [_1125744 = c_Groups_Ozero__class_Ozero(_1125738)]]], (19176 ^ _780205) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125738), _1125740), hAPP(c_Int_Onumber__class_Onumber__of(_1125738), _1125742)) = _1125744, 19179 ^ _780205 : [(19180 ^ _780205) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1125738), _1125742) = c_Groups_Ozero__class_Ozero(_1125738)), -(_1125740 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125738), _1125744), hAPP(c_Int_Onumber__class_Onumber__of(_1125738), _1125742)))], (19186 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1125738), _1125742) = c_Groups_Ozero__class_Ozero(_1125738), -(_1125744 = c_Groups_Ozero__class_Ozero(_1125738))]]]]], (19206 ^ _780205) ^ [_1126348, _1126350, _1126352, _1126354] : [class_Fields_Ofield__inverse__zero(_1126348), class_Int_Onumber(_1126348), 19213 ^ _780205 : [(19230 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126348), _1126350), _1126352) = hAPP(c_Int_Onumber__class_Onumber__of(_1126348), _1126354)), 19233 ^ _780205 : [(19234 ^ _780205) ^ [] : [_1126352 = c_Groups_Ozero__class_Ozero(_1126348)], (19236 ^ _780205) ^ [] : [_1126350 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126348), hAPP(c_Int_Onumber__class_Onumber__of(_1126348), _1126354)), _1126352)]], 19237 ^ _780205 : [(19238 ^ _780205) ^ [] : [-(_1126352 = c_Groups_Ozero__class_Ozero(_1126348))], (19240 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1126348), _1126354) = c_Groups_Ozero__class_Ozero(_1126348)]]], (19214 ^ _780205) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126348), _1126350), _1126352) = hAPP(c_Int_Onumber__class_Onumber__of(_1126348), _1126354), 19217 ^ _780205 : [(19218 ^ _780205) ^ [] : [-(_1126352 = c_Groups_Ozero__class_Ozero(_1126348)), -(_1126350 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126348), hAPP(c_Int_Onumber__class_Onumber__of(_1126348), _1126354)), _1126352))], (19224 ^ _780205) ^ [] : [_1126352 = c_Groups_Ozero__class_Ozero(_1126348), -(hAPP(c_Int_Onumber__class_Onumber__of(_1126348), _1126354) = c_Groups_Ozero__class_Ozero(_1126348))]]]]], (19244 ^ _780205) ^ [_1126943, _1126945, _1126947, _1126949] : [class_Fields_Ofield__inverse__zero(_1126943), class_Int_Onumber(_1126943), 19251 ^ _780205 : [(19268 ^ _780205) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1126943), _1126945) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126943), _1126947), _1126949)), 19271 ^ _780205 : [(19272 ^ _780205) ^ [] : [_1126949 = c_Groups_Ozero__class_Ozero(_1126943)], (19274 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126943), hAPP(c_Int_Onumber__class_Onumber__of(_1126943), _1126945)), _1126949) = _1126947]], 19275 ^ _780205 : [(19276 ^ _780205) ^ [] : [-(_1126949 = c_Groups_Ozero__class_Ozero(_1126943))], (19278 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1126943), _1126945) = c_Groups_Ozero__class_Ozero(_1126943)]]], (19252 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1126943), _1126945) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126943), _1126947), _1126949), 19255 ^ _780205 : [(19256 ^ _780205) ^ [] : [-(_1126949 = c_Groups_Ozero__class_Ozero(_1126943)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126943), hAPP(c_Int_Onumber__class_Onumber__of(_1126943), _1126945)), _1126949) = _1126947)], (19262 ^ _780205) ^ [] : [_1126949 = c_Groups_Ozero__class_Ozero(_1126943), -(hAPP(c_Int_Onumber__class_Onumber__of(_1126943), _1126945) = c_Groups_Ozero__class_Ozero(_1126943))]]]]], (19282 ^ _780205) ^ [_1127538, _1127540, _1127542, _1127544] : [class_Fields_Ofield__inverse__zero(_1127538), class_Int_Onumber(_1127538), 19289 ^ _780205 : [(19306 ^ _780205) ^ [] : [-(_1127540 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127538), _1127542), hAPP(c_Int_Onumber__class_Onumber__of(_1127538), _1127544))), 19309 ^ _780205 : [(19310 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1127538), _1127544) = c_Groups_Ozero__class_Ozero(_1127538)], (19312 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127538), _1127540), hAPP(c_Int_Onumber__class_Onumber__of(_1127538), _1127544)) = _1127542]], 19313 ^ _780205 : [(19314 ^ _780205) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1127538), _1127544) = c_Groups_Ozero__class_Ozero(_1127538))], (19316 ^ _780205) ^ [] : [_1127540 = c_Groups_Ozero__class_Ozero(_1127538)]]], (19290 ^ _780205) ^ [] : [_1127540 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127538), _1127542), hAPP(c_Int_Onumber__class_Onumber__of(_1127538), _1127544)), 19293 ^ _780205 : [(19294 ^ _780205) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1127538), _1127544) = c_Groups_Ozero__class_Ozero(_1127538)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127538), _1127540), hAPP(c_Int_Onumber__class_Onumber__of(_1127538), _1127544)) = _1127542)], (19300 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1127538), _1127544) = c_Groups_Ozero__class_Ozero(_1127538), -(_1127540 = c_Groups_Ozero__class_Ozero(_1127538))]]]]], (19320 ^ _780205) ^ [_1128148, _1128150, _1128152, _1128154] : [class_Fields_Olinordered__field__inverse__zero(_1128148), class_Int_Onumber(_1128148), 19327 ^ _780205 : [(19354 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128148), _1128150), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152))), _1128154))), 19357 ^ _780205 : [(19358 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), c_Groups_Ozero__class_Ozero(_1128148)), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152))))], (19360 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), _1128150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128148), _1128154), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152))))]], 19361 ^ _780205 : [(19362 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), c_Groups_Ozero__class_Ozero(_1128148)), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152)))], (19364 ^ _780205) ^ [] : [19365 ^ _780205 : [(19366 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152)), c_Groups_Ozero__class_Ozero(_1128148))))], (19368 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128148), _1128154), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152))), _1128150))]], 19369 ^ _780205 : [(19370 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152)), c_Groups_Ozero__class_Ozero(_1128148)))], (19372 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), c_Groups_Ozero__class_Ozero(_1128148)), _1128154))]]]]], (19328 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128148), _1128150), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152))), _1128154)), 19331 ^ _780205 : [(19332 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), c_Groups_Ozero__class_Ozero(_1128148)), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), _1128150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128148), _1128154), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152)))))], (19338 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), c_Groups_Ozero__class_Ozero(_1128148)), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152)))), 19341 ^ _780205 : [(19342 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152)), c_Groups_Ozero__class_Ozero(_1128148))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128148), _1128154), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152))), _1128150)))], (19348 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), hAPP(c_Int_Onumber__class_Onumber__of(_1128148), _1128152)), c_Groups_Ozero__class_Ozero(_1128148)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128148), c_Groups_Ozero__class_Ozero(_1128148)), _1128154)))]]]]]]], (19376 ^ _780205) ^ [_1129262, _1129264, _1129266, _1129268] : [class_Fields_Olinordered__field__inverse__zero(_1129262), class_Int_Onumber(_1129262), 19383 ^ _780205 : [(19410 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129262), _1129264), _1129266)), hAPP(c_Int_Onumber__class_Onumber__of(_1129262), _1129268)))), 19413 ^ _780205 : [(19414 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), c_Groups_Ozero__class_Ozero(_1129262)), _1129266)))], (19416 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), _1129264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129262), hAPP(c_Int_Onumber__class_Onumber__of(_1129262), _1129268)), _1129266)))]], 19417 ^ _780205 : [(19418 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), c_Groups_Ozero__class_Ozero(_1129262)), _1129266))], (19420 ^ _780205) ^ [] : [19421 ^ _780205 : [(19422 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), _1129266), c_Groups_Ozero__class_Ozero(_1129262))))], (19424 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129262), hAPP(c_Int_Onumber__class_Onumber__of(_1129262), _1129268)), _1129266)), _1129264))]], 19425 ^ _780205 : [(19426 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), _1129266), c_Groups_Ozero__class_Ozero(_1129262)))], (19428 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), c_Groups_Ozero__class_Ozero(_1129262)), hAPP(c_Int_Onumber__class_Onumber__of(_1129262), _1129268)))]]]]], (19384 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129262), _1129264), _1129266)), hAPP(c_Int_Onumber__class_Onumber__of(_1129262), _1129268))), 19387 ^ _780205 : [(19388 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), c_Groups_Ozero__class_Ozero(_1129262)), _1129266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), _1129264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129262), hAPP(c_Int_Onumber__class_Onumber__of(_1129262), _1129268)), _1129266))))], (19394 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), c_Groups_Ozero__class_Ozero(_1129262)), _1129266))), 19397 ^ _780205 : [(19398 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), _1129266), c_Groups_Ozero__class_Ozero(_1129262))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129262), hAPP(c_Int_Onumber__class_Onumber__of(_1129262), _1129268)), _1129266)), _1129264)))], (19404 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), _1129266), c_Groups_Ozero__class_Ozero(_1129262)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129262), c_Groups_Ozero__class_Ozero(_1129262)), hAPP(c_Int_Onumber__class_Onumber__of(_1129262), _1129268))))]]]]]]], (19432 ^ _780205) ^ [_1130331, _1130333, _1130335, _1130337] : [class_Fields_Olinordered__field__inverse__zero(_1130331), class_Int_Onumber(_1130331), 19439 ^ _780205 : [(19466 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), hAPP(c_Int_Onumber__class_Onumber__of(_1130331), _1130333)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130331), _1130335), _1130337)))), 19469 ^ _780205 : [(19470 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), c_Groups_Ozero__class_Ozero(_1130331)), _1130337)))], (19472 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130331), hAPP(c_Int_Onumber__class_Onumber__of(_1130331), _1130333)), _1130337)), _1130335))]], 19473 ^ _780205 : [(19474 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), c_Groups_Ozero__class_Ozero(_1130331)), _1130337))], (19476 ^ _780205) ^ [] : [19477 ^ _780205 : [(19478 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), _1130337), c_Groups_Ozero__class_Ozero(_1130331))))], (19480 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), _1130335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130331), hAPP(c_Int_Onumber__class_Onumber__of(_1130331), _1130333)), _1130337)))]], 19481 ^ _780205 : [(19482 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), _1130337), c_Groups_Ozero__class_Ozero(_1130331)))], (19484 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), hAPP(c_Int_Onumber__class_Onumber__of(_1130331), _1130333)), c_Groups_Ozero__class_Ozero(_1130331)))]]]]], (19440 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), hAPP(c_Int_Onumber__class_Onumber__of(_1130331), _1130333)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130331), _1130335), _1130337))), 19443 ^ _780205 : [(19444 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), c_Groups_Ozero__class_Ozero(_1130331)), _1130337)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130331), hAPP(c_Int_Onumber__class_Onumber__of(_1130331), _1130333)), _1130337)), _1130335)))], (19450 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), c_Groups_Ozero__class_Ozero(_1130331)), _1130337))), 19453 ^ _780205 : [(19454 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), _1130337), c_Groups_Ozero__class_Ozero(_1130331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), _1130335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130331), hAPP(c_Int_Onumber__class_Onumber__of(_1130331), _1130333)), _1130337))))], (19460 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), _1130337), c_Groups_Ozero__class_Ozero(_1130331)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130331), hAPP(c_Int_Onumber__class_Onumber__of(_1130331), _1130333)), c_Groups_Ozero__class_Ozero(_1130331))))]]]]]]], (19488 ^ _780205) ^ [_1131400, _1131402, _1131404, _1131406] : [class_Fields_Olinordered__field__inverse__zero(_1131400), class_Int_Onumber(_1131400), 19495 ^ _780205 : [(19522 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), _1131402), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131400), _1131404), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406))))), 19525 ^ _780205 : [(19526 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), c_Groups_Ozero__class_Ozero(_1131400)), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406))))], (19528 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131400), _1131402), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406))), _1131404))]], 19529 ^ _780205 : [(19530 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), c_Groups_Ozero__class_Ozero(_1131400)), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406)))], (19532 ^ _780205) ^ [] : [19533 ^ _780205 : [(19534 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406)), c_Groups_Ozero__class_Ozero(_1131400))))], (19536 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), _1131404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131400), _1131402), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406))))]], 19537 ^ _780205 : [(19538 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406)), c_Groups_Ozero__class_Ozero(_1131400)))], (19540 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), _1131402), c_Groups_Ozero__class_Ozero(_1131400)))]]]]], (19496 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), _1131402), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131400), _1131404), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406)))), 19499 ^ _780205 : [(19500 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), c_Groups_Ozero__class_Ozero(_1131400)), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131400), _1131402), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406))), _1131404)))], (19506 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), c_Groups_Ozero__class_Ozero(_1131400)), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406)))), 19509 ^ _780205 : [(19510 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406)), c_Groups_Ozero__class_Ozero(_1131400))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), _1131404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131400), _1131402), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406)))))], (19516 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), hAPP(c_Int_Onumber__class_Onumber__of(_1131400), _1131406)), c_Groups_Ozero__class_Ozero(_1131400)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131400), _1131402), c_Groups_Ozero__class_Ozero(_1131400))))]]]]]]], (19544 ^ _780205) ^ [_1132514, _1132516, _1132518, _1132520] : [class_Fields_Olinordered__field__inverse__zero(_1132514), class_Int_Onumber(_1132514), 19551 ^ _780205 : [(19578 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132514), _1132516), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132514), _1132518), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520))))), 19581 ^ _780205 : [(19582 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132514), c_Groups_Ozero__class_Ozero(_1132514)), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520))))], (19584 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132514), _1132516), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520))), _1132518))]], 19585 ^ _780205 : [(19586 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132514), c_Groups_Ozero__class_Ozero(_1132514)), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520)))], (19588 ^ _780205) ^ [] : [19589 ^ _780205 : [(19590 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132514), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520)), c_Groups_Ozero__class_Ozero(_1132514))))], (19592 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132514), _1132518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132514), _1132516), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520))))]], 19593 ^ _780205 : [(19594 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132514), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520)), c_Groups_Ozero__class_Ozero(_1132514)))], (19596 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132514), _1132516), c_Groups_Ozero__class_Ozero(_1132514)))]]]]], (19552 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132514), _1132516), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132514), _1132518), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520)))), 19555 ^ _780205 : [(19556 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132514), c_Groups_Ozero__class_Ozero(_1132514)), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132514), _1132516), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520))), _1132518)))], (19562 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132514), c_Groups_Ozero__class_Ozero(_1132514)), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520)))), 19565 ^ _780205 : [(19566 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132514), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520)), c_Groups_Ozero__class_Ozero(_1132514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132514), _1132518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132514), _1132516), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520)))))], (19572 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132514), hAPP(c_Int_Onumber__class_Onumber__of(_1132514), _1132520)), c_Groups_Ozero__class_Ozero(_1132514)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132514), _1132516), c_Groups_Ozero__class_Ozero(_1132514))))]]]]]]], (19600 ^ _780205) ^ [_1133628, _1133630, _1133632, _1133634] : [class_Fields_Olinordered__field__inverse__zero(_1133628), class_Int_Onumber(_1133628), 19607 ^ _780205 : [(19634 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133628), hAPP(c_Int_Onumber__class_Onumber__of(_1133628), _1133630)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133628), _1133632), _1133634)))), 19637 ^ _780205 : [(19638 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133628), c_Groups_Ozero__class_Ozero(_1133628)), _1133634)))], (19640 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133628), hAPP(c_Int_Onumber__class_Onumber__of(_1133628), _1133630)), _1133634)), _1133632))]], 19641 ^ _780205 : [(19642 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133628), c_Groups_Ozero__class_Ozero(_1133628)), _1133634))], (19644 ^ _780205) ^ [] : [19645 ^ _780205 : [(19646 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133628), _1133634), c_Groups_Ozero__class_Ozero(_1133628))))], (19648 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133628), _1133632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133628), hAPP(c_Int_Onumber__class_Onumber__of(_1133628), _1133630)), _1133634)))]], 19649 ^ _780205 : [(19650 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133628), _1133634), c_Groups_Ozero__class_Ozero(_1133628)))], (19652 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133628), hAPP(c_Int_Onumber__class_Onumber__of(_1133628), _1133630)), c_Groups_Ozero__class_Ozero(_1133628)))]]]]], (19608 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133628), hAPP(c_Int_Onumber__class_Onumber__of(_1133628), _1133630)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133628), _1133632), _1133634))), 19611 ^ _780205 : [(19612 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133628), c_Groups_Ozero__class_Ozero(_1133628)), _1133634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133628), hAPP(c_Int_Onumber__class_Onumber__of(_1133628), _1133630)), _1133634)), _1133632)))], (19618 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133628), c_Groups_Ozero__class_Ozero(_1133628)), _1133634))), 19621 ^ _780205 : [(19622 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133628), _1133634), c_Groups_Ozero__class_Ozero(_1133628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133628), _1133632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133628), hAPP(c_Int_Onumber__class_Onumber__of(_1133628), _1133630)), _1133634))))], (19628 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133628), _1133634), c_Groups_Ozero__class_Ozero(_1133628)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133628), hAPP(c_Int_Onumber__class_Onumber__of(_1133628), _1133630)), c_Groups_Ozero__class_Ozero(_1133628))))]]]]]]], (19656 ^ _780205) ^ [_1134697, _1134699, _1134701, _1134703] : [class_Fields_Olinordered__field__inverse__zero(_1134697), class_Int_Onumber(_1134697), 19663 ^ _780205 : [(19690 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134697), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134697), _1134699), _1134701)), hAPP(c_Int_Onumber__class_Onumber__of(_1134697), _1134703)))), 19693 ^ _780205 : [(19694 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134697), c_Groups_Ozero__class_Ozero(_1134697)), _1134701)))], (19696 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134697), _1134699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134697), hAPP(c_Int_Onumber__class_Onumber__of(_1134697), _1134703)), _1134701)))]], 19697 ^ _780205 : [(19698 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134697), c_Groups_Ozero__class_Ozero(_1134697)), _1134701))], (19700 ^ _780205) ^ [] : [19701 ^ _780205 : [(19702 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134697), _1134701), c_Groups_Ozero__class_Ozero(_1134697))))], (19704 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134697), hAPP(c_Int_Onumber__class_Onumber__of(_1134697), _1134703)), _1134701)), _1134699))]], 19705 ^ _780205 : [(19706 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134697), _1134701), c_Groups_Ozero__class_Ozero(_1134697)))], (19708 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134697), c_Groups_Ozero__class_Ozero(_1134697)), hAPP(c_Int_Onumber__class_Onumber__of(_1134697), _1134703)))]]]]], (19664 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134697), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134697), _1134699), _1134701)), hAPP(c_Int_Onumber__class_Onumber__of(_1134697), _1134703))), 19667 ^ _780205 : [(19668 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134697), c_Groups_Ozero__class_Ozero(_1134697)), _1134701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134697), _1134699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134697), hAPP(c_Int_Onumber__class_Onumber__of(_1134697), _1134703)), _1134701))))], (19674 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134697), c_Groups_Ozero__class_Ozero(_1134697)), _1134701))), 19677 ^ _780205 : [(19678 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134697), _1134701), c_Groups_Ozero__class_Ozero(_1134697))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134697), hAPP(c_Int_Onumber__class_Onumber__of(_1134697), _1134703)), _1134701)), _1134699)))], (19684 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134697), _1134701), c_Groups_Ozero__class_Ozero(_1134697)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134697), c_Groups_Ozero__class_Ozero(_1134697)), hAPP(c_Int_Onumber__class_Onumber__of(_1134697), _1134703))))]]]]]]], (19712 ^ _780205) ^ [_1135766, _1135768, _1135770, _1135772] : [class_Fields_Olinordered__field__inverse__zero(_1135766), class_Int_Onumber(_1135766), 19719 ^ _780205 : [(19746 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135766), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135766), _1135768), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770))), _1135772))), 19749 ^ _780205 : [(19750 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135766), c_Groups_Ozero__class_Ozero(_1135766)), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770))))], (19752 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135766), _1135768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135766), _1135772), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770))))]], 19753 ^ _780205 : [(19754 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135766), c_Groups_Ozero__class_Ozero(_1135766)), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770)))], (19756 ^ _780205) ^ [] : [19757 ^ _780205 : [(19758 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135766), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770)), c_Groups_Ozero__class_Ozero(_1135766))))], (19760 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135766), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135766), _1135772), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770))), _1135768))]], 19761 ^ _780205 : [(19762 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135766), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770)), c_Groups_Ozero__class_Ozero(_1135766)))], (19764 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135766), c_Groups_Ozero__class_Ozero(_1135766)), _1135772))]]]]], (19720 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135766), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135766), _1135768), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770))), _1135772)), 19723 ^ _780205 : [(19724 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135766), c_Groups_Ozero__class_Ozero(_1135766)), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135766), _1135768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135766), _1135772), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770)))))], (19730 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135766), c_Groups_Ozero__class_Ozero(_1135766)), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770)))), 19733 ^ _780205 : [(19734 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135766), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770)), c_Groups_Ozero__class_Ozero(_1135766))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135766), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135766), _1135772), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770))), _1135768)))], (19740 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135766), hAPP(c_Int_Onumber__class_Onumber__of(_1135766), _1135770)), c_Groups_Ozero__class_Ozero(_1135766)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135766), c_Groups_Ozero__class_Ozero(_1135766)), _1135772)))]]]]]]], (19768 ^ _780205) ^ [_1136880, _1136882, _1136884] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_1136880, _1136882, _1136884)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1136884)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19770 ^ _780205) ^ [_1136921, _1136923, _1136925] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_1136921, _1136923, _1136925)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1136925)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19772 ^ _780205) ^ [_1136964, _1136966, _1136968] : [hBOOL(hAPP(hAPP(c_member(_1136964), _1136966), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1136964, tc_HOL_Obool), _1136968))), 19776 ^ _780205 : [(19777 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1136964), _1136966), 19775 ^ [_1136964, _1136966, _1136968])))], (19779 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1136964, tc_HOL_Obool)), 19775 ^ [_1136964, _1136966, _1136968]), _1136968)))]]], (19781 ^ _780205) ^ [_1137156, _1137158, _1137160, _1137162] : [class_Rings_Olinordered__semidom(_1137156), 19787 ^ _780205 : [(19788 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1137158), 19786 ^ [_1137156, _1137158, _1137160, _1137162]), _1137160)))], (19790 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137156), c_Groups_Ozero__class_Ozero(_1137156)), hAPP(_1137162, 19786 ^ [_1137156, _1137158, _1137160, _1137162])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137156), c_Groups_Ozero__class_Ozero(_1137156)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1137158, _1137156), _1137162), _1137160))))], (19794 ^ _780205) ^ [_1137452, _1137454, _1137456, _1137458] : [class_Rings_Olinordered__semidom(_1137452), 19800 ^ _780205 : [(19801 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1137454), 19799 ^ [_1137452, _1137454, _1137456, _1137458]), _1137456)))], (19803 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137452), c_Groups_Ozero__class_Ozero(_1137452)), hAPP(_1137458, 19799 ^ [_1137452, _1137454, _1137456, _1137458])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137452), c_Groups_Ozero__class_Ozero(_1137452)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1137454, _1137452), _1137458), _1137456))))], (19807 ^ _780205) ^ [_1137748, _1137750] : [class_Int_Onumber__ring(_1137748), -(hAPP(c_Int_Onumber__class_Onumber__of(_1137748), c_Int_Osucc(_1137750)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137748), c_Groups_Oone__class_Oone(_1137748)), hAPP(c_Int_Onumber__class_Onumber__of(_1137748), _1137750)))], (19813 ^ _780205) ^ [_1137867, _1137869, _1137871] : [class_Fields_Olinordered__field(_1137867), 19819 ^ _780205 : [(19820 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137867), c_Groups_Ozero__class_Ozero(_1137867)), 19818 ^ [_1137867, _1137869, _1137871])))], (19822 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137867), _1137869), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137867), _1137871), 19818 ^ [_1137867, _1137869, _1137871])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137867), _1137869), _1137871)))], (19826 ^ _780205) ^ [_1138160, _1138162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138160)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138162))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1138160), _1138162)))], (19832 ^ _780205) ^ [_1138265, _1138267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1138265), _1138267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138265)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138267))))], (19838 ^ _780205) ^ [_1138376, _1138378] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138376)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138378)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1138376), _1138378)))], (19840 ^ _780205) ^ [_1138422, _1138424] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138422)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138424)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1138422), _1138424)))], (19842 ^ _780205) ^ [_1138483, _1138485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138483)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138483), _1138485)))], (19848 ^ _780205) ^ [_1138588, _1138590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138588), _1138590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138588)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138590))))], (19854 ^ _780205) ^ [_1138708] : [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)), _1138708)), _1138708) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (19856 ^ _780205) ^ [_1138752] : [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)), _1138752)), _1138752)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138752), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19862 ^ _780205) ^ [_1138861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138861), 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)), _1138861)), _1138861)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19868 ^ _780205) ^ [] : [-(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))))], (19870 ^ _780205) ^ [_1138994, _1138996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138994)), 19873 ^ _780205 : [(19874 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1138994), _1138996) = c_Groups_Oone__class_Oone(tc_Int_Oint), 19877 ^ _780205 : [(19878 ^ _780205) ^ [] : [-(_1138994 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (19880 ^ _780205) ^ [] : [-(_1138996 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (19882 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1138994), _1138996) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1138994 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1138996 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (19892 ^ _780205) ^ [_1139307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1139307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139307)))], (19898 ^ _780205) ^ [_1139386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1139386)))], (19904 ^ _780205) ^ [_1139471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139471)), -(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)), _1139471))))], (19910 ^ _780205) ^ [_1139560] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1139560), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1139560)], (19912 ^ _780205) ^ [_1139589] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139589) = _1139589)], (19914 ^ _780205) ^ [_1139615, _1139617, _1139619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139615), _1139617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139619), _1139615)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139619), _1139617))))], (19924 ^ _780205) ^ [_1139811, _1139813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139811), _1139813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1139811), _1139813)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19930 ^ _780205) ^ [_1139916, _1139918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1139916), _1139918)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139916), _1139918)))], (19936 ^ _780205) ^ [_1140027, _1140029, _1140031, _1140033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140027), _1140029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1140031), _1140033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140027), _1140031)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140029), _1140033))))], (19946 ^ _780205) ^ [_1140233, _1140235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140233), _1140235)), 19949 ^ _780205 : [(19950 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1140233), _1140235)))], (19952 ^ _780205) ^ [] : [_1140233 = _1140235]]], (19954 ^ _780205) ^ [_1140360, _1140362] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140360), _1140362))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1140360), _1140362)), -(_1140360 = _1140362)], (19964 ^ _780205) ^ [_1140514, _1140516, _1140518] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1140514), _1140516)), _1140518) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140514), _1140518)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140516), _1140518)))], (19966 ^ _780205) ^ [_1140571, _1140573, _1140575] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140571), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1140573), _1140575)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140571), _1140573)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140571), _1140575)))], (19968 ^ _780205) ^ [_1140624, _1140626] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140624), _1140626))), -(_1140624 = _1140626), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140626), _1140624)))], (19978 ^ _780205) ^ [_1140677, _1140679] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140677), _1140679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140679), _1140677))], (19980 ^ _780205) ^ [_1140714, _1140716, _1140718] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140714), _1140716)), _1140718) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140714), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140716), _1140718)))], (19982 ^ _780205) ^ [_1140765, _1140767, _1140769] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140765), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140767), _1140769)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140765), _1140767)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140765), _1140769)))], (19984 ^ _780205) ^ [_1140822, _1140824, _1140826] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140822), _1140824)), _1140826) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140822), _1140826)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140824), _1140826)))], (19986 ^ _780205) ^ [_1140879, _1140881, _1140883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140879), _1140881)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140879), _1140883)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140881), _1140883))))], (19992 ^ _780205) ^ [_1141002, _1141004] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141002), _1141004) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141004), _1141002))], (19994 ^ _780205) ^ [_1141039, _1141041, _1141043] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141039), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141041), _1141043)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141041), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141039), _1141043)))], (19996 ^ _780205) ^ [_1141090, _1141092, _1141094] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141090), _1141092)), _1141094) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141092), _1141094)))], (19998 ^ _780205) ^ [_1141141] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141141), _1141141)))], (20000 ^ _780205) ^ [_1141165, _1141167] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141165), _1141167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141167), _1141165)))], (20006 ^ _780205) ^ [_1141211, _1141213, _1141215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141211), _1141213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141213), _1141215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141211), _1141215)))], (20016 ^ _780205) ^ [_1141374, _1141376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141374), _1141376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141376), _1141374)), -(_1141374 = _1141376)], (20026 ^ _780205) ^ [_1141523, _1141525, _1141527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141523), _1141525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141527), _1141523)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141527), _1141525))))], (20032 ^ _780205) ^ [_1141661, _1141663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141663), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141661), _1141663)))], (20038 ^ _780205) ^ [_1141766, _1141768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141766), _1141768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141766), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141768), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (20044 ^ _780205) ^ [_1141892, _1141894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141892), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1141894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141892), _1141894)))], (20050 ^ _780205) ^ [_1141997, _1141999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1141997), _1141999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141997), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1141999)))], (20056 ^ _780205) ^ [_1142108, _1142110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142108), _1142110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1142108), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1142110)))], (20062 ^ _780205) ^ [_1142232, _1142234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1142232), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1142234), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142232), _1142234)))], (20068 ^ _780205) ^ [_1142337, _1142339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142337), _1142339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1142337), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1142339), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (20074 ^ _780205) ^ [_1142448] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1142448) = _1142448)], (20076 ^ _780205) ^ [_1142474] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1142474), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1142474)], (20088 ^ _780205) ^ [_1142636, _1142638] : [20089 ^ _780205 : [(20090 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142636), _1142638))], (20092 ^ _780205) ^ [] : [_1142636 = _1142638]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142636), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1142638), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (20078 ^ _780205) ^ [_1142518, _1142520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142518), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1142520), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142518), _1142520))), -(_1142518 = _1142520)], (20096 ^ _780205) ^ [_1142785] : [-(c_Int_Osucc(_1142785) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1142785), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20098 ^ _780205) ^ [_1142843, _1142845, _1142847, _1142849, _1142851, _1142853] : [c_Com_Ocom_OLocal(_1142843, _1142845, _1142847) = c_Com_Ocom_OLocal(_1142849, _1142851, _1142853), 20101 ^ _780205 : [(20102 ^ _780205) ^ [] : [-(_1142843 = _1142849)], (20104 ^ _780205) ^ [] : [-(_1142845 = _1142851)], (20106 ^ _780205) ^ [] : [-(_1142847 = _1142853)]]], (20108 ^ _780205) ^ [_1142990, _1142992, _1142994, _1142996, _1142998, _1143000] : [-(c_Com_Ocom_OLocal(_1142990, _1142992, _1142994) = c_Com_Ocom_OLocal(_1142996, _1142998, _1143000)), _1142990 = _1142996, _1142992 = _1142998, _1142994 = _1143000], (20122 ^ _780205) ^ [_1143237, _1143239, _1143241, _1143243, _1143245, _1143247] : [c_Com_Ocom_OCond(_1143237, _1143239, _1143241) = c_Com_Ocom_OLocal(_1143243, _1143245, _1143247)], (20124 ^ _780205) ^ [_1143302, _1143304, _1143306, _1143308, _1143310, _1143312] : [c_Com_Ocom_OLocal(_1143302, _1143304, _1143306) = c_Com_Ocom_OCond(_1143308, _1143310, _1143312)], (20126 ^ _780205) ^ [_1143364, _1143366, _1143368, _1143370, _1143372] : [c_Com_Ocom_OLocal(_1143364, _1143366, _1143368) = c_Com_Ocom_OSemi(_1143370, _1143372)], (20128 ^ _780205) ^ [_1143423, _1143425, _1143427, _1143429, _1143431] : [c_Com_Ocom_OSemi(_1143423, _1143425) = c_Com_Ocom_OLocal(_1143427, _1143429, _1143431)], (20130 ^ _780205) ^ [_1143476, _1143478, _1143480] : [c_Com_Ocom_OLocal(_1143476, _1143478, _1143480) = c_Com_Ocom_OSKIP], (20132 ^ _780205) ^ [_1143522, _1143524, _1143526] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_1143522, _1143524, _1143526)], (20134 ^ _780205) ^ [_1143553, _1143555, _1143557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143553)), _1143553 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1143555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1143553), _1143557)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1143555), _1143553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1143557)))], (20148 ^ _780205) ^ [_1143782, _1143784, _1143786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143782)), _1143782 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1143784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1143782), _1143786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1143784)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1143786), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (20162 ^ _780205) ^ [_1144011, _1144013, _1144015, _1144017, _1144019, _1144021] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1144011), _1144013)), _1144015) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1144017), _1144019)), _1144021), 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), _1144017), _1144019)), _1144021)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1144015), _1144011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144017)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1144017), _1144011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1144019), _1144013)))], (20188 ^ _780205) ^ [_1144516, _1144518, _1144520, _1144522, _1144524] : [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), _1144516), _1144518)), _1144520)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1144516), _1144522)), _1144524))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1144524), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1144516), _1144524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1144516), _1144520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1144522), _1144518)))], (20206 ^ _780205) ^ [_1144871, _1144873, _1144875, _1144877, _1144879, _1144881] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1144871), _1144873)), _1144875) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1144877), _1144879)), _1144881), 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), _1144877), _1144879)), _1144881))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1144881), _1144877)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144875)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1144877)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1144877), _1144871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1144873), _1144879)))], (20232 ^ _780205) ^ [_1145370, _1145372, _1145374, _1145376, _1145378] : [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), _1145370), _1145372)), _1145374)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1145370), _1145376)), _1145378))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145374), _1145370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145378), _1145370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145372), _1145376)))], (20250 ^ _780205) ^ [_1145719, _1145721, _1145723] : [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), _1145719), _1145721)), _1145723)), 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)), _1145723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145721), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20264 ^ _780205) ^ [_1145958] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1145958) = _1145958)], (20266 ^ _780205) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (20268 ^ _780205) ^ [_1146008, _1146010, _1146012] : [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), _1146008), _1146010)), _1146012))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1146012), _1146008)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146010)))], (20282 ^ _780205) ^ [_1146241, _1146243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146241)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146243)), -(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), _1146241), _1146243))))], (20292 ^ _780205) ^ [] : [-(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))))], (20294 ^ _780205) ^ [_1146412, _1146414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146414)), -(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), _1146412), _1146414))))], (20304 ^ _780205) ^ [_1146574, _1146576] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146574))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146574)), _1146576)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1146576))], (20310 ^ _780205) ^ [_1146685, _1146687] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146685)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146685)), _1146687)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1146685))), _1146687))], (20316 ^ _780205) ^ [] : [-(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))))], (20318 ^ _780205) ^ [_1146775] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146775))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146775)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20324 ^ _780205) ^ [_1146866] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146866)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146866)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1146866)))], (20330 ^ _780205) ^ [_1146918, _1146920] : [class_Int_Onumber__ring(_1146918), 20333 ^ _780205 : [(20334 ^ _780205) ^ [] : [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), _1146920))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1146918), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146920)) = hAPP(c_Int_Onumber__class_Onumber__of(_1146918), _1146920))], (20340 ^ _780205) ^ [] : [-(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), _1146920)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1146918), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146920)) = c_Groups_Ozero__class_Ozero(_1146918))]]], (20346 ^ _780205) ^ [_1147158, _1147160, _1147162] : [class_Nat_Osemiring__char__0(_1147158), 20349 ^ _780205 : [(20350 ^ _780205) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1147158), _1147160) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1147158), _1147162), -(_1147160 = _1147162)], (20356 ^ _780205) ^ [] : [_1147160 = _1147162, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1147158), _1147160) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1147158), _1147162))]]], (20362 ^ _780205) ^ [_1147408] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147408)))], (20364 ^ _780205) ^ [] : [-(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)))], (20366 ^ _780205) ^ [_1147454] : [-(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), _1147454))))], (20379 ^ _780205) ^ [_1147664] : [20380 ^ _780205 : [(20381 ^ _780205) ^ [_1147721] : [hBOOL(hAPP(_1147664, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147721)))]], 20383 ^ _780205 : [(20384 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20382 ^ [_1147664])))], (20386 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1147664, 20382 ^ [_1147664])))]]], (20368 ^ _780205) ^ [_1147494] : [-(hBOOL(hAPP(_1147494, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20375 ^ [_1147494])))), 20369 ^ _780205 : [(20370 ^ _780205) ^ [_1147546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147546)), hBOOL(hAPP(_1147494, _1147546))]]], (20388 ^ _780205) ^ [_1147825] : [20390 ^ _780205 : [(20391 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20389 ^ [_1147825])))], (20393 ^ _780205) ^ [] : [hBOOL(hAPP(_1147825, 20389 ^ [_1147825]))]], 20394 ^ _780205 : [(20395 ^ _780205) ^ [_1147952] : [-(hBOOL(hAPP(_1147825, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1147952))))]]], (20397 ^ _780205) ^ [_1147982] : [hBOOL(hAPP(_1147982, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20398 ^ [_1147982]))), 20401 ^ _780205 : [(20402 ^ _780205) ^ [_1148082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148082)), -(hBOOL(hAPP(_1147982, _1148082)))]]], (20408 ^ _780205) ^ [_1148188, _1148190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148188)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148190))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1148188), _1148190)))], (20414 ^ _780205) ^ [_1148293, _1148295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1148293), _1148295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148293)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148295))))], (20420 ^ _780205) ^ [_1148419, _1148421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148419)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148421))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1148419), _1148421)))], (20426 ^ _780205) ^ [_1148524, _1148526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1148524), _1148526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148524)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148526))))], (20432 ^ _780205) ^ [_1148635, _1148637] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148635)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148637)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1148635), _1148637)))], (20434 ^ _780205) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20436 ^ _780205) ^ [_1148705, _1148707] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148705)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148707)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1148705), _1148707)))], (20438 ^ _780205) ^ [] : [-(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)))], (20440 ^ _780205) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20442 ^ _780205) ^ [_1148799] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148799))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148799)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20448 ^ _780205) ^ [_1148890] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148890)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148890)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148890))], (20454 ^ _780205) ^ [] : [-(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))], (20456 ^ _780205) ^ [_1148970] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1148970) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1148970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20462 ^ _780205) ^ [_1149047] : [_1149047 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149047) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20468 ^ _780205) ^ [_1149130] : [-(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), _1149130))))], (20470 ^ _780205) ^ [_1149167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149167)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20472 ^ _780205) ^ [_1149213, _1149215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149213)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1149213), _1149215)))], (20478 ^ _780205) ^ [_1149318, _1149320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1149318), _1149320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149318)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149320))))], (20484 ^ _780205) ^ [_1149444, _1149446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149444)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1149444), _1149446)))], (20490 ^ _780205) ^ [_1149549, _1149551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1149549), _1149551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149549)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149551))))], (20496 ^ _780205) ^ [_1149660, _1149662, _1149664] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149660)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149662)), _1149664)) = 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), _1149660), _1149662))), _1149664))], (20498 ^ _780205) ^ [_1149720, _1149722] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149720)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149722)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1149720), _1149722)))], (20500 ^ _780205) ^ [_1149781, _1149783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1149781), _1149783)), -(_1149783 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149781), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20503 ^ [_1149781, _1149783])))], (20507 ^ _780205) ^ [_1149894, _1149896] : [20508 ^ _780205 : [(20509 ^ _780205) ^ [_1149947] : [_1149896 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149894), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1149947))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1149894), _1149896)))], (20513 ^ _780205) ^ [_1150014, _1150016] : [class_Rings_Olinordered__semidom(_1150014), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150014), c_Groups_Ozero__class_Ozero(_1150014)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150014), _1150016))))], (20519 ^ _780205) ^ [_1150117, _1150119] : [class_Rings_Olinordered__semidom(_1150117), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150117), c_Groups_Ozero__class_Ozero(_1150117)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150117), _1150119))))], (20525 ^ _780205) ^ [_1150220, _1150222] : [class_Rings_Olinordered__semidom(_1150220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150220), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150220), _1150222)), c_Groups_Ozero__class_Ozero(_1150220)))], (20531 ^ _780205) ^ [_1150324, _1150326] : [class_Int_Onumber__ring(_1150324), 20534 ^ _780205 : [(20535 ^ _780205) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150326))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150324), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150326)) = c_Groups_Ozero__class_Ozero(_1150324))], (20541 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150326)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150324), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150326)) = hAPP(c_Int_Onumber__class_Onumber__of(_1150324), _1150326))]]], (20547 ^ _780205) ^ [_1150564, _1150566] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150564)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150566)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150564), _1150566)))], (20549 ^ _780205) ^ [_1150610, _1150612] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150610), _1150612)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150610)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1150612)))], (20551 ^ _780205) ^ [_1150656] : [class_Rings_Osemiring__1(_1150656), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150656), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1150656))], (20557 ^ _780205) ^ [_1150743, _1150745, _1150747] : [class_Rings_Olinordered__semidom(_1150743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150743), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150743), _1150745)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150743), _1150747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150745), _1150747)))], (20567 ^ _780205) ^ [_1150918, _1150920, _1150922] : [class_Rings_Olinordered__semidom(_1150918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150920), _1150922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150918), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150918), _1150920)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1150918), _1150922))))], (20577 ^ _780205) ^ [_1151093, _1151095, _1151097] : [class_Rings_Olinordered__semidom(_1151093), 20580 ^ _780205 : [(20581 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151093), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151093), _1151095)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151093), _1151097))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151095), _1151097)))], (20587 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151095), _1151097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151093), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151093), _1151095)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151093), _1151097))))]]], (20593 ^ _780205) ^ [] : [-(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))], (20595 ^ _780205) ^ [_1151388, _1151390, _1151392] : [class_Rings_Olinordered__semidom(_1151388), 20598 ^ _780205 : [(20599 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151388), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151388), _1151390)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151388), _1151392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1151390), _1151392)))], (20605 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1151390), _1151392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151388), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151388), _1151390)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151388), _1151392))))]]], (20611 ^ _780205) ^ [_1151665, _1151667, _1151669] : [class_Rings_Osemiring__1(_1151665), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1151667), _1151669)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151665), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151665), _1151667)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151665), _1151669)))], (20617 ^ _780205) ^ [_1151800, _1151802, _1151804] : [class_Rings_Osemiring__1(_1151800), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151802), _1151804)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151800), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151800), _1151802)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151800), _1151804)))], (20623 ^ _780205) ^ [_1151935] : [class_Rings_Osemiring__1(_1151935), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1151935), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1151935))], (20629 ^ _780205) ^ [_1152022, _1152024] : [class_Rings_Oring__1(_1152022), -(hBOOL(hAPP(hAPP(c_member(_1152022), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1152022), _1152024)), c_Int_Oring__1__class_OInts(_1152022))))], (20635 ^ _780205) ^ [_1152131] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1152131))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1152131)))], (20641 ^ _780205) ^ [_1152165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1152165)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1152165))], (20647 ^ _780205) ^ [_1152263] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1152263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152263), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20653 ^ _780205) ^ [_1152348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152348), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1152348)))], (20659 ^ _780205) ^ [_1152451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1152451)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1152451 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20665 ^ _780205) ^ [_1152538] : [_1152538 = 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), _1152538)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20671 ^ _780205) ^ [] : [-(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))], (20673 ^ _780205) ^ [_1152664, _1152666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152664), _1152666)), -(_1152666 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1152664), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 20676 ^ [_1152664, _1152666]))))], (20680 ^ _780205) ^ [_1152783, _1152785] : [20681 ^ _780205 : [(20682 ^ _780205) ^ [_1152839] : [_1152785 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1152783), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1152839)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152783), _1152785)))], (20686 ^ _780205) ^ [_1152909] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1152909)) = 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), _1152909)))], (20688 ^ _780205) ^ [_1152944, _1152946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1152944), _1152946)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1152946)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1152944)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152946), _1152944)))], (20694 ^ _780205) ^ [_1153073, _1153075] : [class_Rings_Osemiring__1(_1153073), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1153073), hAPP(c_Nat_OSuc, _1153075)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153073), c_Groups_Oone__class_Oone(_1153073)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1153073), _1153075)))], (20700 ^ _780205) ^ [_1153194, _1153196, _1153198] : [class_Rings_Oring__1(_1153194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1153196), _1153198)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1153194), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1153198), _1153196)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1153194), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1153194), _1153198)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1153194), _1153196)))], (20710 ^ _780205) ^ [_1153393] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1153393))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1153393) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20716 ^ _780205) ^ [_1153496] : [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), _1153496))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153496)))], (20722 ^ _780205) ^ [_1153581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153581)), -(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), _1153581))))], (20728 ^ _780205) ^ [_1153672, _1153674, _1153676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1153672), _1153674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153676)), -(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), _1153676)), _1153672)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1153676)), _1153674))))], (20738 ^ _780205) ^ [_1153865, _1153867] : [class_Rings_Olinordered__semidom(_1153865), 20741 ^ _780205 : [(20742 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153865), c_Groups_Ozero__class_Ozero(_1153865)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1153865), _1153867))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153867)))], (20748 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153865), c_Groups_Ozero__class_Ozero(_1153865)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1153865), _1153867))))]]], (20780 ^ _780205) ^ [_1154518, _1154520] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154518) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154520)), 20783 ^ _780205 : [(20784 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154518))))], (20786 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154520)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 20787 ^ _780205 : [(20788 ^ _780205) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154518)))], (20790 ^ _780205) ^ [] : [20791 ^ _780205 : [(20792 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154520))))], (20794 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154518) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 20795 ^ _780205 : [(20796 ^ _780205) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154520)))], (20798 ^ _780205) ^ [] : [_1154518 = _1154520]]]]], (20754 ^ _780205) ^ [_1154133, _1154135] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154133) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154135), 20757 ^ _780205 : [(20758 ^ _780205) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154133))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154135)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20764 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154133)))), 20767 ^ _780205 : [(20768 ^ _780205) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154135))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154133) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20774 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154135)))), -(_1154133 = _1154135)]]]]], (20802 ^ _780205) ^ [_1154931, _1154933, _1154935] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154931))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154931)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154933)), _1154935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154933)), _1154935))], (20808 ^ _780205) ^ [_1155069, _1155071, _1155073] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1155069)))), 20811 ^ _780205 : [(20812 ^ _780205) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1155071))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155069)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155071)), _1155073)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155069)), _1155073))], (20818 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1155071)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155069)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1155071)), _1155073)) = 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), _1155069), _1155071))), _1155073))]]], (20840 ^ _780205) ^ [_1155701, _1155703, _1155705] : [-(hBOOL(hAPP(_1155701, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1155703), _1155705))))), 20843 ^ _780205 : [(20844 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1155705), _1155703)))], (20846 ^ _780205) ^ [] : [hBOOL(hAPP(_1155701, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155703)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155705))))]], 20847 ^ _780205 : [(20848 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155703), _1155705)))], (20850 ^ _780205) ^ [] : [hBOOL(hAPP(_1155701, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (20824 ^ _780205) ^ [_1155412, _1155414, _1155416] : [hBOOL(hAPP(_1155412, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1155414), _1155416)))), 20827 ^ _780205 : [(20828 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1155416), _1155414)), -(hBOOL(hAPP(_1155412, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155414)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155416)))))], (20834 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1155414), _1155416)), -(hBOOL(hAPP(_1155412, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (20854 ^ _780205) ^ [_1155976, _1155978, _1155980, _1155982, _1155984] : [class_Groups_Oordered__ab__semigroup__add(_1155976), class_Rings_Osemiring__1(_1155976), 20864 ^ _780205 : [(20865 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1155978), 20863 ^ [_1155976, _1155978, _1155980, _1155982, _1155984]), _1155980)))], (20867 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155976), hAPP(_1155982, 20863 ^ [_1155976, _1155978, _1155980, _1155982, _1155984])), _1155984))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155976), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1155978, _1155976), _1155982), _1155980)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155976), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1155976), hAPP(c_Finite__Set_Ocard(_1155978), _1155980))), _1155984))))], (20871 ^ _780205) ^ [_1156375, _1156377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1156375), _1156377)), -(c_Nat__Transfer_Otsub(_1156377, _1156375) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1156377), _1156375))], (20877 ^ _780205) ^ [_1156474, _1156476] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1156474), _1156476))), -(c_Nat__Transfer_Otsub(_1156476, _1156474) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20883 ^ _780205) ^ [_1156526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1156526), 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), _1156526)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20889 ^ _780205) ^ [_1156617] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1156617), 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), _1156617)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1156617)))], (20895 ^ _780205) ^ [_1156675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1156675), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156675)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20901 ^ _780205) ^ [_1156772] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1156772), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156772)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1156772)))], (20907 ^ _780205) ^ [_1156839] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1156839)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156839) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20913 ^ _780205) ^ [_1156930] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1156930) = 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(_1156930)))))], (20919 ^ _780205) ^ [_1157036, _1157038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157036), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157036)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157038)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20925 ^ _780205) ^ [_1157141, _1157143] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157141), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157141)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1157143)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1157141), _1157143)))], (20931 ^ _780205) ^ [_1157220, _1157222] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157220) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157222), -(_1157220 = _1157222)], (20937 ^ _780205) ^ [_1157305, _1157307] : [_1157305 = _1157307, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157305) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157307))], (20943 ^ _780205) ^ [_1157411, _1157413] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157411) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157413), -(_1157411 = _1157413)], (20949 ^ _780205) ^ [_1157496, _1157498] : [_1157496 = _1157498, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157496) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157498))], (20955 ^ _780205) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20957 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (20959 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (20961 ^ _780205) ^ [_1157647] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1157647), c_Int_OPls) = _1157647)], (20963 ^ _780205) ^ [_1157676] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1157676) = _1157676)], (20965 ^ _780205) ^ [_1157702] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1157702) = c_Int_OPls)], (20967 ^ _780205) ^ [_1157728] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1157728), c_Int_OPls) = _1157728)], (20969 ^ _780205) ^ [_1157757] : [-(c_Int_Osucc(c_Int_Opred(_1157757)) = _1157757)], (20971 ^ _780205) ^ [_1157784] : [class_Int_Onumber__ring(_1157784), -(c_Groups_Ozero__class_Ozero(_1157784) = hAPP(c_Int_Onumber__class_Onumber__of(_1157784), c_Int_OPls))], (20977 ^ _780205) ^ [_1157871] : [class_Int_Onumber__ring(_1157871), -(hAPP(c_Int_Onumber__class_Onumber__of(_1157871), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1157871))], (20983 ^ _780205) ^ [_1157958, _1157960] : [class_Int_Onumber__ring(_1157958), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157958), hAPP(c_Int_Onumber__class_Onumber__of(_1157958), c_Int_OPls)), _1157960) = _1157960)], (20989 ^ _780205) ^ [_1158059, _1158061] : [class_Int_Onumber__ring(_1158059), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158059), _1158061), hAPP(c_Int_Onumber__class_Onumber__of(_1158059), c_Int_OPls)) = _1158061)], (20995 ^ _780205) ^ [] : [-(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))))], (20997 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20999 ^ _780205) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21001 ^ _780205) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (21003 ^ _780205) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (21005 ^ _780205) ^ [_1158256, _1158258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1158256)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1158258)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158256)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158258), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1158256))))], (21011 ^ _780205) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (21013 ^ _780205) ^ [_1158422, _1158424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158422), _1158424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1158422)), _1158424)))], (21019 ^ _780205) ^ [_1158519, _1158521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1158519)), _1158521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158519), _1158521)))], (21025 ^ _780205) ^ [_1158622] : [-(c_Int_Opred(_1158622) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1158622), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21027 ^ _780205) ^ [_1158653, _1158655] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1158653), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1158655)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158653), _1158655)))], (21029 ^ _780205) ^ [_1158702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158702), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158702)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21035 ^ _780205) ^ [_1158799] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158799), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1158799)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1158799)))], (21041 ^ _780205) ^ [_1158854, _1158856] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158854), _1158856), hAPP(c_Int_Onumber__class_Onumber__of(_1158854), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1158854)), class_Fields_Ofield__inverse__zero(_1158854), class_Int_Onumber__ring(_1158854)], (21051 ^ _780205) ^ [_1159021] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159021) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159021), c_Int_OPls)))], (21057 ^ _780205) ^ [_1159108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159108), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159108) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21063 ^ _780205) ^ [_1159213] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159213), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159213), c_Int_OPls)))], (21069 ^ _780205) ^ [_1159300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159300), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159300))], (21075 ^ _780205) ^ [_1159408, _1159410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159408)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159410))), 21078 ^ _780205 : [(21085 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159408), _1159410)))], (21079 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159408), _1159410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1159410)))]]], (21087 ^ _780205) ^ [_1159611, _1159613] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159611)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159613)))), 21090 ^ _780205 : [(21091 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159611), _1159613)))], (21093 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1159613))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159611), _1159613))], (21109 ^ _780205) ^ [_1159966, _1159968] : [21110 ^ _780205 : [(21111 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159966), _1159968))], (21113 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159966), 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), _1159966)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159968))))], (21099 ^ _780205) ^ [_1159836, _1159838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159836)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159836), _1159838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159836), c_Int_OPls)))], (21117 ^ _780205) ^ [_1160127, _1160129] : [class_Int_Onumber__ring(_1160127), class_Rings_Olinordered__idom(_1160127), 21124 ^ _780205 : [(21125 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160127), hAPP(c_Int_Onumber__class_Onumber__of(_1160127), _1160129)), c_Groups_Ozero__class_Ozero(_1160127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1160129), c_Int_OPls)))], (21131 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1160129), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160127), hAPP(c_Int_Onumber__class_Onumber__of(_1160127), _1160129)), c_Groups_Ozero__class_Ozero(_1160127))))]]], (21137 ^ _780205) ^ [_1160441, _1160443] : [class_Int_Onumber__ring(_1160441), class_Rings_Olinordered__idom(_1160441), 21144 ^ _780205 : [(21145 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160441), c_Groups_Ozero__class_Ozero(_1160441)), hAPP(c_Int_Onumber__class_Onumber__of(_1160441), _1160443))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1160443)))], (21151 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1160443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160441), c_Groups_Ozero__class_Ozero(_1160441)), hAPP(c_Int_Onumber__class_Onumber__of(_1160441), _1160443))))]]], (21157 ^ _780205) ^ [_1160746, _1160748] : [class_Int_Onumber__ring(_1160746), class_Rings_Olinordered__idom(_1160746), 21164 ^ _780205 : [(21165 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160746), c_Groups_Ozero__class_Ozero(_1160746)), hAPP(c_Int_Onumber__class_Onumber__of(_1160746), _1160748))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1160748)))], (21171 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1160748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160746), c_Groups_Ozero__class_Ozero(_1160746)), hAPP(c_Int_Onumber__class_Onumber__of(_1160746), _1160748))))]]], (21177 ^ _780205) ^ [_1161051, _1161053] : [class_Int_Onumber__ring(_1161051), class_Rings_Olinordered__idom(_1161051), 21184 ^ _780205 : [(21185 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161051), hAPP(c_Int_Onumber__class_Onumber__of(_1161051), _1161053)), c_Groups_Ozero__class_Ozero(_1161051))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161053), c_Int_OPls)))], (21191 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161053), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161051), hAPP(c_Int_Onumber__class_Onumber__of(_1161051), _1161053)), c_Groups_Ozero__class_Ozero(_1161051))))]]], (21197 ^ _780205) ^ [_1161377] : [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), _1161377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1161377)))], (21203 ^ _780205) ^ [_1161462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1161462)), -(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), _1161462))))], (21209 ^ _780205) ^ [_1161562, _1161564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161562), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161562)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161564)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161564))], (21215 ^ _780205) ^ [_1161674, _1161676] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161674), c_Int_OPls))), 21218 ^ _780205 : [(21219 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161676), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161674)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161676)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161674))], (21225 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161676), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161674)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1161676)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1161674), _1161676)))]]], (21231 ^ _780205) ^ [_1161947, _1161949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1161947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1161949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1161947, _1161949))))], (21241 ^ _780205) ^ [_1162094, _1162096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1162094), _1162096)), -(c_Nat__Transfer_Otsub(_1162096, _1162094) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1162096), _1162094))], (21247 ^ _780205) ^ [_1162211, _1162213, _1162215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162211), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162211)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162213)), _1162215)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21253 ^ _780205) ^ [_1162330, _1162332, _1162334] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162330), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162330)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1162332)), _1162334)) = 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), _1162330), _1162332))), _1162334))], (21259 ^ _780205) ^ [_1162408, _1162410] : [class_Int_Onumber__ring(_1162408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1162410)), -(hBOOL(hAPP(hAPP(c_member(_1162408), hAPP(c_Int_Onumber__class_Onumber__of(_1162408), _1162410)), c_Nat_Osemiring__1__class_ONats(_1162408))))], (21269 ^ _780205) ^ [_1162567, _1162569, _1162571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1162567)), 21275 ^ _780205 : [(21276 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1162569, 21274 ^ [_1162567, _1162569, _1162571])))], (21278 ^ _780205) ^ [] : [hBOOL(hAPP(_1162569, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21274 ^ [_1162567, _1162569, _1162571]), _1162567)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1162571)), 21283 ^ _780205 : [(21284 ^ _780205) ^ [_1162856] : [hBOOL(hAPP(_1162569, _1162856)), -(hBOOL(hAPP(_1162569, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1162856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1162571), _1162567)))))]]], (21290 ^ _780205) ^ [_1162979, _1162981, _1162983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1162979)), 21296 ^ _780205 : [(21297 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1162981, 21295 ^ [_1162979, _1162981, _1162983])))], (21299 ^ _780205) ^ [] : [hBOOL(hAPP(_1162981, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21295 ^ [_1162979, _1162981, _1162983]), _1162979)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1162983)), 21304 ^ _780205 : [(21305 ^ _780205) ^ [_1163268] : [hBOOL(hAPP(_1162981, _1163268)), -(hBOOL(hAPP(_1162981, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1163268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1162983), _1162979)))))]]], (21311 ^ _780205) ^ [_1163391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163391)), 21315 ^ _780205 : [(21316 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21314 ^ [_1163391])))], (21318 ^ _780205) ^ [] : [-(_1163391 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21314 ^ [_1163391]))]]], (21320 ^ _780205) ^ [_1163521, _1163523, _1163525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1163525), 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), _1163525), _1163523))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1163521)))))], (21326 ^ _780205) ^ [_1163668, _1163670, _1163672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1163670), 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), _1163670), _1163672))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1163668))), _1163672)))], (21332 ^ _780205) ^ [_1163815, _1163817] : [class_Groups_Oordered__ab__group__add__abs(_1163815), -(hAPP(c_Groups_Oabs__class_Oabs(_1163815), hAPP(c_Groups_Oabs__class_Oabs(_1163815), _1163817)) = hAPP(c_Groups_Oabs__class_Oabs(_1163815), _1163817))], (21338 ^ _780205) ^ [_1163920, _1163922, _1163924] : [class_Groups_Oordered__ab__group__add__abs(_1163920), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163920), hAPP(c_Groups_Oabs__class_Oabs(_1163920), _1163922)), _1163924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163920), _1163922), _1163924)))], (21348 ^ _780205) ^ [_1164089, _1164091] : [class_Groups_Oordered__ab__group__add__abs(_1164089), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164089), _1164091), hAPP(c_Groups_Oabs__class_Oabs(_1164089), _1164091))))], (21354 ^ _780205) ^ [_1164188] : [class_Groups_Oordered__ab__group__add__abs(_1164188), -(hAPP(c_Groups_Oabs__class_Oabs(_1164188), c_Groups_Ozero__class_Ozero(_1164188)) = c_Groups_Ozero__class_Ozero(_1164188))], (21360 ^ _780205) ^ [_1164279, _1164281] : [class_Groups_Oordered__ab__group__add__abs(_1164279), 21363 ^ _780205 : [(21364 ^ _780205) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1164279), _1164281) = c_Groups_Ozero__class_Ozero(_1164279), -(_1164281 = c_Groups_Ozero__class_Ozero(_1164279))], (21370 ^ _780205) ^ [] : [_1164281 = c_Groups_Ozero__class_Ozero(_1164279), -(hAPP(c_Groups_Oabs__class_Oabs(_1164279), _1164281) = c_Groups_Ozero__class_Ozero(_1164279))]]], (21376 ^ _780205) ^ [_1164511, _1164513, _1164515] : [class_Groups_Oordered__ab__group__add__abs(_1164511), -(hAPP(c_Groups_Oabs__class_Oabs(_1164511), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164511), hAPP(c_Groups_Oabs__class_Oabs(_1164511), _1164513)), hAPP(c_Groups_Oabs__class_Oabs(_1164511), _1164515))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164511), hAPP(c_Groups_Oabs__class_Oabs(_1164511), _1164513)), hAPP(c_Groups_Oabs__class_Oabs(_1164511), _1164515)))], (21382 ^ _780205) ^ [_1164670, _1164672] : [class_Rings_Olinordered__idom(_1164670), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164670), hAPP(c_Groups_Oabs__class_Oabs(_1164670), _1164672)), hAPP(c_Groups_Oabs__class_Oabs(_1164670), _1164672)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164670), _1164672), _1164672))], (21388 ^ _780205) ^ [_1164797, _1164799, _1164801] : [class_Rings_Olinordered__idom(_1164797), -(hAPP(c_Groups_Oabs__class_Oabs(_1164797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164797), _1164799), _1164801)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164797), hAPP(c_Groups_Oabs__class_Oabs(_1164797), _1164799)), hAPP(c_Groups_Oabs__class_Oabs(_1164797), _1164801)))], (21394 ^ _780205) ^ [_1164936, _1164938, _1164940] : [class_Groups_Oordered__ab__group__add__abs(_1164936), -(hAPP(c_Groups_Oabs__class_Oabs(_1164936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1164936), _1164938), _1164940)) = hAPP(c_Groups_Oabs__class_Oabs(_1164936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1164936), _1164940), _1164938)))], (21400 ^ _780205) ^ [_1165065] : [class_Rings_Olinordered__idom(_1165065), -(hAPP(c_Groups_Oabs__class_Oabs(_1165065), c_Groups_Oone__class_Oone(_1165065)) = c_Groups_Oone__class_Oone(_1165065))], (21406 ^ _780205) ^ [_1165156, _1165158] : [class_Rings_Olinordered__idom(_1165156), -(hAPP(c_Groups_Oabs__class_Oabs(_1165156), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1165156), _1165158)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1165156), _1165158))], (21412 ^ _780205) ^ [_1165261, _1165263, _1165265] : [class_Fields_Olinordered__field__inverse__zero(_1165261), -(hAPP(c_Groups_Oabs__class_Oabs(_1165261), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165261), _1165263), _1165265)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165261), hAPP(c_Groups_Oabs__class_Oabs(_1165261), _1165263)), hAPP(c_Groups_Oabs__class_Oabs(_1165261), _1165265)))], (21418 ^ _780205) ^ [_1165400] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1165400)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1165400))], (21420 ^ _780205) ^ [_1165432, _1165434] : [class_Groups_Oordered__ab__group__add__abs(_1165432), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165432), c_Groups_Ozero__class_Ozero(_1165432)), hAPP(c_Groups_Oabs__class_Oabs(_1165432), _1165434))))], (21426 ^ _780205) ^ [_1165535, _1165537] : [class_Groups_Oordered__ab__group__add__abs(_1165535), 21429 ^ _780205 : [(21430 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165535), hAPP(c_Groups_Oabs__class_Oabs(_1165535), _1165537)), c_Groups_Ozero__class_Ozero(_1165535))), -(_1165537 = c_Groups_Ozero__class_Ozero(_1165535))], (21436 ^ _780205) ^ [] : [_1165537 = c_Groups_Ozero__class_Ozero(_1165535), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165535), hAPP(c_Groups_Oabs__class_Oabs(_1165535), _1165537)), c_Groups_Ozero__class_Ozero(_1165535))))]]], (21442 ^ _780205) ^ [_1165788, _1165790] : [class_Groups_Oordered__ab__group__add__abs(_1165788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165788), c_Groups_Ozero__class_Ozero(_1165788)), _1165790)), -(hAPP(c_Groups_Oabs__class_Oabs(_1165788), _1165790) = _1165790)], (21452 ^ _780205) ^ [_1165943, _1165945] : [class_Groups_Oordered__ab__group__add__abs(_1165943), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165943), hAPP(c_Groups_Oabs__class_Oabs(_1165943), _1165945)), c_Groups_Ozero__class_Ozero(_1165943)))], (21458 ^ _780205) ^ [_1166047, _1166049] : [class_Groups_Oordered__ab__group__add__abs(_1166047), 21461 ^ _780205 : [(21462 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166047), c_Groups_Ozero__class_Ozero(_1166047)), hAPP(c_Groups_Oabs__class_Oabs(_1166047), _1166049))), _1166049 = c_Groups_Ozero__class_Ozero(_1166047)], (21468 ^ _780205) ^ [] : [-(_1166049 = c_Groups_Ozero__class_Ozero(_1166047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166047), c_Groups_Ozero__class_Ozero(_1166047)), hAPP(c_Groups_Oabs__class_Oabs(_1166047), _1166049))))]]], (21474 ^ _780205) ^ [_1166262, _1166264] : [class_Groups_Oordered__ab__group__add__abs(_1166262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166262), c_Groups_Ozero__class_Ozero(_1166262)), _1166264)), -(hAPP(c_Groups_Oabs__class_Oabs(_1166262), _1166264) = _1166264)], (21484 ^ _780205) ^ [_1166417, _1166419, _1166421] : [class_Groups_Oordered__ab__group__add__abs(_1166417), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166417), hAPP(c_Groups_Oabs__class_Oabs(_1166417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166417), _1166419), _1166421))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166417), hAPP(c_Groups_Oabs__class_Oabs(_1166417), _1166419)), hAPP(c_Groups_Oabs__class_Oabs(_1166417), _1166421)))))], (21490 ^ _780205) ^ [_1166570, _1166572, _1166574, _1166576, _1166578] : [class_Rings_Olinordered__idom(_1166570), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166570), hAPP(c_Groups_Oabs__class_Oabs(_1166570), _1166572)), _1166574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166570), hAPP(c_Groups_Oabs__class_Oabs(_1166570), _1166576)), _1166578)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166570), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166570), hAPP(c_Groups_Oabs__class_Oabs(_1166570), _1166572)), hAPP(c_Groups_Oabs__class_Oabs(_1166570), _1166576))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166570), _1166574), _1166578))))], (21504 ^ _780205) ^ [_1166881, _1166883, _1166885] : [class_Groups_Oordered__ab__group__add__abs(_1166881), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166881), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1166881), hAPP(c_Groups_Oabs__class_Oabs(_1166881), _1166883)), hAPP(c_Groups_Oabs__class_Oabs(_1166881), _1166885))), hAPP(c_Groups_Oabs__class_Oabs(_1166881), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1166881), _1166885), _1166883)))))], (21510 ^ _780205) ^ [_1167034, _1167036, _1167038] : [class_Groups_Oordered__ab__group__add__abs(_1167034), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167034), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1167034), hAPP(c_Groups_Oabs__class_Oabs(_1167034), _1167036)), hAPP(c_Groups_Oabs__class_Oabs(_1167034), _1167038))), hAPP(c_Groups_Oabs__class_Oabs(_1167034), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1167034), _1167036), _1167038)))))], (21516 ^ _780205) ^ [_1167187, _1167189, _1167191] : [class_Groups_Oordered__ab__group__add__abs(_1167187), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167187), hAPP(c_Groups_Oabs__class_Oabs(_1167187), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1167187), hAPP(c_Groups_Oabs__class_Oabs(_1167187), _1167189)), hAPP(c_Groups_Oabs__class_Oabs(_1167187), _1167191)))), hAPP(c_Groups_Oabs__class_Oabs(_1167187), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1167187), _1167189), _1167191)))))], (21522 ^ _780205) ^ [_1167350, _1167352, _1167354] : [class_Fields_Olinordered__field(_1167350), -(_1167352 = c_Groups_Ozero__class_Ozero(_1167350)), -(hAPP(c_Groups_Oabs__class_Oabs(_1167350), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1167350), _1167354), _1167352)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1167350), hAPP(c_Groups_Oabs__class_Oabs(_1167350), _1167354)), hAPP(c_Groups_Oabs__class_Oabs(_1167350), _1167352)))], (21532 ^ _780205) ^ [_1167508, _1167510] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1167508), _1167510)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1167508) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (21538 ^ _780205) ^ [_1167609, _1167611, _1167613] : [class_Rings_Olinordered__idom(_1167609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167609), c_Groups_Ozero__class_Ozero(_1167609)), _1167611)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167609), hAPP(c_Groups_Oabs__class_Oabs(_1167609), _1167613)), _1167611) = hAPP(c_Groups_Oabs__class_Oabs(_1167609), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167609), _1167613), _1167611)))], (21548 ^ _780205) ^ [_1167810, _1167812, _1167814] : [class_Rings_Oordered__ring__abs(_1167810), -(hAPP(c_Groups_Oabs__class_Oabs(_1167810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167810), _1167812), _1167814)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167810), hAPP(c_Groups_Oabs__class_Oabs(_1167810), _1167812)), hAPP(c_Groups_Oabs__class_Oabs(_1167810), _1167814))), 21555 ^ _780205 : [(21556 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167810), c_Groups_Ozero__class_Ozero(_1167810)), _1167812))], (21558 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167810), _1167812), c_Groups_Ozero__class_Ozero(_1167810)))]], 21559 ^ _780205 : [(21560 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167810), c_Groups_Ozero__class_Ozero(_1167810)), _1167814))], (21562 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167810), _1167814), c_Groups_Ozero__class_Ozero(_1167810)))]]], (21566 ^ _780205) ^ [_1168205, _1168207, _1168209, _1168211, _1168213] : [class_Groups_Oordered__ab__group__add__abs(_1168205), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168205), hAPP(c_Groups_Oabs__class_Oabs(_1168205), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168205), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1168205), _1168207), _1168209)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1168205), _1168211), _1168213)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1168205), hAPP(c_Groups_Oabs__class_Oabs(_1168205), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168205), _1168207), _1168211))), hAPP(c_Groups_Oabs__class_Oabs(_1168205), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168205), _1168209), _1168213))))))], (21572 ^ _780205) ^ [_1168426, _1168428, _1168430] : [class_Groups_Oordered__ab__group__add__abs(_1168426), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168426), hAPP(c_Groups_Oabs__class_Oabs(_1168426), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168426), _1168428), _1168430))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1168426), hAPP(c_Groups_Oabs__class_Oabs(_1168426), _1168428)), hAPP(c_Groups_Oabs__class_Oabs(_1168426), _1168430)))))], (21578 ^ _780205) ^ [_1168579, _1168581, _1168583] : [class_Fields_Olinordered__field__inverse__zero(_1168579), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), c_Groups_Ozero__class_Ozero(_1168579)), _1168581)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168579), hAPP(c_Groups_Oabs__class_Oabs(_1168579), _1168583)), _1168581) = hAPP(c_Groups_Oabs__class_Oabs(_1168579), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168579), _1168583), _1168581)))], (21588 ^ _780205) ^ [_1168792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1168792)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1168792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21594 ^ _780205) ^ [_1168879] : [_1168879 = 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), _1168879)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (21600 ^ _780205) ^ [_1168972] : [class_Rings_Osemiring__1(_1168972), -(hBOOL(hAPP(hAPP(c_member(_1168972), c_Groups_Ozero__class_Ozero(_1168972)), c_Nat_Osemiring__1__class_ONats(_1168972))))], (21606 ^ _780205) ^ [_1169067, _1169069, _1169071] : [class_Rings_Osemiring__1(_1169067), hBOOL(hAPP(hAPP(c_member(_1169067), _1169069), c_Nat_Osemiring__1__class_ONats(_1169067))), hBOOL(hAPP(hAPP(c_member(_1169067), _1169071), c_Nat_Osemiring__1__class_ONats(_1169067))), -(hBOOL(hAPP(hAPP(c_member(_1169067), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169067), _1169069), _1169071)), c_Nat_Osemiring__1__class_ONats(_1169067))))], (21620 ^ _780205) ^ [_1169322, _1169324, _1169326] : [class_Rings_Osemiring__1(_1169322), hBOOL(hAPP(hAPP(c_member(_1169322), _1169324), c_Nat_Osemiring__1__class_ONats(_1169322))), hBOOL(hAPP(hAPP(c_member(_1169322), _1169326), c_Nat_Osemiring__1__class_ONats(_1169322))), -(hBOOL(hAPP(hAPP(c_member(_1169322), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169322), _1169324), _1169326)), c_Nat_Osemiring__1__class_ONats(_1169322))))], (21634 ^ _780205) ^ [_1169577] : [class_Rings_Osemiring__1(_1169577), -(hBOOL(hAPP(hAPP(c_member(_1169577), c_Groups_Oone__class_Oone(_1169577)), c_Nat_Osemiring__1__class_ONats(_1169577))))], (21640 ^ _780205) ^ [_1169672, _1169674] : [class_Rings_Osemiring__1(_1169672), -(hBOOL(hAPP(hAPP(c_member(_1169672), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1169672), _1169674)), c_Nat_Osemiring__1__class_ONats(_1169672))))], (21646 ^ _780205) ^ [_1169775, _1169777, _1169779] : [21648 ^ _780205 : [(21649 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21647 ^ [_1169775, _1169777, _1169779]), _1169775)))], (21651 ^ _780205) ^ [] : [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(_1169777, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 21647 ^ [_1169775, _1169777, _1169779]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1169777, 21647 ^ [_1169775, _1169777, _1169779])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1169777, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1169779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1169779), hAPP(_1169777, _1169775))), 21661 ^ _780205 : [(21662 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 21660 ^ [_1169775, _1169777, _1169779]), _1169775)))], (21664 ^ _780205) ^ [] : [-(hAPP(_1169777, 21660 ^ [_1169775, _1169777, _1169779]) = _1169779)]]], (21666 ^ _780205) ^ [_1170225, _1170227, _1170229] : [21668 ^ _780205 : [(21669 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21667 ^ [_1170225, _1170227, _1170229]), _1170225)))], (21671 ^ _780205) ^ [] : [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(_1170227, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 21667 ^ [_1170225, _1170227, _1170229]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1170227, 21667 ^ [_1170225, _1170227, _1170229])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1170227, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1170229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1170229), hAPP(_1170227, _1170225))), 21681 ^ _780205 : [(21682 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 21680 ^ [_1170225, _1170227, _1170229]), _1170225)))], (21684 ^ _780205) ^ [] : [-(hAPP(_1170227, 21680 ^ [_1170225, _1170227, _1170229]) = _1170229)]]], (21686 ^ _780205) ^ [_1170675, _1170677, _1170679, _1170681] : [21688 ^ _780205 : [(21689 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1170675), 21687 ^ [_1170675, _1170677, _1170679, _1170681])))], (21691 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21687 ^ [_1170675, _1170677, _1170679, _1170681]), _1170677)))], (21693 ^ _780205) ^ [] : [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(_1170679, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 21687 ^ [_1170675, _1170677, _1170679, _1170681]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1170679, 21687 ^ [_1170675, _1170677, _1170679, _1170681])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170675), _1170677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1170679, _1170675)), _1170681)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1170681), hAPP(_1170679, _1170677))), 21707 ^ _780205 : [(21708 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1170675), 21706 ^ [_1170675, _1170677, _1170679, _1170681])))], (21710 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 21706 ^ [_1170675, _1170677, _1170679, _1170681]), _1170677)))], (21712 ^ _780205) ^ [] : [-(hAPP(_1170679, 21706 ^ [_1170675, _1170677, _1170679, _1170681]) = _1170681)]]], (21714 ^ _780205) ^ [_1171301, _1171303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1171301)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1171303)), _1171301) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171303), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171301), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (21720 ^ _780205) ^ [_1171424, _1171426, _1171428, _1171430] : [_1171424 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1171426), _1171428)), _1171430), -(_1171426 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1171424, _1171426) = _1171430), 21727 ^ _780205 : [(21728 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171426)))], (21730 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171430), _1171426))]], 21735 ^ _780205 : [(21736 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171426))], (21738 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171426), _1171430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171430), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (21750 ^ _780205) ^ [_1171889, _1171891, _1171893, _1171895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171889)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171891), _1171893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1171893), 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), _1171891), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1171895, _1171889))), _1171893)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21764 ^ _780205) ^ [_1172163, _1172165] : [c_Int_OBit1(_1172163) = c_Int_OBit1(_1172165), -(_1172163 = _1172165)], (21770 ^ _780205) ^ [_1172244, _1172246] : [_1172244 = _1172246, -(c_Int_OBit1(_1172244) = c_Int_OBit1(_1172246))], (21776 ^ _780205) ^ [_1172331, _1172333, _1172335] : [class_Divides_Osemiring__div(_1172331), -(c_Divides_Odiv__class_Omod(_1172331, c_Divides_Odiv__class_Omod(_1172331, _1172333, _1172335), _1172335) = c_Divides_Odiv__class_Omod(_1172331, _1172333, _1172335))], (21782 ^ _780205) ^ [_1172432, _1172434] : [class_Divides_Osemiring__div(_1172432), -(c_Divides_Odiv__class_Omod(_1172432, c_Groups_Ozero__class_Ozero(_1172432), _1172434) = c_Groups_Ozero__class_Ozero(_1172432))], (21788 ^ _780205) ^ [_1172523, _1172525] : [class_Divides_Osemiring__div(_1172523), -(c_Divides_Odiv__class_Omod(_1172523, _1172525, c_Groups_Ozero__class_Ozero(_1172523)) = _1172525)], (21794 ^ _780205) ^ [_1172610, _1172612] : [class_Divides_Osemiring__div(_1172610), -(c_Divides_Odiv__class_Omod(_1172610, _1172612, _1172612) = c_Groups_Ozero__class_Ozero(_1172610))], (21800 ^ _780205) ^ [_1172697, _1172699, _1172701] : [class_Divides_Osemiring__div(_1172697), -(c_Divides_Odiv__class_Omod(_1172697, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172697), _1172699), _1172701), _1172701) = c_Divides_Odiv__class_Omod(_1172697, _1172699, _1172701))], (21806 ^ _780205) ^ [_1172806, _1172808, _1172810] : [class_Divides_Osemiring__div(_1172806), -(c_Divides_Odiv__class_Omod(_1172806, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172806), _1172808), _1172810), _1172808) = c_Divides_Odiv__class_Omod(_1172806, _1172810, _1172808))], (21812 ^ _780205) ^ [_1172915, _1172917, _1172919, _1172921] : [class_Divides_Osemiring__div(_1172915), -(c_Divides_Odiv__class_Omod(_1172915, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172915), _1172917), _1172919), _1172921) = c_Divides_Odiv__class_Omod(_1172915, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172915), _1172917), c_Divides_Odiv__class_Omod(_1172915, _1172919, _1172921)), _1172921))], (21818 ^ _780205) ^ [_1173050, _1173052, _1173054, _1173056] : [class_Divides_Osemiring__div(_1173050), -(c_Divides_Odiv__class_Omod(_1173050, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173050), _1173052), _1173054), _1173056) = c_Divides_Odiv__class_Omod(_1173050, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173050), c_Divides_Odiv__class_Omod(_1173050, _1173052, _1173056)), _1173054), _1173056))], (21824 ^ _780205) ^ [_1173185, _1173187, _1173189, _1173191] : [class_Divides_Osemiring__div(_1173185), -(c_Divides_Odiv__class_Omod(_1173185, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173185), _1173187), _1173189), _1173191) = c_Divides_Odiv__class_Omod(_1173185, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173185), c_Divides_Odiv__class_Omod(_1173185, _1173187, _1173191)), c_Divides_Odiv__class_Omod(_1173185, _1173189, _1173191)), _1173191))], (21830 ^ _780205) ^ [_1173328, _1173330, _1173332, _1173334] : [class_Divides_Osemiring__div(_1173328), -(c_Divides_Odiv__class_Omod(_1173328, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173328), _1173330), c_Divides_Odiv__class_Omod(_1173328, _1173332, _1173334)), _1173334) = c_Divides_Odiv__class_Omod(_1173328, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173328), _1173330), _1173332), _1173334))], (21836 ^ _780205) ^ [_1173463, _1173465, _1173467, _1173469] : [class_Divides_Osemiring__div(_1173463), -(c_Divides_Odiv__class_Omod(_1173463, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173463), c_Divides_Odiv__class_Omod(_1173463, _1173465, _1173467)), _1173469), _1173467) = c_Divides_Odiv__class_Omod(_1173463, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173463), _1173465), _1173469), _1173467))], (21842 ^ _780205) ^ [_1173598, _1173600, _1173602, _1173604, _1173606, _1173608] : [class_Divides_Osemiring__div(_1173598), c_Divides_Odiv__class_Omod(_1173598, _1173600, _1173602) = c_Divides_Odiv__class_Omod(_1173598, _1173604, _1173602), c_Divides_Odiv__class_Omod(_1173598, _1173606, _1173602) = c_Divides_Odiv__class_Omod(_1173598, _1173608, _1173602), -(c_Divides_Odiv__class_Omod(_1173598, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173598), _1173600), _1173606), _1173602) = c_Divides_Odiv__class_Omod(_1173598, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173598), _1173604), _1173608), _1173602))], (21856 ^ _780205) ^ [_1173881, _1173883, _1173885, _1173887, _1173889, _1173891] : [class_Divides_Osemiring__div(_1173881), c_Divides_Odiv__class_Omod(_1173881, _1173883, _1173885) = c_Divides_Odiv__class_Omod(_1173881, _1173887, _1173885), c_Divides_Odiv__class_Omod(_1173881, _1173889, _1173885) = c_Divides_Odiv__class_Omod(_1173881, _1173891, _1173885), -(c_Divides_Odiv__class_Omod(_1173881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173881), _1173883), _1173889), _1173885) = c_Divides_Odiv__class_Omod(_1173881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173881), _1173887), _1173891), _1173885))], (21870 ^ _780205) ^ [_1174164, _1174166, _1174168, _1174170] : [class_Divides_Osemiring__div(_1174164), -(c_Divides_Odiv__class_Omod(_1174164, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174164), c_Divides_Odiv__class_Omod(_1174164, _1174166, _1174168)), _1174170), _1174168) = c_Divides_Odiv__class_Omod(_1174164, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174164), _1174166), _1174170), _1174168))], (21876 ^ _780205) ^ [_1174299, _1174301, _1174303, _1174305] : [class_Divides_Osemiring__div(_1174299), -(c_Divides_Odiv__class_Omod(_1174299, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174299), _1174301), _1174303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174299), _1174305), _1174303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174299), c_Divides_Odiv__class_Omod(_1174299, _1174301, _1174305)), _1174303))], (21882 ^ _780205) ^ [_1174442, _1174444, _1174446, _1174448] : [class_Divides_Osemiring__div(_1174442), -(c_Divides_Odiv__class_Omod(_1174442, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174442), _1174444), _1174446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174442), _1174444), _1174448)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174442), _1174444), c_Divides_Odiv__class_Omod(_1174442, _1174446, _1174448)))], (21888 ^ _780205) ^ [_1174585, _1174587, _1174589, _1174591] : [class_Divides_Osemiring__div(_1174585), -(c_Divides_Odiv__class_Omod(_1174585, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174585), _1174587), _1174589), _1174591) = c_Divides_Odiv__class_Omod(_1174585, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174585), c_Divides_Odiv__class_Omod(_1174585, _1174587, _1174591)), c_Divides_Odiv__class_Omod(_1174585, _1174589, _1174591)), _1174591))], (21894 ^ _780205) ^ [_1174728, _1174730, _1174732, _1174734] : [class_Divides_Osemiring__div(_1174728), -(c_Divides_Odiv__class_Omod(_1174728, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174728), _1174730), _1174732), _1174734) = c_Divides_Odiv__class_Omod(_1174728, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174728), c_Divides_Odiv__class_Omod(_1174728, _1174730, _1174734)), _1174732), _1174734))], (21900 ^ _780205) ^ [_1174863, _1174865, _1174867, _1174869] : [class_Divides_Osemiring__div(_1174863), -(c_Divides_Odiv__class_Omod(_1174863, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174863), _1174865), _1174867), _1174869) = c_Divides_Odiv__class_Omod(_1174863, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174863), _1174865), c_Divides_Odiv__class_Omod(_1174863, _1174867, _1174869)), _1174869))], (21906 ^ _780205) ^ [_1174998, _1175000, _1175002, _1175004] : [class_Divides_Oring__div(_1174998), -(c_Divides_Odiv__class_Omod(_1174998, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1174998), _1175000), _1175002), _1175004) = c_Divides_Odiv__class_Omod(_1174998, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1174998), _1175000), c_Divides_Odiv__class_Omod(_1174998, _1175002, _1175004)), _1175004))], (21912 ^ _780205) ^ [_1175133, _1175135, _1175137, _1175139] : [class_Divides_Oring__div(_1175133), -(c_Divides_Odiv__class_Omod(_1175133, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1175133), _1175135), _1175137), _1175139) = c_Divides_Odiv__class_Omod(_1175133, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1175133), c_Divides_Odiv__class_Omod(_1175133, _1175135, _1175139)), _1175137), _1175139))], (21918 ^ _780205) ^ [_1175268, _1175270, _1175272, _1175274] : [class_Divides_Oring__div(_1175268), -(c_Divides_Odiv__class_Omod(_1175268, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1175268), _1175270), _1175272), _1175274) = c_Divides_Odiv__class_Omod(_1175268, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1175268), c_Divides_Odiv__class_Omod(_1175268, _1175270, _1175274)), c_Divides_Odiv__class_Omod(_1175268, _1175272, _1175274)), _1175274))], (21924 ^ _780205) ^ [_1175411, _1175413, _1175415, _1175417, _1175419, _1175421] : [class_Divides_Oring__div(_1175411), c_Divides_Odiv__class_Omod(_1175411, _1175413, _1175415) = c_Divides_Odiv__class_Omod(_1175411, _1175417, _1175415), c_Divides_Odiv__class_Omod(_1175411, _1175419, _1175415) = c_Divides_Odiv__class_Omod(_1175411, _1175421, _1175415), -(c_Divides_Odiv__class_Omod(_1175411, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1175411), _1175413), _1175419), _1175415) = c_Divides_Odiv__class_Omod(_1175411, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1175411), _1175417), _1175421), _1175415))], (21938 ^ _780205) ^ [_1175694] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1175694) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21940 ^ _780205) ^ [_1175721] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1175721, _1175721) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21942 ^ _780205) ^ [_1175763, _1175765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1175763)), c_Int_OBit1(_1175765))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1175763), _1175765)))], (21948 ^ _780205) ^ [_1175864, _1175866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1175864), _1175866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1175864)), c_Int_OBit1(_1175866))))], (21954 ^ _780205) ^ [_1175986, _1175988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1175986)), c_Int_OBit1(_1175988))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1175986), _1175988)))], (21960 ^ _780205) ^ [_1176087, _1176089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176087), _1176089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1176087)), c_Int_OBit1(_1176089))))], (21966 ^ _780205) ^ [_1176209, _1176211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1176209)), c_Int_OBit1(_1176211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176209), _1176211)))], (21972 ^ _780205) ^ [_1176310, _1176312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176310), _1176312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1176310)), c_Int_OBit1(_1176312))))], (21978 ^ _780205) ^ [_1176432, _1176434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1176432)), c_Int_OBit1(_1176434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176432), _1176434)))], (21984 ^ _780205) ^ [_1176533, _1176535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176533), _1176535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1176533)), c_Int_OBit1(_1176535))))], (21990 ^ _780205) ^ [_1176649] : [c_Int_OBit1(_1176649) = c_Int_OPls], (21992 ^ _780205) ^ [_1176683] : [c_Int_OPls = c_Int_OBit1(_1176683)], (21994 ^ _780205) ^ [_1176708, _1176710, _1176712] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1176708), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176710, _1176712)), _1176712) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1176708), _1176710), _1176712))], (21996 ^ _780205) ^ [_1176759, _1176761, _1176763] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1176759), _1176761), _1176763) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1176759), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176761, _1176763)), _1176763))], (21998 ^ _780205) ^ [_1176810, _1176812, _1176814] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1176810), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176812, _1176814)), _1176814) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1176810), _1176812), _1176814))], (22000 ^ _780205) ^ [_1176861, _1176863, _1176865] : [-(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, _1176861, _1176863)), _1176865), _1176863) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1176861), _1176865), _1176863))], (22002 ^ _780205) ^ [_1176912, _1176914, _1176916] : [class_Divides_Osemiring__div(_1176912), -(c_Divides_Odiv__class_Omod(_1176912, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176912), _1176914), _1176916), _1176916) = c_Groups_Ozero__class_Ozero(_1176912))], (22008 ^ _780205) ^ [_1177017, _1177019, _1177021] : [class_Divides_Osemiring__div(_1177017), -(c_Divides_Odiv__class_Omod(_1177017, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177017), _1177019), _1177021), _1177019) = c_Groups_Ozero__class_Ozero(_1177017))], (22014 ^ _780205) ^ [_1177122, _1177124, _1177126, _1177128] : [class_Divides_Osemiring__div(_1177122), -(c_Divides_Odiv__class_Omod(_1177122, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177122), _1177124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177122), _1177126), _1177128)), _1177128) = c_Divides_Odiv__class_Omod(_1177122, _1177124, _1177128))], (22020 ^ _780205) ^ [_1177249, _1177251, _1177253, _1177255] : [class_Divides_Osemiring__div(_1177249), -(c_Divides_Odiv__class_Omod(_1177249, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177249), _1177251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177249), _1177253), _1177255)), _1177253) = c_Divides_Odiv__class_Omod(_1177249, _1177251, _1177253))], (22026 ^ _780205) ^ [_1177376, _1177378] : [class_Divides_Osemiring__div(_1177376), -(c_Divides_Odiv__class_Omod(_1177376, _1177378, c_Groups_Oone__class_Oone(_1177376)) = c_Groups_Ozero__class_Ozero(_1177376))], (22032 ^ _780205) ^ [_1177467, _1177469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177467)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177469)), -(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, _1177467, _1177469))))], (22042 ^ _780205) ^ [_1177616, _1177618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1177616, _1177618)), _1177616)))], (22048 ^ _780205) ^ [_1177715, _1177717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1177717, _1177715)), _1177715)))], (22054 ^ _780205) ^ [_1177814, _1177816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177814), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177814), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1177816, _1177814))))], (22060 ^ _780205) ^ [_1177931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1177931)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177931), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22066 ^ _780205) ^ [_1178026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178026), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1178026)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22072 ^ _780205) ^ [_1178142, _1178144] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178142, _1178144) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1178142 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178144), 22075 ^ [_1178142, _1178144]))], (22079 ^ _780205) ^ [_1178247, _1178249] : [22080 ^ _780205 : [(22081 ^ _780205) ^ [_1178296] : [_1178247 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178249), _1178296)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1178247, _1178249) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22085 ^ _780205) ^ [_1178371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1178371))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1178371)))], (22091 ^ _780205) ^ [_1178454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1178454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1178454))))], (22097 ^ _780205) ^ [_1178555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1178555)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178555), c_Int_OPls)))], (22103 ^ _780205) ^ [_1178650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178650), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1178650)), c_Int_OPls)))], (22109 ^ _780205) ^ [_1178751] : [-(c_Int_OBit1(_1178751) = 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)), _1178751)), _1178751))], (22111 ^ _780205) ^ [_1178797] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1178797)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178797))))], (22117 ^ _780205) ^ [_1178892] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178892))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1178892)))))], (22123 ^ _780205) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (22125 ^ _780205) ^ [_1179011, _1179013] : [class_Int_Onumber__ring(_1179011), -(hAPP(c_Int_Onumber__class_Onumber__of(_1179011), c_Int_OBit1(_1179013)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179011), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179011), c_Groups_Oone__class_Oone(_1179011)), hAPP(c_Int_Onumber__class_Onumber__of(_1179011), _1179013))), hAPP(c_Int_Onumber__class_Onumber__of(_1179011), _1179013)))], (22131 ^ _780205) ^ [_1179156, _1179158] : [class_Int_Onumber__ring(_1179156), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179156), hAPP(c_Int_Onumber__class_Onumber__of(_1179156), c_Int_OBit1(c_Int_OPls))), _1179158) = _1179158)], (22137 ^ _780205) ^ [_1179257, _1179259] : [class_Int_Onumber__ring(_1179257), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179257), _1179259), hAPP(c_Int_Onumber__class_Onumber__of(_1179257), c_Int_OBit1(c_Int_OPls))) = _1179259)], (22143 ^ _780205) ^ [_1179358, _1179360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179358), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179360), _1179358)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179358, _1179360) = _1179358)], (22153 ^ _780205) ^ [_1179515, _1179517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179515), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22156 ^ _780205 : [(22157 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179517, _1179515)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22159 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179515), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179517, _1179515))))]]], (22161 ^ _780205) ^ [_1179664, _1179666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179664), 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, _1179666, _1179664)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22167 ^ _780205) ^ [_1179769, _1179771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179769), _1179771)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179769, _1179771) = _1179769)], (22177 ^ _780205) ^ [_1179920, _1179922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179920)), 22180 ^ _780205 : [(22181 ^ _780205) ^ [] : [-(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, _1179922, _1179920))))], (22183 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179922, _1179920)), _1179920)))]]], (22185 ^ _780205) ^ [_1180057, _1180059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180057)), -(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, _1180059, _1180057))))], (22191 ^ _780205) ^ [_1180150] : [class_Int_Onumber__ring(_1180150), -(c_Groups_Oone__class_Oone(_1180150) = hAPP(c_Int_Onumber__class_Onumber__of(_1180150), c_Int_OBit1(c_Int_OPls)))], (22197 ^ _780205) ^ [_1180237] : [class_Int_Onumber__ring(_1180237), -(hAPP(c_Int_Onumber__class_Onumber__of(_1180237), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1180237))], (22203 ^ _780205) ^ [_1180336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1180336))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1180336)))], (22209 ^ _780205) ^ [_1180419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1180419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1180419))))], (22215 ^ _780205) ^ [_1180520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1180520)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180520), c_Int_OPls)))], (22221 ^ _780205) ^ [_1180615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180615), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1180615)), c_Int_OPls)))], (22227 ^ _780205) ^ [_1180716, _1180718] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180716), _1180718), hAPP(c_Int_Onumber__class_Onumber__of(_1180716), c_Int_OBit1(c_Int_OPls))) = _1180718), class_Fields_Ofield(_1180716), class_Int_Onumber__ring(_1180716)], (22237 ^ _780205) ^ [_1180867, _1180869] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180867), _1180869), hAPP(c_Int_Onumber__class_Onumber__of(_1180867), c_Int_OBit1(c_Int_OPls))) = _1180869), class_Fields_Ofield(_1180867), class_Int_Onumber__ring(_1180867)], (22247 ^ _780205) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (22249 ^ _780205) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (22251 ^ _780205) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (22253 ^ _780205) ^ [_1181072, _1181074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181072)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181072), _1181074)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181072, _1181074) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181072), _1181074))], (22263 ^ _780205) ^ [] : [-(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)))], (22265 ^ _780205) ^ [] : [-(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)))))], (22267 ^ _780205) ^ [] : [-(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))))))], (22269 ^ _780205) ^ [_1181301] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1181301))) = 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)))), _1181301))], (22271 ^ _780205) ^ [] : [-(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)))))], (22273 ^ _780205) ^ [_1181354, _1181356] : [class_Int_Onumber__ring(_1181354), class_Rings_Olinordered__idom(_1181354), 22280 ^ _780205 : [(22281 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181354), hAPP(c_Int_Onumber__class_Onumber__of(_1181354), _1181356)), c_Groups_Oone__class_Oone(_1181354))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181356), c_Int_OBit1(c_Int_OPls))))], (22287 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181356), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181354), hAPP(c_Int_Onumber__class_Onumber__of(_1181354), _1181356)), c_Groups_Oone__class_Oone(_1181354))))]]], (22293 ^ _780205) ^ [_1181668, _1181670] : [class_Int_Onumber__ring(_1181668), class_Rings_Olinordered__idom(_1181668), 22300 ^ _780205 : [(22301 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181668), c_Groups_Oone__class_Oone(_1181668)), hAPP(c_Int_Onumber__class_Onumber__of(_1181668), _1181670))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1181670)))], (22307 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1181670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181668), c_Groups_Oone__class_Oone(_1181668)), hAPP(c_Int_Onumber__class_Onumber__of(_1181668), _1181670))))]]], (22313 ^ _780205) ^ [_1181973, _1181975] : [class_Int_Onumber__ring(_1181973), class_Rings_Olinordered__idom(_1181973), 22320 ^ _780205 : [(22321 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181973), c_Groups_Oone__class_Oone(_1181973)), hAPP(c_Int_Onumber__class_Onumber__of(_1181973), _1181975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1181975)))], (22327 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1181975)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181973), c_Groups_Oone__class_Oone(_1181973)), hAPP(c_Int_Onumber__class_Onumber__of(_1181973), _1181975))))]]], (22333 ^ _780205) ^ [_1182278, _1182280] : [class_Int_Onumber__ring(_1182278), class_Rings_Olinordered__idom(_1182278), 22340 ^ _780205 : [(22341 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182278), hAPP(c_Int_Onumber__class_Onumber__of(_1182278), _1182280)), c_Groups_Oone__class_Oone(_1182278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182280), c_Int_OBit1(c_Int_OPls))))], (22347 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182280), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182278), hAPP(c_Int_Onumber__class_Onumber__of(_1182278), _1182280)), c_Groups_Oone__class_Oone(_1182278))))]]], (22353 ^ _780205) ^ [_1182592, _1182594] : [class_Int_Onumber__ring(_1182592), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182592), hAPP(c_Int_Onumber__class_Onumber__of(_1182592), _1182594)), c_Groups_Oone__class_Oone(_1182592)) = hAPP(c_Int_Onumber__class_Onumber__of(_1182592), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1182594), c_Int_OBit1(c_Int_OPls))))], (22359 ^ _780205) ^ [_1182719, _1182721] : [class_Int_Onumber__ring(_1182719), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182719), c_Groups_Oone__class_Oone(_1182719)), hAPP(c_Int_Onumber__class_Onumber__of(_1182719), _1182721)) = hAPP(c_Int_Onumber__class_Onumber__of(_1182719), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1182721)))], (22411 ^ _780205) ^ [_1183735, _1183737, _1183739] : [-(hBOOL(hAPP(_1183735, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183737, _1183739)))), 22414 ^ _780205 : [(22415 ^ _780205) ^ [] : [-(_1183739 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22417 ^ _780205) ^ [] : [hBOOL(hAPP(_1183735, _1183737))]], 22420 ^ _780205 : [(22421 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183739)))], (22425 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22423 ^ [_1183735, _1183737, _1183739])))], (22427 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 22423 ^ [_1183735, _1183737, _1183739]), _1183739)))], (22429 ^ _780205) ^ [] : [-(_1183737 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1183739), 22422 ^ [_1183735, _1183737, _1183739])), 22423 ^ [_1183735, _1183737, _1183739]))], (22431 ^ _780205) ^ [] : [hBOOL(hAPP(_1183735, 22423 ^ [_1183735, _1183737, _1183739]))]], 22432 ^ _780205 : [(22433 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183739), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22437 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183739), 22435 ^ [_1183735, _1183737, _1183739])))], (22439 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 22435 ^ [_1183735, _1183737, _1183739]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22441 ^ _780205) ^ [] : [-(_1183737 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1183739), 22434 ^ [_1183735, _1183737, _1183739])), 22435 ^ [_1183735, _1183737, _1183739]))], (22443 ^ _780205) ^ [] : [hBOOL(hAPP(_1183735, 22435 ^ [_1183735, _1183737, _1183739]))]]], (22365 ^ _780205) ^ [_1182858, _1182860, _1182862] : [hBOOL(hAPP(_1182858, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1182860, _1182862))), 22368 ^ _780205 : [(22369 ^ _780205) ^ [] : [_1182862 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1182858, _1182860)))], (22375 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182862)), 22378 ^ _780205 : [(22379 ^ _780205) ^ [_1183188, _1183190] : [-(hBOOL(hAPP(_1182858, _1183188))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183188), _1182862)), _1182860 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182862), _1183190)), _1183188)]]], (22393 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182862), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22396 ^ _780205 : [(22397 ^ _780205) ^ [_1183480, _1183482] : [-(hBOOL(hAPP(_1182858, _1183480))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182862), _1183480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1183480), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1182860 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182862), _1183482)), _1183480)]]]]], (22447 ^ _780205) ^ [_1184447, _1184449, _1184451, _1184453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184449), _1184451)), -(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), _1184451), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1184453, _1184447))), _1184449))))], (22461 ^ _780205) ^ [_1184694, _1184696, _1184698, _1184700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184696), _1184698)), -(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), _1184698), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1184700, _1184694))), _1184696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1184698), _1184694))))], (22475 ^ _780205) ^ [_1184959, _1184961, _1184963, _1184965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184959)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184961), _1184963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1184963), 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), _1184961), _1184959)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1184961), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1184965, _1184959))), _1184963))))], (22489 ^ _780205) ^ [_1185230, _1185232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185230), 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)))), _1185232)), 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)))), _1185230)) = 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), _1185232), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1185230))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22495 ^ _780205) ^ [_1185390, _1185392] : [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), _1185390))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1185392)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1185390))) = 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), _1185392), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1185390)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22501 ^ _780205) ^ [_1185537, _1185539] : [-(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), _1185537)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1185539)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1185537))) = 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), _1185539)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1185537)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22507 ^ _780205) ^ [_1185619, _1185621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185619)), -(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)))), _1185621)), 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)))), _1185619)) = 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, _1185621, _1185619))))], (22513 ^ _780205) ^ [] : [-(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)))], (22515 ^ _780205) ^ [_1185764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185764)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1185764) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1185764), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22521 ^ _780205) ^ [_1185863, _1185865] : [class_Int_Onumber__ring(_1185863), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1185863), hAPP(c_Int_Onumber__class_Onumber__of(_1185863), _1185865)), c_Groups_Oone__class_Oone(_1185863)) = hAPP(c_Int_Onumber__class_Onumber__of(_1185863), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1185865), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (22527 ^ _780205) ^ [_1185990, _1185992] : [-(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), _1185990))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185992))))], (22529 ^ _780205) ^ [_1186029, _1186031] : [-(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, _1186029)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186031))))], (22531 ^ _780205) ^ [_1186071, _1186073] : [class_Int_Onumber__ring(_1186071), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186071), hAPP(c_Int_Onumber__class_Onumber__of(_1186071), c_Int_OMin)), _1186073) = hAPP(c_Groups_Ouminus__class_Ouminus(_1186071), _1186073))], (22537 ^ _780205) ^ [_1186182, _1186184] : [class_Int_Onumber__ring(_1186182), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186182), _1186184), hAPP(c_Int_Onumber__class_Onumber__of(_1186182), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1186182), _1186184))], (22543 ^ _780205) ^ [_1186293, _1186295, _1186297] : [class_Int_Onumber__ring(_1186293), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186293), hAPP(c_Groups_Ouminus__class_Ouminus(_1186293), hAPP(c_Int_Onumber__class_Onumber__of(_1186293), _1186295))), _1186297) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186293), hAPP(c_Int_Onumber__class_Onumber__of(_1186293), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186295))), _1186297))], (22549 ^ _780205) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (22551 ^ _780205) ^ [_1186456, _1186458] : [class_Int_Onumber__ring(_1186456), -(hAPP(c_Int_Onumber__class_Onumber__of(_1186456), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186458)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1186456), hAPP(c_Int_Onumber__class_Onumber__of(_1186456), _1186458)))], (22557 ^ _780205) ^ [_1186567, _1186569] : [class_Int_Onumber__ring(_1186567), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1186567), hAPP(c_Int_Onumber__class_Onumber__of(_1186567), _1186569)) = hAPP(c_Int_Onumber__class_Onumber__of(_1186567), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186569)))], (22563 ^ _780205) ^ [] : [-(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))], (22565 ^ _780205) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22567 ^ _780205) ^ [_1186714] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186714)) = _1186714)], (22569 ^ _780205) ^ [_1186743] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1186743)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1186743)))], (22571 ^ _780205) ^ [_1186785] : [c_Int_OMin = c_Int_OBit0(_1186785)], (22573 ^ _780205) ^ [_1186819] : [c_Int_OBit0(_1186819) = c_Int_OMin], (22575 ^ _780205) ^ [_1186859, _1186861] : [c_Int_OBit0(_1186859) = c_Int_OBit0(_1186861), -(_1186859 = _1186861)], (22581 ^ _780205) ^ [_1186940, _1186942] : [_1186940 = _1186942, -(c_Int_OBit0(_1186940) = c_Int_OBit0(_1186942))], (22587 ^ _780205) ^ [_1187027, _1187029] : [class_Groups_Ogroup__add(_1187027), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1187027), hAPP(c_Groups_Ouminus__class_Ouminus(_1187027), _1187029)) = _1187029)], (22593 ^ _780205) ^ [_1187122, _1187124, _1187126] : [class_Groups_Ogroup__add(_1187122), 22596 ^ _780205 : [(22597 ^ _780205) ^ [] : [_1187124 = hAPP(c_Groups_Ouminus__class_Ouminus(_1187122), _1187126), -(_1187126 = hAPP(c_Groups_Ouminus__class_Ouminus(_1187122), _1187124))], (22603 ^ _780205) ^ [] : [_1187126 = hAPP(c_Groups_Ouminus__class_Ouminus(_1187122), _1187124), -(_1187124 = hAPP(c_Groups_Ouminus__class_Ouminus(_1187122), _1187126))]]], (22609 ^ _780205) ^ [_1187363, _1187365, _1187367] : [class_Groups_Ogroup__add(_1187363), 22612 ^ _780205 : [(22613 ^ _780205) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1187363), _1187365) = _1187367, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1187363), _1187367) = _1187365)], (22619 ^ _780205) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1187363), _1187367) = _1187365, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1187363), _1187365) = _1187367)]]], (22625 ^ _780205) ^ [_1187604, _1187606, _1187608] : [class_Groups_Ogroup__add(_1187604), 22628 ^ _780205 : [(22629 ^ _780205) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1187604), _1187606) = hAPP(c_Groups_Ouminus__class_Ouminus(_1187604), _1187608), -(_1187606 = _1187608)], (22635 ^ _780205) ^ [] : [_1187606 = _1187608, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1187604), _1187606) = hAPP(c_Groups_Ouminus__class_Ouminus(_1187604), _1187608))]]], (22641 ^ _780205) ^ [_1187845, _1187847] : [class_Lattices_Oboolean__algebra(_1187845), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1187845), hAPP(c_Groups_Ouminus__class_Ouminus(_1187845), _1187847)) = _1187847)], (22647 ^ _780205) ^ [_1187940, _1187942, _1187944, _1187946] : [class_Groups_Ouminus(_1187940), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1187942, _1187940)), _1187944), _1187946) = hAPP(c_Groups_Ouminus__class_Ouminus(_1187940), hAPP(_1187944, _1187946)))], (22653 ^ _780205) ^ [_1188057, _1188059, _1188061] : [class_Lattices_Oboolean__algebra(_1188057), 22656 ^ _780205 : [(22657 ^ _780205) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1188057), _1188059) = hAPP(c_Groups_Ouminus__class_Ouminus(_1188057), _1188061), -(_1188059 = _1188061)], (22663 ^ _780205) ^ [] : [_1188059 = _1188061, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1188057), _1188059) = hAPP(c_Groups_Ouminus__class_Ouminus(_1188057), _1188061))]]], (22669 ^ _780205) ^ [_1188310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1188310)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1188310), c_Int_OMin)))], (22675 ^ _780205) ^ [_1188405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1188405), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1188405)), c_Int_OMin)))], (22681 ^ _780205) ^ [_1188506] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1188506) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1188506))], (22683 ^ _780205) ^ [_1188547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1188547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1188547)))], (22689 ^ _780205) ^ [_1188630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1188630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1188630))))], (22695 ^ _780205) ^ [_1188719] : [class_Int_Onumber__ring(_1188719), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1188719), c_Groups_Oone__class_Oone(_1188719)) = hAPP(c_Int_Onumber__class_Onumber__of(_1188719), c_Int_OMin))], (22701 ^ _780205) ^ [_1188816] : [class_Int_Onumber__ring(_1188816), -(hAPP(c_Int_Onumber__class_Onumber__of(_1188816), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1188816), c_Groups_Oone__class_Oone(_1188816)))], (22707 ^ _780205) ^ [_1188925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1188925)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1188925), c_Int_OMin)))], (22713 ^ _780205) ^ [_1189020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1189020), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1189020)), c_Int_OMin)))], (22719 ^ _780205) ^ [_1189133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1189133))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1189133)))], (22725 ^ _780205) ^ [_1189216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1189216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1189216))))], (22731 ^ _780205) ^ [_1189305, _1189307] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1189305), _1189307), hAPP(c_Int_Onumber__class_Onumber__of(_1189305), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1189305), _1189307)), class_Fields_Ofield__inverse__zero(_1189305), class_Int_Onumber__ring(_1189305)], (22741 ^ _780205) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (22743 ^ _780205) ^ [_1189484] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1189484)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1189484)))], (22745 ^ _780205) ^ [_1189517] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1189517)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1189517)))], (22747 ^ _780205) ^ [_1189550, _1189552, _1189554] : [class_Lattices_Oboolean__algebra(_1189550), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189550), _1189552), _1189554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189550), hAPP(c_Groups_Ouminus__class_Ouminus(_1189550), _1189554)), hAPP(c_Groups_Ouminus__class_Ouminus(_1189550), _1189552))))], (22757 ^ _780205) ^ [_1189729, _1189731, _1189733] : [class_Lattices_Oboolean__algebra(_1189729), 22760 ^ _780205 : [(22761 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189729), hAPP(c_Groups_Ouminus__class_Ouminus(_1189729), _1189731)), hAPP(c_Groups_Ouminus__class_Ouminus(_1189729), _1189733))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189729), _1189733), _1189731)))], (22767 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189729), _1189733), _1189731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189729), hAPP(c_Groups_Ouminus__class_Ouminus(_1189729), _1189731)), hAPP(c_Groups_Ouminus__class_Ouminus(_1189729), _1189733))))]]], (22773 ^ _780205) ^ [_1190012, _1190014, _1190016] : [class_Groups_Oordered__ab__group__add(_1190012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190012), _1190014), _1190016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190012), hAPP(c_Groups_Ouminus__class_Ouminus(_1190012), _1190016)), hAPP(c_Groups_Ouminus__class_Ouminus(_1190012), _1190014))))], (22783 ^ _780205) ^ [_1190191, _1190193, _1190195] : [class_Groups_Oordered__ab__group__add(_1190191), 22786 ^ _780205 : [(22787 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190191), hAPP(c_Groups_Ouminus__class_Ouminus(_1190191), _1190193)), hAPP(c_Groups_Ouminus__class_Ouminus(_1190191), _1190195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190191), _1190195), _1190193)))], (22793 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190191), _1190195), _1190193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190191), hAPP(c_Groups_Ouminus__class_Ouminus(_1190191), _1190193)), hAPP(c_Groups_Ouminus__class_Ouminus(_1190191), _1190195))))]]], (22799 ^ _780205) ^ [_1190474, _1190476, _1190478] : [class_Groups_Oordered__ab__group__add(_1190474), 22802 ^ _780205 : [(22803 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190474), hAPP(c_Groups_Ouminus__class_Ouminus(_1190474), _1190476)), _1190478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190474), hAPP(c_Groups_Ouminus__class_Ouminus(_1190474), _1190478)), _1190476)))], (22809 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190474), hAPP(c_Groups_Ouminus__class_Ouminus(_1190474), _1190478)), _1190476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190474), hAPP(c_Groups_Ouminus__class_Ouminus(_1190474), _1190476)), _1190478)))]]], (22815 ^ _780205) ^ [_1190757, _1190759, _1190761] : [class_Groups_Oordered__ab__group__add(_1190757), 22818 ^ _780205 : [(22819 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190757), _1190759), hAPP(c_Groups_Ouminus__class_Ouminus(_1190757), _1190761))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190757), _1190761), hAPP(c_Groups_Ouminus__class_Ouminus(_1190757), _1190759))))], (22825 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190757), _1190761), hAPP(c_Groups_Ouminus__class_Ouminus(_1190757), _1190759))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190757), _1190759), hAPP(c_Groups_Ouminus__class_Ouminus(_1190757), _1190761))))]]], (22831 ^ _780205) ^ [_1191040] : [class_Groups_Ogroup__add(_1191040), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1191040), c_Groups_Ozero__class_Ozero(_1191040)) = c_Groups_Ozero__class_Ozero(_1191040))], (22837 ^ _780205) ^ [_1191131, _1191133] : [class_Groups_Ogroup__add(_1191131), 22840 ^ _780205 : [(22841 ^ _780205) ^ [] : [c_Groups_Ozero__class_Ozero(_1191131) = hAPP(c_Groups_Ouminus__class_Ouminus(_1191131), _1191133), -(c_Groups_Ozero__class_Ozero(_1191131) = _1191133)], (22847 ^ _780205) ^ [] : [c_Groups_Ozero__class_Ozero(_1191131) = _1191133, -(c_Groups_Ozero__class_Ozero(_1191131) = hAPP(c_Groups_Ouminus__class_Ouminus(_1191131), _1191133))]]], (22853 ^ _780205) ^ [_1191363, _1191365] : [class_Groups_Olinordered__ab__group__add(_1191363), 22856 ^ _780205 : [(22857 ^ _780205) ^ [] : [_1191365 = hAPP(c_Groups_Ouminus__class_Ouminus(_1191363), _1191365), -(_1191365 = c_Groups_Ozero__class_Ozero(_1191363))], (22863 ^ _780205) ^ [] : [_1191365 = c_Groups_Ozero__class_Ozero(_1191363), -(_1191365 = hAPP(c_Groups_Ouminus__class_Ouminus(_1191363), _1191365))]]], (22869 ^ _780205) ^ [_1191589, _1191591] : [class_Groups_Ogroup__add(_1191589), 22872 ^ _780205 : [(22873 ^ _780205) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1191589), _1191591) = c_Groups_Ozero__class_Ozero(_1191589), -(_1191591 = c_Groups_Ozero__class_Ozero(_1191589))], (22879 ^ _780205) ^ [] : [_1191591 = c_Groups_Ozero__class_Ozero(_1191589), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1191589), _1191591) = c_Groups_Ozero__class_Ozero(_1191589))]]], (22885 ^ _780205) ^ [_1191821, _1191823] : [class_Groups_Olinordered__ab__group__add(_1191821), 22888 ^ _780205 : [(22889 ^ _780205) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1191821), _1191823) = _1191823, -(_1191823 = c_Groups_Ozero__class_Ozero(_1191821))], (22895 ^ _780205) ^ [] : [_1191823 = c_Groups_Ozero__class_Ozero(_1191821), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1191821), _1191823) = _1191823)]]], (22901 ^ _780205) ^ [_1192047, _1192049, _1192051] : [class_Groups_Oordered__ab__group__add(_1192047), 22904 ^ _780205 : [(22905 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192047), _1192049), hAPP(c_Groups_Ouminus__class_Ouminus(_1192047), _1192051))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192047), _1192051), hAPP(c_Groups_Ouminus__class_Ouminus(_1192047), _1192049))))], (22911 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192047), _1192051), hAPP(c_Groups_Ouminus__class_Ouminus(_1192047), _1192049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192047), _1192049), hAPP(c_Groups_Ouminus__class_Ouminus(_1192047), _1192051))))]]], (22917 ^ _780205) ^ [_1192330, _1192332, _1192334] : [class_Groups_Oordered__ab__group__add(_1192330), 22920 ^ _780205 : [(22921 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192330), hAPP(c_Groups_Ouminus__class_Ouminus(_1192330), _1192332)), _1192334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192330), hAPP(c_Groups_Ouminus__class_Ouminus(_1192330), _1192334)), _1192332)))], (22927 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192330), hAPP(c_Groups_Ouminus__class_Ouminus(_1192330), _1192334)), _1192332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192330), hAPP(c_Groups_Ouminus__class_Ouminus(_1192330), _1192332)), _1192334)))]]], (22933 ^ _780205) ^ [_1192613, _1192615, _1192617] : [class_Groups_Oordered__ab__group__add(_1192613), 22936 ^ _780205 : [(22937 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192613), hAPP(c_Groups_Ouminus__class_Ouminus(_1192613), _1192615)), hAPP(c_Groups_Ouminus__class_Ouminus(_1192613), _1192617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192613), _1192617), _1192615)))], (22943 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192613), _1192617), _1192615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192613), hAPP(c_Groups_Ouminus__class_Ouminus(_1192613), _1192615)), hAPP(c_Groups_Ouminus__class_Ouminus(_1192613), _1192617))))]]], (22949 ^ _780205) ^ [_1192896, _1192898, _1192900] : [class_Groups_Oab__group__add(_1192896), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1192896), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192896), _1192898), _1192900)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192896), hAPP(c_Groups_Ouminus__class_Ouminus(_1192896), _1192898)), hAPP(c_Groups_Ouminus__class_Ouminus(_1192896), _1192900)))], (22955 ^ _780205) ^ [_1193035, _1193037, _1193039] : [class_Groups_Ogroup__add(_1193035), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1193035), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1193035), _1193037), _1193039)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1193035), hAPP(c_Groups_Ouminus__class_Ouminus(_1193035), _1193039)), hAPP(c_Groups_Ouminus__class_Ouminus(_1193035), _1193037)))], (22961 ^ _780205) ^ [_1193174, _1193176, _1193178] : [class_Groups_Ogroup__add(_1193174), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1193174), _1193176), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1193174), hAPP(c_Groups_Ouminus__class_Ouminus(_1193174), _1193176)), _1193178)) = _1193178)], (22967 ^ _780205) ^ [_1193293, _1193295, _1193297] : [class_Groups_Ogroup__add(_1193293), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1193293), hAPP(c_Groups_Ouminus__class_Ouminus(_1193293), _1193295)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1193293), _1193295), _1193297)) = _1193297)], (22973 ^ _780205) ^ [_1193412, _1193414, _1193416] : [class_Rings_Oidom(_1193412), 22976 ^ _780205 : [(22987 ^ _780205) ^ [] : [22988 ^ _780205 : [(22989 ^ _780205) ^ [] : [_1193414 = _1193416], (22991 ^ _780205) ^ [] : [_1193414 = hAPP(c_Groups_Ouminus__class_Ouminus(_1193412), _1193416)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193412), _1193414), _1193414) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193412), _1193416), _1193416))], (22977 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193412), _1193414), _1193414) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193412), _1193416), _1193416), -(_1193414 = _1193416), -(_1193414 = hAPP(c_Groups_Ouminus__class_Ouminus(_1193412), _1193416))]]], (22995 ^ _780205) ^ [_1193731, _1193733, _1193735] : [class_Rings_Oring(_1193731), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193731), hAPP(c_Groups_Ouminus__class_Ouminus(_1193731), _1193733)), hAPP(c_Groups_Ouminus__class_Ouminus(_1193731), _1193735)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193731), _1193733), _1193735))], (23001 ^ _780205) ^ [_1193860, _1193862, _1193864] : [class_Rings_Oring(_1193860), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193860), hAPP(c_Groups_Ouminus__class_Ouminus(_1193860), _1193862)), _1193864) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193860), _1193862), hAPP(c_Groups_Ouminus__class_Ouminus(_1193860), _1193864)))], (23007 ^ _780205) ^ [_1193989, _1193991, _1193993] : [class_Rings_Oring(_1193989), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1193989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193989), _1193991), _1193993)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193989), hAPP(c_Groups_Ouminus__class_Ouminus(_1193989), _1193991)), _1193993))], (23013 ^ _780205) ^ [_1194118, _1194120, _1194122] : [class_Rings_Oring(_1194118), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1194118), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194118), _1194120), _1194122)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194118), _1194120), hAPP(c_Groups_Ouminus__class_Ouminus(_1194118), _1194122)))], (23019 ^ _780205) ^ [_1194247, _1194249, _1194251] : [class_Groups_Oab__group__add(_1194247), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1194247), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1194247), _1194249), _1194251)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1194247), _1194251), _1194249))], (23025 ^ _780205) ^ [_1194366, _1194368] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1194366), _1194368) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1194366, _1194368)), _1194368))], (23027 ^ _780205) ^ [_1194409, _1194411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1194409), _1194411)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1194409, _1194411) = _1194409)], (23033 ^ _780205) ^ [_1194504, _1194506, _1194508] : [class_Divides_Oring__div(_1194504), -(c_Divides_Odiv__class_Omod(_1194504, hAPP(c_Groups_Ouminus__class_Ouminus(_1194504), _1194506), _1194508) = c_Divides_Odiv__class_Omod(_1194504, hAPP(c_Groups_Ouminus__class_Ouminus(_1194504), c_Divides_Odiv__class_Omod(_1194504, _1194506, _1194508)), _1194508))], (23039 ^ _780205) ^ [_1194625, _1194627, _1194629, _1194631] : [class_Divides_Oring__div(_1194625), c_Divides_Odiv__class_Omod(_1194625, _1194627, _1194629) = c_Divides_Odiv__class_Omod(_1194625, _1194631, _1194629), -(c_Divides_Odiv__class_Omod(_1194625, hAPP(c_Groups_Ouminus__class_Ouminus(_1194625), _1194627), _1194629) = c_Divides_Odiv__class_Omod(_1194625, hAPP(c_Groups_Ouminus__class_Ouminus(_1194625), _1194631), _1194629))], (23049 ^ _780205) ^ [_1194812, _1194814] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1194812, _1194814)), _1194812)))], (23051 ^ _780205) ^ [_1194861, _1194863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1194861)), c_Int_OBit0(_1194863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194861), _1194863)))], (23057 ^ _780205) ^ [_1194962, _1194964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194962), _1194964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1194962)), c_Int_OBit0(_1194964))))], (23063 ^ _780205) ^ [_1195084, _1195086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1195084)), c_Int_OBit0(_1195086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195084), _1195086)))], (23069 ^ _780205) ^ [_1195185, _1195187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195185), _1195187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1195185)), c_Int_OBit0(_1195187))))], (23075 ^ _780205) ^ [_1195307, _1195309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1195307)), c_Int_OBit0(_1195309))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195307), _1195309)))], (23081 ^ _780205) ^ [_1195408, _1195410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195408), _1195410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1195408)), c_Int_OBit0(_1195410))))], (23087 ^ _780205) ^ [_1195530, _1195532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1195530)), c_Int_OBit0(_1195532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195530), _1195532)))], (23093 ^ _780205) ^ [_1195631, _1195633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195631), _1195633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1195631)), c_Int_OBit0(_1195633))))], (23099 ^ _780205) ^ [] : [-(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))], (23101 ^ _780205) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (23103 ^ _780205) ^ [_1195786] : [c_Int_OPls = c_Int_OBit0(_1195786), -(c_Int_OPls = _1195786)], (23109 ^ _780205) ^ [_1195861] : [c_Int_OPls = _1195861, -(c_Int_OPls = c_Int_OBit0(_1195861))], (23115 ^ _780205) ^ [_1195954] : [c_Int_OBit0(_1195954) = c_Int_OPls, -(_1195954 = c_Int_OPls)], (23121 ^ _780205) ^ [_1196029] : [_1196029 = c_Int_OPls, -(c_Int_OBit0(_1196029) = c_Int_OPls)], (23127 ^ _780205) ^ [_1196122, _1196124] : [c_Int_OBit0(_1196122) = c_Int_OBit1(_1196124)], (23129 ^ _780205) ^ [_1196163, _1196165] : [c_Int_OBit1(_1196163) = c_Int_OBit0(_1196165)], (23131 ^ _780205) ^ [_1196192, _1196194, _1196196] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196192), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1196194, _1196196)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196192), _1196194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196192), _1196196)))], (23133 ^ _780205) ^ [_1196245, _1196247, _1196249] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1196245, _1196247)), _1196249) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196245), _1196249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196247), _1196249)))], (23135 ^ _780205) ^ [_1196298] : [-(c_Int_OBit0(_1196298) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1196298), _1196298))], (23137 ^ _780205) ^ [_1196329, _1196331] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1196329)), c_Int_OBit0(_1196331)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1196329), _1196331)))], (23139 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (23141 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (23143 ^ _780205) ^ [_1196414, _1196416, _1196418] : [class_Rings_Odivision__ring(_1196414), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1196414), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196414), _1196416), _1196418)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196414), hAPP(c_Groups_Ouminus__class_Ouminus(_1196414), _1196416)), _1196418))], (23149 ^ _780205) ^ [_1196543, _1196545, _1196547] : [class_Fields_Ofield__inverse__zero(_1196543), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1196543), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196543), _1196545), _1196547)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196543), _1196545), hAPP(c_Groups_Ouminus__class_Ouminus(_1196543), _1196547)))], (23155 ^ _780205) ^ [_1196672, _1196674, _1196676] : [class_Fields_Ofield__inverse__zero(_1196672), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196672), hAPP(c_Groups_Ouminus__class_Ouminus(_1196672), _1196674)), hAPP(c_Groups_Ouminus__class_Ouminus(_1196672), _1196676)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196672), _1196674), _1196676))], (23161 ^ _780205) ^ [_1196801, _1196803] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1196801)), _1196803) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1196801), _1196803)))], (23163 ^ _780205) ^ [_1196842, _1196844] : [class_Groups_Oordered__ab__group__add__abs(_1196842), -(hAPP(c_Groups_Oabs__class_Oabs(_1196842), hAPP(c_Groups_Ouminus__class_Ouminus(_1196842), _1196844)) = hAPP(c_Groups_Oabs__class_Oabs(_1196842), _1196844))], (23169 ^ _780205) ^ [] : [c_Int_OMin = c_Int_OPls], (23171 ^ _780205) ^ [] : [c_Int_OPls = c_Int_OMin], (23173 ^ _780205) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (23175 ^ _780205) ^ [_1197025] : [c_Int_OMin = c_Int_OBit1(_1197025), -(c_Int_OMin = _1197025)], (23181 ^ _780205) ^ [_1197100] : [c_Int_OMin = _1197100, -(c_Int_OMin = c_Int_OBit1(_1197100))], (23187 ^ _780205) ^ [_1197193] : [c_Int_OBit1(_1197193) = c_Int_OMin, -(_1197193 = c_Int_OMin)], (23193 ^ _780205) ^ [_1197268] : [_1197268 = c_Int_OMin, -(c_Int_OBit1(_1197268) = c_Int_OMin)], (23199 ^ _780205) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (23201 ^ _780205) ^ [_1197367, _1197369] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1197367), _1197369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197367)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197369)))], (23203 ^ _780205) ^ [_1197413] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197413)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197413)))], (23205 ^ _780205) ^ [_1197448, _1197450] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1197448)), c_Int_OBit0(_1197450)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1197448), _1197450)))], (23207 ^ _780205) ^ [_1197491, _1197493] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197491)), _1197493) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1197491), _1197493)))], (23209 ^ _780205) ^ [_1197534, _1197536] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1197534, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197536)) = 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), _1197534), _1197536)))], (23211 ^ _780205) ^ [_1197576, _1197578] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197576), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197578)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1197576, _1197578)))], (23213 ^ _780205) ^ [_1197618, _1197620] : [-(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, _1197618, _1197620)), _1197620) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197618), _1197620))], (23215 ^ _780205) ^ [_1197661, _1197663] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1197661), hAPP(c_Int_Onumber__class_Onumber__of(_1197661), c_Int_OMin)), _1197663) = hAPP(c_Groups_Ouminus__class_Ouminus(_1197661), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1197661), c_Groups_Oone__class_Oone(_1197661)), _1197663))), class_Fields_Ofield__inverse__zero(_1197661), class_Int_Onumber__ring(_1197661)], (23225 ^ _780205) ^ [_1197842] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1197842)), 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, _1197842, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (23227 ^ _780205) ^ [_1197879, _1197881] : [class_Groups_Oordered__ab__group__add(_1197879), 23230 ^ _780205 : [(23231 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197879), c_Groups_Ozero__class_Ozero(_1197879)), hAPP(c_Groups_Ouminus__class_Ouminus(_1197879), _1197881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197879), _1197881), c_Groups_Ozero__class_Ozero(_1197879))))], (23237 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197879), _1197881), c_Groups_Ozero__class_Ozero(_1197879))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197879), c_Groups_Ozero__class_Ozero(_1197879)), hAPP(c_Groups_Ouminus__class_Ouminus(_1197879), _1197881))))]]], (23243 ^ _780205) ^ [_1198153, _1198155] : [class_Groups_Olinordered__ab__group__add(_1198153), 23246 ^ _780205 : [(23247 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198153), _1198155), hAPP(c_Groups_Ouminus__class_Ouminus(_1198153), _1198155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198153), _1198155), c_Groups_Ozero__class_Ozero(_1198153))))], (23253 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198153), _1198155), c_Groups_Ozero__class_Ozero(_1198153))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198153), _1198155), hAPP(c_Groups_Ouminus__class_Ouminus(_1198153), _1198155))))]]], (23259 ^ _780205) ^ [_1198421, _1198423] : [class_Groups_Oordered__ab__group__add(_1198421), 23262 ^ _780205 : [(23263 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198421), hAPP(c_Groups_Ouminus__class_Ouminus(_1198421), _1198423)), c_Groups_Ozero__class_Ozero(_1198421))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198421), c_Groups_Ozero__class_Ozero(_1198421)), _1198423)))], (23269 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198421), c_Groups_Ozero__class_Ozero(_1198421)), _1198423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198421), hAPP(c_Groups_Ouminus__class_Ouminus(_1198421), _1198423)), c_Groups_Ozero__class_Ozero(_1198421))))]]], (23275 ^ _780205) ^ [_1198695, _1198697] : [class_Groups_Olinordered__ab__group__add(_1198695), 23278 ^ _780205 : [(23279 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198695), hAPP(c_Groups_Ouminus__class_Ouminus(_1198695), _1198697)), _1198697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198695), c_Groups_Ozero__class_Ozero(_1198695)), _1198697)))], (23285 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198695), c_Groups_Ozero__class_Ozero(_1198695)), _1198697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198695), hAPP(c_Groups_Ouminus__class_Ouminus(_1198695), _1198697)), _1198697)))]]], (23291 ^ _780205) ^ [_1198963, _1198965] : [class_Rings_Olinordered__idom(_1198963), 23294 ^ _780205 : [(23295 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198963), _1198965), hAPP(c_Groups_Ouminus__class_Ouminus(_1198963), _1198965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198963), _1198965), c_Groups_Ozero__class_Ozero(_1198963))))], (23301 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198963), _1198965), c_Groups_Ozero__class_Ozero(_1198963))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198963), _1198965), hAPP(c_Groups_Ouminus__class_Ouminus(_1198963), _1198965))))]]], (23307 ^ _780205) ^ [_1199231, _1199233] : [class_Groups_Oordered__ab__group__add(_1199231), 23310 ^ _780205 : [(23311 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199231), c_Groups_Ozero__class_Ozero(_1199231)), hAPP(c_Groups_Ouminus__class_Ouminus(_1199231), _1199233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199231), _1199233), c_Groups_Ozero__class_Ozero(_1199231))))], (23317 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199231), _1199233), c_Groups_Ozero__class_Ozero(_1199231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199231), c_Groups_Ozero__class_Ozero(_1199231)), hAPP(c_Groups_Ouminus__class_Ouminus(_1199231), _1199233))))]]], (23323 ^ _780205) ^ [_1199505, _1199507] : [class_Groups_Oordered__ab__group__add(_1199505), 23326 ^ _780205 : [(23327 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199505), hAPP(c_Groups_Ouminus__class_Ouminus(_1199505), _1199507)), c_Groups_Ozero__class_Ozero(_1199505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199505), c_Groups_Ozero__class_Ozero(_1199505)), _1199507)))], (23333 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199505), c_Groups_Ozero__class_Ozero(_1199505)), _1199507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199505), hAPP(c_Groups_Ouminus__class_Ouminus(_1199505), _1199507)), c_Groups_Ozero__class_Ozero(_1199505))))]]], (23339 ^ _780205) ^ [_1199779, _1199781] : [class_Groups_Olinordered__ab__group__add(_1199779), 23342 ^ _780205 : [(23343 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199779), hAPP(c_Groups_Ouminus__class_Ouminus(_1199779), _1199781)), _1199781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199779), c_Groups_Ozero__class_Ozero(_1199779)), _1199781)))], (23349 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199779), c_Groups_Ozero__class_Ozero(_1199779)), _1199781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199779), hAPP(c_Groups_Ouminus__class_Ouminus(_1199779), _1199781)), _1199781)))]]], (23355 ^ _780205) ^ [_1200047, _1200049] : [class_Groups_Ogroup__add(_1200047), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200047), _1200049), hAPP(c_Groups_Ouminus__class_Ouminus(_1200047), _1200049)) = c_Groups_Ozero__class_Ozero(_1200047))], (23361 ^ _780205) ^ [_1200152, _1200154, _1200156] : [class_Groups_Ogroup__add(_1200152), 23364 ^ _780205 : [(23365 ^ _780205) ^ [] : [_1200154 = hAPP(c_Groups_Ouminus__class_Ouminus(_1200152), _1200156), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200152), _1200154), _1200156) = c_Groups_Ozero__class_Ozero(_1200152))], (23371 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200152), _1200154), _1200156) = c_Groups_Ozero__class_Ozero(_1200152), -(_1200154 = hAPP(c_Groups_Ouminus__class_Ouminus(_1200152), _1200156))]]], (23377 ^ _780205) ^ [_1200408, _1200410] : [class_Groups_Ogroup__add(_1200408), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200408), hAPP(c_Groups_Ouminus__class_Ouminus(_1200408), _1200410)), _1200410) = c_Groups_Ozero__class_Ozero(_1200408))], (23383 ^ _780205) ^ [_1200513, _1200515] : [class_Groups_Oab__group__add(_1200513), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200513), hAPP(c_Groups_Ouminus__class_Ouminus(_1200513), _1200515)), _1200515) = c_Groups_Ozero__class_Ozero(_1200513))], (23389 ^ _780205) ^ [_1200618, _1200620, _1200622] : [class_Groups_Ogroup__add(_1200618), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200618), _1200620), _1200622) = c_Groups_Ozero__class_Ozero(_1200618), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1200618), _1200620) = _1200622)], (23399 ^ _780205) ^ [_1200779, _1200781] : [class_Groups_Ogroup__add(_1200779), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1200779), c_Groups_Ozero__class_Ozero(_1200779)), _1200781) = hAPP(c_Groups_Ouminus__class_Ouminus(_1200779), _1200781))], (23405 ^ _780205) ^ [_1200884, _1200886, _1200888] : [class_Rings_Ocomm__ring__1(_1200884), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1200884), _1200886), _1200888) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200884), _1200886), hAPP(c_Groups_Ouminus__class_Ouminus(_1200884), _1200888)))], (23411 ^ _780205) ^ [_1201003, _1201005, _1201007] : [class_Groups_Ogroup__add(_1201003), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201003), _1201005), _1201007) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201003), _1201005), hAPP(c_Groups_Ouminus__class_Ouminus(_1201003), _1201007)))], (23417 ^ _780205) ^ [_1201122, _1201124, _1201126] : [class_Groups_Oab__group__add(_1201122), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201122), _1201124), _1201126) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201122), _1201124), hAPP(c_Groups_Ouminus__class_Ouminus(_1201122), _1201126)))], (23423 ^ _780205) ^ [_1201241, _1201243, _1201245] : [class_Groups_Ogroup__add(_1201241), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201241), _1201243), hAPP(c_Groups_Ouminus__class_Ouminus(_1201241), _1201245)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201241), _1201243), _1201245))], (23429 ^ _780205) ^ [_1201360, _1201362] : [class_Rings_Ocomm__ring__1(_1201360), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1201360), _1201362) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201360), hAPP(c_Groups_Ouminus__class_Ouminus(_1201360), c_Groups_Oone__class_Oone(_1201360))), _1201362))], (23435 ^ _780205) ^ [_1201475, _1201477] : [class_Rings_Oring__1__no__zero__divisors(_1201475), 23438 ^ _780205 : [(23449 ^ _780205) ^ [] : [23450 ^ _780205 : [(23451 ^ _780205) ^ [] : [_1201477 = c_Groups_Oone__class_Oone(_1201475)], (23453 ^ _780205) ^ [] : [_1201477 = hAPP(c_Groups_Ouminus__class_Ouminus(_1201475), c_Groups_Oone__class_Oone(_1201475))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201475), _1201477), _1201477) = c_Groups_Oone__class_Oone(_1201475))], (23439 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201475), _1201477), _1201477) = c_Groups_Oone__class_Oone(_1201475), -(_1201477 = c_Groups_Oone__class_Oone(_1201475)), -(_1201477 = hAPP(c_Groups_Ouminus__class_Ouminus(_1201475), c_Groups_Oone__class_Oone(_1201475)))]]], (23457 ^ _780205) ^ [_1201782, _1201784] : [class_Lattices_Oboolean__algebra(_1201782), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1201782), hAPP(c_Groups_Ouminus__class_Ouminus(_1201782), _1201784)), _1201784) = c_Orderings_Obot__class_Obot(_1201782))], (23463 ^ _780205) ^ [_1201887, _1201889] : [class_Lattices_Oboolean__algebra(_1201887), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1201887), _1201889), hAPP(c_Groups_Ouminus__class_Ouminus(_1201887), _1201889)) = c_Orderings_Obot__class_Obot(_1201887))], (23469 ^ _780205) ^ [_1201992, _1201994, _1201996] : [class_Lattices_Oboolean__algebra(_1201992), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1201992), _1201994), _1201996) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1201992), _1201994), hAPP(c_Groups_Ouminus__class_Ouminus(_1201992), _1201996)))], (23475 ^ _780205) ^ [_1202120, _1202122] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1202120, _1202122)) = _1202122, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1202120), _1202122) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23481 ^ _780205) ^ [_1202219, _1202221] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1202219, _1202221)) = _1202221), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1202219), _1202221) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1202219, _1202221)))], (23487 ^ _780205) ^ [_1202278] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1202278, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23489 ^ _780205) ^ [_1202305, _1202307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1202307, _1202305)), _1202305)))], (23495 ^ _780205) ^ [_1202404, _1202406, _1202408] : [class_Lattices_Oboolean__algebra(_1202404), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1202404), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1202404), _1202406), _1202408)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1202404), hAPP(c_Groups_Ouminus__class_Ouminus(_1202404), _1202406)), hAPP(c_Groups_Ouminus__class_Ouminus(_1202404), _1202408)))], (23501 ^ _780205) ^ [_1202543, _1202545, _1202547] : [class_Lattices_Oboolean__algebra(_1202543), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1202543), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1202543), _1202545), _1202547)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1202543), hAPP(c_Groups_Ouminus__class_Ouminus(_1202543), _1202545)), hAPP(c_Groups_Ouminus__class_Ouminus(_1202543), _1202547)))], (23507 ^ _780205) ^ [_1202682, _1202684, _1202686] : [class_Rings_Odivision__ring(_1202682), -(_1202684 = c_Groups_Ozero__class_Ozero(_1202682)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1202682), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202682), _1202686), _1202684)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202682), _1202686), hAPP(c_Groups_Ouminus__class_Ouminus(_1202682), _1202684)))], (23517 ^ _780205) ^ [_1202830, _1202832, _1202834] : [class_Rings_Odivision__ring(_1202830), -(_1202832 = c_Groups_Ozero__class_Ozero(_1202830)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202830), hAPP(c_Groups_Ouminus__class_Ouminus(_1202830), _1202834)), hAPP(c_Groups_Ouminus__class_Ouminus(_1202830), _1202832)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202830), _1202834), _1202832))], (23527 ^ _780205) ^ [_1202978, _1202980, _1202982] : [class_Groups_Oordered__ab__group__add__abs(_1202978), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202978), hAPP(c_Groups_Oabs__class_Oabs(_1202978), _1202980)), _1202982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202978), hAPP(c_Groups_Ouminus__class_Ouminus(_1202978), _1202980)), _1202982)))], (23537 ^ _780205) ^ [_1203157, _1203159, _1203161] : [class_Groups_Oordered__ab__group__add__abs(_1203157), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203157), _1203159), _1203161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203157), hAPP(c_Groups_Ouminus__class_Ouminus(_1203157), _1203159)), _1203161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203157), hAPP(c_Groups_Oabs__class_Oabs(_1203157), _1203159)), _1203161)))], (23551 ^ _780205) ^ [_1203404, _1203406, _1203408] : [class_Groups_Oordered__ab__group__add__abs(_1203404), 23554 ^ _780205 : [(23555 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203404), hAPP(c_Groups_Oabs__class_Oabs(_1203404), _1203406)), _1203408)), 23558 ^ _780205 : [(23559 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203404), _1203406), _1203408)))], (23561 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203404), hAPP(c_Groups_Ouminus__class_Ouminus(_1203404), _1203406)), _1203408)))]]], (23563 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203404), hAPP(c_Groups_Oabs__class_Oabs(_1203404), _1203406)), _1203408))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203404), _1203406), _1203408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203404), hAPP(c_Groups_Ouminus__class_Ouminus(_1203404), _1203406)), _1203408))]]], (23573 ^ _780205) ^ [_1203782, _1203784] : [class_Groups_Oordered__ab__group__add__abs(_1203782), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203782), hAPP(c_Groups_Ouminus__class_Ouminus(_1203782), _1203784)), hAPP(c_Groups_Oabs__class_Oabs(_1203782), _1203784))))], (23579 ^ _780205) ^ [_1203891, _1203893, _1203895] : [class_Rings_Olinordered__idom(_1203891), 23582 ^ _780205 : [(23583 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203891), hAPP(c_Groups_Oabs__class_Oabs(_1203891), _1203893)), _1203895)), 23586 ^ _780205 : [(23587 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203891), _1203893), _1203895)))], (23589 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203891), hAPP(c_Groups_Ouminus__class_Ouminus(_1203891), _1203893)), _1203895)))]]], (23591 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203891), hAPP(c_Groups_Oabs__class_Oabs(_1203891), _1203893)), _1203895))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203891), _1203893), _1203895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203891), hAPP(c_Groups_Ouminus__class_Ouminus(_1203891), _1203893)), _1203895))]]], (23601 ^ _780205) ^ [_1204284, _1204286] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1204284, _1204286) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1204284 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1204286), 23604 ^ [_1204284, _1204286]))], (23608 ^ _780205) ^ [_1204389, _1204391] : [23609 ^ _780205 : [(23610 ^ _780205) ^ [_1204438] : [_1204389 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1204391), _1204438)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1204389, _1204391) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23614 ^ _780205) ^ [_1204513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1204513)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204513), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23620 ^ _780205) ^ [_1204608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204608), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1204608)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23626 ^ _780205) ^ [_1204718, _1204720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204718), _1204720)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1204718, _1204720) = _1204718)], (23632 ^ _780205) ^ [_1204807, _1204809] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204807), _1204809))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1204807, _1204809) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1204807), _1204809), _1204809))], (23638 ^ _780205) ^ [_1204860, _1204862] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204860), _1204862))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1204860, _1204862) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1204860), _1204862), _1204862))], (23644 ^ _780205) ^ [_1204915, _1204917, _1204919] : [-(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), _1204915), _1204917)), _1204919), _1204917) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1204919, _1204917))], (23646 ^ _780205) ^ [_1204974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1204974)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204974), c_Int_OPls)))], (23652 ^ _780205) ^ [_1205069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205069), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1205069)), c_Int_OPls)))], (23658 ^ _780205) ^ [_1205182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1205182))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1205182)))], (23664 ^ _780205) ^ [_1205265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1205265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1205265))))], (23670 ^ _780205) ^ [_1205369, _1205371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1205369)), c_Int_OBit1(_1205371))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205369), _1205371)))], (23676 ^ _780205) ^ [_1205470, _1205472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205470), _1205472)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1205470)), c_Int_OBit1(_1205472))))], (23682 ^ _780205) ^ [_1205592, _1205594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1205592)), c_Int_OBit1(_1205594))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205592), _1205594)))], (23688 ^ _780205) ^ [_1205693, _1205695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205693), _1205695)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1205693)), c_Int_OBit1(_1205695))))], (23694 ^ _780205) ^ [_1205800, _1205802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205800), _1205802)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1205802, _1205800) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1205802), _1205800), _1205800))], (23700 ^ _780205) ^ [_1205927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1205927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1205927)))], (23706 ^ _780205) ^ [_1206010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1206010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1206010))))], (23712 ^ _780205) ^ [_1206111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1206111)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206111), c_Int_OPls)))], (23718 ^ _780205) ^ [_1206206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206206), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1206206)), c_Int_OPls)))], (23724 ^ _780205) ^ [_1206322, _1206324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1206322)), c_Int_OBit0(_1206324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206322), _1206324)))], (23730 ^ _780205) ^ [_1206423, _1206425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206423), _1206425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1206423)), c_Int_OBit0(_1206425))))], (23736 ^ _780205) ^ [_1206545, _1206547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1206545)), c_Int_OBit0(_1206547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206545), _1206547)))], (23742 ^ _780205) ^ [_1206646, _1206648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206646), _1206648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1206646)), c_Int_OBit0(_1206648))))], (23748 ^ _780205) ^ [_1206753, _1206755] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1206753)), c_Int_OBit0(_1206755)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1206753), _1206755)))], (23750 ^ _780205) ^ [_1206796, _1206798] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1206796)), c_Int_OBit1(_1206798)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1206796), _1206798)))], (23752 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23754 ^ _780205) ^ [_1206857] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1206857)), _1206857) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23756 ^ _780205) ^ [_1206904, _1206906] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206904)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206906), 23759 ^ _780205 : [(23760 ^ _780205) ^ [] : [-(_1206904 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23762 ^ _780205) ^ [] : [-(_1206906 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23764 ^ _780205) ^ [_1207021, _1207023] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207021)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207023)), _1207021 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1207023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23774 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (23776 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (23778 ^ _780205) ^ [_1207224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1207224)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1207224), c_Int_OMin)))], (23784 ^ _780205) ^ [_1207319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1207319), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1207319)), c_Int_OMin)))], (23790 ^ _780205) ^ [_1207432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1207432))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1207432)))], (23796 ^ _780205) ^ [_1207515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1207515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1207515))))], (23802 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (23804 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (23806 ^ _780205) ^ [_1207658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1207658))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1207658)))], (23812 ^ _780205) ^ [_1207741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1207741)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1207741))))], (23818 ^ _780205) ^ [_1207842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1207842)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1207842), c_Int_OMin)))], (23824 ^ _780205) ^ [_1207937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1207937), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1207937)), c_Int_OMin)))], (23830 ^ _780205) ^ [_1208038] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1208038)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1208038)))], (23832 ^ _780205) ^ [_1208071, _1208073] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1208071)), c_Int_OBit0(_1208073)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1208071), _1208073)))], (23834 ^ _780205) ^ [_1208114, _1208116] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1208114)), c_Int_OBit1(_1208116)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1208114), _1208116)))], (23836 ^ _780205) ^ [_1208157, _1208159] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1208157, _1208159)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208157), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208159)))], (23838 ^ _780205) ^ [_1208199, _1208201] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208199), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208201)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1208199, _1208201)))], (23840 ^ _780205) ^ [] : [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)], (23842 ^ _780205) ^ [_1208277, _1208279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208277)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208279))))], (23844 ^ _780205) ^ [_1208315, _1208317] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208315, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1208317)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208315, _1208317) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23850 ^ _780205) ^ [_1208405, _1208407] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1208405), _1208407) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208405, _1208407) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23856 ^ _780205) ^ [_1208496, _1208498] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1208496), _1208498) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1208496), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1208498)))], (23858 ^ _780205) ^ [_1208536, _1208538] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1208536), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1208538)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1208536), _1208538))], (23860 ^ _780205) ^ [_1208576, _1208578] : [class_Rings_Oring__1(_1208576), hBOOL(hAPP(hAPP(c_member(_1208576), _1208578), c_Int_Oring__1__class_OInts(_1208576))), -(hBOOL(hAPP(hAPP(c_member(_1208576), hAPP(c_Groups_Ouminus__class_Ouminus(_1208576), _1208578)), c_Int_Oring__1__class_OInts(_1208576))))], (23870 ^ _780205) ^ [_1208761] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1208761)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1208761))))], (23876 ^ _780205) ^ [_1208856] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1208856))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1208856)))))], (23882 ^ _780205) ^ [_1208957] : [-(c_Int_Opred(c_Int_OBit0(_1208957)) = c_Int_OBit1(c_Int_Opred(_1208957)))], (23884 ^ _780205) ^ [_1208988] : [-(c_Int_Opred(c_Int_OBit1(_1208988)) = c_Int_OBit0(_1208988))], (23886 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (23888 ^ _780205) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (23890 ^ _780205) ^ [_1209053] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1209053)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1209053))))], (23892 ^ _780205) ^ [_1209088] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1209088), c_Int_OMin) = c_Int_Opred(_1209088))], (23894 ^ _780205) ^ [_1209119] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1209119) = c_Int_Opred(_1209119))], (23896 ^ _780205) ^ [_1209147] : [-(c_Int_Osucc(c_Int_OBit1(_1209147)) = c_Int_OBit0(c_Int_Osucc(_1209147)))], (23898 ^ _780205) ^ [_1209178] : [-(c_Int_Osucc(c_Int_OBit0(_1209178)) = c_Int_OBit1(_1209178))], (23900 ^ _780205) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (23902 ^ _780205) ^ [_1209225] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1209225), c_Int_OMin) = c_Int_Osucc(_1209225))], (23904 ^ _780205) ^ [_1209268] : [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, _1209268, 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, _1209268, 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))], (23910 ^ _780205) ^ [_1209359] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1209359, 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, _1209359, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (23916 ^ _780205) ^ [_1209456, _1209458] : [class_Int_Onumber__ring(_1209456), -(hAPP(c_Int_Onumber__class_Onumber__of(_1209456), c_Int_OBit0(_1209458)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209456), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209456), c_Groups_Ozero__class_Ozero(_1209456)), hAPP(c_Int_Onumber__class_Onumber__of(_1209456), _1209458))), hAPP(c_Int_Onumber__class_Onumber__of(_1209456), _1209458)))], (23922 ^ _780205) ^ [_1209601, _1209603] : [class_Groups_Oordered__ab__group__add__abs(_1209601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209601), _1209603), c_Groups_Ozero__class_Ozero(_1209601))), -(hAPP(c_Groups_Oabs__class_Oabs(_1209601), _1209603) = hAPP(c_Groups_Ouminus__class_Ouminus(_1209601), _1209603))], (23932 ^ _780205) ^ [_1209766, _1209768] : [class_Groups_Oordered__ab__group__add__abs(_1209766), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209766), hAPP(c_Groups_Ouminus__class_Ouminus(_1209766), hAPP(c_Groups_Oabs__class_Oabs(_1209766), _1209768))), c_Groups_Ozero__class_Ozero(_1209766))))], (23938 ^ _780205) ^ [_1209879, _1209881] : [class_Groups_Oabs__if(_1209879), 23941 ^ _780205 : [(23942 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209879), _1209881), c_Groups_Ozero__class_Ozero(_1209879))), -(hAPP(c_Groups_Oabs__class_Oabs(_1209879), _1209881) = hAPP(c_Groups_Ouminus__class_Ouminus(_1209879), _1209881))], (23948 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209879), _1209881), c_Groups_Ozero__class_Ozero(_1209879)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1209879), _1209881) = _1209881)]]], (23954 ^ _780205) ^ [_1210119, _1210121] : [class_Groups_Oordered__ab__group__add__abs(_1210119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210119), _1210121), c_Groups_Ozero__class_Ozero(_1210119))), -(hAPP(c_Groups_Oabs__class_Oabs(_1210119), _1210121) = hAPP(c_Groups_Ouminus__class_Ouminus(_1210119), _1210121))], (23964 ^ _780205) ^ [_1210284, _1210286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1210284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1210286, _1210284)), _1210284)))], (23970 ^ _780205) ^ [_1210383, _1210385, _1210387] : [-(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), _1210383), _1210385)), _1210387)), _1210385) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1210387), _1210385))], (23972 ^ _780205) ^ [_1210451, _1210453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1210451)), c_Int_OBit0(_1210453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210451), _1210453)))], (23978 ^ _780205) ^ [_1210552, _1210554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210552), _1210554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1210552)), c_Int_OBit0(_1210554))))], (23984 ^ _780205) ^ [_1210674, _1210676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1210674)), c_Int_OBit0(_1210676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210674), _1210676)))], (23990 ^ _780205) ^ [_1210775, _1210777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210775), _1210777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1210775)), c_Int_OBit0(_1210777))))], (23996 ^ _780205) ^ [_1210897, _1210899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1210897)), c_Int_OBit1(_1210899))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210897), _1210899)))], (24002 ^ _780205) ^ [_1210998, _1211000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210998), _1211000)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1210998)), c_Int_OBit1(_1211000))))], (24008 ^ _780205) ^ [_1211120, _1211122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1211120)), c_Int_OBit1(_1211122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211120), _1211122)))], (24014 ^ _780205) ^ [_1211221, _1211223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211221), _1211223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1211221)), c_Int_OBit1(_1211223))))], (24020 ^ _780205) ^ [_1211328, _1211330, _1211332] : [class_Int_Onumber__ring(_1211328), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1211328), hAPP(c_Int_Onumber__class_Onumber__of(_1211328), _1211330)), hAPP(c_Int_Onumber__class_Onumber__of(_1211328), _1211332)) = hAPP(c_Int_Onumber__class_Onumber__of(_1211328), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1211330), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1211332))))], (24026 ^ _780205) ^ [_1211469, _1211471] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1211469)), _1211471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1211469), _1211471))), _1211471))], (24028 ^ _780205) ^ [_1211516] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1211516), hAPP(c_Int_Onumber__class_Onumber__of(_1211516), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1211516)), class_Int_Onumber__ring(_1211516), class_Rings_Olinordered__idom(_1211516)], (24038 ^ _780205) ^ [_1211676, _1211678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211676)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211678)))), 24041 ^ _780205 : [(24042 ^ _780205) ^ [] : [-(_1211676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24044 ^ _780205) ^ [] : [-(_1211678 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (24046 ^ _780205) ^ [_1211803, _1211805] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211803)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211805))))), _1211803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1211805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24056 ^ _780205) ^ [_1211962] : [-(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), _1211962))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24058 ^ _780205) ^ [_1211996] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1211996, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24060 ^ _780205) ^ [_1212023] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1212023)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1212023)))], (24062 ^ _780205) ^ [_1212056, _1212058] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1212056), _1212058) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1212056 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1212056 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (24072 ^ _780205) ^ [_1212173, _1212175] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1212173), _1212175) = c_Groups_Oone__class_Oone(tc_Int_Oint), 24077 ^ _780205 : [(24078 ^ _780205) ^ [] : [-(_1212173 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (24080 ^ _780205) ^ [] : [-(_1212175 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 24081 ^ _780205 : [(24082 ^ _780205) ^ [] : [-(_1212173 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (24084 ^ _780205) ^ [] : [-(_1212175 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (24086 ^ _780205) ^ [_1212357, _1212359] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1212357), _1212359) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 24087 ^ _780205 : [(24088 ^ _780205) ^ [] : [_1212357 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1212359 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (24094 ^ _780205) ^ [] : [_1212357 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1212359 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (24102 ^ _780205) ^ [_1212583, _1212585] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1212583)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1212585)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1212583), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1212585))))], (24104 ^ _780205) ^ [_1212641, _1212643] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212641, _1212643) = 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), _1212641), _1212643) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24110 ^ _780205) ^ [_1212734, _1212736] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212734, _1212736) = 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), _1212734), _1212736) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1212736), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212734, _1212736)))], (24116 ^ _780205) ^ [_1212802, _1212804] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212802, _1212804) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212802, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1212804)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24122 ^ _780205) ^ [_1212895, _1212897] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212895, _1212897) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212895, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1212897)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1212895, _1212897)), _1212897))], (24128 ^ _780205) ^ [_1212960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212960), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1212960) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1212960))], (24134 ^ _780205) ^ [_1213051] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213051), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1213051) = _1213051)], (24140 ^ _780205) ^ [_1213095] : [-(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, _1213095))))))], (24142 ^ _780205) ^ [_1213129, _1213131] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1213129)), c_Int_OBit1(_1213131)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1213129)), _1213131)))], (24144 ^ _780205) ^ [_1213174, _1213176] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1213174)), c_Int_OBit1(_1213176)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213174), c_Int_Osucc(_1213176))))], (24146 ^ _780205) ^ [] : [-(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))], (24148 ^ _780205) ^ [_1213237, _1213239] : [class_Int_Onumber__ring(_1213237), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213237), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1213237), c_Groups_Oone__class_Oone(_1213237)), c_Groups_Oone__class_Oone(_1213237))), hAPP(c_Int_Onumber__class_Onumber__of(_1213237), _1213239)) = hAPP(c_Int_Onumber__class_Onumber__of(_1213237), c_Int_OBit0(_1213239)))], (24154 ^ _780205) ^ [_1213376, _1213378] : [class_Int_Onumber__ring(_1213376), class_Rings_Olinordered__idom(_1213376), 24161 ^ _780205 : [(24162 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213376), hAPP(c_Int_Onumber__class_Onumber__of(_1213376), _1213378)), c_Groups_Ozero__class_Ozero(_1213376))), -(hAPP(c_Groups_Oabs__class_Oabs(_1213376), hAPP(c_Int_Onumber__class_Onumber__of(_1213376), _1213378)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1213376), hAPP(c_Int_Onumber__class_Onumber__of(_1213376), _1213378)))], (24168 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213376), hAPP(c_Int_Onumber__class_Onumber__of(_1213376), _1213378)), c_Groups_Ozero__class_Ozero(_1213376)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1213376), hAPP(c_Int_Onumber__class_Onumber__of(_1213376), _1213378)) = hAPP(c_Int_Onumber__class_Onumber__of(_1213376), _1213378))]]], (24198 ^ _780205) ^ [_1214179, _1214181, _1214183] : [-(hBOOL(hAPP(_1214179, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1214181, _1214183)))), 24201 ^ _780205 : [(24202 ^ _780205) ^ [] : [-(_1214183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24204 ^ _780205) ^ [] : [hBOOL(hAPP(_1214179, _1214181))]], 24205 ^ _780205 : [(24206 ^ _780205) ^ [] : [_1214183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24210 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24208 ^ [_1214179, _1214181, _1214183]), _1214183)))], (24212 ^ _780205) ^ [] : [-(_1214181 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214183), 24207 ^ [_1214179, _1214181, _1214183])), 24208 ^ [_1214179, _1214181, _1214183]))], (24214 ^ _780205) ^ [] : [hBOOL(hAPP(_1214179, 24208 ^ [_1214179, _1214181, _1214183]))]]], (24174 ^ _780205) ^ [_1213746, _1213748, _1213750] : [hBOOL(hAPP(_1213746, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1213748, _1213750))), 24177 ^ _780205 : [(24178 ^ _780205) ^ [] : [_1213750 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1213746, _1213748)))], (24184 ^ _780205) ^ [] : [-(_1213750 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24187 ^ _780205 : [(24188 ^ _780205) ^ [_1213994, _1213996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1213994), _1213750)), _1213748 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1213750), _1213996)), _1213994), -(hBOOL(hAPP(_1213746, _1213994)))]]]]], (24218 ^ _780205) ^ [_1214588, _1214590, _1214592, _1214594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1214590), _1214592)), -(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), _1214592), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1214594, _1214588))), _1214590)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214592), _1214588))))], (24228 ^ _780205) ^ [_1214793, _1214795, _1214797, _1214799] : [class_Int_Onumber__ring(_1214793), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214793), hAPP(c_Int_Onumber__class_Onumber__of(_1214793), _1214795)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1214793), _1214797), hAPP(c_Int_Onumber__class_Onumber__of(_1214793), _1214799))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214793), hAPP(c_Int_Onumber__class_Onumber__of(_1214793), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214795), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214799)))), _1214797))], (24234 ^ _780205) ^ [_1214968] : [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), _1214968))), 24237 ^ _780205 : [(24238 ^ _780205) ^ [] : [-(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(_1214968)))))], (24240 ^ _780205) ^ [] : [-(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(_1214968)))))]]], (24242 ^ _780205) ^ [_1215107, _1215109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1215107)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215107), _1215109)), _1215107) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (24248 ^ _780205) ^ [_1215214, _1215216] : [class_Int_Onumber__ring(_1215214), -(hAPP(c_Int_Onumber__class_Onumber__of(_1215214), c_Int_Opred(_1215216)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215214), hAPP(c_Groups_Ouminus__class_Ouminus(_1215214), c_Groups_Oone__class_Oone(_1215214))), hAPP(c_Int_Onumber__class_Onumber__of(_1215214), _1215216)))], (24254 ^ _780205) ^ [_1215352] : [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, _1215352)))))], (24256 ^ _780205) ^ [_1215386] : [-(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, _1215386)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24258 ^ _780205) ^ [_1215423, _1215425] : [class_Int_Onumber__ring(_1215423), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215423), _1215425), hAPP(c_Int_Onumber__class_Onumber__of(_1215423), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215423), _1215425), _1215425))], (24264 ^ _780205) ^ [_1215540, _1215542] : [class_Int_Onumber__ring(_1215540), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215540), hAPP(c_Int_Onumber__class_Onumber__of(_1215540), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1215542) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215540), _1215542), _1215542))], (24270 ^ _780205) ^ [_1215657] : [class_Int_Onumber__ring(_1215657), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215657), c_Groups_Oone__class_Oone(_1215657)), c_Groups_Oone__class_Oone(_1215657)) = hAPP(c_Int_Onumber__class_Onumber__of(_1215657), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (24276 ^ _780205) ^ [_1215764, _1215766] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1215764, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1215766)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1215764, 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)))), _1215766)))], (24278 ^ _780205) ^ [_1215809, _1215811] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1215809))), _1215811) = 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)))), _1215809), _1215811))], (24280 ^ _780205) ^ [_1215854, _1215856] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1215854))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1215856)) = 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)))), _1215854), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1215856)))], (24282 ^ _780205) ^ [] : [-(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))))], (24284 ^ _780205) ^ [] : [-(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))))], (24286 ^ _780205) ^ [] : [-(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))))))], (24288 ^ _780205) ^ [_1215959] : [-(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)))), _1215959) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1215959)))], (24290 ^ _780205) ^ [_1215991] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1215991), 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, _1215991)))], (24292 ^ _780205) ^ [_1216026] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1216026), 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), _1216026), _1216026))], (24294 ^ _780205) ^ [_1216061] : [-(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)))), _1216061) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1216061), _1216061))], (24296 ^ _780205) ^ [] : [-(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)))))], (24298 ^ _780205) ^ [] : [-(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))))], (24300 ^ _780205) ^ [_1216129, _1216131] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1216129)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1216131))) = 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), _1216129), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1216131))))], (24302 ^ _780205) ^ [_1216181, _1216183] : [class_Fields_Olinordered__field__inverse__zero(_1216181), class_Int_Onumber__ring(_1216181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216181), c_Groups_Ozero__class_Ozero(_1216181)), _1216183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216181), c_Groups_Ozero__class_Ozero(_1216181)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216181), _1216183), hAPP(c_Int_Onumber__class_Onumber__of(_1216181), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (24316 ^ _780205) ^ [_1216422, _1216424] : [class_Fields_Olinordered__field__inverse__zero(_1216422), class_Int_Onumber__ring(_1216422), 24323 ^ _780205 : [(24324 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216422), c_Groups_Ozero__class_Ozero(_1216422)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216422), _1216424), hAPP(c_Int_Onumber__class_Onumber__of(_1216422), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216422), c_Groups_Ozero__class_Ozero(_1216422)), _1216424)))], (24330 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216422), c_Groups_Ozero__class_Ozero(_1216422)), _1216424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216422), c_Groups_Ozero__class_Ozero(_1216422)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216422), _1216424), hAPP(c_Int_Onumber__class_Onumber__of(_1216422), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (24336 ^ _780205) ^ [_1216772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1216772), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1216772 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1216772 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24346 ^ _780205) ^ [_1216870, _1216872] : [class_Int_Onumber__ring(_1216870), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216870), c_Groups_Oone__class_Oone(_1216870)), hAPP(c_Int_Onumber__class_Onumber__of(_1216870), _1216872)) = hAPP(c_Int_Onumber__class_Onumber__of(_1216870), 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), _1216872))))], (24352 ^ _780205) ^ [_1216997, _1216999] : [class_Int_Onumber__ring(_1216997), 24355 ^ _780205 : [(24356 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1216997), _1216999) = c_Groups_Oone__class_Oone(_1216997), -(c_Int_Oiszero(_1216997, hAPP(c_Int_Onumber__class_Onumber__of(_1216997), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216999), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (24362 ^ _780205) ^ [] : [c_Int_Oiszero(_1216997, hAPP(c_Int_Onumber__class_Onumber__of(_1216997), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216999), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1216997), _1216999) = c_Groups_Oone__class_Oone(_1216997))]]], (24368 ^ _780205) ^ [_1217256, _1217258] : [class_Int_Onumber__ring(_1217256), 24371 ^ _780205 : [(24372 ^ _780205) ^ [] : [c_Groups_Oone__class_Oone(_1217256) = hAPP(c_Int_Onumber__class_Onumber__of(_1217256), _1217258), -(c_Int_Oiszero(_1217256, hAPP(c_Int_Onumber__class_Onumber__of(_1217256), 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), _1217258)))))], (24378 ^ _780205) ^ [] : [c_Int_Oiszero(_1217256, hAPP(c_Int_Onumber__class_Onumber__of(_1217256), 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), _1217258)))), -(c_Groups_Oone__class_Oone(_1217256) = hAPP(c_Int_Onumber__class_Onumber__of(_1217256), _1217258))]]], (24384 ^ _780205) ^ [_1217524, _1217526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217524)), -(c_SMT_Oz3mod(_1217526, _1217524) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1217526, _1217524))], (24390 ^ _780205) ^ [_1217613, _1217615] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217613))), -(c_SMT_Oz3mod(_1217615, _1217613) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1217615, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1217613)))], (24396 ^ _780205) ^ [_1217663, _1217665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1217663), 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)))), _1217665))), 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)))), _1217663)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1217665), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1217663))], (24402 ^ _780205) ^ [_1217804, _1217806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217804)), -(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)))), _1217806))), 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)))), _1217804)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1217806), _1217804))], (24408 ^ _780205) ^ [_1217927, _1217929] : [class_Rings_Osemiring__1(_1217927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217929)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217927), 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)))), _1217929))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217927), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217927), hAPP(c_Int_Onat, _1217929))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217927), hAPP(c_Int_Onat, _1217929))))], (24418 ^ _780205) ^ [_1218124, _1218126, _1218128] : [-(hBOOL(hAPP(hAPP(c_member(_1218124), _1218126), _1218128))), -(hBOOL(hAPP(hAPP(c_member(_1218124), _1218126), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218124, tc_HOL_Obool)), _1218128))))], (24424 ^ _780205) ^ [_1218184, _1218186, _1218188] : [hBOOL(hAPP(hAPP(c_member(_1218184), _1218186), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218184, tc_HOL_Obool)), _1218188))), hBOOL(hAPP(hAPP(c_member(_1218184), _1218186), _1218188))], (24430 ^ _780205) ^ [_1218308, _1218310, _1218312] : [hBOOL(hAPP(hAPP(c_member(_1218308), _1218310), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218308, tc_HOL_Obool)), _1218312))), hBOOL(hAPP(hAPP(c_member(_1218308), _1218310), _1218312))], (24436 ^ _780205) ^ [_1218450, _1218452, _1218454] : [hBOOL(hAPP(hAPP(c_member(_1218450), _1218452), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218450, tc_HOL_Obool)), _1218454))), hBOOL(hAPP(hAPP(c_member(_1218450), _1218452), _1218454))], (24442 ^ _780205) ^ [_1218568, _1218570, _1218572] : [-(hBOOL(hAPP(hAPP(c_member(_1218568), _1218570), _1218572))), -(hBOOL(hAPP(hAPP(c_member(_1218568), _1218570), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218568, tc_HOL_Obool)), _1218572))))], (24448 ^ _780205) ^ [_1218630] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218630) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24450 ^ _780205) ^ [_1218656, _1218658, _1218660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218656, tc_HOL_Obool)), _1218658), _1218660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218656, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218656, tc_HOL_Obool)), _1218660)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218656, tc_HOL_Obool)), _1218658))))], (24456 ^ _780205) ^ [_1218825, _1218827, _1218829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218825, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218825, tc_HOL_Obool)), _1218827)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218825, tc_HOL_Obool)), _1218829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218825, tc_HOL_Obool)), _1218829), _1218827)))], (24462 ^ _780205) ^ [_1218972, _1218974, _1218976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218972, tc_HOL_Obool)), _1218976), _1218974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218972, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218972, tc_HOL_Obool)), _1218974)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1218972, tc_HOL_Obool)), _1218976))))], (24468 ^ _780205) ^ [_1219125] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1219125)) = _1219125)], (24470 ^ _780205) ^ [_1219154, _1219156] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1219154)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1219156)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1219154), _1219156))], (24472 ^ _780205) ^ [_1219197, _1219199] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1219197), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1219199)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1219197)), _1219199))], (24474 ^ _780205) ^ [_1219240, _1219242] : [class_Divides_Osemiring__div(_1219240), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1219240), c_Groups_Ozero__class_Ozero(_1219240)), _1219242) = c_Groups_Ozero__class_Ozero(_1219240))], (24480 ^ _780205) ^ [_1219339, _1219341] : [class_Divides_Osemiring__div(_1219339), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1219339), _1219341), c_Groups_Ozero__class_Ozero(_1219339)) = c_Groups_Ozero__class_Ozero(_1219339))], (24486 ^ _780205) ^ [_1219438, _1219440, _1219442, _1219444] : [-(hAPP(c_Set_Ovimage(_1219438, _1219440, _1219442), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1219440, tc_HOL_Obool)), _1219444)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1219438, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1219438, _1219440, _1219442), _1219444)))], (24488 ^ _780205) ^ [_1219497, _1219499] : [class_Divides_Osemiring__div(_1219497), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1219497), _1219499), c_Groups_Oone__class_Oone(_1219497)) = _1219499)], (24494 ^ _780205) ^ [_1219592] : [class_Rings_Osemiring__1(_1219592), -(c_Int_Oiszero(_1219592, c_Groups_Ozero__class_Ozero(_1219592)))], (24500 ^ _780205) ^ [_1219669, _1219671] : [class_Rings_Osemiring__1(_1219669), 24503 ^ _780205 : [(24504 ^ _780205) ^ [] : [c_Int_Oiszero(_1219669, _1219671), -(_1219671 = c_Groups_Ozero__class_Ozero(_1219669))], (24510 ^ _780205) ^ [] : [_1219671 = c_Groups_Ozero__class_Ozero(_1219669), -(c_Int_Oiszero(_1219669, _1219671))]]], (24516 ^ _780205) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24518 ^ _780205) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24520 ^ _780205) ^ [_1219916, _1219918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219916)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219918)), -(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), _1219916), _1219918))))], (24530 ^ _780205) ^ [_1220069] : [class_Rings_Osemiring__1(_1220069), c_Int_Oiszero(_1220069, c_Groups_Oone__class_Oone(_1220069))], (24536 ^ _780205) ^ [_1220147, _1220149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220147)), 24539 ^ _780205 : [(24540 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1220149), _1220147)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1220149), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24546 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1220149), 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), _1220149), _1220147)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (24552 ^ _780205) ^ [_1220406, _1220408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1220406), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24555 ^ _780205 : [(24556 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1220408), _1220406)), 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)), _1220408)))], (24562 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1220408), _1220406)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (24568 ^ _780205) ^ [_1220662, _1220664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1220662), 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)), _1220664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1220662), _1220664)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24578 ^ _780205) ^ [_1220827, _1220829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220829)), 24585 ^ _780205 : [(24586 ^ _780205) ^ [] : [hAPP(c_Int_Onat, _1220827) = hAPP(c_Int_Onat, _1220829), -(_1220827 = _1220829)], (24592 ^ _780205) ^ [] : [_1220827 = _1220829, -(hAPP(c_Int_Onat, _1220827) = hAPP(c_Int_Onat, _1220829))]]], (24598 ^ _780205) ^ [_1221112, _1221114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221112)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221114)), 24605 ^ _780205 : [(24606 ^ _780205) ^ [] : [hAPP(c_Int_Onat, _1221112) = hAPP(c_Int_Onat, _1221114), -(_1221112 = _1221114)], (24612 ^ _780205) ^ [] : [_1221112 = _1221114, -(hAPP(c_Int_Onat, _1221112) = hAPP(c_Int_Onat, _1221114))]]], (24629 ^ _780205) ^ [_1221594] : [24631 ^ _780205 : [(24632 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24630 ^ [_1221594])))], (24634 ^ _780205) ^ [] : [hBOOL(hAPP(_1221594, hAPP(c_Int_Onat, 24630 ^ [_1221594])))]], 24635 ^ _780205 : [(24636 ^ _780205) ^ [_1221727] : [-(hBOOL(hAPP(_1221594, _1221727)))]]], (24618 ^ _780205) ^ [_1221409] : [hBOOL(hAPP(_1221409, 24619 ^ [_1221409])), 24622 ^ _780205 : [(24623 ^ _780205) ^ [_1221503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221503)), -(hBOOL(hAPP(_1221409, hAPP(c_Int_Onat, _1221503))))]]], (24638 ^ _780205) ^ [_1221772] : [24639 ^ _780205 : [(24640 ^ _780205) ^ [_1221829] : [hBOOL(hAPP(_1221772, _1221829))]], 24642 ^ _780205 : [(24643 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24641 ^ [_1221772])))], (24645 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1221772, hAPP(c_Int_Onat, 24641 ^ [_1221772]))))]]], (24647 ^ _780205) ^ [_1221915] : [-(hBOOL(hAPP(_1221915, 24654 ^ [_1221915]))), 24648 ^ _780205 : [(24649 ^ _780205) ^ [_1221967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221967)), hBOOL(hAPP(_1221915, hAPP(c_Int_Onat, _1221967)))]]], (24658 ^ _780205) ^ [_1222090] : [-(_1222090 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222090), _1222090) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (24664 ^ _780205) ^ [_1222145, _1222147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1222145, tc_HOL_Obool)), _1222147), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222145, tc_HOL_Obool)), _1222147))), -(_1222147 = c_Orderings_Obot__class_Obot(tc_fun(_1222145, tc_HOL_Obool)))], (24670 ^ _780205) ^ [_1222264, _1222266] : [_1222266 = c_Orderings_Obot__class_Obot(tc_fun(_1222264, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1222264, tc_HOL_Obool)), _1222266), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222264, tc_HOL_Obool)), _1222266))))], (24676 ^ _780205) ^ [_1222389, _1222391] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222389, tc_HOL_Obool)), _1222391), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222389, tc_HOL_Obool)), _1222391)) = c_Orderings_Obot__class_Obot(tc_fun(_1222389, tc_HOL_Obool)))], (24678 ^ _780205) ^ [_1222438, _1222440] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222438, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222438, tc_HOL_Obool)), _1222440)), _1222440) = c_Orderings_Obot__class_Obot(tc_fun(_1222438, tc_HOL_Obool)))], (24680 ^ _780205) ^ [_1222487, _1222489] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1222487))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1222489))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222487)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222489)))], (24682 ^ _780205) ^ [_1222540, _1222542] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1222540, _1222542)), _1222542) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24684 ^ _780205) ^ [_1222573] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222573), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24686 ^ _780205) ^ [_1222599] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1222599, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1222599)], (24688 ^ _780205) ^ [_1222628] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1222628) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222628)))], (24690 ^ _780205) ^ [_1222660] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222660)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1222660))], (24692 ^ _780205) ^ [_1222692, _1222694, _1222696] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222692, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222692, tc_HOL_Obool)), _1222694), _1222696)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222692, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222692, tc_HOL_Obool)), _1222694)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222692, tc_HOL_Obool)), _1222696)))], (24694 ^ _780205) ^ [_1222765, _1222767, _1222769] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222765, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222765, tc_HOL_Obool)), _1222767), _1222769)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222765, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222765, tc_HOL_Obool)), _1222767)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222765, tc_HOL_Obool)), _1222769)))], (24696 ^ _780205) ^ [_1222838, _1222840, _1222842] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1222838), _1222840)), _1222842) = 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), _1222838), _1222842)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222840), _1222842))), 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, _1222838, _1222842)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1222840, _1222842))), _1222842)))], (24698 ^ _780205) ^ [_1222921, _1222923, _1222925] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222921, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222921, tc_HOL_Obool)), _1222923), _1222925)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222921, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222921, tc_HOL_Obool)), _1222923)), _1222925))], (24700 ^ _780205) ^ [_1222986, _1222988, _1222990] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222986, tc_HOL_Obool)), _1222988), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1222986, tc_HOL_Obool)), _1222990)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222986, tc_HOL_Obool)), _1222988), _1222990))], (24702 ^ _780205) ^ [_1223043, _1223045, _1223047] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1223043, tc_HOL_Obool)), _1223045), _1223047) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1223043, tc_HOL_Obool)), _1223045), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1223043, tc_HOL_Obool)), _1223047)))], (24704 ^ _780205) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (24706 ^ _780205) ^ [_1223118] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1223118)), -(hAPP(c_Int_Onat, _1223118) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24712 ^ _780205) ^ [_1223199] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1223199))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1223199)) = _1223199)], (24718 ^ _780205) ^ [_1223241, _1223243, _1223245, _1223247] : [class_Divides_Osemiring__div(_1223241), 24721 ^ _780205 : [(24722 ^ _780205) ^ [] : [_1223243 = c_Groups_Ozero__class_Ozero(_1223241), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223241), _1223243), _1223245)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223241), _1223243), _1223247)) = c_Groups_Ozero__class_Ozero(_1223241))], (24728 ^ _780205) ^ [] : [-(_1223243 = c_Groups_Ozero__class_Ozero(_1223241)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223241), _1223243), _1223245)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223241), _1223243), _1223247)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223241), _1223245), _1223247))]]], (24734 ^ _780205) ^ [_1223547, _1223549, _1223551] : [class_Divides_Osemiring__div(_1223547), -(_1223549 = c_Groups_Ozero__class_Ozero(_1223547)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223547), _1223551), _1223549)), _1223549) = _1223551)], (24744 ^ _780205) ^ [_1223675, _1223677, _1223679] : [class_Divides_Osemiring__div(_1223675), -(_1223677 = c_Groups_Ozero__class_Ozero(_1223675)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223675), _1223677), _1223679)), _1223677) = _1223679)], (24754 ^ _780205) ^ [_1223803, _1223805, _1223807, _1223809] : [class_Divides_Osemiring__div(_1223803), -(_1223805 = c_Groups_Ozero__class_Ozero(_1223803)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223803), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223803), _1223807), _1223805)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223803), _1223809), _1223805)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223803), _1223807), _1223809))], (24764 ^ _780205) ^ [_1223965, _1223967, _1223969, _1223971] : [class_Divides_Osemiring__div(_1223965), -(_1223967 = c_Groups_Ozero__class_Ozero(_1223965)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223965), _1223967), _1223969)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223965), _1223967), _1223971)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1223965), _1223969), _1223971))], (24774 ^ _780205) ^ [_1224127, _1224129] : [class_Divides_Osemiring__div(_1224127), -(_1224129 = c_Groups_Ozero__class_Ozero(_1224127)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1224127), _1224129), _1224129) = c_Groups_Oone__class_Oone(_1224127))], (24784 ^ _780205) ^ [_1224241, _1224243, _1224245] : [class_Divides_Osemiring__div(_1224241), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1224241), c_Divides_Odiv__class_Omod(_1224241, _1224243, _1224245)), _1224245) = c_Groups_Ozero__class_Ozero(_1224241))], (24790 ^ _780205) ^ [_1224346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224346), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1224346) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24796 ^ _780205) ^ [_1224449] : [hAPP(c_Int_Onat, _1224449) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224449), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24802 ^ _780205) ^ [_1224536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224536), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1224536) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24808 ^ _780205) ^ [_1224629, _1224631, _1224633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224629), _1224631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224633), 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), _1224631), _1224633)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1224629), _1224633))))], (24818 ^ _780205) ^ [_1224816, _1224818, _1224820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224816), _1224818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1224816), _1224820)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1224818), _1224820))))], (24828 ^ _780205) ^ [_1224997, _1224999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224997), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224999), _1224997)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1224997), _1224999) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24838 ^ _780205) ^ [_1225158, _1225160, _1225162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225158), 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)), _1225160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225160), _1225162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1225158), _1225160)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1225158), _1225162))))], (24852 ^ _780205) ^ [_1225403, _1225405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225403), 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)), _1225405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1225403), _1225405)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24862 ^ _780205) ^ [_1225568, _1225570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225568), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24865 ^ _780205 : [(24866 ^ _780205) ^ [] : [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), _1225570), _1225568))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225570), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24872 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225570), 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), _1225570), _1225568))))]]], (24878 ^ _780205) ^ [_1225824, _1225826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225824), _1225826)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1225824), _1225826) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24888 ^ _780205) ^ [_1225979, _1225981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225981), 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), _1225979), _1225981)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24898 ^ _780205) ^ [_1226144, _1226146, _1226148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226146), _1226148)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1226144), _1226148)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1226144), _1226146))))], (24912 ^ _780205) ^ [_1226383, _1226385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226383)), 24915 ^ _780205 : [(24916 ^ _780205) ^ [] : [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), _1226383), _1226385))), 24919 ^ _780205 : [(24920 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226385), _1226383)))], (24922 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226385)))]]], (24924 ^ _780205) ^ [] : [-(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), _1226383), _1226385)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226385), _1226383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226385))]]], (24934 ^ _780205) ^ [_1226711, _1226713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226711)), 24937 ^ _780205 : [(24938 ^ _780205) ^ [] : [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), _1226713), _1226711))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226711), _1226713)))], (24944 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226711), _1226713)), -(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), _1226713), _1226711))))]]], (24950 ^ _780205) ^ [_1226961, _1226963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226961)), 24953 ^ _780205 : [(24954 ^ _780205) ^ [] : [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), _1226963), _1226961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226963)))], (24960 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226963)), -(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), _1226963), _1226961))))]]], (24966 ^ _780205) ^ [_1227217, _1227219] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1227217), _1227219) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1227219 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24975 ^ _780205 : [(24976 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227217)))], (24978 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227217), _1227219)))]], 24979 ^ _780205 : [(24980 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227217), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24982 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227219), _1227217)))]]], (24984 ^ _780205) ^ [_1227448, _1227450] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1227448), _1227450) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24985 ^ _780205 : [(24986 ^ _780205) ^ [] : [_1227450 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (24988 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227448), _1227450))], (24994 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227448), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227450), _1227448))]]], (25002 ^ _780205) ^ [_1227758, _1227760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227758)), hAPP(c_Int_Onat, _1227760))), 25005 ^ _780205 : [(25006 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227760)))], (25008 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227758), _1227760)))]]], (25010 ^ _780205) ^ [_1227893, _1227895] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227893)), hAPP(c_Int_Onat, _1227895)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227893), _1227895))], (25020 ^ _780205) ^ [_1228060, _1228062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228060)), 25023 ^ _780205 : [(25024 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1228062)), hAPP(c_Int_Onat, _1228060))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228062), _1228060)))], (25030 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228062), _1228060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1228062)), hAPP(c_Int_Onat, _1228060))))]]], (25036 ^ _780205) ^ [_1228319, _1228321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228321)), 25043 ^ _780205 : [(25044 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1228319)), hAPP(c_Int_Onat, _1228321))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228319), _1228321)))], (25050 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228319), _1228321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1228319)), hAPP(c_Int_Onat, _1228321))))]]], (25056 ^ _780205) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25058 ^ _780205) ^ [_1228652, _1228654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1228654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1228652), _1228654)), _1228652)))], (25068 ^ _780205) ^ [_1228811, _1228813, _1228815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228811)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1228813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228815), _1228811)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1228813), _1228815)), _1228811))], (25074 ^ _780205) ^ [_1228942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228942)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1228942)) = _1228942)], (25080 ^ _780205) ^ [_1229048, _1229050] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229048) = _1229050, 25083 ^ _780205 : [(25084 ^ _780205) ^ [] : [-(_1229048 = hAPP(c_Int_Onat, _1229050))], (25086 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229050)))]]], (25088 ^ _780205) ^ [_1229163, _1229165] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229163) = _1229165), _1229163 = hAPP(c_Int_Onat, _1229165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229165))], (25098 ^ _780205) ^ [_1229316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229316)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1229316)) = _1229316)], (25104 ^ _780205) ^ [_1229401] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229401))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1229401)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25110 ^ _780205) ^ [_1229460, _1229462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1229460), hAPP(c_Int_Onat, _1229462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229460)), _1229462)))], (25116 ^ _780205) ^ [_1229565, _1229567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229565)), _1229567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1229565), hAPP(c_Int_Onat, _1229567))))], (25122 ^ _780205) ^ [_1229694, _1229696, _1229698] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1229694, tc_HOL_Obool)), _1229696), _1229698) = c_Orderings_Obot__class_Obot(tc_fun(_1229694, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1229694, tc_HOL_Obool)), _1229696), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1229694, tc_HOL_Obool)), _1229698))))], (25128 ^ _780205) ^ [_1229837, _1229839, _1229841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1229837, tc_HOL_Obool)), _1229839), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1229837, tc_HOL_Obool)), _1229841))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1229837, tc_HOL_Obool)), _1229839), _1229841) = c_Orderings_Obot__class_Obot(tc_fun(_1229837, tc_HOL_Obool)))], (25134 ^ _780205) ^ [_1229986, _1229988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229988)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1229986, _1229988)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1229986), hAPP(c_Int_Onat, _1229988)))], (25144 ^ _780205) ^ [_1230157, _1230159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230159)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1230157), hAPP(c_Int_Onat, _1230159)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230157, _1230159)))], (25154 ^ _780205) ^ [_1230328] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230328))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25156 ^ _780205) ^ [_1230360, _1230362, _1230364] : [-(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), _1230360), _1230362)), _1230362)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230360, _1230362))), _1230364) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1230360), _1230364))], (25158 ^ _780205) ^ [_1230421, _1230423, _1230425] : [-(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), _1230421), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230423), _1230421))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230423, _1230421))), _1230425) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1230423), _1230425))], (25160 ^ _780205) ^ [_1230482, _1230484, _1230486] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230482), _1230484)), _1230486) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230482), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230484), _1230486))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230482), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230484, _1230486))), _1230486)))], (25162 ^ _780205) ^ [_1230555, _1230557] : [-(_1230555 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230557), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230555), _1230557))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230555, _1230557)))], (25164 ^ _780205) ^ [_1230602] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230602), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230602))], (25166 ^ _780205) ^ [_1230634, _1230636] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230634, _1230636) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1230634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230634), _1230636)), _1230636)))], (25168 ^ _780205) ^ [_1230681, _1230683] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230681), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230683), _1230681)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1230683), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230683, _1230681)))], (25170 ^ _780205) ^ [_1230728, _1230730] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230728), _1230730))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1230728))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1230730))))], (25172 ^ _780205) ^ [_1230783, _1230785, _1230787, _1230789] : [class_Divides_Osemiring__div(_1230783), -(_1230785 = c_Groups_Ozero__class_Ozero(_1230783)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230783), _1230787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230783), _1230789), _1230785))), _1230785) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230783), _1230789), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230783), _1230787), _1230785)))], (25182 ^ _780205) ^ [_1230961, _1230963, _1230965, _1230967] : [class_Divides_Osemiring__div(_1230961), -(_1230963 = c_Groups_Ozero__class_Ozero(_1230961)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230961), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230961), _1230965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230961), _1230963), _1230967))), _1230963) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230961), _1230967), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230961), _1230965), _1230963)))], (25192 ^ _780205) ^ [_1231139, _1231141, _1231143] : [class_Divides_Osemiring__div(_1231139), -(_1231141 = c_Groups_Ozero__class_Ozero(_1231139)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231139), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231139), _1231143), _1231141)), _1231141) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231139), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231139), _1231143), _1231141)), c_Groups_Oone__class_Oone(_1231139)))], (25202 ^ _780205) ^ [_1231303, _1231305, _1231307] : [class_Divides_Osemiring__div(_1231303), -(_1231305 = c_Groups_Ozero__class_Ozero(_1231303)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231303), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231303), _1231305), _1231307)), _1231305) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231303), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231303), _1231307), _1231305)), c_Groups_Oone__class_Oone(_1231303)))], (25212 ^ _780205) ^ [_1231467, _1231469, _1231471, _1231473] : [class_Divides_Osemiring__div(_1231467), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231467), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231467), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231467), _1231469), _1231471)), _1231471)), c_Divides_Odiv__class_Omod(_1231467, _1231469, _1231471))), _1231473) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231467), _1231469), _1231473))], (25218 ^ _780205) ^ [_1231634, _1231636, _1231638, _1231640] : [class_Divides_Osemiring__div(_1231634), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231634), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231634), _1231636), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231634), _1231638), _1231636))), c_Divides_Odiv__class_Omod(_1231634, _1231638, _1231636))), _1231640) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231634), _1231638), _1231640))], (25224 ^ _780205) ^ [_1231801, _1231803, _1231805] : [class_Divides_Osemiring__div(_1231801), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231801), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231801), _1231803), _1231805)), _1231805)), c_Divides_Odiv__class_Omod(_1231801, _1231803, _1231805)) = _1231803)], (25230 ^ _780205) ^ [_1231934, _1231936, _1231938] : [class_Divides_Osemiring__div(_1231934), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231934), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231934), _1231936), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231934), _1231938), _1231936))), c_Divides_Odiv__class_Omod(_1231934, _1231938, _1231936)) = _1231938)], (25236 ^ _780205) ^ [_1232067, _1232069, _1232071] : [class_Divides_Osemiring__div(_1232067), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1232067), c_Divides_Odiv__class_Omod(_1232067, _1232069, _1232071)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232067), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1232067), _1232069), _1232071)), _1232071)) = _1232069)], (25242 ^ _780205) ^ [_1232200] : [class_Int_Onumber__ring(_1232200), -(c_Int_Oiszero(_1232200, hAPP(c_Int_Onumber__class_Onumber__of(_1232200), c_Int_OPls)))], (25248 ^ _780205) ^ [_1232283, _1232285] : [c_Int_Oiszero(_1232283, hAPP(c_Int_Onumber__class_Onumber__of(_1232283), c_Int_OBit1(_1232285))), class_Int_Onumber__ring(_1232283), class_Int_Oring__char__0(_1232283)], (25258 ^ _780205) ^ [_1232423, _1232425] : [class_Int_Onumber__ring(_1232423), class_Int_Oring__char__0(_1232423), 25265 ^ _780205 : [(25266 ^ _780205) ^ [] : [c_Int_Oiszero(_1232423, hAPP(c_Int_Onumber__class_Onumber__of(_1232423), c_Int_OBit0(_1232425))), -(c_Int_Oiszero(_1232423, hAPP(c_Int_Onumber__class_Onumber__of(_1232423), _1232425)))], (25272 ^ _780205) ^ [] : [c_Int_Oiszero(_1232423, hAPP(c_Int_Onumber__class_Onumber__of(_1232423), _1232425)), -(c_Int_Oiszero(_1232423, hAPP(c_Int_Onumber__class_Onumber__of(_1232423), c_Int_OBit0(_1232425))))]]], (25278 ^ _780205) ^ [_1232716] : [class_Int_Onumber__ring(_1232716), c_Int_Oiszero(_1232716, hAPP(c_Int_Onumber__class_Onumber__of(_1232716), c_Int_OMin))], (25284 ^ _780205) ^ [_1232812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1232812))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232812)))], (25290 ^ _780205) ^ [_1232897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1232897))))], (25296 ^ _780205) ^ [_1232988, _1232990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232988)), 25299 ^ _780205 : [(25300 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1232988)), hAPP(c_Int_Onat, _1232990))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232988), _1232990)))], (25306 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232988), _1232990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1232988)), hAPP(c_Int_Onat, _1232990))))]]], (25312 ^ _780205) ^ [_1233247, _1233249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233249)), 25319 ^ _780205 : [(25320 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1233247)), hAPP(c_Int_Onat, _1233249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233247), _1233249)))], (25326 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233247), _1233249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1233247)), hAPP(c_Int_Onat, _1233249))))]]], (25348 ^ _780205) ^ [_1233769, _1233771] : [-(_1233769 = hAPP(c_Int_Onat, _1233771)), 25351 ^ _780205 : [(25352 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233771)))], (25354 ^ _780205) ^ [] : [_1233771 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233769)]], 25355 ^ _780205 : [(25356 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233771))], (25358 ^ _780205) ^ [] : [_1233769 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (25332 ^ _780205) ^ [_1233577, _1233579] : [_1233577 = hAPP(c_Int_Onat, _1233579), 25335 ^ _780205 : [(25336 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233579)), -(_1233579 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233577))], (25342 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233579))), -(_1233577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25378 ^ _780205) ^ [_1234200, _1234202] : [-(hAPP(c_Int_Onat, _1234200) = _1234202), 25381 ^ _780205 : [(25382 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234200)))], (25384 ^ _780205) ^ [] : [_1234200 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234202)]], 25385 ^ _780205 : [(25386 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234200))], (25388 ^ _780205) ^ [] : [_1234202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (25362 ^ _780205) ^ [_1234008, _1234010] : [hAPP(c_Int_Onat, _1234008) = _1234010, 25365 ^ _780205 : [(25366 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234008)), -(_1234008 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234010))], (25372 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234008))), -(_1234010 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25392 ^ _780205) ^ [_1234424, _1234426] : [25393 ^ _780205 : [(25394 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234424))], (25396 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234426))]], 25397 ^ _780205 : [(25398 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1234424)), hAPP(c_Int_Onat, _1234426))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234424), _1234426)))], (25404 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234424), _1234426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1234424)), hAPP(c_Int_Onat, _1234426))))]]], (25426 ^ _780205) ^ [_1235003, _1235005] : [-(hBOOL(hAPP(_1235003, hAPP(c_Int_Onat, _1235005)))), 25430 ^ _780205 : [(25431 ^ _780205) ^ [] : [-(_1235005 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 25429 ^ [_1235003, _1235005]))], (25433 ^ _780205) ^ [] : [hBOOL(hAPP(_1235003, 25429 ^ [_1235003, _1235005]))]], 25434 ^ _780205 : [(25435 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235005), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25437 ^ _780205) ^ [] : [hBOOL(hAPP(_1235003, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (25410 ^ _780205) ^ [_1234740, _1234742] : [hBOOL(hAPP(_1234740, hAPP(c_Int_Onat, _1234742))), 25413 ^ _780205 : [(25414 ^ _780205) ^ [_1234840] : [_1234742 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234840), -(hBOOL(hAPP(_1234740, _1234840)))], (25420 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234742), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1234740, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (25441 ^ _780205) ^ [_1235266, _1235268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235268)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235266), _1235268)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1235266)), hAPP(c_Int_Onat, _1235268)))], (25451 ^ _780205) ^ [_1235445, _1235447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235447)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1235445)), hAPP(c_Int_Onat, _1235447)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235445), _1235447)))], (25461 ^ _780205) ^ [_1235639, _1235641] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235639) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235641), 25464 ^ _780205 : [(25465 ^ _780205) ^ [] : [-(_1235639 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235641)))], (25467 ^ _780205) ^ [] : [-(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), _1235641))))]]], (25469 ^ _780205) ^ [_1235772, _1235774] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235772) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235774)), _1235772 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235774)), 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), _1235774)))], (25479 ^ _780205) ^ [_1235937, _1235939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235937)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235937), _1235939)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1235937)), hAPP(c_Int_Onat, _1235939)))], (25485 ^ _780205) ^ [_1236060, _1236062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236062)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1236060)), hAPP(c_Int_Onat, _1236062)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236060), _1236062)))], (25495 ^ _780205) ^ [_1236239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236239)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1236239) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (25501 ^ _780205) ^ [_1236324, _1236326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236324), _1236326)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1236326), _1236324)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1236326)), hAPP(c_Int_Onat, _1236324)))], (25511 ^ _780205) ^ [] : [-(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)))))], (25513 ^ _780205) ^ [_1236527, _1236529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236529)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1236527)), hAPP(c_Int_Onat, _1236529)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1236527, _1236529)))], (25523 ^ _780205) ^ [_1236712] : [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, _1236712))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1236712)))], (25529 ^ _780205) ^ [_1236797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1236797)), -(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, _1236797))))], (25581 ^ _780205) ^ [_1237866, _1237868, _1237870] : [-(hBOOL(hAPP(_1237866, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1237868), _1237870)))), 25584 ^ _780205 : [(25585 ^ _780205) ^ [] : [-(_1237870 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25587 ^ _780205) ^ [] : [hBOOL(hAPP(_1237866, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 25590 ^ _780205 : [(25591 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237870)))], (25595 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25593 ^ [_1237866, _1237868, _1237870])))], (25597 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 25593 ^ [_1237866, _1237868, _1237870]), _1237870)))], (25599 ^ _780205) ^ [] : [-(_1237868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237870), 25592 ^ [_1237866, _1237868, _1237870])), 25593 ^ [_1237866, _1237868, _1237870]))], (25601 ^ _780205) ^ [] : [hBOOL(hAPP(_1237866, 25592 ^ [_1237866, _1237868, _1237870]))]], 25602 ^ _780205 : [(25603 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237870), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25607 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237870), 25605 ^ [_1237866, _1237868, _1237870])))], (25609 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 25605 ^ [_1237866, _1237868, _1237870]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25611 ^ _780205) ^ [] : [-(_1237868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237870), 25604 ^ [_1237866, _1237868, _1237870])), 25605 ^ [_1237866, _1237868, _1237870]))], (25613 ^ _780205) ^ [] : [hBOOL(hAPP(_1237866, 25604 ^ [_1237866, _1237868, _1237870]))]]], (25535 ^ _780205) ^ [_1236906, _1236908, _1236910] : [hBOOL(hAPP(_1236906, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1236908), _1236910))), 25538 ^ _780205 : [(25539 ^ _780205) ^ [] : [_1236910 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1236906, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25545 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236910)), 25548 ^ _780205 : [(25549 ^ _780205) ^ [_1237240] : [-(hBOOL(hAPP(_1236906, _1237240))), 25550 ^ _780205 : [(25551 ^ _780205) ^ [_1237311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237311), _1236910)), _1236908 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236910), _1237240)), _1237311)]]]]], (25563 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236910), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 25566 ^ _780205 : [(25567 ^ _780205) ^ [_1237570] : [-(hBOOL(hAPP(_1236906, _1237570))), 25568 ^ _780205 : [(25569 ^ _780205) ^ [_1237644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236910), _1237644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237644), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1236908 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236910), _1237570)), _1237644)]]]]]]], (25617 ^ _780205) ^ [_1238580, _1238582, _1238584, _1238586] : [_1238580 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1238582), _1238584)), _1238586), -(_1238582 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1238580), _1238582) = _1238584), 25624 ^ _780205 : [(25625 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238582)))], (25627 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238586), _1238582))]], 25632 ^ _780205 : [(25633 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238582))], (25635 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238582), _1238586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1238586), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (25647 ^ _780205) ^ [_1239049, _1239051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239049)), 25650 ^ _780205 : [(25651 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1239049)), _1239051)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239049), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239051))))], (25657 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239049), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239051))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1239049)), _1239051)))]]], (25663 ^ _780205) ^ [_1239308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239308)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1239308)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1239308)))], (25669 ^ _780205) ^ [_1239411, _1239413, _1239415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239411)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1239413, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1239415), _1239411)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1239415), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1239413), _1239415), _1239411))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1239413, _1239415)))], (25675 ^ _780205) ^ [] : [-(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)))))], (25677 ^ _780205) ^ [_1239584, _1239586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239584), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1239584), _1239586)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1239584))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1239586))))], (25683 ^ _780205) ^ [_1239724, _1239726] : [-(_1239724 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25686 ^ _780205 : [(25687 ^ _780205) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1239726, _1239724) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1239726), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1239724)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1239726), _1239724)))], (25693 ^ _780205) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1239726, _1239724) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1239726), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1239724)) = 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), _1239726), _1239724))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (25699 ^ _780205) ^ [_1239997, _1239999] : [-(_1239997 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25702 ^ _780205 : [(25703 ^ _780205) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1239999, _1239997) = 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), _1239999)), _1239997) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1239999), _1239997)))], (25709 ^ _780205) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1239999, _1239997) = 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), _1239999)), _1239997) = 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), _1239999), _1239997))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (25715 ^ _780205) ^ [_1240280, _1240282] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1240280))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1240280), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1240282)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25721 ^ _780205) ^ [_1240382, _1240384] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1240382)))), 25724 ^ _780205 : [(25725 ^ _780205) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1240384))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1240382), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1240384)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1240382))], (25731 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1240384)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1240382), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1240384)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1240382), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1240384))))]]], (25737 ^ _780205) ^ [_1240655] : [class_Int_Onumber__ring(_1240655), c_Int_Oiszero(_1240655, hAPP(c_Int_Onumber__class_Onumber__of(_1240655), c_Int_OBit1(c_Int_OPls)))], (25743 ^ _780205) ^ [_1240739, _1240741, _1240743] : [class_Int_Onumber__ring(_1240739), 25746 ^ _780205 : [(25747 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1240739), _1240741) = hAPP(c_Int_Onumber__class_Onumber__of(_1240739), _1240743), -(c_Int_Oiszero(_1240739, hAPP(c_Int_Onumber__class_Onumber__of(_1240739), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1240741), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1240743)))))], (25753 ^ _780205) ^ [] : [c_Int_Oiszero(_1240739, hAPP(c_Int_Onumber__class_Onumber__of(_1240739), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1240741), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1240743)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1240739), _1240741) = hAPP(c_Int_Onumber__class_Onumber__of(_1240739), _1240743))]]], (25759 ^ _780205) ^ [] : [-(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))))], (25761 ^ _780205) ^ [_1241040, _1241042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1241040), _1241042)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1241040), _1241042) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (25771 ^ _780205) ^ [_1241207, _1241209, _1241211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241207)), 25774 ^ _780205 : [(25793 ^ _780205) ^ [] : [25796 ^ _780205 : [(25797 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25795 ^ [_1241207, _1241209, _1241211])))], (25799 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 25795 ^ [_1241207, _1241209, _1241211]), _1241207)))], (25801 ^ _780205) ^ [] : [-(_1241211 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241207), 25794 ^ [_1241207, _1241209, _1241211])), 25795 ^ [_1241207, _1241209, _1241211]))], (25803 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1241209, 25794 ^ [_1241207, _1241209, _1241211]), 25795 ^ [_1241207, _1241209, _1241211]))]], -(hBOOL(hAPP(hAPP(_1241209, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1241211), _1241207)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241211, _1241207))))], (25775 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1241209, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1241211), _1241207)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241211, _1241207))), 25778 ^ _780205 : [(25779 ^ _780205) ^ [_1241408, _1241410] : [-(hBOOL(hAPP(hAPP(_1241209, _1241410), _1241408))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241408), _1241207)), _1241211 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241207), _1241410)), _1241408)]]]]], (25807 ^ _780205) ^ [_1241922, _1241924, _1241926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241922), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 25810 ^ _780205 : [(25829 ^ _780205) ^ [] : [25832 ^ _780205 : [(25833 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241922), 25831 ^ [_1241922, _1241924, _1241926])))], (25835 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 25831 ^ [_1241922, _1241924, _1241926]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25837 ^ _780205) ^ [] : [-(_1241926 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241922), 25830 ^ [_1241922, _1241924, _1241926])), 25831 ^ [_1241922, _1241924, _1241926]))], (25839 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1241924, 25830 ^ [_1241922, _1241924, _1241926]), 25831 ^ [_1241922, _1241924, _1241926]))]], -(hBOOL(hAPP(hAPP(_1241924, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1241926), _1241922)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241926, _1241922))))], (25811 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1241924, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1241926), _1241922)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241926, _1241922))), 25814 ^ _780205 : [(25815 ^ _780205) ^ [_1242132, _1242134] : [-(hBOOL(hAPP(hAPP(_1241924, _1242134), _1242132))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241922), _1242132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1242132), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1241926 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241922), _1242134)), _1242132)]]]]], (25843 ^ _780205) ^ [_1242664, _1242666] : [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), _1242664))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1242666))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1242664))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1242666)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1242664)))], (25849 ^ _780205) ^ [_1242801, _1242803] : [-(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), _1242801)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1242803))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1242801))) = 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), _1242803)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1242801)))], (25855 ^ _780205) ^ [_1242884] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1242884))), -(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), _1242884)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25861 ^ _780205) ^ [_1242977] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1242977)))), -(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), _1242977)) = 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), _1242977))))], (25867 ^ _780205) ^ [_1243035, _1243037] : [class_Int_Onumber__ring(_1243035), 25870 ^ _780205 : [(25871 ^ _780205) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1243035), _1243037) = c_Groups_Ozero__class_Ozero(_1243035), -(c_Int_Oiszero(_1243035, hAPP(c_Int_Onumber__class_Onumber__of(_1243035), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1243037), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (25877 ^ _780205) ^ [] : [c_Int_Oiszero(_1243035, hAPP(c_Int_Onumber__class_Onumber__of(_1243035), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1243037), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1243035), _1243037) = c_Groups_Ozero__class_Ozero(_1243035))]]], (25883 ^ _780205) ^ [_1243294, _1243296] : [class_Int_Onumber__ring(_1243294), 25886 ^ _780205 : [(25887 ^ _780205) ^ [] : [c_Groups_Ozero__class_Ozero(_1243294) = hAPP(c_Int_Onumber__class_Onumber__of(_1243294), _1243296), -(c_Int_Oiszero(_1243294, hAPP(c_Int_Onumber__class_Onumber__of(_1243294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243296)))))], (25893 ^ _780205) ^ [] : [c_Int_Oiszero(_1243294, hAPP(c_Int_Onumber__class_Onumber__of(_1243294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243296)))), -(c_Groups_Ozero__class_Ozero(_1243294) = hAPP(c_Int_Onumber__class_Onumber__of(_1243294), _1243296))]]], (25899 ^ _780205) ^ [_1243562, _1243564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243562)), -(c_SMT_Oz3div(_1243564, _1243562) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243564), _1243562))], (25905 ^ _780205) ^ [_1243655, _1243657] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243655))), -(c_SMT_Oz3div(_1243657, _1243655) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243657), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243655))))], (25911 ^ _780205) ^ [_1243710, _1243712] : [-(c_Int_Onat__aux(_1243710, _1243712) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1243710)), _1243712))], (25913 ^ _780205) ^ [_1243756, _1243758] : [_1243756 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1243756, _1243758) = _1243758)], (25919 ^ _780205) ^ [_1243833, _1243835] : [-(_1243833 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1243833, _1243835) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1243833), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1243835)))], (25925 ^ _780205) ^ [] : [-(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))))], (25927 ^ _780205) ^ [_1243904, _1243906] : [class_Int_Onumber__ring(_1243904), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1243904), hAPP(c_Int_Onumber__class_Onumber__of(_1243904), 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)))), _1243906))) = hAPP(c_Int_Onumber__class_Onumber__of(_1243904), c_Int_OMin))], (25933 ^ _780205) ^ [_1244027, _1244029] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1244027, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1244027, tc_HOL_Obool)), _1244029)) = _1244029)], (25935 ^ _780205) ^ [_1244086, _1244088, _1244090] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1244086, tc_HOL_Obool)), _1244088) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1244086, tc_HOL_Obool)), _1244090), -(_1244088 = _1244090)], (25941 ^ _780205) ^ [_1244193, _1244195, _1244197] : [_1244195 = _1244197, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1244193, tc_HOL_Obool)), _1244195) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1244193, tc_HOL_Obool)), _1244197))], (25947 ^ _780205) ^ [_1244306, _1244308, _1244310, _1244312] : [class_Rings_Ocomm__semiring__1(_1244306), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1244306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244306), _1244308), _1244310)), _1244312) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244306), hAPP(hAPP(c_Power_Opower__class_Opower(_1244306), _1244308), _1244312)), hAPP(hAPP(c_Power_Opower__class_Opower(_1244306), _1244310), _1244312)))], (25953 ^ _780205) ^ [_1244465, _1244467, _1244469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1244465), _1244467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1244465), _1244469)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1244467), _1244469))))], (25959 ^ _780205) ^ [_1244588, _1244590] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1244588), _1244590)), _1244588)))], (25961 ^ _780205) ^ [_1244624, _1244626] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1244624), _1244626)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1244624)), _1244626))], (25963 ^ _780205) ^ [_1244667, _1244669] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1244667)), _1244669) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1244667), _1244669)))], (25965 ^ _780205) ^ [_1244710, _1244712] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1244710)), _1244712) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1244710), _1244712)))], (25967 ^ _780205) ^ [_1244753, _1244755, _1244757] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1244753), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244755), _1244757)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1244753), _1244755)), _1244757))], (25969 ^ _780205) ^ [_1244804, _1244806, _1244808, _1244810] : [class_Rings_Ocomm__semiring__1(_1244804), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1244804), hAPP(hAPP(c_Power_Opower__class_Opower(_1244804), _1244806), _1244808)), _1244810) = hAPP(hAPP(c_Power_Opower__class_Opower(_1244804), _1244806), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244808), _1244810)))], (25975 ^ _780205) ^ [_1244943, _1244945, _1244947] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1244943), _1244945)), _1244947) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1244943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244945), _1244947)))], (25977 ^ _780205) ^ [_1244994, _1244996] : [class_Rings_Ocomm__semiring__1(_1244994), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1244994), _1244996), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1244996)], (25983 ^ _780205) ^ [_1245085, _1245087, _1245089] : [-(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, _1245085, _1245087)), _1245089), _1245087) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1245085), _1245089), _1245087))], (25985 ^ _780205) ^ [_1245136, _1245138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245136)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1245136), _1245138)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1245136)), _1245138))], (25991 ^ _780205) ^ [_1245253, _1245255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245253)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1245253)), _1245255) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1245253), _1245255)))], (25997 ^ _780205) ^ [_1245370] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1245370), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1245370)], (25999 ^ _780205) ^ [_1245399, _1245401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1245399), _1245401)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1245399), _1245401) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26005 ^ _780205) ^ [_1245510, _1245512, _1245514] : [_1245510 = 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), _1245510), _1245512)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1245510), _1245514)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26011 ^ _780205) ^ [_1245619, _1245621, _1245623] : [-(_1245619 = 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), _1245619), _1245621)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1245619), _1245623)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1245621), _1245623))], (26017 ^ _780205) ^ [_1245683, _1245685, _1245687] : [class_Rings_Ocomm__semiring__1(_1245683), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1245683), _1245685), hAPP(c_Nat_OSuc, _1245687)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245683), _1245685), hAPP(hAPP(c_Power_Opower__class_Opower(_1245683), _1245685), _1245687)))], (26023 ^ _780205) ^ [_1245814, _1245816, _1245818] : [class_Rings_Ocomm__semiring__1(_1245814), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245814), _1245816), hAPP(hAPP(c_Power_Opower__class_Opower(_1245814), _1245816), _1245818)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1245814), _1245816), hAPP(c_Nat_OSuc, _1245818)))], (26029 ^ _780205) ^ [_1245945, _1245947, _1245949] : [class_Rings_Ocomm__semiring__1(_1245945), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1245945), hAPP(hAPP(c_Power_Opower__class_Opower(_1245945), _1245947), _1245949)), _1245947) = hAPP(hAPP(c_Power_Opower__class_Opower(_1245945), _1245947), hAPP(c_Nat_OSuc, _1245949)))], (26035 ^ _780205) ^ [_1246076, _1246078] : [class_Rings_Ocomm__semiring__1(_1246076), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1246076), _1246078), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1246076))], (26041 ^ _780205) ^ [_1246171, _1246173, _1246175, _1246177] : [class_Rings_Ocomm__semiring__1(_1246171), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246171), hAPP(hAPP(c_Power_Opower__class_Opower(_1246171), _1246173), _1246175)), hAPP(hAPP(c_Power_Opower__class_Opower(_1246171), _1246173), _1246177)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1246171), _1246173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1246175), _1246177)))], (26047 ^ _780205) ^ [_1246326, _1246328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246326)), -(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), _1246326), _1246328))))], (26053 ^ _780205) ^ [_1246423, _1246425, _1246427] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1246423), _1246425)), _1246427) = 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), _1246423), _1246427)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1246425), _1246427))), 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, _1246423, _1246427)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1246425, _1246427))), _1246427)))], (26055 ^ _780205) ^ [_1246506, _1246508] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1246506), _1246508)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1246506)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1246508)))], (26057 ^ _780205) ^ [_1246552, _1246554] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1246552)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1246554)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1246552), _1246554)))], (26059 ^ _780205) ^ [_1246598, _1246600, _1246602] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1246598), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1246600), _1246602)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1246598), _1246600)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1246598), _1246602)))], (26061 ^ _780205) ^ [_1246655, _1246657, _1246659] : [class_Rings_Oring__1(_1246655), hBOOL(hAPP(hAPP(c_member(_1246655), _1246657), c_Int_Oring__1__class_OInts(_1246655))), -(hBOOL(hAPP(hAPP(c_member(_1246655), hAPP(hAPP(c_Power_Opower__class_Opower(_1246655), _1246657), _1246659)), c_Int_Oring__1__class_OInts(_1246655))))], (26071 ^ _780205) ^ [_1246847, _1246849] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1246847))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1246847)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1246849)) = 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), _1246849)))], (26077 ^ _780205) ^ [_1246964, _1246966] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1246964)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1246964)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1246966)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1246964)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1246966))))], (26083 ^ _780205) ^ [_1247043, _1247045] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1247043))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1247043)), _1247045) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1247045))], (26089 ^ _780205) ^ [_1247148, _1247150] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1247148)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1247148)), _1247150) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1247148)), _1247150)))], (26095 ^ _780205) ^ [_1247212, _1247214, _1247216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1247212)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1247212), _1247214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247216), _1247214)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247216), _1247212))))], (26105 ^ _780205) ^ [_1247393, _1247395, _1247397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1247393)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247393), _1247395)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247393), _1247397)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247395), _1247397))], (26111 ^ _780205) ^ [_1247524, _1247526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1247524)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247524), _1247526)), _1247524) = _1247526)], (26117 ^ _780205) ^ [_1247629, _1247631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1247629)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247631), _1247629)), _1247629) = _1247631)], (26123 ^ _780205) ^ [_1247734, _1247736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1247734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1247736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247736), _1247734)), _1247736)))], (26133 ^ _780205) ^ [_1247893, _1247895, _1247897] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247893, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247895), _1247897)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247895), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247893), _1247895), _1247897))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247893, _1247895)))], (26135 ^ _780205) ^ [_1247956, _1247958, _1247960] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247956), _1247958)), _1247960) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247956), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247958), _1247960))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247956), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247958, _1247960))), _1247960)))], (26137 ^ _780205) ^ [_1248029, _1248031] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1248029), _1248031)), _1248031) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1248029), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248029, _1248031)))], (26139 ^ _780205) ^ [_1248076, _1248078] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248076), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1248078), _1248076)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1248078), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248078, _1248076)))], (26141 ^ _780205) ^ [_1248123, _1248125] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248123, _1248125) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1248123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1248123), _1248125)), _1248125)))], (26143 ^ _780205) ^ [_1248170, _1248172] : [-(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), _1248170)), _1248172))))], (26145 ^ _780205) ^ [_1248206, _1248208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248206)), 26148 ^ _780205 : [(26149 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1248208), _1248206)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1248208), _1248206) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26155 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1248208), _1248206))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1248208), _1248206) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1248208), _1248206)), _1248206)))]]], (26161 ^ _780205) ^ [_1248460, _1248462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1248462), _1248460))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1248462), _1248460) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1248462), _1248460)), _1248460)))], (26195 ^ _780205) ^ [_1249063, _1249065, _1249067] : [-(hBOOL(hAPP(_1249063, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1249065), _1249067)))), 26198 ^ _780205 : [(26199 ^ _780205) ^ [] : [-(_1249067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26201 ^ _780205) ^ [] : [hBOOL(hAPP(_1249063, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 26202 ^ _780205 : [(26203 ^ _780205) ^ [] : [_1249067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26207 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26205 ^ [_1249063, _1249065, _1249067]), _1249067)))], (26209 ^ _780205) ^ [] : [-(_1249065 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1249067), 26204 ^ [_1249063, _1249065, _1249067])), 26205 ^ [_1249063, _1249065, _1249067]))], (26211 ^ _780205) ^ [] : [hBOOL(hAPP(_1249063, 26204 ^ [_1249063, _1249065, _1249067]))]]], (26171 ^ _780205) ^ [_1248626, _1248628, _1248630] : [hBOOL(hAPP(_1248626, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1248628), _1248630))), 26174 ^ _780205 : [(26175 ^ _780205) ^ [] : [_1248630 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1248626, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26181 ^ _780205) ^ [] : [-(_1248630 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 26184 ^ _780205 : [(26185 ^ _780205) ^ [_1248878, _1248880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1248878), _1248630)), _1248628 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248630), _1248880)), _1248878), -(hBOOL(hAPP(_1248626, _1248880)))]]]]], (26215 ^ _780205) ^ [_1249485, _1249487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249487)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1249485)), hAPP(c_Int_Onat, _1249487)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1249485), _1249487)))], (26225 ^ _780205) ^ [_1249664, _1249666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249664)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1249664), _1249666)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1249664)), hAPP(c_Int_Onat, _1249666)))], (26231 ^ _780205) ^ [_1249787, _1249789] : [class_Groups_Omonoid__mult(_1249787), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1249787), _1249789), 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(_1249787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249787), _1249789), _1249789)), _1249789))], (26237 ^ _780205) ^ [_1249910, _1249912] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1249910), hAPP(hAPP(c_Power_Opower__class_Opower(_1249910), hAPP(c_Int_Onumber__class_Onumber__of(_1249910), c_Int_OMin)), _1249912)) = c_Groups_Oone__class_Oone(_1249910)), class_Int_Onumber__ring(_1249910), class_Rings_Olinordered__idom(_1249910)], (26247 ^ _780205) ^ [_1250084, _1250086] : [_1250084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1250086), _1250084) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (26253 ^ _780205) ^ [_1250167, _1250169] : [-(_1250167 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1250169), _1250167) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1250169), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1250169), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1250167), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (26269 ^ _780205) ^ [_1250393, _1250395] : [26270 ^ _780205 : [(26271 ^ _780205) ^ [] : [-(_1250393 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26273 ^ _780205) ^ [] : [_1250395 = 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), _1250393)), _1250395))))], (26259 ^ _780205) ^ [_1250244, _1250246] : [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), _1250244)), _1250246))), _1250244 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1250246 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26277 ^ _780205) ^ [_1250529, _1250531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1250529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1250529), _1250531)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1250531), _1250529) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1250531), _1250529)), _1250529)))], (26287 ^ _780205) ^ [_1250714, _1250716, _1250718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1250714)), 26290 ^ _780205 : [(26301 ^ _780205) ^ [] : [_1250716 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1250718), _1250714), 26304 ^ _780205 : [(26305 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1250714), _1250716)), _1250718)))], (26307 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1250718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1250714), hAPP(c_Nat_OSuc, _1250716)))))]]], (26291 ^ _780205) ^ [] : [-(_1250716 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1250718), _1250714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1250714), _1250716)), _1250718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1250718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1250714), hAPP(c_Nat_OSuc, _1250716))))]]], (26309 ^ _780205) ^ [_1251116, _1251118, _1251120] : [hBOOL(hAPP(_1251116, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1251118), _1251120))), 26314 ^ _780205 : [(26315 ^ _780205) ^ [] : [-(_1251120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26317 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1251116, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 26319 ^ _780205 : [(26320 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251120), 26318 ^ [_1251116, _1251118, _1251120])), _1251118)))], (26322 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1251118), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251120), hAPP(c_Nat_OSuc, 26318 ^ [_1251116, _1251118, _1251120])))))], (26324 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1251116, 26318 ^ [_1251116, _1251118, _1251120])))]]], (26326 ^ _780205) ^ [_1251420, _1251422, _1251424] : [-(hBOOL(hAPP(_1251420, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1251422), _1251424)))), 26327 ^ _780205 : [(26328 ^ _780205) ^ [] : [_1251424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1251420, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26334 ^ _780205) ^ [_1251588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251424), _1251588)), _1251422)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1251422), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251424), hAPP(c_Nat_OSuc, _1251588)))), hBOOL(hAPP(_1251420, _1251588))]]], (26346 ^ _780205) ^ [_1251818, _1251820] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1251818), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1251820)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1251818), 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)))), _1251820)))], (26348 ^ _780205) ^ [_1251867, _1251869] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1251867)))), _1251869) = 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)))), _1251867)), _1251869))], (26350 ^ _780205) ^ [_1251916, _1251918] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1251916)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1251918)) = 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)))), _1251916)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1251918)))], (26352 ^ _780205) ^ [_1251971] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1251971))), 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), _1251971), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (26354 ^ _780205) ^ [_1252015] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1252015), _1252015)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1252015)], (26356 ^ _780205) ^ [_1252050] : [class_Rings_Osemiring__1(_1252050), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252050), c_Groups_Ozero__class_Ozero(_1252050)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1252050))], (26362 ^ _780205) ^ [_1252147, _1252149] : [class_Rings_Oring__1__no__zero__divisors(_1252147), 26365 ^ _780205 : [(26366 ^ _780205) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1252147), _1252149), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1252147), -(_1252149 = c_Groups_Ozero__class_Ozero(_1252147))], (26372 ^ _780205) ^ [] : [_1252149 = c_Groups_Ozero__class_Ozero(_1252147), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252147), _1252149), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1252147))]]], (26378 ^ _780205) ^ [_1252388, _1252390] : [class_Rings_Ocomm__semiring__1(_1252388), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252388), _1252390), _1252390) = hAPP(hAPP(c_Power_Opower__class_Opower(_1252388), _1252390), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (26384 ^ _780205) ^ [_1252495, _1252497] : [class_Groups_Omonoid__mult(_1252495), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252495), _1252497), 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(_1252495), _1252497), _1252497))], (26390 ^ _780205) ^ [_1252602] : [class_Rings_Osemiring__1(_1252602), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252602), c_Groups_Oone__class_Oone(_1252602)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1252602))], (26396 ^ _780205) ^ [_1252699, _1252701] : [class_Rings_Oring__1(_1252699), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252699), hAPP(c_Groups_Ouminus__class_Ouminus(_1252699), _1252701)), 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(_1252699), _1252701), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (26402 ^ _780205) ^ [_1252816, _1252818, _1252820] : [class_Groups_Omonoid__mult(_1252816), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252816), _1252818), 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)))), _1252820)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1252816), hAPP(hAPP(c_Power_Opower__class_Opower(_1252816), _1252818), _1252820)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (26408 ^ _780205) ^ [_1252947, _1252949] : [class_Rings_Olinordered__idom(_1252947), -(hAPP(c_Groups_Oabs__class_Oabs(_1252947), hAPP(hAPP(c_Power_Opower__class_Opower(_1252947), _1252949), 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(_1252947), _1252949), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (26414 ^ _780205) ^ [_1253064, _1253066] : [class_Rings_Olinordered__idom(_1253064), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1253064), hAPP(c_Groups_Oabs__class_Oabs(_1253064), _1253066)), 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(_1253064), _1253066), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (26420 ^ _780205) ^ [_1253181, _1253183, _1253185] : [class_Rings_Olinordered__semidom(_1253181), hAPP(hAPP(c_Power_Opower__class_Opower(_1253181), _1253183), 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(_1253181), _1253185), 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(_1253181), c_Groups_Ozero__class_Ozero(_1253181)), _1253183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253181), c_Groups_Ozero__class_Ozero(_1253181)), _1253185)), -(_1253183 = _1253185)], (26438 ^ _780205) ^ [_1253488, _1253490, _1253492] : [class_Rings_Olinordered__semidom(_1253488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253488), hAPP(hAPP(c_Power_Opower__class_Opower(_1253488), _1253490), 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(_1253488), _1253492), 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(_1253488), c_Groups_Ozero__class_Ozero(_1253488)), _1253492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253488), _1253490), _1253492)))], (26452 ^ _780205) ^ [_1253751, _1253753] : [class_Rings_Olinordered__idom(_1253751), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253751), c_Groups_Ozero__class_Ozero(_1253751)), hAPP(hAPP(c_Power_Opower__class_Opower(_1253751), _1253753), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (26458 ^ _780205) ^ [_1253860, _1253862] : [class_Rings_Olinordered__idom(_1253860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253860), hAPP(hAPP(c_Power_Opower__class_Opower(_1253860), _1253862), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1253860)))], (26464 ^ _780205) ^ [_1253970, _1253972] : [class_Rings_Olinordered__idom(_1253970), 26467 ^ _780205 : [(26468 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253970), c_Groups_Ozero__class_Ozero(_1253970)), hAPP(hAPP(c_Power_Opower__class_Opower(_1253970), _1253972), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1253972 = c_Groups_Ozero__class_Ozero(_1253970)], (26474 ^ _780205) ^ [] : [-(_1253972 = c_Groups_Ozero__class_Ozero(_1253970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253970), c_Groups_Ozero__class_Ozero(_1253970)), hAPP(hAPP(c_Power_Opower__class_Opower(_1253970), _1253972), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (26480 ^ _780205) ^ [_1254194, _1254196, _1254198] : [class_Rings_Olinordered__idom(_1254194), 26483 ^ _780205 : [(26484 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254194), hAPP(hAPP(c_Power_Opower__class_Opower(_1254194), _1254196), 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(_1254194), _1254198), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1254194), 26487 ^ _780205 : [(26488 ^ _780205) ^ [] : [-(_1254196 = c_Groups_Ozero__class_Ozero(_1254194))], (26490 ^ _780205) ^ [] : [-(_1254198 = c_Groups_Ozero__class_Ozero(_1254194))]]], (26492 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254194), hAPP(hAPP(c_Power_Opower__class_Opower(_1254194), _1254196), 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(_1254194), _1254198), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1254194)), _1254196 = c_Groups_Ozero__class_Ozero(_1254194), _1254198 = c_Groups_Ozero__class_Ozero(_1254194)]]], (26502 ^ _780205) ^ [_1254569, _1254571] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1254569), hAPP(c_Int_Onumber__class_Onumber__of(_1254569), _1254571)), 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(_1254569), hAPP(c_Int_Onumber__class_Onumber__of(_1254569), _1254571)), hAPP(c_Int_Onumber__class_Onumber__of(_1254569), _1254571))), class_Groups_Omonoid__mult(_1254569), class_Int_Onumber(_1254569)], (26512 ^ _780205) ^ [_1254756, _1254758] : [class_Rings_Oring__1__no__zero__divisors(_1254756), 26515 ^ _780205 : [(26526 ^ _780205) ^ [] : [26527 ^ _780205 : [(26528 ^ _780205) ^ [] : [_1254758 = c_Groups_Oone__class_Oone(_1254756)], (26530 ^ _780205) ^ [] : [_1254758 = hAPP(c_Groups_Ouminus__class_Ouminus(_1254756), c_Groups_Oone__class_Oone(_1254756))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1254756), _1254758), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1254756))], (26516 ^ _780205) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1254756), _1254758), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1254756), -(_1254758 = c_Groups_Oone__class_Oone(_1254756)), -(_1254758 = hAPP(c_Groups_Ouminus__class_Ouminus(_1254756), c_Groups_Oone__class_Oone(_1254756)))]]], (26534 ^ _780205) ^ [_1255072, _1255074] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1255072))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1255072)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1255074)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26540 ^ _780205) ^ [_1255177, _1255179] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1255177)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1255177)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1255179)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1255177)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1255179))))], (26546 ^ _780205) ^ [_1255247, _1255249, _1255251] : [class_Rings_Ocomm__semiring__1(_1255247), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1255247), _1255249), 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)))), _1255251)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1255247), hAPP(hAPP(c_Power_Opower__class_Opower(_1255247), _1255249), _1255251)), hAPP(hAPP(c_Power_Opower__class_Opower(_1255247), _1255249), _1255251)))], (26552 ^ _780205) ^ [_1255394, _1255396, _1255398] : [class_Rings_Oring__1(_1255394), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1255394), hAPP(c_Groups_Ouminus__class_Ouminus(_1255394), _1255396)), 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)))), _1255398)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1255394), _1255396), 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)))), _1255398)))], (26558 ^ _780205) ^ [_1255525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1255525)), -(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), _1255525), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (26564 ^ _780205) ^ [_1255620, _1255622, _1255624] : [class_Rings_Olinordered__semidom(_1255620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255620), hAPP(hAPP(c_Power_Opower__class_Opower(_1255620), _1255622), 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(_1255620), _1255624), 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(_1255620), c_Groups_Ozero__class_Ozero(_1255620)), _1255624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255620), _1255622), _1255624)))], (26578 ^ _780205) ^ [_1255883] : [-(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), _1255883)) = 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), _1255883))))], (26580 ^ _780205) ^ [_1255921, _1255923, _1255925] : [class_Rings_Olinordered__idom(_1255921), 26583 ^ _780205 : [(26584 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255921), hAPP(hAPP(c_Power_Opower__class_Opower(_1255921), _1255923), 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(_1255921), _1255925), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1255921))), 26587 ^ _780205 : [(26588 ^ _780205) ^ [] : [-(_1255923 = c_Groups_Ozero__class_Ozero(_1255921))], (26590 ^ _780205) ^ [] : [-(_1255925 = c_Groups_Ozero__class_Ozero(_1255921))]]], (26592 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255921), hAPP(hAPP(c_Power_Opower__class_Opower(_1255921), _1255923), 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(_1255921), _1255925), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1255921)))), _1255923 = c_Groups_Ozero__class_Ozero(_1255921), _1255925 = c_Groups_Ozero__class_Ozero(_1255921)]]], (26602 ^ _780205) ^ [_1256317, _1256319, _1256321] : [class_Rings_Olinordered__idom(_1256317), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256317), c_Groups_Ozero__class_Ozero(_1256317)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256317), hAPP(hAPP(c_Power_Opower__class_Opower(_1256317), _1256319), 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(_1256317), _1256321), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (26608 ^ _780205) ^ [_1256460, _1256462, _1256464] : [class_Rings_Olinordered__idom(_1256460), 26611 ^ _780205 : [(26622 ^ _780205) ^ [] : [26623 ^ _780205 : [(26624 ^ _780205) ^ [] : [-(_1256462 = c_Groups_Ozero__class_Ozero(_1256460))], (26626 ^ _780205) ^ [] : [-(_1256464 = c_Groups_Ozero__class_Ozero(_1256460))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256460), c_Groups_Ozero__class_Ozero(_1256460)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256460), hAPP(hAPP(c_Power_Opower__class_Opower(_1256460), _1256462), 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(_1256460), _1256464), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (26612 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256460), c_Groups_Ozero__class_Ozero(_1256460)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256460), hAPP(hAPP(c_Power_Opower__class_Opower(_1256460), _1256462), 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(_1256460), _1256464), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1256462 = c_Groups_Ozero__class_Ozero(_1256460), _1256464 = c_Groups_Ozero__class_Ozero(_1256460)]]], (26630 ^ _780205) ^ [_1256835, _1256837, _1256839] : [class_Rings_Olinordered__idom(_1256835), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256835), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256835), hAPP(hAPP(c_Power_Opower__class_Opower(_1256835), _1256837), 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(_1256835), _1256839), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1256835)))], (26636 ^ _780205) ^ [_1256979, _1256981, _1256983] : [class_Int_Onumber__ring(_1256979), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1256979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256979), _1256981), _1256983)), 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(_1256979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256979), hAPP(hAPP(c_Power_Opower__class_Opower(_1256979), _1256981), 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(_1256979), _1256983), 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(_1256979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1256979), hAPP(c_Int_Onumber__class_Onumber__of(_1256979), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1256981)), _1256983)))], (26642 ^ _780205) ^ [_1257194, _1257196, _1257198] : [class_Rings_Olinordered__idom(_1257194), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257194), c_Groups_Ozero__class_Ozero(_1257194)), hAPP(hAPP(c_Power_Opower__class_Opower(_1257194), _1257196), 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)))), _1257198)))))], (26648 ^ _780205) ^ [_1257311, _1257313, _1257315] : [class_Rings_Ocomm__semiring__1(_1257311), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1257311), _1257313), 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)))), _1257315))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257311), _1257313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257311), hAPP(hAPP(c_Power_Opower__class_Opower(_1257311), _1257313), _1257315)), hAPP(hAPP(c_Power_Opower__class_Opower(_1257311), _1257313), _1257315))))], (26654 ^ _780205) ^ [_1257480, _1257482, _1257484] : [class_Groups_Omonoid__mult(_1257480), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1257480), _1257482), 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)))), _1257484))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257480), _1257482), hAPP(hAPP(c_Power_Opower__class_Opower(_1257480), hAPP(hAPP(c_Power_Opower__class_Opower(_1257480), _1257482), _1257484)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (26660 ^ _780205) ^ [_1257633, _1257635] : [class_Rings_Oring__1(_1257633), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1257633), hAPP(c_Groups_Ouminus__class_Ouminus(_1257633), c_Groups_Oone__class_Oone(_1257633))), 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)))), _1257635)) = c_Groups_Oone__class_Oone(_1257633))], (26666 ^ _780205) ^ [_1257748, _1257750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1257748)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257750)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1257750), _1257748)), _1257750) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1257750), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1257748), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (26676 ^ _780205) ^ [_1257933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1257933)), -(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), _1257933), 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)))))))], (26682 ^ _780205) ^ [_1258040, _1258042, _1258044] : [class_Int_Onumber__ring(_1258040), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1258040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1258040), _1258042), _1258044)), 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(_1258040), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1258040), hAPP(hAPP(c_Power_Opower__class_Opower(_1258040), _1258042), 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(_1258040), _1258044), 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(_1258040), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1258040), hAPP(c_Int_Onumber__class_Onumber__of(_1258040), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1258042)), _1258044)))], (26688 ^ _780205) ^ [_1258255, _1258257, _1258259] : [class_Rings_Olinordered__idom(_1258255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258255), c_Groups_Ozero__class_Ozero(_1258255)), hAPP(hAPP(c_Power_Opower__class_Opower(_1258255), _1258257), 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)))), _1258259))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258255), c_Groups_Ozero__class_Ozero(_1258255)), _1258257)))], (26698 ^ _780205) ^ [_1258450, _1258452, _1258454] : [class_Rings_Olinordered__idom(_1258450), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258450), _1258452), c_Groups_Ozero__class_Ozero(_1258450))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258450), hAPP(hAPP(c_Power_Opower__class_Opower(_1258450), _1258452), 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)))), _1258454)))), c_Groups_Ozero__class_Ozero(_1258450))))], (26708 ^ _780205) ^ [_1258645, _1258647] : [class_Rings_Oring__1(_1258645), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1258645), hAPP(c_Groups_Ouminus__class_Ouminus(_1258645), c_Groups_Oone__class_Oone(_1258645))), 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)))), _1258647))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1258645), c_Groups_Oone__class_Oone(_1258645)))], (26714 ^ _780205) ^ [_1258776, _1258778] : [class_Int_Onumber__ring(_1258776), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1258776), hAPP(c_Int_Onumber__class_Onumber__of(_1258776), 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)))), _1258778)) = c_Groups_Oone__class_Oone(_1258776))], (26720 ^ _780205) ^ [_1258893] : [_1258893 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1258893) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26726 ^ _780205) ^ [_1258969] : [-(_1258969 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 26729 ^ _780205 : [(26730 ^ _780205) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1258969, 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, _1258969) = 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), _1258969), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (26736 ^ _780205) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1258969, 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, _1258969) = 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), _1258969), 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)))]]], (26742 ^ _780205) ^ [_1259229, _1259231, _1259233, _1259235] : [class_Rings_Olinordered__semidom(_1259229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259229), _1259231), _1259233)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259229), c_Groups_Ozero__class_Ozero(_1259229)), _1259231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1259235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259229), hAPP(hAPP(c_Power_Opower__class_Opower(_1259229), _1259231), _1259235)), hAPP(hAPP(c_Power_Opower__class_Opower(_1259229), _1259233), _1259235))))], (26760 ^ _780205) ^ [_1259558, _1259560, _1259562, _1259564] : [class_Fields_Ofield(_1259558), -(_1259560 = c_Groups_Ozero__class_Ozero(_1259558)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1259562), _1259564)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1259558), _1259560), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1259564), _1259562)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1259558), hAPP(hAPP(c_Power_Opower__class_Opower(_1259558), _1259560), _1259564)), hAPP(hAPP(c_Power_Opower__class_Opower(_1259558), _1259560), _1259562)))], (26774 ^ _780205) ^ [_1259842, _1259844, _1259846] : [class_Rings_Olinordered__semidom(_1259842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259842), c_Groups_Oone__class_Oone(_1259842)), _1259844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1259846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259842), c_Groups_Oone__class_Oone(_1259842)), hAPP(hAPP(c_Power_Opower__class_Opower(_1259842), _1259844), _1259846))))], (26788 ^ _780205) ^ [_1260083, _1260085, _1260087, _1260089] : [class_Rings_Olinordered__semidom(_1260083), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260083), c_Groups_Oone__class_Oone(_1260083)), _1260085)), 26795 ^ _780205 : [(26796 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260083), hAPP(hAPP(c_Power_Opower__class_Opower(_1260083), _1260085), _1260087)), hAPP(hAPP(c_Power_Opower__class_Opower(_1260083), _1260085), _1260089))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1260087), _1260089)))], (26802 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1260087), _1260089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260083), hAPP(hAPP(c_Power_Opower__class_Opower(_1260083), _1260085), _1260087)), hAPP(hAPP(c_Power_Opower__class_Opower(_1260083), _1260085), _1260089))))]]], (26808 ^ _780205) ^ [_1260458, _1260460, _1260462] : [class_Rings_Oring__1__no__zero__divisors(_1260458), -(_1260460 = c_Groups_Ozero__class_Ozero(_1260458)), hAPP(hAPP(c_Power_Opower__class_Opower(_1260458), _1260460), _1260462) = c_Groups_Ozero__class_Ozero(_1260458)], (26818 ^ _780205) ^ [_1260617] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1260617) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26830 ^ _780205) ^ [_1260756, _1260758] : [26831 ^ _780205 : [(26832 ^ _780205) ^ [] : [_1260758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26834 ^ _780205) ^ [] : [_1260756 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1260756), _1260758) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26820 ^ _780205) ^ [_1260658, _1260660] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1260658), _1260660) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1260660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1260658 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26848 ^ _780205) ^ [_1261006, _1261008] : [26849 ^ _780205 : [(26850 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1261006))], (26852 ^ _780205) ^ [] : [_1261008 = 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), _1261006), _1261008))))], (26838 ^ _780205) ^ [_1260900, _1260902] : [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), _1260900), _1260902))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1260900))), -(_1260902 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26856 ^ _780205) ^ [_1261143, _1261145, _1261147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1261143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1261143), _1261145)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1261143), _1261147))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1261145), _1261147)))], (26866 ^ _780205) ^ [_1261324, _1261326, _1261328, _1261330] : [class_Groups_Ocomm__monoid__mult(_1261324), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1261324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1261324), _1261326), _1261328)), _1261330) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1261324), hAPP(hAPP(c_Power_Opower__class_Opower(_1261324), _1261326), _1261330)), hAPP(hAPP(c_Power_Opower__class_Opower(_1261324), _1261328), _1261330)))], (26872 ^ _780205) ^ [_1261483, _1261485, _1261487] : [class_Groups_Omonoid__mult(_1261483), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1261483), hAPP(hAPP(c_Power_Opower__class_Opower(_1261483), _1261485), _1261487)), _1261485) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1261483), _1261485), hAPP(hAPP(c_Power_Opower__class_Opower(_1261483), _1261485), _1261487)))], (26878 ^ _780205) ^ [_1261624, _1261626] : [class_Groups_Omonoid__mult(_1261624), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1261624), c_Groups_Oone__class_Oone(_1261624)), _1261626) = c_Groups_Oone__class_Oone(_1261624))], (26884 ^ _780205) ^ [_1261723, _1261725, _1261727] : [class_Rings_Osemiring__1(_1261723), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1261723), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1261725), _1261727)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1261723), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1261723), _1261725)), _1261727))], (26890 ^ _780205) ^ [_1261848, _1261850, _1261852, _1261854] : [class_Groups_Omonoid__mult(_1261848), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1261848), _1261850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1261852), _1261854)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1261848), hAPP(hAPP(c_Power_Opower__class_Opower(_1261848), _1261850), _1261852)), _1261854))], (26896 ^ _780205) ^ [_1261987, _1261989, _1261991, _1261993] : [class_Fields_Ofield__inverse__zero(_1261987), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1261987), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1261987), _1261989), _1261991)), _1261993) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1261987), hAPP(hAPP(c_Power_Opower__class_Opower(_1261987), _1261989), _1261993)), hAPP(hAPP(c_Power_Opower__class_Opower(_1261987), _1261991), _1261993)))], (26902 ^ _780205) ^ [_1262146, _1262148, _1262150] : [class_Rings_Olinordered__idom(_1262146), -(hAPP(c_Groups_Oabs__class_Oabs(_1262146), hAPP(hAPP(c_Power_Opower__class_Opower(_1262146), _1262148), _1262150)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1262146), hAPP(c_Groups_Oabs__class_Oabs(_1262146), _1262148)), _1262150))], (26908 ^ _780205) ^ [_1262275, _1262277] : [class_Groups_Omonoid__mult(_1262275), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1262275), _1262277), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1262277)], (26914 ^ _780205) ^ [_1262366, _1262368, _1262370] : [class_Rings_Olinordered__semidom(_1262366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262366), c_Groups_Ozero__class_Ozero(_1262366)), _1262368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262366), c_Groups_Ozero__class_Ozero(_1262366)), hAPP(hAPP(c_Power_Opower__class_Opower(_1262366), _1262368), _1262370))))], (26924 ^ _780205) ^ [_1262549, _1262551, _1262553, _1262555] : [class_Rings_Olinordered__semidom(_1262549), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262549), _1262551), _1262553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262549), c_Groups_Ozero__class_Ozero(_1262549)), _1262551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262549), hAPP(hAPP(c_Power_Opower__class_Opower(_1262549), _1262551), _1262555)), hAPP(hAPP(c_Power_Opower__class_Opower(_1262549), _1262553), _1262555))))], (26938 ^ _780205) ^ [_1262818, _1262820, _1262822] : [class_Rings_Olinordered__semidom(_1262818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262818), c_Groups_Ozero__class_Ozero(_1262818)), _1262820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262818), c_Groups_Ozero__class_Ozero(_1262818)), hAPP(hAPP(c_Power_Opower__class_Opower(_1262818), _1262820), _1262822))))], (26948 ^ _780205) ^ [_1263001, _1263003, _1263005] : [class_Power_Opower(_1263001), class_Rings_Omult__zero(_1263001), class_Rings_Ono__zero__divisors(_1263001), class_Rings_Ozero__neq__one(_1263001), 26963 ^ _780205 : [(26964 ^ _780205) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1263001), _1263003), _1263005) = c_Groups_Ozero__class_Ozero(_1263001), 26967 ^ _780205 : [(26968 ^ _780205) ^ [] : [-(_1263003 = c_Groups_Ozero__class_Ozero(_1263001))], (26970 ^ _780205) ^ [] : [_1263005 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (26972 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1263001), _1263003), _1263005) = c_Groups_Ozero__class_Ozero(_1263001)), _1263003 = c_Groups_Ozero__class_Ozero(_1263001), -(_1263005 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (26982 ^ _780205) ^ [_1263493, _1263495, _1263497] : [class_Rings_Olinordered__semidom(_1263493), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263493), c_Groups_Oone__class_Oone(_1263493)), _1263495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263493), c_Groups_Oone__class_Oone(_1263493)), hAPP(hAPP(c_Power_Opower__class_Opower(_1263493), _1263495), _1263497))))], (26992 ^ _780205) ^ [_1263676, _1263678] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1263676), c_Groups_Ozero__class_Ozero(_1263676)), hAPP(c_Nat_OSuc, _1263678)) = c_Groups_Ozero__class_Ozero(_1263676)), class_Power_Opower(_1263676), class_Rings_Osemiring__0(_1263676)], (27002 ^ _780205) ^ [_1263831, _1263833, _1263835, _1263837] : [class_Rings_Olinordered__semidom(_1263831), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263831), c_Groups_Oone__class_Oone(_1263831)), _1263833)), 27009 ^ _780205 : [(27010 ^ _780205) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1263831), _1263833), _1263835) = hAPP(hAPP(c_Power_Opower__class_Opower(_1263831), _1263833), _1263837), -(_1263835 = _1263837)], (27016 ^ _780205) ^ [] : [_1263835 = _1263837, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1263831), _1263833), _1263835) = hAPP(hAPP(c_Power_Opower__class_Opower(_1263831), _1263833), _1263837))]]], (27022 ^ _780205) ^ [_1264170, _1264172, _1264174] : [class_Power_Opower(_1264170), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1264170), _1264172), hAPP(c_Nat_OSuc, _1264174)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264170), _1264172), hAPP(hAPP(c_Power_Opower__class_Opower(_1264170), _1264172), _1264174)))], (27028 ^ _780205) ^ [_1264301, _1264303, _1264305] : [class_Groups_Omonoid__mult(_1264301), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1264301), _1264303), hAPP(c_Nat_OSuc, _1264305)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264301), hAPP(hAPP(c_Power_Opower__class_Opower(_1264301), _1264303), _1264305)), _1264303))], (27034 ^ _780205) ^ [_1264432, _1264434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1264432)), -(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), _1264432), _1264434))))], (27040 ^ _780205) ^ [_1264529, _1264531] : [class_Power_Opower(_1264529), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1264529), _1264531), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1264529))], (27046 ^ _780205) ^ [_1264624, _1264626, _1264628, _1264630] : [class_Groups_Omonoid__mult(_1264624), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1264624), _1264626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1264628), _1264630)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264624), hAPP(hAPP(c_Power_Opower__class_Opower(_1264624), _1264626), _1264628)), hAPP(hAPP(c_Power_Opower__class_Opower(_1264624), _1264626), _1264630)))], (27052 ^ _780205) ^ [_1264779, _1264781, _1264783, _1264785] : [class_Fields_Ofield(_1264779), -(_1264781 = c_Groups_Ozero__class_Ozero(_1264779)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1264779), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264779), _1264783), _1264781)), _1264785) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264779), hAPP(hAPP(c_Power_Opower__class_Opower(_1264779), _1264783), _1264785)), hAPP(hAPP(c_Power_Opower__class_Opower(_1264779), _1264781), _1264785)))], (27062 ^ _780205) ^ [_1264957, _1264959, _1264961] : [class_Fields_Ofield__inverse__zero(_1264957), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264957), c_Groups_Oone__class_Oone(_1264957)), hAPP(hAPP(c_Power_Opower__class_Opower(_1264957), _1264959), _1264961)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1264957), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264957), c_Groups_Oone__class_Oone(_1264957)), _1264959)), _1264961))], (27068 ^ _780205) ^ [_1265106, _1265108, _1265110] : [class_Rings_Olinordered__idom(_1265106), -(hAPP(c_Groups_Oabs__class_Oabs(_1265106), hAPP(hAPP(c_Power_Opower__class_Opower(_1265106), hAPP(c_Groups_Ouminus__class_Ouminus(_1265106), _1265108)), _1265110)) = hAPP(c_Groups_Oabs__class_Oabs(_1265106), hAPP(hAPP(c_Power_Opower__class_Opower(_1265106), _1265108), _1265110)))], (27074 ^ _780205) ^ [_1265245, _1265247, _1265249, _1265251] : [class_Rings_Olinordered__semidom(_1265245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265245), hAPP(hAPP(c_Power_Opower__class_Opower(_1265245), _1265247), _1265249)), hAPP(hAPP(c_Power_Opower__class_Opower(_1265245), _1265251), _1265249))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265245), c_Groups_Ozero__class_Ozero(_1265245)), _1265251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265245), _1265247), _1265251)))], (27088 ^ _780205) ^ [_1265514, _1265516, _1265518, _1265520] : [class_Rings_Olinordered__semidom(_1265514), hAPP(hAPP(c_Power_Opower__class_Opower(_1265514), _1265516), hAPP(c_Nat_OSuc, _1265518)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1265514), _1265520), hAPP(c_Nat_OSuc, _1265518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265514), c_Groups_Ozero__class_Ozero(_1265514)), _1265516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265514), c_Groups_Ozero__class_Ozero(_1265514)), _1265520)), -(_1265516 = _1265520)], (27106 ^ _780205) ^ [_1265841, _1265843, _1265845, _1265847] : [class_Rings_Olinordered__semidom(_1265841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265841), hAPP(hAPP(c_Power_Opower__class_Opower(_1265841), _1265843), hAPP(c_Nat_OSuc, _1265845))), hAPP(hAPP(c_Power_Opower__class_Opower(_1265841), _1265847), hAPP(c_Nat_OSuc, _1265845)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265841), c_Groups_Ozero__class_Ozero(_1265841)), _1265847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265841), _1265843), _1265847)))], (27120 ^ _780205) ^ [_1266122, _1266124, _1266126] : [class_Rings_Olinordered__semidom(_1266122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266122), c_Groups_Oone__class_Oone(_1266122)), _1266124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266122), c_Groups_Oone__class_Oone(_1266122)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266122), _1266124), hAPP(hAPP(c_Power_Opower__class_Opower(_1266122), _1266124), _1266126)))))], (27130 ^ _780205) ^ [_1266321, _1266323, _1266325] : [class_Rings_Olinordered__semidom(_1266321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266321), c_Groups_Oone__class_Oone(_1266321)), _1266323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266321), hAPP(hAPP(c_Power_Opower__class_Opower(_1266321), _1266323), _1266325)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266321), _1266323), hAPP(hAPP(c_Power_Opower__class_Opower(_1266321), _1266323), _1266325)))))], (27140 ^ _780205) ^ [_1266532, _1266534] : [class_Power_Opower(_1266532), class_Rings_Osemiring__0(_1266532), 27147 ^ _780205 : [(27148 ^ _780205) ^ [] : [_1266534 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1266532), c_Groups_Ozero__class_Ozero(_1266532)), _1266534) = c_Groups_Oone__class_Oone(_1266532))], (27154 ^ _780205) ^ [] : [-(_1266534 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1266532), c_Groups_Ozero__class_Ozero(_1266532)), _1266534) = c_Groups_Ozero__class_Ozero(_1266532))]]], (27160 ^ _780205) ^ [_1266806, _1266808, _1266810] : [class_Rings_Olinordered__semidom(_1266806), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266806), c_Groups_Oone__class_Oone(_1266806)), _1266808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266806), c_Groups_Oone__class_Oone(_1266806)), hAPP(hAPP(c_Power_Opower__class_Opower(_1266806), _1266808), hAPP(c_Nat_OSuc, _1266810)))))], (27170 ^ _780205) ^ [_1266995, _1266997, _1266999, _1267001] : [class_Rings_Olinordered__semidom(_1266995), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266995), c_Groups_Oone__class_Oone(_1266995)), _1266997)), 27177 ^ _780205 : [(27178 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266995), hAPP(hAPP(c_Power_Opower__class_Opower(_1266995), _1266997), _1266999)), hAPP(hAPP(c_Power_Opower__class_Opower(_1266995), _1266997), _1267001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1266999), _1267001)))], (27184 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1266999), _1267001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266995), hAPP(hAPP(c_Power_Opower__class_Opower(_1266995), _1266997), _1266999)), hAPP(hAPP(c_Power_Opower__class_Opower(_1266995), _1266997), _1267001))))]]], (27190 ^ _780205) ^ [_1267370, _1267372, _1267374, _1267376] : [class_Rings_Olinordered__semidom(_1267370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267370), c_Groups_Oone__class_Oone(_1267370)), _1267372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267370), hAPP(hAPP(c_Power_Opower__class_Opower(_1267370), _1267372), _1267374)), hAPP(hAPP(c_Power_Opower__class_Opower(_1267370), _1267372), _1267376))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1267374), _1267376)))], (27204 ^ _780205) ^ [_1267635, _1267637, _1267639, _1267641] : [class_Rings_Olinordered__semidom(_1267635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1267637), _1267639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267635), c_Groups_Oone__class_Oone(_1267635)), _1267641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267635), hAPP(hAPP(c_Power_Opower__class_Opower(_1267635), _1267641), _1267637)), hAPP(hAPP(c_Power_Opower__class_Opower(_1267635), _1267641), _1267639))))], (27218 ^ _780205) ^ [_1267900, _1267902, _1267904] : [class_Rings_Olinordered__idom(_1267900), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267900), c_Groups_Ozero__class_Ozero(_1267900)), hAPP(hAPP(c_Power_Opower__class_Opower(_1267900), hAPP(c_Groups_Oabs__class_Oabs(_1267900), _1267902)), _1267904))))], (27224 ^ _780205) ^ [_1268021, _1268023, _1268025, _1268027] : [class_Rings_Olinordered__semidom(_1268021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1268023), _1268025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268021), c_Groups_Oone__class_Oone(_1268021)), _1268027)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268021), hAPP(hAPP(c_Power_Opower__class_Opower(_1268021), _1268027), _1268023)), hAPP(hAPP(c_Power_Opower__class_Opower(_1268021), _1268027), _1268025))))], (27238 ^ _780205) ^ [_1268286, _1268288, _1268290] : [class_Rings_Oring__1(_1268286), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1268286), hAPP(c_Groups_Ouminus__class_Ouminus(_1268286), _1268288)), _1268290) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1268286), hAPP(hAPP(c_Power_Opower__class_Opower(_1268286), hAPP(c_Groups_Ouminus__class_Ouminus(_1268286), c_Groups_Oone__class_Oone(_1268286))), _1268290)), hAPP(hAPP(c_Power_Opower__class_Opower(_1268286), _1268288), _1268290)))], (27244 ^ _780205) ^ [_1268451, _1268453, _1268455] : [class_Rings_Olinordered__semidom(_1268451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268451), c_Groups_Ozero__class_Ozero(_1268451)), _1268453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268451), _1268453), c_Groups_Oone__class_Oone(_1268451))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1268451), _1268453), hAPP(hAPP(c_Power_Opower__class_Opower(_1268451), _1268453), _1268455))), hAPP(hAPP(c_Power_Opower__class_Opower(_1268451), _1268453), _1268455))))], (27258 ^ _780205) ^ [_1268734, _1268736, _1268738, _1268740] : [class_Rings_Olinordered__semidom(_1268734), hAPP(hAPP(c_Power_Opower__class_Opower(_1268734), _1268736), _1268738) = hAPP(hAPP(c_Power_Opower__class_Opower(_1268734), _1268740), _1268738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268734), c_Groups_Ozero__class_Ozero(_1268734)), _1268736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268734), c_Groups_Ozero__class_Ozero(_1268734)), _1268740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1268738)), -(_1268736 = _1268740)], (27280 ^ _780205) ^ [_1269109, _1269111, _1269113] : [class_Rings_Olinordered__semidom(_1269109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269109), c_Groups_Ozero__class_Ozero(_1269109)), _1269111)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269109), _1269111), c_Groups_Oone__class_Oone(_1269109))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269109), hAPP(hAPP(c_Power_Opower__class_Opower(_1269109), _1269111), hAPP(c_Nat_OSuc, _1269113))), c_Groups_Oone__class_Oone(_1269109))))], (27294 ^ _780205) ^ [_1269370, _1269372, _1269374, _1269376] : [class_Rings_Olinordered__semidom(_1269370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1269372), _1269374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269370), c_Groups_Ozero__class_Ozero(_1269370)), _1269376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269370), _1269376), c_Groups_Oone__class_Oone(_1269370))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269370), hAPP(hAPP(c_Power_Opower__class_Opower(_1269370), _1269376), _1269374)), hAPP(hAPP(c_Power_Opower__class_Opower(_1269370), _1269376), _1269372))))], (27312 ^ _780205) ^ [_1269709, _1269711, _1269713, _1269715] : [class_Rings_Olinordered__semidom(_1269709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1269711), _1269713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269709), c_Groups_Ozero__class_Ozero(_1269709)), _1269715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269709), _1269715), c_Groups_Oone__class_Oone(_1269709))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269709), hAPP(hAPP(c_Power_Opower__class_Opower(_1269709), _1269715), _1269713)), hAPP(hAPP(c_Power_Opower__class_Opower(_1269709), _1269715), _1269711))))], (27330 ^ _780205) ^ [_1270048, _1270050, _1270052, _1270054] : [class_Rings_Olinordered__semidom(_1270048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270048), c_Groups_Oone__class_Oone(_1270048)), _1270050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270048), hAPP(hAPP(c_Power_Opower__class_Opower(_1270048), _1270050), _1270052)), hAPP(hAPP(c_Power_Opower__class_Opower(_1270048), _1270050), _1270054))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1270052), _1270054)))], (27344 ^ _780205) ^ [_1270313, _1270315] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1270313), _1270315)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1270313, tc_HOL_Obool)), hAPP(c_Set_OPow(_1270313), _1270315)) = 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(_1270313), _1270315)))], (27350 ^ _780205) ^ [_1270440] : [class_Power_Opower(_1270440), -(c_Power_Opower__class_Opower(_1270440) = c_Power_Opower_Opower(_1270440, c_Groups_Oone__class_Oone(_1270440), c_Groups_Otimes__class_Otimes(_1270440)))], (27356 ^ _780205) ^ [] : [-(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))], (27358 ^ _780205) ^ [_1270551, _1270553] : [class_Rings_Oring__1(_1270551), 27361 ^ _780205 : [(27362 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1270553), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1270551), _1270553) = hAPP(c_Groups_Ouminus__class_Ouminus(_1270551), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1270551), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1270553)))))], (27368 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1270553), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1270551), _1270553) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1270551), hAPP(c_Int_Onat, _1270553)))]]], (27374 ^ _780205) ^ [_1270813, _1270815] : [-(c_Nitpick_Oint__lcm(_1270813, _1270815) = 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), _1270813)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1270815)))))], (27376 ^ _780205) ^ [_1270859, _1270861, _1270863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270859, tc_HOL_Obool)), _1270861), _1270863)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1270859, tc_HOL_Obool)), _1270861), hAPP(c_Set_OPow(_1270859), _1270863))))], (27382 ^ _780205) ^ [_1270988, _1270990, _1270992] : [class_Int_Oring__char__0(_1270988), 27385 ^ _780205 : [(27386 ^ _780205) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1270988), _1270990) = hAPP(c_Int_Oring__1__class_Oof__int(_1270988), _1270992), -(_1270990 = _1270992)], (27392 ^ _780205) ^ [] : [_1270990 = _1270992, -(hAPP(c_Int_Oring__1__class_Oof__int(_1270988), _1270990) = hAPP(c_Int_Oring__1__class_Oof__int(_1270988), _1270992))]]], (27398 ^ _780205) ^ [_1271229, _1271231] : [class_Int_Onumber__ring(_1271229), -(hAPP(c_Int_Onumber__class_Onumber__of(_1271229), _1271231) = hAPP(c_Int_Oring__1__class_Oof__int(_1271229), _1271231))], (27404 ^ _780205) ^ [_1271324] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1271324) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1271324))], (27406 ^ _780205) ^ [_1271353] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1271353)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1271353))], (27408 ^ _780205) ^ [_1271385, _1271387] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1271385, tc_HOL_Obool)), _1271387), hAPP(c_Set_OPow(_1271385), _1271387))))], (27410 ^ _780205) ^ [_1271425, _1271427] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1271425, tc_HOL_Obool), hAPP(c_Set_OPow(_1271425), _1271427)) = _1271427)], (27412 ^ _780205) ^ [_1271473, _1271475] : [hAPP(c_Set_OPow(_1271473), _1271475) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1271473, tc_HOL_Obool), tc_HOL_Obool))], (27414 ^ _780205) ^ [_1271511] : [class_Rings_Oring__1(_1271511), -(hAPP(c_Int_Oring__1__class_Oof__int(_1271511), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1271511))], (27420 ^ _780205) ^ [_1271598, _1271600] : [class_Int_Oring__char__0(_1271598), 27423 ^ _780205 : [(27424 ^ _780205) ^ [] : [c_Groups_Ozero__class_Ozero(_1271598) = hAPP(c_Int_Oring__1__class_Oof__int(_1271598), _1271600), -(_1271600 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27430 ^ _780205) ^ [] : [_1271600 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1271598) = hAPP(c_Int_Oring__1__class_Oof__int(_1271598), _1271600))]]], (27436 ^ _780205) ^ [_1271824, _1271826] : [class_Int_Oring__char__0(_1271824), 27439 ^ _780205 : [(27440 ^ _780205) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1271824), _1271826) = c_Groups_Ozero__class_Ozero(_1271824), -(_1271826 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27446 ^ _780205) ^ [] : [_1271826 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1271824), _1271826) = c_Groups_Ozero__class_Ozero(_1271824))]]], (27452 ^ _780205) ^ [_1272050, _1272052, _1272054] : [class_Rings_Olinordered__idom(_1272050), 27455 ^ _780205 : [(27456 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272050), hAPP(c_Int_Oring__1__class_Oof__int(_1272050), _1272052)), hAPP(c_Int_Oring__1__class_Oof__int(_1272050), _1272054))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1272052), _1272054)))], (27462 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1272052), _1272054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272050), hAPP(c_Int_Oring__1__class_Oof__int(_1272050), _1272052)), hAPP(c_Int_Oring__1__class_Oof__int(_1272050), _1272054))))]]], (27468 ^ _780205) ^ [_1272327, _1272329, _1272331] : [class_Rings_Olinordered__idom(_1272327), 27471 ^ _780205 : [(27472 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272327), hAPP(c_Int_Oring__1__class_Oof__int(_1272327), _1272329)), hAPP(c_Int_Oring__1__class_Oof__int(_1272327), _1272331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1272329), _1272331)))], (27478 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1272329), _1272331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272327), hAPP(c_Int_Oring__1__class_Oof__int(_1272327), _1272329)), hAPP(c_Int_Oring__1__class_Oof__int(_1272327), _1272331))))]]], (27484 ^ _780205) ^ [_1272604, _1272606, _1272608] : [class_Rings_Oring__1(_1272604), -(hAPP(c_Int_Oring__1__class_Oof__int(_1272604), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1272606), _1272608)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272604), hAPP(c_Int_Oring__1__class_Oof__int(_1272604), _1272606)), hAPP(c_Int_Oring__1__class_Oof__int(_1272604), _1272608)))], (27490 ^ _780205) ^ [_1272739, _1272741] : [class_Int_Onumber__ring(_1272739), -(hAPP(c_Int_Oring__1__class_Oof__int(_1272739), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1272741)) = hAPP(c_Int_Onumber__class_Onumber__of(_1272739), _1272741))], (27496 ^ _780205) ^ [_1272840, _1272842, _1272844] : [class_Rings_Oring__1(_1272840), -(hAPP(c_Int_Oring__1__class_Oof__int(_1272840), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1272842), _1272844)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272840), hAPP(c_Int_Oring__1__class_Oof__int(_1272840), _1272842)), hAPP(c_Int_Oring__1__class_Oof__int(_1272840), _1272844)))], (27502 ^ _780205) ^ [_1272975] : [class_Rings_Oring__1(_1272975), -(hAPP(c_Int_Oring__1__class_Oof__int(_1272975), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1272975))], (27508 ^ _780205) ^ [_1273062, _1273064, _1273066] : [class_Rings_Oring__1(_1273062), -(hAPP(c_Int_Oring__1__class_Oof__int(_1273062), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1273064), _1273066)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1273062), hAPP(c_Int_Oring__1__class_Oof__int(_1273062), _1273064)), hAPP(c_Int_Oring__1__class_Oof__int(_1273062), _1273066)))], (27514 ^ _780205) ^ [_1273197, _1273199] : [class_Rings_Oring__1(_1273197), -(hAPP(c_Int_Oring__1__class_Oof__int(_1273197), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1273199)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1273197), _1273199))], (27520 ^ _780205) ^ [_1273298, _1273300] : [class_Rings_Oring__1(_1273298), -(hAPP(c_Int_Oring__1__class_Oof__int(_1273298), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1273300)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1273298), hAPP(c_Int_Oring__1__class_Oof__int(_1273298), _1273300)))], (27526 ^ _780205) ^ [_1273409, _1273411] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1273409, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1273409, tc_HOL_Obool))), hAPP(c_Set_OPow(_1273409), _1273411))))], (27528 ^ _780205) ^ [_1273472, _1273474, _1273476] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1273472, tc_HOL_Obool)), _1273474), hAPP(c_Set_OPow(_1273472), _1273476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273472, tc_HOL_Obool)), _1273474), _1273476)))], (27534 ^ _780205) ^ [_1273597, _1273599, _1273601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273597, tc_HOL_Obool)), _1273599), _1273601)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1273597, tc_HOL_Obool)), _1273599), hAPP(c_Set_OPow(_1273597), _1273601))))], (27540 ^ _780205) ^ [_1273728, _1273730, _1273732] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1273728, tc_HOL_Obool)), _1273730), hAPP(c_Set_OPow(_1273728), _1273732))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273728, tc_HOL_Obool)), _1273730), _1273732)))], (27546 ^ _780205) ^ [_1273857, _1273859] : [class_Rings_Oring__1(_1273857), -(hBOOL(hAPP(hAPP(c_member(_1273857), hAPP(c_Int_Oring__1__class_Oof__int(_1273857), _1273859)), c_Int_Oring__1__class_OInts(_1273857))))], (27552 ^ _780205) ^ [_1273960, _1273962, _1273964] : [class_Rings_Oring__1(_1273960), -(hAPP(c_Int_Oring__1__class_Oof__int(_1273960), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1273962), _1273964)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1273960), hAPP(c_Int_Oring__1__class_Oof__int(_1273960), _1273962)), _1273964))], (27558 ^ _780205) ^ [_1274085, _1274087, _1274089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1274085, tc_HOL_Obool)), _1274087), _1274089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1274085, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1274085), _1274087)), hAPP(c_Set_OPow(_1274085), _1274089))))], (27564 ^ _780205) ^ [_1274245, _1274247] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1274245, tc_HOL_Obool)), hAPP(c_Set_OPow(_1274245), _1274247))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1274245), _1274247)))], (27570 ^ _780205) ^ [_1274350, _1274352] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1274350), _1274352)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1274350, tc_HOL_Obool)), hAPP(c_Set_OPow(_1274350), _1274352))))], (27576 ^ _780205) ^ [_1274461, _1274463] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1274461, tc_HOL_Obool), tc_HOL_Obool)), _1274463), hAPP(c_Set_OPow(_1274461), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1274461, tc_HOL_Obool), _1274463)))))], (27578 ^ _780205) ^ [_1274510, _1274512, _1274514, _1274516] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1274510, _1274512, _1274514), _1274516), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1274512)], (27580 ^ _780205) ^ [_1274549, _1274551, _1274553, _1274555, _1274557] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1274549, _1274551, _1274553), _1274555), hAPP(c_Nat_OSuc, _1274557)) = hAPP(hAPP(_1274553, _1274555), hAPP(hAPP(c_Power_Opower_Opower(_1274549, _1274551, _1274553), _1274555), _1274557)))], (27582 ^ _780205) ^ [_1274609, _1274611, _1274613] : [-(hAPP(c_Set_OPow(_1274609), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1274609, tc_HOL_Obool)), _1274611), _1274613)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1274609, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1274609), _1274611)), hAPP(c_Set_OPow(_1274609), _1274613)))], (27584 ^ _780205) ^ [_1274676] : [class_Int_Onumber__ring(_1274676), -(hAPP(c_Int_Oring__1__class_Oof__int(_1274676), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1274676), c_Int_OMin))], (27590 ^ _780205) ^ [_1274769] : [-(hAPP(c_Set_OPow(_1274769), c_Orderings_Obot__class_Obot(tc_fun(_1274769, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1274769, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1274769, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1274769, tc_HOL_Obool), tc_HOL_Obool))))], (27592 ^ _780205) ^ [_1274826, _1274828] : [class_Rings_Olinordered__idom(_1274826), 27595 ^ _780205 : [(27596 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274826), hAPP(c_Int_Oring__1__class_Oof__int(_1274826), _1274828)), c_Groups_Ozero__class_Ozero(_1274826))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1274828), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27602 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1274828), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274826), hAPP(c_Int_Oring__1__class_Oof__int(_1274826), _1274828)), c_Groups_Ozero__class_Ozero(_1274826))))]]], (27608 ^ _780205) ^ [_1275088, _1275090] : [class_Rings_Olinordered__idom(_1275088), 27611 ^ _780205 : [(27612 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275088), c_Groups_Ozero__class_Ozero(_1275088)), hAPP(c_Int_Oring__1__class_Oof__int(_1275088), _1275090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275090)))], (27618 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275088), c_Groups_Ozero__class_Ozero(_1275088)), hAPP(c_Int_Oring__1__class_Oof__int(_1275088), _1275090))))]]], (27624 ^ _780205) ^ [_1275341, _1275343] : [class_Rings_Olinordered__idom(_1275341), 27627 ^ _780205 : [(27628 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275341), c_Groups_Ozero__class_Ozero(_1275341)), hAPP(c_Int_Oring__1__class_Oof__int(_1275341), _1275343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275343)))], (27634 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275341), c_Groups_Ozero__class_Ozero(_1275341)), hAPP(c_Int_Oring__1__class_Oof__int(_1275341), _1275343))))]]], (27640 ^ _780205) ^ [_1275594, _1275596] : [class_Rings_Olinordered__idom(_1275594), 27643 ^ _780205 : [(27644 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275594), hAPP(c_Int_Oring__1__class_Oof__int(_1275594), _1275596)), c_Groups_Ozero__class_Ozero(_1275594))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275596), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27650 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275596), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275594), hAPP(c_Int_Oring__1__class_Oof__int(_1275594), _1275596)), c_Groups_Ozero__class_Ozero(_1275594))))]]], (27656 ^ _780205) ^ [_1275856, _1275858] : [class_Rings_Oring__1(_1275856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275858)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1275856), hAPP(c_Int_Onat, _1275858)) = hAPP(c_Int_Oring__1__class_Oof__int(_1275856), _1275858))], (27666 ^ _780205) ^ [_1276013, _1276015, _1276017] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1276013, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1276013, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1276013), _1276015)), hAPP(c_Set_OPow(_1276013), _1276017))), hAPP(c_Set_OPow(_1276013), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276013, tc_HOL_Obool)), _1276015), _1276017)))))], (27668 ^ _780205) ^ [_1276093, _1276095] : [-(c_Nitpick_Onat__lcm(_1276093, _1276095) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1276093), _1276095)), c_Nitpick_Onat__gcd(_1276093, _1276095)))], (27670 ^ _780205) ^ [_1276136] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1276136)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1276136)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27672 ^ _780205) ^ [_1276171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276171), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1276171 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 27675 ^ [_1276171]))))], (27679 ^ _780205) ^ [] : [-(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))], (27681 ^ _780205) ^ [_1276302, _1276304] : [class_Groups_Osgn__if(_1276302), 27684 ^ _780205 : [(27685 ^ _780205) ^ [] : [_1276304 = c_Groups_Ozero__class_Ozero(_1276302), -(c_Groups_Osgn__class_Osgn(_1276302, _1276304) = c_Groups_Ozero__class_Ozero(_1276302))], (27691 ^ _780205) ^ [] : [-(_1276304 = c_Groups_Ozero__class_Ozero(_1276302)), 27694 ^ _780205 : [(27695 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276302), c_Groups_Ozero__class_Ozero(_1276302)), _1276304)), -(c_Groups_Osgn__class_Osgn(_1276302, _1276304) = c_Groups_Oone__class_Oone(_1276302))], (27701 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276302), c_Groups_Ozero__class_Ozero(_1276302)), _1276304))), -(c_Groups_Osgn__class_Osgn(_1276302, _1276304) = hAPP(c_Groups_Ouminus__class_Ouminus(_1276302), c_Groups_Oone__class_Oone(_1276302)))]]]]], (27707 ^ _780205) ^ [_1276714, _1276716] : [c_Code__Numeral_OSuc__code__numeral(_1276714) = c_Code__Numeral_OSuc__code__numeral(_1276716), -(_1276714 = _1276716)], (27713 ^ _780205) ^ [_1276795, _1276797] : [_1276795 = _1276797, -(c_Code__Numeral_OSuc__code__numeral(_1276795) = c_Code__Numeral_OSuc__code__numeral(_1276797))], (27719 ^ _780205) ^ [_1276882, _1276884] : [class_Rings_Olinordered__idom(_1276882), -(c_Groups_Osgn__class_Osgn(_1276882, c_Groups_Osgn__class_Osgn(_1276882, _1276884)) = c_Groups_Osgn__class_Osgn(_1276882, _1276884))], (27725 ^ _780205) ^ [_1276975, _1276977] : [class_Rings_Olinordered__idom(_1276975), 27728 ^ _780205 : [(27729 ^ _780205) ^ [] : [c_Groups_Osgn__class_Osgn(_1276975, _1276977) = c_Groups_Ozero__class_Ozero(_1276975), -(_1276977 = c_Groups_Ozero__class_Ozero(_1276975))], (27735 ^ _780205) ^ [] : [_1276977 = c_Groups_Ozero__class_Ozero(_1276975), -(c_Groups_Osgn__class_Osgn(_1276975, _1276977) = c_Groups_Ozero__class_Ozero(_1276975))]]], (27741 ^ _780205) ^ [_1277201] : [class_Groups_Osgn__if(_1277201), -(c_Groups_Osgn__class_Osgn(_1277201, c_Groups_Ozero__class_Ozero(_1277201)) = c_Groups_Ozero__class_Ozero(_1277201))], (27747 ^ _780205) ^ [_1277288, _1277290, _1277292] : [class_Rings_Olinordered__idom(_1277288), -(c_Groups_Osgn__class_Osgn(_1277288, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277288), _1277290), _1277292)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277288), c_Groups_Osgn__class_Osgn(_1277288, _1277290)), c_Groups_Osgn__class_Osgn(_1277288, _1277292)))], (27753 ^ _780205) ^ [_1277424] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1277424)], (27755 ^ _780205) ^ [_1277458] : [c_Code__Numeral_OSuc__code__numeral(_1277458) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (27757 ^ _780205) ^ [_1277483, _1277485] : [class_Rings_Olinordered__idom(_1277483), 27760 ^ _780205 : [(27761 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277483), c_Groups_Osgn__class_Osgn(_1277483, _1277485)), c_Groups_Ozero__class_Ozero(_1277483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277483), _1277485), c_Groups_Ozero__class_Ozero(_1277483))))], (27767 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277483), _1277485), c_Groups_Ozero__class_Ozero(_1277483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277483), c_Groups_Osgn__class_Osgn(_1277483, _1277485)), c_Groups_Ozero__class_Ozero(_1277483))))]]], (27773 ^ _780205) ^ [_1277751, _1277753] : [class_Rings_Olinordered__idom(_1277751), 27776 ^ _780205 : [(27777 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277751), c_Groups_Ozero__class_Ozero(_1277751)), c_Groups_Osgn__class_Osgn(_1277751, _1277753))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277751), c_Groups_Ozero__class_Ozero(_1277751)), _1277753)))], (27783 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277751), c_Groups_Ozero__class_Ozero(_1277751)), _1277753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277751), c_Groups_Ozero__class_Ozero(_1277751)), c_Groups_Osgn__class_Osgn(_1277751, _1277753))))]]], (27789 ^ _780205) ^ [_1278019] : 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hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279626), _1279628), _1279630) = c_Orderings_Otop__class_Otop(_1279626), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1279626), _1279628) = _1279630)], (27909 ^ _780205) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (27911 ^ _780205) ^ [_1279879, _1279881, _1279883] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1279879, _1279881, _1279883, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1279881)], (27913 ^ _780205) ^ [_1279911, _1279913] : [-(hBOOL(hAPP(hAPP(c_member(_1279911), _1279913), c_Orderings_Otop__class_Otop(tc_fun(_1279911, tc_HOL_Obool)))))], (27915 ^ _780205) ^ [_1279948, _1279950] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1279948, _1279950)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1279948, _1279950), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279950), c_Orderings_Otop__class_Otop(tc_fun(_1279950, 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tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1280737, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1280737, tc_HOL_Obool)))], (27957 ^ _780205) ^ [_1280779, _1280781, _1280783] : [class_Orderings_Otop(_1280779), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1280781, _1280779)), _1280783) = c_Orderings_Otop__class_Otop(_1280779))], (27963 ^ _780205) ^ [_1280876] : [class_Complete__Lattice_Ocomplete__lattice(_1280876), -(c_Complete__Lattice_OSup__class_OSup(_1280876, c_Orderings_Otop__class_Otop(tc_fun(_1280876, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1280876))], (27969 ^ _780205) ^ [_1280969, _1280971] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1280969, tc_HOL_Obool)), _1280971), c_Orderings_Otop__class_Otop(tc_fun(_1280969, tc_HOL_Obool))) = _1280971)], (27971 ^ _780205) ^ [_1281010, _1281012] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1281010, tc_HOL_Obool)), 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c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27981 ^ _780205) ^ [_1281217, _1281219] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1281217, _1281219)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1281217, _1281219), tc_HOL_Obool)))), 27984 ^ _780205 : [(27985 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281217), c_Orderings_Otop__class_Otop(tc_fun(_1281217, tc_HOL_Obool)))))], (27987 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281219), c_Orderings_Otop__class_Otop(tc_fun(_1281219, tc_HOL_Obool)))))]]], (27989 ^ _780205) ^ [_1281382, _1281384] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1281382, _1281384)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1281382, _1281384), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281382), c_Orderings_Otop__class_Otop(tc_fun(_1281382, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281384), c_Orderings_Otop__class_Otop(tc_fun(_1281384, tc_HOL_Obool))))], (27999 ^ _780205) ^ [_1281579, _1281581, _1281583] : [-(hAPP(c_Set_Ovimage(_1281579, _1281581, _1281583), c_Orderings_Otop__class_Otop(tc_fun(_1281581, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1281579, tc_HOL_Obool)))], (28001 ^ _780205) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (28003 ^ _780205) ^ [_1281641, _1281643] : [c_Nat__Transfer_Ois__nat(_1281641), c_Nat__Transfer_Ois__nat(_1281643), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1281641), _1281643)))], (28013 ^ _780205) ^ [_1281776] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1281776)))], (28015 ^ _780205) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28017 ^ _780205) ^ [_1281819, _1281821] : [c_Nat__Transfer_Ois__nat(_1281819), c_Nat__Transfer_Ois__nat(_1281821), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1281819), _1281821)))], (28027 ^ _780205) ^ [_1281954, _1281956] : [c_Nat__Transfer_Ois__nat(_1281954), c_Nat__Transfer_Ois__nat(_1281956), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1281954, _1281956)))], (28037 ^ _780205) ^ [_1282085, _1282087] : [c_Nat__Transfer_Ois__nat(_1282085), c_Nat__Transfer_Ois__nat(_1282087), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1282085), _1282087)))], (28047 ^ _780205) ^ [_1282220, _1282222] : [class_Orderings_Otop(_1282220), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282220), _1282222), c_Orderings_Otop__class_Otop(_1282220))))], (28053 ^ _780205) ^ [_1282313, _1282315] : [class_Lattices_Obounded__lattice__top(_1282313), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282313), _1282315), c_Orderings_Otop__class_Otop(_1282313)) = c_Orderings_Otop__class_Otop(_1282313))], (28059 ^ _780205) ^ [_1282412, _1282414] : [class_Lattices_Obounded__lattice__top(_1282412), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282412), c_Orderings_Otop__class_Otop(_1282412)), _1282414) = c_Orderings_Otop__class_Otop(_1282412))], (28065 ^ _780205) ^ [_1282511, _1282513] : [class_Lattices_Obounded__lattice__top(_1282511), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282511), c_Orderings_Otop__class_Otop(_1282511)), _1282513) = _1282513)], (28071 ^ _780205) ^ [_1282606, _1282608] : [class_Lattices_Obounded__lattice__top(_1282606), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282606), _1282608), c_Orderings_Otop__class_Otop(_1282606)) = _1282608)], (28077 ^ _780205) ^ [_1282701, _1282703, _1282705] : [class_Lattices_Obounded__lattice__top(_1282701), 28080 ^ _780205 : [(28081 ^ _780205) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282701), _1282703), _1282705) = c_Orderings_Otop__class_Otop(_1282701), 28084 ^ _780205 : [(28085 ^ _780205) ^ [] : [-(_1282703 = c_Orderings_Otop__class_Otop(_1282701))], (28087 ^ _780205) ^ [] : [-(_1282705 = c_Orderings_Otop__class_Otop(_1282701))]]], (28089 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1282701), _1282703), _1282705) = c_Orderings_Otop__class_Otop(_1282701)), _1282703 = c_Orderings_Otop__class_Otop(_1282701), _1282705 = c_Orderings_Otop__class_Otop(_1282701)]]], (28099 ^ _780205) ^ [_1283028, _1283030] : [c_Nat__Transfer_Ois__nat(_1283028), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1283028), _1283030)))], (28105 ^ _780205) ^ [_1283113, _1283115] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1283113, tc_HOL_Obool)), _1283115), c_Orderings_Otop__class_Otop(tc_fun(_1283113, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1283113, tc_HOL_Obool)))], (28107 ^ _780205) ^ [_1283159, _1283161] : [c_Nat__Transfer_Ois__nat(_1283159), c_Nat__Transfer_Ois__nat(_1283161), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1283159, _1283161)))], (28117 ^ _780205) ^ [_1283288, _1283290] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283288), c_Orderings_Otop__class_Otop(tc_fun(_1283288, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1283288), _1283290) = hAPP(c_Finite__Set_Ocard(_1283288), c_Orderings_Otop__class_Otop(tc_fun(_1283288, tc_HOL_Obool))), -(_1283290 = c_Orderings_Otop__class_Otop(tc_fun(_1283288, tc_HOL_Obool)))], (28127 ^ _780205) ^ [_1283475] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283475, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1283475, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1283475, tc_HOL_Obool)))], (28129 ^ _780205) ^ [_1283516] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283516, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1283516, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1283516, tc_HOL_Obool)))], (28131 ^ _780205) ^ [_1283557, _1283559] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283557), _1283559)), 28134 ^ _780205 : [(28135 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283557), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283557, tc_HOL_Obool)), _1283559))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283557), c_Orderings_Otop__class_Otop(tc_fun(_1283557, tc_HOL_Obool)))))], (28141 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283557), c_Orderings_Otop__class_Otop(tc_fun(_1283557, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283557), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283557, tc_HOL_Obool)), _1283559))))]]], (28147 ^ _780205) ^ [_1283835, _1283837] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283835, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283835, tc_HOL_Obool)), _1283837)), _1283837) = c_Orderings_Otop__class_Otop(tc_fun(_1283835, tc_HOL_Obool)))], (28149 ^ _780205) ^ [_1283884, _1283886] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283884, tc_HOL_Obool)), _1283886), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283884, tc_HOL_Obool)), _1283886)) = c_Orderings_Otop__class_Otop(tc_fun(_1283884, tc_HOL_Obool)))], (28151 ^ _780205) ^ [_1283933, _1283935] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283933, tc_HOL_Obool)), _1283935) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1283933, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1283933, tc_HOL_Obool))), _1283935))], (28153 ^ _780205) ^ [_1283994] : [c_Nat__Transfer_Ois__nat(_1283994), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1283994)))], (28159 ^ _780205) ^ [_1284067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284067)), -(c_Nat__Transfer_Ois__nat(_1284067))], (28165 ^ _780205) ^ [_1284146] : [class_Lattices_Oboolean__algebra(_1284146), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1284146), c_Orderings_Obot__class_Obot(_1284146)) = c_Orderings_Otop__class_Otop(_1284146))], (28171 ^ _780205) ^ [_1284237] : [class_Lattices_Oboolean__algebra(_1284237), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1284237), c_Orderings_Otop__class_Otop(_1284237)) = c_Orderings_Obot__class_Obot(_1284237))], (28177 ^ _780205) ^ [_1284328, _1284330] : [class_Lattices_Oboolean__algebra(_1284328), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284328), _1284330), hAPP(c_Groups_Ouminus__class_Ouminus(_1284328), _1284330)) = c_Orderings_Otop__class_Otop(_1284328))], (28183 ^ _780205) ^ [_1284433, _1284435] : [class_Lattices_Oboolean__algebra(_1284433), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284433), hAPP(c_Groups_Ouminus__class_Ouminus(_1284433), _1284435)), _1284435) = c_Orderings_Otop__class_Otop(_1284433))], (28189 ^ _780205) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (28191 ^ _780205) ^ [_1284556] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284556), c_Orderings_Otop__class_Otop(tc_fun(_1284556, 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(_1284556), c_Orderings_Otop__class_Otop(tc_fun(_1284556, tc_HOL_Obool))))))], (28197 ^ _780205) ^ [] : [-(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))))], (28199 ^ _780205) ^ [_1284691, _1284693] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1284691, _1284693)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1284691, _1284693), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1284693), c_Orderings_Otop__class_Otop(tc_fun(_1284693, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1284691), c_Orderings_Otop__class_Otop(tc_fun(_1284691, tc_HOL_Obool)))))], (28209 ^ _780205) ^ [_1284851, _1284853] : [class_Complete__Lattice_Ocomplete__lattice(_1284851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284851), _1284853)), -(c_Complete__Lattice_OInf__class_OInf(_1284851, _1284853) = hAPP(hAPP(c_Finite__Set_Ofold(_1284851, _1284851, c_Lattices_Osemilattice__inf__class_Oinf(_1284851)), c_Orderings_Otop__class_Otop(_1284851)), _1284853))], (28219 ^ _780205) ^ [_1285020, _1285022, _1285024] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1285020, _1285022) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1285024, _1285022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1285024), _1285020)), -(_1285020 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1285024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1285022), 28226 ^ [_1285020, _1285022, _1285024])))], (28230 ^ _780205) ^ [_1285217, _1285219, _1285221] : [28232 ^ _780205 : [(28233 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 28231 ^ [_1285217, _1285219, _1285221]), _1285217)))], (28235 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1285219, 28231 ^ [_1285217, _1285219, _1285221])))], (28237 ^ _780205) ^ [] : [hBOOL(hAPP(_1285219, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 28231 ^ [_1285217, _1285219, _1285221]), _1285217)))]], hBOOL(hAPP(_1285219, _1285221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1285221), _1285217)), -(hBOOL(hAPP(_1285219, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28249 ^ _780205) ^ [_1285588, _1285590] : [28250 ^ _780205 : [(28251 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1285588), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (28253 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1285590), _1285588))]], -(c_Random_Olog(_1285588, _1285590) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (28257 ^ _780205) ^ [_1285723, _1285725] : [-(c_Random_Olog(_1285723, _1285725) = 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(_1285723, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1285725), _1285723)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1285723), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1285725), _1285723)))], (28267 ^ _780205) ^ [_1285793, _1285795] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1285793), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1285793, tc_HOL_Obool), _1285795)))), 28268 ^ _780205 : [(28269 ^ _780205) ^ [_1285857] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1285793, tc_HOL_Obool)), _1285857), _1285795)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285793), _1285857))]]], (28277 ^ _780205) ^ [_1286001, _1286003] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1286001, tc_HOL_Obool)), _1286003)))], (28279 ^ _780205) ^ [_1286033, _1286035, _1286037, _1286039] : [hBOOL(hAPP(hAPP(c_member(_1286033), _1286035), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1286033, tc_HOL_Obool), _1286037))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1286033, tc_HOL_Obool)), _1286039), _1286037)), -(hBOOL(hAPP(hAPP(c_member(_1286033), _1286035), _1286039)))], (28289 ^ _780205) ^ [_1286230, _1286232, _1286234, _1286236] : [hBOOL(hAPP(hAPP(c_member(_1286230), _1286232), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1286230, tc_HOL_Obool), _1286234))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1286230, tc_HOL_Obool)), _1286236), _1286234)), -(hBOOL(hAPP(hAPP(c_member(_1286230), _1286232), _1286236)))], (28299 ^ _780205) ^ [_1286427] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1286427, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1286427, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1286427, tc_HOL_Obool)))], (28301 ^ _780205) ^ [_1286469] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1286469, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1286469, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1286469, tc_HOL_Obool)))], (28303 ^ _780205) ^ [_1286511, _1286513, _1286515] : [class_Complete__Lattice_Ocomplete__lattice(_1286511), 28306 ^ _780205 : [(28317 ^ _780205) ^ [] : [28319 ^ _780205 : [(28320 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1286511), 28318 ^ [_1286511, _1286513, _1286515]), _1286515)))], (28322 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286511), _1286513), 28318 ^ [_1286511, _1286513, _1286515]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286511), _1286513), c_Complete__Lattice_OInf__class_OInf(_1286511, _1286515))))], (28307 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286511), _1286513), c_Complete__Lattice_OInf__class_OInf(_1286511, _1286515))), 28310 ^ _780205 : [(28311 ^ _780205) ^ [_1286669] : [hBOOL(hAPP(hAPP(c_member(_1286511), _1286669), _1286515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286511), _1286513), _1286669)))]]]]], (28326 ^ _780205) ^ [_1286945, _1286947, _1286949] : [class_Complete__Lattice_Ocomplete__lattice(_1286945), class_Orderings_Olinorder(_1286945), 28333 ^ _780205 : [(28334 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286945), c_Complete__Lattice_OInf__class_OInf(_1286945, _1286947)), _1286949)), 28338 ^ _780205 : [(28339 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1286945), 28337 ^ [_1286945, _1286947, _1286949]), _1286947)))], (28341 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286945), 28337 ^ [_1286945, _1286947, _1286949]), _1286949)))]]], (28343 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286945), c_Complete__Lattice_OInf__class_OInf(_1286945, _1286947)), _1286949))), 28344 ^ _780205 : [(28345 ^ _780205) ^ [_1287251] : [hBOOL(hAPP(hAPP(c_member(_1286945), _1287251), _1286947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286945), _1287251), _1286949))]]]]], (28353 ^ _780205) ^ [_1287405] : [class_Complete__Lattice_Ocomplete__lattice(_1287405), -(c_Complete__Lattice_OInf__class_OInf(_1287405, c_Orderings_Otop__class_Otop(tc_fun(_1287405, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1287405))], (28359 ^ _780205) ^ [_1287498, _1287500, _1287502] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1287498, tc_HOL_Obool)), _1287500), _1287502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287498, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1287498, tc_HOL_Obool), _1287502)), _1287500)))], (28365 ^ _780205) ^ [_1287629, _1287631, _1287633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1287629, tc_HOL_Obool), tc_HOL_Obool)), _1287631), _1287633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287629, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1287629, tc_HOL_Obool), _1287633)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1287629, tc_HOL_Obool), _1287631))))], (28371 ^ _780205) ^ [_1287778, _1287780, _1287782] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1287778, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1287778, tc_HOL_Obool)), _1287780), _1287782)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1287778, tc_HOL_Obool)), _1287780), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1287778, tc_HOL_Obool), _1287782)))], (28373 ^ _780205) ^ [_1287839, _1287841, _1287843] : [class_Complete__Lattice_Ocomplete__lattice(_1287839), hBOOL(hAPP(hAPP(c_member(_1287839), _1287841), _1287843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287839), c_Complete__Lattice_OInf__class_OInf(_1287839, _1287843)), _1287841)))], (28383 ^ _780205) ^ [_1288004, _1288006, _1288008] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1288004, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1288004, tc_HOL_Obool), tc_HOL_Obool)), _1288006), _1288008)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288004, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1288004, tc_HOL_Obool), _1288006)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1288004, tc_HOL_Obool), _1288008)))], (28385 ^ _780205) ^ [_1288074, _1288076] : [class_Complete__Lattice_Ocomplete__lattice(_1288074), -(c_Complete__Lattice_OInf__class_OInf(_1288074, hAPP(hAPP(c_Set_Oinsert(_1288074), _1288076), c_Orderings_Obot__class_Obot(tc_fun(_1288074, tc_HOL_Obool)))) = _1288076)], (28391 ^ _780205) ^ [_1288181] : [class_Complete__Lattice_Ocomplete__lattice(_1288181), -(c_Complete__Lattice_OInf__class_OInf(_1288181, c_Orderings_Obot__class_Obot(tc_fun(_1288181, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1288181))], (28397 ^ _780205) ^ [_1288274, _1288276, _1288278] : [class_Complete__Lattice_Ocomplete__lattice(_1288274), -(c_Complete__Lattice_OInf__class_OInf(_1288274, hAPP(hAPP(c_Set_Oinsert(_1288274), _1288276), _1288278)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1288274), _1288276), c_Complete__Lattice_OInf__class_OInf(_1288274, _1288278)))], (28403 ^ _780205) ^ [_1288395, _1288397, _1288399] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1288395, tc_HOL_Obool)), _1288397), _1288399) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1288395, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1288395, tc_HOL_Obool)), _1288397), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1288395, tc_HOL_Obool)), _1288399), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1288395, tc_HOL_Obool), tc_HOL_Obool))))))], (28405 ^ _780205) ^ [_1288469, _1288471, _1288473] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288469, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288469, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1288469, tc_HOL_Obool), _1288471)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1288469, tc_HOL_Obool), _1288473))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1288469, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1288469, tc_HOL_Obool), tc_HOL_Obool)), _1288471), _1288473)))))], (28407 ^ _780205) ^ [_1288549, _1288551, _1288553] : [class_Complete__Lattice_Ocomplete__lattice(_1288549), -(c_Complete__Lattice_OInf__class_OInf(_1288549, hAPP(hAPP(c_Set_Oinsert(_1288549), _1288551), hAPP(hAPP(c_Set_Oinsert(_1288549), _1288553), c_Orderings_Obot__class_Obot(tc_fun(_1288549, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1288549), _1288551), _1288553))], (28413 ^ _780205) ^ [_1288690, _1288692, _1288694] : [class_Complete__Lattice_Ocomplete__lattice(_1288690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288690), _1288692)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1288690), _1288694), c_Complete__Lattice_OInf__class_OInf(_1288690, _1288692)) = hAPP(hAPP(c_Finite__Set_Ofold(_1288690, _1288690, c_Lattices_Osemilattice__inf__class_Oinf(_1288690)), _1288694), _1288692))], (28423 ^ _780205) ^ [_1288875, _1288877] : [class_Complete__Lattice_Ocomplete__lattice(_1288875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288875), _1288877)), -(_1288877 = c_Orderings_Obot__class_Obot(tc_fun(_1288875, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1288875, _1288877) = c_Complete__Lattice_OInf__class_OInf(_1288875, _1288877))], (28437 ^ _780205) ^ [_1289059, _1289061, _1289063] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1289059), _1289061)), -(c_Random_Ominus__shift(_1289063, _1289059, _1289061) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1289063), _1289059)), _1289061))], (28443 ^ _780205) ^ [_1289174, _1289176, _1289178] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1289174), _1289176))), -(c_Random_Ominus__shift(_1289178, _1289174, _1289176) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1289174), _1289176))], (28449 ^ _780205) ^ [_1289238, _1289240] : [_1289238 = _1289240, -(c_Random_Oinc__shift(_1289238, _1289240) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (28455 ^ _780205) ^ [_1289315, _1289317] : [-(_1289315 = _1289317), -(c_Random_Oinc__shift(_1289315, _1289317) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1289317), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (28461 ^ _780205) ^ [_1289362, _1289364] : [-(hBOOL(hAPP(hAPP(c_member(_1289362), _1289364), c_Orderings_Otop__class_Otop(tc_fun(_1289362, tc_HOL_Obool)))))], (28463 ^ _780205) ^ [_1289399, _1289401, _1289403] : [class_Divides_Osemiring__div(_1289399), -(_1289401 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1289399), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289399), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1289399), _1289401), _1289403)), _1289403)), c_Divides_Odiv__class_Omod(_1289399, _1289401, _1289403)))], (28469 ^ _780205) ^ [_1289532, _1289534, _1289536] : [28471 ^ _780205 : [(28472 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1289532, tc_HOL_Obool)), 28470 ^ [_1289532, _1289534, _1289536]), _1289534)))], (28474 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289532, tc_HOL_Obool)), 28470 ^ [_1289532, _1289534, _1289536]), _1289536))]], -(_1289534 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1289532, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289532, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1289532, tc_HOL_Obool), _1289534)), _1289536)))], (28482 ^ _780205) ^ [_1289794, _1289796, _1289798] : [28484 ^ _780205 : [(28485 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1289794, tc_HOL_Obool)), 28483 ^ [_1289794, _1289796, _1289798]), _1289796)))], (28487 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1289794), _1289798), 28483 ^ [_1289794, _1289796, _1289798]))]], -(hBOOL(hAPP(hAPP(c_member(_1289794), _1289798), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1289794, tc_HOL_Obool), _1289796))))], (28491 ^ _780205) ^ [_1290010, _1290012] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1290010, _1290012)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1290012)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28493 ^ _780205) ^ [_1290050, _1290052] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1290050, _1290052)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1290052)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28495 ^ _780205) ^ [_1290109, _1290111, _1290113, _1290115] : [c_Com_Ocom_OWhile(_1290109, _1290111) = c_Com_Ocom_OWhile(_1290113, _1290115), 28498 ^ _780205 : [(28499 ^ _780205) ^ [] : [-(_1290109 = _1290113)], (28501 ^ _780205) ^ [] : [-(_1290111 = _1290115)]]], (28503 ^ _780205) ^ [_1290224, _1290226, _1290228, _1290230] : [-(c_Com_Ocom_OWhile(_1290224, _1290226) = c_Com_Ocom_OWhile(_1290228, _1290230)), _1290224 = _1290228, _1290226 = _1290230], (28513 ^ _780205) ^ [_1290396, _1290398, _1290400, _1290402, _1290404] : [c_Com_Ocom_OCond(_1290396, _1290398, _1290400) = c_Com_Ocom_OWhile(_1290402, _1290404)], (28515 ^ _780205) ^ [_1290455, _1290457, _1290459, _1290461, _1290463] : [c_Com_Ocom_OWhile(_1290455, _1290457) = c_Com_Ocom_OCond(_1290459, _1290461, _1290463)], (28517 ^ _780205) ^ [_1290511, _1290513, _1290515, _1290517] : [c_Com_Ocom_OSemi(_1290511, _1290513) = c_Com_Ocom_OWhile(_1290515, _1290517)], (28519 ^ _780205) ^ [_1290564, _1290566, _1290568, _1290570] : [c_Com_Ocom_OWhile(_1290564, _1290566) = c_Com_Ocom_OSemi(_1290568, _1290570)], (28521 ^ _780205) ^ [_1290620, _1290622, _1290624, _1290626, _1290628] : [c_Com_Ocom_OLocal(_1290620, _1290622, _1290624) = c_Com_Ocom_OWhile(_1290626, _1290628)], (28523 ^ _780205) ^ [_1290679, _1290681, _1290683, _1290685, _1290687] : [c_Com_Ocom_OWhile(_1290679, _1290681) = c_Com_Ocom_OLocal(_1290683, _1290685, _1290687)], (28525 ^ _780205) ^ [_1290729, _1290731] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_1290729, _1290731)], (28527 ^ _780205) ^ [_1290769, _1290771] : [c_Com_Ocom_OWhile(_1290769, _1290771) = c_Com_Ocom_OSKIP], (28529 ^ _780205) ^ [_1290797, _1290799] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1290797), _1290799) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1290797), _1290799))], (28531 ^ _780205) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (28533 ^ _780205) ^ [_1290852, _1290854, _1290856, _1290858, _1290860, _1290862] : [-(c_Nitpick_Opair__box_Opair__box__size(_1290852, _1290854, _1290856, _1290858, c_Nitpick_Opair__box_OPairBox(_1290852, _1290854, _1290860, _1290862)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1290856, _1290860)), hAPP(_1290858, _1290862))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28535 ^ _780205) ^ [_1290914] : [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), _1290914))), 28538 ^ _780205 : [(28539 ^ _780205) ^ [] : [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), _1290914)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1290914)) = 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), _1290914))))], (28545 ^ _780205) ^ [] : [-(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), _1290914))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1290914)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1290914)), 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), _1290914)))))]]], (28551 ^ _780205) ^ [_1291231, _1291233, _1291235, _1291237, _1291239, _1291241] : [c_Nitpick_Opair__box_OPairBox(_1291231, _1291233, _1291235, _1291237) = c_Nitpick_Opair__box_OPairBox(_1291231, _1291233, _1291239, _1291241), 28554 ^ _780205 : [(28555 ^ _780205) ^ [] : [-(_1291235 = _1291239)], (28557 ^ _780205) ^ [] : [-(_1291237 = _1291241)]]], (28559 ^ _780205) ^ [_1291358, _1291360, _1291362, _1291364, _1291366, _1291368] : [-(c_Nitpick_Opair__box_OPairBox(_1291358, _1291360, _1291362, _1291364) = c_Nitpick_Opair__box_OPairBox(_1291358, _1291360, _1291366, _1291368)), _1291362 = _1291366, _1291364 = _1291368], (28569 ^ _780205) ^ [_1291525, _1291527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1291525), 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)), _1291527)), -(c_Divides_OnegDivAlg(_1291525, _1291527) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1291525), _1291527)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1291525, _1291527)))], (28579 ^ _780205) ^ [_1291706] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1291706) = 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), _1291706), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (28581 ^ _780205) ^ [_1291750, _1291752] : [28582 ^ _780205 : [(28583 ^ _780205) ^ [] : [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), _1291750), _1291752)))], (28585 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1291752), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1291750, _1291752) = 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), _1291750), _1291752)))], (28589 ^ _780205) ^ [_1291909, _1291911] : [-(c_Divides_OnegDivAlg(_1291909, _1291911) = hAPP(c_Divides_Oadjust(_1291911), c_Divides_OnegDivAlg(_1291909, 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)))), _1291911)))), -(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), _1291909), _1291911)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1291911), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28599 ^ _780205) ^ [_1291981, _1291983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291981)), 28602 ^ _780205 : [(28603 ^ _780205) ^ [] : [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), _1291983), _1291981))), -(c_Divides_OnegDivAlg(_1291983, _1291981) = 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), _1291983), _1291981)))], (28609 ^ _780205) ^ [] : [-(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), _1291983), _1291981)))), -(c_Divides_OnegDivAlg(_1291983, _1291981) = hAPP(c_Divides_Oadjust(_1291981), c_Divides_OnegDivAlg(_1291983, 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)))), _1291981))))]]], (28615 ^ _780205) ^ [_1292245, _1292247] : [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), _1292245))), 28618 ^ _780205 : [(28619 ^ _780205) ^ [] : [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), _1292247)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292245)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292247), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292245)) = 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), _1292247)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292245))))], (28625 ^ _780205) ^ [] : [-(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), _1292247)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292245))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292247), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292245)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292245)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292247), 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), _1292245)))))]]], (28631 ^ _780205) ^ [_1292593] : [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), _1292593))), 28634 ^ _780205 : [(28635 ^ _780205) ^ [] : [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), _1292593))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292593)) = 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)))], (28641 ^ _780205) ^ [] : [-(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), _1292593)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292593)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292593)), 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), _1292593)))))]]], (28647 ^ _780205) ^ [_1292862, _1292864] : [28648 ^ _780205 : [(28649 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1292862), _1292864))], (28651 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1292864), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1292862, _1292864) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292862))], (28655 ^ _780205) ^ [_1293003, _1293005] : [-(c_Divides_OposDivAlg(_1293003, _1293005) = hAPP(c_Divides_Oadjust(_1293005), c_Divides_OposDivAlg(_1293003, 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)))), _1293005)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293003), _1293005))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1293005), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28665 ^ _780205) ^ [_1293096, _1293098, _1293100, _1293102, _1293104] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1293096, _1293098, _1293100), _1293102), _1293104)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1293096, _1293098)), hAPP(hAPP(c_Product__Type_OPair(_1293096, _1293098), _1293102), _1293104)), _1293100)))], (28671 ^ _780205) ^ [_1293231, _1293233, _1293235, _1293237, _1293239] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1293231, _1293233)), hAPP(hAPP(c_Product__Type_OPair(_1293231, _1293233), _1293237), _1293239)), _1293235)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1293231, _1293233, _1293235), _1293237), _1293239)))], (28677 ^ _780205) ^ [_1293372, _1293374] : [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), _1293372))), 28680 ^ _780205 : [(28681 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1293374)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1293372))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1293374), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1293372)) = 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), _1293374)))], (28687 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1293374)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1293372)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1293374), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1293372)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1293372)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1293374), 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), _1293372)))))]]], (28693 ^ _780205) ^ [_1293690] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1293690) = 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)))], (28695 ^ _780205) ^ [_1293716, _1293718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293718)), -(c_Divides_OposDivAlg(_1293716, _1293718) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1293716), _1293718)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1293716, _1293718)))], (28705 ^ _780205) ^ [_1293891, _1293893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293891)), 28708 ^ _780205 : [(28709 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293893), _1293891)), -(c_Divides_OposDivAlg(_1293893, _1293891) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293893))], (28715 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293893), _1293891))), -(c_Divides_OposDivAlg(_1293893, _1293891) = hAPP(c_Divides_Oadjust(_1293891), c_Divides_OposDivAlg(_1293893, 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)))), _1293891))))]]], (28721 ^ _780205) ^ [_1294131, _1294133] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1294131, _1294133) = 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), _1294131), _1294133)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1294131, _1294133)))], (28723 ^ _780205) ^ [_1294190, _1294192] : [c_Nitpick_Orefl_H(_1294190, _1294192), 28726 ^ _780205 : [(28727 ^ _780205) ^ [_1294268] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1294190, _1294190)), hAPP(hAPP(c_Product__Type_OPair(_1294190, _1294190), _1294268), _1294268)), _1294192)))]]], (28729 ^ _780205) ^ [_1294310, _1294312] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1294310, _1294310)), hAPP(hAPP(c_Product__Type_OPair(_1294310, _1294310), 28730 ^ [_1294310, _1294312]), 28730 ^ [_1294310, _1294312])), _1294312)), -(c_Nitpick_Orefl_H(_1294310, _1294312))], (28736 ^ _780205) ^ [_1294477, _1294479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1294477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1294477), _1294479)), -(c_Divides_Odivmod__nat(_1294479, _1294477) = 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), _1294479), _1294477)), _1294477))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1294479), _1294477), _1294477)))], (28746 ^ _780205) ^ [_1294688, _1294690, _1294692, _1294694] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1294688, _1294690)), c_Nitpick_Opair__box_OPairBox(_1294688, _1294690, _1294692, _1294694)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28748 ^ _780205) ^ [_1294730] : [-(c_Divides_Odivmod__nat(_1294730, 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)), _1294730))], (28750 ^ _780205) ^ [_1294759, _1294761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1294759), _1294761)), -(c_Divides_Odivmod__nat(_1294759, _1294761) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1294759))], (28756 ^ _780205) ^ [_1294858, _1294860] : [-(c_Divides_Odivmod__nat(_1294858, _1294860) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1294858), _1294860)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1294858, _1294860)))], (28758 ^ _780205) ^ [_1294902, _1294904, _1294906, _1294908, _1294910] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1294902, _1294904), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294906), _1294908))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1294904)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1294910), _1294902), _1294904), 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), _1294910), _1294906)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1294910), _1294908)), _1294904))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1294910), _1294908), _1294904)))))], (28768 ^ _780205) ^ [_1295171, _1295173, _1295175, _1295177, _1295179] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1295171, _1295173), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1295175), _1295177))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1295173)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1295179)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1295171, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1295173), _1295179)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1295175), _1295179)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1295173), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1295175, _1295179))), _1295177)))))], (28782 ^ _780205) ^ [_1295478, _1295480, _1295482, _1295484, _1295486, _1295488] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1295478, _1295480, _1295482, _1295484, c_Nitpick_Opair__box_OPairBox(_1295478, _1295480, _1295486, _1295488)) = hAPP(hAPP(_1295484, _1295486), _1295488))], (28784 ^ _780205) ^ [_1295528, _1295530, _1295532, _1295534, _1295536, _1295538] : [-(c_Nitpick_Opair__box_Opair__box__case(_1295528, _1295530, _1295532, _1295534, c_Nitpick_Opair__box_OPairBox(_1295528, _1295530, _1295536, _1295538)) = hAPP(hAPP(_1295534, _1295536), _1295538))], (28786 ^ _780205) ^ [_1295578, _1295580, _1295582, _1295584] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1295578, _1295580), _1295582)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1295578, _1295580), _1295584)), -(_1295582 = _1295584)], (28796 ^ _780205) ^ [_1295735, _1295737, _1295739] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1295735, _1295737), _1295739)), -(c_Divides_Odivmod__nat(_1295735, _1295737) = _1295739)], (28802 ^ _780205) ^ [_1295830, _1295832] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1295830, _1295832), c_Divides_Odivmod__nat(_1295830, _1295832))))], (28804 ^ _780205) ^ [_1295863, _1295865, _1295867, _1295869] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1295863, _1295865), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1295867), _1295869))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1295863, _1295865) = _1295869)], (28810 ^ _780205) ^ [_1295974, _1295976, _1295978, _1295980] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1295974, _1295976), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1295978), _1295980))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1295974), _1295976) = _1295978)], (28816 ^ _780205) ^ [_1296089, _1296091] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1296089, _1296091), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1296089), _1296091)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1296089, _1296091)))))], (28818 ^ _780205) ^ [_1296135, _1296137, _1296139, _1296141, _1296143, _1296145, _1296147] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1296135, _1296137), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1296139), _1296141))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1296143, _1296137), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1296145), _1296147))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1296137)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1296135), _1296143), _1296137), 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), _1296139), _1296145)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1296141), _1296147)), _1296137))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1296141), _1296147), _1296137)))))], (28832 ^ _780205) ^ [_1296496, _1296498] : [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), _1296496), _1296498))), 28835 ^ _780205 : [(28836 ^ _780205) ^ [] : [28837 ^ _780205 : [(28838 ^ _780205) ^ [] : [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), _1296496), _1296498)))], (28840 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296498), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1296496, _1296498) = 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), _1296496), _1296498)))], (28844 ^ _780205) ^ [] : [-(c_Divides_OnegDivAlg(_1296496, _1296498) = hAPP(c_Divides_Oadjust(_1296498), c_Divides_OnegDivAlg(_1296496, 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)))), _1296498)))), -(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), _1296496), _1296498)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296498), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (28854 ^ _780205) ^ [_1296852, _1296854] : [_1296852 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1296854, _1296852) = 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), _1296854)))], (28860 ^ _780205) ^ [_1296941, _1296943] : [-(_1296941 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1296943, _1296941) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1296943), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1296941)))], (28866 ^ _780205) ^ [_1296991, _1296993] : [-(c_Divides_Opdivmod(_1296991, _1296993) = 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), _1296991)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1296993))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1296991), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1296993))))], (28868 ^ _780205) ^ [_1297047, _1297049, _1297051, _1297053, _1297055] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1297047, _1297049), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1297051), _1297053))), -(_1297049 = 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)), _1297055)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1297047, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1297049), _1297055)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1297051), _1297055)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1297049), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1297051, _1297055))), _1297053)))))], (28882 ^ _780205) ^ [_1297353, _1297355, _1297357, _1297359, _1297361, _1297363] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1297353, _1297355), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1297357), _1297359))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1297353, _1297355), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1297361), _1297363))), -(_1297355 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1297359 = _1297363)], (28896 ^ _780205) ^ [_1297557, _1297559, _1297561, _1297563, _1297565, _1297567] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1297557, _1297559), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1297561), _1297563))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1297557, _1297559), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1297565), _1297567))), -(_1297559 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1297561 = _1297565)], (28910 ^ _780205) ^ [_1297761, _1297763, _1297765] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1297761, _1297761), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1297763), _1297765))), -(_1297761 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1297765 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28920 ^ _780205) ^ [_1297873] : [-(_1297873 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1297873), 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)))))], (28926 ^ _780205) ^ [_1297912, _1297914, _1297916] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1297912, _1297912), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1297914), _1297916))), -(_1297912 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1297914 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (28936 ^ _780205) ^ [_1298028, _1298030, _1298032, _1298034] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1298028, _1298030), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1298032), _1298034))), -(_1298030 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1298028, _1298030) = _1298034)], (28946 ^ _780205) ^ [_1298154, _1298156, _1298158, _1298160] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1298154, _1298156), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1298158), _1298160))), -(_1298156 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1298154), _1298156) = _1298158)], (28956 ^ _780205) ^ [_1298284, _1298286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1298284), 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)), _1298286)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1298284, _1298286), c_Divides_OnegDivAlg(_1298284, _1298286))))], (28966 ^ _780205) ^ [_1298439, _1298441] : [-(_1298439 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1298441, _1298439), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1298441), _1298439)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1298441, _1298439)))))], (28972 ^ _780205) ^ [_1298496, _1298498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298498)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1298496, _1298498), c_Divides_OposDivAlg(_1298496, _1298498))))], (28982 ^ _780205) ^ [_1298649, _1298651, _1298653, _1298655, _1298657, _1298659, _1298661] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1298649, _1298651), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1298653), _1298655))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1298657, _1298651), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1298659), _1298661))), -(_1298651 = 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), _1298649), _1298657), _1298651), 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), _1298653), _1298659)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1298655), _1298661)), _1298651))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1298655), _1298661), _1298651)))))], (28996 ^ _780205) ^ [_1298959, _1298961, _1298963, _1298965] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1298959, _1298961), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1298963), _1298965))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1298959), _1298961), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1298965), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1298963)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1298963)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1298965), 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), _1298961), _1298965))))))], (29002 ^ _780205) ^ [_1299186, _1299188, _1299190, _1299192] : [_1299186 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1299188), _1299190)), _1299192), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1299186, _1299188), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1299190), _1299192)))), 29009 ^ _780205 : [(29010 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299188)))], (29012 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299192), _1299188))]], 29017 ^ _780205 : [(29018 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299188))], (29020 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299188), _1299192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1299192), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (29028 ^ _780205) ^ [_1299648, _1299650, _1299652, _1299654, _1299656] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1299648, _1299650), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1299652), _1299654))), -(_1299650 = 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), _1299656), _1299648), _1299650), 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), _1299656), _1299652)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1299656), _1299654)), _1299650))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1299656), _1299654), _1299650)))))], (29038 ^ _780205) ^ [_1299870, _1299872] : [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), _1299870), _1299872))), 29041 ^ _780205 : [(29042 ^ _780205) ^ [] : [29043 ^ _780205 : [(29044 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299870), _1299872))], (29046 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1299872), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1299870, _1299872) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299870))], (29050 ^ _780205) ^ [] : [-(c_Divides_OposDivAlg(_1299870, _1299872) = hAPP(c_Divides_Oadjust(_1299872), c_Divides_OposDivAlg(_1299870, 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)))), _1299872)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299870), _1299872))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1299872), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29060 ^ _780205) ^ [_1300193, _1300195, _1300197] : [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), _1300193), _1300195))), -(hBOOL(hAPP(hAPP(_1300197, _1300193), _1300195))), 29067 ^ _780205 : [(29068 ^ _780205) ^ [] : [-(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), 29065 ^ [_1300193, _1300195, _1300197]), 29066 ^ [_1300193, _1300195, _1300197]))))], (29080 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1300197, 29065 ^ [_1300193, _1300195, _1300197]), 29066 ^ [_1300193, _1300195, _1300197]))], (29070 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1300197, 29065 ^ [_1300193, _1300195, _1300197]), 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)))), 29066 ^ [_1300193, _1300195, _1300197])))), -(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), 29065 ^ [_1300193, _1300195, _1300197]), 29066 ^ [_1300193, _1300195, _1300197])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 29066 ^ [_1300193, _1300195, _1300197]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29084 ^ _780205) ^ [_1300688, _1300690, _1300692] : [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), _1300688), _1300690))), -(hBOOL(hAPP(hAPP(_1300692, _1300688), _1300690))), 29091 ^ _780205 : [(29092 ^ _780205) ^ [] : [-(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), 29089 ^ [_1300688, _1300690, _1300692]), 29090 ^ [_1300688, _1300690, _1300692]))))], (29104 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1300692, 29089 ^ [_1300688, _1300690, _1300692]), 29090 ^ [_1300688, _1300690, _1300692]))], (29094 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1300692, 29089 ^ [_1300688, _1300690, _1300692]), 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)))), 29090 ^ [_1300688, _1300690, _1300692])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 29089 ^ [_1300688, _1300690, _1300692]), 29090 ^ [_1300688, _1300690, _1300692]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 29090 ^ [_1300688, _1300690, _1300692]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29108 ^ _780205) ^ [_1301174, _1301176, _1301178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301174, tc_fun(_1301174, tc_HOL_Obool))), _1301176), _1301178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301174, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1301174, _1301178)), c_Wellfounded_Oaccp(_1301174, _1301176))))], (29114 ^ _780205) ^ [_1301311, _1301313, _1301315, _1301317, _1301319, _1301321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301311, tc_fun(_1301313, tc_HOL_Obool))), _1301315), _1301317)), hBOOL(hAPP(hAPP(_1301315, _1301319), _1301321)), -(hBOOL(hAPP(hAPP(_1301317, _1301319), _1301321)))], (29124 ^ _780205) ^ [_1301502, _1301504, _1301506, _1301508, _1301510, _1301512] : [hBOOL(hAPP(hAPP(_1301502, _1301504), _1301506)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301508, tc_fun(_1301510, tc_HOL_Obool))), _1301502), _1301512)), -(hBOOL(hAPP(hAPP(_1301512, _1301504), _1301506)))], (29144 ^ _780205) ^ [_1301897, _1301899, _1301901] : [29146 ^ _780205 : [(29147 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1301899, 29145 ^ [_1301897, _1301899, _1301901]), _1301901)))], (29149 ^ _780205) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1301897, _1301899), 29145 ^ [_1301897, _1301899, _1301901]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1301897, _1301899), _1301901)))], (29134 ^ _780205) ^ [_1301711, _1301713, _1301715] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1301711, _1301713), _1301715)), 29137 ^ _780205 : [(29138 ^ _780205) ^ [_1301796] : [hBOOL(hAPP(hAPP(_1301713, _1301796), _1301715)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1301711, _1301713), _1301796)))]]], (29163 ^ _780205) ^ [_1302287, _1302289, _1302291] : [29165 ^ _780205 : [(29166 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1302289, 29164 ^ [_1302287, _1302289, _1302291]), _1302291)))], (29168 ^ _780205) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1302287, _1302289), 29164 ^ [_1302287, _1302289, _1302291]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1302287, _1302289), _1302291)))], (29153 ^ _780205) ^ [_1302101, _1302103, _1302105] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1302101, _1302103), _1302105)), 29156 ^ _780205 : [(29157 ^ _780205) ^ [_1302186] : [hBOOL(hAPP(hAPP(_1302103, _1302186), _1302105)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1302101, _1302103), _1302186)))]]], (29172 ^ _780205) ^ [_1302473, _1302475, _1302477, _1302479] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1302473, _1302475), _1302477)), hBOOL(hAPP(hAPP(_1302475, _1302479), _1302477)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1302473, _1302475), _1302479)))], (29182 ^ _780205) ^ [_1302640, _1302642] : [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), _1302640), _1302642))), 29185 ^ _780205 : [(29186 ^ _780205) ^ [] : [_1302642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1302640, _1302642) = _1302640)], (29192 ^ _780205) ^ [] : [-(_1302642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1302640, _1302642) = c_Nitpick_Onat__gcd(_1302642, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1302640, _1302642)))]]], (29198 ^ _780205) ^ [_1302858] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1302858)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1302858)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29200 ^ _780205) ^ [_1302915, _1302917, _1302919, _1302921] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1302915, _1302915)), hAPP(hAPP(c_Product__Type_OPair(_1302915, _1302915), _1302917), _1302919)), hAPP(c_Wellfounded_Omeasure(_1302915), _1302921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1302921, _1302917)), hAPP(_1302921, _1302919))))], (29206 ^ _780205) ^ [_1303062, _1303064, _1303066, _1303068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1303068, _1303064)), hAPP(_1303068, _1303066))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1303062, _1303062)), hAPP(hAPP(c_Product__Type_OPair(_1303062, _1303062), _1303064), _1303066)), hAPP(c_Wellfounded_Omeasure(_1303062), _1303068))))], (29212 ^ _780205) ^ [_1303215, _1303217, _1303219, _1303221, _1303223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1303215, _1303217)), hAPP(_1303215, _1303219))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1303221, _1303221)), hAPP(hAPP(c_Product__Type_OPair(_1303221, _1303221), _1303217), _1303219)), _1303223)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1303221, _1303221)), hAPP(hAPP(c_Product__Type_OPair(_1303221, _1303221), _1303217), _1303219)), c_Wellfounded_Omlex__prod(_1303221, _1303215, _1303223))))], (29222 ^ _780205) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29224 ^ _780205) ^ [_1303480, _1303482, _1303484, _1303486, _1303488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1303480, _1303482)), hAPP(_1303480, _1303484))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1303486, _1303486)), hAPP(hAPP(c_Product__Type_OPair(_1303486, _1303486), _1303482), _1303484)), c_Wellfounded_Omlex__prod(_1303486, _1303480, _1303488))))], (29230 ^ _780205) ^ [_1303631, _1303633, _1303635] : [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), _1303631), _1303633))), -(hBOOL(hAPP(hAPP(_1303635, _1303631), _1303633))), 29237 ^ _780205 : [(29238 ^ _780205) ^ [] : [-(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), 29235 ^ [_1303631, _1303633, _1303635]), 29236 ^ [_1303631, _1303633, _1303635]))))], (29246 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1303635, 29235 ^ [_1303631, _1303633, _1303635]), 29236 ^ [_1303631, _1303633, _1303635]))], (29240 ^ _780205) ^ [] : [-(29236 ^ [_1303631, _1303633, _1303635] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1303635, 29236 ^ [_1303631, _1303633, _1303635]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 29235 ^ [_1303631, _1303633, _1303635], 29236 ^ [_1303631, _1303633, _1303635]))))]]], (29250 ^ _780205) ^ [_1304053] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1304053)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1304053)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29278 ^ _780205) ^ [_1304470, _1304472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1304470))), 29281 ^ _780205 : [(29282 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1304472)), -(c_Divides_Odivmod__int(_1304470, _1304472) = c_Divides_OnegDivAlg(_1304470, _1304472))], (29288 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1304472))), -(c_Divides_Odivmod__int(_1304470, _1304472) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1304470), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1304472))))]]], (29252 ^ _780205) ^ [_1304100, _1304102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1304100)), 29255 ^ _780205 : [(29256 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1304102)), -(c_Divides_Odivmod__int(_1304100, _1304102) = c_Divides_OposDivAlg(_1304100, _1304102))], (29262 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1304102))), 29265 ^ _780205 : [(29266 ^ _780205) ^ [] : [_1304100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1304100, _1304102) = 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)))], (29272 ^ _780205) ^ [] : [-(_1304100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1304100, _1304102) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1304100), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1304102))))]]]]], (29294 ^ _780205) ^ [_1304698] : [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), _1304698))), -(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), _1304698)) = 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), _1304698))))], (29300 ^ _780205) ^ [_1304815, _1304817] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304815, _1304817) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1304815, _1304817)))], (29302 ^ _780205) ^ [_1304850] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1304850) = _1304850)], (29304 ^ _780205) ^ [] : [-(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))], (29306 ^ _780205) ^ [_1304894, _1304896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1304894)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1304896), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304894, _1304896) = 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), _1304894), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1304896)))))], (29316 ^ _780205) ^ [_1305075, _1305077] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1305075), _1305077)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1305075), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1305077)))], (29318 ^ _780205) ^ [_1305118, _1305120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1305118), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1305120), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1305118, _1305120) = 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), _1305118), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1305120)))))], (29328 ^ _780205) ^ [_1305305, _1305307, _1305309] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1305305), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1305307)), _1305309)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1305305, _1305307), hAPP(c_Divides_OnegateSnd, _1305309))))], (29334 ^ _780205) ^ [_1305422, _1305424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1305422), 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)), _1305424)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1305422, _1305424) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1305422, _1305424)))], (29344 ^ _780205) ^ [_1305581, _1305583] : [-(_1305581 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1305583, _1305581), c_Divides_Odivmod__int(_1305583, _1305581))))], (29350 ^ _780205) ^ [_1305625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1305625)), 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), _1305625)) = 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), _1305625))))))], (29356 ^ _780205) ^ [_1305760, _1305762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1305760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1305762)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1305760, _1305762) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1305760, _1305762)))], (29366 ^ _780205) ^ [_1305917, _1305919] : [-(c_Divides_Odivmod__int(_1305917, _1305919) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1305917), _1305919)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1305917, _1305919)))], (29368 ^ _780205) ^ [_1305961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1305961)), 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), _1305961)) = 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), _1305961))))))], (29374 ^ _780205) ^ [_1306094, _1306096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306094), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1306096), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1306094), _1306096) = 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), _1306094), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1306096)))))], (29384 ^ _780205) ^ [_1306285, _1306287, _1306289, _1306291, _1306293] : [hAPP(c_Product__Type_Osnd(_1306285, _1306287), hAPP(hAPP(c_Product__Type_OPair(_1306285, _1306287), _1306289), _1306291)) = _1306293, -(_1306291 = _1306293)], (29390 ^ _780205) ^ [_1306398, _1306400, _1306402, _1306404] : [-(hAPP(c_Product__Type_Osnd(_1306398, _1306400), hAPP(hAPP(c_Product__Type_OPair(_1306398, _1306400), _1306402), _1306404)) = _1306404)], (29392 ^ _780205) ^ [_1306463, _1306465, _1306467, _1306469] : [_1306463 = _1306465, 29395 ^ _780205 : [(29396 ^ _780205) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1306467, _1306469), _1306463) = hAPP(c_Product__Type_Ofst(_1306467, _1306469), _1306465))], (29398 ^ _780205) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1306467, _1306469), _1306463) = hAPP(c_Product__Type_Osnd(_1306467, _1306469), _1306465))]]], (29400 ^ _780205) ^ [_1306614, _1306616, _1306618, _1306620] : [-(_1306614 = _1306616), hAPP(c_Product__Type_Ofst(_1306618, _1306620), _1306614) = hAPP(c_Product__Type_Ofst(_1306618, _1306620), _1306616), hAPP(c_Product__Type_Osnd(_1306618, _1306620), _1306614) = hAPP(c_Product__Type_Osnd(_1306618, _1306620), _1306616)], (29410 ^ _780205) ^ [_1306801, _1306803, _1306805, _1306807] : [hAPP(c_Product__Type_Ofst(_1306801, _1306803), _1306805) = hAPP(c_Product__Type_Ofst(_1306801, _1306803), _1306807), hAPP(c_Product__Type_Osnd(_1306801, _1306803), _1306805) = hAPP(c_Product__Type_Osnd(_1306801, _1306803), _1306807), -(_1306805 = _1306807)], (29420 ^ _780205) ^ [_1306986, _1306988, _1306990, _1306992] : [-(hAPP(c_Product__Type_Ofst(_1306986, _1306988), hAPP(hAPP(c_Product__Type_OPair(_1306986, _1306988), _1306990), _1306992)) = _1306990)], (29422 ^ _780205) ^ [_1307030, _1307032, _1307034, _1307036, _1307038] : [hAPP(c_Product__Type_Ofst(_1307030, _1307032), hAPP(hAPP(c_Product__Type_OPair(_1307030, _1307032), _1307034), _1307036)) = _1307038, -(_1307034 = _1307038)], (29428 ^ _780205) ^ [_1307143, _1307145, _1307147] : [-(_1307143 = hAPP(hAPP(c_Product__Type_OPair(_1307145, _1307147), hAPP(c_Product__Type_Ofst(_1307145, _1307147), _1307143)), hAPP(c_Product__Type_Osnd(_1307145, _1307147), _1307143)))], (29430 ^ _780205) ^ [_1307191, _1307193, _1307195] : [-(hAPP(hAPP(c_Product__Type_OPair(_1307191, _1307193), hAPP(c_Product__Type_Ofst(_1307191, _1307193), _1307195)), hAPP(c_Product__Type_Osnd(_1307191, _1307193), _1307195)) = _1307195)], (29432 ^ _780205) ^ [_1307239, _1307241] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1307239), _1307241) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1307239, _1307241)))], (29434 ^ _780205) ^ [_1307276, _1307278] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1307276, _1307278) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1307276, _1307278)))], (29436 ^ _780205) ^ [_1307311, _1307313, _1307315, _1307317, _1307319, _1307321] : [hAPP(hAPP(c_Product__Type_OPair(_1307311, _1307313), _1307315), _1307317) = hAPP(hAPP(c_Product__Type_OPair(_1307311, _1307313), _1307319), _1307321), 29439 ^ _780205 : [(29440 ^ _780205) ^ [] : [-(_1307315 = _1307319)], (29442 ^ _780205) ^ [] : [-(_1307317 = _1307321)]]], (29444 ^ _780205) ^ [_1307489, _1307491, _1307493, _1307495, _1307497, _1307499] : [hAPP(hAPP(c_Product__Type_OPair(_1307489, _1307491), _1307493), _1307495) = hAPP(hAPP(c_Product__Type_OPair(_1307489, _1307491), _1307497), _1307499), 29447 ^ _780205 : [(29448 ^ _780205) ^ [] : [-(_1307493 = _1307497)], (29450 ^ _780205) ^ [] : [-(_1307495 = _1307499)]]], (29452 ^ _780205) ^ [_1307632, _1307634, _1307636, _1307638, _1307640, _1307642] : [-(hAPP(hAPP(c_Product__Type_OPair(_1307632, _1307634), _1307636), _1307638) = hAPP(hAPP(c_Product__Type_OPair(_1307632, _1307634), _1307640), _1307642)), _1307636 = _1307640, _1307638 = _1307642], (29462 ^ _780205) ^ [_1307833, _1307835, _1307837] : [hBOOL(hAPP(_1307833, 29463 ^ [_1307833, _1307835, _1307837])), 29466 ^ _780205 : [(29467 ^ _780205) ^ [_1307944, _1307946] : [-(hBOOL(hAPP(_1307833, hAPP(hAPP(c_Product__Type_OPair(_1307835, _1307837), _1307946), _1307944))))]]], (29469 ^ _780205) ^ [_1307980, _1307982, _1307984] : [hBOOL(hAPP(_1307980, hAPP(hAPP(c_Product__Type_OPair(_1307982, _1307984), 29470 ^ [_1307980, _1307982, _1307984]), 29471 ^ [_1307980, _1307982, _1307984]))), 29474 ^ _780205 : [(29475 ^ _780205) ^ [_1308127] : [-(hBOOL(hAPP(_1307980, _1308127)))]]], (29477 ^ _780205) ^ [_1308158, _1308160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1308158), 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)), _1308160)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1308158), _1308160) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1308158, _1308160)))], (29487 ^ _780205) ^ [_1308325, _1308327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1308325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1308327)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1308325), _1308327) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1308325, _1308327)))], (29497 ^ _780205) ^ [_1308486] : [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), _1308486))), -(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), _1308486)) = 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), _1308486))))], (29503 ^ _780205) ^ [_1308601, _1308603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1308601)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1308603), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1308601), _1308603) = 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), _1308601), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1308603)))))], (29513 ^ _780205) ^ [_1308786, _1308788, _1308790, _1308792, _1308794] : [-(c_Product__Type_Oprod_Oprod__size(_1308786, _1308788, _1308790, _1308792, _1308794) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1308790, hAPP(c_Product__Type_Ofst(_1308786, _1308788), _1308794))), hAPP(_1308792, hAPP(c_Product__Type_Osnd(_1308786, _1308788), _1308794)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29515 ^ _780205) ^ [_1308853, _1308855, _1308857, _1308859, _1308861, _1308863] : [hBOOL(hAPP(_1308853, _1308855)), hBOOL(hAPP(_1308857, _1308859)), 29522 ^ _780205 : [(29523 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1308853, hAPP(c_Product__Type_Ofst(_1308861, _1308863), hAPP(hAPP(c_Product__Type_OPair(_1308861, _1308863), _1308855), _1308859)))))], (29525 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1308857, hAPP(c_Product__Type_Osnd(_1308861, _1308863), hAPP(hAPP(c_Product__Type_OPair(_1308861, _1308863), _1308855), _1308859)))))]]], (29527 ^ _780205) ^ [_1309100, _1309102, _1309104, _1309106, _1309108] : [hBOOL(hAPP(hAPP(_1309100, _1309102), _1309104)), -(hBOOL(hAPP(hAPP(_1309100, hAPP(c_Product__Type_Osnd(_1309106, _1309108), hAPP(hAPP(c_Product__Type_OPair(_1309106, _1309108), _1309104), _1309102))), hAPP(c_Product__Type_Ofst(_1309106, _1309108), hAPP(hAPP(c_Product__Type_OPair(_1309106, _1309108), _1309104), _1309102)))))], (29533 ^ _780205) ^ [_1309263, _1309265, _1309267, _1309269, _1309271, _1309273] : [-(c_Product__Type_Oprod_Oprod__rec(_1309263, _1309265, _1309267, _1309269, hAPP(hAPP(c_Product__Type_OPair(_1309263, _1309265), _1309271), _1309273)) = hAPP(hAPP(_1309269, _1309271), _1309273))], (29535 ^ _780205) ^ [_1309317, _1309319] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1309317), _1309319) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1309317, _1309319)))], (29569 ^ _780205) ^ [_1309908, _1309910, _1309912] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1309908, _1309910), _1309912))), _1309908 = 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), _1309912)), _1309910)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1309912)), 29576 ^ _780205 : [(29577 ^ _780205) ^ [] : [-(_1309910 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29579 ^ _780205) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1309912) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 29580 ^ _780205 : [(29581 ^ _780205) ^ [] : [_1309910 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29583 ^ _780205) ^ [] : [29584 ^ _780205 : [(29585 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1309910)))], (29587 ^ _780205) ^ [] : [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), _1309912))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1309912)), _1309910))]], 29592 ^ _780205 : [(29593 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1309910))], (29595 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1309910), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1309912))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1309912)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (29537 ^ _780205) ^ [_1309372, _1309374, _1309376] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1309372, _1309374), _1309376)), 29540 ^ _780205 : [(29541 ^ _780205) ^ [] : [-(_1309372 = 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), _1309376)), _1309374)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1309376)))], (29543 ^ _780205) ^ [] : [_1309374 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1309376) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29549 ^ _780205) ^ [] : [-(_1309374 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29552 ^ _780205 : [(29553 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1309374)), 29556 ^ _780205 : [(29557 ^ _780205) ^ [] : [-(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), _1309376))))], (29559 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1309376)), _1309374)))]]], (29561 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1309374))), 29564 ^ _780205 : [(29565 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1309374), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1309376))))], (29567 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1309376)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (29603 ^ _780205) ^ [_1310517, _1310519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1310517)), -(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(_1310517), _1310519))), _1310517)))], (29609 ^ _780205) ^ [_1310657, _1310659, _1310661, _1310663, _1310665, _1310667, _1310669, _1310671] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1310657, _1310659), tc_prod(_1310657, _1310659))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1310657, _1310659), tc_prod(_1310657, _1310659)), hAPP(hAPP(c_Product__Type_OPair(_1310657, _1310659), _1310661), _1310663)), hAPP(hAPP(c_Product__Type_OPair(_1310657, _1310659), _1310665), _1310667))), c_Wellfounded_Olex__prod(_1310657, _1310659, _1310669, _1310671))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1310657, _1310657)), hAPP(hAPP(c_Product__Type_OPair(_1310657, _1310657), _1310661), _1310665)), _1310669))), 29616 ^ _780205 : [(29617 ^ _780205) ^ [] : [-(_1310661 = _1310665)], (29619 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1310659, _1310659)), hAPP(hAPP(c_Product__Type_OPair(_1310659, _1310659), _1310663), _1310667)), _1310671)))]]], (29621 ^ _780205) ^ [_1310982, _1310984, _1310986, _1310988, _1310990, _1310992, _1310994, _1310996] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1310982, _1310984), tc_prod(_1310982, _1310984))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1310982, _1310984), tc_prod(_1310982, _1310984)), hAPP(hAPP(c_Product__Type_OPair(_1310982, _1310984), _1310986), _1310988)), hAPP(hAPP(c_Product__Type_OPair(_1310982, _1310984), _1310990), _1310992))), c_Wellfounded_Olex__prod(_1310982, _1310984, _1310994, _1310996)))), 29622 ^ _780205 : [(29623 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1310982, _1310982)), hAPP(hAPP(c_Product__Type_OPair(_1310982, _1310982), _1310986), _1310990)), _1310994))], (29625 ^ _780205) ^ [] : [_1310986 = _1310990, hBOOL(hAPP(hAPP(c_member(tc_prod(_1310984, _1310984)), hAPP(hAPP(c_Product__Type_OPair(_1310984, _1310984), _1310988), _1310992)), _1310996))]]], (29633 ^ _780205) ^ [_1311375, _1311377, _1311379] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1311375, tc_HOL_Obool), tc_fun(_1311375, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1311375, tc_HOL_Obool), tc_fun(_1311375, tc_HOL_Obool)), _1311377), _1311379)), c_Wellfounded_Ofinite__psubset(_1311375))), 29636 ^ _780205 : [(29637 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1311375, tc_HOL_Obool)), _1311377), _1311379)))], (29639 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311375), _1311379)))]]], (29641 ^ _780205) ^ [_1311570, _1311572, _1311574] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1311570, tc_HOL_Obool), tc_fun(_1311570, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1311570, tc_HOL_Obool), tc_fun(_1311570, tc_HOL_Obool)), _1311572), _1311574)), c_Wellfounded_Ofinite__psubset(_1311570)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1311570, tc_HOL_Obool)), _1311572), _1311574)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311570), _1311574))], (29651 ^ _780205) ^ [_1311799, _1311801, _1311803, _1311805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1311799), _1311801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1311803), _1311805)), -(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), _1311799), _1311803)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1311801), _1311805))), c_FunDef_Opair__less)))], (29661 ^ _780205) ^ [_1312002, _1312004, _1312006, _1312008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1312002), _1312004)), -(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), _1312002), _1312006)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1312004), _1312008))), c_FunDef_Opair__less)))], (29667 ^ _780205) ^ [_1312139, _1312141, _1312143, _1312145, _1312147, _1312149, _1312151] : [hBOOL(hAPP(_1312139, _1312141)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1312143, _1312143)), hAPP(hAPP(c_Product__Type_OPair(_1312143, _1312143), _1312145), _1312147)), hAPP(_1312149, _1312141))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1312151, _1312143), tc_prod(_1312151, _1312143))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1312151, _1312143), tc_prod(_1312151, _1312143)), hAPP(hAPP(c_Product__Type_OPair(_1312151, _1312143), _1312141), _1312145)), hAPP(hAPP(c_Product__Type_OPair(_1312151, _1312143), _1312141), _1312147))), c_Recdef_Osame__fst(_1312151, _1312143, _1312139, _1312149))))], (29677 ^ _780205) ^ [_1312444, _1312446, _1312448, _1312450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1312444), _1312446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1312448), _1312450)), -(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), _1312444), _1312448)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1312446), _1312450))), c_FunDef_Opair__leq)))], (29687 ^ _780205) ^ [_1312647, _1312649, _1312651, _1312653] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1312647), _1312649)), 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)), _1312651), _1312647)), 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)), _1312653), _1312649)), 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)), _1312651), _1312653)), _1312649)), c_FunDef_Omax__strict)))], (29701 ^ _780205) ^ [_1312928, _1312930, _1312932, _1312934] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1312928), _1312930)), 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)), _1312928), _1312932)), 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)), _1312930), _1312934)), 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)), _1312930), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1312932), _1312934))), c_FunDef_Omin__strict)))], (29715 ^ _780205) ^ [_1313205] : [-(_1313205 = 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)), _1313205), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (29721 ^ _780205) ^ [_1313250] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1313250)), -(_1313250 = 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))), _1313250)), c_FunDef_Omax__strict)))], (29731 ^ _780205) ^ [_1313360, _1313362, _1313364, _1313366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1313360), _1313362)), -(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), _1313360), _1313364)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1313362), _1313366))), c_FunDef_Opair__leq)))], (29737 ^ _780205) ^ [_1313497, _1313499, _1313501, _1313503] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1313497), _1313499)), 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)), _1313497), _1313501)), 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)), _1313499), _1313503)), 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)), _1313499), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1313501), _1313503))), c_FunDef_Omin__weak)))], (29751 ^ _780205) ^ [_1313778, _1313780, _1313782, _1313784] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1313778), _1313780)), 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)), _1313782), _1313778)), 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)), _1313784), _1313780)), 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)), _1313782), _1313784)), _1313780)), c_FunDef_Omax__weak)))], (29765 ^ _780205) ^ [_1314059] : [-(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)), _1314059), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (29767 ^ _780205) ^ [_1314093] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1314093)), -(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))), _1314093)), c_FunDef_Omax__weak)))], (29773 ^ _780205) ^ [_1314188, _1314190, _1314192] : [_1314188 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1314190, _1314190), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1314190, _1314190), tc_HOL_Obool)), _1314188), _1314192)))], (29779 ^ _780205) ^ [] : [-(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)))))], (29781 ^ _780205) ^ [] : [-(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)))))], (29783 ^ _780205) ^ [] : [-(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)))], (29785 ^ _780205) ^ [] : [-(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)))], (29787 ^ _780205) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (29789 ^ _780205) ^ [_1314399, _1314401, _1314403, _1314405, _1314407, _1314409] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1314399, tc_HOL_Obool), tc_fun(_1314399, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1314399, tc_HOL_Obool), tc_fun(_1314399, tc_HOL_Obool)), _1314401), _1314403)), c_Wellfounded_Omax__ext(_1314399, _1314405))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1314399, tc_HOL_Obool), tc_fun(_1314399, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1314399, tc_HOL_Obool), tc_fun(_1314399, tc_HOL_Obool)), _1314407), _1314409)), c_Wellfounded_Omax__ext(_1314399, _1314405))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1314399, tc_HOL_Obool), tc_fun(_1314399, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1314399, tc_HOL_Obool), tc_fun(_1314399, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1314399, tc_HOL_Obool)), _1314401), _1314407)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1314399, tc_HOL_Obool)), _1314403), _1314409))), c_Wellfounded_Omax__ext(_1314399, _1314405))))], (29799 ^ _780205) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (29801 ^ _780205) ^ [_1314825, _1314827] : [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), _1314825), _1314827)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1314825), _1314827)))], (29807 ^ _780205) ^ [_1314930, _1314932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1314930), _1314932)), -(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), _1314930), _1314932)), c_Wellfounded_Oless__than)))], (29813 ^ _780205) ^ [_1315062, _1315064, _1315066, _1315068] : [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), _1315062), _1315064)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1315066), _1315068))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1315062), _1315068) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1315066), _1315064))], (29819 ^ _780205) ^ [_1315209, _1315211, _1315213, _1315215] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1315209), _1315215) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1315213), _1315211), -(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), _1315209), _1315211)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1315213), _1315215))), c_Int_Ointrel)))], (29825 ^ _780205) ^ [_1315362, _1315364, _1315366, _1315368] : [c_FunDef_Oreduction__pair(_1315362, _1315364), -(c_FunDef_Oreduction__pair(_1315366, hAPP(hAPP(c_FunDef_Orp__inv__image(_1315362, _1315366), _1315364), _1315368)))], (29831 ^ _780205) ^ [_1315461, _1315463, _1315465, _1315467] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1315461), _1315463)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315461), _1315465)), -(_1315465 = c_Orderings_Obot__class_Obot(tc_fun(_1315461, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1315461, tc_HOL_Obool), tc_fun(_1315461, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1315461, tc_HOL_Obool), tc_fun(_1315461, tc_HOL_Obool)), _1315463), _1315465)), c_Wellfounded_Omax__ext(_1315461, _1315467)))), 29845 ^ _780205 : [(29846 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1315461), 29844 ^ [_1315461, _1315463, _1315465, _1315467]), _1315463)))], (29848 ^ _780205) ^ [_1315866] : [hBOOL(hAPP(hAPP(c_member(_1315461), _1315866), _1315465)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1315461, _1315461)), hAPP(hAPP(c_Product__Type_OPair(_1315461, _1315461), 29844 ^ [_1315461, _1315463, _1315465, _1315467]), _1315866)), _1315467))]]], (29856 ^ _780205) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (29858 ^ _780205) ^ [_1316125, _1316127] : [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)), _1316125), 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)), _1316127), 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)), _1316125), _1316127)), c_Int_Ointrel)))], (29864 ^ _780205) ^ [_1316256, _1316258] : [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)), _1316256), _1316258)), 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)), _1316256), 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)), _1316258), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (29870 ^ _780205) ^ [_1316393] : [-(c_Nitpick_Ozero__frac(_1316393) = c_Nitpick_OAbs__Frac(_1316393, 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))))], (29872 ^ _780205) ^ [_1316421] : [-(c_Wellfounded_Omeasure(_1316421) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1316421), c_Wellfounded_Oless__than))], (29874 ^ _780205) ^ [_1316452, _1316454, _1316456] : [-(hAPP(c_Divides_Oadjust(_1316452), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1316454), _1316456)) = 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), _1316456), _1316452)), 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)))), _1316454)), 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)))), _1316454)), _1316456))))], (29876 ^ _780205) ^ [_1316532, _1316534, _1316536, _1316538] : [class_Groups_Oordered__ab__group__add__abs(_1316532), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316532), hAPP(c_Groups_Oabs__class_Oabs(_1316532), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316534, _1316532), _1316536), _1316538))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316534, _1316532), hAPP(hAPP(c_COMBB(_1316532, _1316532, _1316534), c_Groups_Oabs__class_Oabs(_1316532)), _1316536)), _1316538))))], (29882 ^ _780205) ^ [_1316695, _1316697, _1316699, _1316701] : [class_Groups_Oordered__ab__group__add__abs(_1316695), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316695), c_Groups_Ozero__class_Ozero(_1316695)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316697, _1316695), hAPP(hAPP(c_COMBB(_1316695, _1316695, _1316697), c_Groups_Oabs__class_Oabs(_1316695)), _1316699)), _1316701))))], (29888 ^ _780205) ^ [_1316834, _1316836, _1316838, _1316840, _1316842] : [class_Groups_Ocomm__monoid__mult(_1316834), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316836), _1316838)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1316836, _1316834), hAPP(hAPP(c_COMBS(_1316836, _1316834, _1316834), hAPP(hAPP(c_COMBB(_1316834, tc_fun(_1316834, _1316834), _1316836), c_Groups_Otimes__class_Otimes(_1316834)), _1316840)), _1316842)), _1316838) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1316834), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1316836, _1316834), _1316840), _1316838)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1316836, _1316834), _1316842), _1316838)))], (29898 ^ _780205) ^ [_1317101, _1317103, _1317105, _1317107, _1317109] : [class_Groups_Ocomm__monoid__add(_1317101), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317103), _1317105)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1317103, _1317101), hAPP(hAPP(c_COMBS(_1317103, _1317101, _1317101), hAPP(hAPP(c_COMBB(_1317101, tc_fun(_1317101, _1317101), _1317103), c_Groups_Oplus__class_Oplus(_1317101)), _1317107)), _1317109)), _1317105) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1317101), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1317103, _1317101), _1317107), _1317105)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1317103, _1317101), _1317109), _1317105)))], (29908 ^ _780205) ^ [_1317368, _1317370, _1317372, _1317374, _1317376] : [class_Fields_Ofield__inverse__zero(_1317368), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317370), _1317372)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317370, _1317368), hAPP(hAPP(c_COMBS(_1317370, _1317368, _1317368), hAPP(hAPP(c_COMBB(_1317368, tc_fun(_1317368, _1317368), _1317370), c_Rings_Oinverse__class_Odivide(_1317368)), _1317374)), _1317376)), _1317372) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1317368), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317370, _1317368), _1317374), _1317372)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317370, _1317368), _1317376), _1317372)))], (29918 ^ _780205) ^ [_1317635] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1317635)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1317635)), 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))))], (29920 ^ _780205) ^ [_1317672, _1317674, _1317676, _1317678] : [class_Groups_Oab__group__add(_1317672), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1317674, _1317672), hAPP(hAPP(c_COMBB(_1317672, _1317672, _1317674), c_Groups_Ouminus__class_Ouminus(_1317672)), _1317676)), _1317678) = hAPP(c_Groups_Ouminus__class_Ouminus(_1317672), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1317674, _1317672), _1317676), _1317678)))], (29926 ^ _780205) ^ [_1317821, _1317823, _1317825, _1317827] : [class_Groups_Ouminus(_1317821), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1317823, _1317821)), _1317825), _1317827) = hAPP(c_Groups_Ouminus__class_Ouminus(_1317821), hAPP(_1317825, _1317827)))], (29932 ^ _780205) ^ [_1317938, _1317940, _1317942] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317938, tc_Nat_Onat), _1317940), _1317942)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317938, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1317938), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1317940)), _1317942))], (29934 ^ _780205) ^ [_1317996, _1317998, _1318000] : [class_Groups_Ocomm__monoid__mult(_1317996), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317998, _1317996), hAPP(c_COMBK(_1317996, _1317998), c_Groups_Oone__class_Oone(_1317996))), _1318000) = c_Groups_Oone__class_Oone(_1317996))], (29940 ^ _780205) ^ [_1318111, _1318113, _1318115, _1318117] : [class_Groups_Oordered__ab__group__add__abs(_1318111), -(hAPP(c_Groups_Oabs__class_Oabs(_1318111), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318113, _1318111), hAPP(hAPP(c_COMBB(_1318111, _1318111, _1318113), c_Groups_Oabs__class_Oabs(_1318111)), _1318115)), _1318117)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318113, _1318111), hAPP(hAPP(c_COMBB(_1318111, _1318111, _1318113), c_Groups_Oabs__class_Oabs(_1318111)), _1318115)), _1318117))], (29946 ^ _780205) ^ [_1318284, _1318286, _1318288, _1318290] : [class_Fields_Olinordered__field(_1318284), -(hAPP(c_Groups_Oabs__class_Oabs(_1318284), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318286, _1318284), _1318288), _1318290)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1318286, _1318284), hAPP(hAPP(c_COMBB(_1318284, _1318284, _1318286), c_Groups_Oabs__class_Oabs(_1318284)), _1318288)), _1318290))], (29952 ^ _780205) ^ [_1318433, _1318435, _1318437, _1318439, _1318441] : [class_Rings_Osemiring__0(_1318433), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318433), _1318435), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318437, _1318433), _1318439), _1318441)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318437, _1318433), hAPP(hAPP(c_COMBB(_1318433, _1318433, _1318437), hAPP(c_Groups_Otimes__class_Otimes(_1318433), _1318435)), _1318439)), _1318441))], (29958 ^ _780205) ^ [_1318596, _1318598, _1318600, _1318602, _1318604] : [class_Rings_Osemiring__0(_1318596), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318596), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318598, _1318596), _1318600), _1318602)), _1318604) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318598, _1318596), hAPP(hAPP(c_COMBC(_1318598, _1318596, _1318596), hAPP(hAPP(c_COMBB(_1318596, tc_fun(_1318596, _1318596), _1318598), c_Groups_Otimes__class_Otimes(_1318596)), _1318600)), _1318604)), _1318602))], (29964 ^ _780205) ^ [_1318779, _1318781, _1318783, _1318785, _1318787, _1318789, _1318791] : [class_Rings_Osemiring__0(_1318779), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318779), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318781, _1318779), _1318783), _1318785)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318787, _1318779), _1318789), _1318791)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318781, _1318779), hAPP(hAPP(c_COMBC(_1318781, tc_fun(_1318787, tc_HOL_Obool), _1318779), hAPP(hAPP(c_COMBB(tc_fun(_1318787, _1318779), tc_fun(tc_fun(_1318787, tc_HOL_Obool), _1318779), _1318781), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318787, _1318779)), hAPP(hAPP(c_COMBC(_1318781, tc_fun(_1318787, _1318779), tc_fun(_1318787, _1318779)), hAPP(hAPP(c_COMBB(tc_fun(_1318779, _1318779), tc_fun(tc_fun(_1318787, _1318779), tc_fun(_1318787, _1318779)), _1318781), c_COMBB(_1318779, _1318779, _1318787)), hAPP(hAPP(c_COMBB(_1318779, tc_fun(_1318779, _1318779), _1318781), c_Groups_Otimes__class_Otimes(_1318779)), _1318783))), _1318789))), _1318791)), _1318785))], (29970 ^ _780205) ^ [_1319118, _1319120, _1319122, _1319124, _1319126] : [class_Lattices_Olattice(_1319118), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319120, _1319118)), _1319122), _1319124), _1319126) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319118), hAPP(_1319122, _1319126)), hAPP(_1319124, _1319126)))], (29976 ^ _780205) ^ [_1319255, _1319257, _1319259, _1319261, _1319263] : [class_Groups_Ocomm__monoid__mult(_1319255), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319257, _1319255), hAPP(hAPP(c_COMBS(_1319257, _1319255, _1319255), hAPP(hAPP(c_COMBB(_1319255, tc_fun(_1319255, _1319255), _1319257), c_Groups_Otimes__class_Otimes(_1319255)), _1319259)), _1319261)), _1319263) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319255), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319257, _1319255), _1319259), _1319263)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319257, _1319255), _1319261), _1319263)))], (29982 ^ _780205) ^ [_1319456, _1319458, _1319460, _1319462, _1319464] : [c_Finite__Set_Ofun__left__comm(_1319456, _1319458, _1319460), -(c_Finite__Set_Ofun__left__comm(_1319462, _1319458, hAPP(hAPP(c_COMBB(_1319456, tc_fun(_1319458, _1319458), _1319462), _1319460), _1319464)))], (29988 ^ _780205) ^ [_1319569, _1319571, _1319573, _1319575, _1319577, _1319579] : [class_Groups_Ocomm__monoid__add(_1319569), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319571, _1319569), hAPP(hAPP(c_COMBC(_1319571, tc_fun(_1319573, tc_HOL_Obool), _1319569), hAPP(hAPP(c_COMBB(tc_fun(_1319573, _1319569), tc_fun(tc_fun(_1319573, tc_HOL_Obool), _1319569), _1319571), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319573, _1319569)), _1319575)), _1319577)), _1319579) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319573, _1319569), hAPP(hAPP(c_COMBC(_1319573, tc_fun(_1319571, tc_HOL_Obool), _1319569), hAPP(hAPP(c_COMBB(tc_fun(_1319571, _1319569), tc_fun(tc_fun(_1319571, tc_HOL_Obool), _1319569), _1319573), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319571, _1319569)), hAPP(c_COMBC(_1319571, _1319573, _1319569), _1319575))), _1319579)), _1319577))], (29994 ^ _780205) ^ [_1319842, _1319844, _1319846, _1319848, _1319850] : [c_Finite__Set_Ofun__left__comm__idem(_1319842, _1319844, _1319846), -(c_Finite__Set_Ofun__left__comm__idem(_1319848, _1319844, hAPP(hAPP(c_COMBB(_1319842, tc_fun(_1319844, _1319844), _1319848), _1319846), _1319850)))], (30000 ^ _780205) ^ [_1319955, _1319957, _1319959, _1319961, _1319963] : [class_Fields_Ofield(_1319955), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319955), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319957, _1319955), _1319959), _1319961)), _1319963) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1319957, _1319955), hAPP(hAPP(c_COMBC(_1319957, _1319955, _1319955), hAPP(hAPP(c_COMBB(_1319955, tc_fun(_1319955, _1319955), _1319957), c_Rings_Oinverse__class_Odivide(_1319955)), _1319959)), _1319963)), _1319961))], (30006 ^ _780205) ^ [_1320138, _1320140, _1320142, _1320144] : [-(hAPP(c_Finite__Set_Ofold__image(_1320138, _1320140, _1320142), _1320144) = c_Finite__Set_Ofold(_1320140, _1320138, hAPP(hAPP(c_COMBB(_1320138, tc_fun(_1320138, _1320138), _1320140), _1320142), _1320144)))], (30008 ^ _780205) ^ [_1320191, _1320193, _1320195] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320191, tc_Nat_Onat), _1320193), _1320195)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320191, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1320191), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1320193)), _1320195))], (30010 ^ _780205) ^ [_1320249, _1320251, _1320253] : [class_Groups_Ocomm__monoid__add(_1320249), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320251, _1320249), hAPP(c_COMBK(_1320249, _1320251), c_Groups_Ozero__class_Ozero(_1320249))), _1320253) = c_Groups_Ozero__class_Ozero(_1320249))], (30016 ^ _780205) ^ [_1320364, _1320366, _1320368, _1320370, _1320372] : [class_Groups_Ominus(_1320364), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320366, _1320364)), _1320368), _1320370), _1320372) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1320364), hAPP(_1320368, _1320372)), hAPP(_1320370, _1320372)))], (30022 ^ _780205) ^ [_1320501, _1320503, _1320505, _1320507, _1320509] : [class_Groups_Oab__group__add(_1320501), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320503, _1320501), hAPP(hAPP(c_COMBS(_1320503, _1320501, _1320501), hAPP(hAPP(c_COMBB(_1320501, tc_fun(_1320501, _1320501), _1320503), c_Groups_Ominus__class_Ominus(_1320501)), _1320505)), _1320507)), _1320509) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1320501), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320503, _1320501), _1320505), _1320509)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320503, _1320501), _1320507), _1320509)))], (30028 ^ _780205) ^ [_1320702, _1320704, _1320706, _1320708] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1320702), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1320704, tc_Int_Oint), _1320706), _1320708)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1320704, _1320702), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1320702, _1320704), c_Int_Oring__1__class_Oof__int(_1320702)), _1320706)), _1320708)), class_Groups_Ocomm__monoid__mult(_1320702), class_Rings_Oring__1(_1320702)], (30038 ^ _780205) ^ [_1320905, _1320907, _1320909, _1320911] : [class_Rings_Oring__1(_1320905), -(hAPP(c_Int_Oring__1__class_Oof__int(_1320905), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320907, tc_Int_Oint), _1320909), _1320911)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1320907, _1320905), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1320905, _1320907), c_Int_Oring__1__class_Oof__int(_1320905)), _1320909)), _1320911))], (30044 ^ _780205) ^ [_1321054, _1321056, _1321058, _1321060, _1321062] : [class_Groups_Ocomm__monoid__add(_1321054), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1321056, _1321054), hAPP(hAPP(c_COMBS(_1321056, _1321054, _1321054), hAPP(hAPP(c_COMBB(_1321054, tc_fun(_1321054, _1321054), _1321056), c_Groups_Oplus__class_Oplus(_1321054)), _1321058)), _1321060)), _1321062) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1321054), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1321056, _1321054), _1321058), _1321062)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1321056, _1321054), _1321060), _1321062)))], (30050 ^ _780205) ^ [_1321276, _1321278, _1321280, _1321282] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321276, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1321276, tc_fun(_1321276, tc_HOL_Obool), tc_HOL_Obool), c_member(_1321276)), _1321278)), hAPP(hAPP(c_COMBC(_1321276, tc_fun(_1321276, tc_HOL_Obool), tc_HOL_Obool), c_member(_1321276)), _1321280)), _1321282)), -(hBOOL(hAPP(hAPP(c_member(_1321276), _1321282), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321276, tc_HOL_Obool)), _1321278), _1321280))))], (30056 ^ _780205) ^ [_1321475, _1321477, _1321479, _1321481] : [hBOOL(hAPP(hAPP(c_member(_1321475), _1321481), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321475, tc_HOL_Obool)), _1321477), _1321479))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321475, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1321475, tc_fun(_1321475, tc_HOL_Obool), tc_HOL_Obool), c_member(_1321475)), _1321477)), hAPP(hAPP(c_COMBC(_1321475, tc_fun(_1321475, tc_HOL_Obool), tc_HOL_Obool), c_member(_1321475)), _1321479)), _1321481)))], (30062 ^ _780205) ^ [_1321698, _1321700, _1321702] : [hAPP(hAPP(c_COMBC(_1321698, tc_fun(_1321698, tc_HOL_Obool), tc_HOL_Obool), c_member(_1321698)), _1321700) = hAPP(hAPP(c_COMBC(_1321698, tc_fun(_1321698, tc_HOL_Obool), tc_HOL_Obool), c_member(_1321698)), _1321702), -(_1321700 = _1321702)], (30068 ^ _780205) ^ [_1321833, _1321835, _1321837] : [_1321835 = _1321837, -(hAPP(hAPP(c_COMBC(_1321833, tc_fun(_1321833, tc_HOL_Obool), tc_HOL_Obool), c_member(_1321833)), _1321835) = hAPP(hAPP(c_COMBC(_1321833, tc_fun(_1321833, tc_HOL_Obool), tc_HOL_Obool), c_member(_1321833)), _1321837))], (30074 ^ _780205) ^ [_1321992, _1321994, _1321996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1321992, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1321992, tc_fun(_1321992, tc_HOL_Obool), tc_HOL_Obool), c_member(_1321992)), _1321994)), hAPP(hAPP(c_COMBC(_1321992, tc_fun(_1321992, tc_HOL_Obool), tc_HOL_Obool), c_member(_1321992)), _1321996))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1321992, tc_HOL_Obool)), _1321994), _1321996)))], (30080 ^ _780205) ^ [_1322167, _1322169, _1322171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322167, tc_HOL_Obool)), _1322169), _1322171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322167, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1322167, tc_fun(_1322167, tc_HOL_Obool), tc_HOL_Obool), c_member(_1322167)), _1322169)), hAPP(hAPP(c_COMBC(_1322167, tc_fun(_1322167, tc_HOL_Obool), tc_HOL_Obool), c_member(_1322167)), _1322171))))], (30086 ^ _780205) ^ [_1322369, _1322371, _1322373, _1322375] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322369, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1322369, tc_fun(_1322369, tc_HOL_Obool), tc_HOL_Obool), c_member(_1322369)), _1322371)), hAPP(hAPP(c_COMBC(_1322369, tc_fun(_1322369, tc_HOL_Obool), tc_HOL_Obool), c_member(_1322369)), _1322373)), _1322375)), -(hBOOL(hAPP(hAPP(c_member(_1322369), _1322375), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322369, tc_HOL_Obool)), _1322371), _1322373))))], (30092 ^ _780205) ^ [_1322568, _1322570, _1322572, _1322574] : [hBOOL(hAPP(hAPP(c_member(_1322568), _1322574), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322568, tc_HOL_Obool)), _1322570), _1322572))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322568, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1322568, tc_fun(_1322568, tc_HOL_Obool), tc_HOL_Obool), c_member(_1322568)), _1322570)), hAPP(hAPP(c_COMBC(_1322568, tc_fun(_1322568, tc_HOL_Obool), tc_HOL_Obool), c_member(_1322568)), _1322572)), _1322574)))], (30098 ^ _780205) ^ [_1322800, _1322802, _1322804, _1322806, _1322808, _1322810] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322800, tc_fun(_1322802, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1322800, tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_fun(_1322802, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1322802, tc_fun(tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_fun(_1322802, tc_HOL_Obool)), _1322800), c_COMBC(_1322802, tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1322802, tc_prod(_1322800, _1322802)), tc_fun(_1322802, tc_fun(tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_HOL_Obool)), _1322800), hAPP(c_COMBB(tc_prod(_1322800, _1322802), tc_fun(tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_HOL_Obool), _1322802), c_member(tc_prod(_1322800, _1322802)))), c_Product__Type_OPair(_1322800, _1322802)))), _1322804)), hAPP(hAPP(c_COMBC(_1322800, tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_fun(_1322802, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1322802, tc_fun(tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_fun(_1322802, tc_HOL_Obool)), _1322800), c_COMBC(_1322802, tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1322802, tc_prod(_1322800, _1322802)), tc_fun(_1322802, tc_fun(tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_HOL_Obool)), _1322800), hAPP(c_COMBB(tc_prod(_1322800, _1322802), tc_fun(tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool), tc_HOL_Obool), _1322802), c_member(tc_prod(_1322800, _1322802)))), c_Product__Type_OPair(_1322800, _1322802)))), _1322806)), _1322808), _1322810)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1322800, _1322802)), hAPP(hAPP(c_Product__Type_OPair(_1322800, _1322802), _1322808), _1322810)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1322800, _1322802), tc_HOL_Obool)), _1322804), _1322806))))], (30104 ^ _780205) ^ [_1323457, _1323459, _1323461, _1323463, _1323465, _1323467] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1323457, _1323459)), hAPP(hAPP(c_Product__Type_OPair(_1323457, _1323459), _1323465), _1323467)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool)), _1323461), _1323463))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1323457, tc_fun(_1323459, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1323457, tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_fun(_1323459, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1323459, tc_fun(tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_fun(_1323459, tc_HOL_Obool)), _1323457), c_COMBC(_1323459, tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1323459, tc_prod(_1323457, _1323459)), tc_fun(_1323459, tc_fun(tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_HOL_Obool)), _1323457), hAPP(c_COMBB(tc_prod(_1323457, _1323459), tc_fun(tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_HOL_Obool), _1323459), c_member(tc_prod(_1323457, _1323459)))), c_Product__Type_OPair(_1323457, _1323459)))), _1323461)), hAPP(hAPP(c_COMBC(_1323457, tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_fun(_1323459, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1323459, tc_fun(tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_fun(_1323459, tc_HOL_Obool)), _1323457), c_COMBC(_1323459, tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1323459, tc_prod(_1323457, _1323459)), tc_fun(_1323459, tc_fun(tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_HOL_Obool)), _1323457), hAPP(c_COMBB(tc_prod(_1323457, _1323459), tc_fun(tc_fun(tc_prod(_1323457, _1323459), tc_HOL_Obool), tc_HOL_Obool), _1323459), c_member(tc_prod(_1323457, _1323459)))), c_Product__Type_OPair(_1323457, _1323459)))), _1323463)), _1323465), _1323467)))], (30110 ^ _780205) ^ [_1324147, _1324149, _1324151, _1324153, _1324155, _1324157] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324147, tc_fun(_1324149, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1324147, tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_fun(_1324149, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324149, tc_fun(tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_fun(_1324149, tc_HOL_Obool)), _1324147), c_COMBC(_1324149, tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324149, tc_prod(_1324147, _1324149)), tc_fun(_1324149, tc_fun(tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_HOL_Obool)), _1324147), hAPP(c_COMBB(tc_prod(_1324147, _1324149), tc_fun(tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_HOL_Obool), _1324149), c_member(tc_prod(_1324147, _1324149)))), c_Product__Type_OPair(_1324147, _1324149)))), _1324151)), hAPP(hAPP(c_COMBC(_1324147, tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_fun(_1324149, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324149, tc_fun(tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_fun(_1324149, tc_HOL_Obool)), _1324147), c_COMBC(_1324149, tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324149, tc_prod(_1324147, _1324149)), tc_fun(_1324149, tc_fun(tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_HOL_Obool)), _1324147), hAPP(c_COMBB(tc_prod(_1324147, _1324149), tc_fun(tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool), tc_HOL_Obool), _1324149), c_member(tc_prod(_1324147, _1324149)))), c_Product__Type_OPair(_1324147, _1324149)))), _1324153)), _1324155), _1324157)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1324147, _1324149)), hAPP(hAPP(c_Product__Type_OPair(_1324147, _1324149), _1324155), _1324157)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1324147, _1324149), tc_HOL_Obool)), _1324151), _1324153))))], (30116 ^ _780205) ^ [_1324804, _1324806, _1324808, _1324810, _1324812, _1324814] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1324804, _1324806)), hAPP(hAPP(c_Product__Type_OPair(_1324804, _1324806), _1324812), _1324814)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool)), _1324808), _1324810))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324804, tc_fun(_1324806, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1324804, tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_fun(_1324806, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324806, tc_fun(tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_fun(_1324806, tc_HOL_Obool)), _1324804), c_COMBC(_1324806, tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324806, tc_prod(_1324804, _1324806)), tc_fun(_1324806, tc_fun(tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_HOL_Obool)), _1324804), hAPP(c_COMBB(tc_prod(_1324804, _1324806), tc_fun(tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_HOL_Obool), _1324806), c_member(tc_prod(_1324804, _1324806)))), c_Product__Type_OPair(_1324804, _1324806)))), _1324808)), hAPP(hAPP(c_COMBC(_1324804, tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_fun(_1324806, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324806, tc_fun(tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_fun(_1324806, tc_HOL_Obool)), _1324804), c_COMBC(_1324806, tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324806, tc_prod(_1324804, _1324806)), tc_fun(_1324806, tc_fun(tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_HOL_Obool)), _1324804), hAPP(c_COMBB(tc_prod(_1324804, _1324806), tc_fun(tc_fun(tc_prod(_1324804, _1324806), tc_HOL_Obool), tc_HOL_Obool), _1324806), c_member(tc_prod(_1324804, _1324806)))), c_Product__Type_OPair(_1324804, _1324806)))), _1324810)), _1324812), _1324814)))], (30122 ^ _780205) ^ [_1325488, _1325490, _1325492, _1325494] : [hAPP(hAPP(c_COMBC(_1325488, tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_fun(_1325490, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1325490, tc_fun(tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_fun(_1325490, tc_HOL_Obool)), _1325488), c_COMBC(_1325490, tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1325490, tc_prod(_1325488, _1325490)), tc_fun(_1325490, tc_fun(tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_HOL_Obool)), _1325488), hAPP(c_COMBB(tc_prod(_1325488, _1325490), tc_fun(tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_HOL_Obool), _1325490), c_member(tc_prod(_1325488, _1325490)))), c_Product__Type_OPair(_1325488, _1325490)))), _1325492) = hAPP(hAPP(c_COMBC(_1325488, tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_fun(_1325490, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1325490, tc_fun(tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_fun(_1325490, tc_HOL_Obool)), _1325488), c_COMBC(_1325490, tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1325490, tc_prod(_1325488, _1325490)), tc_fun(_1325490, tc_fun(tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_HOL_Obool)), _1325488), hAPP(c_COMBB(tc_prod(_1325488, _1325490), tc_fun(tc_fun(tc_prod(_1325488, _1325490), tc_HOL_Obool), tc_HOL_Obool), _1325490), c_member(tc_prod(_1325488, _1325490)))), c_Product__Type_OPair(_1325488, _1325490)))), _1325494), -(_1325492 = _1325494)], (30128 ^ _780205) ^ [_1326037, _1326039, _1326041, _1326043] : [_1326041 = _1326043, -(hAPP(hAPP(c_COMBC(_1326037, tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_fun(_1326039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1326039, tc_fun(tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_fun(_1326039, tc_HOL_Obool)), _1326037), c_COMBC(_1326039, tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1326039, tc_prod(_1326037, _1326039)), tc_fun(_1326039, tc_fun(tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_HOL_Obool)), _1326037), hAPP(c_COMBB(tc_prod(_1326037, _1326039), tc_fun(tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_HOL_Obool), _1326039), c_member(tc_prod(_1326037, _1326039)))), c_Product__Type_OPair(_1326037, _1326039)))), _1326041) = hAPP(hAPP(c_COMBC(_1326037, tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_fun(_1326039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1326039, tc_fun(tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_fun(_1326039, tc_HOL_Obool)), _1326037), c_COMBC(_1326039, tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1326039, tc_prod(_1326037, _1326039)), tc_fun(_1326039, tc_fun(tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_HOL_Obool)), _1326037), hAPP(c_COMBB(tc_prod(_1326037, _1326039), tc_fun(tc_fun(tc_prod(_1326037, _1326039), tc_HOL_Obool), tc_HOL_Obool), _1326039), c_member(tc_prod(_1326037, _1326039)))), c_Product__Type_OPair(_1326037, _1326039)))), _1326043))], (30134 ^ _780205) ^ [_1326592] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1326592) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1326592)))], (30136 ^ _780205) ^ [_1326624, _1326626, _1326628, _1326630, _1326632] : [class_Lattices_Olattice(_1326624), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326626, _1326624)), _1326628), _1326630), _1326632) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1326624), hAPP(_1326628, _1326632)), hAPP(_1326630, _1326632)))], (30142 ^ _780205) ^ [_1326761, _1326763, _1326765] : [class_Orderings_Obot(_1326761), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1326763, _1326761)), _1326765) = c_Orderings_Obot__class_Obot(_1326761))], (30148 ^ _780205) ^ [_1326879, _1326881, _1326883, _1326885] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1326879, tc_fun(_1326881, tc_HOL_Obool))), _1326883), _1326885)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1326879, _1326881)), hAPP(hAPP(c_Product__Type_OPair(_1326879, _1326881), _1326883), _1326885)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1326879, _1326881), tc_HOL_Obool)))))], (30154 ^ _780205) ^ [_1327036, _1327038, _1327040, _1327042] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1327036, _1327038)), hAPP(hAPP(c_Product__Type_OPair(_1327036, _1327038), _1327040), _1327042)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1327036, _1327038), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1327036, tc_fun(_1327038, tc_HOL_Obool))), _1327040), _1327042)))], (30160 ^ _780205) ^ [_1327214, _1327216] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1327214, tc_HOL_Obool)), _1327216)), -(hBOOL(hAPP(hAPP(c_member(_1327214), _1327216), c_Orderings_Obot__class_Obot(tc_fun(_1327214, tc_HOL_Obool)))))], (30166 ^ _780205) ^ [_1327325, _1327327] : [hBOOL(hAPP(hAPP(c_member(_1327325), _1327327), c_Orderings_Obot__class_Obot(tc_fun(_1327325, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1327325, tc_HOL_Obool)), _1327327)))], (30172 ^ _780205) ^ [_1327442, _1327444, _1327446, _1327448] : [class_Rings_Osemiring__1(_1327442), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1327442), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1327444, tc_Nat_Onat), _1327446), _1327448)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1327444, _1327442), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1327442, _1327444), c_Nat_Osemiring__1__class_Oof__nat(_1327442)), _1327446)), _1327448))], (30178 ^ _780205) ^ [_1327591, _1327593, _1327595] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1327591, tc_Nat_Onat), _1327593), _1327595) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1327591, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1327591), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1327593)), _1327595)))], (30180 ^ _780205) ^ [_1327649, _1327651] : [-(hAPP(c_Finite__Set_Ocard(_1327649), _1327651) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1327649, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1327649), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1327651))], (30182 ^ _780205) ^ [_1327694, _1327696, _1327698, _1327700] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1327694), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327696, tc_Nat_Onat), _1327698), _1327700)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327696, _1327694), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1327694, _1327696), c_Nat_Osemiring__1__class_Oof__nat(_1327694)), _1327698)), _1327700)), class_Groups_Ocomm__monoid__mult(_1327694), class_Rings_Osemiring__1(_1327694)], (30192 ^ _780205) ^ [_1327897, _1327899, _1327901] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327897, tc_Nat_Onat), _1327899), _1327901) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327897, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1327897), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1327899)), _1327901)))], (30194 ^ _780205) ^ [_1327955, _1327957, _1327959, _1327961, _1327963] : [class_Groups_Ocomm__monoid__add(_1327955), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327957), _1327959)), 30201 ^ _780205 : [(30202 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1327957), _1327961), _1327959)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1327957, _1327955), hAPP(hAPP(c_COMBC(_1327957, _1327955, _1327955), hAPP(hAPP(c_COMBS(_1327957, _1327955, tc_fun(_1327955, _1327955)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1327955, tc_fun(_1327955, _1327955)), _1327957), c_If(_1327955)), hAPP(c_fequal, _1327961))), _1327963)), c_Groups_Ozero__class_Ozero(_1327955))), _1327959) = hAPP(_1327963, _1327961))], (30208 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327957), _1327961), _1327959))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1327957, _1327955), hAPP(hAPP(c_COMBC(_1327957, _1327955, _1327955), hAPP(hAPP(c_COMBS(_1327957, _1327955, tc_fun(_1327955, _1327955)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1327955, tc_fun(_1327955, _1327955)), _1327957), c_If(_1327955)), hAPP(c_fequal, _1327961))), _1327963)), c_Groups_Ozero__class_Ozero(_1327955))), _1327959) = c_Groups_Ozero__class_Ozero(_1327955))]]], (30214 ^ _780205) ^ [_1328465, _1328467, _1328469, _1328471, _1328473] : [class_Groups_Ocomm__monoid__add(_1328465), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328467), _1328469)), 30221 ^ _780205 : [(30222 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1328467), _1328471), _1328469)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1328467, _1328465), hAPP(hAPP(c_COMBC(_1328467, _1328465, _1328465), hAPP(hAPP(c_COMBS(_1328467, _1328465, tc_fun(_1328465, _1328465)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1328465, tc_fun(_1328465, _1328465)), _1328467), c_If(_1328465)), hAPP(hAPP(c_COMBC(_1328467, _1328467, tc_HOL_Obool), c_fequal), _1328471))), _1328473)), c_Groups_Ozero__class_Ozero(_1328465))), _1328469) = hAPP(_1328473, _1328471))], (30228 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1328467), _1328471), _1328469))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1328467, _1328465), hAPP(hAPP(c_COMBC(_1328467, _1328465, _1328465), hAPP(hAPP(c_COMBS(_1328467, _1328465, tc_fun(_1328465, _1328465)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1328465, tc_fun(_1328465, _1328465)), _1328467), c_If(_1328465)), hAPP(hAPP(c_COMBC(_1328467, _1328467, tc_HOL_Obool), c_fequal), _1328471))), _1328473)), c_Groups_Ozero__class_Ozero(_1328465))), _1328469) = c_Groups_Ozero__class_Ozero(_1328465))]]], (30234 ^ _780205) ^ [_1329003, _1329005, _1329007, _1329009, _1329011] : [class_Groups_Ocomm__monoid__mult(_1329003), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329005), _1329007)), 30241 ^ _780205 : [(30242 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1329005), _1329009), _1329007)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329005, _1329003), hAPP(hAPP(c_COMBC(_1329005, _1329003, _1329003), hAPP(hAPP(c_COMBS(_1329005, _1329003, tc_fun(_1329003, _1329003)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1329003, tc_fun(_1329003, _1329003)), _1329005), c_If(_1329003)), hAPP(c_fequal, _1329009))), _1329011)), c_Groups_Oone__class_Oone(_1329003))), _1329007) = hAPP(_1329011, _1329009))], (30248 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329005), _1329009), _1329007))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329005, _1329003), hAPP(hAPP(c_COMBC(_1329005, _1329003, _1329003), hAPP(hAPP(c_COMBS(_1329005, _1329003, tc_fun(_1329003, _1329003)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1329003, tc_fun(_1329003, _1329003)), _1329005), c_If(_1329003)), hAPP(c_fequal, _1329009))), _1329011)), c_Groups_Oone__class_Oone(_1329003))), _1329007) = c_Groups_Oone__class_Oone(_1329003))]]], (30254 ^ _780205) ^ [_1329513, _1329515, _1329517, _1329519, _1329521] : [class_Groups_Ocomm__monoid__mult(_1329513), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329515), _1329517)), 30261 ^ _780205 : [(30262 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1329515), _1329519), _1329517)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329515, _1329513), hAPP(hAPP(c_COMBC(_1329515, _1329513, _1329513), hAPP(hAPP(c_COMBS(_1329515, _1329513, tc_fun(_1329513, _1329513)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1329513, tc_fun(_1329513, _1329513)), _1329515), c_If(_1329513)), hAPP(hAPP(c_COMBC(_1329515, _1329515, tc_HOL_Obool), c_fequal), _1329519))), _1329521)), c_Groups_Oone__class_Oone(_1329513))), _1329517) = hAPP(_1329521, _1329519))], (30268 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329515), _1329519), _1329517))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329515, _1329513), hAPP(hAPP(c_COMBC(_1329515, _1329513, _1329513), hAPP(hAPP(c_COMBS(_1329515, _1329513, tc_fun(_1329513, _1329513)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1329513, tc_fun(_1329513, _1329513)), _1329515), c_If(_1329513)), hAPP(hAPP(c_COMBC(_1329515, _1329515, tc_HOL_Obool), c_fequal), _1329519))), _1329521)), c_Groups_Oone__class_Oone(_1329513))), _1329517) = c_Groups_Oone__class_Oone(_1329513))]]], (30274 ^ _780205) ^ [_1330066, _1330068, _1330070, _1330072] : [hBOOL(hAPP(hAPP(c_member(_1330066), _1330068), _1330070)), -(hAPP(c_Set_Ovimage(_1330072, _1330066, hAPP(c_COMBK(_1330066, _1330072), _1330068)), _1330070) = c_Orderings_Otop__class_Otop(tc_fun(_1330072, tc_HOL_Obool)))], (30280 ^ _780205) ^ [_1330191, _1330193, _1330195, _1330197] : [-(hBOOL(hAPP(hAPP(c_member(_1330191), _1330193), _1330195))), -(hAPP(c_Set_Ovimage(_1330197, _1330191, hAPP(c_COMBK(_1330191, _1330197), _1330193)), _1330195) = c_Orderings_Obot__class_Obot(tc_fun(_1330197, tc_HOL_Obool)))], (30286 ^ _780205) ^ [_1330258, _1330260, _1330262, _1330264] : [class_Rings_Osemiring__1(_1330258), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1330260, _1330258), hAPP(c_COMBK(_1330258, _1330260), _1330262)), _1330264) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330258), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1330258), hAPP(c_Finite__Set_Ocard(_1330260), _1330264))), _1330262))], (30292 ^ _780205) ^ [_1330403, _1330405, _1330407] : [class_Int_Onumber__ring(_1330403), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1330403), _1330405), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1330407))) = hAPP(hAPP(c_HOL_OLet(_1330403, _1330403), hAPP(hAPP(c_Power_Opower__class_Opower(_1330403), _1330405), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330407))), hAPP(hAPP(c_COMBS(_1330403, _1330403, _1330403), c_Groups_Otimes__class_Otimes(_1330403)), c_COMBI(_1330403))))], (30298 ^ _780205) ^ [_1330574, _1330576, _1330578, _1330580, _1330582] : [class_Groups_Ocomm__monoid__mult(_1330574), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330576), _1330578)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1330574, _1330576, c_Groups_Otimes__class_Otimes(_1330574)), hAPP(hAPP(c_COMBS(_1330576, _1330574, _1330574), hAPP(hAPP(c_COMBB(_1330574, tc_fun(_1330574, _1330574), _1330576), c_Groups_Otimes__class_Otimes(_1330574)), _1330580)), _1330582)), c_Groups_Oone__class_Oone(_1330574)), _1330578) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330574), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1330574, _1330576, c_Groups_Otimes__class_Otimes(_1330574)), _1330580), c_Groups_Oone__class_Oone(_1330574)), _1330578)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1330574, _1330576, c_Groups_Otimes__class_Otimes(_1330574)), _1330582), c_Groups_Oone__class_Oone(_1330574)), _1330578)))], (30308 ^ _780205) ^ [_1330889, _1330891, _1330893, _1330895] : [class_Groups_Ocomm__monoid__mult(_1330889), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330891), _1330893)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1330891, _1330889), hAPP(c_COMBK(_1330889, _1330891), _1330895)), _1330893) = hAPP(hAPP(c_Power_Opower__class_Opower(_1330889), _1330895), hAPP(c_Finite__Set_Ocard(_1330891), _1330893)))], (30318 ^ _780205) ^ [_1331088, _1331090] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1331088), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1331090))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1331088), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1331090))), 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))))], (30320 ^ _780205) ^ [_1331160, _1331162, _1331164, _1331166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331160, tc_fun(_1331162, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1331160, tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_fun(_1331162, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1331162, tc_fun(tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_fun(_1331162, tc_HOL_Obool)), _1331160), c_COMBC(_1331162, tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1331162, tc_prod(_1331160, _1331162)), tc_fun(_1331162, tc_fun(tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_HOL_Obool)), _1331160), hAPP(c_COMBB(tc_prod(_1331160, _1331162), tc_fun(tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_HOL_Obool), _1331162), c_member(tc_prod(_1331160, _1331162)))), c_Product__Type_OPair(_1331160, _1331162)))), _1331164)), hAPP(hAPP(c_COMBC(_1331160, tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_fun(_1331162, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1331162, tc_fun(tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_fun(_1331162, tc_HOL_Obool)), _1331160), c_COMBC(_1331162, tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1331162, tc_prod(_1331160, _1331162)), tc_fun(_1331162, tc_fun(tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_HOL_Obool)), _1331160), hAPP(c_COMBB(tc_prod(_1331160, _1331162), tc_fun(tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool), tc_HOL_Obool), _1331162), c_member(tc_prod(_1331160, _1331162)))), c_Product__Type_OPair(_1331160, _1331162)))), _1331166))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1331160, _1331162), tc_HOL_Obool)), _1331164), _1331166)))], (30326 ^ _780205) ^ [_1331761, _1331763, _1331765, _1331767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool)), _1331765), _1331767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331761, tc_fun(_1331763, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1331761, tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_fun(_1331763, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1331763, tc_fun(tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_fun(_1331763, tc_HOL_Obool)), _1331761), c_COMBC(_1331763, tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1331763, tc_prod(_1331761, _1331763)), tc_fun(_1331763, tc_fun(tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_HOL_Obool)), _1331761), hAPP(c_COMBB(tc_prod(_1331761, _1331763), tc_fun(tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_HOL_Obool), _1331763), c_member(tc_prod(_1331761, _1331763)))), c_Product__Type_OPair(_1331761, _1331763)))), _1331765)), hAPP(hAPP(c_COMBC(_1331761, tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_fun(_1331763, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1331763, tc_fun(tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_fun(_1331763, tc_HOL_Obool)), _1331761), c_COMBC(_1331763, tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1331763, tc_prod(_1331761, _1331763)), tc_fun(_1331763, tc_fun(tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_HOL_Obool)), _1331761), hAPP(c_COMBB(tc_prod(_1331761, _1331763), tc_fun(tc_fun(tc_prod(_1331761, _1331763), tc_HOL_Obool), tc_HOL_Obool), _1331763), c_member(tc_prod(_1331761, _1331763)))), c_Product__Type_OPair(_1331761, _1331763)))), _1331767))))], (30332 ^ _780205) ^ [_1332368, _1332370, _1332372, _1332374] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1332368, _1332370, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1332368)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1332368), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1332368), hAPP(c_COMBK(tc_HOL_Obool, tc_Com_Ostate), c_fFalse))), _1332372), _1332374)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1332368), tc_HOL_Obool)))))], (30334 ^ _780205) ^ [_1332450, _1332452, _1332454] : [hBOOL(hAPP(c_Predicate_OPowp(_1332450, hAPP(hAPP(c_COMBC(_1332450, tc_fun(_1332450, tc_HOL_Obool), tc_HOL_Obool), c_member(_1332450)), _1332452)), _1332454)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1332450, tc_HOL_Obool)), _1332454), hAPP(c_Set_OPow(_1332450), _1332452))))], (30340 ^ _780205) ^ [_1332595, _1332597, _1332599] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1332595, tc_HOL_Obool)), _1332599), hAPP(c_Set_OPow(_1332595), _1332597))), -(hBOOL(hAPP(c_Predicate_OPowp(_1332595, hAPP(hAPP(c_COMBC(_1332595, tc_fun(_1332595, tc_HOL_Obool), tc_HOL_Obool), c_member(_1332595)), _1332597)), _1332599)))], (30346 ^ _780205) ^ [_1332746, _1332748, _1332750, _1332752, _1332754] : [class_Groups_Ocomm__monoid__add(_1332746), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332748), _1332750)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1332748, _1332746), _1332752), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332748, tc_HOL_Obool)), _1332750), _1332754)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1332748, _1332746), hAPP(hAPP(c_COMBC(_1332748, _1332746, _1332746), hAPP(hAPP(c_COMBS(_1332748, _1332746, tc_fun(_1332746, _1332746)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1332746, tc_fun(_1332746, _1332746)), _1332748), c_If(_1332746)), hAPP(hAPP(c_COMBC(_1332748, tc_fun(_1332748, tc_HOL_Obool), tc_HOL_Obool), c_member(_1332748)), _1332754))), _1332752)), c_Groups_Ozero__class_Ozero(_1332746))), _1332750))], (30356 ^ _780205) ^ [_1333067, _1333069, _1333071] : [class_Int_Onumber__ring(_1333067), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1333067), hAPP(c_Int_Onumber__class_Onumber__of(_1333067), _1333069)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1333071))) = hAPP(hAPP(c_HOL_OLet(_1333067, _1333067), hAPP(hAPP(c_Power_Opower__class_Opower(_1333067), hAPP(c_Int_Onumber__class_Onumber__of(_1333067), _1333069)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1333071))), hAPP(hAPP(c_COMBS(_1333067, _1333067, _1333067), c_Groups_Otimes__class_Otimes(_1333067)), c_COMBI(_1333067))))], (30362 ^ _780205) ^ [_1333258, _1333260] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333258), _1333260)), -(hAPP(c_Finite__Set_Ocard(_1333258), _1333260) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1333258, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1333258), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1333260))], (30368 ^ _780205) ^ [_1333400, _1333402] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333400), _1333402)), -(hAPP(c_Finite__Set_Ocard(_1333400), _1333402) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1333400, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1333400), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1333402))], (30374 ^ _780205) ^ [_1333527, _1333529] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1333527), _1333529))), -(hAPP(c_Finite__Set_Ocard(_1333527), _1333529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30380 ^ _780205) ^ [_1333574] : [-(c_Finite__Set_Ofun__left__comm__idem(_1333574, tc_fun(_1333574, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1333574, tc_HOL_Obool), tc_fun(tc_fun(_1333574, tc_HOL_Obool), tc_fun(_1333574, tc_HOL_Obool)), _1333574), hAPP(c_COMBC(tc_fun(_1333574, tc_HOL_Obool), tc_fun(_1333574, tc_HOL_Obool), tc_fun(_1333574, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1333574, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1333574, tc_fun(_1333574, tc_HOL_Obool), tc_fun(_1333574, tc_HOL_Obool)), c_Set_Oinsert(_1333574)), c_Orderings_Obot__class_Obot(tc_fun(_1333574, tc_HOL_Obool))))))], (30382 ^ _780205) ^ [_1333688, _1333690, _1333692, _1333694, _1333696, _1333698] : [hBOOL(hAPP(hAPP(c_member(_1333688), _1333690), _1333692)), 30385 ^ _780205 : [(30386 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1333688), _1333694), _1333692)), -(hAPP(c_Set_Ovimage(_1333696, _1333688, hAPP(hAPP(c_COMBC(_1333696, _1333688, _1333688), hAPP(hAPP(c_COMBC(_1333696, _1333688, tc_fun(_1333688, _1333688)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1333688, tc_fun(_1333688, _1333688)), _1333696), c_If(_1333688)), hAPP(hAPP(c_COMBC(_1333696, tc_fun(_1333696, tc_HOL_Obool), tc_HOL_Obool), c_member(_1333696)), _1333698))), _1333690)), _1333694)), _1333692) = c_Orderings_Otop__class_Otop(tc_fun(_1333696, tc_HOL_Obool)))], (30392 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333688), _1333694), _1333692))), -(hAPP(c_Set_Ovimage(_1333696, _1333688, hAPP(hAPP(c_COMBC(_1333696, _1333688, _1333688), hAPP(hAPP(c_COMBC(_1333696, _1333688, tc_fun(_1333688, _1333688)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1333688, tc_fun(_1333688, _1333688)), _1333696), c_If(_1333688)), hAPP(hAPP(c_COMBC(_1333696, tc_fun(_1333696, tc_HOL_Obool), tc_HOL_Obool), c_member(_1333696)), _1333698))), _1333690)), _1333694)), _1333692) = _1333698)]]], (30398 ^ _780205) ^ [_1334179, _1334181, _1334183, _1334185, _1334187, _1334189] : [-(hBOOL(hAPP(hAPP(c_member(_1334179), _1334181), _1334183))), 30401 ^ _780205 : [(30402 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1334179), _1334185), _1334183)), -(hAPP(c_Set_Ovimage(_1334187, _1334179, hAPP(hAPP(c_COMBC(_1334187, _1334179, _1334179), hAPP(hAPP(c_COMBC(_1334187, _1334179, tc_fun(_1334179, _1334179)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1334179, tc_fun(_1334179, _1334179)), _1334187), c_If(_1334179)), hAPP(hAPP(c_COMBC(_1334187, tc_fun(_1334187, tc_HOL_Obool), tc_HOL_Obool), c_member(_1334187)), _1334189))), _1334181)), _1334185)), _1334183) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1334187, tc_HOL_Obool)), _1334189))], (30408 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1334179), _1334185), _1334183))), -(hAPP(c_Set_Ovimage(_1334187, _1334179, hAPP(hAPP(c_COMBC(_1334187, _1334179, _1334179), hAPP(hAPP(c_COMBC(_1334187, _1334179, tc_fun(_1334179, _1334179)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1334179, tc_fun(_1334179, _1334179)), _1334187), c_If(_1334179)), hAPP(hAPP(c_COMBC(_1334187, tc_fun(_1334187, tc_HOL_Obool), tc_HOL_Obool), c_member(_1334187)), _1334189))), _1334181)), _1334185)), _1334183) = c_Orderings_Obot__class_Obot(tc_fun(_1334187, tc_HOL_Obool)))]]], (30414 ^ _780205) ^ [_1334693, _1334695] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1334693)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1334695)), hAPP(c_Int_Onat, _1334693)) = hAPP(c_Int_Onat, _1334695))], (30420 ^ _780205) ^ [_1334798, _1334800] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1334798))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1334800)), hAPP(c_Int_Onat, _1334798)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1334800), _1334798)), 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)))], (30426 ^ _780205) ^ [_1334862, _1334864, _1334866, _1334868, _1334870] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1334862, _1334864, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1334862)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1334862), hAPP(hAPP(c_COMBC(_1334862, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1334862), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1334862), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _1334866))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _1334868))), c_Com_Ocom_OWhile(_1334868, _1334870)), _1334866)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1334862), tc_HOL_Obool)))))], (30428 ^ _780205) ^ [_1334958, _1334960, _1334962] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1334958), _1334960)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334958, tc_HOL_Obool)), _1334962), _1334960) = hAPP(hAPP(c_Finite__Set_Ofold(_1334958, tc_fun(_1334958, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1334958, tc_HOL_Obool), tc_fun(tc_fun(_1334958, tc_HOL_Obool), tc_fun(_1334958, tc_HOL_Obool)), _1334958), hAPP(c_COMBC(tc_fun(_1334958, tc_HOL_Obool), tc_fun(_1334958, tc_HOL_Obool), tc_fun(_1334958, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1334958, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1334958, tc_fun(_1334958, tc_HOL_Obool), tc_fun(_1334958, tc_HOL_Obool)), c_Set_Oinsert(_1334958)), c_Orderings_Obot__class_Obot(tc_fun(_1334958, tc_HOL_Obool))))), _1334962), _1334960))], (30434 ^ _780205) ^ [_1335240, _1335242] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1335240) = hAPP(c_Nat_OSuc, _1335242), -(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(_1335240))), 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)), _1335242))))))], (30440 ^ _780205) ^ [_1335363, _1335365] : [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(_1335363))), 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)), _1335365))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1335363) = hAPP(c_Nat_OSuc, _1335365))], (30446 ^ _780205) ^ [_1335507, _1335509] : [hAPP(c_Nat_OSuc, _1335507) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1335509), -(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(_1335509))), 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)), _1335507))))))], (30452 ^ _780205) ^ [_1335630, _1335632] : [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(_1335632))), 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)), _1335630))))), -(hAPP(c_Nat_OSuc, _1335630) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1335632))], (30458 ^ _780205) ^ [_1335765] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1335765))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1335765)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30464 ^ _780205) ^ [_1335854] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1335854)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1335854)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1335854)), 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)))))], (30470 ^ _780205) ^ [_1335924, _1335926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1335924)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1335926))), -(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(_1335926))), 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), _1335924)), c_Int_Onat))))))], (30476 ^ _780205) ^ [_1336069, _1336071] : [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(_1336071))), 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), _1336069)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1336069)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1336071))))], (30482 ^ _780205) ^ [_1336235, _1336237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1336235)), hAPP(c_Nat_OSuc, _1336237))), -(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(_1336235))), 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)), _1336237)))))], (30488 ^ _780205) ^ [_1336362, _1336364] : [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(_1336362))), 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)), _1336364)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1336362)), hAPP(c_Nat_OSuc, _1336364))))], (30494 ^ _780205) ^ [_1336510, _1336512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1336510)), hAPP(c_Nat_OSuc, _1336512))), -(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(_1336510))), 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)), _1336512)))))], (30500 ^ _780205) ^ [_1336637, _1336639] : [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(_1336637))), 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)), _1336639)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1336637)), hAPP(c_Nat_OSuc, _1336639))))], (30506 ^ _780205) ^ [_1336785, _1336787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1336785)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1336787))), -(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(_1336787))), 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), _1336785)), c_Int_Onat))))))], (30512 ^ _780205) ^ [_1336930, _1336932] : [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(_1336932))), 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), _1336930)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1336930)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1336932))))], (30518 ^ _780205) ^ [_1337081, _1337083, _1337085] : [class_Int_Onumber__ring(_1337081), 30521 ^ _780205 : [(30522 ^ _780205) ^ [] : [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), _1337083))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337081), _1337085), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1337083))) = hAPP(hAPP(c_HOL_OLet(_1337081, _1337081), hAPP(hAPP(c_Power_Opower__class_Opower(_1337081), _1337085), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1337083))), hAPP(hAPP(c_COMBS(_1337081, _1337081, _1337081), hAPP(hAPP(c_COMBB(_1337081, tc_fun(_1337081, _1337081), _1337081), c_Groups_Otimes__class_Otimes(_1337081)), hAPP(c_Groups_Otimes__class_Otimes(_1337081), _1337085))), c_COMBI(_1337081))))], (30528 ^ _780205) ^ [] : [-(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), _1337083)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337081), _1337085), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1337083))) = c_Groups_Oone__class_Oone(_1337081))]]], (30534 ^ _780205) ^ [_1337439, _1337441, _1337443, _1337445, _1337447, _1337449] : [class_Groups_Ocomm__monoid__mult(_1337439), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337441), _1337443)), 30541 ^ _780205 : [(30542 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1337441), _1337445), _1337443)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337441, _1337439), hAPP(hAPP(c_COMBC(_1337441, _1337439, _1337439), hAPP(hAPP(c_COMBS(_1337441, _1337439, tc_fun(_1337439, _1337439)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1337439, tc_fun(_1337439, _1337439)), _1337441), c_If(_1337439)), hAPP(hAPP(c_COMBC(_1337441, _1337441, tc_HOL_Obool), c_fequal), _1337445))), _1337447)), _1337449)), _1337443) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337439), hAPP(_1337447, _1337445)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337439), _1337449), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1337441), _1337443)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (30548 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1337441), _1337445), _1337443))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337441, _1337439), hAPP(hAPP(c_COMBC(_1337441, _1337439, _1337439), hAPP(hAPP(c_COMBS(_1337441, _1337439, tc_fun(_1337439, _1337439)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1337439, tc_fun(_1337439, _1337439)), _1337441), c_If(_1337439)), hAPP(hAPP(c_COMBC(_1337441, _1337441, tc_HOL_Obool), c_fequal), _1337445))), _1337447)), _1337449)), _1337443) = hAPP(hAPP(c_Power_Opower__class_Opower(_1337439), _1337449), hAPP(c_Finite__Set_Ocard(_1337441), _1337443)))]]], (30554 ^ _780205) ^ [_1338060, _1338062] : [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), _1338060))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1338062), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1338060))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1338062), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1338060))), 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), _1338062))), c_COMBI(tc_Int_Oint))))], (30560 ^ _780205) ^ [_1338217, _1338219] : [-(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), _1338217)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1338219), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1338217))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (30566 ^ _780205) ^ [_1338271, _1338273] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1338271)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1338273)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1338273))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), c_Nat_OSuc), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1338271)), c_Int_Onat)))))], (30568 ^ _780205) ^ [_1338334, _1338336] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1338334)), hAPP(c_Nat_OSuc, _1338336)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1338334))), 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)), _1338336)))))], (30570 ^ _780205) ^ [_1338391, _1338393, _1338395] : [class_Int_Onumber__ring(_1338391), 30573 ^ _780205 : [(30574 ^ _780205) ^ [] : [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), _1338393))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1338391), hAPP(c_Int_Onumber__class_Onumber__of(_1338391), _1338395)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1338393))) = hAPP(hAPP(c_HOL_OLet(_1338391, _1338391), hAPP(hAPP(c_Power_Opower__class_Opower(_1338391), hAPP(c_Int_Onumber__class_Onumber__of(_1338391), _1338395)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1338393))), hAPP(hAPP(c_COMBS(_1338391, _1338391, _1338391), hAPP(hAPP(c_COMBB(_1338391, tc_fun(_1338391, _1338391), _1338391), c_Groups_Otimes__class_Otimes(_1338391)), hAPP(c_Groups_Otimes__class_Otimes(_1338391), hAPP(c_Int_Onumber__class_Onumber__of(_1338391), _1338395)))), c_COMBI(_1338391))))], (30580 ^ _780205) ^ [] : [-(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), _1338393)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1338391), hAPP(c_Int_Onumber__class_Onumber__of(_1338391), _1338395)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1338393))) = c_Groups_Oone__class_Oone(_1338391))]]], (30586 ^ _780205) ^ [_1338798, _1338800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338798), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1338800)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1338798)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1338800))], (30592 ^ _780205) ^ [_1338909, _1338911] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338909), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1338911)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1338909)) = 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), _1338911), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1338909)))), 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)))], (30598 ^ _780205) ^ [_1338982] : [-(c_Nitpick_Oone__frac(_1338982) = c_Nitpick_OAbs__Frac(_1338982, 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))))], (30600 ^ _780205) ^ [_1339010, _1339012] : [-(c_Nitpick_Onumber__of__frac(_1339010, _1339012) = c_Nitpick_OAbs__Frac(_1339010, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1339012), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (30602 ^ _780205) ^ [_1339071, _1339073, _1339075, _1339077, _1339079] : [hBOOL(hAPP(hAPP(c_member(_1339071), _1339073), hAPP(c_Relation_OImage(_1339075, _1339071, _1339077), hAPP(hAPP(c_Set_Oinsert(_1339075), _1339079), c_Orderings_Obot__class_Obot(tc_fun(_1339075, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1339075, _1339071)), hAPP(hAPP(c_Product__Type_OPair(_1339075, _1339071), _1339079), _1339073)), _1339077)))], (30608 ^ _780205) ^ [_1339242, _1339244, _1339246, _1339248, _1339250] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1339246, _1339242)), hAPP(hAPP(c_Product__Type_OPair(_1339246, _1339242), _1339250), _1339244)), _1339248)), -(hBOOL(hAPP(hAPP(c_member(_1339242), _1339244), hAPP(c_Relation_OImage(_1339246, _1339242, _1339248), hAPP(hAPP(c_Set_Oinsert(_1339246), _1339250), c_Orderings_Obot__class_Obot(tc_fun(_1339246, tc_HOL_Obool)))))))], (30614 ^ _780205) ^ [_1339428, _1339430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1339428), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1339430, _1339428) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1339430), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1339428)))], (30620 ^ _780205) ^ [_1339534, _1339536] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1339534), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 30623 ^ _780205 : [(30624 ^ _780205) ^ [] : [30625 ^ _780205 : [(30626 ^ _780205) ^ [] : [_1339536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (30628 ^ _780205) ^ [] : [_1339534 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1339536, _1339534) = 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)))], (30632 ^ _780205) ^ [] : [-(c_Nitpick_Onorm__frac(_1339536, _1339534) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1339536), _1339534)), 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), _1339536))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1339534)))), -(_1339536 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1339534 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (30642 ^ _780205) ^ [_1339832, _1339834, _1339836, _1339838, _1339840, _1339842] : [30643 ^ _780205 : [(30644 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1339832, _1339834), _1339836))], (30646 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1339838, _1339834), _1339836))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339840, tc_fun(_1339842, tc_HOL_Obool))), _1339838), _1339832), _1339834), _1339836)))], (30650 ^ _780205) ^ [_1340015, _1340017, _1340019, _1340021, _1340023, _1340025] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340015, tc_fun(_1340017, tc_HOL_Obool))), _1340019), _1340021), _1340023), _1340025)), -(hBOOL(hAPP(hAPP(_1340019, _1340023), _1340025))), -(hBOOL(hAPP(hAPP(_1340021, _1340023), _1340025)))], (30660 ^ _780205) ^ [_1340173, _1340175, _1340177, _1340179, _1340181, _1340183] : [hBOOL(hAPP(hAPP(_1340173, _1340175), _1340177)), hBOOL(hAPP(hAPP(_1340179, _1340175), _1340177)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340181, tc_fun(_1340183, tc_HOL_Obool))), _1340173), _1340179), _1340175), _1340177)))], (30670 ^ _780205) ^ [_1340376, _1340378, _1340380, _1340382, _1340384, _1340386] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340376, tc_fun(_1340378, tc_HOL_Obool))), _1340380), _1340382), _1340384), _1340386)), 30673 ^ _780205 : [(30674 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1340380, _1340384), _1340386)))], (30676 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1340382, _1340384), _1340386)))]]], (30678 ^ _780205) ^ [_1340567, _1340569, _1340571, _1340573] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1340567, tc_fun(_1340569, tc_HOL_Obool))), _1340571), _1340573))], (30680 ^ _780205) ^ [_1340609, _1340611, _1340613, _1340615, _1340617, _1340619] : [hBOOL(hAPP(hAPP(_1340609, _1340611), _1340613)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340615, tc_fun(_1340617, tc_HOL_Obool))), _1340619), _1340609), _1340611), _1340613)))], (30686 ^ _780205) ^ [_1340742, _1340744, _1340746, _1340748, _1340750, _1340752] : [hBOOL(hAPP(hAPP(_1340742, _1340744), _1340746)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340748, tc_fun(_1340750, tc_HOL_Obool))), _1340742), _1340752), _1340744), _1340746)))], (30692 ^ _780205) ^ [_1340875, _1340877, _1340879, _1340881, _1340883, _1340885] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340875, tc_fun(_1340877, tc_HOL_Obool))), _1340879), _1340881), _1340883), _1340885)), -(hBOOL(hAPP(hAPP(_1340879, _1340883), _1340885)))], (30698 ^ _780205) ^ [_1341008, _1341010, _1341012, _1341014, _1341016, _1341018] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341008, tc_fun(_1341010, tc_HOL_Obool))), _1341012), _1341014), _1341016), _1341018)), -(hBOOL(hAPP(hAPP(_1341014, _1341016), _1341018)))], (30704 ^ _780205) ^ [_1341141, _1341143, _1341145] : [-(hAPP(c_Relation_OImage(_1341141, _1341143, _1341145), c_Orderings_Obot__class_Obot(tc_fun(_1341141, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1341143, tc_HOL_Obool)))], (30706 ^ _780205) ^ [_1341185, _1341187, _1341189, _1341191, _1341193] : [-(hAPP(c_Relation_OImage(_1341185, _1341187, _1341189), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341185, tc_HOL_Obool)), _1341191), _1341193)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341187, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1341185, _1341187, _1341189), _1341191)), hAPP(c_Relation_OImage(_1341185, _1341187, _1341189), _1341193)))], (30708 ^ _780205) ^ [_1341259, _1341261, _1341263, _1341265, _1341267] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341259, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1341261, _1341259, _1341263), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341261, tc_HOL_Obool)), _1341265), _1341267))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341259, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1341261, _1341259, _1341263), _1341265)), hAPP(c_Relation_OImage(_1341261, _1341259, _1341263), _1341267)))))], (30710 ^ _780205) ^ [_1341343, _1341345, _1341347, _1341349, _1341351, _1341353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1341343, _1341345), tc_HOL_Obool)), _1341347), _1341349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341343, tc_HOL_Obool)), _1341351), _1341353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1341345, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1341343, _1341345, _1341347), _1341351)), hAPP(c_Relation_OImage(_1341343, _1341345, _1341349), _1341353))))], (30720 ^ _780205) ^ [_1341582, _1341584, _1341586, _1341588, _1341590] : [-(hAPP(c_Relation_OImage(_1341582, _1341584, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1341582, _1341584), tc_HOL_Obool)), _1341586), _1341588)), _1341590) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341584, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1341582, _1341584, _1341586), _1341590)), hAPP(c_Relation_OImage(_1341582, _1341584, _1341588), _1341590)))], (30722 ^ _780205) ^ [_1341686, _1341688, _1341690, _1341692, _1341694, _1341696] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1341686, _1341686)), hAPP(hAPP(c_Product__Type_OPair(_1341686, _1341686), _1341688), _1341690)), hAPP(hAPP(c_Relation_Oinv__image(_1341692, _1341686), _1341694), _1341696))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1341692, _1341692)), hAPP(hAPP(c_Product__Type_OPair(_1341692, _1341692), hAPP(_1341696, _1341688)), hAPP(_1341696, _1341690))), _1341694)))], (30728 ^ _780205) ^ [_1341873, _1341875, _1341877, _1341879, _1341881, _1341883] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1341879, _1341879)), hAPP(hAPP(c_Product__Type_OPair(_1341879, _1341879), hAPP(_1341883, _1341875)), hAPP(_1341883, _1341877))), _1341881)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1341873, _1341873)), hAPP(hAPP(c_Product__Type_OPair(_1341873, _1341873), _1341875), _1341877)), hAPP(hAPP(c_Relation_Oinv__image(_1341879, _1341873), _1341881), _1341883))))], (30734 ^ _780205) ^ [_1342090, _1342092, _1342094, _1342096, _1342098] : [hBOOL(hAPP(hAPP(c_member(_1342090), _1342092), hAPP(c_Relation_OImage(_1342094, _1342090, _1342096), _1342098))), 30738 ^ _780205 : [(30739 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1342094), 30737 ^ [_1342090, _1342092, _1342094, _1342096, _1342098]), _1342098)))], (30741 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1342094, _1342090)), hAPP(hAPP(c_Product__Type_OPair(_1342094, _1342090), 30737 ^ [_1342090, _1342092, _1342094, _1342096, _1342098]), _1342092)), _1342096)))]]], (30743 ^ _780205) ^ [_1342306, _1342308, _1342310, _1342312, _1342314] : [-(hBOOL(hAPP(hAPP(c_member(_1342306), _1342308), hAPP(c_Relation_OImage(_1342310, _1342306, _1342312), _1342314)))), 30744 ^ _780205 : [(30745 ^ _780205) ^ [_1342392] : [hBOOL(hAPP(hAPP(c_member(_1342310), _1342392), _1342314)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1342310, _1342306)), hAPP(hAPP(c_Product__Type_OPair(_1342310, _1342306), _1342392), _1342308)), _1342312))]]], (30753 ^ _780205) ^ [_1342572, _1342574, _1342576, _1342578, _1342580, _1342582] : [hBOOL(hAPP(hAPP(c_member(_1342572), _1342574), _1342576)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1342572, _1342578)), hAPP(hAPP(c_Product__Type_OPair(_1342572, _1342578), _1342574), _1342580)), _1342582)), -(hBOOL(hAPP(hAPP(c_member(_1342578), _1342580), hAPP(c_Relation_OImage(_1342572, _1342578, _1342582), _1342576))))], (30763 ^ _780205) ^ [_1342797, _1342799] : [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), _1342797), _1342799))), 30766 ^ _780205 : [(30767 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342799), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1342797, _1342799) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1342797), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1342799)))], (30773 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342799), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 30776 ^ _780205 : [(30777 ^ _780205) ^ [] : [30778 ^ _780205 : [(30779 ^ _780205) ^ [] : [_1342797 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (30781 ^ _780205) ^ [] : [_1342799 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1342797, _1342799) = 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)))], (30785 ^ _780205) ^ [] : [-(c_Nitpick_Onorm__frac(_1342797, _1342799) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1342797), _1342799)), 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), _1342797))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1342799)))), -(_1342797 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1342799 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (30795 ^ _780205) ^ [_1343289, _1343291] : [class_Rings_Oring__1(_1343289), 30798 ^ _780205 : [(30799 ^ _780205) ^ [] : [_1343291 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1343289), _1343291) = c_Groups_Ozero__class_Ozero(_1343289))], (30805 ^ _780205) ^ [] : [-(_1343291 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30808 ^ _780205 : [(30809 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1343291), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1343289), _1343291) = hAPP(c_Groups_Ouminus__class_Ouminus(_1343289), hAPP(c_Int_Oring__1__class_Oof__int(_1343289), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1343291))))], (30815 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1343291), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1343289), _1343291) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1343289), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1343289, _1343289)), tc_fun(tc_Int_Oint, _1343289)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1343289, _1343289), _1343289), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1343289, _1343289)), tc_fun(tc_Int_Oint, _1343289)), tc_Int_Oint), c_COMBB(tc_fun(_1343289, _1343289), _1343289, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1343289, tc_fun(tc_fun(_1343289, _1343289), _1343289), tc_Int_Oint), c_HOL_OLet(_1343289, _1343289)), c_Int_Oring__1__class_Oof__int(_1343289)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1343289, _1343289), tc_fun(_1343289, _1343289)), hAPP(hAPP(c_COMBB(tc_fun(_1343289, tc_fun(_1343289, _1343289)), tc_fun(tc_fun(_1343289, _1343289), tc_fun(_1343289, _1343289)), tc_Int_Oint), c_COMBS(_1343289, _1343289, _1343289)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1343289, _1343289), tc_fun(_1343289, tc_fun(_1343289, _1343289))), hAPP(hAPP(c_COMBB(tc_fun(_1343289, tc_fun(_1343289, _1343289)), tc_fun(tc_fun(_1343289, _1343289), tc_fun(_1343289, tc_fun(_1343289, _1343289))), tc_Int_Oint), c_COMBB(_1343289, tc_fun(_1343289, _1343289), _1343289)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1343289, tc_fun(_1343289, _1343289)), tc_Int_Oint), c_If(_1343289)), 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(_1343289, _1343289, _1343289), c_Groups_Oplus__class_Oplus(_1343289)), c_COMBI(_1343289))))), hAPP(hAPP(c_COMBC(_1343289, _1343289, _1343289), hAPP(hAPP(c_COMBB(_1343289, tc_fun(_1343289, _1343289), _1343289), c_Groups_Oplus__class_Oplus(_1343289)), hAPP(hAPP(c_COMBS(_1343289, _1343289, _1343289), c_Groups_Oplus__class_Oplus(_1343289)), c_COMBI(_1343289)))), c_Groups_Oone__class_Oone(_1343289))))), c_Divides_Odivmod__int(_1343291, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (30821 ^ _780205) ^ [_1344223, _1344225, _1344227, _1344229] : [c_Wellfounded_Omax__extp(_1344223, hAPP(hAPP(c_COMBC(_1344223, tc_fun(tc_prod(_1344223, _1344223), tc_HOL_Obool), tc_fun(_1344223, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344223, tc_fun(tc_fun(tc_prod(_1344223, _1344223), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1344223, _1344223), tc_HOL_Obool), tc_fun(_1344223, tc_HOL_Obool)), _1344223), c_COMBC(_1344223, tc_fun(tc_prod(_1344223, _1344223), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344223, tc_prod(_1344223, _1344223)), tc_fun(_1344223, tc_fun(tc_fun(tc_prod(_1344223, _1344223), tc_HOL_Obool), tc_HOL_Obool)), _1344223), hAPP(c_COMBB(tc_prod(_1344223, _1344223), tc_fun(tc_fun(tc_prod(_1344223, _1344223), tc_HOL_Obool), tc_HOL_Obool), _1344223), c_member(tc_prod(_1344223, _1344223)))), c_Product__Type_OPair(_1344223, _1344223)))), _1344225), _1344227, _1344229), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1344223, tc_HOL_Obool), tc_fun(_1344223, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1344223, tc_HOL_Obool), tc_fun(_1344223, tc_HOL_Obool)), _1344227), _1344229)), c_Wellfounded_Omax__ext(_1344223, _1344225))))], (30827 ^ _780205) ^ [_1344608, _1344610, _1344612, _1344614] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1344608, tc_HOL_Obool), tc_fun(_1344608, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1344608, tc_HOL_Obool), tc_fun(_1344608, tc_HOL_Obool)), _1344612), _1344614)), c_Wellfounded_Omax__ext(_1344608, _1344610))), -(c_Wellfounded_Omax__extp(_1344608, hAPP(hAPP(c_COMBC(_1344608, tc_fun(tc_prod(_1344608, _1344608), tc_HOL_Obool), tc_fun(_1344608, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344608, tc_fun(tc_fun(tc_prod(_1344608, _1344608), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1344608, _1344608), tc_HOL_Obool), tc_fun(_1344608, tc_HOL_Obool)), _1344608), c_COMBC(_1344608, tc_fun(tc_prod(_1344608, _1344608), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344608, tc_prod(_1344608, _1344608)), tc_fun(_1344608, tc_fun(tc_fun(tc_prod(_1344608, _1344608), tc_HOL_Obool), tc_HOL_Obool)), _1344608), hAPP(c_COMBB(tc_prod(_1344608, _1344608), tc_fun(tc_fun(tc_prod(_1344608, _1344608), tc_HOL_Obool), tc_HOL_Obool), _1344608), c_member(tc_prod(_1344608, _1344608)))), c_Product__Type_OPair(_1344608, _1344608)))), _1344610), _1344612, _1344614))], (30833 ^ _780205) ^ [_1344999, _1345001, _1345003, _1345005, _1345007] : [-(c_Nat_Onat_Onat__case(_1344999, _1345001, _1345003, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1345005)), _1345007)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1344999), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1345005))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1344999, _1344999), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1344999, tc_fun(_1344999, _1344999)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1344999, tc_fun(_1344999, _1344999)), tc_Int_Oint), c_If(_1344999)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1344999, _1345001, _1345003, _1345007))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1344999, tc_Int_Oint), _1345003), 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)), _1345007)))))], (30835 ^ _780205) ^ [_1345117, _1345119, _1345121, _1345123, _1345125, _1345127] : [_1345117 = _1345119, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345121, _1345123, _1345125), _1345127), _1345117) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345121, _1345123, _1345125), _1345127), _1345119))], (30841 ^ _780205) ^ [_1345242, _1345244, _1345246, _1345248, _1345250, _1345252] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345242, _1345244, _1345246), _1345248), hAPP(hAPP(c_Product__Type_OPair(_1345242, _1345244), _1345250), _1345252)) = hAPP(hAPP(_1345248, _1345250), _1345252))], (30843 ^ _780205) ^ [_1345300, _1345302, _1345304, _1345306, _1345308, _1345310] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345300, _1345302, _1345304), _1345306), hAPP(hAPP(c_Product__Type_OPair(_1345300, _1345302), _1345308), _1345310)) = hAPP(hAPP(_1345306, _1345308), _1345310))], (30845 ^ _780205) ^ [_1345358, _1345360, _1345362, _1345364, _1345366, _1345368, _1345370, _1345372] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345358, _1345360, _1345362), _1345364), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345366, _1345368, tc_prod(_1345358, _1345360)), _1345370), _1345372)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345366, _1345368, _1345362), hAPP(hAPP(c_COMBB(tc_fun(_1345368, tc_prod(_1345358, _1345360)), tc_fun(_1345368, _1345362), _1345366), hAPP(c_COMBB(tc_prod(_1345358, _1345360), _1345362, _1345368), hAPP(c_Product__Type_Oprod_Oprod__case(_1345358, _1345360, _1345362), _1345364))), _1345370)), _1345372))], (30847 ^ _780205) ^ [_1345464, _1345466, _1345468, _1345470] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1345464, _1345466, _1345468), hAPP(hAPP(c_COMBB(tc_fun(_1345466, tc_prod(_1345464, _1345466)), tc_fun(_1345466, _1345468), _1345464), hAPP(c_COMBB(tc_prod(_1345464, _1345466), _1345468, _1345466), _1345470)), c_Product__Type_OPair(_1345464, _1345466))) = _1345470)], (30849 ^ _780205) ^ [_1345532, _1345534, _1345536] : [-(hAPP(c_Product__Type_Ofst(_1345532, _1345534), _1345536) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345532, _1345534, _1345532), c_COMBK(_1345532, _1345534)), _1345536))], (30851 ^ _780205) ^ [_1345578, _1345580, _1345582] : [-(hAPP(c_Product__Type_Osnd(_1345578, _1345580), _1345582) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345578, _1345580, _1345580), hAPP(c_COMBK(tc_fun(_1345580, _1345580), _1345578), c_COMBI(_1345580))), _1345582))], (30853 ^ _780205) ^ [_1345632, _1345634, _1345636] : [-(c_Nat_Onat_Onat__case(_1345632, _1345634, _1345636, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1345634)], (30855 ^ _780205) ^ [_1345664, _1345666, _1345668, _1345670] : [-(c_Nat_Onat_Onat__case(_1345664, _1345666, _1345668, hAPP(c_Nat_OSuc, _1345670)) = hAPP(_1345668, _1345670))], (30857 ^ _780205) ^ [_1345704, _1345706, _1345708, _1345710, _1345712] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345704, _1345706, _1345708), _1345710), _1345712) = hAPP(hAPP(_1345710, hAPP(c_Product__Type_Ofst(_1345704, _1345706), _1345712)), hAPP(c_Product__Type_Osnd(_1345704, _1345706), _1345712)))], (30859 ^ _780205) ^ [_1345763, _1345765, _1345767, _1345769, _1345771, _1345773] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1345763, _1345765), _1345765, _1345767), hAPP(hAPP(c_COMBB(_1345769, tc_fun(_1345765, _1345767), tc_prod(_1345763, _1345765)), _1345771), hAPP(hAPP(c_COMBB(_1345763, _1345769, tc_prod(_1345763, _1345765)), _1345773), c_Product__Type_Ofst(_1345763, _1345765)))), c_Product__Type_Osnd(_1345763, _1345765)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1345763, _1345765, _1345767), hAPP(hAPP(c_COMBB(_1345769, tc_fun(_1345765, _1345767), _1345763), _1345771), _1345773)))], (30861 ^ _780205) ^ [_1345864, _1345866, _1345868, _1345870, _1345872] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345864, _1345866, _1345868), _1345870), _1345872) = hAPP(hAPP(_1345870, hAPP(c_Product__Type_Ofst(_1345864, _1345866), _1345872)), hAPP(c_Product__Type_Osnd(_1345864, _1345866), _1345872)))], (30863 ^ _780205) ^ [_1345923, _1345925, _1345927, _1345929, _1345931] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1345923, _1345925, _1345927), _1345929), _1345931) = hAPP(hAPP(_1345929, hAPP(c_Product__Type_Ofst(_1345923, _1345925), _1345931)), hAPP(c_Product__Type_Osnd(_1345923, _1345925), _1345931)))], (30865 ^ _780205) ^ [_1345997, _1345999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1345997)), _1345999)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1345997), _1345999)))], (30871 ^ _780205) ^ [_1346100, _1346102] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1346100), _1346102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1346100)), _1346102)))], (30877 ^ _780205) ^ [_1346209, _1346211] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1346209), hAPP(c_Nat_OSuc, _1346211)) = 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), _1346209), _1346211)))], (30879 ^ _780205) ^ [_1346254, _1346256] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1346254)), _1346256) = 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), _1346254)), _1346256))], (30881 ^ _780205) ^ [_1346299, _1346301] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1346299), hAPP(c_Nat_OSuc, _1346301)) = 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)), _1346301)), _1346299))], (30883 ^ _780205) ^ [_1346344, _1346346] : [-(c_Divides_Odivmod__int__rel(_1346344, _1346346) = 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, _1346344))), 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), _1346346)))))), 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)), _1346346))), 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)), _1346346))))), 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)), _1346346)))), 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), _1346346))), 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))))))))], (30885 ^ _780205) ^ [_1346459, _1346461, _1346463] : [-(c_Wellfounded_Omlex__prod(_1346459, _1346461, _1346463) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1346459), _1346459), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1346459, c_Wellfounded_Oless__than, _1346463)), hAPP(hAPP(c_COMBS(_1346459, _1346459, tc_prod(tc_Nat_Onat, _1346459)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1346459, tc_prod(tc_Nat_Onat, _1346459)), _1346459), c_Product__Type_OPair(tc_Nat_Onat, _1346459)), _1346461)), c_COMBI(_1346459))))], (30887 ^ _780205) ^ [_1346541, _1346543, _1346545, _1346547] : [-(c_Nat_Onat_Onat__case(_1346541, _1346543, _1346545, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1346547)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1346541), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1346547))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1346541, _1346541), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1346541, tc_fun(_1346541, _1346541)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1346541, tc_fun(_1346541, _1346541)), tc_Int_Oint), c_If(_1346541)), c_Nat__Numeral_Oneg)), _1346543)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1346541, tc_Int_Oint), _1346545), c_Int_Onat))))], (30889 ^ _780205) ^ [_1346643] : [-(c_Divides_Oadjust(_1346643) = 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)), _1346643))))), 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)), _1346643))))), 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))))))))], (30891 ^ _780205) ^ [] : [-(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)))))], (30893 ^ _780205) ^ [_1346731, _1346733] : [_1346731 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1346731, _1346733) = 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)))], (30899 ^ _780205) ^ [_1346809, _1346811] : [-(_1346809 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30902 ^ _780205 : [(30903 ^ _780205) ^ [] : [_1346811 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1346809, _1346811) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346809))], (30909 ^ _780205) ^ [] : [-(_1346811 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1346809, _1346811) = 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, _1346811))), 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)), _1346811)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346809))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1346811), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1346809), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1346809, _1346811)), 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), _1346811))))), c_Divides_Opdivmod(_1346809, _1346811)))))]]], (30915 ^ _780205) ^ [_1347178, _1347180] : [_1347178 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1347178, _1347180) = 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)))], (30921 ^ _780205) ^ [_1347256, _1347258] : [-(_1347256 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30924 ^ _780205 : [(30925 ^ _780205) ^ [] : [_1347258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1347256, _1347258) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1347256))], (30931 ^ _780205) ^ [] : [-(_1347258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1347256, _1347258) = 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, _1347258))), 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, _1347256)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1347258))), c_Divides_Opdivmod(_1347256, _1347258)), 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), _1347258))))), c_Divides_Opdivmod(_1347256, _1347258)))))]]], (30937 ^ _780205) ^ [_1347568, _1347570, _1347572] : [class_Rings_Oring__1(_1347568), -(hAPP(c_Int_Oring__1__class_Oof__int(_1347568), 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), _1347570), _1347572)), 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(_1347568), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1347568), _1347570)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1347568), _1347572)))], (30943 ^ _780205) ^ [_1347727, _1347729, _1347731, _1347733, _1347735, _1347737, _1347739] : [hBOOL(hAPP(hAPP(c_member(_1347727), _1347729), hAPP(hAPP(_1347731, _1347733), _1347735))), -(hBOOL(hAPP(hAPP(c_member(_1347727), _1347729), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1347737, _1347739, tc_fun(_1347727, tc_HOL_Obool)), _1347731), hAPP(hAPP(c_Product__Type_OPair(_1347737, _1347739), _1347733), _1347735)))))], (30949 ^ _780205) ^ [_1347898, _1347900, _1347902, _1347904, _1347906] : [hBOOL(hAPP(hAPP(_1347898, _1347900), _1347902)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1347904, _1347906, tc_HOL_Obool), _1347898), hAPP(hAPP(c_Product__Type_OPair(_1347904, _1347906), _1347900), _1347902))))], (30955 ^ _780205) ^ [_1348027, _1348029, _1348031, _1348033, _1348035] : [hBOOL(hAPP(hAPP(_1348027, _1348029), _1348031)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1348033, _1348035, tc_HOL_Obool), _1348027), hAPP(hAPP(c_Product__Type_OPair(_1348033, _1348035), _1348029), _1348031))))], (30961 ^ _780205) ^ [_1348156, _1348158, _1348160, _1348162, _1348164, _1348166, _1348168] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1348156, _1348158, tc_fun(_1348160, tc_HOL_Obool)), _1348162), hAPP(hAPP(c_Product__Type_OPair(_1348156, _1348158), _1348164), _1348166)), _1348168)), -(hBOOL(hAPP(hAPP(hAPP(_1348162, _1348164), _1348166), _1348168)))], (30967 ^ _780205) ^ [_1348307, _1348309, _1348311, _1348313, _1348315] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1348307, _1348309, tc_HOL_Obool), _1348311), hAPP(hAPP(c_Product__Type_OPair(_1348307, _1348309), _1348313), _1348315))), -(hBOOL(hAPP(hAPP(_1348311, _1348313), _1348315)))], (30973 ^ _780205) ^ [_1348436, _1348438, _1348440, _1348442, _1348444, _1348446] : [-(hAPP(c_Product__Type_Oapsnd(_1348436, _1348438, _1348440, _1348442), hAPP(hAPP(c_Product__Type_OPair(_1348440, _1348436), _1348444), _1348446)) = hAPP(hAPP(c_Product__Type_OPair(_1348440, _1348438), _1348444), hAPP(_1348442, _1348446)))], (30975 ^ _780205) ^ [_1348498, _1348500, _1348502, _1348504, _1348506] : [-(hAPP(c_Product__Type_Ofst(_1348498, _1348500), hAPP(c_Product__Type_Oapsnd(_1348502, _1348500, _1348498, _1348504), _1348506)) = hAPP(c_Product__Type_Ofst(_1348498, _1348502), _1348506))], (30977 ^ _780205) ^ [_1348549, _1348551, _1348553, _1348555, _1348557] : [-(hAPP(c_Product__Type_Osnd(_1348549, _1348551), hAPP(c_Product__Type_Oapsnd(_1348553, _1348551, _1348549, _1348555), _1348557)) = hAPP(_1348555, hAPP(c_Product__Type_Osnd(_1348549, _1348553), _1348557)))], (30979 ^ _780205) ^ [_1348630, _1348632, _1348634, _1348636, _1348638, _1348640] : [hAPP(c_Product__Type_Oapsnd(_1348630, _1348632, _1348634, _1348636), _1348638) = hAPP(c_Product__Type_Oapsnd(_1348630, _1348632, _1348634, _1348640), _1348638), -(hAPP(_1348636, hAPP(c_Product__Type_Osnd(_1348634, _1348630), _1348638)) = hAPP(_1348640, hAPP(c_Product__Type_Osnd(_1348634, _1348630), _1348638)))], (30985 ^ _780205) ^ [_1348779, _1348781, _1348783, _1348785, _1348787, _1348789] : [hAPP(_1348785, hAPP(c_Product__Type_Osnd(_1348783, _1348779), _1348787)) = hAPP(_1348789, hAPP(c_Product__Type_Osnd(_1348783, _1348779), _1348787)), -(hAPP(c_Product__Type_Oapsnd(_1348779, _1348781, _1348783, _1348785), _1348787) = hAPP(c_Product__Type_Oapsnd(_1348779, _1348781, _1348783, _1348789), _1348787))], (30991 ^ _780205) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (30993 ^ _780205) ^ [_1348952, _1348954] : [-(c_FunDef_Orp__inv__image(_1348952, _1348954) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool), tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool), tc_fun(tc_fun(_1348954, _1348952), tc_prod(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool), tc_fun(tc_fun(_1348954, _1348952), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool), tc_fun(tc_fun(_1348954, _1348952), tc_prod(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1348954, _1348952), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)), tc_fun(tc_fun(_1348954, _1348952), tc_prod(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool), tc_fun(tc_fun(_1348954, _1348952), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool), tc_fun(tc_fun(_1348954, _1348952), tc_prod(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool))))), tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1348954, _1348952), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)), tc_fun(tc_fun(_1348954, _1348952), tc_prod(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool))), tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1348954, _1348952), tc_fun(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1348954, _1348952), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)), tc_fun(tc_fun(_1348954, _1348952), tc_prod(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)))), tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool)), c_COMBS(tc_fun(_1348954, _1348952), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1348954, _1348952), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)), tc_fun(tc_fun(_1348954, _1348952), tc_fun(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)))), tc_fun(tc_prod(_1348952, _1348952), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool))), tc_fun(_1348954, _1348952)), c_Product__Type_OPair(tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool), tc_fun(tc_prod(_1348954, _1348954), tc_HOL_Obool)))), c_Relation_Oinv__image(_1348952, _1348954))))), c_Relation_Oinv__image(_1348952, _1348954))))], (30995 ^ _780205) ^ [_1349474, _1349476] : [30996 ^ _780205 : [(30997 ^ _780205) ^ [] : [_1349474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30999 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1349476), _1349474))]], -(c_Divides_Odivmod__nat(_1349476, _1349474) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1349476))], (31003 ^ _780205) ^ [_1349605, _1349607] : [-(c_Divides_Odivmod__nat(_1349607, _1349605) = 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), _1349607), _1349605), _1349605))), -(_1349605 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1349607), _1349605)))], (31013 ^ _780205) ^ [_1349670, _1349672] : [-(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), _1349670), _1349672)), 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), _1349672), _1349670)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (31015 ^ _780205) ^ [] : [-(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))))))], (31017 ^ _780205) ^ [_1349752] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1349752) = 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), _1349752), 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))))))], (31019 ^ _780205) ^ [_1349796, _1349798, _1349800, _1349802] : [-(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), _1349796), _1349798)), 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), _1349800), _1349802)), 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), _1349796), _1349800)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1349798), _1349802))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (31021 ^ _780205) ^ [_1349897, _1349899] : [-(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), _1349897), _1349899)), 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), _1349897), _1349899))], (31023 ^ _780205) ^ [_1349970, _1349972, _1349974, _1349976] : [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), _1349970), _1349972)), 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), _1349974), _1349976)), 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), _1349970), _1349976)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1349974), _1349972))))], (31029 ^ _780205) ^ [_1350163, _1350165, _1350167, _1350169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1350163), _1350169)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1350167), _1350165))), -(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), _1350163), _1350165)), 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), _1350167), _1350169)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (31035 ^ _780205) ^ [_1350383, _1350385, _1350387, _1350389] : [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), _1350383), _1350385)), 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), _1350387), _1350389)), 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), _1350383), _1350389)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1350387), _1350385))))], (31041 ^ _780205) ^ [_1350576, _1350578, _1350580, _1350582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1350576), _1350582)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1350580), _1350578))), -(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), _1350576), _1350578)), 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), _1350580), _1350582)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (31047 ^ _780205) ^ [_1350775, _1350777, _1350779, _1350781] : [-(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), _1350775), _1350777)), 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), _1350779), _1350781)), 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), _1350775), _1350779)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1350777), _1350781))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1350775), _1350781)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1350777), _1350779)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (31049 ^ _780205) ^ [] : [-(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))))))], (31051 ^ _780205) ^ [_1350918, _1350920, _1350922, _1350924, _1350926] : [-(hAPP(c_Nat_Onat_Onat__rec(_1350918, _1350920, _1350922), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1350924)), _1350926)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1350918), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1350924))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1350918, _1350918), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1350918, tc_fun(_1350918, _1350918)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1350918, tc_fun(_1350918, _1350918)), tc_Int_Oint), c_If(_1350918)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1350918, _1350920, _1350922), _1350926))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1350918, _1350918), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1350918, _1350918), tc_Int_Oint), _1350922), 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)), _1350926))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1350918, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1350918, _1350920, _1350922)), 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)), _1350926))))))], (31053 ^ _780205) ^ [_1351070, _1351072] : [class_Rings_Osemiring__1(_1351070), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1351070), _1351072) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1351070, hAPP(hAPP(c_COMBC(_1351070, _1351070, _1351070), c_Groups_Oplus__class_Oplus(_1351070)), c_Groups_Oone__class_Oone(_1351070)), _1351072, c_Groups_Ozero__class_Ozero(_1351070)))], (31059 ^ _780205) ^ [_1351197, _1351199, _1351201, _1351203] : [-(hAPP(c_Nat_Onat_Onat__rec(_1351197, _1351199, _1351201), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1351203)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1351197), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1351203))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1351197, _1351197), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1351197, tc_fun(_1351197, _1351197)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1351197, tc_fun(_1351197, _1351197)), tc_Int_Oint), c_If(_1351197)), c_Nat__Numeral_Oneg)), _1351199)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1351197, _1351197), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1351197, _1351197), tc_Int_Oint), _1351201), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1351197, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1351197, _1351199, _1351201)), c_Int_Onat)))))], (31061 ^ _780205) ^ [_1351328] : [class_Orderings_Olinorder(_1351328), -(c_Orderings_Oord_Omax(_1351328, hAPP(c_COMBC(_1351328, _1351328, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1351328))) = c_Orderings_Oord__class_Omin(_1351328))], (31067 ^ _780205) ^ [_1351429, _1351431, _1351433] : [-(hAPP(c_Nat_Onat_Onat__rec(_1351429, _1351431, _1351433), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1351431)], (31069 ^ _780205) ^ [_1351463, _1351465, _1351467, _1351469] : [-(hAPP(c_Nat_Onat_Onat__rec(_1351463, _1351465, _1351467), hAPP(c_Nat_OSuc, _1351469)) = hAPP(hAPP(_1351467, _1351469), hAPP(c_Nat_Onat_Onat__rec(_1351463, _1351465, _1351467), _1351469)))], (31071 ^ _780205) ^ [_1351515, _1351517, _1351519] : [class_Rings_Osemiring__1(_1351515), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1351515, _1351517, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1351519) = _1351519)], (31077 ^ _780205) ^ [_1351602, _1351604, _1351606, _1351608] : [class_Rings_Osemiring__1(_1351602), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1351602, _1351604, hAPP(c_Nat_OSuc, _1351606), _1351608) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1351602, _1351604, _1351606, hAPP(_1351604, _1351608)))], (31083 ^ _780205) ^ [_1351713, _1351715, _1351717] : [31085 ^ _780205 : [(31086 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1351713), 31084 ^ [_1351713, _1351715, _1351717]), _1351715)))], (31088 ^ _780205) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1351717, 31084 ^ [_1351713, _1351715, _1351717]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351713, tc_Int_Oint), _1351717), _1351715) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351713, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1351713), c_Int_Onat), _1351717)), _1351715)))], (31092 ^ _780205) ^ [_1351958, _1351960] : [c_Relation_Oirrefl(_1351958, _1351960), 31095 ^ _780205 : [(31096 ^ _780205) ^ [_1352040] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1351958, _1351958)), hAPP(hAPP(c_Product__Type_OPair(_1351958, _1351958), _1352040), _1352040)), _1351960))]]], (31098 ^ _780205) ^ [_1352080, _1352082] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1352080, _1352080)), hAPP(hAPP(c_Product__Type_OPair(_1352080, _1352080), 31099 ^ [_1352080, _1352082]), 31099 ^ [_1352080, _1352082])), _1352082))), -(c_Relation_Oirrefl(_1352080, _1352082))], (31105 ^ _780205) ^ [_1352151, _1352153, _1352155] : [31107 ^ _780205 : [(31108 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1352151), 31106 ^ [_1352151, _1352153, _1352155]), _1352153)))], (31110 ^ _780205) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1352155, 31106 ^ [_1352151, _1352153, _1352155]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352151, tc_Int_Oint), _1352155), _1352153) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352151, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1352151), c_Int_Onat), _1352155)), _1352153)))], (31114 ^ _780205) ^ [_1352381, _1352383, _1352385] : [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), _1352381), _1352383))), -(hBOOL(hAPP(hAPP(_1352385, _1352381), _1352383))), 31121 ^ _780205 : [(31122 ^ _780205) ^ [] : [-(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), 31119 ^ [_1352381, _1352383, _1352385]), 31120 ^ [_1352381, _1352383, _1352385]))))], (31130 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1352385, 31119 ^ [_1352381, _1352383, _1352385]), 31120 ^ [_1352381, _1352383, _1352385]))], (31124 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 31120 ^ [_1352381, _1352383, _1352385]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1352385, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 31119 ^ [_1352381, _1352383, _1352385])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 31120 ^ [_1352381, _1352383, _1352385]))))]]], (31134 ^ _780205) ^ [_1352854, _1352856, _1352858] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1352854), _1352856), _1352858) = c_Nitpick_OAbs__Frac(_1352854, c_Nitpick_Onorm__frac(_1352856, _1352858)))], (31138 ^ _780205) ^ [_1352895] : [-(_1352895 = 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), 31135 ^ [_1352895]), 31136 ^ [_1352895])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (31140 ^ _780205) ^ [_1352946, _1352948, _1352950] : [-(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), _1352946)), 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))), _1352948))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1352950))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1352950)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1352946), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1352946), 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), _1352950), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1352948)))))], (31142 ^ _780205) ^ [_1353033, _1353035, _1353037, _1353039] : [-(hAPP(c_Relation_OField(_1353033), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1353033, _1353033)), hAPP(hAPP(c_Product__Type_OPair(_1353033, _1353033), _1353035), _1353037)), _1353039)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353033, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1353033), _1353035), hAPP(hAPP(c_Set_Oinsert(_1353033), _1353037), c_Orderings_Obot__class_Obot(tc_fun(_1353033, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1353033), _1353039)))], (31144 ^ _780205) ^ [_1353124] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1353124))))], (31146 ^ _780205) ^ [] : [-(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)))], (31148 ^ _780205) ^ [_1353170, _1353172, _1353174] : [class_Orderings_Olinorder(_1353170), 31151 ^ _780205 : [(31152 ^ _780205) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1353170), _1353172) = hAPP(c_SetInterval_Oord__class_OlessThan(_1353170), _1353174), -(_1353172 = _1353174)], (31158 ^ _780205) ^ [] : [_1353172 = _1353174, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1353170), _1353172) = hAPP(c_SetInterval_Oord__class_OlessThan(_1353170), _1353174))]]], (31164 ^ _780205) ^ [_1353411] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1353411)) = _1353411)], (31166 ^ _780205) ^ [_1353440] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1353440)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1353440), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1353440)))], (31168 ^ _780205) ^ [_1353478, _1353480, _1353482] : [class_Orderings_Oord(_1353478), 31171 ^ _780205 : [(31172 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1353478), _1353480), hAPP(c_SetInterval_Oord__class_OlessThan(_1353478), _1353482))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353478), _1353480), _1353482)))], (31178 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1353478), _1353480), _1353482)), -(hBOOL(hAPP(hAPP(c_member(_1353478), _1353480), hAPP(c_SetInterval_Oord__class_OlessThan(_1353478), _1353482))))]]], (31184 ^ _780205) ^ [_1353746, _1353748, _1353750] : [class_Orderings_Olinorder(_1353746), 31187 ^ _780205 : [(31188 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1353746, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1353746), _1353748)), hAPP(c_SetInterval_Oord__class_OlessThan(_1353746), _1353750))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1353746), _1353748), _1353750)))], (31194 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1353746), _1353748), _1353750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1353746, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1353746), _1353748)), hAPP(c_SetInterval_Oord__class_OlessThan(_1353746), _1353750))))]]], (31200 ^ _780205) ^ [_1354038, _1354040, _1354042] : [class_Groups_Ocomm__monoid__add(_1354038), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354038), _1354040), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1354042))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354038), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354038), _1354040), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1354042))), hAPP(_1354040, _1354042)))], (31206 ^ _780205) ^ [_1354191, _1354193, _1354195] : [class_Orderings_Olinorder(_1354191), 31209 ^ _780205 : [(31210 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1354191, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1354191), _1354193)), hAPP(c_SetInterval_Oord__class_OlessThan(_1354191), _1354195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354191), _1354193), _1354195)))], (31216 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1354191), _1354193), _1354195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1354191, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1354191), _1354193)), hAPP(c_SetInterval_Oord__class_OlessThan(_1354191), _1354195))))]]], (31222 ^ _780205) ^ [_1354483, _1354485] : [class_Orderings_Oorder(_1354483), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354483, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1354483), _1354485), c_Orderings_Obot__class_Obot(tc_fun(_1354483, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1354483), _1354485)) = hAPP(hAPP(c_Set_Oinsert(_1354483), _1354485), c_Orderings_Obot__class_Obot(tc_fun(_1354483, tc_HOL_Obool))))], (31239 ^ _780205) ^ [_1354841] : [31241 ^ _780205 : [(31242 ^ _780205) ^ [_1354917] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 31240 ^ [_1354841, _1354917]), _1354841)))], (31244 ^ _780205) ^ [_1354951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31240 ^ [_1354841, _1354951]), _1354951))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1354841)))], (31228 ^ _780205) ^ [_1354654] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1354654)), 31232 ^ _780205 : [(31233 ^ _780205) ^ [_1354734] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1354734), _1354654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1354734), 31231 ^ [_1354654])))]]], (31248 ^ _780205) ^ [_1355020] : [-(hAPP(c_Relation_OField(_1355020), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1355020, _1355020), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1355020, tc_HOL_Obool)))], (31250 ^ _780205) ^ [_1355061, _1355063, _1355065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1355061, _1355061), tc_HOL_Obool)), _1355063), _1355065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1355061, tc_HOL_Obool)), hAPP(c_Relation_OField(_1355061), _1355063)), hAPP(c_Relation_OField(_1355061), _1355065))))], (31267 ^ _780205) ^ [_1355405] : [31269 ^ _780205 : [(31270 ^ _780205) ^ [_1355481] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 31268 ^ [_1355405, _1355481]), _1355405)))], (31272 ^ _780205) ^ [_1355515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 31268 ^ [_1355405, _1355515]), _1355515))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1355405)))], (31256 ^ _780205) ^ [_1355218] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1355218)), 31260 ^ _780205 : [(31261 ^ _780205) ^ [_1355298] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1355298), _1355218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1355298), 31259 ^ [_1355218])))]]], (31276 ^ _780205) ^ [_1355584, _1355586, _1355588] : [-(hAPP(c_Relation_OField(_1355584), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1355584, _1355584), tc_HOL_Obool)), _1355586), _1355588)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1355584, tc_HOL_Obool)), hAPP(c_Relation_OField(_1355584), _1355586)), hAPP(c_Relation_OField(_1355584), _1355588)))], (31278 ^ _780205) ^ [_1355651, _1355653] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1355651, _1355651)), _1355653)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1355651), hAPP(c_Relation_OField(_1355651), _1355653))))], (31284 ^ _780205) ^ [_1355760, _1355762, _1355764, _1355766] : [class_Rings_Ocomm__semiring__1(_1355760), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355760), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355760), c_Groups_Oone__class_Oone(_1355760)), c_Groups_Oone__class_Oone(_1355760))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355760), hAPP(hAPP(c_COMBB(_1355760, _1355760, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1355760), _1355762)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1355760, _1355760), hAPP(hAPP(c_COMBB(_1355760, tc_fun(_1355760, _1355760), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1355760)), c_Nat_Osemiring__1__class_Oof__nat(_1355760))), _1355764))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1355766))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355760), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1355760), _1355766)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355760), _1355762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355760), _1355762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1355760), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1355760), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1355766), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1355764)))))], (31290 ^ _780205) ^ [_1356083, _1356085, _1356087] : [-(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), _1356083)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1356085))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1356087))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1356087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1356083), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1356083), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1356087), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1356085)))))], (31292 ^ _780205) ^ [_1356185, _1356187, _1356189, _1356191] : [hBOOL(hAPP(hAPP(c_member(_1356185), _1356187), c_SetInterval_Oord_OatMost(_1356185, _1356189, _1356191))), -(hBOOL(hAPP(hAPP(_1356189, _1356187), _1356191)))], (31298 ^ _780205) ^ [_1356294, _1356296, _1356298, _1356300] : [hBOOL(hAPP(hAPP(_1356298, _1356296), _1356300)), -(hBOOL(hAPP(hAPP(c_member(_1356294), _1356296), c_SetInterval_Oord_OatMost(_1356294, _1356298, _1356300))))], (31304 ^ _780205) ^ [_1356430, _1356432, _1356434, _1356436] : [hBOOL(hAPP(hAPP(c_member(_1356430), _1356432), c_SetInterval_Oord_OatLeast(_1356430, _1356434, _1356436))), -(hBOOL(hAPP(hAPP(_1356434, _1356436), _1356432)))], (31310 ^ _780205) ^ [_1356539, _1356541, _1356543, _1356545] : [hBOOL(hAPP(hAPP(_1356543, _1356545), _1356541)), -(hBOOL(hAPP(hAPP(c_member(_1356539), _1356541), c_SetInterval_Oord_OatLeast(_1356539, _1356543, _1356545))))], (31316 ^ _780205) ^ [_1356675, _1356677, _1356679, _1356681] : [hBOOL(hAPP(hAPP(c_member(_1356675), _1356677), c_SetInterval_Oord_OlessThan(_1356675, _1356679, _1356681))), -(hBOOL(hAPP(hAPP(_1356679, _1356677), _1356681)))], (31322 ^ _780205) ^ [_1356784, _1356786, _1356788, _1356790] : [hBOOL(hAPP(hAPP(_1356788, _1356786), _1356790)), -(hBOOL(hAPP(hAPP(c_member(_1356784), _1356786), c_SetInterval_Oord_OlessThan(_1356784, _1356788, _1356790))))], (31328 ^ _780205) ^ [_1356920, _1356922, _1356924, _1356926] : [hBOOL(hAPP(hAPP(c_member(_1356920), _1356922), c_SetInterval_Oord_OgreaterThan(_1356920, _1356924, _1356926))), -(hBOOL(hAPP(hAPP(_1356924, _1356926), _1356922)))], (31334 ^ _780205) ^ [_1357029, _1357031, _1357033, _1357035] : [hBOOL(hAPP(hAPP(_1357033, _1357035), _1357031)), -(hBOOL(hAPP(hAPP(c_member(_1357029), _1357031), c_SetInterval_Oord_OgreaterThan(_1357029, _1357033, _1357035))))], (31340 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (31342 ^ _780205) ^ [_1357195, _1357197, _1357199, _1357201, _1357203, _1357205] : [hBOOL(hAPP(hAPP(c_member(_1357195), _1357197), c_SetInterval_Oord_OgreaterThanAtMost(_1357195, _1357199, _1357201, _1357203, _1357205))), 31345 ^ _780205 : [(31346 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1357201, _1357203), _1357197)))], (31348 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1357199, _1357197), _1357205)))]]], (31350 ^ _780205) ^ [_1357348, _1357350, _1357352, _1357354, _1357356, _1357358] : [-(hBOOL(hAPP(hAPP(c_member(_1357348), _1357350), c_SetInterval_Oord_OgreaterThanAtMost(_1357348, _1357352, _1357354, _1357356, _1357358)))), hBOOL(hAPP(hAPP(_1357354, _1357356), _1357350)), hBOOL(hAPP(hAPP(_1357352, _1357350), _1357358))], (31360 ^ _780205) ^ [_1357568, _1357570, _1357572, _1357574, _1357576, _1357578] : [hBOOL(hAPP(hAPP(c_member(_1357568), _1357570), c_SetInterval_Oord_OatLeastLessThan(_1357568, _1357572, _1357574, _1357576, _1357578))), 31363 ^ _780205 : [(31364 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1357572, _1357576), _1357570)))], (31366 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1357574, _1357570), _1357578)))]]], (31368 ^ _780205) ^ [_1357721, _1357723, _1357725, _1357727, _1357729, _1357731] : [-(hBOOL(hAPP(hAPP(c_member(_1357721), _1357723), c_SetInterval_Oord_OatLeastLessThan(_1357721, _1357725, _1357727, _1357729, _1357731)))), hBOOL(hAPP(hAPP(_1357725, _1357729), _1357723)), hBOOL(hAPP(hAPP(_1357727, _1357723), _1357731))], (31378 ^ _780205) ^ [_1357938, _1357940, _1357942, _1357944, _1357946] : [hBOOL(hAPP(hAPP(c_member(_1357938), _1357940), c_SetInterval_Oord_OgreaterThanLessThan(_1357938, _1357942, _1357944, _1357946))), 31381 ^ _780205 : [(31382 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1357942, _1357944), _1357940)))], (31384 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1357942, _1357940), _1357946)))]]], (31386 ^ _780205) ^ [_1358087, _1358089, _1358091, _1358093, _1358095] : [-(hBOOL(hAPP(hAPP(c_member(_1358087), _1358089), c_SetInterval_Oord_OgreaterThanLessThan(_1358087, _1358091, _1358093, _1358095)))), hBOOL(hAPP(hAPP(_1358091, _1358093), _1358089)), hBOOL(hAPP(hAPP(_1358091, _1358089), _1358095))], (31396 ^ _780205) ^ [_1358298, _1358300, _1358302, _1358304, _1358306] : [hBOOL(hAPP(hAPP(c_member(_1358298), _1358300), c_SetInterval_Oord_OatLeastAtMost(_1358298, _1358302, _1358304, _1358306))), 31399 ^ _780205 : [(31400 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1358302, _1358304), _1358300)))], (31402 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1358302, _1358300), _1358306)))]]], (31404 ^ _780205) ^ [_1358447, _1358449, _1358451, _1358453, _1358455] : [-(hBOOL(hAPP(hAPP(c_member(_1358447), _1358449), c_SetInterval_Oord_OatLeastAtMost(_1358447, _1358451, _1358453, _1358455)))), hBOOL(hAPP(hAPP(_1358451, _1358453), _1358449)), hBOOL(hAPP(hAPP(_1358451, _1358449), _1358455))], (31414 ^ _780205) ^ [_1358634, _1358636, _1358638, _1358640, _1358642] : [class_Groups_Oordered__ab__group__add(_1358634), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358636), _1358638)), 31424 ^ _780205 : [(31425 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358636), 31423 ^ [_1358634, _1358636, _1358638, _1358640, _1358642]), _1358638)))], (31427 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358634), c_Groups_Ozero__class_Ozero(_1358634)), hAPP(_1358640, 31423 ^ [_1358634, _1358636, _1358638, _1358640, _1358642])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358636, _1358634), _1358640), _1358638) = c_Groups_Ozero__class_Ozero(_1358634), hBOOL(hAPP(hAPP(c_member(_1358636), _1358642), _1358638)), -(hAPP(_1358640, _1358642) = c_Groups_Ozero__class_Ozero(_1358634))], (31439 ^ _780205) ^ [_1359132, _1359134, _1359136, _1359138, _1359140, _1359142] : [class_Groups_Oordered__ab__group__add(_1359132), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359134), _1359136)), 31449 ^ _780205 : [(31450 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359134), 31448 ^ [_1359132, _1359134, _1359136, _1359138, _1359140, _1359142]), _1359136)))], (31452 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359132), c_Groups_Ozero__class_Ozero(_1359132)), hAPP(_1359138, 31448 ^ [_1359132, _1359134, _1359136, _1359138, _1359140, _1359142])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359134, _1359132), _1359138), _1359136) = _1359140, hBOOL(hAPP(hAPP(c_member(_1359134), _1359142), _1359136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359132), hAPP(_1359138, _1359142)), _1359140)))], (31464 ^ _780205) ^ [_1359652, _1359654] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1359652)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1359654)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1359654))), 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, _1359652))), 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), _1359652)), c_Int_Onat)))))], (31466 ^ _780205) ^ [_1359724, _1359726] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1359724)), hAPP(c_Nat_OSuc, _1359726)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1359724))), 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, _1359726))), 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)), _1359726)))))], (31468 ^ _780205) ^ [_1359790, _1359792, _1359794, _1359796] : [class_Orderings_Olinorder(_1359790), 31471 ^ _780205 : [(31482 ^ _780205) ^ [] : [31483 ^ _780205 : [(31484 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359790), _1359792), _1359794))], (31486 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359790), _1359792), _1359796))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359790), _1359792), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359790), _1359794), _1359796))))], (31472 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359790), _1359792), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359790), _1359794), _1359796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359790), _1359792), _1359794))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359790), _1359792), _1359796)))]]], (31490 ^ _780205) ^ [_1360139, _1360141, _1360143, _1360145] : [class_Orderings_Olinorder(_1360139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360139), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360139), _1360141), _1360143)), _1360145)), 31497 ^ _780205 : [(31498 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360139), _1360141), _1360145)))], (31500 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360139), _1360143), _1360145)))]]], (31502 ^ _780205) ^ [_1360362, _1360364, _1360366, _1360368, _1360370] : [class_Orderings_Olinorder(_1360362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360362), _1360364), _1360366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360362), _1360368), _1360370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360362), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360362), _1360364), _1360368)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360362), _1360366), _1360370))))], (31516 ^ _780205) ^ [_1360633, _1360635, _1360637, _1360639] : [class_Orderings_Olinorder(_1360633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360633), _1360635), _1360637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360633), _1360639), _1360637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360633), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360633), _1360635), _1360639)), _1360637)))], (31530 ^ _780205) ^ [_1360882, _1360884, _1360886, _1360888] : [class_Orderings_Olinorder(_1360882), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360882), _1360884), _1360886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360882), _1360888), _1360886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360882), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360882), _1360884), _1360888)), _1360886)))], (31544 ^ _780205) ^ [_1361131, _1361133, _1361135] : [class_Orderings_Olinorder(_1361131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361131), _1361133), _1361135)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361131), _1361135), _1361133) = _1361135)], (31554 ^ _780205) ^ [_1361292, _1361294, _1361296] : [class_Orderings_Olinorder(_1361292), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361292), _1361294), _1361296)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361292), _1361294), _1361296) = _1361296)], (31564 ^ _780205) ^ [_1361453, _1361455, _1361457, _1361459] : [class_Orderings_Olinorder(_1361453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361453), _1361455), _1361457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361453), _1361455), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361453), _1361459), _1361457))))], (31574 ^ _780205) ^ [_1361632, _1361634, _1361636, _1361638] : [class_Orderings_Olinorder(_1361632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361632), _1361634), _1361636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361632), _1361634), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361632), _1361636), _1361638))))], (31584 ^ _780205) ^ [_1361811, _1361813, _1361815, _1361817] : [class_Orderings_Olinorder(_1361811), 31587 ^ _780205 : [(31588 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361811), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361811), _1361813), _1361815)), _1361817)), 31591 ^ _780205 : [(31592 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361811), _1361813), _1361817)))], (31594 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361811), _1361815), _1361817)))]]], (31596 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361811), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361811), _1361813), _1361815)), _1361817))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361811), _1361813), _1361817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361811), _1361815), _1361817))]]], (31606 ^ _780205) ^ [_1362191, _1362193, _1362195] : [class_Orderings_Olinorder(_1362191), 31609 ^ _780205 : [(31610 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362191), _1362193), _1362195)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362191), _1362193), _1362195) = _1362195)], (31616 ^ _780205) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362191), _1362193), _1362195) = _1362195, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362191), _1362193), _1362195)))]]], (31622 ^ _780205) ^ [_1362447, _1362449, _1362451] : [class_Orderings_Olinorder(_1362447), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362447), _1362449), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362447), _1362451), _1362449))))], (31628 ^ _780205) ^ [_1362554, _1362556, _1362558] : [class_Orderings_Olinorder(_1362554), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362554), _1362556), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362554), _1362556), _1362558))))], (31634 ^ _780205) ^ [_1362661] : [class_Orderings_Olinorder(_1362661), -(c_Finite__Set_Ofun__left__comm__idem(_1362661, _1362661, c_Orderings_Oord__class_Omax(_1362661)))], (31640 ^ _780205) ^ [_1362740, _1362742, _1362744, _1362746] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1362740), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362740), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362740), _1362742), _1362744)), _1362746) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362740), _1362742), _1362746)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362740), _1362744), _1362746)))], (31646 ^ _780205) ^ [_1362899, _1362901, _1362903, _1362905] : [class_Orderings_Olinorder(_1362899), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362899), _1362901), _1362903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362899), _1362901), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362899), _1362903), _1362905))))], (31656 ^ _780205) ^ [_1363078, _1363080, _1363082, _1363084] : [class_Orderings_Olinorder(_1363078), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363078), _1363080), _1363082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363078), _1363080), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363078), _1363084), _1363082))))], (31666 ^ _780205) ^ [_1363257, _1363259, _1363261, _1363263] : [class_Orderings_Olinorder(_1363257), 31669 ^ _780205 : [(31680 ^ _780205) ^ [] : [31681 ^ _780205 : [(31682 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363257), _1363259), _1363261))], (31684 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363257), _1363259), _1363263))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363257), _1363259), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363257), _1363261), _1363263))))], (31670 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363257), _1363259), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363257), _1363261), _1363263))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363257), _1363259), _1363261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363257), _1363259), _1363263)))]]], (31688 ^ _780205) ^ [_1363606, _1363608, _1363610, _1363612] : [class_Orderings_Olinorder(_1363606), 31691 ^ _780205 : [(31692 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363606), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363606), _1363608), _1363610)), _1363612)), 31695 ^ _780205 : [(31696 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363606), _1363608), _1363612)))], (31698 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363606), _1363610), _1363612)))]]], (31700 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363606), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363606), _1363608), _1363610)), _1363612))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363606), _1363608), _1363612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363606), _1363610), _1363612))]]], (31710 ^ _780205) ^ [_1363986, _1363988, _1363990, _1363992] : [class_Groups_Oordered__ab__group__add(_1363986), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363986), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363986), _1363988), _1363990)), _1363992) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363986), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363986), _1363988), _1363992)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363986), _1363990), _1363992)))], (31716 ^ _780205) ^ [_1364145, _1364147] : [class_Orderings_Olinorder(_1364145), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364145), _1364147), _1364147) = _1364147)], (31722 ^ _780205) ^ [_1364236, _1364238, _1364240] : [class_Orderings_Olinorder(_1364236), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364236), _1364238), _1364240) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364236), _1364240), _1364238))], (31728 ^ _780205) ^ [_1364345, _1364347, _1364349] : [class_Orderings_Olinorder(_1364345), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364345), _1364347), _1364349) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364345), _1364349), _1364347))], (31734 ^ _780205) ^ [_1364454, _1364456, _1364458] : [class_Orderings_Olinorder(_1364454), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364454), _1364456), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364454), _1364456), _1364458)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364454), _1364456), _1364458))], (31740 ^ _780205) ^ [_1364579, _1364581, _1364583] : [class_Orderings_Olinorder(_1364579), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364579), _1364581), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364579), _1364581), _1364583)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364579), _1364581), _1364583))], (31746 ^ _780205) ^ [_1364704, _1364706, _1364708, _1364710] : [class_Orderings_Olinorder(_1364704), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364704), _1364706), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364704), _1364708), _1364710)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364704), _1364708), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364704), _1364706), _1364710)))], (31752 ^ _780205) ^ [_1364847, _1364849, _1364851, _1364853] : [class_Orderings_Olinorder(_1364847), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364847), _1364849), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364847), _1364851), _1364853)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364847), _1364851), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364847), _1364849), _1364853)))], (31758 ^ _780205) ^ [_1364990, _1364992, _1364994, _1364996] : [class_Orderings_Olinorder(_1364990), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364990), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364990), _1364992), _1364994)), _1364996) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364990), _1364992), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364990), _1364994), _1364996)))], (31764 ^ _780205) ^ [_1365133, _1365135, _1365137, _1365139] : [class_Orderings_Olinorder(_1365133), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365133), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365133), _1365135), _1365137)), _1365139) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365133), _1365135), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365133), _1365137), _1365139)))], (31770 ^ _780205) ^ [_1365276, _1365278] : [class_Orderings_Olinorder(_1365276), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365276), _1365278), _1365278) = _1365278)], (31776 ^ _780205) ^ [_1365367, _1365369, _1365371, _1365373] : [class_Orderings_Olinorder(_1365367), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365367), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365367), _1365369), _1365371)), _1365373) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365367), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365367), _1365369), _1365373)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365367), _1365371), _1365373)))], (31782 ^ _780205) ^ [_1365526, _1365528, _1365530, _1365532] : [class_Orderings_Olinorder(_1365526), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365526), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365526), _1365528), _1365530)), _1365532) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365526), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365526), _1365528), _1365532)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365526), _1365530), _1365532)))], (31788 ^ _780205) ^ [_1365685, _1365687, _1365689, _1365691] : [class_Orderings_Olinorder(_1365685), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365685), _1365687), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365685), _1365689), _1365691)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365685), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365685), _1365687), _1365689)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365685), _1365687), _1365691)))], (31794 ^ _780205) ^ [_1365844, _1365846, _1365848, _1365850] : [class_Orderings_Olinorder(_1365844), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365844), _1365846), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365844), _1365848), _1365850)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365844), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365844), _1365846), _1365848)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1365844), _1365846), _1365850)))], (31800 ^ _780205) ^ [_1366003, _1366005, _1366007] : [class_Orderings_Olinorder(_1366003), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1366003), _1366005), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366003), _1366005), _1366007)) = _1366005)], (31806 ^ _780205) ^ [_1366112, _1366114, _1366116] : [class_Orderings_Olinorder(_1366112), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366112), _1366114), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1366112), _1366114), _1366116)) = _1366114)], (31812 ^ _780205) ^ [_1366221, _1366223] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1366221)), hAPP(c_Nat_OSuc, _1366223)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1366221), _1366223)))], (31814 ^ _780205) ^ [_1366267] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1366267) = _1366267)], (31816 ^ _780205) ^ [_1366293] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1366293), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1366293)], (31818 ^ _780205) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (31820 ^ _780205) ^ [_1366340] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1366340) = c_Orderings_Oord__class_Omax(_1366340)), class_Lattices_Osemilattice__sup(_1366340), class_Orderings_Olinorder(_1366340)], (31830 ^ _780205) ^ [_1366469, _1366471, _1366473] : [class_Int_Onumber(_1366469), class_Orderings_Oord(_1366469), 31837 ^ _780205 : [(31838 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366469), hAPP(c_Int_Onumber__class_Onumber__of(_1366469), _1366471)), hAPP(c_Int_Onumber__class_Onumber__of(_1366469), _1366473))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366469), hAPP(c_Int_Onumber__class_Onumber__of(_1366469), _1366471)), hAPP(c_Int_Onumber__class_Onumber__of(_1366469), _1366473)) = hAPP(c_Int_Onumber__class_Onumber__of(_1366469), _1366473))], (31844 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366469), hAPP(c_Int_Onumber__class_Onumber__of(_1366469), _1366471)), hAPP(c_Int_Onumber__class_Onumber__of(_1366469), _1366473)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366469), hAPP(c_Int_Onumber__class_Onumber__of(_1366469), _1366471)), hAPP(c_Int_Onumber__class_Onumber__of(_1366469), _1366473)) = hAPP(c_Int_Onumber__class_Onumber__of(_1366469), _1366471))]]], (31850 ^ _780205) ^ [_1366861, _1366863, _1366865, _1366867] : [class_Orderings_Olinorder(_1366861), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366861), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366861), _1366863), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1366861), _1366865), _1366867))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1366861), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366861), _1366863), _1366865)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366861), _1366863), _1366867)))))], (31856 ^ _780205) ^ [_1367034, _1367036, _1367038, _1367040] : [class_Orderings_Olinorder(_1367034), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367034), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367034), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367034), _1367036), _1367038)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367034), _1367036), _1367040))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367034), _1367036), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367034), _1367038), _1367040)))))], (31862 ^ _780205) ^ [_1367207, _1367209, _1367211] : [class_Groups_Olinordered__ab__group__add(_1367207), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1367207), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367207), _1367209), _1367211)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367207), hAPP(c_Groups_Ouminus__class_Ouminus(_1367207), _1367209)), hAPP(c_Groups_Ouminus__class_Ouminus(_1367207), _1367211)))], (31868 ^ _780205) ^ [_1367346, _1367348, _1367350] : [class_Groups_Olinordered__ab__group__add(_1367346), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1367346), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367346), _1367348), _1367350)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367346), hAPP(c_Groups_Ouminus__class_Ouminus(_1367346), _1367348)), hAPP(c_Groups_Ouminus__class_Ouminus(_1367346), _1367350)))], (31874 ^ _780205) ^ [_1367485, _1367487] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1367485), _1367487)), _1367487) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1367485), _1367487))], (31876 ^ _780205) ^ [_1367528, _1367530] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1367528)), _1367530) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1367528), 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), _1367528)), _1367530))], (31878 ^ _780205) ^ [_1367576, _1367578] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1367576), hAPP(c_Nat_OSuc, _1367578)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1367578), 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)), _1367578)), _1367576))], (31880 ^ _780205) ^ [_1367624] : [class_Orderings_Oord(_1367624), -(c_Orderings_Oord__class_Omax(_1367624) = c_Orderings_Oord_Omax(_1367624, c_Orderings_Oord__class_Oless__eq(_1367624)))], (31886 ^ _780205) ^ [_1367711, _1367713, _1367715, _1367717] : [class_Orderings_Olinorder(_1367711), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367711), _1367713)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1367711, _1367711, c_Orderings_Oord__class_Omax(_1367711)), _1367715), hAPP(hAPP(c_Set_Oinsert(_1367711), _1367717), _1367713)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367711), _1367717), hAPP(hAPP(c_Finite__Set_Ofold(_1367711, _1367711, c_Orderings_Oord__class_Omax(_1367711)), _1367715), _1367713)))], (31896 ^ _780205) ^ [_1367934] : [class_Orderings_Olinorder(_1367934), -(c_Orderings_Oord_Omin(_1367934, hAPP(c_COMBC(_1367934, _1367934, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1367934))) = c_Orderings_Oord__class_Omax(_1367934))], (31902 ^ _780205) ^ [_1368035, _1368037, _1368039, _1368041] : [class_Orderings_Olinorder(_1368035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368035), _1368037)), hBOOL(hAPP(hAPP(c_member(_1368035), _1368039), _1368037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368035), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1368035), _1368039), _1368041)), hAPP(hAPP(c_Finite__Set_Ofold(_1368035, _1368035, c_Orderings_Oord__class_Omax(_1368035)), _1368041), _1368037))))], (31916 ^ _780205) ^ [_1368302, _1368304, _1368306] : [class_Orderings_Olinorder(_1368302), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368302), _1368304)), hBOOL(hAPP(hAPP(c_member(_1368302), _1368306), _1368304)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1368302), _1368306), c_Big__Operators_Olattice_OInf__fin(_1368302, c_Orderings_Oord__class_Omin(_1368302), _1368304)) = _1368306)], (31930 ^ _780205) ^ [_1368537, _1368539, _1368541] : [class_Orderings_Olinorder(_1368537), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368537), _1368539)), hBOOL(hAPP(hAPP(c_member(_1368537), _1368541), _1368539)), 31941 ^ _780205 : [(31942 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368537, tc_HOL_Obool)), _1368539), hAPP(hAPP(c_Set_Oinsert(_1368537), _1368541), c_Orderings_Obot__class_Obot(tc_fun(_1368537, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1368537, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1368537, _1368539) = _1368541)], (31948 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368537, tc_HOL_Obool)), _1368539), hAPP(hAPP(c_Set_Oinsert(_1368537), _1368541), c_Orderings_Obot__class_Obot(tc_fun(_1368537, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1368537, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1368537, _1368539) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1368537), _1368541), c_Big__Operators_Olinorder__class_OMax(_1368537, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368537, tc_HOL_Obool)), _1368539), hAPP(hAPP(c_Set_Oinsert(_1368537), _1368541), c_Orderings_Obot__class_Obot(tc_fun(_1368537, tc_HOL_Obool)))))))]]], (31954 ^ _780205) ^ [_1369043, _1369045] : [class_Orderings_Olinorder(_1369043), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369043), _1369045)), -(_1369045 = c_Orderings_Obot__class_Obot(tc_fun(_1369043, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369043), c_Big__Operators_Olattice_OInf__fin(_1369043, c_Orderings_Oord__class_Omin(_1369043), _1369045)), c_Big__Operators_Olattice_OSup__fin(_1369043, c_Orderings_Oord__class_Omax(_1369043), _1369045))))], (31968 ^ _780205) ^ [_1369241, _1369243, _1369245] : [class_Orderings_Olinorder(_1369241), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369241), _1369243)), hBOOL(hAPP(hAPP(c_member(_1369241), _1369245), _1369243)), 31979 ^ _780205 : [(31980 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369241, tc_HOL_Obool)), _1369243), hAPP(hAPP(c_Set_Oinsert(_1369241), _1369245), c_Orderings_Obot__class_Obot(tc_fun(_1369241, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1369241, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1369241, c_Orderings_Oord__class_Omax(_1369241), _1369243) = _1369245)], (31986 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369241, tc_HOL_Obool)), _1369243), hAPP(hAPP(c_Set_Oinsert(_1369241), _1369245), c_Orderings_Obot__class_Obot(tc_fun(_1369241, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1369241, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1369241, c_Orderings_Oord__class_Omax(_1369241), _1369243) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1369241), _1369245), c_Big__Operators_Olattice_OSup__fin(_1369241, c_Orderings_Oord__class_Omax(_1369241), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369241, tc_HOL_Obool)), _1369243), hAPP(hAPP(c_Set_Oinsert(_1369241), _1369245), c_Orderings_Obot__class_Obot(tc_fun(_1369241, tc_HOL_Obool)))))))]]], (31992 ^ _780205) ^ [_1369765, _1369767, _1369769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1369765, 31993 ^ [_1369765, _1369767, _1369769])), hAPP(_1369767, 31993 ^ [_1369765, _1369767, _1369769]))), -(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), _1369767), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1369769))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1369765), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1369769))) = 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)), _1369767)), _1369765)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1369769)))], (31999 ^ _780205) ^ [_1369998, _1370000] : [class_Orderings_Olinorder(_1369998), -(c_Big__Operators_Olinorder__class_OMax(_1369998, hAPP(hAPP(c_Set_Oinsert(_1369998), _1370000), c_Orderings_Obot__class_Obot(tc_fun(_1369998, tc_HOL_Obool)))) = _1370000)], (32005 ^ _780205) ^ [_1370105, _1370107, _1370109] : [class_Orderings_Olinorder(_1370105), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370105), _1370107)), hBOOL(hAPP(hAPP(c_member(_1370105), _1370109), _1370107)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1370105), _1370109), c_Big__Operators_Olattice_OSup__fin(_1370105, c_Orderings_Oord__class_Omax(_1370105), _1370107)) = c_Big__Operators_Olattice_OSup__fin(_1370105, c_Orderings_Oord__class_Omax(_1370105), _1370107))], (32019 ^ _780205) ^ [_1370352, _1370354, _1370356] : [class_Orderings_Olinorder(_1370352), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370352), _1370354)), hBOOL(hAPP(hAPP(c_member(_1370352), _1370356), _1370354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370352), _1370356), c_Big__Operators_Olinorder__class_OMax(_1370352, _1370354))))], (32033 ^ _780205) ^ [_1370579, _1370581] : [class_Orderings_Olinorder(_1370579), -(c_Big__Operators_Olattice_OSup__fin(_1370579, c_Orderings_Oord__class_Omax(_1370579), hAPP(hAPP(c_Set_Oinsert(_1370579), _1370581), c_Orderings_Obot__class_Obot(tc_fun(_1370579, tc_HOL_Obool)))) = _1370581)], (32039 ^ _780205) ^ [_1370692, _1370694] : [class_Orderings_Olinorder(_1370692), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370692), _1370694)), -(_1370694 = c_Orderings_Obot__class_Obot(tc_fun(_1370692, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1370692), c_Big__Operators_Olinorder__class_OMax(_1370692, _1370694)), _1370694)))], (32053 ^ _780205) ^ [_1370872, _1370874, _1370876] : [class_Orderings_Olinorder(_1370872), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370872), _1370874)), hBOOL(hAPP(hAPP(c_member(_1370872), _1370876), _1370874)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1370872), _1370876), c_Big__Operators_Olinorder__class_OMax(_1370872, _1370874)) = c_Big__Operators_Olinorder__class_OMax(_1370872, _1370874))], (32067 ^ _780205) ^ [_1371107, _1371109] : [class_Orderings_Olinorder(_1371107), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371107), _1371109)), -(c_Big__Operators_Olattice_OSup__fin(_1371107, c_Orderings_Oord__class_Omax(_1371107), _1371109) = hAPP(c_Finite__Set_Ofold1(_1371107, c_Orderings_Oord__class_Omax(_1371107)), _1371109))], (32077 ^ _780205) ^ [_1371270, _1371272] : [class_Orderings_Olinorder(_1371270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371270), _1371272)), -(c_Big__Operators_Olinorder__class_OMax(_1371270, _1371272) = hAPP(c_Finite__Set_Ofold1(_1371270, c_Orderings_Oord__class_Omax(_1371270)), _1371272))], (32087 ^ _780205) ^ [_1371427, _1371429, _1371431] : [class_Orderings_Olinorder(_1371427), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371427), _1371429)), -(_1371429 = c_Orderings_Obot__class_Obot(tc_fun(_1371427, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1371427, c_Orderings_Oord__class_Omax(_1371427), hAPP(hAPP(c_Set_Oinsert(_1371427), _1371431), _1371429)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371427), _1371431), c_Big__Operators_Olattice_OSup__fin(_1371427, c_Orderings_Oord__class_Omax(_1371427), _1371429)))], (32101 ^ _780205) ^ [_1371647, _1371649, _1371651] : [class_Orderings_Olinorder(_1371647), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371647), _1371649)), -(_1371651 = c_Orderings_Obot__class_Obot(tc_fun(_1371647, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1371647, tc_HOL_Obool)), _1371651), _1371649)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371647), c_Big__Operators_Olattice_OSup__fin(_1371647, c_Orderings_Oord__class_Omax(_1371647), _1371651)), c_Big__Operators_Olattice_OSup__fin(_1371647, c_Orderings_Oord__class_Omax(_1371647), _1371649)) = c_Big__Operators_Olattice_OSup__fin(_1371647, c_Orderings_Oord__class_Omax(_1371647), _1371649))], (32119 ^ _780205) ^ [_1371979, _1371981, _1371983] : [class_Orderings_Olinorder(_1371979), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371979), _1371981)), hBOOL(hAPP(hAPP(c_member(_1371979), _1371983), _1371981)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1371979), _1371983), c_Big__Operators_Olattice_OSup__fin(_1371979, c_Orderings_Oord__class_Omax(_1371979), _1371981)) = _1371983)], (32133 ^ _780205) ^ [_1372214, _1372216, _1372218] : [class_Orderings_Olinorder(_1372214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372214), _1372216)), -(_1372216 = c_Orderings_Obot__class_Obot(tc_fun(_1372214, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372214), _1372218)), -(_1372218 = c_Orderings_Obot__class_Obot(tc_fun(_1372214, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1372214, c_Orderings_Oord__class_Omax(_1372214), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372214, tc_HOL_Obool)), _1372216), _1372218)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372214), c_Big__Operators_Olattice_OSup__fin(_1372214, c_Orderings_Oord__class_Omax(_1372214), _1372216)), c_Big__Operators_Olattice_OSup__fin(_1372214, c_Orderings_Oord__class_Omax(_1372214), _1372218)))], (32155 ^ _780205) ^ [_1372581, _1372583, _1372585] : [class_Orderings_Olinorder(_1372581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1372581, tc_HOL_Obool)), _1372583), _1372585)), -(_1372583 = c_Orderings_Obot__class_Obot(tc_fun(_1372581, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372581), _1372585)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372581), c_Big__Operators_Olinorder__class_OMax(_1372581, _1372583)), c_Big__Operators_Olinorder__class_OMax(_1372581, _1372585))))], (32173 ^ _780205) ^ [_1372887, _1372889, _1372891] : [class_Orderings_Olinorder(_1372887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372887), _1372889)), -(c_Big__Operators_Olattice_OSup__fin(_1372887, c_Orderings_Oord__class_Omax(_1372887), hAPP(hAPP(c_Set_Oinsert(_1372887), _1372891), _1372889)) = hAPP(hAPP(c_Finite__Set_Ofold(_1372887, _1372887, c_Orderings_Oord__class_Omax(_1372887)), _1372891), _1372889))], (32183 ^ _780205) ^ [_1373078, _1373080, _1373082] : [class_Orderings_Olinorder(_1373078), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373078), _1373080)), -(_1373080 = c_Orderings_Obot__class_Obot(tc_fun(_1373078, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1373078, hAPP(hAPP(c_Set_Oinsert(_1373078), _1373082), _1373080)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373078), _1373082), c_Big__Operators_Olinorder__class_OMax(_1373078, _1373080)))], (32197 ^ _780205) ^ [_1373286, _1373288, _1373290] : [class_Orderings_Olinorder(_1373286), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373286), _1373288)), -(_1373290 = c_Orderings_Obot__class_Obot(tc_fun(_1373286, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373286, tc_HOL_Obool)), _1373290), _1373288)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373286), c_Big__Operators_Olinorder__class_OMax(_1373286, _1373290)), c_Big__Operators_Olinorder__class_OMax(_1373286, _1373288)) = c_Big__Operators_Olinorder__class_OMax(_1373286, _1373288))], (32215 ^ _780205) ^ [_1373600, _1373602, _1373604] : [class_Orderings_Olinorder(_1373600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373600), _1373602)), -(_1373602 = c_Orderings_Obot__class_Obot(tc_fun(_1373600, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373600), _1373604)), -(_1373604 = c_Orderings_Obot__class_Obot(tc_fun(_1373600, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1373600, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1373600, tc_HOL_Obool)), _1373602), _1373604)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373600), c_Big__Operators_Olinorder__class_OMax(_1373600, _1373602)), c_Big__Operators_Olinorder__class_OMax(_1373600, _1373604)))], (32237 ^ _780205) ^ [_1373949, _1373951, _1373953] : [class_Orderings_Olinorder(_1373949), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373949), _1373951)), -(c_Big__Operators_Olinorder__class_OMax(_1373949, hAPP(hAPP(c_Set_Oinsert(_1373949), _1373953), _1373951)) = hAPP(hAPP(c_Finite__Set_Ofold(_1373949, _1373949, c_Orderings_Oord__class_Omax(_1373949)), _1373953), _1373951))], (32247 ^ _780205) ^ [_1374134, _1374136, _1374138] : [class_Orderings_Olinorder(_1374134), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374134), _1374136)), -(hBOOL(hAPP(hAPP(c_member(_1374134), _1374138), _1374136))), -(_1374136 = c_Orderings_Obot__class_Obot(tc_fun(_1374134, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1374134, c_Orderings_Oord__class_Omax(_1374134), hAPP(hAPP(c_Set_Oinsert(_1374134), _1374138), _1374136)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1374134), _1374138), c_Big__Operators_Olattice_OSup__fin(_1374134, c_Orderings_Oord__class_Omax(_1374134), _1374136)))], (32265 ^ _780205) ^ [_1374383, _1374385, _1374387] : [class_Orderings_Olinorder(_1374383), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374383), _1374385)), 32272 ^ _780205 : [(32273 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374383, tc_HOL_Obool)), _1374385), hAPP(hAPP(c_Set_Oinsert(_1374383), _1374387), c_Orderings_Obot__class_Obot(tc_fun(_1374383, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1374383, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1374383, c_Orderings_Oord__class_Omax(_1374383), hAPP(hAPP(c_Set_Oinsert(_1374383), _1374387), _1374385)) = _1374387)], (32279 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374383, tc_HOL_Obool)), _1374385), hAPP(hAPP(c_Set_Oinsert(_1374383), _1374387), c_Orderings_Obot__class_Obot(tc_fun(_1374383, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1374383, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1374383, c_Orderings_Oord__class_Omax(_1374383), hAPP(hAPP(c_Set_Oinsert(_1374383), _1374387), _1374385)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1374383), _1374387), c_Big__Operators_Olattice_OSup__fin(_1374383, c_Orderings_Oord__class_Omax(_1374383), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374383, tc_HOL_Obool)), _1374385), hAPP(hAPP(c_Set_Oinsert(_1374383), _1374387), c_Orderings_Obot__class_Obot(tc_fun(_1374383, tc_HOL_Obool)))))))]]], (32285 ^ _780205) ^ [_1374871, _1374873, _1374875] : [class_Orderings_Olinorder(_1374871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374871), _1374873)), -(_1374873 = c_Orderings_Obot__class_Obot(tc_fun(_1374871, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374871), _1374875)), -(_1374875 = c_Orderings_Obot__class_Obot(tc_fun(_1374871, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1374871, tc_HOL_Obool)), _1374873), _1374875) = c_Orderings_Obot__class_Obot(tc_fun(_1374871, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1374871, c_Orderings_Oord__class_Omax(_1374871), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1374871, tc_HOL_Obool)), _1374873), _1374875)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1374871), c_Big__Operators_Olattice_OSup__fin(_1374871, c_Orderings_Oord__class_Omax(_1374871), _1374873)), c_Big__Operators_Olattice_OSup__fin(_1374871, c_Orderings_Oord__class_Omax(_1374871), _1374875)))], (32311 ^ _780205) ^ [_1375366, _1375368, _1375370] : [class_Orderings_Olinorder(_1375366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375366), _1375368)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375366), _1375370)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1375366, tc_HOL_Obool)), _1375368), _1375370) = c_Orderings_Obot__class_Obot(tc_fun(_1375366, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1375366), c_Big__Operators_Olattice_OSup__fin(_1375366, c_Orderings_Oord__class_Omax(_1375366), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1375366, tc_HOL_Obool)), _1375368), _1375370))), c_Big__Operators_Olattice_OSup__fin(_1375366, c_Orderings_Oord__class_Omax(_1375366), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1375366, tc_HOL_Obool)), _1375368), _1375370))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1375366), c_Big__Operators_Olattice_OSup__fin(_1375366, c_Orderings_Oord__class_Omax(_1375366), _1375368)), c_Big__Operators_Olattice_OSup__fin(_1375366, c_Orderings_Oord__class_Omax(_1375366), _1375370)))], (32329 ^ _780205) ^ [_1375738, _1375740, _1375742] : [class_Orderings_Olinorder(_1375738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375738), _1375740)), -(hBOOL(hAPP(hAPP(c_member(_1375738), _1375742), _1375740))), -(c_Big__Operators_Olattice_OSup__fin(_1375738, c_Orderings_Oord__class_Omax(_1375738), hAPP(hAPP(c_Set_Oinsert(_1375738), _1375742), _1375740)) = hAPP(hAPP(c_Finite__Set_Ofold(_1375738, _1375738, c_Orderings_Oord__class_Omax(_1375738)), _1375742), _1375740))], (32343 ^ _780205) ^ [_1375958, _1375960, _1375962] : [class_Orderings_Olinorder(_1375958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375958), _1375960)), -(hBOOL(hAPP(hAPP(c_member(_1375958), _1375962), _1375960))), -(_1375960 = c_Orderings_Obot__class_Obot(tc_fun(_1375958, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1375958, hAPP(hAPP(c_Set_Oinsert(_1375958), _1375962), _1375960)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1375958), _1375962), c_Big__Operators_Olinorder__class_OMax(_1375958, _1375960)))], (32361 ^ _780205) ^ [_1376195, _1376197, _1376199] : [class_Orderings_Olinorder(_1376195), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376195), _1376197)), 32368 ^ _780205 : [(32369 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1376195, tc_HOL_Obool)), _1376197), hAPP(hAPP(c_Set_Oinsert(_1376195), _1376199), c_Orderings_Obot__class_Obot(tc_fun(_1376195, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1376195, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1376195, hAPP(hAPP(c_Set_Oinsert(_1376195), _1376199), _1376197)) = _1376199)], (32375 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1376195, tc_HOL_Obool)), _1376197), hAPP(hAPP(c_Set_Oinsert(_1376195), _1376199), c_Orderings_Obot__class_Obot(tc_fun(_1376195, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1376195, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1376195, hAPP(hAPP(c_Set_Oinsert(_1376195), _1376199), _1376197)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376195), _1376199), c_Big__Operators_Olinorder__class_OMax(_1376195, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1376195, tc_HOL_Obool)), _1376197), hAPP(hAPP(c_Set_Oinsert(_1376195), _1376199), c_Orderings_Obot__class_Obot(tc_fun(_1376195, tc_HOL_Obool)))))))]]], (32381 ^ _780205) ^ [_1376665, _1376667, _1376669] : [class_Orderings_Olinorder(_1376665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376665), _1376667)), -(_1376667 = c_Orderings_Obot__class_Obot(tc_fun(_1376665, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376665), _1376669)), -(_1376669 = c_Orderings_Obot__class_Obot(tc_fun(_1376665, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376665, tc_HOL_Obool)), _1376667), _1376669) = c_Orderings_Obot__class_Obot(tc_fun(_1376665, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1376665, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1376665, tc_HOL_Obool)), _1376667), _1376669)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376665), c_Big__Operators_Olinorder__class_OMax(_1376665, _1376667)), c_Big__Operators_Olinorder__class_OMax(_1376665, _1376669)))], (32407 ^ _780205) ^ [_1377142, _1377144, _1377146] : [class_Orderings_Olinorder(_1377142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377142), _1377144)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377142), _1377146)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377142, tc_HOL_Obool)), _1377144), _1377146) = c_Orderings_Obot__class_Obot(tc_fun(_1377142, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1377142), c_Big__Operators_Olinorder__class_OMax(_1377142, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377142, tc_HOL_Obool)), _1377144), _1377146))), c_Big__Operators_Olinorder__class_OMax(_1377142, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377142, tc_HOL_Obool)), _1377144), _1377146))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1377142), c_Big__Operators_Olinorder__class_OMax(_1377142, _1377144)), c_Big__Operators_Olinorder__class_OMax(_1377142, _1377146)))], (32425 ^ _780205) ^ [_1377490, _1377492, _1377494] : [class_Orderings_Olinorder(_1377490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377490), _1377492)), -(hBOOL(hAPP(hAPP(c_member(_1377490), _1377494), _1377492))), -(c_Big__Operators_Olinorder__class_OMax(_1377490, hAPP(hAPP(c_Set_Oinsert(_1377490), _1377494), _1377492)) = hAPP(hAPP(c_Finite__Set_Ofold(_1377490, _1377490, c_Orderings_Oord__class_Omax(_1377490)), _1377494), _1377492))], (32439 ^ _780205) ^ [_1377704, _1377706] : [class_Orderings_Olinorder(_1377704), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377704), _1377706)), -(_1377706 = c_Orderings_Obot__class_Obot(tc_fun(_1377704, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1377704), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1377704), 32452 ^ [_1377704, _1377706]), 32453 ^ [_1377704, _1377706])), hAPP(hAPP(c_Set_Oinsert(_1377704), 32452 ^ [_1377704, _1377706]), hAPP(hAPP(c_Set_Oinsert(_1377704), 32453 ^ [_1377704, _1377706]), c_Orderings_Obot__class_Obot(tc_fun(_1377704, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1377704), c_Big__Operators_Olattice_OSup__fin(_1377704, c_Orderings_Oord__class_Omax(_1377704), _1377706)), _1377706)))], (32459 ^ _780205) ^ [_1378154, _1378156] : [class_Orderings_Olinorder(_1378154), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378154), _1378156)), -(_1378156 = c_Orderings_Obot__class_Obot(tc_fun(_1378154, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1378154), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1378154), 32472 ^ [_1378154, _1378156]), 32473 ^ [_1378154, _1378156])), hAPP(hAPP(c_Set_Oinsert(_1378154), 32472 ^ [_1378154, _1378156]), hAPP(hAPP(c_Set_Oinsert(_1378154), 32473 ^ [_1378154, _1378156]), c_Orderings_Obot__class_Obot(tc_fun(_1378154, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1378154), c_Big__Operators_Olinorder__class_OMax(_1378154, _1378156)), _1378156)))], (32479 ^ _780205) ^ [_1378598, _1378600, _1378602, _1378604, _1378606, _1378608, _1378610] : [-(hAPP(c_Product__Type_Oapfst(_1378598, _1378600, _1378602, _1378604), hAPP(c_Product__Type_Oapsnd(_1378606, _1378602, _1378598, _1378608), _1378610)) = hAPP(hAPP(c_Product__Type_OPair(_1378600, _1378602), hAPP(_1378604, hAPP(c_Product__Type_Ofst(_1378598, _1378606), _1378610))), hAPP(_1378608, hAPP(c_Product__Type_Osnd(_1378598, _1378606), _1378610))))], (32481 ^ _780205) ^ [_1378676, _1378678, _1378680, _1378682, _1378684, _1378686, _1378688] : [-(hAPP(c_Product__Type_Oapsnd(_1378676, _1378678, _1378680, _1378682), hAPP(c_Product__Type_Oapfst(_1378684, _1378680, _1378676, _1378686), _1378688)) = hAPP(hAPP(c_Product__Type_OPair(_1378680, _1378678), hAPP(_1378686, hAPP(c_Product__Type_Ofst(_1378684, _1378676), _1378688))), hAPP(_1378682, hAPP(c_Product__Type_Osnd(_1378684, _1378676), _1378688))))], (32483 ^ _780205) ^ [_1378754, _1378756, _1378758, _1378760, _1378762, _1378764] : [-(hAPP(c_Product__Type_Oapfst(_1378754, _1378756, _1378758, _1378760), hAPP(hAPP(c_Product__Type_OPair(_1378754, _1378758), _1378762), _1378764)) = hAPP(hAPP(c_Product__Type_OPair(_1378756, _1378758), hAPP(_1378760, _1378762)), _1378764))], (32485 ^ _780205) ^ [_1378843, _1378845, _1378847, _1378849, _1378851, _1378853] : [hAPP(c_Product__Type_Oapfst(_1378843, _1378845, _1378847, _1378849), _1378851) = hAPP(c_Product__Type_Oapfst(_1378843, _1378845, _1378847, _1378853), _1378851), -(hAPP(_1378849, hAPP(c_Product__Type_Ofst(_1378843, _1378847), _1378851)) = hAPP(_1378853, hAPP(c_Product__Type_Ofst(_1378843, _1378847), _1378851)))], (32491 ^ _780205) ^ [_1378992, _1378994, _1378996, _1378998, _1379000, _1379002] : [hAPP(_1378998, hAPP(c_Product__Type_Ofst(_1378992, _1378996), _1379000)) = hAPP(_1379002, hAPP(c_Product__Type_Ofst(_1378992, _1378996), _1379000)), -(hAPP(c_Product__Type_Oapfst(_1378992, _1378994, _1378996, _1378998), _1379000) = hAPP(c_Product__Type_Oapfst(_1378992, _1378994, _1378996, _1379002), _1379000))], (32497 ^ _780205) ^ [_1379147, _1379149, _1379151, _1379153, _1379155] : [-(hAPP(c_Product__Type_Ofst(_1379147, _1379149), hAPP(c_Product__Type_Oapfst(_1379151, _1379147, _1379149, _1379153), _1379155)) = hAPP(_1379153, hAPP(c_Product__Type_Ofst(_1379151, _1379149), _1379155)))], (32499 ^ _780205) ^ [_1379201, _1379203, _1379205, _1379207, _1379209] : [-(hAPP(c_Product__Type_Osnd(_1379201, _1379203), hAPP(c_Product__Type_Oapfst(_1379205, _1379201, _1379203, _1379207), _1379209)) = hAPP(c_Product__Type_Osnd(_1379205, _1379203), _1379209))], (32501 ^ _780205) ^ [_1379252, _1379254, _1379256, _1379258, _1379260, _1379262, _1379264] : [-(hAPP(c_Product__Type_Oapsnd(_1379252, _1379254, _1379256, _1379258), hAPP(c_Product__Type_Oapfst(_1379260, _1379256, _1379252, _1379262), _1379264)) = hAPP(c_Product__Type_Oapfst(_1379260, _1379256, _1379254, _1379262), hAPP(c_Product__Type_Oapsnd(_1379252, _1379254, _1379260, _1379258), _1379264)))], (32503 ^ _780205) ^ [_1379319, _1379321, _1379323, _1379325] : [class_Groups_Oab__group__add(_1379319), 32506 ^ _780205 : [(32507 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1379321), _1379323)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379319), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1379319, _1379319), hAPP(hAPP(c_COMBB(_1379319, tc_fun(_1379319, _1379319), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1379319)), _1379325)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1379319, tc_Nat_Onat), _1379325), 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, _1379321, _1379323)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1379319), hAPP(_1379325, _1379321)), hAPP(_1379325, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1379323), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (32513 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1379321), _1379323))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379319), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1379319, _1379319), hAPP(hAPP(c_COMBB(_1379319, tc_fun(_1379319, _1379319), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1379319)), _1379325)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1379319, tc_Nat_Onat), _1379325), 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, _1379321, _1379323)) = c_Groups_Ozero__class_Ozero(_1379319))]]], (32519 ^ _780205) ^ [_1379757, _1379759] : [class_Rings_Ocomm__semiring__1(_1379757), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379757), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379757), c_Groups_Oone__class_Oone(_1379757)), c_Groups_Oone__class_Oone(_1379757))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1379757), c_Nat_Osemiring__1__class_Oof__nat(_1379757)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1379759))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379757), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1379757), _1379759)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379757), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1379757), _1379759)), c_Groups_Oone__class_Oone(_1379757))))], (32525 ^ _780205) ^ [_1379958, _1379960, _1379962, _1379964] : [class_Complete__Lattice_Ocomplete__lattice(_1379958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379960), _1379962)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1379960, _1379958), _1379962), _1379964) = hAPP(hAPP(c_Finite__Set_Ofold(_1379960, _1379958, hAPP(hAPP(c_COMBB(_1379958, tc_fun(_1379958, _1379958), _1379960), c_Lattices_Osemilattice__inf__class_Oinf(_1379958)), _1379964)), c_Orderings_Otop__class_Otop(_1379958)), _1379962))], (32535 ^ _780205) ^ [_1380173, _1380175, _1380177, _1380179] : [class_Complete__Lattice_Ocomplete__lattice(_1380173), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380175), _1380177)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380175, _1380173), _1380177), _1380179) = hAPP(hAPP(c_Finite__Set_Ofold(_1380175, _1380173, hAPP(hAPP(c_COMBB(_1380173, tc_fun(_1380173, _1380173), _1380175), c_Lattices_Osemilattice__sup__class_Osup(_1380173)), _1380179)), c_Orderings_Obot__class_Obot(_1380173)), _1380177))], (32545 ^ _780205) ^ [_1380388, _1380390, _1380392, _1380394, _1380396, _1380398] : [hBOOL(hAPP(hAPP(c_member(_1380388), _1380390), _1380392)), hBOOL(hAPP(hAPP(_1380394, _1380390), _1380396)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380388, tc_fun(_1380398, tc_HOL_Obool)), _1380392), _1380394), _1380396)))], (32555 ^ _780205) ^ [_1380585, _1380587, _1380589, _1380591, _1380593, _1380595] : [hBOOL(hAPP(hAPP(c_member(_1380585), _1380587), _1380589)), hBOOL(hAPP(hAPP(c_member(_1380591), _1380593), hAPP(_1380595, _1380587))), -(hBOOL(hAPP(hAPP(c_member(_1380591), _1380593), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380585, tc_fun(_1380591, tc_HOL_Obool)), _1380589), _1380595))))], (32565 ^ _780205) ^ [_1380802, _1380804, _1380806, _1380808, _1380810, _1380812] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380802, tc_fun(_1380804, tc_HOL_Obool)), _1380806), _1380808), _1380810)), -(hBOOL(hAPP(hAPP(_1380808, _1380812), _1380810))), hBOOL(hAPP(hAPP(c_member(_1380802), _1380812), _1380806))], (32575 ^ _780205) ^ [_1381003, _1381005, _1381007, _1381009, _1381011, _1381013] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1381003, tc_fun(_1381005, tc_HOL_Obool)), _1381007), _1381009), _1381011)), hBOOL(hAPP(hAPP(c_member(_1381003), _1381013), _1381007)), -(hBOOL(hAPP(hAPP(_1381009, _1381013), _1381011)))], (32585 ^ _780205) ^ [_1381200, _1381202, _1381204, _1381206, _1381208, _1381210] : [hBOOL(hAPP(hAPP(c_member(_1381200), _1381202), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1381204, tc_fun(_1381200, tc_HOL_Obool)), _1381206), _1381208))), hBOOL(hAPP(hAPP(c_member(_1381204), _1381210), _1381206)), -(hBOOL(hAPP(hAPP(c_member(_1381200), _1381202), hAPP(_1381208, _1381210))))], (32595 ^ _780205) ^ [_1381417, _1381419, _1381421, _1381423, _1381425, _1381427] : [hBOOL(hAPP(hAPP(c_member(_1381417), _1381419), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1381421, tc_fun(_1381417, tc_HOL_Obool)), _1381423), _1381425))), -(hBOOL(hAPP(hAPP(c_member(_1381417), _1381419), hAPP(_1381425, _1381427)))), hBOOL(hAPP(hAPP(c_member(_1381421), _1381427), _1381423))], (32605 ^ _780205) ^ [_1381638, _1381640, _1381642, _1381644, _1381646, _1381648, _1381650, _1381652] : [hBOOL(hAPP(hAPP(c_member(_1381638), _1381640), _1381642)), hBOOL(hAPP(hAPP(hAPP(_1381644, _1381640), _1381646), _1381648)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381638, tc_fun(_1381650, tc_fun(_1381652, tc_HOL_Obool))), _1381642), _1381644), _1381646), _1381648)))], (32615 ^ _780205) ^ [_1381861, _1381863, _1381865, _1381867, _1381869, _1381871, _1381873, _1381875] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1381861, tc_fun(_1381863, tc_fun(_1381865, tc_HOL_Obool))), _1381867), _1381869), _1381871), _1381873)), hBOOL(hAPP(hAPP(c_member(_1381861), _1381875), _1381867)), -(hBOOL(hAPP(hAPP(hAPP(_1381869, _1381875), _1381871), _1381873)))], (32625 ^ _780205) ^ [_1382084, _1382086, _1382088, _1382090, _1382092, _1382094, _1382096, _1382098] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382084, tc_fun(_1382086, tc_fun(_1382088, tc_HOL_Obool))), _1382090), _1382092), _1382094), _1382096)), -(hBOOL(hAPP(hAPP(hAPP(_1382092, _1382098), _1382094), _1382096))), hBOOL(hAPP(hAPP(c_member(_1382084), _1382098), _1382090))], (32635 ^ _780205) ^ [_1382311, _1382313, _1382315, _1382317] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1382315), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382311, tc_fun(_1382315, tc_HOL_Obool)), _1382313), _1382317)))), 32636 ^ _780205 : [(32637 ^ _780205) ^ [_1382385] : [hBOOL(hAPP(hAPP(c_member(_1382311), _1382385), _1382313)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382315), hAPP(_1382317, _1382385)))]]], (32645 ^ _780205) ^ [_1382539, _1382541] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1382539, _1382541))))], (32647 ^ _780205) ^ [_1382570, _1382572, _1382574, _1382576, _1382578] : [-(hAPP(hAPP(c_Set_Oinsert(_1382570), _1382572), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382574, tc_fun(_1382570, tc_HOL_Obool)), _1382576), _1382578)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382574, tc_fun(_1382570, tc_HOL_Obool)), _1382576), hAPP(hAPP(c_COMBB(tc_fun(_1382570, tc_HOL_Obool), tc_fun(_1382570, tc_HOL_Obool), _1382574), hAPP(c_Set_Oinsert(_1382570), _1382572)), _1382578)))], (32649 ^ _780205) ^ [_1382654, _1382656, _1382658, _1382660, _1382662] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382654, tc_fun(_1382656, tc_HOL_Obool)), _1382658), hAPP(hAPP(c_COMBB(tc_fun(_1382656, tc_HOL_Obool), tc_fun(_1382656, tc_HOL_Obool), _1382654), hAPP(c_Set_Oinsert(_1382656), _1382660)), _1382662)) = hAPP(hAPP(c_Set_Oinsert(_1382656), _1382660), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382654, tc_fun(_1382656, tc_HOL_Obool)), _1382658), _1382662)))], (32651 ^ _780205) ^ [_1382738, _1382740, _1382742, _1382744] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1382738), _1382740)), 32654 ^ _780205 : [(32665 ^ _780205) ^ [] : [32667 ^ _780205 : [(32668 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382738), 32666 ^ [_1382738, _1382740, _1382742, _1382744]), _1382740)))], (32670 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1382742), hAPP(_1382744, 32666 ^ [_1382738, _1382740, _1382742, _1382744])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1382742), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382738, tc_fun(_1382742, tc_HOL_Obool)), _1382740), _1382744))))], (32655 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1382742), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382738, tc_fun(_1382742, tc_HOL_Obool)), _1382740), _1382744))), 32658 ^ _780205 : [(32659 ^ _780205) ^ [_1382922] : [hBOOL(hAPP(hAPP(c_member(_1382738), _1382922), _1382740)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1382742), hAPP(_1382744, _1382922))))]]]]], (32684 ^ _780205) ^ [_1383463, _1383465, _1383467, _1383469] : [32686 ^ _780205 : [(32687 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1383463), 32685 ^ [_1383463, _1383465, _1383467, _1383469]), _1383467)))], (32689 ^ _780205) ^ [] : [hAPP(_1383469, 32685 ^ [_1383463, _1383465, _1383467, _1383469]) = c_Orderings_Obot__class_Obot(tc_fun(_1383465, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383463, tc_fun(_1383465, tc_HOL_Obool)), _1383467), _1383469) = c_Orderings_Obot__class_Obot(tc_fun(_1383465, tc_HOL_Obool)))], (32674 ^ _780205) ^ [_1383234, _1383236, _1383238, _1383240] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383234, tc_fun(_1383236, tc_HOL_Obool)), _1383238), _1383240) = c_Orderings_Obot__class_Obot(tc_fun(_1383236, tc_HOL_Obool)), 32677 ^ _780205 : [(32678 ^ _780205) ^ [_1383350] : [hBOOL(hAPP(hAPP(c_member(_1383234), _1383350), _1383238)), -(hAPP(_1383240, _1383350) = c_Orderings_Obot__class_Obot(tc_fun(_1383236, tc_HOL_Obool)))]]], (32693 ^ _780205) ^ [_1383708, _1383710, _1383712, _1383714] : [_1383708 = c_Orderings_Obot__class_Obot(tc_fun(_1383710, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383710, tc_fun(_1383712, tc_HOL_Obool)), _1383708), hAPP(c_COMBK(tc_fun(_1383712, tc_HOL_Obool), _1383710), _1383714)) = c_Orderings_Obot__class_Obot(tc_fun(_1383712, tc_HOL_Obool)))], (32699 ^ _780205) ^ [_1383845, _1383847, _1383849, _1383851] : [-(_1383845 = c_Orderings_Obot__class_Obot(tc_fun(_1383847, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383847, tc_fun(_1383849, tc_HOL_Obool)), _1383845), hAPP(c_COMBK(tc_fun(_1383849, tc_HOL_Obool), _1383847), _1383851)) = _1383851)], (32705 ^ _780205) ^ [_1383913, _1383915, _1383917] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383913, tc_fun(_1383915, tc_HOL_Obool)), _1383917), hAPP(c_COMBK(tc_fun(_1383915, tc_HOL_Obool), _1383913), c_Orderings_Obot__class_Obot(tc_fun(_1383915, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1383915, tc_HOL_Obool)))], (32717 ^ _780205) ^ [_1384221, _1384223, _1384225, _1384227] : [32719 ^ _780205 : [(32720 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1384223), 32718 ^ [_1384221, _1384223, _1384225, _1384227]), _1384225)))], (32722 ^ _780205) ^ [] : [hAPP(_1384227, 32718 ^ [_1384221, _1384223, _1384225, _1384227]) = c_Orderings_Obot__class_Obot(tc_fun(_1384221, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1384221, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384223, tc_fun(_1384221, tc_HOL_Obool)), _1384225), _1384227))], (32707 ^ _780205) ^ [_1383992, _1383994, _1383996, _1383998] : [c_Orderings_Obot__class_Obot(tc_fun(_1383992, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383994, tc_fun(_1383992, tc_HOL_Obool)), _1383996), _1383998), 32710 ^ _780205 : [(32711 ^ _780205) ^ [_1384108] : [hBOOL(hAPP(hAPP(c_member(_1383994), _1384108), _1383996)), -(hAPP(_1383998, _1384108) = c_Orderings_Obot__class_Obot(tc_fun(_1383992, tc_HOL_Obool)))]]], (32726 ^ _780205) ^ [_1384469, _1384471, _1384473, _1384475, _1384477] : [_1384469 = c_Orderings_Obot__class_Obot(tc_fun(_1384471, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384473, tc_HOL_Obool)), _1384475), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384471, tc_fun(_1384473, tc_HOL_Obool)), _1384469), _1384477)) = _1384475)], (32732 ^ _780205) ^ [_1384602, _1384604, _1384606, _1384608, _1384610] : [-(_1384602 = c_Orderings_Obot__class_Obot(tc_fun(_1384604, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384606, tc_HOL_Obool)), _1384608), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384604, tc_fun(_1384606, tc_HOL_Obool)), _1384602), _1384610)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384604, tc_fun(_1384606, tc_HOL_Obool)), _1384602), hAPP(hAPP(c_COMBB(tc_fun(_1384606, tc_HOL_Obool), tc_fun(_1384606, tc_HOL_Obool), _1384604), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384606, tc_HOL_Obool)), _1384608)), _1384610)))], (32738 ^ _780205) ^ [_1384710, _1384712] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1384710, tc_HOL_Obool), _1384712) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1384710, tc_HOL_Obool), tc_fun(_1384710, tc_HOL_Obool)), _1384712), c_COMBI(tc_fun(_1384710, tc_HOL_Obool))))], (32740 ^ _780205) ^ [_1384761, _1384763, _1384765, _1384767] : [-(hAPP(c_Set_OPow(_1384761), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384763, tc_fun(_1384761, tc_HOL_Obool)), _1384765), _1384767)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384763, tc_fun(tc_fun(_1384761, tc_HOL_Obool), tc_HOL_Obool)), _1384765), hAPP(hAPP(c_COMBB(tc_fun(_1384761, tc_HOL_Obool), tc_fun(tc_fun(_1384761, tc_HOL_Obool), tc_HOL_Obool), _1384763), c_Set_OPow(_1384761)), _1384767)))], (32742 ^ _780205) ^ [_1384843, _1384845, _1384847, _1384849] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1384843, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384845, tc_fun(_1384843, tc_HOL_Obool)), _1384847), _1384849)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384845, tc_fun(_1384843, tc_HOL_Obool)), _1384847), hAPP(hAPP(c_COMBB(tc_fun(_1384843, tc_HOL_Obool), tc_fun(_1384843, tc_HOL_Obool), _1384845), c_Groups_Ouminus__class_Ouminus(tc_fun(_1384843, tc_HOL_Obool))), _1384849)))], (32744 ^ _780205) ^ [_1384925, _1384927, _1384929, _1384931] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1384925, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1384927, tc_fun(_1384925, tc_HOL_Obool)), _1384929), _1384931)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384927, tc_fun(_1384925, tc_HOL_Obool)), _1384929), hAPP(hAPP(c_COMBB(tc_fun(_1384925, tc_HOL_Obool), tc_fun(_1384925, tc_HOL_Obool), _1384927), c_Groups_Ouminus__class_Ouminus(tc_fun(_1384925, tc_HOL_Obool))), _1384931)))], (32746 ^ _780205) ^ [_1385007, _1385009, _1385011, _1385013, _1385015, _1385017] : [class_Complete__Lattice_Ocomplete__lattice(_1385007), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385009, tc_fun(_1385011, _1385007)), _1385013), _1385015), _1385017) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385009, _1385007), _1385013), hAPP(hAPP(c_COMBC(_1385009, _1385011, _1385007), _1385015), _1385017)))], (32752 ^ _780205) ^ [_1385158, _1385160, _1385162, _1385164, _1385166, _1385168] : [class_Complete__Lattice_Ocomplete__lattice(_1385158), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385160, tc_fun(_1385162, _1385158)), _1385164), _1385166), _1385168) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385160, _1385158), _1385164), hAPP(hAPP(c_COMBC(_1385160, _1385162, _1385158), _1385166), _1385168)))], (32758 ^ _780205) ^ [_1385309, _1385311, _1385313, _1385315, _1385317, _1385319] : [class_Complete__Lattice_Ocomplete__lattice(_1385309), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385311, _1385309), _1385313), hAPP(hAPP(c_COMBB(tc_fun(_1385315, _1385309), _1385309, _1385311), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385315, _1385309), _1385317)), _1385319)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385315, _1385309), _1385317), hAPP(hAPP(c_COMBB(tc_fun(_1385311, _1385309), _1385309, _1385315), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385311, _1385309), _1385313)), hAPP(c_COMBC(_1385311, _1385315, _1385309), _1385319))))], (32764 ^ _780205) ^ [_1385518, _1385520, _1385522, _1385524, _1385526, _1385528] : [class_Complete__Lattice_Ocomplete__lattice(_1385518), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385520, _1385518), _1385522), hAPP(hAPP(c_COMBB(tc_fun(_1385524, _1385518), _1385518, _1385520), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385524, _1385518), _1385526)), _1385528)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385524, _1385518), _1385526), hAPP(hAPP(c_COMBB(tc_fun(_1385520, _1385518), _1385518, _1385524), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385520, _1385518), _1385522)), hAPP(c_COMBC(_1385520, _1385524, _1385518), _1385528))))], (32770 ^ _780205) ^ [_1385727, _1385729, _1385731, _1385733] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1385727, tc_HOL_Obool), tc_fun(_1385729, tc_HOL_Obool)), _1385731), hAPP(hAPP(c_COMBC(tc_fun(_1385727, tc_HOL_Obool), tc_fun(_1385727, tc_fun(_1385729, tc_HOL_Obool)), tc_fun(_1385729, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385727, tc_fun(_1385729, tc_HOL_Obool))), _1385733)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385727, tc_fun(_1385729, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1385727, tc_HOL_Obool), _1385731)), _1385733))], (32772 ^ _780205) ^ [_1385817, _1385819, _1385821, _1385823] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1385817, tc_HOL_Obool), tc_fun(_1385819, tc_HOL_Obool)), _1385821), hAPP(hAPP(c_COMBC(tc_fun(_1385817, tc_HOL_Obool), tc_fun(_1385817, tc_fun(_1385819, tc_HOL_Obool)), tc_fun(_1385819, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385817, tc_fun(_1385819, tc_HOL_Obool))), _1385823)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385817, tc_fun(_1385819, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1385817, tc_HOL_Obool), _1385821)), _1385823))], (32774 ^ _780205) ^ [_1385907, _1385909, _1385911, _1385913] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385907, tc_fun(_1385909, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1385907, tc_HOL_Obool), _1385911)), _1385913) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1385907, tc_HOL_Obool), tc_fun(_1385909, tc_HOL_Obool)), _1385911), hAPP(hAPP(c_COMBC(tc_fun(_1385907, tc_HOL_Obool), tc_fun(_1385907, tc_fun(_1385909, tc_HOL_Obool)), tc_fun(_1385909, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385907, tc_fun(_1385909, tc_HOL_Obool))), _1385913)))], (32776 ^ _780205) ^ [_1385997, _1385999, _1386001, _1386003] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385997, tc_fun(_1385999, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1385997, tc_HOL_Obool), _1386001)), _1386003) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1385997, tc_HOL_Obool), tc_fun(_1385999, tc_HOL_Obool)), _1386001), hAPP(hAPP(c_COMBC(tc_fun(_1385997, tc_HOL_Obool), tc_fun(_1385997, tc_fun(_1385999, tc_HOL_Obool)), tc_fun(_1385999, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385997, tc_fun(_1385999, tc_HOL_Obool))), _1386003)))], (32778 ^ _780205) ^ [_1386087, _1386089, _1386091, _1386093, _1386095] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386087, tc_fun(_1386089, tc_HOL_Obool)), _1386091), hAPP(hAPP(c_COMBB(tc_fun(_1386089, tc_HOL_Obool), tc_fun(_1386089, tc_HOL_Obool), _1386087), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386089, tc_HOL_Obool)), _1386093)), _1386095)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386089, tc_HOL_Obool)), _1386093), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1386087, tc_fun(_1386089, tc_HOL_Obool)), _1386091), _1386095)))], (32780 ^ _780205) ^ [_1386177, _1386179, _1386181, _1386183, _1386185] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386177, tc_fun(_1386179, tc_HOL_Obool)), _1386181), hAPP(hAPP(c_COMBC(_1386177, tc_fun(_1386179, tc_HOL_Obool), tc_fun(_1386179, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1386179, tc_HOL_Obool), tc_fun(tc_fun(_1386179, tc_HOL_Obool), tc_fun(_1386179, tc_HOL_Obool)), _1386177), c_Groups_Ominus__class_Ominus(tc_fun(_1386179, tc_HOL_Obool))), _1386183)), _1386185)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386179, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386177, tc_fun(_1386179, tc_HOL_Obool)), _1386181), _1386183)), _1386185))], (32782 ^ _780205) ^ [_1386286, _1386288, _1386290, _1386292, _1386294] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386286, tc_HOL_Obool)), _1386288), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1386290, tc_fun(_1386286, tc_HOL_Obool)), _1386292), _1386294)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386290, tc_fun(_1386286, tc_HOL_Obool)), _1386292), hAPP(hAPP(c_COMBB(tc_fun(_1386286, tc_HOL_Obool), tc_fun(_1386286, tc_HOL_Obool), _1386290), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386286, tc_HOL_Obool)), _1386288)), _1386294)))], (32784 ^ _780205) ^ [_1386376, _1386378, _1386380, _1386382, _1386384] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386376, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386378, tc_fun(_1386376, tc_HOL_Obool)), _1386380), _1386382)), _1386384) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386378, tc_fun(_1386376, tc_HOL_Obool)), _1386380), hAPP(hAPP(c_COMBC(_1386378, tc_fun(_1386376, tc_HOL_Obool), tc_fun(_1386376, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1386376, tc_HOL_Obool), tc_fun(tc_fun(_1386376, tc_HOL_Obool), tc_fun(_1386376, tc_HOL_Obool)), _1386378), c_Groups_Ominus__class_Ominus(tc_fun(_1386376, tc_HOL_Obool))), _1386382)), _1386384)))], (32786 ^ _780205) ^ [_1386509, _1386511, _1386513, _1386515, _1386517] : [hBOOL(hAPP(hAPP(c_member(_1386509), _1386511), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386513, tc_fun(_1386509, tc_HOL_Obool)), _1386515), _1386517))), 32790 ^ _780205 : [(32791 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1386513), 32789 ^ [_1386509, _1386511, _1386513, _1386515, _1386517]), _1386515)))], (32793 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1386509), _1386511), hAPP(_1386517, 32789 ^ [_1386509, _1386511, _1386513, _1386515, _1386517]))))]]], (32795 ^ _780205) ^ [_1386717, _1386719, _1386721, _1386723, _1386725] : [-(hBOOL(hAPP(hAPP(c_member(_1386717), _1386719), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386721, tc_fun(_1386717, tc_HOL_Obool)), _1386723), _1386725)))), 32796 ^ _780205 : [(32797 ^ _780205) ^ [_1386799] : [hBOOL(hAPP(hAPP(c_member(_1386721), _1386799), _1386723)), hBOOL(hAPP(hAPP(c_member(_1386717), _1386719), hAPP(_1386725, _1386799)))]]], (32815 ^ _780205) ^ [_1387233, _1387235, _1387237, _1387239, _1387241] : [32817 ^ _780205 : [(32818 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1387237), 32816 ^ [_1387233, _1387235, _1387237, _1387239, _1387241]), _1387239)))], (32820 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1387233), _1387235), hAPP(_1387241, 32816 ^ [_1387233, _1387235, _1387237, _1387239, _1387241])))]], -(hBOOL(hAPP(hAPP(c_member(_1387233), _1387235), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1387237, tc_fun(_1387233, tc_HOL_Obool)), _1387239), _1387241))))], (32805 ^ _780205) ^ [_1386990, _1386992, _1386994, _1386996, _1386998] : [hBOOL(hAPP(hAPP(c_member(_1386990), _1386992), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1386994, tc_fun(_1386990, tc_HOL_Obool)), _1386996), _1386998))), 32808 ^ _780205 : [(32809 ^ _780205) ^ [_1387114] : [hBOOL(hAPP(hAPP(c_member(_1386994), _1387114), _1386996)), -(hBOOL(hAPP(hAPP(c_member(_1386990), _1386992), hAPP(_1386998, _1387114))))]]], (32834 ^ _780205) ^ [_1387763, _1387765, _1387767, _1387769, _1387771] : [32836 ^ _780205 : [(32837 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1387765), 32835 ^ [_1387763, _1387765, _1387767, _1387769, _1387771]), _1387767)))], (32839 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387763, tc_HOL_Obool)), hAPP(_1387769, 32835 ^ [_1387763, _1387765, _1387767, _1387769, _1387771])), _1387771))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387763, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387765, tc_fun(_1387763, tc_HOL_Obool)), _1387767), _1387769)), _1387771)))], (32824 ^ _780205) ^ [_1387505, _1387507, _1387509, _1387511, _1387513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387505, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1387507, tc_fun(_1387505, tc_HOL_Obool)), _1387509), _1387511)), _1387513)), 32827 ^ _780205 : [(32828 ^ _780205) ^ [_1387638] : [hBOOL(hAPP(hAPP(c_member(_1387507), _1387638), _1387509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387505, tc_HOL_Obool)), hAPP(_1387511, _1387638)), _1387513)))]]], (32853 ^ _780205) ^ [_1388308, _1388310, _1388312, _1388314, _1388316] : [32855 ^ _780205 : [(32856 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388312), 32854 ^ [_1388308, _1388310, _1388312, _1388314, _1388316]), _1388314)))], (32858 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388308, tc_HOL_Obool)), _1388310), hAPP(_1388316, 32854 ^ [_1388308, _1388310, _1388312, _1388314, _1388316])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388308, tc_HOL_Obool)), _1388310), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388312, tc_fun(_1388308, tc_HOL_Obool)), _1388314), _1388316))))], (32843 ^ _780205) ^ [_1388050, _1388052, _1388054, _1388056, _1388058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388050, tc_HOL_Obool)), _1388052), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388054, tc_fun(_1388050, tc_HOL_Obool)), _1388056), _1388058))), 32846 ^ _780205 : [(32847 ^ _780205) ^ [_1388183] : [hBOOL(hAPP(hAPP(c_member(_1388054), _1388183), _1388056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388050, tc_HOL_Obool)), _1388052), hAPP(_1388058, _1388183))))]]], (32862 ^ _780205) ^ [_1388571, _1388573, _1388575, _1388577] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1388571, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388573, tc_fun(tc_fun(_1388571, tc_HOL_Obool), tc_HOL_Obool)), _1388575), hAPP(hAPP(c_COMBB(tc_fun(_1388571, tc_HOL_Obool), tc_fun(tc_fun(_1388571, tc_HOL_Obool), tc_HOL_Obool), _1388573), c_Set_OPow(_1388571)), _1388577))), hAPP(c_Set_OPow(_1388571), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388573, tc_fun(_1388571, tc_HOL_Obool)), _1388575), _1388577)))))], (32864 ^ _780205) ^ [_1388666, _1388668, _1388670, _1388672, _1388674, _1388676] : [-(hAPP(c_Set_Ovimage(_1388666, _1388668, _1388670), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388672, tc_fun(_1388668, tc_HOL_Obool)), _1388674), _1388676)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388672, tc_fun(_1388666, tc_HOL_Obool)), _1388674), hAPP(hAPP(c_COMBB(tc_fun(_1388668, tc_HOL_Obool), tc_fun(_1388666, tc_HOL_Obool), _1388672), c_Set_Ovimage(_1388666, _1388668, _1388670)), _1388676)))], (32866 ^ _780205) ^ [_1388750, _1388752, _1388754, _1388756, _1388758, _1388760] : [-(hAPP(c_Set_Ovimage(_1388750, _1388752, _1388754), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388756, tc_fun(_1388752, tc_HOL_Obool)), _1388758), _1388760)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388756, tc_fun(_1388750, tc_HOL_Obool)), _1388758), hAPP(hAPP(c_COMBB(tc_fun(_1388752, tc_HOL_Obool), tc_fun(_1388750, tc_HOL_Obool), _1388756), c_Set_Ovimage(_1388750, _1388752, _1388754)), _1388760)))], (32868 ^ _780205) ^ [_1388834, _1388836, _1388838, _1388840, _1388842, _1388844] : [-(hAPP(c_Relation_OImage(_1388834, _1388836, _1388838), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388840, tc_fun(_1388834, tc_HOL_Obool)), _1388842), _1388844)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388840, tc_fun(_1388836, tc_HOL_Obool)), _1388842), hAPP(hAPP(c_COMBB(tc_fun(_1388834, tc_HOL_Obool), tc_fun(_1388836, tc_HOL_Obool), _1388840), c_Relation_OImage(_1388834, _1388836, _1388838)), _1388844)))], (32870 ^ _780205) ^ [_1388918, _1388920, _1388922, _1388924, _1388926] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388918, tc_fun(_1388920, tc_HOL_Obool)), _1388922), hAPP(hAPP(c_COMBB(tc_fun(_1388920, tc_HOL_Obool), tc_fun(_1388920, tc_HOL_Obool), _1388918), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388920, tc_HOL_Obool)), _1388924)), _1388926)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388920, tc_HOL_Obool)), _1388924), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388918, tc_fun(_1388920, tc_HOL_Obool)), _1388922), _1388926)))], (32872 ^ _780205) ^ [_1389008, _1389010, _1389012, _1389014, _1389016] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389008, tc_fun(_1389010, tc_HOL_Obool)), _1389012), hAPP(hAPP(c_COMBC(_1389008, tc_fun(_1389010, tc_HOL_Obool), tc_fun(_1389010, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1389010, tc_HOL_Obool), tc_fun(tc_fun(_1389010, tc_HOL_Obool), tc_fun(_1389010, tc_HOL_Obool)), _1389008), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389010, tc_HOL_Obool))), _1389014)), _1389016)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389010, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389008, tc_fun(_1389010, tc_HOL_Obool)), _1389012), _1389014)), _1389016))], (32874 ^ _780205) ^ [_1389117, _1389119, _1389121, _1389123, _1389125] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389117, tc_fun(_1389119, tc_HOL_Obool)), _1389121), hAPP(hAPP(c_COMBS(_1389117, tc_fun(_1389119, tc_HOL_Obool), tc_fun(_1389119, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1389119, tc_HOL_Obool), tc_fun(tc_fun(_1389119, tc_HOL_Obool), tc_fun(_1389119, tc_HOL_Obool)), _1389117), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389119, tc_HOL_Obool))), _1389123)), _1389125)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389119, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389117, tc_fun(_1389119, tc_HOL_Obool)), _1389121), _1389123)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389117, tc_fun(_1389119, tc_HOL_Obool)), _1389121), _1389125)))], (32876 ^ _780205) ^ [_1389238, _1389240, _1389242, _1389244, _1389246] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389238, tc_HOL_Obool)), _1389240), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389242, tc_fun(_1389238, tc_HOL_Obool)), _1389244), _1389246)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389242, tc_fun(_1389238, tc_HOL_Obool)), _1389244), hAPP(hAPP(c_COMBB(tc_fun(_1389238, tc_HOL_Obool), tc_fun(_1389238, tc_HOL_Obool), _1389242), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389238, tc_HOL_Obool)), _1389240)), _1389246)))], (32878 ^ _780205) ^ [_1389328, _1389330, _1389332, _1389334, _1389336] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389328, tc_HOL_Obool)), _1389330), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389332, tc_fun(_1389328, tc_HOL_Obool)), _1389334), _1389336)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389332, tc_fun(_1389328, tc_HOL_Obool)), _1389334), hAPP(hAPP(c_COMBB(tc_fun(_1389328, tc_HOL_Obool), tc_fun(_1389328, tc_HOL_Obool), _1389332), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389328, tc_HOL_Obool)), _1389330)), _1389336)))], (32880 ^ _780205) ^ [_1389418, _1389420, _1389422, _1389424, _1389426] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389418, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389420, tc_fun(_1389418, tc_HOL_Obool)), _1389422), _1389424)), _1389426) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389420, tc_fun(_1389418, tc_HOL_Obool)), _1389422), hAPP(hAPP(c_COMBC(_1389420, tc_fun(_1389418, tc_HOL_Obool), tc_fun(_1389418, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1389418, tc_HOL_Obool), tc_fun(tc_fun(_1389418, tc_HOL_Obool), tc_fun(_1389418, tc_HOL_Obool)), _1389420), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389418, tc_HOL_Obool))), _1389424)), _1389426)))], (32882 ^ _780205) ^ [_1389527, _1389529, _1389531, _1389533, _1389535, _1389537, _1389539] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389527, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389529, tc_fun(_1389527, tc_HOL_Obool)), _1389531), _1389533)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389535, tc_fun(_1389527, tc_HOL_Obool)), _1389537), _1389539)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389529, tc_fun(_1389527, tc_HOL_Obool)), _1389531), hAPP(hAPP(c_COMBB(tc_fun(_1389535, tc_fun(_1389527, tc_HOL_Obool)), tc_fun(_1389527, tc_HOL_Obool), _1389529), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389535, tc_fun(_1389527, tc_HOL_Obool)), _1389537)), hAPP(hAPP(c_COMBC(_1389529, tc_fun(_1389535, tc_fun(_1389527, tc_HOL_Obool)), tc_fun(_1389535, tc_fun(_1389527, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1389527, tc_HOL_Obool), tc_fun(_1389527, tc_HOL_Obool)), tc_fun(tc_fun(_1389535, tc_fun(_1389527, tc_HOL_Obool)), tc_fun(_1389535, tc_fun(_1389527, tc_HOL_Obool))), _1389529), c_COMBB(tc_fun(_1389527, tc_HOL_Obool), tc_fun(_1389527, tc_HOL_Obool), _1389535)), hAPP(hAPP(c_COMBB(tc_fun(_1389527, tc_HOL_Obool), tc_fun(tc_fun(_1389527, tc_HOL_Obool), tc_fun(_1389527, tc_HOL_Obool)), _1389529), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389527, tc_HOL_Obool))), _1389533))), _1389539))))], (32884 ^ _780205) ^ [_1389730, _1389732] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1389730, tc_HOL_Obool), _1389732) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1389730, tc_HOL_Obool), tc_fun(_1389730, tc_HOL_Obool)), _1389732), c_COMBI(tc_fun(_1389730, tc_HOL_Obool))))], (32896 ^ _780205) ^ [_1390031, _1390033, _1390035, _1390037] : [32898 ^ _780205 : [(32899 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1390033), 32897 ^ [_1390031, _1390033, _1390035, _1390037]), _1390035)))], (32901 ^ _780205) ^ [] : [hAPP(_1390037, 32897 ^ [_1390031, _1390033, _1390035, _1390037]) = c_Orderings_Otop__class_Otop(tc_fun(_1390031, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1390031, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390033, tc_fun(_1390031, tc_HOL_Obool)), _1390035), _1390037))], (32886 ^ _780205) ^ [_1389802, _1389804, _1389806, _1389808] : [c_Orderings_Otop__class_Otop(tc_fun(_1389802, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389804, tc_fun(_1389802, tc_HOL_Obool)), _1389806), _1389808), 32889 ^ _780205 : [(32890 ^ _780205) ^ [_1389918] : [hBOOL(hAPP(hAPP(c_member(_1389804), _1389918), _1389806)), -(hAPP(_1389808, _1389918) = c_Orderings_Otop__class_Otop(tc_fun(_1389802, tc_HOL_Obool)))]]], (32915 ^ _780205) ^ [_1390511, _1390513, _1390515, _1390517] : [32917 ^ _780205 : [(32918 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1390511), 32916 ^ [_1390511, _1390513, _1390515, _1390517]), _1390515)))], (32920 ^ _780205) ^ [] : [hAPP(_1390517, 32916 ^ [_1390511, _1390513, _1390515, _1390517]) = c_Orderings_Otop__class_Otop(tc_fun(_1390513, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390511, tc_fun(_1390513, tc_HOL_Obool)), _1390515), _1390517) = c_Orderings_Otop__class_Otop(tc_fun(_1390513, tc_HOL_Obool)))], (32905 ^ _780205) ^ [_1390282, _1390284, _1390286, _1390288] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390282, tc_fun(_1390284, tc_HOL_Obool)), _1390286), _1390288) = c_Orderings_Otop__class_Otop(tc_fun(_1390284, tc_HOL_Obool)), 32908 ^ _780205 : [(32909 ^ _780205) ^ [_1390398] : [hBOOL(hAPP(hAPP(c_member(_1390282), _1390398), _1390286)), -(hAPP(_1390288, _1390398) = c_Orderings_Otop__class_Otop(tc_fun(_1390284, tc_HOL_Obool)))]]], (32924 ^ _780205) ^ [_1390759, _1390761, _1390763, _1390765, _1390767] : [_1390759 = c_Orderings_Obot__class_Obot(tc_fun(_1390761, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390761, tc_fun(_1390763, tc_HOL_Obool)), _1390759), hAPP(hAPP(c_COMBB(tc_fun(_1390763, tc_HOL_Obool), tc_fun(_1390763, tc_HOL_Obool), _1390761), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1390763, tc_HOL_Obool)), _1390765)), _1390767)) = c_Orderings_Otop__class_Otop(tc_fun(_1390763, tc_HOL_Obool)))], (32930 ^ _780205) ^ [_1390928, _1390930, _1390932, _1390934, _1390936] : [-(_1390928 = c_Orderings_Obot__class_Obot(tc_fun(_1390930, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390930, tc_fun(_1390932, tc_HOL_Obool)), _1390928), hAPP(hAPP(c_COMBB(tc_fun(_1390932, tc_HOL_Obool), tc_fun(_1390932, tc_HOL_Obool), _1390930), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1390932, tc_HOL_Obool)), _1390934)), _1390936)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1390932, tc_HOL_Obool)), _1390934), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390930, tc_fun(_1390932, tc_HOL_Obool)), _1390928), _1390936)))], (32936 ^ _780205) ^ [_1391036, _1391038, _1391040, _1391042, _1391044, _1391046, _1391048] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391036, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391038, tc_fun(_1391036, tc_HOL_Obool)), _1391040), _1391042)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391044, tc_fun(_1391036, tc_HOL_Obool)), _1391046), _1391048)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391038, tc_fun(_1391036, tc_HOL_Obool)), _1391040), hAPP(hAPP(c_COMBB(tc_fun(_1391044, tc_fun(_1391036, tc_HOL_Obool)), tc_fun(_1391036, tc_HOL_Obool), _1391038), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391044, tc_fun(_1391036, tc_HOL_Obool)), _1391046)), hAPP(hAPP(c_COMBC(_1391038, tc_fun(_1391044, tc_fun(_1391036, tc_HOL_Obool)), tc_fun(_1391044, tc_fun(_1391036, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1391036, tc_HOL_Obool), tc_fun(_1391036, tc_HOL_Obool)), tc_fun(tc_fun(_1391044, tc_fun(_1391036, tc_HOL_Obool)), tc_fun(_1391044, tc_fun(_1391036, tc_HOL_Obool))), _1391038), c_COMBB(tc_fun(_1391036, tc_HOL_Obool), tc_fun(_1391036, tc_HOL_Obool), _1391044)), hAPP(hAPP(c_COMBB(tc_fun(_1391036, tc_HOL_Obool), tc_fun(tc_fun(_1391036, tc_HOL_Obool), tc_fun(_1391036, tc_HOL_Obool)), _1391038), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391036, tc_HOL_Obool))), _1391042))), _1391048))))], (32938 ^ _780205) ^ [_1391239, _1391241, _1391243, _1391245, _1391247] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391239, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391241, tc_fun(_1391239, tc_HOL_Obool)), _1391243), _1391245)), _1391247) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391241, tc_fun(_1391239, tc_HOL_Obool)), _1391243), hAPP(hAPP(c_COMBC(_1391241, tc_fun(_1391239, tc_HOL_Obool), tc_fun(_1391239, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391239, tc_HOL_Obool), tc_fun(tc_fun(_1391239, tc_HOL_Obool), tc_fun(_1391239, tc_HOL_Obool)), _1391241), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391239, tc_HOL_Obool))), _1391245)), _1391247)))], (32940 ^ _780205) ^ [_1391348, _1391350, _1391352, _1391354, _1391356] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391348, tc_fun(_1391350, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391348, tc_HOL_Obool)), _1391352), _1391354)), _1391356) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391350, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391348, tc_fun(_1391350, tc_HOL_Obool)), _1391352), _1391356)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391348, tc_fun(_1391350, tc_HOL_Obool)), _1391354), _1391356)))], (32942 ^ _780205) ^ [_1391437, _1391439, _1391441, _1391443, _1391445] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391437, tc_HOL_Obool)), _1391439), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391441, tc_fun(_1391437, tc_HOL_Obool)), _1391443), _1391445)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391441, tc_fun(_1391437, tc_HOL_Obool)), _1391443), hAPP(hAPP(c_COMBB(tc_fun(_1391437, tc_HOL_Obool), tc_fun(_1391437, tc_HOL_Obool), _1391441), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391437, tc_HOL_Obool)), _1391439)), _1391445)))], (32944 ^ _780205) ^ [_1391527, _1391529, _1391531, _1391533, _1391535] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391527, tc_HOL_Obool)), _1391529), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391531, tc_fun(_1391527, tc_HOL_Obool)), _1391533), _1391535)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391531, tc_fun(_1391527, tc_HOL_Obool)), _1391533), hAPP(hAPP(c_COMBB(tc_fun(_1391527, tc_HOL_Obool), tc_fun(_1391527, tc_HOL_Obool), _1391531), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391527, tc_HOL_Obool)), _1391529)), _1391535)))], (32946 ^ _780205) ^ [_1391617, _1391619, _1391621, _1391623, _1391625] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391617, tc_fun(_1391619, tc_HOL_Obool)), _1391621), hAPP(hAPP(c_COMBS(_1391617, tc_fun(_1391619, tc_HOL_Obool), tc_fun(_1391619, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391619, tc_HOL_Obool), tc_fun(tc_fun(_1391619, tc_HOL_Obool), tc_fun(_1391619, tc_HOL_Obool)), _1391617), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391619, tc_HOL_Obool))), _1391623)), _1391625)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391619, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391617, tc_fun(_1391619, tc_HOL_Obool)), _1391621), _1391623)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391617, tc_fun(_1391619, tc_HOL_Obool)), _1391621), _1391625)))], (32948 ^ _780205) ^ [_1391738, _1391740, _1391742, _1391744, _1391746] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391738, tc_fun(_1391740, tc_HOL_Obool)), _1391742), hAPP(hAPP(c_COMBC(_1391738, tc_fun(_1391740, tc_HOL_Obool), tc_fun(_1391740, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391740, tc_HOL_Obool), tc_fun(tc_fun(_1391740, tc_HOL_Obool), tc_fun(_1391740, tc_HOL_Obool)), _1391738), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391740, tc_HOL_Obool))), _1391744)), _1391746)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391740, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391738, tc_fun(_1391740, tc_HOL_Obool)), _1391742), _1391744)), _1391746))], (32950 ^ _780205) ^ [_1391847, _1391849, _1391851, _1391853, _1391855] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391847, tc_fun(_1391849, tc_HOL_Obool)), _1391851), hAPP(hAPP(c_COMBB(tc_fun(_1391849, tc_HOL_Obool), tc_fun(_1391849, tc_HOL_Obool), _1391847), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391849, tc_HOL_Obool)), _1391853)), _1391855)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391849, tc_HOL_Obool)), _1391853), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391847, tc_fun(_1391849, tc_HOL_Obool)), _1391851), _1391855)))], (32952 ^ _780205) ^ [_1391964, _1391966, _1391968, _1391970, _1391972, _1391974] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391964, tc_fun(_1391966, tc_fun(_1391968, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1391964, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1391966, _1391968), tc_HOL_Obool), tc_fun(_1391966, tc_fun(_1391968, tc_HOL_Obool)), _1391964), hAPP(c_COMBC(_1391966, tc_fun(tc_prod(_1391966, _1391968), tc_HOL_Obool), tc_fun(_1391968, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391968, tc_fun(tc_fun(tc_prod(_1391966, _1391968), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1391966, _1391968), tc_HOL_Obool), tc_fun(_1391968, tc_HOL_Obool)), _1391966), c_COMBC(_1391968, tc_fun(tc_prod(_1391966, _1391968), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1391968, tc_prod(_1391966, _1391968)), tc_fun(_1391968, tc_fun(tc_fun(tc_prod(_1391966, _1391968), tc_HOL_Obool), tc_HOL_Obool)), _1391966), hAPP(c_COMBB(tc_prod(_1391966, _1391968), tc_fun(tc_fun(tc_prod(_1391966, _1391968), tc_HOL_Obool), tc_HOL_Obool), _1391968), c_member(tc_prod(_1391966, _1391968)))), c_Product__Type_OPair(_1391966, _1391968))))), _1391970)), _1391972), _1391974)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1391966, _1391968)), hAPP(hAPP(c_Product__Type_OPair(_1391966, _1391968), _1391972), _1391974)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1391964, tc_fun(tc_prod(_1391966, _1391968), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1391964, tc_HOL_Obool))), _1391970))))], (32958 ^ _780205) ^ [_1392447, _1392449, _1392451, _1392453, _1392455, _1392457] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1392449, _1392451)), hAPP(hAPP(c_Product__Type_OPair(_1392449, _1392451), _1392455), _1392457)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392447, tc_fun(tc_prod(_1392449, _1392451), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1392447, tc_HOL_Obool))), _1392453))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1392447, tc_fun(_1392449, tc_fun(_1392451, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1392447, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1392449, _1392451), tc_HOL_Obool), tc_fun(_1392449, tc_fun(_1392451, tc_HOL_Obool)), _1392447), hAPP(c_COMBC(_1392449, tc_fun(tc_prod(_1392449, _1392451), tc_HOL_Obool), tc_fun(_1392451, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392451, tc_fun(tc_fun(tc_prod(_1392449, _1392451), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1392449, _1392451), tc_HOL_Obool), tc_fun(_1392451, tc_HOL_Obool)), _1392449), c_COMBC(_1392451, tc_fun(tc_prod(_1392449, _1392451), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392451, tc_prod(_1392449, _1392451)), tc_fun(_1392451, tc_fun(tc_fun(tc_prod(_1392449, _1392451), tc_HOL_Obool), tc_HOL_Obool)), _1392449), hAPP(c_COMBB(tc_prod(_1392449, _1392451), tc_fun(tc_fun(tc_prod(_1392449, _1392451), tc_HOL_Obool), tc_HOL_Obool), _1392451), c_member(tc_prod(_1392449, _1392451)))), c_Product__Type_OPair(_1392449, _1392451))))), _1392453)), _1392455), _1392457)))], (32964 ^ _780205) ^ [_1392963, _1392965, _1392967, _1392969, _1392971, _1392973] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392963, tc_fun(_1392965, tc_fun(_1392967, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1392963, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1392965, _1392967), tc_HOL_Obool), tc_fun(_1392965, tc_fun(_1392967, tc_HOL_Obool)), _1392963), hAPP(c_COMBC(_1392965, tc_fun(tc_prod(_1392965, _1392967), tc_HOL_Obool), tc_fun(_1392967, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392967, tc_fun(tc_fun(tc_prod(_1392965, _1392967), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1392965, _1392967), tc_HOL_Obool), tc_fun(_1392967, tc_HOL_Obool)), _1392965), c_COMBC(_1392967, tc_fun(tc_prod(_1392965, _1392967), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392967, tc_prod(_1392965, _1392967)), tc_fun(_1392967, tc_fun(tc_fun(tc_prod(_1392965, _1392967), tc_HOL_Obool), tc_HOL_Obool)), _1392965), hAPP(c_COMBB(tc_prod(_1392965, _1392967), tc_fun(tc_fun(tc_prod(_1392965, _1392967), tc_HOL_Obool), tc_HOL_Obool), _1392967), c_member(tc_prod(_1392965, _1392967)))), c_Product__Type_OPair(_1392965, _1392967))))), _1392969)), _1392971), _1392973)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1392965, _1392967)), hAPP(hAPP(c_Product__Type_OPair(_1392965, _1392967), _1392971), _1392973)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392963, tc_fun(tc_prod(_1392965, _1392967), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1392963, tc_HOL_Obool))), _1392969))))], (32970 ^ _780205) ^ [_1393446, _1393448, _1393450, _1393452, _1393454, _1393456] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1393448, _1393450)), hAPP(hAPP(c_Product__Type_OPair(_1393448, _1393450), _1393454), _1393456)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393446, tc_fun(tc_prod(_1393448, _1393450), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1393446, tc_HOL_Obool))), _1393452))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393446, tc_fun(_1393448, tc_fun(_1393450, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1393446, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1393448, _1393450), tc_HOL_Obool), tc_fun(_1393448, tc_fun(_1393450, tc_HOL_Obool)), _1393446), hAPP(c_COMBC(_1393448, tc_fun(tc_prod(_1393448, _1393450), tc_HOL_Obool), tc_fun(_1393450, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393450, tc_fun(tc_fun(tc_prod(_1393448, _1393450), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1393448, _1393450), tc_HOL_Obool), tc_fun(_1393450, tc_HOL_Obool)), _1393448), c_COMBC(_1393450, tc_fun(tc_prod(_1393448, _1393450), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393450, tc_prod(_1393448, _1393450)), tc_fun(_1393450, tc_fun(tc_fun(tc_prod(_1393448, _1393450), tc_HOL_Obool), tc_HOL_Obool)), _1393448), hAPP(c_COMBB(tc_prod(_1393448, _1393450), tc_fun(tc_fun(tc_prod(_1393448, _1393450), tc_HOL_Obool), tc_HOL_Obool), _1393450), c_member(tc_prod(_1393448, _1393450)))), c_Product__Type_OPair(_1393448, _1393450))))), _1393452)), _1393454), _1393456)))], (32976 ^ _780205) ^ [_1393935, _1393937, _1393939, _1393941, _1393943] : [class_Complete__Lattice_Ocomplete__lattice(_1393935), 32979 ^ _780205 : [(32990 ^ _780205) ^ [] : [32992 ^ _780205 : [(32993 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1393937), 32991 ^ [_1393935, _1393937, _1393939, _1393941, _1393943]), _1393939)))], (32995 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393935), hAPP(_1393941, 32991 ^ [_1393935, _1393937, _1393939, _1393941, _1393943])), _1393943))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393935), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393937, _1393935), _1393939), _1393941)), _1393943)))], (32980 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393935), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393937, _1393935), _1393939), _1393941)), _1393943)), 32983 ^ _780205 : [(32984 ^ _780205) ^ [_1394116] : [hBOOL(hAPP(hAPP(c_member(_1393937), _1394116), _1393939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393935), hAPP(_1393941, _1394116)), _1393943)))]]]]], (32999 ^ _780205) ^ [_1394429, _1394431, _1394433, _1394435, _1394437] : [class_Complete__Lattice_Ocomplete__lattice(_1394429), 33002 ^ _780205 : [(33013 ^ _780205) ^ [] : [33015 ^ _780205 : [(33016 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394433), 33014 ^ [_1394429, _1394431, _1394433, _1394435, _1394437]), _1394435)))], (33018 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394429), _1394431), hAPP(_1394437, 33014 ^ [_1394429, _1394431, _1394433, _1394435, _1394437])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394429), _1394431), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394433, _1394429), _1394435), _1394437))))], (33003 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394429), _1394431), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394433, _1394429), _1394435), _1394437))), 33006 ^ _780205 : [(33007 ^ _780205) ^ [_1394610] : [hBOOL(hAPP(hAPP(c_member(_1394433), _1394610), _1394435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394429), _1394431), hAPP(_1394437, _1394610))))]]]]], (33022 ^ _780205) ^ [_1394923, _1394925, _1394927, _1394929, _1394931] : [class_Complete__Lattice_Ocomplete__lattice(_1394923), class_Orderings_Olinorder(_1394923), 33029 ^ _780205 : [(33030 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394923), _1394925), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394927, _1394923), _1394929), _1394931))), 33034 ^ _780205 : [(33035 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394927), 33033 ^ [_1394923, _1394925, _1394927, _1394929, _1394931]), _1394929)))], (33037 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394923), _1394925), hAPP(_1394931, 33033 ^ [_1394923, _1394925, _1394927, _1394929, _1394931]))))]]], (33039 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394923), _1394925), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394927, _1394923), _1394929), _1394931)))), 33040 ^ _780205 : [(33041 ^ _780205) ^ [_1395271] : [hBOOL(hAPP(hAPP(c_member(_1394927), _1395271), _1394929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394923), _1394925), hAPP(_1394931, _1395271)))]]]]], (33049 ^ _780205) ^ [_1395441, _1395443, _1395445, _1395447, _1395449] : [class_Complete__Lattice_Ocomplete__lattice(_1395441), class_Orderings_Olinorder(_1395441), 33056 ^ _780205 : [(33057 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395441), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395443, _1395441), _1395445), _1395447)), _1395449)), 33061 ^ _780205 : [(33062 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1395443), 33060 ^ [_1395441, _1395443, _1395445, _1395447, _1395449]), _1395445)))], (33064 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395441), hAPP(_1395447, 33060 ^ [_1395441, _1395443, _1395445, _1395447, _1395449])), _1395449)))]]], (33066 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395441), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395443, _1395441), _1395445), _1395447)), _1395449))), 33067 ^ _780205 : [(33068 ^ _780205) ^ [_1395789] : [hBOOL(hAPP(hAPP(c_member(_1395443), _1395789), _1395445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395441), hAPP(_1395447, _1395789)), _1395449))]]]]], (33076 ^ _780205) ^ [_1395959, _1395961, _1395963, _1395965, _1395967, _1395969] : [hBOOL(hAPP(hAPP(c_member(_1395959), _1395961), _1395963)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395959, tc_fun(_1395965, tc_HOL_Obool)), _1395963), hAPP(hAPP(c_COMBB(tc_fun(_1395965, tc_HOL_Obool), tc_fun(_1395965, tc_HOL_Obool), _1395959), hAPP(c_Set_Oinsert(_1395965), _1395967)), _1395969)) = hAPP(hAPP(c_Set_Oinsert(_1395965), _1395967), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395959, tc_fun(_1395965, tc_HOL_Obool)), _1395963), _1395969)))], (33082 ^ _780205) ^ [_1396164, _1396166, _1396168, _1396170, _1396172] : [hBOOL(hAPP(hAPP(c_member(_1396164), _1396166), _1396168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1396170, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396164, tc_fun(_1396170, tc_HOL_Obool)), _1396168), _1396172)), hAPP(_1396172, _1396166))))], (33088 ^ _780205) ^ [_1396332, _1396334, _1396336, _1396338] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396332, tc_fun(_1396334, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1396332, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1396334, tc_HOL_Obool), tc_fun(_1396334, tc_HOL_Obool), _1396332), hAPP(c_COMBC(_1396334, tc_fun(_1396334, tc_HOL_Obool), tc_HOL_Obool), c_member(_1396334))), _1396336)), _1396338)), -(hBOOL(hAPP(hAPP(c_member(_1396334), _1396338), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396332, tc_fun(_1396334, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1396332, tc_HOL_Obool))), _1396336))))], (33094 ^ _780205) ^ [_1396551, _1396553, _1396555, _1396557] : [hBOOL(hAPP(hAPP(c_member(_1396553), _1396557), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396551, tc_fun(_1396553, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1396551, tc_HOL_Obool))), _1396555))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396551, tc_fun(_1396553, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1396551, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1396553, tc_HOL_Obool), tc_fun(_1396553, tc_HOL_Obool), _1396551), hAPP(c_COMBC(_1396553, tc_fun(_1396553, tc_HOL_Obool), tc_HOL_Obool), c_member(_1396553))), _1396555)), _1396557)))], (33100 ^ _780205) ^ [_1396776, _1396778, _1396780, _1396782, _1396784] : [hBOOL(hAPP(hAPP(c_member(_1396776), _1396778), _1396780)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396782, tc_HOL_Obool)), hAPP(_1396784, _1396778)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396776, tc_fun(_1396782, tc_HOL_Obool)), _1396780), _1396784)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1396776, tc_fun(_1396782, tc_HOL_Obool)), _1396780), _1396784))], (33106 ^ _780205) ^ [_1396949, _1396951, _1396953, _1396955] : [class_Complete__Lattice_Ocomplete__lattice(_1396949), -(_1396951 = c_Orderings_Obot__class_Obot(tc_fun(_1396953, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396953, _1396949), _1396951), hAPP(c_COMBK(_1396949, _1396953), _1396955)) = _1396955)], (33116 ^ _780205) ^ [_1397083, _1397085, _1397087, _1397089] : [class_Complete__Lattice_Ocomplete__lattice(_1397083), -(_1397085 = c_Orderings_Obot__class_Obot(tc_fun(_1397087, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397087, _1397083), _1397085), hAPP(c_COMBK(_1397083, _1397087), _1397089)) = _1397089)], (33126 ^ _780205) ^ [_1397217, _1397219, _1397221, _1397223, _1397225, _1397227] : [hBOOL(hAPP(hAPP(c_member(_1397217), _1397219), _1397221)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397217, tc_fun(_1397223, tc_HOL_Obool)), _1397221), hAPP(hAPP(c_COMBB(tc_fun(_1397223, tc_HOL_Obool), tc_fun(_1397223, tc_HOL_Obool), _1397217), hAPP(c_Set_Oinsert(_1397223), _1397225)), _1397227)) = hAPP(hAPP(c_Set_Oinsert(_1397223), _1397225), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397217, tc_fun(_1397223, tc_HOL_Obool)), _1397221), _1397227)))], (33132 ^ _780205) ^ [_1397437, _1397439, _1397441, _1397443] : [_1397437 = c_Orderings_Obot__class_Obot(tc_fun(_1397439, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397439, tc_fun(_1397441, tc_HOL_Obool)), _1397437), hAPP(c_COMBK(tc_fun(_1397441, tc_HOL_Obool), _1397439), _1397443)) = c_Orderings_Otop__class_Otop(tc_fun(_1397441, tc_HOL_Obool)))], (33138 ^ _780205) ^ [_1397574, _1397576, _1397578, _1397580] : [-(_1397574 = c_Orderings_Obot__class_Obot(tc_fun(_1397576, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397576, tc_fun(_1397578, tc_HOL_Obool)), _1397574), hAPP(c_COMBK(tc_fun(_1397578, tc_HOL_Obool), _1397576), _1397580)) = _1397580)], (33144 ^ _780205) ^ [_1397642, _1397644, _1397646] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397642, tc_fun(_1397644, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1397642, tc_HOL_Obool))), _1397646) = c_Orderings_Otop__class_Otop(tc_fun(_1397644, tc_HOL_Obool)))], (33146 ^ _780205) ^ [_1397709, _1397711, _1397713, _1397715, _1397717] : [_1397709 = c_Orderings_Obot__class_Obot(tc_fun(_1397711, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397713, tc_HOL_Obool)), _1397715), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397711, tc_fun(_1397713, tc_HOL_Obool)), _1397709), _1397717)) = _1397715)], (33152 ^ _780205) ^ [_1397842, _1397844, _1397846, _1397848, _1397850] : [-(_1397842 = c_Orderings_Obot__class_Obot(tc_fun(_1397844, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397846, tc_HOL_Obool)), _1397848), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397844, tc_fun(_1397846, tc_HOL_Obool)), _1397842), _1397850)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397844, tc_fun(_1397846, tc_HOL_Obool)), _1397842), hAPP(hAPP(c_COMBB(tc_fun(_1397846, tc_HOL_Obool), tc_fun(_1397846, tc_HOL_Obool), _1397844), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397846, tc_HOL_Obool)), _1397848)), _1397850)))], (33158 ^ _780205) ^ [_1397968, _1397970, _1397972, _1397974, _1397976] : [_1397968 = c_Orderings_Obot__class_Obot(tc_fun(_1397970, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397972, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1397970, tc_fun(_1397972, tc_HOL_Obool)), _1397968), _1397974)), _1397976) = _1397976)], (33164 ^ _780205) ^ [_1398101, _1398103, _1398105, _1398107, _1398109] : [-(_1398101 = c_Orderings_Obot__class_Obot(tc_fun(_1398103, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398105, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1398103, tc_fun(_1398105, tc_HOL_Obool)), _1398101), _1398107)), _1398109) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1398103, tc_fun(_1398105, tc_HOL_Obool)), _1398101), hAPP(hAPP(c_COMBC(_1398103, tc_fun(_1398105, tc_HOL_Obool), tc_fun(_1398105, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1398105, tc_HOL_Obool), tc_fun(tc_fun(_1398105, tc_HOL_Obool), tc_fun(_1398105, tc_HOL_Obool)), _1398103), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398105, tc_HOL_Obool))), _1398107)), _1398109)))], (33170 ^ _780205) ^ [_1398228, _1398230, _1398232, _1398234, _1398236] : [hBOOL(hAPP(hAPP(c_member(_1398228), _1398230), _1398232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398234, tc_HOL_Obool)), hAPP(_1398236, _1398230)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398228, tc_fun(_1398234, tc_HOL_Obool)), _1398232), _1398236))))], (33176 ^ _780205) ^ [_1398396, _1398398, _1398400, _1398402] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398396, tc_fun(_1398398, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1398396, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1398398, tc_HOL_Obool), tc_fun(_1398398, tc_HOL_Obool), _1398396), hAPP(c_COMBC(_1398398, tc_fun(_1398398, tc_HOL_Obool), tc_HOL_Obool), c_member(_1398398))), _1398400)), _1398402)), -(hBOOL(hAPP(hAPP(c_member(_1398398), _1398402), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398396, tc_fun(_1398398, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1398396, tc_HOL_Obool))), _1398400))))], (33182 ^ _780205) ^ [_1398615, _1398617, _1398619, _1398621] : [hBOOL(hAPP(hAPP(c_member(_1398617), _1398621), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398615, tc_fun(_1398617, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1398615, tc_HOL_Obool))), _1398619))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398615, tc_fun(_1398617, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1398615, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1398617, tc_HOL_Obool), tc_fun(_1398617, tc_HOL_Obool), _1398615), hAPP(c_COMBC(_1398617, tc_fun(_1398617, tc_HOL_Obool), tc_HOL_Obool), c_member(_1398617))), _1398619)), _1398621)))], (33188 ^ _780205) ^ [_1398840, _1398842, _1398844, _1398846, _1398848] : [hBOOL(hAPP(hAPP(c_member(_1398840), _1398842), _1398844)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398846, tc_HOL_Obool)), hAPP(_1398848, _1398842)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398840, tc_fun(_1398846, tc_HOL_Obool)), _1398844), _1398848)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398840, tc_fun(_1398846, tc_HOL_Obool)), _1398844), _1398848))], (33194 ^ _780205) ^ [_1399013, _1399015, _1399017, _1399019, _1399021] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1399013, tc_fun(_1399015, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1399013), _1399017), _1399019)), _1399021) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399015, tc_HOL_Obool)), hAPP(_1399021, _1399017)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1399013, tc_fun(_1399015, tc_HOL_Obool)), _1399019), _1399021)))], (33196 ^ _780205) ^ [_1399108, _1399110, _1399112, _1399114, _1399116] : [_1399108 = c_Orderings_Obot__class_Obot(tc_fun(_1399110, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399110, tc_fun(_1399112, tc_HOL_Obool)), _1399108), hAPP(hAPP(c_COMBB(tc_fun(_1399112, tc_HOL_Obool), tc_fun(_1399112, tc_HOL_Obool), _1399110), hAPP(c_Set_Oinsert(_1399112), _1399114)), _1399116)) = c_Orderings_Obot__class_Obot(tc_fun(_1399112, tc_HOL_Obool)))], (33202 ^ _780205) ^ [_1399271, _1399273, _1399275, _1399277, _1399279] : [-(_1399271 = c_Orderings_Obot__class_Obot(tc_fun(_1399273, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399273, tc_fun(_1399275, tc_HOL_Obool)), _1399271), hAPP(hAPP(c_COMBB(tc_fun(_1399275, tc_HOL_Obool), tc_fun(_1399275, tc_HOL_Obool), _1399273), hAPP(c_Set_Oinsert(_1399275), _1399277)), _1399279)) = hAPP(hAPP(c_Set_Oinsert(_1399275), _1399277), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399273, tc_fun(_1399275, tc_HOL_Obool)), _1399271), _1399279)))], (33208 ^ _780205) ^ [_1399373, _1399375] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399373, tc_fun(_1399373, tc_HOL_Obool)), _1399375), hAPP(hAPP(c_COMBC(_1399373, tc_fun(_1399373, tc_HOL_Obool), tc_fun(_1399373, tc_HOL_Obool)), c_Set_Oinsert(_1399373)), c_Orderings_Obot__class_Obot(tc_fun(_1399373, tc_HOL_Obool)))) = _1399375)], (33210 ^ _780205) ^ [_1399451, _1399453, _1399455, _1399457, _1399459] : [_1399451 = c_Orderings_Obot__class_Obot(tc_fun(_1399453, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1399455), _1399457), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399453, tc_fun(_1399455, tc_HOL_Obool)), _1399451), _1399459)) = hAPP(hAPP(c_Set_Oinsert(_1399455), _1399457), c_Orderings_Obot__class_Obot(tc_fun(_1399455, tc_HOL_Obool))))], (33216 ^ _780205) ^ [_1399604, _1399606, _1399608, _1399610, _1399612] : [-(_1399604 = c_Orderings_Obot__class_Obot(tc_fun(_1399606, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1399608), _1399610), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399606, tc_fun(_1399608, tc_HOL_Obool)), _1399604), _1399612)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399606, tc_fun(_1399608, tc_HOL_Obool)), _1399604), hAPP(hAPP(c_COMBB(tc_fun(_1399608, tc_HOL_Obool), tc_fun(_1399608, tc_HOL_Obool), _1399606), hAPP(c_Set_Oinsert(_1399608), _1399610)), _1399612)))], (33222 ^ _780205) ^ [_1399706, _1399708, _1399710, _1399712, _1399714] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1399706, tc_fun(_1399708, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399706, tc_HOL_Obool)), _1399710), _1399712)), _1399714) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399708, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1399706, tc_fun(_1399708, tc_HOL_Obool)), _1399710), _1399714)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1399706, tc_fun(_1399708, tc_HOL_Obool)), _1399712), _1399714)))], (33224 ^ _780205) ^ [_1399813, _1399815, _1399817, _1399819, _1399821] : [_1399813 = c_Orderings_Obot__class_Obot(tc_fun(_1399815, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399817, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399815, tc_fun(_1399817, tc_HOL_Obool)), _1399813), _1399819)), _1399821) = _1399821)], (33230 ^ _780205) ^ [_1399946, _1399948, _1399950, _1399952, _1399954] : [-(_1399946 = c_Orderings_Obot__class_Obot(tc_fun(_1399948, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399950, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399948, tc_fun(_1399950, tc_HOL_Obool)), _1399946), _1399952)), _1399954) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399948, tc_fun(_1399950, tc_HOL_Obool)), _1399946), hAPP(hAPP(c_COMBC(_1399948, tc_fun(_1399950, tc_HOL_Obool), tc_fun(_1399950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1399950, tc_HOL_Obool), tc_fun(tc_fun(_1399950, tc_HOL_Obool), tc_fun(_1399950, tc_HOL_Obool)), _1399948), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399950, tc_HOL_Obool))), _1399952)), _1399954)))], (33236 ^ _780205) ^ [_1400091, _1400093, _1400095, _1400097, _1400099] : [_1400091 = c_Orderings_Obot__class_Obot(tc_fun(_1400093, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400095, tc_HOL_Obool)), _1400097), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400093, tc_fun(_1400095, tc_HOL_Obool)), _1400091), _1400099)) = _1400097)], (33242 ^ _780205) ^ [_1400224, _1400226, _1400228, _1400230, _1400232] : [-(_1400224 = c_Orderings_Obot__class_Obot(tc_fun(_1400226, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400228, tc_HOL_Obool)), _1400230), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400226, tc_fun(_1400228, tc_HOL_Obool)), _1400224), _1400232)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400226, tc_fun(_1400228, tc_HOL_Obool)), _1400224), hAPP(hAPP(c_COMBB(tc_fun(_1400228, tc_HOL_Obool), tc_fun(_1400228, tc_HOL_Obool), _1400226), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400228, tc_HOL_Obool)), _1400230)), _1400232)))], (33248 ^ _780205) ^ [_1400350, _1400352, _1400354, _1400356, _1400358] : [_1400350 = c_Orderings_Obot__class_Obot(tc_fun(_1400352, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400352, tc_fun(_1400354, tc_HOL_Obool)), _1400350), hAPP(hAPP(c_COMBC(_1400352, tc_fun(_1400354, tc_HOL_Obool), tc_fun(_1400354, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1400354, tc_HOL_Obool), tc_fun(tc_fun(_1400354, tc_HOL_Obool), tc_fun(_1400354, tc_HOL_Obool)), _1400352), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400354, tc_HOL_Obool))), _1400356)), _1400358)) = c_Orderings_Obot__class_Obot(tc_fun(_1400354, tc_HOL_Obool)))], (33254 ^ _780205) ^ [_1400557, _1400559, _1400561, _1400563, _1400565] : [-(_1400557 = c_Orderings_Obot__class_Obot(tc_fun(_1400559, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400559, tc_fun(_1400561, tc_HOL_Obool)), _1400557), hAPP(hAPP(c_COMBC(_1400559, tc_fun(_1400561, tc_HOL_Obool), tc_fun(_1400561, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1400561, tc_HOL_Obool), tc_fun(tc_fun(_1400561, tc_HOL_Obool), tc_fun(_1400561, tc_HOL_Obool)), _1400559), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400561, tc_HOL_Obool))), _1400563)), _1400565)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400561, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400559, tc_fun(_1400561, tc_HOL_Obool)), _1400557), _1400563)), _1400565))], (33260 ^ _780205) ^ [_1400702, _1400704, _1400706, _1400708, _1400710] : [_1400702 = c_Orderings_Obot__class_Obot(tc_fun(_1400704, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400704, tc_fun(_1400706, tc_HOL_Obool)), _1400702), hAPP(hAPP(c_COMBB(tc_fun(_1400706, tc_HOL_Obool), tc_fun(_1400706, tc_HOL_Obool), _1400704), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400706, tc_HOL_Obool)), _1400708)), _1400710)) = c_Orderings_Obot__class_Obot(tc_fun(_1400706, tc_HOL_Obool)))], (33266 ^ _780205) ^ [_1400871, _1400873, _1400875, _1400877, _1400879] : [-(_1400871 = c_Orderings_Obot__class_Obot(tc_fun(_1400873, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400873, tc_fun(_1400875, tc_HOL_Obool)), _1400871), hAPP(hAPP(c_COMBB(tc_fun(_1400875, tc_HOL_Obool), tc_fun(_1400875, tc_HOL_Obool), _1400873), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400875, tc_HOL_Obool)), _1400877)), _1400879)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400875, tc_HOL_Obool)), _1400877), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400873, tc_fun(_1400875, tc_HOL_Obool)), _1400871), _1400879)))], (33272 ^ _780205) ^ [_1400979, _1400981, _1400983, _1400985, _1400987] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400979, tc_fun(_1400981, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1400979), _1400983), _1400985)), _1400987) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400981, tc_HOL_Obool)), hAPP(_1400987, _1400983)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400979, tc_fun(_1400981, tc_HOL_Obool)), _1400985), _1400987)))], (33274 ^ _780205) ^ [_1401056, _1401058, _1401060, _1401062, _1401064, _1401066] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401056, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1401058, _1401056, _1401060), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401062, tc_fun(_1401058, tc_HOL_Obool)), _1401064), _1401066))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401062, tc_fun(_1401056, tc_HOL_Obool)), _1401064), hAPP(hAPP(c_COMBB(tc_fun(_1401058, tc_HOL_Obool), tc_fun(_1401056, tc_HOL_Obool), _1401062), c_Relation_OImage(_1401058, _1401056, _1401060)), _1401066)))))], (33276 ^ _780205) ^ [_1401150, _1401152, _1401154] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401150, tc_HOL_Obool)), _1401152), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1401150, tc_HOL_Obool), _1401154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1401150, tc_HOL_Obool), tc_fun(_1401150, tc_HOL_Obool)), _1401154), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401150, tc_HOL_Obool)), _1401152)))], (33278 ^ _780205) ^ [_1401217, _1401219, _1401221] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401217, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1401217, tc_HOL_Obool), _1401219)), _1401221) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1401217, tc_HOL_Obool), tc_fun(_1401217, tc_HOL_Obool)), _1401219), hAPP(hAPP(c_COMBC(tc_fun(_1401217, tc_HOL_Obool), tc_fun(_1401217, tc_HOL_Obool), tc_fun(_1401217, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401217, tc_HOL_Obool))), _1401221)))], (33280 ^ _780205) ^ [_1401300, _1401302, _1401304] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1401300, tc_HOL_Obool)), _1401302), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1401300, tc_HOL_Obool), _1401304)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1401300, tc_HOL_Obool), tc_fun(_1401300, tc_HOL_Obool)), _1401304), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1401300, tc_HOL_Obool)), _1401302)))], (33282 ^ _780205) ^ [_1401367, _1401369, _1401371] : [class_Orderings_Oorder(_1401367), 33285 ^ _780205 : [(33286 ^ _780205) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1401367, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1401367, _1401369, _1401371), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401367), _1401369), _1401371))], (33292 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401367), _1401369), _1401371))), -(c_Orderings_Obot__class_Obot(tc_fun(_1401367, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1401367, _1401369, _1401371))]]], (33298 ^ _780205) ^ [_1401586, _1401588, _1401590] : [class_Orderings_Oorder(_1401586), 33301 ^ _780205 : [(33302 ^ _780205) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1401586, _1401588, _1401590) = c_Orderings_Obot__class_Obot(tc_fun(_1401586, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401586), _1401588), _1401590))], (33308 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401586), _1401588), _1401590))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1401586, _1401588, _1401590) = c_Orderings_Obot__class_Obot(tc_fun(_1401586, tc_HOL_Obool)))]]], (33314 ^ _780205) ^ [_1401805, _1401807, _1401809] : [class_Orderings_Oorder(_1401805), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401805), _1401807), _1401809)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1401805, _1401809, _1401807) = c_Orderings_Obot__class_Obot(tc_fun(_1401805, tc_HOL_Obool)))], (33324 ^ _780205) ^ [_1401968, _1401970, _1401972, _1401974, _1401976] : [class_Orderings_Oorder(_1401968), 33327 ^ _780205 : [(33328 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401968, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1401968, _1401970, _1401972)), c_SetInterval_Oord__class_OatLeastAtMost(_1401968, _1401974, _1401976))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401968), _1401970), _1401972)), 33335 ^ _780205 : [(33336 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401968), _1401974), _1401970)))], (33338 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401968), _1401972), _1401976)))]]], (33340 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401968, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1401968, _1401970, _1401972)), c_SetInterval_Oord__class_OatLeastAtMost(_1401968, _1401974, _1401976)))), 33341 ^ _780205 : [(33342 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401968), _1401970), _1401972)))], (33344 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401968), _1401974), _1401970)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401968), _1401972), _1401976))]]]]], (33352 ^ _780205) ^ [_1402471, _1402473] : [class_Orderings_Oorder(_1402471), -(c_SetInterval_Oord__class_OatLeastAtMost(_1402471, _1402473, _1402473) = hAPP(hAPP(c_Set_Oinsert(_1402471), _1402473), c_Orderings_Obot__class_Obot(tc_fun(_1402471, tc_HOL_Obool))))], (33358 ^ _780205) ^ [_1402580, _1402582, _1402584, _1402586] : [class_Orderings_Oorder(_1402580), 33361 ^ _780205 : [(33362 ^ _780205) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1402580, _1402582, _1402584) = hAPP(hAPP(c_Set_Oinsert(_1402580), _1402586), c_Orderings_Obot__class_Obot(tc_fun(_1402580, tc_HOL_Obool))), 33365 ^ _780205 : [(33366 ^ _780205) ^ [] : [-(_1402582 = _1402584)], (33368 ^ _780205) ^ [] : [-(_1402584 = _1402586)]]], (33370 ^ _780205) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1402580, _1402582, _1402584) = hAPP(hAPP(c_Set_Oinsert(_1402580), _1402586), c_Orderings_Obot__class_Obot(tc_fun(_1402580, tc_HOL_Obool)))), _1402582 = _1402584, _1402584 = _1402586]]], (33380 ^ _780205) ^ [_1402924, _1402926, _1402928] : [class_Orderings_Oorder(_1402924), _1402926 = _1402928, -(c_SetInterval_Oord__class_OatLeastAtMost(_1402924, _1402926, _1402928) = hAPP(hAPP(c_Set_Oinsert(_1402924), _1402926), c_Orderings_Obot__class_Obot(tc_fun(_1402924, tc_HOL_Obool))))], (33390 ^ _780205) ^ [_1403089, _1403091, _1403093, _1403095] : [-(hAPP(c_Set_Ovimage(_1403089, _1403091, _1403093), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1403091, tc_HOL_Obool), _1403095)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1403091, tc_HOL_Obool), tc_fun(_1403089, tc_HOL_Obool)), _1403095), c_Set_Ovimage(_1403089, _1403091, _1403093)))], (33392 ^ _780205) ^ [_1403150, _1403152, _1403154, _1403156] : [class_Groups_Ocomm__monoid__add(_1403150), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1403150), _1403152), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1403154), hAPP(c_Nat_OSuc, _1403156))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1403150), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1403150, tc_Nat_Onat), _1403152), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1403154, _1403156)))], (33398 ^ _780205) ^ [_1403313, _1403315, _1403317, _1403319, _1403321] : [class_Groups_Ocomm__monoid__add(_1403313), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1403313), _1403315), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1403317), _1403319), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1403321), _1403319))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1403313), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1403313, tc_Nat_Onat), _1403315), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1403319))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1403317, _1403321)))], (33404 ^ _780205) ^ [] : [-(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)))], (33406 ^ _780205) ^ [_1403514, _1403516, _1403518, _1403520, _1403522] : [class_Complete__Lattice_Ocomplete__lattice(_1403514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403516, tc_HOL_Obool)), _1403518), _1403520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403514), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1403516, _1403514), _1403520), _1403522)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1403516, _1403514), _1403518), _1403522))))], (33416 ^ _780205) ^ [_1403723, _1403725, _1403727, _1403729, _1403731] : [class_Complete__Lattice_Ocomplete__lattice(_1403723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403725, tc_HOL_Obool)), _1403727), _1403729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403723), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403725, _1403723), _1403727), _1403731)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403725, _1403723), _1403729), _1403731))))], (33426 ^ _780205) ^ [_1403950, _1403952, _1403954, _1403956, _1403958] : [_1403950 = c_Orderings_Obot__class_Obot(tc_fun(_1403952, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1403952, tc_fun(_1403954, tc_HOL_Obool)), _1403950), hAPP(hAPP(c_COMBB(tc_fun(_1403954, tc_HOL_Obool), tc_fun(_1403954, tc_HOL_Obool), _1403952), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1403954, tc_HOL_Obool)), _1403956)), _1403958)) = c_Orderings_Otop__class_Otop(tc_fun(_1403954, tc_HOL_Obool)))], (33432 ^ _780205) ^ [_1404119, _1404121, _1404123, _1404125, _1404127] : [-(_1404119 = c_Orderings_Obot__class_Obot(tc_fun(_1404121, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404121, tc_fun(_1404123, tc_HOL_Obool)), _1404119), hAPP(hAPP(c_COMBB(tc_fun(_1404123, tc_HOL_Obool), tc_fun(_1404123, tc_HOL_Obool), _1404121), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404123, tc_HOL_Obool)), _1404125)), _1404127)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404123, tc_HOL_Obool)), _1404125), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404121, tc_fun(_1404123, tc_HOL_Obool)), _1404119), _1404127)))], (33438 ^ _780205) ^ [_1404245, _1404247, _1404249, _1404251, _1404253] : [_1404245 = c_Orderings_Obot__class_Obot(tc_fun(_1404247, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404247, tc_fun(_1404249, tc_HOL_Obool)), _1404245), hAPP(hAPP(c_COMBC(_1404247, tc_fun(_1404249, tc_HOL_Obool), tc_fun(_1404249, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404249, tc_HOL_Obool), tc_fun(tc_fun(_1404249, tc_HOL_Obool), tc_fun(_1404249, tc_HOL_Obool)), _1404247), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404249, tc_HOL_Obool))), _1404251)), _1404253)) = c_Orderings_Otop__class_Otop(tc_fun(_1404249, tc_HOL_Obool)))], (33444 ^ _780205) ^ [_1404452, _1404454, _1404456, _1404458, _1404460] : [-(_1404452 = c_Orderings_Obot__class_Obot(tc_fun(_1404454, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404454, tc_fun(_1404456, tc_HOL_Obool)), _1404452), hAPP(hAPP(c_COMBC(_1404454, tc_fun(_1404456, tc_HOL_Obool), tc_fun(_1404456, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404456, tc_HOL_Obool), tc_fun(tc_fun(_1404456, tc_HOL_Obool), tc_fun(_1404456, tc_HOL_Obool)), _1404454), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404456, tc_HOL_Obool))), _1404458)), _1404460)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404456, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404454, tc_fun(_1404456, tc_HOL_Obool)), _1404452), _1404458)), _1404460))], (33450 ^ _780205) ^ [_1404597, _1404599, _1404601, _1404603, _1404605] : [_1404597 = c_Orderings_Obot__class_Obot(tc_fun(_1404599, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404599, tc_fun(_1404601, tc_HOL_Obool)), _1404597), hAPP(hAPP(c_COMBC(_1404599, tc_fun(_1404601, tc_HOL_Obool), tc_fun(_1404601, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404601, tc_HOL_Obool), tc_fun(tc_fun(_1404601, tc_HOL_Obool), tc_fun(_1404601, tc_HOL_Obool)), _1404599), c_Groups_Ominus__class_Ominus(tc_fun(_1404601, tc_HOL_Obool))), _1404603)), _1404605)) = c_Orderings_Otop__class_Otop(tc_fun(_1404601, tc_HOL_Obool)))], (33456 ^ _780205) ^ [_1404804, _1404806, _1404808, _1404810, _1404812] : [-(_1404804 = c_Orderings_Obot__class_Obot(tc_fun(_1404806, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404806, tc_fun(_1404808, tc_HOL_Obool)), _1404804), hAPP(hAPP(c_COMBC(_1404806, tc_fun(_1404808, tc_HOL_Obool), tc_fun(_1404808, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404808, tc_HOL_Obool), tc_fun(tc_fun(_1404808, tc_HOL_Obool), tc_fun(_1404808, tc_HOL_Obool)), _1404806), c_Groups_Ominus__class_Ominus(tc_fun(_1404808, tc_HOL_Obool))), _1404810)), _1404812)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1404808, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404806, tc_fun(_1404808, tc_HOL_Obool)), _1404804), _1404810)), _1404812))], (33462 ^ _780205) ^ [_1404949, _1404951, _1404953, _1404955, _1404957] : [_1404949 = c_Orderings_Obot__class_Obot(tc_fun(_1404951, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1404953, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404951, tc_fun(_1404953, tc_HOL_Obool)), _1404949), _1404955)), _1404957) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1404953, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1404953, tc_HOL_Obool))), _1404957))], (33468 ^ _780205) ^ [_1405114, _1405116, _1405118, _1405120, _1405122] : [-(_1405114 = c_Orderings_Obot__class_Obot(tc_fun(_1405116, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1405118, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1405116, tc_fun(_1405118, tc_HOL_Obool)), _1405114), _1405120)), _1405122) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1405116, tc_fun(_1405118, tc_HOL_Obool)), _1405114), hAPP(hAPP(c_COMBC(_1405116, tc_fun(_1405118, tc_HOL_Obool), tc_fun(_1405118, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405118, tc_HOL_Obool), tc_fun(tc_fun(_1405118, tc_HOL_Obool), tc_fun(_1405118, tc_HOL_Obool)), _1405116), c_Groups_Ominus__class_Ominus(tc_fun(_1405118, tc_HOL_Obool))), _1405120)), _1405122)))], (33474 ^ _780205) ^ [_1405241, _1405243, _1405245, _1405247] : [-(hAPP(c_Relation_OImage(_1405241, _1405243, _1405245), _1405247) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405241, tc_fun(_1405243, tc_HOL_Obool)), _1405247), hAPP(hAPP(c_COMBB(tc_fun(_1405241, tc_HOL_Obool), tc_fun(_1405243, tc_HOL_Obool), _1405241), c_Relation_OImage(_1405241, _1405243, _1405245)), hAPP(hAPP(c_COMBC(_1405241, tc_fun(_1405241, tc_HOL_Obool), tc_fun(_1405241, tc_HOL_Obool)), c_Set_Oinsert(_1405241)), c_Orderings_Obot__class_Obot(tc_fun(_1405241, tc_HOL_Obool))))))], (33476 ^ _780205) ^ [_1405332, _1405334, _1405336, _1405338] : [-(hAPP(c_Set_Ovimage(_1405332, _1405334, _1405336), _1405338) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405334, tc_fun(_1405332, tc_HOL_Obool)), _1405338), hAPP(hAPP(c_COMBB(tc_fun(_1405334, tc_HOL_Obool), tc_fun(_1405332, tc_HOL_Obool), _1405334), c_Set_Ovimage(_1405332, _1405334, _1405336)), hAPP(hAPP(c_COMBC(_1405334, tc_fun(_1405334, tc_HOL_Obool), tc_fun(_1405334, tc_HOL_Obool)), c_Set_Oinsert(_1405334)), c_Orderings_Obot__class_Obot(tc_fun(_1405334, tc_HOL_Obool))))))], (33478 ^ _780205) ^ [_1405423, _1405425] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1405423, _1405425)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1405425)), _1405423))], (33480 ^ _780205) ^ [_1405464, _1405466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1405464), hAPP(c_Nat_OSuc, _1405466))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1405464, hAPP(c_Nat_OSuc, _1405466)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1405466)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1405464, _1405466)))], (33486 ^ _780205) ^ [_1405597, _1405599, _1405601, _1405603, _1405605] : [class_Complete__Lattice_Ocomplete__lattice(_1405597), hBOOL(hAPP(hAPP(c_member(_1405599), _1405601), _1405603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405597), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1405599, _1405597), _1405603), _1405605)), hAPP(_1405605, _1405601))))], (33496 ^ _780205) ^ [_1405788, _1405790, _1405792, _1405794, _1405796] : [class_Complete__Lattice_Ocomplete__lattice(_1405788), hBOOL(hAPP(hAPP(c_member(_1405790), _1405792), _1405794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405788), hAPP(_1405796, _1405792)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405790, _1405788), _1405794), _1405796))))], (33506 ^ _780205) ^ [_1405979, _1405981] : [hAPP(_1405979, 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), _1405979), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1405981)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1405979), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1405981)))], (33512 ^ _780205) ^ [_1406102, _1406104, _1406106, _1406108, _1406110] : [class_Orderings_Olinorder(_1406102), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406102, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1406102, _1406104, _1406106)), c_SetInterval_Oord__class_OatLeastAtMost(_1406102, _1406108, _1406110)) = c_SetInterval_Oord__class_OatLeastAtMost(_1406102, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1406102), _1406104), _1406108), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1406102), _1406106), _1406110)))], (33518 ^ _780205) ^ [_1406261, _1406263, _1406265, _1406267, _1406269] : [class_Orderings_Oorder(_1406261), 33521 ^ _780205 : [(33522 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1406261, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1406261, _1406263, _1406265)), c_SetInterval_Oord__class_OatLeastAtMost(_1406261, _1406267, _1406269))), 33525 ^ _780205 : [(33540 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406261), _1406267), _1406269)))], (33526 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406261), _1406263), _1406265)), 33529 ^ _780205 : [(33530 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406261), _1406267), _1406263)))], (33532 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406261), _1406265), _1406269)))], (33534 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406261), _1406267), _1406263))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406261), _1406265), _1406269)))]]]]], (33542 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1406261, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1406261, _1406263, _1406265)), c_SetInterval_Oord__class_OatLeastAtMost(_1406261, _1406267, _1406269)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406261), _1406267), _1406269)), 33545 ^ _780205 : [(33546 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406261), _1406263), _1406265)))], (33548 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406261), _1406267), _1406263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406261), _1406265), _1406269)), 33555 ^ _780205 : [(33556 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406261), _1406267), _1406263))], (33558 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406261), _1406265), _1406269))]]]]]]], (33564 ^ _780205) ^ [_1407032, _1407034, _1407036] : [class_Orderings_Oorder(_1407032), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407032, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1407032), _1407034)), c_SetInterval_Oord__class_OatLeastAtMost(_1407032, _1407034, _1407036)) = c_Orderings_Obot__class_Obot(tc_fun(_1407032, tc_HOL_Obool)))], (33570 ^ _780205) ^ [_1407159, _1407161, _1407163, _1407165] : [class_Groups_Ocomm__monoid__add(_1407159), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1407161), _1407163)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1407159), _1407165), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1407161, _1407163)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1407159), hAPP(_1407165, _1407161)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1407159), _1407165), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1407161), _1407163))))], (33580 ^ _780205) ^ [_1407384, _1407386, _1407388, _1407390] : [class_Groups_Ocomm__monoid__add(_1407384), 33583 ^ _780205 : [(33584 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1407386)), _1407388)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1407384), _1407390), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1407388, hAPP(c_Nat_OSuc, _1407386))) = c_Groups_Ozero__class_Ozero(_1407384))], (33590 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1407386)), _1407388))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1407384), _1407390), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1407388, hAPP(c_Nat_OSuc, _1407386))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1407384), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1407384), _1407390), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1407388, _1407386))), hAPP(_1407390, hAPP(c_Nat_OSuc, _1407386))))]]], (33596 ^ _780205) ^ [_1407720, _1407722, _1407724, _1407726, _1407728] : [class_Complete__Lattice_Ocomplete__lattice(_1407720), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407722), _1407724)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1407720), _1407726), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407722, _1407720), _1407724), _1407728)) = hAPP(hAPP(c_Finite__Set_Ofold(_1407722, _1407720, hAPP(hAPP(c_COMBB(_1407720, tc_fun(_1407720, _1407720), _1407722), c_Lattices_Osemilattice__sup__class_Osup(_1407720)), _1407728)), _1407726), _1407724))], (33606 ^ _780205) ^ [_1407951, _1407953, _1407955, _1407957, _1407959] : [class_Complete__Lattice_Ocomplete__lattice(_1407951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407953), _1407955)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1407951), _1407957), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1407953, _1407951), _1407955), _1407959)) = hAPP(hAPP(c_Finite__Set_Ofold(_1407953, _1407951, hAPP(hAPP(c_COMBB(_1407951, tc_fun(_1407951, _1407951), _1407953), c_Lattices_Osemilattice__inf__class_Oinf(_1407951)), _1407959)), _1407957), _1407955))], (33616 ^ _780205) ^ [_1408182, _1408184, _1408186, _1408188, _1408190] : [class_Groups_Ocomm__monoid__add(_1408182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1408184), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408186), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1408182), _1408188), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1408184, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408186), _1408190))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1408182), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1408182), _1408188), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1408184, _1408186))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1408182), _1408188), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408186), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1408186), _1408190)))))], (33626 ^ _780205) ^ [_1408473] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1408473) = 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, _1408473)), 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))))))))], (33628 ^ _780205) ^ [_1408526, _1408528] : [33636 ^ _780205 : [(33637 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 33635 ^ [_1408526, _1408528]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1408526))))], (33639 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1408528, 33635 ^ [_1408526, _1408528])))]], 33629 ^ _780205 : [(33630 ^ _780205) ^ [_1408595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1408595), _1408526)), hBOOL(hAPP(_1408528, _1408595))]]], (33641 ^ _780205) ^ [_1408756, _1408758] : [33649 ^ _780205 : [(33650 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 33648 ^ [_1408756, _1408758]), _1408756)))], (33652 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1408758, 33648 ^ [_1408756, _1408758])))]], 33642 ^ _780205 : [(33643 ^ _780205) ^ [_1408825] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1408825), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1408756))), hBOOL(hAPP(_1408758, _1408825))]]], (33654 ^ _780205) ^ [_1409011, _1409013] : [33656 ^ _780205 : [(33657 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 33655 ^ [_1409011, _1409013]), _1409011)))], (33659 ^ _780205) ^ [] : [hBOOL(hAPP(_1409013, 33655 ^ [_1409011, _1409013]))]], 33660 ^ _780205 : [(33661 ^ _780205) ^ [_1409162] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1409162), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1409011))), -(hBOOL(hAPP(_1409013, _1409162)))]]], (33667 ^ _780205) ^ [_1409265, _1409267] : [33669 ^ _780205 : [(33670 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 33668 ^ [_1409265, _1409267]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1409265))))], (33672 ^ _780205) ^ [] : [hBOOL(hAPP(_1409267, 33668 ^ [_1409265, _1409267]))]], 33673 ^ _780205 : [(33674 ^ _780205) ^ [_1409420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1409420), _1409265)), -(hBOOL(hAPP(_1409267, _1409420)))]]], (33680 ^ _780205) ^ [_1409521] : [-(hAPP(c_Int_Onat, _1409521) = 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, _1409521)), 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)))))))], (33682 ^ _780205) ^ [_1409589, _1409591, _1409593, _1409595, _1409597, _1409599, _1409601] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409589, tc_fun(_1409591, tc_fun(_1409593, tc_HOL_Obool))), _1409595), _1409597), _1409599), _1409601)), 33686 ^ _780205 : [(33687 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409589), 33685 ^ [_1409589, _1409591, _1409593, _1409595, _1409597, _1409599, _1409601]), _1409595)))], (33689 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1409597, 33685 ^ [_1409589, _1409591, _1409593, _1409595, _1409597, _1409599, _1409601]), _1409599), _1409601)))]]], (33691 ^ _780205) ^ [_1409807, _1409809, _1409811, _1409813, _1409815, _1409817, _1409819] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409807, tc_fun(_1409809, tc_fun(_1409811, tc_HOL_Obool))), _1409813), _1409815), _1409817), _1409819))), 33692 ^ _780205 : [(33693 ^ _780205) ^ [_1409892] : [hBOOL(hAPP(hAPP(c_member(_1409807), _1409892), _1409813)), hBOOL(hAPP(hAPP(hAPP(_1409815, _1409892), _1409817), _1409819))]]], (33711 ^ _780205) ^ [_1410337, _1410339, _1410341, _1410343, _1410345, _1410347, _1410349] : [33713 ^ _780205 : [(33714 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1410337), 33712 ^ [_1410337, _1410339, _1410341, _1410343, _1410345, _1410347, _1410349]), _1410343)))], (33716 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1410345, 33712 ^ [_1410337, _1410339, _1410341, _1410343, _1410345, _1410347, _1410349]), _1410347), _1410349))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410337, tc_fun(_1410339, tc_fun(_1410341, tc_HOL_Obool))), _1410343), _1410345), _1410347), _1410349)))], (33701 ^ _780205) ^ [_1410090, _1410092, _1410094, _1410096, _1410098, _1410100, _1410102] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410090, tc_fun(_1410092, tc_fun(_1410094, tc_HOL_Obool))), _1410096), _1410098), _1410100), _1410102)), 33704 ^ _780205 : [(33705 ^ _780205) ^ [_1410218] : [hBOOL(hAPP(hAPP(c_member(_1410090), _1410218), _1410096)), -(hBOOL(hAPP(hAPP(hAPP(_1410098, _1410218), _1410100), _1410102)))]]], (33720 ^ _780205) ^ [_1410621, _1410623, _1410625, _1410627, _1410629] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410621, tc_fun(_1410623, tc_HOL_Obool)), _1410625), _1410627), _1410629)), 33724 ^ _780205 : [(33725 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1410621), 33723 ^ [_1410621, _1410623, _1410625, _1410627, _1410629]), _1410625)))], (33727 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1410627, 33723 ^ [_1410621, _1410623, _1410625, _1410627, _1410629]), _1410629)))]]], (33729 ^ _780205) ^ [_1410809, _1410811, _1410813, _1410815, _1410817] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410809, tc_fun(_1410811, tc_HOL_Obool)), _1410813), _1410815), _1410817))), 33730 ^ _780205 : [(33731 ^ _780205) ^ [_1410881] : [hBOOL(hAPP(hAPP(c_member(_1410809), _1410881), _1410813)), hBOOL(hAPP(hAPP(_1410815, _1410881), _1410817))]]], (33749 ^ _780205) ^ [_1411275, _1411277, _1411279, _1411281, _1411283] : [33751 ^ _780205 : [(33752 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411275), 33750 ^ [_1411275, _1411277, _1411279, _1411281, _1411283]), _1411279)))], (33754 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1411281, 33750 ^ [_1411275, _1411277, _1411279, _1411281, _1411283]), _1411283))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411275, tc_fun(_1411277, tc_HOL_Obool)), _1411279), _1411281), _1411283)))], (33739 ^ _780205) ^ [_1411057, _1411059, _1411061, _1411063, _1411065] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411057, tc_fun(_1411059, tc_HOL_Obool)), _1411061), _1411063), _1411065)), 33742 ^ _780205 : [(33743 ^ _780205) ^ [_1411166] : [hBOOL(hAPP(hAPP(c_member(_1411057), _1411166), _1411061)), -(hBOOL(hAPP(hAPP(_1411063, _1411166), _1411065)))]]], (33758 ^ _780205) ^ [_1411498, _1411500, _1411502, _1411504, _1411506, _1411508] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411498, tc_fun(_1411500, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411502, tc_fun(_1411498, tc_HOL_Obool)), _1411504), _1411506)), _1411508) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411502, tc_fun(_1411500, tc_HOL_Obool)), _1411504), hAPP(hAPP(c_COMBC(_1411502, tc_fun(_1411498, tc_fun(_1411500, tc_HOL_Obool)), tc_fun(_1411500, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411498, tc_HOL_Obool), tc_fun(tc_fun(_1411498, tc_fun(_1411500, tc_HOL_Obool)), tc_fun(_1411500, tc_HOL_Obool)), _1411502), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411498, tc_fun(_1411500, tc_HOL_Obool))), _1411506)), _1411508)))], (33760 ^ _780205) ^ [_1411617, _1411619, _1411621, _1411623, _1411625, _1411627] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411617, tc_fun(_1411619, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411621, tc_fun(_1411617, tc_HOL_Obool)), _1411623), _1411625)), _1411627) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411621, tc_fun(_1411619, tc_HOL_Obool)), _1411623), hAPP(hAPP(c_COMBC(_1411621, tc_fun(_1411617, tc_fun(_1411619, tc_HOL_Obool)), tc_fun(_1411619, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411617, tc_HOL_Obool), tc_fun(tc_fun(_1411617, tc_fun(_1411619, tc_HOL_Obool)), tc_fun(_1411619, tc_HOL_Obool)), _1411621), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411617, tc_fun(_1411619, tc_HOL_Obool))), _1411625)), _1411627)))], (33762 ^ _780205) ^ [_1411736, _1411738, _1411740, _1411742, _1411744, _1411746] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411736, tc_fun(_1411738, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411740, tc_fun(_1411736, tc_HOL_Obool)), _1411742), _1411744)), _1411746) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411740, tc_fun(_1411738, tc_HOL_Obool)), _1411742), hAPP(hAPP(c_COMBC(_1411740, tc_fun(_1411736, tc_fun(_1411738, tc_HOL_Obool)), tc_fun(_1411738, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411736, tc_HOL_Obool), tc_fun(tc_fun(_1411736, tc_fun(_1411738, tc_HOL_Obool)), tc_fun(_1411738, tc_HOL_Obool)), _1411740), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411736, tc_fun(_1411738, tc_HOL_Obool))), _1411744)), _1411746)))], (33764 ^ _780205) ^ [_1411855, _1411857, _1411859, _1411861, _1411863, _1411865] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411855, tc_fun(_1411857, tc_HOL_Obool)), _1411859), hAPP(hAPP(c_COMBC(_1411855, tc_fun(_1411861, tc_fun(_1411857, tc_HOL_Obool)), tc_fun(_1411857, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411861, tc_HOL_Obool), tc_fun(tc_fun(_1411861, tc_fun(_1411857, tc_HOL_Obool)), tc_fun(_1411857, tc_HOL_Obool)), _1411855), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411861, tc_fun(_1411857, tc_HOL_Obool))), _1411863)), _1411865)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411861, tc_fun(_1411857, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411855, tc_fun(_1411861, tc_HOL_Obool)), _1411859), _1411863)), _1411865))], (33766 ^ _780205) ^ [_1411974, _1411976, _1411978, _1411980, _1411982, _1411984] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411974, tc_fun(_1411976, tc_HOL_Obool)), _1411978), hAPP(hAPP(c_COMBC(_1411974, tc_fun(_1411980, tc_fun(_1411976, tc_HOL_Obool)), tc_fun(_1411976, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411980, tc_HOL_Obool), tc_fun(tc_fun(_1411980, tc_fun(_1411976, tc_HOL_Obool)), tc_fun(_1411976, tc_HOL_Obool)), _1411974), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411980, tc_fun(_1411976, tc_HOL_Obool))), _1411982)), _1411984)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411980, tc_fun(_1411976, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411974, tc_fun(_1411980, tc_HOL_Obool)), _1411978), _1411982)), _1411984))], (33785 ^ _780205) ^ [_1412553, _1412555, _1412557, _1412559, _1412561] : [33787 ^ _780205 : [(33788 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412555), 33786 ^ [_1412553, _1412555, _1412557, _1412559, _1412561]), _1412557)))], (33791 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412553), 33789 ^ [_1412553, _1412555, _1412557, _1412559, _1412561]), hAPP(_1412559, 33786 ^ [_1412553, _1412555, _1412557, _1412559, _1412561]))))], (33793 ^ _780205) ^ [] : [hBOOL(hAPP(_1412561, 33789 ^ [_1412553, _1412555, _1412557, _1412559, _1412561]))]], 33794 ^ _780205 : [(33795 ^ _780205) ^ [_1412863] : [hBOOL(hAPP(hAPP(c_member(_1412553), _1412863), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412555, tc_fun(_1412553, tc_HOL_Obool)), _1412557), _1412559))), -(hBOOL(hAPP(_1412561, _1412863)))]]], (33768 ^ _780205) ^ [_1412117, _1412119, _1412121, _1412123, _1412125] : [33770 ^ _780205 : [(33771 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412117), 33769 ^ [_1412117, _1412119, _1412121, _1412123, _1412125]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412119, tc_fun(_1412117, tc_HOL_Obool)), _1412121), _1412123))))], (33773 ^ _780205) ^ [] : [hBOOL(hAPP(_1412125, 33769 ^ [_1412117, _1412119, _1412121, _1412123, _1412125]))]], 33774 ^ _780205 : [(33775 ^ _780205) ^ [_1412339] : [hBOOL(hAPP(hAPP(c_member(_1412119), _1412339), _1412121)), 33778 ^ _780205 : [(33779 ^ _780205) ^ [_1412436] : [hBOOL(hAPP(hAPP(c_member(_1412117), _1412436), hAPP(_1412123, _1412339))), -(hBOOL(hAPP(_1412125, _1412436)))]]]]], (33801 ^ _780205) ^ [_1413013, _1413015] : [hAPP(c_Int_ORep__Integ, _1413013) = hAPP(c_Int_ORep__Integ, _1413015), -(_1413013 = _1413015)], (33807 ^ _780205) ^ [_1413098, _1413100] : [_1413098 = _1413100, -(hAPP(c_Int_ORep__Integ, _1413098) = hAPP(c_Int_ORep__Integ, _1413100))], (33813 ^ _780205) ^ [_1413189] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1413189)) = _1413189)], (33815 ^ _780205) ^ [_1413227, _1413229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413227), _1413229)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1413229, _1413227) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (33821 ^ _780205) ^ [_1413316, _1413318] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413316), _1413318))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1413318, _1413316) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1413318), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413318), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1413316)))], (33827 ^ _780205) ^ [_1413379, _1413381] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1413379, _1413381)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1413381), _1413379)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (33829 ^ _780205) ^ [_1413426, _1413428, _1413430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1413426)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413428), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1413430)), 33836 ^ _780205 : [(33837 ^ _780205) ^ [_1413634] : [33839 ^ _780205 : [(33840 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33838 ^ [_1413426, _1413428, _1413430, _1413634]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1413426))))], (33843 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33841 ^ [_1413426, _1413428, _1413430, _1413634]), _1413430)))], (33845 ^ _780205) ^ [] : [-(_1413634 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33841 ^ [_1413426, _1413428, _1413430, _1413634]), 33838 ^ [_1413426, _1413428, _1413430, _1413634]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1413634), _1413428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413634), _1413426)), _1413428)))]]], (33853 ^ _780205) ^ [_1413910, _1413912, _1413914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1413910)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1413912), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1413914)), 33860 ^ _780205 : [(33861 ^ _780205) ^ [_1414118] : [33863 ^ _780205 : [(33864 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33862 ^ [_1413910, _1413912, _1413914, _1414118]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1413910))))], (33867 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33865 ^ [_1413910, _1413912, _1413914, _1414118]), _1413914)))], (33869 ^ _780205) ^ [] : [-(_1414118 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33865 ^ [_1413910, _1413912, _1413914, _1414118]), 33862 ^ [_1413910, _1413912, _1413914, _1414118]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1413912), _1414118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1413912), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1414118), _1413910))))]]], (33877 ^ _780205) ^ [_1414394, _1414396, _1414398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1414394)), 33880 ^ _780205 : [(33881 ^ _780205) ^ [_1414528] : [33883 ^ _780205 : [(33884 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33882 ^ [_1414394, _1414396, _1414398, _1414528]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1414394))))], (33887 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33885 ^ [_1414394, _1414396, _1414398, _1414528]), _1414396)))], (33889 ^ _780205) ^ [] : [-(_1414528 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33885 ^ [_1414394, _1414396, _1414398, _1414528]), 33882 ^ [_1414394, _1414396, _1414398, _1414528]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1414398), _1414528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1414398), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1414528), _1414394))))]]], (33897 ^ _780205) ^ [_1414802, _1414804] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1414802, _1414804))))], (33899 ^ _780205) ^ [_1414833, _1414835, _1414837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1414833)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1414835), _1414837)), 33906 ^ _780205 : [(33907 ^ _780205) ^ [_1415023] : [33909 ^ _780205 : [(33910 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33908 ^ [_1414833, _1414835, _1414837, _1415023]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1414833))))], (33913 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33911 ^ [_1414833, _1414835, _1414837, _1415023]), _1414837)))], (33915 ^ _780205) ^ [] : [-(_1415023 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33911 ^ [_1414833, _1414835, _1414837, _1415023]), 33908 ^ [_1414833, _1414835, _1414837, _1415023]))]], -(_1415023 = _1414835), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1415023), _1414833) = _1414835]]], (33923 ^ _780205) ^ [_1415283, _1415285, _1415287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1415283)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1415285), _1415287)), 33930 ^ _780205 : [(33931 ^ _780205) ^ [_1415473] : [33933 ^ _780205 : [(33934 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33932 ^ [_1415283, _1415285, _1415287, _1415473]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1415283))))], (33937 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33935 ^ [_1415283, _1415285, _1415287, _1415473]), _1415287)))], (33939 ^ _780205) ^ [] : [-(_1415473 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33935 ^ [_1415283, _1415285, _1415287, _1415473]), 33932 ^ [_1415283, _1415285, _1415287, _1415473]))]], -(_1415473 = _1415285), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1415473), _1415283) = _1415285]]], (33947 ^ _780205) ^ [_1415733, _1415735, _1415737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1415733)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1415735), _1415737)), 33954 ^ _780205 : [(33955 ^ _780205) ^ [_1415929] : [33957 ^ _780205 : [(33958 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33956 ^ [_1415733, _1415735, _1415737, _1415929]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1415733))))], (33961 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33959 ^ [_1415733, _1415735, _1415737, _1415929]), _1415737)))], (33963 ^ _780205) ^ [] : [-(_1415929 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33959 ^ [_1415733, _1415735, _1415737, _1415929]), 33956 ^ [_1415733, _1415735, _1415737, _1415929]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1415735), _1415929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1415735), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1415929), _1415733))))]]], (33971 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (33973 ^ _780205) ^ [_1416229, _1416231, _1416233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1416229)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1416231), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1416233)), 33983 ^ _780205 : [(33984 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33982 ^ [_1416229, _1416231, _1416233]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1416229))))], (33987 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33985 ^ [_1416229, _1416231, _1416233]), _1416233)))], (33989 ^ _780205) ^ [] : [-(_1416231 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33985 ^ [_1416229, _1416231, _1416233]), 33982 ^ [_1416229, _1416231, _1416233]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1416231), _1416229) = _1416231)], (33993 ^ _780205) ^ [_1416568, _1416570, _1416572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1416568)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1416570), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1416572)), 34003 ^ _780205 : [(34004 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34002 ^ [_1416568, _1416570, _1416572]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1416568))))], (34007 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34005 ^ [_1416568, _1416570, _1416572]), _1416572)))], (34009 ^ _780205) ^ [] : [-(_1416570 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 34005 ^ [_1416568, _1416570, _1416572]), 34002 ^ [_1416568, _1416570, _1416572]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1416570), _1416568) = _1416570)], (34013 ^ _780205) ^ [_1416907, _1416909, _1416911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1416907)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1416909), _1416911)), 34020 ^ _780205 : [(34021 ^ _780205) ^ [_1417103] : [34023 ^ _780205 : [(34024 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34022 ^ [_1416907, _1416909, _1416911, _1417103]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1416907))))], (34027 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34025 ^ [_1416907, _1416909, _1416911, _1417103]), _1416911)))], (34029 ^ _780205) ^ [] : [-(_1417103 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 34025 ^ [_1416907, _1416909, _1416911, _1417103]), 34022 ^ [_1416907, _1416909, _1416911, _1417103]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417103), _1416909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1417103), _1416907)), _1416909)))]]], (34037 ^ _780205) ^ [_1417379, _1417381, _1417383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1417379)), 34040 ^ _780205 : [(34041 ^ _780205) ^ [_1417513] : [34043 ^ _780205 : [(34044 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34042 ^ [_1417379, _1417381, _1417383, _1417513]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1417379))))], (34047 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34045 ^ [_1417379, _1417381, _1417383, _1417513]), _1417381)))], (34049 ^ _780205) ^ [] : [-(_1417513 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 34045 ^ [_1417379, _1417381, _1417383, _1417513]), 34042 ^ [_1417379, _1417381, _1417383, _1417513]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1417513), _1417383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1417513), _1417379)), _1417383)))]]], (34057 ^ _780205) ^ [_1417787, _1417789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1417787)), 34066 ^ _780205 : [(34067 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1417789, 34062 ^ [_1417787, _1417789])))], (34069 ^ _780205) ^ [] : [hBOOL(hAPP(_1417789, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 34062 ^ [_1417787, _1417789]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 34063 ^ [_1417787, _1417789]), _1417787))))]], 34070 ^ _780205 : [(34071 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1417789, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 34062 ^ [_1417787, _1417789]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 34063 ^ [_1417787, _1417789]), _1417787)))))], (34073 ^ _780205) ^ [] : [hBOOL(hAPP(_1417789, 34062 ^ [_1417787, _1417789]))]], 34074 ^ _780205 : [(34075 ^ _780205) ^ [] : [34076 ^ _780205 : [(34077 ^ _780205) ^ [_1418219] : [hBOOL(hAPP(_1417789, _1418219))]], 34079 ^ _780205 : [(34080 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34078 ^ [_1417787, _1417789]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1417787))))], (34082 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1417789, 34078 ^ [_1417787, _1417789])))]]], (34084 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1417789, 34091 ^ [_1417787, _1417789]))), 34085 ^ _780205 : [(34086 ^ _780205) ^ [_1418334] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1418334), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1417787))), hBOOL(hAPP(_1417789, _1418334))]]]]], (34095 ^ _780205) ^ [_1418481, _1418483, _1418485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1418481)), 34098 ^ _780205 : [(34099 ^ _780205) ^ [_1418615] : [34101 ^ _780205 : [(34102 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34100 ^ [_1418481, _1418483, _1418485, _1418615]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1418481))))], (34105 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34103 ^ [_1418481, _1418483, _1418485, _1418615]), _1418483)))], (34107 ^ _780205) ^ [] : [-(_1418615 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 34103 ^ [_1418481, _1418483, _1418485, _1418615]), 34100 ^ [_1418481, _1418483, _1418485, _1418615]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1418485), _1418615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1418485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1418615), _1418481))))]]], (34115 ^ _780205) ^ [_1418889, _1418891, _1418893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1418889)), 34118 ^ _780205 : [(34119 ^ _780205) ^ [_1419023] : [34121 ^ _780205 : [(34122 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34120 ^ [_1418889, _1418891, _1418893, _1419023]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1418889))))], (34125 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 34123 ^ [_1418889, _1418891, _1418893, _1419023]), _1418891)))], (34127 ^ _780205) ^ [] : [-(_1419023 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 34123 ^ [_1418889, _1418891, _1418893, _1419023]), 34120 ^ [_1418889, _1418891, _1418893, _1419023]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1419023), _1418893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1419023), _1418889)), _1418893)))]]], (34135 ^ _780205) ^ [_1419297, _1419299] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1419297, _1419299)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1419299), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1419297), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (34137 ^ _780205) ^ [_1419344, _1419346] : [-(c_Relation_OId__on(_1419344, _1419346) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419344, tc_fun(tc_prod(_1419344, _1419344), tc_HOL_Obool)), _1419346), hAPP(hAPP(c_COMBC(_1419344, tc_fun(tc_prod(_1419344, _1419344), tc_HOL_Obool), tc_fun(tc_prod(_1419344, _1419344), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1419344, _1419344), tc_fun(tc_fun(tc_prod(_1419344, _1419344), tc_HOL_Obool), tc_fun(tc_prod(_1419344, _1419344), tc_HOL_Obool)), _1419344), c_Set_Oinsert(tc_prod(_1419344, _1419344))), hAPP(hAPP(c_COMBS(_1419344, _1419344, tc_prod(_1419344, _1419344)), c_Product__Type_OPair(_1419344, _1419344)), c_COMBI(_1419344)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1419344, _1419344), tc_HOL_Obool)))))], (34139 ^ _780205) ^ [_1419468, _1419470] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1419468, _1419470))))], (34141 ^ _780205) ^ [_1419499, _1419501] : [-(c_Relation_OId__on(_1419499, _1419501) = hAPP(c_Product__Type_Oprod_Oprod__case(_1419499, _1419499, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1419499, tc_HOL_Obool, tc_fun(_1419499, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419499, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1419499, tc_HOL_Obool)), _1419499), c_COMBC(_1419499, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419499, tc_HOL_Obool), tc_fun(_1419499, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1419499), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1419499), c_fconj)), c_fequal))), _1419501)))], (34143 ^ _780205) ^ [_1419593, _1419595, _1419597] : [class_Orderings_Oorder(_1419593), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1419593), _1419595), _1419597)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1419593, _1419597, _1419595) = c_Orderings_Obot__class_Obot(tc_fun(_1419593, tc_HOL_Obool)))], (34153 ^ _780205) ^ [_1419756] : [-(c_Relation_OId__on(_1419756, c_Orderings_Obot__class_Obot(tc_fun(_1419756, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1419756, _1419756), tc_HOL_Obool)))], (34155 ^ _780205) ^ [_1419795, _1419797, _1419799] : [-(hAPP(c_Relation_OImage(_1419795, _1419795, c_Relation_OId__on(_1419795, _1419797)), _1419799) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419795, tc_HOL_Obool)), _1419797), _1419799))], (34157 ^ _780205) ^ [_1419843, _1419845, _1419847, _1419849] : [class_Orderings_Oorder(_1419843), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419843, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1419843, _1419845, _1419847)), c_SetInterval_Oord__class_OatLeastAtMost(_1419843, _1419847, _1419849)) = c_Orderings_Obot__class_Obot(tc_fun(_1419843, tc_HOL_Obool)))], (34163 ^ _780205) ^ [_1419970, _1419972, _1419974, _1419976] : [class_Orderings_Oorder(_1419970), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419970, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1419970, _1419972, _1419974)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1419970, _1419974, _1419976)) = c_Orderings_Obot__class_Obot(tc_fun(_1419970, tc_HOL_Obool)))], (34169 ^ _780205) ^ [_1420097, _1420099, _1420101, _1420103, _1420105] : [class_Orderings_Olinorder(_1420097), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420097, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1420097, _1420099, _1420101)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1420097, _1420103, _1420105)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1420097, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1420097), _1420099), _1420103), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1420097), _1420101), _1420105)))], (34175 ^ _780205) ^ [_1420277, _1420279, _1420281, _1420283] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1420277, _1420277)), hAPP(hAPP(c_Product__Type_OPair(_1420277, _1420277), _1420279), _1420281)), c_Relation_OId__on(_1420277, _1420283))), 34178 ^ _780205 : [(34179 ^ _780205) ^ [] : [-(_1420279 = _1420281)], (34181 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1420277), _1420279), _1420283)))]]], (34183 ^ _780205) ^ [_1420438, _1420440, _1420442, _1420444] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1420438, _1420438)), hAPP(hAPP(c_Product__Type_OPair(_1420438, _1420438), _1420440), _1420442)), c_Relation_OId__on(_1420438, _1420444)))), _1420440 = _1420442, hBOOL(hAPP(hAPP(c_member(_1420438), _1420440), _1420444))], (34193 ^ _780205) ^ [_1420635, _1420637, _1420639, _1420641] : [_1420635 = _1420637, hBOOL(hAPP(hAPP(c_member(_1420639), _1420635), _1420641)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1420639, _1420639)), hAPP(hAPP(c_Product__Type_OPair(_1420639, _1420639), _1420635), _1420637)), c_Relation_OId__on(_1420639, _1420641))))], (34203 ^ _780205) ^ [_1420830, _1420832, _1420834] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1420830, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1420832)), _1420834) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420830, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1420830, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1420832)), _1420834)), hAPP(_1420834, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34205 ^ _780205) ^ [_1420902, _1420904, _1420906, _1420908] : [class_Orderings_Olinorder(_1420902), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420902), _1420904), _1420906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420902), _1420906), _1420908)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420902, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1420902, _1420904, _1420906)), c_SetInterval_Oord__class_OatLeastAtMost(_1420902, _1420906, _1420908)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1420902, _1420904, _1420908))], (34219 ^ _780205) ^ [_1421167, _1421169, _1421171] : [class_Orderings_Olinorder(_1421167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421167), _1421169), _1421171)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421167, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1421167, _1421169, _1421171)), hAPP(hAPP(c_Set_Oinsert(_1421167), _1421171), c_Orderings_Obot__class_Obot(tc_fun(_1421167, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1421167, _1421169, _1421171))], (34229 ^ _780205) ^ [_1421376, _1421378] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1421376, _1421378))))], (34231 ^ _780205) ^ [_1421407, _1421409] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1421407, _1421409))))], (34233 ^ _780205) ^ [_1421438, _1421440] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1421438, _1421440))))], (34235 ^ _780205) ^ [_1421469] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1421469))))], (34237 ^ _780205) ^ [_1421497, _1421499, _1421501] : [class_Orderings_Oorder(_1421497), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421497, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1421497), _1421499)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1421497, _1421499, _1421501)) = c_Orderings_Obot__class_Obot(tc_fun(_1421497, tc_HOL_Obool)))], (34243 ^ _780205) ^ [_1421624, _1421626, _1421628] : [class_Orderings_Olinorder(_1421624), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421624), _1421626), _1421628)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421624, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1421624), _1421626)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1421624, _1421626, _1421628)) = hAPP(c_SetInterval_Oord__class_OatMost(_1421624), _1421628))], (34253 ^ _780205) ^ [_1421819, _1421821, _1421823] : [class_Orderings_Olinorder(_1421819), 34256 ^ _780205 : [(34257 ^ _780205) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1421819), _1421821) = hAPP(c_SetInterval_Oord__class_OatMost(_1421819), _1421823), -(_1421821 = _1421823)], (34263 ^ _780205) ^ [] : [_1421821 = _1421823, -(hAPP(c_SetInterval_Oord__class_OatMost(_1421819), _1421821) = hAPP(c_SetInterval_Oord__class_OatMost(_1421819), _1421823))]]], (34269 ^ _780205) ^ [_1422060, _1422062, _1422064] : [class_Orderings_Oorder(_1422060), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422060), _1422062), _1422064)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1422060, _1422064, _1422062) = c_Orderings_Obot__class_Obot(tc_fun(_1422060, tc_HOL_Obool)))], (34279 ^ _780205) ^ [_1422223, _1422225, _1422227] : [class_Orderings_Oorder(_1422223), 34282 ^ _780205 : [(34283 ^ _780205) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1422223, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1422223, _1422225, _1422227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422223), _1422225), _1422227))], (34289 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422223), _1422225), _1422227))), -(c_Orderings_Obot__class_Obot(tc_fun(_1422223, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1422223, _1422225, _1422227))]]], (34295 ^ _780205) ^ [_1422442, _1422444, _1422446] : 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^ _780205) ^ [_1423115, _1423117] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1423115), _1423117) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1423115, _1423117))], (34337 ^ _780205) ^ [_1423151] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1423151)) = hAPP(c_Nat_OSuc, _1423151))], (34339 ^ _780205) ^ [_1423183] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1423183)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1423183)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1423183)))], (34341 ^ _780205) ^ [_1423224, _1423226, _1423228] : [class_Orderings_Oord(_1423224), 34344 ^ _780205 : [(34345 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1423224), _1423226), hAPP(c_SetInterval_Oord__class_OatMost(_1423224), _1423228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423224), _1423226), _1423228)))], (34351 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423224), _1423226), _1423228)), -(hBOOL(hAPP(hAPP(c_member(_1423224), _1423226), hAPP(c_SetInterval_Oord__class_OatMost(_1423224), _1423228))))]]], (34357 ^ _780205) ^ [_1423492, _1423494, _1423496] : [class_Orderings_Oorder(_1423492), 34360 ^ _780205 : [(34361 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423492, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1423492), _1423494)), hAPP(c_SetInterval_Oord__class_OatMost(_1423492), _1423496))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423492), _1423494), _1423496)))], (34367 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423492), _1423494), _1423496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423492, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1423492), _1423494)), hAPP(c_SetInterval_Oord__class_OatMost(_1423492), _1423496))))]]], (34373 ^ _780205) ^ [_1423784, _1423786] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1423784, _1423786)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1423786), _1423784))], (34375 ^ _780205) ^ [_1423822, _1423824, _1423826, _1423828] : [class_Orderings_Olinorder(_1423822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423822), _1423824), _1423826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423822), _1423826), _1423828)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1423822, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1423822, _1423824, _1423826)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1423822, _1423826, _1423828)) = c_SetInterval_Oord__class_OatLeastAtMost(_1423822, _1423824, _1423828))], (34389 ^ _780205) ^ [_1424087, _1424089] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1424087), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1424089) = 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c_SetInterval_Oord__class_OgreaterThanAtMost(_1424271, _1424273, _1424275)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1424271, _1424277, _1424279)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1424271, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1424271), _1424273), _1424277), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424271), _1424275), _1424279)))], (34405 ^ _780205) ^ [_1424430, _1424432, _1424434] : [class_Groups_Ocomm__monoid__add(_1424430), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424430), _1424432), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1424434))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424430), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424430), _1424432), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1424434))), hAPP(_1424432, hAPP(c_Nat_OSuc, _1424434))))], (34411 ^ _780205) ^ [] : [-(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))))], (34413 ^ _780205) ^ [_1424607, _1424609, _1424611, _1424613] : [class_Orderings_Oorder(_1424607), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424607, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1424607, _1424609, _1424611)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1424607, _1424611, _1424613)) = c_Orderings_Obot__class_Obot(tc_fun(_1424607, tc_HOL_Obool)))], (34419 ^ _780205) ^ [_1424734, _1424736] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1424734, _1424736)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1424736), hAPP(c_Nat_OSuc, _1424734)))], (34421 ^ _780205) ^ [_1424775, _1424777, _1424779, _1424781] : [class_Orderings_Olinorder(_1424775), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424775, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1424775), _1424777)), c_SetInterval_Oord__class_OatLeastAtMost(_1424775, _1424779, _1424781)) = c_SetInterval_Oord__class_OatLeastAtMost(_1424775, _1424779, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424775), _1424777), _1424781)))], (34427 ^ _780205) ^ [_1424918, _1424920, _1424922, _1424924] : [class_Orderings_Olinorder(_1424918), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424918, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1424918, _1424920, _1424922)), hAPP(c_SetInterval_Oord__class_OatMost(_1424918), _1424924)) = c_SetInterval_Oord__class_OatLeastAtMost(_1424918, _1424920, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424918), _1424922), _1424924)))], (34433 ^ _780205) ^ [_1425061, _1425063] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1425061, _1425063)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1425063), _1425061)))], (34435 ^ _780205) ^ [_1425102, _1425104, _1425106, _1425108] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1425102, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1425104)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1425102, tc_HOL_Obool), tc_Nat_Onat), _1425106), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1425108))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1425102, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1425108, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1425104), _1425108))), _1425106))], (34437 ^ _780205) ^ [_1425184, _1425186, _1425188] : [class_Orderings_Oorder(_1425184), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425184, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1425184), _1425186)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1425184, _1425186, _1425188)) = c_Orderings_Obot__class_Obot(tc_fun(_1425184, tc_HOL_Obool)))], (34443 ^ _780205) ^ [_1425311, _1425313, _1425315, _1425317] : [class_Orderings_Olinorder(_1425311), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425311), _1425313), _1425315)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425311), _1425315), _1425317)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1425311, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1425311, _1425313, _1425315)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1425311, _1425315, _1425317)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1425311, _1425313, _1425317))], (34457 ^ _780205) ^ [_1425576, _1425578, _1425580, _1425582] : [class_Groups_Ocomm__monoid__add(_1425576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1425578), _1425580)), 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-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426328, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1426328), _1426330), c_Orderings_Obot__class_Obot(tc_fun(_1426328, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1426328, _1426330, _1426332)) = c_SetInterval_Oord__class_OatLeastAtMost(_1426328, _1426330, _1426332))], (34503 ^ _780205) ^ [_1426537, _1426539, _1426541] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1426537), _1426539), _1426541) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426537, tc_fun(tc_fun(_1426537, tc_HOL_Obool), tc_HOL_Obool)), _1426539), hAPP(hAPP(c_COMBC(_1426537, tc_fun(tc_fun(_1426537, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1426537, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1426537, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1426537, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1426537, tc_HOL_Obool), tc_HOL_Obool)), _1426537), c_Set_Oinsert(tc_fun(_1426537, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1426537, tc_HOL_Obool), tc_fun(_1426537, tc_HOL_Obool), _1426537), c_Relation_OImage(_1426537, _1426537, _1426541)), hAPP(hAPP(c_COMBC(_1426537, tc_fun(_1426537, tc_HOL_Obool), tc_fun(_1426537, tc_HOL_Obool)), c_Set_Oinsert(_1426537)), c_Orderings_Obot__class_Obot(tc_fun(_1426537, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1426537, tc_HOL_Obool), tc_HOL_Obool)))))], (34505 ^ _780205) ^ [_1426693, _1426695, _1426697] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1426693, _1426693)), _1426695), c_Relation_OId__on(_1426693, _1426697))), 34509 ^ _780205 : [(34510 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1426693), 34508 ^ [_1426693, _1426695, _1426697]), _1426697)))], (34512 ^ _780205) ^ [] : [-(_1426695 = hAPP(hAPP(c_Product__Type_OPair(_1426693, _1426693), 34508 ^ [_1426693, _1426695, _1426697]), 34508 ^ [_1426693, _1426695, _1426697]))]]], (34514 ^ _780205) ^ [_1426892, _1426894, _1426896, _1426898, _1426900] : [hBOOL(hAPP(hAPP(c_member(_1426892), _1426894), hAPP(c_Relation_OImage(_1426896, _1426892, _1426898), _1426900))), 34518 ^ _780205 : [(34519 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1426896, _1426892)), hAPP(hAPP(c_Product__Type_OPair(_1426896, _1426892), 34517 ^ [_1426892, _1426894, _1426896, _1426898, _1426900]), _1426894)), _1426898)))], (34521 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1426896), 34517 ^ [_1426892, _1426894, _1426896, _1426898, _1426900]), _1426900)))]]], (34523 ^ _780205) ^ [_1427134, _1427136, _1427138] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427134), _1427136), _1427138) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427134, tc_HOL_Obool), tc_HOL_Obool)), -(_1427136 = c_Orderings_Obot__class_Obot(tc_fun(_1427134, tc_HOL_Obool)))], (34529 ^ _780205) ^ [_1427251, _1427253, _1427255] : [_1427253 = c_Orderings_Obot__class_Obot(tc_fun(_1427251, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427251), _1427253), _1427255) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427251, tc_HOL_Obool), tc_HOL_Obool)))], (34535 ^ _780205) ^ [_1427392, _1427394, _1427396] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427392, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427392), _1427394), _1427396), -(_1427394 = c_Orderings_Obot__class_Obot(tc_fun(_1427392, tc_HOL_Obool)))], (34541 ^ _780205) ^ [_1427509, _1427511, _1427513] : [_1427511 = c_Orderings_Obot__class_Obot(tc_fun(_1427509, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427509, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427509), _1427511), _1427513))], (34547 ^ _780205) ^ [_1427632, _1427634] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427632), c_Orderings_Obot__class_Obot(tc_fun(_1427632, tc_HOL_Obool))), _1427634) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427632, tc_HOL_Obool), tc_HOL_Obool)))], (34549 ^ _780205) ^ [_1427678, _1427680, _1427682, _1427684] : [hBOOL(hAPP(hAPP(c_member(_1427678), _1427680), _1427682)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1427678, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1427678, _1427678, _1427684), hAPP(hAPP(c_Set_Oinsert(_1427678), _1427680), c_Orderings_Obot__class_Obot(tc_fun(_1427678, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427678), _1427682), _1427684))))], (34555 ^ _780205) ^ [_1427849, _1427851, _1427853] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1427849), hAPP(hAPP(c_Set_Oinsert(_1427849), _1427851), c_Orderings_Obot__class_Obot(tc_fun(_1427849, tc_HOL_Obool)))), _1427853) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1427849, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1427849, _1427849, _1427853), hAPP(hAPP(c_Set_Oinsert(_1427849), _1427851), c_Orderings_Obot__class_Obot(tc_fun(_1427849, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1427849, tc_HOL_Obool), tc_HOL_Obool))))], (34557 ^ _780205) ^ [_1427936, _1427938, _1427940, _1427942, _1427944, _1427946] : [c_Equiv__Relations_Oequiv(_1427936, _1427938, _1427940), hBOOL(hAPP(hAPP(c_member(_1427936), _1427942), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427936, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1427936, _1427936, _1427940), hAPP(hAPP(c_Set_Oinsert(_1427936), _1427944), c_Orderings_Obot__class_Obot(tc_fun(_1427936, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1427936, _1427936, _1427940), hAPP(hAPP(c_Set_Oinsert(_1427936), _1427946), c_Orderings_Obot__class_Obot(tc_fun(_1427936, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1427936, _1427936)), hAPP(hAPP(c_Product__Type_OPair(_1427936, _1427936), _1427944), _1427946)), _1427940)))], (34567 ^ _780205) ^ [_1428237, _1428239, _1428241, _1428243, _1428245] : [c_Equiv__Relations_Oequiv(_1428237, _1428239, _1428241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428237, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1428237, _1428237, _1428241), hAPP(hAPP(c_Set_Oinsert(_1428237), _1428243), c_Orderings_Obot__class_Obot(tc_fun(_1428237, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1428237, _1428237, _1428241), hAPP(hAPP(c_Set_Oinsert(_1428237), _1428245), c_Orderings_Obot__class_Obot(tc_fun(_1428237, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1428237), _1428243), _1428239)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1428237, _1428237)), hAPP(hAPP(c_Product__Type_OPair(_1428237, _1428237), _1428245), _1428243)), _1428241)))], (34581 ^ _780205) ^ [_1428590, _1428592, _1428594, _1428596] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1428590, tc_HOL_Obool)), _1428592), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1428590), _1428594), _1428596))), 34585 ^ _780205 : [(34586 ^ _780205) ^ [] : [-(_1428592 = hAPP(c_Relation_OImage(_1428590, _1428590, _1428596), hAPP(hAPP(c_Set_Oinsert(_1428590), 34584 ^ [_1428590, _1428592, _1428594, _1428596]), c_Orderings_Obot__class_Obot(tc_fun(_1428590, tc_HOL_Obool)))))], (34588 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1428590), 34584 ^ [_1428590, _1428592, _1428594, _1428596]), _1428594)))]]], (34590 ^ _780205) ^ [] : [-(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))], (34592 ^ _780205) ^ [_1428836, _1428838, _1428840] : [c_Equiv__Relations_Oequiv(_1428836, _1428838, _1428840), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1428836, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1428836), _1428838), _1428840)) = _1428838)], (34598 ^ _780205) ^ [_1428945, _1428947, _1428949, _1428951] : [c_Equiv__Relations_Oequiv(_1428945, _1428947, _1428949), hBOOL(hAPP(hAPP(c_member(_1428945), _1428951), _1428947)), -(hBOOL(hAPP(hAPP(c_member(_1428945), _1428951), hAPP(c_Relation_OImage(_1428945, _1428945, _1428949), hAPP(hAPP(c_Set_Oinsert(_1428945), _1428951), c_Orderings_Obot__class_Obot(tc_fun(_1428945, tc_HOL_Obool)))))))], (34608 ^ _780205) ^ [_1429152, _1429154, _1429156, _1429158, _1429160] : [c_Equiv__Relations_Oequiv(_1429152, _1429154, _1429156), hBOOL(hAPP(hAPP(c_member(tc_fun(_1429152, tc_HOL_Obool)), _1429158), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1429152), _1429154), _1429156))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1429152, tc_HOL_Obool)), _1429160), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1429152), _1429154), _1429156))), -(_1429158 = _1429160), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429152, tc_HOL_Obool)), _1429158), _1429160) = c_Orderings_Obot__class_Obot(tc_fun(_1429152, tc_HOL_Obool)))], (34626 ^ _780205) ^ [_1429470, _1429472, _1429474, _1429476, _1429478] : [c_Equiv__Relations_Oequiv(_1429470, _1429472, _1429474), hBOOL(hAPP(hAPP(c_member(tc_prod(_1429470, _1429470)), hAPP(hAPP(c_Product__Type_OPair(_1429470, _1429470), _1429476), _1429478)), _1429474)), -(hAPP(c_Relation_OImage(_1429470, _1429470, _1429474), hAPP(hAPP(c_Set_Oinsert(_1429470), _1429476), c_Orderings_Obot__class_Obot(tc_fun(_1429470, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1429470, _1429470, _1429474), hAPP(hAPP(c_Set_Oinsert(_1429470), _1429478), c_Orderings_Obot__class_Obot(tc_fun(_1429470, tc_HOL_Obool)))))], (34636 ^ _780205) ^ [_1429731, _1429733, _1429735, _1429737, _1429739, _1429741, _1429743] : [c_Equiv__Relations_Oequiv(_1429731, _1429733, _1429735), hBOOL(hAPP(hAPP(c_member(tc_fun(_1429731, tc_HOL_Obool)), _1429737), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1429731), _1429733), _1429735))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1429731, tc_HOL_Obool)), _1429739), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1429731), _1429733), _1429735))), hBOOL(hAPP(hAPP(c_member(_1429731), _1429741), _1429737)), hBOOL(hAPP(hAPP(c_member(_1429731), _1429743), _1429739)), 34655 ^ _780205 : [(34656 ^ _780205) ^ [] : [_1429737 = _1429739, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1429731, _1429731)), hAPP(hAPP(c_Product__Type_OPair(_1429731, _1429731), _1429741), _1429743)), _1429735)))], (34662 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1429731, _1429731)), hAPP(hAPP(c_Product__Type_OPair(_1429731, _1429731), _1429741), _1429743)), _1429735)), -(_1429737 = _1429739)]]], (34668 ^ _780205) ^ [_1430375, _1430377, _1430379, _1430381, _1430383, _1430385, _1430387] : [c_Equiv__Relations_Oequiv(_1430375, _1430377, _1430379), hBOOL(hAPP(hAPP(c_member(tc_fun(_1430375, tc_HOL_Obool)), _1430381), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1430375), _1430377), _1430379))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1430375, tc_HOL_Obool)), _1430383), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1430375), _1430377), _1430379))), hBOOL(hAPP(hAPP(c_member(_1430375), _1430385), _1430381)), hBOOL(hAPP(hAPP(c_member(_1430375), _1430387), _1430383)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1430375, _1430375)), hAPP(hAPP(c_Product__Type_OPair(_1430375, _1430375), _1430385), _1430387)), _1430379)), -(_1430381 = _1430383)], (34694 ^ _780205) ^ [_1430912, _1430914, _1430916, _1430918, _1430920] : [c_Equiv__Relations_Oequiv(_1430912, _1430914, _1430916), 34697 ^ _780205 : [(34698 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1430912, _1430912)), hAPP(hAPP(c_Product__Type_OPair(_1430912, _1430912), _1430918), _1430920)), _1430916)), 34701 ^ _780205 : [(34702 ^ _780205) ^ [] : [-(hAPP(c_Relation_OImage(_1430912, _1430912, _1430916), hAPP(hAPP(c_Set_Oinsert(_1430912), _1430918), c_Orderings_Obot__class_Obot(tc_fun(_1430912, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1430912, _1430912, _1430916), hAPP(hAPP(c_Set_Oinsert(_1430912), _1430920), c_Orderings_Obot__class_Obot(tc_fun(_1430912, tc_HOL_Obool)))))], (34704 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1430912), _1430918), _1430914)))], (34706 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1430912), _1430920), _1430914)))]]], (34708 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1430912, _1430912)), hAPP(hAPP(c_Product__Type_OPair(_1430912, _1430912), _1430918), _1430920)), _1430916))), hAPP(c_Relation_OImage(_1430912, _1430912, _1430916), hAPP(hAPP(c_Set_Oinsert(_1430912), _1430918), c_Orderings_Obot__class_Obot(tc_fun(_1430912, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1430912, _1430912, _1430916), hAPP(hAPP(c_Set_Oinsert(_1430912), _1430920), c_Orderings_Obot__class_Obot(tc_fun(_1430912, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1430912), _1430918), _1430914)), hBOOL(hAPP(hAPP(c_member(_1430912), _1430920), _1430914))]]], (34722 ^ _780205) ^ [_1431512, _1431514, _1431516, _1431518, _1431520] : [c_Equiv__Relations_Oequiv(_1431512, _1431514, _1431516), hBOOL(hAPP(hAPP(c_member(_1431512), _1431518), _1431514)), hBOOL(hAPP(hAPP(c_member(_1431512), _1431520), _1431514)), 34733 ^ _780205 : [(34734 ^ _780205) ^ [] : [hAPP(c_Relation_OImage(_1431512, _1431512, _1431516), hAPP(hAPP(c_Set_Oinsert(_1431512), _1431518), c_Orderings_Obot__class_Obot(tc_fun(_1431512, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1431512, _1431512, _1431516), hAPP(hAPP(c_Set_Oinsert(_1431512), _1431520), c_Orderings_Obot__class_Obot(tc_fun(_1431512, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1431512, _1431512)), hAPP(hAPP(c_Product__Type_OPair(_1431512, _1431512), _1431518), _1431520)), _1431516)))], (34740 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1431512, _1431512)), hAPP(hAPP(c_Product__Type_OPair(_1431512, _1431512), _1431518), _1431520)), _1431516)), -(hAPP(c_Relation_OImage(_1431512, _1431512, _1431516), hAPP(hAPP(c_Set_Oinsert(_1431512), _1431518), c_Orderings_Obot__class_Obot(tc_fun(_1431512, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1431512, _1431512, _1431516), hAPP(hAPP(c_Set_Oinsert(_1431512), _1431520), c_Orderings_Obot__class_Obot(tc_fun(_1431512, tc_HOL_Obool)))))]]], (34746 ^ _780205) ^ [_1432060, _1432062, _1432064, _1432066, _1432068] : [hAPP(c_Relation_OImage(_1432060, _1432060, _1432062), hAPP(hAPP(c_Set_Oinsert(_1432060), _1432064), c_Orderings_Obot__class_Obot(tc_fun(_1432060, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1432060, _1432060, _1432062), hAPP(hAPP(c_Set_Oinsert(_1432060), _1432066), c_Orderings_Obot__class_Obot(tc_fun(_1432060, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1432060, _1432068, _1432062), hBOOL(hAPP(hAPP(c_member(_1432060), _1432066), _1432068)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1432060, _1432060)), hAPP(hAPP(c_Product__Type_OPair(_1432060, _1432060), _1432064), _1432066)), _1432062)))], (34760 ^ _780205) ^ [_1432393, _1432395, _1432397, _1432399, _1432401] : [c_Equiv__Relations_Oequiv(_1432393, _1432395, _1432397), hBOOL(hAPP(hAPP(c_member(tc_prod(_1432393, _1432393)), hAPP(hAPP(c_Product__Type_OPair(_1432393, _1432393), _1432399), _1432401)), _1432397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432393, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1432393, _1432393, _1432397), hAPP(hAPP(c_Set_Oinsert(_1432393), _1432399), c_Orderings_Obot__class_Obot(tc_fun(_1432393, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1432393, _1432393, _1432397), hAPP(hAPP(c_Set_Oinsert(_1432393), _1432401), c_Orderings_Obot__class_Obot(tc_fun(_1432393, tc_HOL_Obool)))))))], (34770 ^ _780205) ^ [_1432674, _1432676, _1432678, _1432680, _1432682] : [c_Equiv__Relations_Oequiv(_1432674, _1432676, _1432678), hBOOL(hAPP(hAPP(c_member(_1432674), _1432680), _1432676)), hBOOL(hAPP(hAPP(c_member(_1432674), _1432682), _1432676)), 34781 ^ _780205 : [(34782 ^ _780205) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1432674), hAPP(hAPP(c_Set_Oinsert(_1432674), _1432680), c_Orderings_Obot__class_Obot(tc_fun(_1432674, tc_HOL_Obool)))), _1432678) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1432674), hAPP(hAPP(c_Set_Oinsert(_1432674), _1432682), c_Orderings_Obot__class_Obot(tc_fun(_1432674, tc_HOL_Obool)))), _1432678), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1432674, _1432674)), hAPP(hAPP(c_Product__Type_OPair(_1432674, _1432674), _1432680), _1432682)), _1432678)))], (34788 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1432674, _1432674)), hAPP(hAPP(c_Product__Type_OPair(_1432674, _1432674), _1432680), _1432682)), _1432678)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1432674), hAPP(hAPP(c_Set_Oinsert(_1432674), _1432680), c_Orderings_Obot__class_Obot(tc_fun(_1432674, tc_HOL_Obool)))), _1432678) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1432674), hAPP(hAPP(c_Set_Oinsert(_1432674), _1432682), c_Orderings_Obot__class_Obot(tc_fun(_1432674, tc_HOL_Obool)))), _1432678))]]], (34794 ^ _780205) ^ [_1433228, _1433230, _1433232, _1433234, _1433236, _1433238, _1433240, _1433242, _1433244, _1433246] : [c_Equiv__Relations_Oequiv(_1433228, _1433230, _1433232), c_Equiv__Relations_Oequiv(_1433234, _1433236, _1433238), c_Equiv__Relations_Ocongruent2(_1433228, _1433234, tc_fun(_1433240, tc_HOL_Obool), _1433232, _1433238, _1433242), hBOOL(hAPP(hAPP(c_member(_1433228), _1433244), _1433230)), hBOOL(hAPP(hAPP(c_member(_1433234), _1433246), _1433236)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433228, tc_fun(_1433240, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1433228, _1433228, _1433232), hAPP(hAPP(c_Set_Oinsert(_1433228), _1433244), c_Orderings_Obot__class_Obot(tc_fun(_1433228, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1433234, tc_fun(_1433240, tc_HOL_Obool)), tc_fun(_1433240, tc_HOL_Obool), _1433228), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433234, tc_fun(_1433240, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1433234, _1433234, _1433238), hAPP(hAPP(c_Set_Oinsert(_1433234), _1433246), c_Orderings_Obot__class_Obot(tc_fun(_1433234, tc_HOL_Obool)))))), _1433242)) = hAPP(hAPP(_1433242, _1433244), _1433246))], (34816 ^ _780205) ^ [_1433811, _1433813, _1433815, _1433817, _1433819, _1433821] : [c_Equiv__Relations_Oequiv(_1433811, _1433813, _1433815), c_Equiv__Relations_Ocongruent(_1433811, tc_fun(_1433817, tc_HOL_Obool), _1433815, _1433819), hBOOL(hAPP(hAPP(c_member(_1433811), _1433821), _1433813)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433811, tc_fun(_1433817, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1433811, _1433811, _1433815), hAPP(hAPP(c_Set_Oinsert(_1433811), _1433821), c_Orderings_Obot__class_Obot(tc_fun(_1433811, tc_HOL_Obool))))), _1433819) = hAPP(_1433819, _1433821))], (34830 ^ _780205) ^ [_1434127, _1434129] : [c_Equiv__Relations_Oequiv(_1434127, c_Orderings_Otop__class_Otop(tc_fun(_1434127, tc_HOL_Obool)), _1434129), -(c_Equiv__Relations_Oequivp(_1434127, hAPP(hAPP(c_COMBC(_1434127, tc_fun(tc_prod(_1434127, _1434127), tc_HOL_Obool), tc_fun(_1434127, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1434127, tc_fun(tc_fun(tc_prod(_1434127, _1434127), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1434127, _1434127), tc_HOL_Obool), tc_fun(_1434127, tc_HOL_Obool)), _1434127), c_COMBC(_1434127, tc_fun(tc_prod(_1434127, _1434127), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1434127, tc_prod(_1434127, _1434127)), tc_fun(_1434127, tc_fun(tc_fun(tc_prod(_1434127, _1434127), tc_HOL_Obool), tc_HOL_Obool)), _1434127), hAPP(c_COMBB(tc_prod(_1434127, _1434127), tc_fun(tc_fun(tc_prod(_1434127, _1434127), tc_HOL_Obool), tc_HOL_Obool), _1434127), c_member(tc_prod(_1434127, _1434127)))), c_Product__Type_OPair(_1434127, _1434127)))), _1434129)))], (34836 ^ _780205) ^ [_1434448, _1434450] : [c_Equiv__Relations_Oequivp(_1434448, hAPP(hAPP(c_COMBC(_1434448, tc_fun(tc_prod(_1434448, _1434448), tc_HOL_Obool), tc_fun(_1434448, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1434448, tc_fun(tc_fun(tc_prod(_1434448, _1434448), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1434448, _1434448), tc_HOL_Obool), tc_fun(_1434448, tc_HOL_Obool)), _1434448), c_COMBC(_1434448, tc_fun(tc_prod(_1434448, _1434448), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1434448, tc_prod(_1434448, _1434448)), tc_fun(_1434448, tc_fun(tc_fun(tc_prod(_1434448, _1434448), tc_HOL_Obool), tc_HOL_Obool)), _1434448), hAPP(c_COMBB(tc_prod(_1434448, _1434448), tc_fun(tc_fun(tc_prod(_1434448, _1434448), tc_HOL_Obool), tc_HOL_Obool), _1434448), c_member(tc_prod(_1434448, _1434448)))), c_Product__Type_OPair(_1434448, _1434448)))), _1434450)), -(c_Equiv__Relations_Oequiv(_1434448, c_Orderings_Otop__class_Otop(tc_fun(_1434448, tc_HOL_Obool)), _1434450))], (34842 ^ _780205) ^ [_1434775, _1434777, _1434779, _1434781, _1434783] : [c_Equiv__Relations_Oequivp(_1434775, _1434777), hBOOL(hAPP(hAPP(_1434777, _1434779), _1434781)), hBOOL(hAPP(hAPP(_1434777, _1434781), _1434783)), -(hBOOL(hAPP(hAPP(_1434777, _1434779), _1434783)))], (34856 ^ _780205) ^ [_1435004, _1435006, _1435008, _1435010] : [c_Equiv__Relations_Oequivp(_1435004, _1435006), hBOOL(hAPP(hAPP(_1435006, _1435008), _1435010)), -(hBOOL(hAPP(hAPP(_1435006, _1435010), _1435008)))], (34866 ^ _780205) ^ [_1435161, _1435163, _1435165] : [c_Equiv__Relations_Oequivp(_1435161, _1435163), -(hBOOL(hAPP(hAPP(_1435163, _1435165), _1435165)))], (34888 ^ _780205) ^ [_1435563, _1435565] : [-(c_Equiv__Relations_Oequivp(_1435563, _1435565)), 34893 ^ _780205 : [(34894 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1435565, 34889 ^ [_1435563, _1435565]), 34890 ^ [_1435563, _1435565])))], (34896 ^ _780205) ^ [] : [hAPP(_1435565, 34889 ^ [_1435563, _1435565]) = hAPP(_1435565, 34890 ^ [_1435563, _1435565])]], 34897 ^ _780205 : [(34898 ^ _780205) ^ [] : [-(hAPP(_1435565, 34889 ^ [_1435563, _1435565]) = hAPP(_1435565, 34890 ^ [_1435563, _1435565]))], (34900 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1435565, 34889 ^ [_1435563, _1435565]), 34890 ^ [_1435563, _1435565]))]]], (34872 ^ _780205) ^ [_1435265, _1435267] : [c_Equiv__Relations_Oequivp(_1435265, _1435267), 34875 ^ _780205 : [(34876 ^ _780205) ^ [_1435359, _1435361] : [hBOOL(hAPP(hAPP(_1435267, _1435361), _1435359)), -(hAPP(_1435267, _1435361) = hAPP(_1435267, _1435359))], (34882 ^ _780205) ^ [_1435458, _1435460] : [hAPP(_1435267, _1435460) = hAPP(_1435267, _1435458), -(hBOOL(hAPP(hAPP(_1435267, _1435460), _1435458)))]]], (34904 ^ _780205) ^ [_1435892] : [-(c_Equiv__Relations_Oequivp(_1435892, c_fequal))], (34906 ^ _780205) ^ [_1435915, _1435917, _1435919, _1435921, _1435923, _1435925, _1435927, _1435929] : [c_Equiv__Relations_Oequiv(_1435915, _1435917, _1435919), c_Equiv__Relations_Ocongruent2(_1435915, _1435921, _1435923, _1435919, _1435925, _1435927), hBOOL(hAPP(hAPP(c_member(_1435915), _1435929), _1435917)), -(c_Equiv__Relations_Ocongruent(_1435921, _1435923, _1435925, hAPP(_1435927, _1435929)))], (34920 ^ _780205) ^ [_1436166, _1436168, _1436170, _1436172, _1436174, _1436176, _1436178, _1436180, _1436182, _1436184] : [c_Equiv__Relations_Ocongruent2(_1436166, _1436168, _1436170, _1436172, _1436174, _1436176), hBOOL(hAPP(hAPP(c_member(tc_prod(_1436166, _1436166)), hAPP(hAPP(c_Product__Type_OPair(_1436166, _1436166), _1436178), _1436180)), _1436172)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1436168, _1436168)), hAPP(hAPP(c_Product__Type_OPair(_1436168, _1436168), _1436182), _1436184)), _1436174)), -(hAPP(hAPP(_1436176, _1436178), _1436182) = hAPP(hAPP(_1436176, _1436180), _1436184))], (34934 ^ _780205) ^ [_1436503, _1436505, _1436507, _1436509, _1436511, _1436513] : [c_Equiv__Relations_Ocongruent(_1436503, _1436505, _1436507, _1436509), hBOOL(hAPP(hAPP(c_member(tc_prod(_1436503, _1436503)), hAPP(hAPP(c_Product__Type_OPair(_1436503, _1436503), _1436511), _1436513)), _1436507)), -(hAPP(_1436509, _1436511) = hAPP(_1436509, _1436513))], (34944 ^ _780205) ^ [_1436702, _1436704, _1436706, _1436708, _1436710, _1436712, _1436714, _1436716, _1436718] : [c_Equiv__Relations_Oequiv(_1436702, _1436704, _1436706), c_Equiv__Relations_Oequiv(_1436708, _1436710, _1436712), c_Equiv__Relations_Ocongruent2(_1436702, _1436708, tc_fun(_1436714, tc_HOL_Obool), _1436706, _1436712, _1436716), hBOOL(hAPP(hAPP(c_member(_1436708), _1436718), _1436710)), -(c_Equiv__Relations_Ocongruent(_1436702, tc_fun(_1436714, tc_HOL_Obool), _1436706, hAPP(hAPP(c_COMBB(tc_fun(_1436708, tc_fun(_1436714, tc_HOL_Obool)), tc_fun(_1436714, tc_HOL_Obool), _1436702), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1436708, tc_fun(_1436714, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1436708, _1436708, _1436712), hAPP(hAPP(c_Set_Oinsert(_1436708), _1436718), c_Orderings_Obot__class_Obot(tc_fun(_1436708, tc_HOL_Obool)))))), _1436716)))], (34962 ^ _780205) ^ [_1437129, _1437131, _1437133, _1437135, _1437137, _1437139, _1437141] : [c_Equiv__Relations_Oequiv(_1437129, _1437131, _1437133), c_Equiv__Relations_Ocongruent(_1437129, tc_fun(_1437135, tc_HOL_Obool), _1437133, _1437137), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1437129, tc_fun(_1437135, tc_HOL_Obool)), _1437139), _1437137) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1437129, tc_fun(_1437135, tc_HOL_Obool)), _1437141), _1437137), hBOOL(hAPP(hAPP(c_member(tc_fun(_1437129, tc_HOL_Obool)), _1437139), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1437129), _1437131), _1437133))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1437129, tc_HOL_Obool)), _1437141), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1437129), _1437131), _1437133))), 34984 ^ _780205 : [(34985 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1437129), 34983 ^ [_1437129, _1437131, _1437133, _1437135, _1437137, _1437139, _1437141]), _1437131)))], (34988 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1437129), 34986 ^ [_1437129, _1437131, _1437133, _1437135, _1437137, _1437139, _1437141]), _1437131)))], (34990 ^ _780205) ^ [] : [-(hAPP(_1437137, 34983 ^ [_1437129, _1437131, _1437133, _1437135, _1437137, _1437139, _1437141]) = hAPP(_1437137, 34986 ^ [_1437129, _1437131, _1437133, _1437135, _1437137, _1437139, _1437141]))], (34992 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1437129, _1437129)), hAPP(hAPP(c_Product__Type_OPair(_1437129, _1437129), 34983 ^ [_1437129, _1437131, _1437133, _1437135, _1437137, _1437139, _1437141]), 34986 ^ [_1437129, _1437131, _1437133, _1437135, _1437137, _1437139, _1437141])), _1437133))]], -(_1437139 = _1437141)], (34996 ^ _780205) ^ [_1438099, _1438101, _1438103, _1438105, _1438107, _1438109, _1438111, _1438113, _1438115, _1438117, _1438119] : [c_Equiv__Relations_Oequiv(_1438099, _1438101, _1438103), c_Equiv__Relations_Oequiv(_1438105, _1438107, _1438109), c_Equiv__Relations_Ocongruent2(_1438099, _1438105, tc_fun(_1438111, tc_HOL_Obool), _1438103, _1438109, _1438113), hBOOL(hAPP(hAPP(c_member(tc_fun(_1438099, tc_HOL_Obool)), _1438115), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1438099), _1438101), _1438103))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1438105, tc_HOL_Obool)), _1438117), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1438105), _1438107), _1438109))), 35018 ^ _780205 : [(35019 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438099), 35017 ^ [_1438099, _1438101, _1438103, _1438105, _1438107, _1438109, _1438111, _1438113, _1438115, _1438117, _1438119]), _1438101)))], (35022 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438105), 35020 ^ [_1438099, _1438101, _1438103, _1438105, _1438107, _1438109, _1438111, _1438113, _1438115, _1438117, _1438119]), _1438107)))], (35024 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1438111, tc_HOL_Obool)), hAPP(hAPP(_1438113, 35017 ^ [_1438099, _1438101, _1438103, _1438105, _1438107, _1438109, _1438111, _1438113, _1438115, _1438117, _1438119]), 35020 ^ [_1438099, _1438101, _1438103, _1438105, _1438107, _1438109, _1438111, _1438113, _1438115, _1438117, _1438119])), _1438119))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1438111, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1438099, tc_fun(_1438111, tc_HOL_Obool)), _1438115), hAPP(hAPP(c_COMBB(tc_fun(_1438105, tc_fun(_1438111, tc_HOL_Obool)), tc_fun(_1438111, tc_HOL_Obool), _1438099), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1438105, tc_fun(_1438111, tc_HOL_Obool)), _1438117)), _1438113))), _1438119)))], (35028 ^ _780205) ^ [_1439101, _1439103, _1439105, _1439107, _1439109, _1439111, _1439113] : [c_Equiv__Relations_Oequiv(_1439101, _1439103, _1439105), c_Equiv__Relations_Ocongruent(_1439101, tc_fun(_1439107, tc_HOL_Obool), _1439105, _1439109), hBOOL(hAPP(hAPP(c_member(tc_fun(_1439101, tc_HOL_Obool)), _1439111), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1439101), _1439103), _1439105))), 35042 ^ _780205 : [(35043 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1439101), 35041 ^ [_1439101, _1439103, _1439105, _1439107, _1439109, _1439111, _1439113]), _1439103)))], (35045 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1439107, tc_HOL_Obool)), hAPP(_1439109, 35041 ^ [_1439101, _1439103, _1439105, _1439107, _1439109, _1439111, _1439113])), _1439113))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1439107, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1439101, tc_fun(_1439107, tc_HOL_Obool)), _1439111), _1439109)), _1439113)))], (35049 ^ _780205) ^ [] : [-(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))], (35051 ^ _780205) ^ [_1439630, _1439632, _1439634] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1439630), _1439632)), c_Fun_Oinj__on(_1439630, tc_fun(tc_fun(_1439630, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1439630, tc_fun(tc_prod(_1439630, _1439630), tc_HOL_Obool), tc_fun(tc_fun(_1439630, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1439630, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1439630, _1439630), tc_HOL_Obool), tc_fun(tc_fun(_1439630, tc_HOL_Obool), tc_HOL_Obool)), _1439630), c_Equiv__Relations_Oquotient(_1439630)), hAPP(hAPP(c_COMBC(_1439630, tc_fun(_1439630, tc_HOL_Obool), tc_fun(_1439630, tc_HOL_Obool)), c_Set_Oinsert(_1439630)), c_Orderings_Obot__class_Obot(tc_fun(_1439630, tc_HOL_Obool))))), _1439634), _1439632), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1439630, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1439630), _1439632), _1439634)) = hAPP(c_Finite__Set_Ocard(_1439630), _1439632))], (35061 ^ _780205) ^ [_1439979, _1439981, _1439983] : [class_Fields_Ofield(_1439979), -(_1439981 = c_Groups_Oone__class_Oone(_1439979)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1439979), hAPP(c_Power_Opower__class_Opower(_1439979), _1439981)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1439983)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1439979), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1439979), hAPP(hAPP(c_Power_Opower__class_Opower(_1439979), _1439981), _1439983)), c_Groups_Oone__class_Oone(_1439979))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1439979), _1439981), c_Groups_Oone__class_Oone(_1439979))))], (35071 ^ _780205) ^ [_1440181, _1440183] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1440181), _1440183))))], (35073 ^ _780205) ^ [_1440214, _1440216, _1440218, _1440220, _1440222] : [class_Orderings_Olinorder(_1440214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440214), _1440216), _1440218)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440214), _1440220), _1440222)), 35084 ^ _780205 : [(35085 ^ _780205) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440214, _1440216), _1440218) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440214, _1440220), _1440222), 35088 ^ _780205 : [(35089 ^ _780205) ^ [] : [-(_1440216 = _1440220)], (35091 ^ _780205) ^ [] : [-(_1440218 = _1440222)]]], (35093 ^ _780205) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440214, _1440216), _1440218) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440214, _1440220), _1440222)), _1440216 = _1440220, _1440218 = _1440222]]], (35103 ^ _780205) ^ [_1440695, _1440697, _1440699, _1440701, _1440703] : [class_Orderings_Olinorder(_1440695), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440695, _1440697), _1440699) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440695, _1440701), _1440703), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440695), _1440697), _1440699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440695), _1440701), _1440703)), -(_1440697 = _1440701)], (35121 ^ _780205) ^ [_1441002, _1441004, _1441006, _1441008, _1441010] : [class_Orderings_Olinorder(_1441002), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1441002, _1441004), _1441006) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1441002, _1441008), _1441010), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441002), _1441004), _1441006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441002), _1441008), _1441010)), -(_1441006 = _1441010)], (35139 ^ _780205) ^ [_1441324, _1441326] : [35147 ^ _780205 : [(35148 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35146 ^ [_1441324, _1441326]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1441324))))], (35150 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1441326, 35146 ^ [_1441324, _1441326])))]], 35140 ^ _780205 : [(35141 ^ _780205) ^ [_1441392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1441392), _1441324)), hBOOL(hAPP(_1441326, _1441392))]]], (35152 ^ _780205) ^ [_1441552, _1441554] : [35160 ^ _780205 : [(35161 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 35159 ^ [_1441552, _1441554]), _1441552)))], (35163 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1441554, 35159 ^ [_1441552, _1441554])))]], 35153 ^ _780205 : [(35154 ^ _780205) ^ [_1441620] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1441620), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1441552))), hBOOL(hAPP(_1441554, _1441620))]]], (35165 ^ _780205) ^ [_1441804, _1441806] : [35167 ^ _780205 : [(35168 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 35166 ^ [_1441804, _1441806]), _1441804)))], (35170 ^ _780205) ^ [] : [hBOOL(hAPP(_1441806, 35166 ^ [_1441804, _1441806]))]], 35171 ^ _780205 : [(35172 ^ _780205) ^ [_1441954] : 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hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1442311), _1442313)) = 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, _1442309), _1442311)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442311), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1442311), _1442313))))], (35197 ^ _780205) ^ [_1442470, _1442472] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442470), hAPP(c_Nat_OSuc, _1442472)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1442470, _1442472))], (35199 ^ _780205) ^ [_1442508] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442508), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (35201 ^ _780205) ^ [_1442537] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1442537) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1442537))], (35203 ^ _780205) ^ [_1442566, _1442568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1442566), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442568), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1442568), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1442566))))), -(_1442566 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442568), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1442568), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1442566))))], (35209 ^ _780205) ^ [_1442713, _1442715] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442713), _1442715)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1442715), _1442713))], (35211 ^ _780205) ^ [_1442753, _1442755, _1442757] : [class_Orderings_Oorder(_1442753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442753), _1442755), _1442757)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1442753, _1442757), _1442755) = c_Orderings_Obot__class_Obot(tc_fun(_1442753, tc_HOL_Obool)))], (35221 ^ _780205) ^ [_1442920, _1442922, _1442924] : [class_Orderings_Oorder(_1442920), 35224 ^ _780205 : [(35225 ^ _780205) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1442920, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1442920, _1442922), _1442924), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1442920), _1442922), _1442924))], (35231 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1442920), _1442922), _1442924))), -(c_Orderings_Obot__class_Obot(tc_fun(_1442920, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1442920, _1442922), _1442924))]]], (35237 ^ _780205) ^ [_1443145, _1443147, _1443149] : [class_Orderings_Oorder(_1443145), 35240 ^ _780205 : [(35241 ^ _780205) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443145, _1443147), _1443149) = c_Orderings_Obot__class_Obot(tc_fun(_1443145, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1443145), _1443147), _1443149))], (35247 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1443145), _1443147), _1443149))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443145, _1443147), _1443149) = c_Orderings_Obot__class_Obot(tc_fun(_1443145, tc_HOL_Obool)))]]], (35253 ^ _780205) ^ [_1443370, _1443372, _1443374, _1443376, _1443378] : [class_Orderings_Olinorder(_1443370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443370, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443370, _1443372), _1443374)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443370, _1443376), _1443378))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443370), _1443374), _1443372))), 35264 ^ _780205 : [(35265 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443370), _1443376), _1443372)))], (35267 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443370), _1443374), _1443378)))]]], (35269 ^ _780205) ^ [_1443651, _1443653, _1443655, _1443657] : [class_Groups_Ocomm__monoid__add(_1443651), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1443651), _1443653), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1443655)), hAPP(c_Nat_OSuc, _1443657))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1443651), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1443651, tc_Nat_Onat), _1443653), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1443655), _1443657)))], (35275 ^ _780205) ^ [_1443822, _1443824, _1443826, _1443828] : [class_Orderings_Olinorder(_1443822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443822), _1443824), _1443826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443822), _1443826), _1443828)), 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c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1444105))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444103), _1444107)))], (35295 ^ _780205) ^ [_1444290, _1444292, _1444294, _1444296] : [class_Orderings_Olinorder(_1444290), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444290), _1444292), _1444294)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1444290, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444290, _1444292), _1444296)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444290, _1444292), _1444294)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444290, _1444294), _1444296))], (35305 ^ _780205) ^ [_1444497, _1444499, _1444501, _1444503] : [class_Orderings_Oorder(_1444497), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444497, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444497, _1444499), _1444501)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444497, _1444501), _1444503)) = c_Orderings_Obot__class_Obot(tc_fun(_1444497, tc_HOL_Obool)))], (35311 ^ _780205) ^ [_1444632, _1444634] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1444632)), _1444634) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1444632, _1444634))], (35313 ^ _780205) ^ [_1444670, _1444672, _1444674, _1444676] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1444670), _1444672)), c_Fun_Oinj__on(_1444674, _1444670, _1444676, c_Orderings_Otop__class_Otop(tc_fun(_1444674, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1444674), hAPP(c_Set_Ovimage(_1444674, _1444670, _1444676), _1444672))))], (35323 ^ _780205) ^ [_1444851, _1444853, _1444855, _1444857, _1444859] : [class_Groups_Ocomm__monoid__add(_1444851), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1444853), _1444855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1444855), _1444857)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1444851), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1444851), _1444859), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444853), _1444855))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1444851), _1444859), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444855), _1444857))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1444851), _1444859), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444853), _1444857)))], (35337 ^ _780205) ^ [_1445174, _1445176, _1445178, _1445180, _1445182] : [class_Groups_Oab__group__add(_1445174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1445176), _1445178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1445178), _1445180)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1445174), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1445174), _1445182), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1445176), _1445180))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1445174), _1445182), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1445176), _1445178))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1445174), _1445182), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1445178), _1445180)))], (35351 ^ _780205) ^ [_1445497] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1445497), hAPP(c_Nat_OSuc, _1445497)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1445497), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (35353 ^ _780205) ^ [_1445535] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1445535)), c_Int_OInteg)))], (35355 ^ _780205) ^ [_1445566, _1445568] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1445566, 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(_1445566, tc_HOL_Obool)), tc_fun(_1445566, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1445566, tc_HOL_Obool)), tc_fun(_1445566, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1445566, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1445568)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1445566, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1445568))], (35357 ^ _780205) ^ [_1445662, _1445664, _1445666, _1445668] : [class_Orderings_Olinorder(_1445662), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445662), _1445664), _1445666)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445662), _1445666), _1445668)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445662, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1445662, _1445664), _1445666)), c_SetInterval_Oord__class_OatLeastAtMost(_1445662, _1445666, _1445668)) = c_SetInterval_Oord__class_OatLeastAtMost(_1445662, _1445664, _1445668))], (35371 ^ _780205) ^ [_1445931, _1445933, _1445935, _1445937] : [class_Orderings_Oorder(_1445931), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445931, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1445931, _1445933), _1445935)), c_SetInterval_Oord__class_OatLeastAtMost(_1445931, _1445935, _1445937)) = c_Orderings_Obot__class_Obot(tc_fun(_1445931, tc_HOL_Obool)))], (35377 ^ _780205) ^ [_1446062, _1446064, _1446066, _1446068, _1446070] : [class_Orderings_Olinorder(_1446062), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446062, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446062, _1446064), _1446066)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446062, _1446068), _1446070)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446062, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1446062), _1446064), _1446068)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1446062), _1446066), _1446070)))], (35383 ^ _780205) ^ [_1446233, _1446235, _1446237] : [class_Orderings_Olinorder(_1446233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446233), _1446235), _1446237)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446233, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1446233), _1446235)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446233, _1446235), _1446237)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1446233), _1446237))], (35393 ^ _780205) ^ [_1446432, _1446434, _1446436] : [class_Orderings_Oorder(_1446432), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446432, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1446432), _1446434)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446432, _1446434), _1446436)) = c_Orderings_Obot__class_Obot(tc_fun(_1446432, tc_HOL_Obool)))], (35399 ^ _780205) ^ [_1446563, _1446565, _1446567, _1446569] : [class_Orderings_Oorder(_1446563), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446563, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1446563, _1446565, _1446567)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446563, _1446567), _1446569)) = c_Orderings_Obot__class_Obot(tc_fun(_1446563, tc_HOL_Obool)))], (35405 ^ _780205) ^ [_1446694, _1446696, _1446698] : [class_Groups_Ocomm__monoid__add(_1446694), hAPP(_1446696, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1446694), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1446694), _1446696), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1446698)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1446694), _1446696), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1446698)))], (35415 ^ _780205) ^ [_1446883, _1446885, _1446887, _1446889] : [class_Groups_Ocomm__monoid__add(_1446883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1446885), _1446887)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1446883), _1446889), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1446885), _1446887)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1446883), hAPP(_1446889, _1446885)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1446883), _1446889), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1446885)), _1446887))))], (35425 ^ _780205) ^ [_1447125, _1447127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1447125), _1447127)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1447125), hAPP(c_Nat_OSuc, _1447127)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1447127), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1447125), _1447127)))], (35431 ^ _780205) ^ [_1447248, _1447250] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1447248), _1447250))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1447248), hAPP(c_Nat_OSuc, _1447250)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (35437 ^ _780205) ^ [_1447300, _1447302, _1447304, _1447306] : [class_Groups_Ocomm__monoid__add(_1447300), 35440 ^ _780205 : [(35441 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1447302), _1447304)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1447300), _1447306), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1447304), hAPP(c_Nat_OSuc, _1447302))) = c_Groups_Ozero__class_Ozero(_1447300))], (35447 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1447302), _1447304))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1447300), _1447306), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1447304), hAPP(c_Nat_OSuc, _1447302))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1447300), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1447300), _1447306), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1447304), _1447302))), hAPP(_1447306, _1447302)))]]], (35453 ^ _780205) ^ [_1447630, _1447632, _1447634, _1447636] : [class_Orderings_Olinorder(_1447630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447630), _1447632), _1447634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1447630), _1447634), _1447636)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1447630, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1447630, _1447632, _1447634)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1447630, _1447634), _1447636)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1447630, _1447632, _1447636))], (35467 ^ _780205) ^ [_1447899, _1447901, _1447903, _1447905] : [c_Fun_Oinj__on(_1447899, tc_fun(tc_fun(_1447899, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1447899, tc_fun(tc_prod(_1447899, _1447899), tc_HOL_Obool), tc_fun(tc_fun(_1447899, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447899, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1447899, _1447899), tc_HOL_Obool), tc_fun(tc_fun(_1447899, tc_HOL_Obool), tc_HOL_Obool)), _1447899), c_Equiv__Relations_Oquotient(_1447899)), hAPP(hAPP(c_COMBC(_1447899, tc_fun(_1447899, tc_HOL_Obool), tc_fun(_1447899, tc_HOL_Obool)), c_Set_Oinsert(_1447899)), c_Orderings_Obot__class_Obot(tc_fun(_1447899, tc_HOL_Obool))))), _1447901), _1447903), hBOOL(hAPP(hAPP(c_member(_1447899), _1447905), _1447903)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447899), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1447899, tc_HOL_Obool)), _1447903), hAPP(hAPP(c_Set_Oinsert(_1447899), _1447905), c_Orderings_Obot__class_Obot(tc_fun(_1447899, tc_HOL_Obool))))), _1447901) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1447899, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447899), _1447903), _1447901)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447899), hAPP(hAPP(c_Set_Oinsert(_1447899), _1447905), c_Orderings_Obot__class_Obot(tc_fun(_1447899, tc_HOL_Obool)))), _1447901)))], (35477 ^ _780205) ^ [_1448366, _1448368, _1448370] : [class_Orderings_Olinorder(_1448366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1448366), _1448368), _1448370)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448366, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1448366, _1448368), _1448370)), hAPP(hAPP(c_Set_Oinsert(_1448366), _1448370), c_Orderings_Obot__class_Obot(tc_fun(_1448366, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1448366, _1448368, _1448370))], (35487 ^ _780205) ^ [_1448579, _1448581, _1448583] : [class_Orderings_Olinorder(_1448579), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448579), _1448581), _1448583)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448579, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1448579), _1448581), c_Orderings_Obot__class_Obot(tc_fun(_1448579, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1448579, _1448581, _1448583)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1448579, _1448581), _1448583))], (35497 ^ _780205) ^ [_1448792, _1448794, _1448796, _1448798] : [class_Orderings_Olinorder(_1448792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1448792), _1448794), _1448796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448792), _1448796), _1448798)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448792, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1448792, _1448794, _1448796)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1448792, _1448796, _1448798)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1448792, _1448794), _1448798))], (35511 ^ _780205) ^ [_1449061, _1449063] : [class_Groups_Oordered__ab__group__add(_1449061), -(c_Fun_Oinj__on(_1449061, _1449061, c_Groups_Ouminus__class_Ouminus(_1449061), _1449063))], (35517 ^ _780205) ^ [_1449144, _1449146, _1449148] : [-(c_Fun_Oinj__on(_1449144, _1449146, _1449148, c_Orderings_Obot__class_Obot(tc_fun(_1449144, tc_HOL_Obool))))], (35519 ^ _780205) ^ [_1449178] : [-(c_Fun_Oinj__on(_1449178, tc_fun(_1449178, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1449178, tc_fun(_1449178, tc_HOL_Obool), tc_fun(_1449178, tc_HOL_Obool)), c_Set_Oinsert(_1449178)), c_Orderings_Obot__class_Obot(tc_fun(_1449178, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1449178, tc_HOL_Obool))))], (35521 ^ _780205) ^ [_1449234, _1449236] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1449234), _1449236))))], (35523 ^ _780205) ^ [_1449267, _1449269] : [-(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)), _1449267), _1449269))], (35525 ^ _780205) ^ [_1449297] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1449297))], (35527 ^ _780205) ^ [_1449322] : [class_Nat_Osemiring__char__0(_1449322), -(c_Fun_Oinj__on(tc_Nat_Onat, _1449322, c_Nat_Osemiring__1__class_Oof__nat(_1449322), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (35533 ^ _780205) ^ [] : [-(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))))], (35535 ^ _780205) ^ [_1449421, _1449423, _1449425] : [-(c_Fun_Oinj__on(tc_prod(_1449421, _1449423), tc_prod(_1449423, _1449421), hAPP(c_Product__Type_Oprod_Oprod__case(_1449421, _1449423, tc_prod(_1449423, _1449421)), hAPP(c_COMBC(_1449423, _1449421, tc_prod(_1449423, _1449421)), c_Product__Type_OPair(_1449423, _1449421))), _1449425))], (35537 ^ _780205) ^ [_1449479] : [-(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)), _1449479))))], (35557 ^ _780205) ^ [_1449913, _1449915, _1449917, _1449919] : [35559 ^ _780205 : [(35560 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1449913), 35558 ^ [_1449913, _1449915, _1449917, _1449919]), _1449919)))], (35563 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1449913), 35561 ^ [_1449913, _1449915, _1449917, _1449919]), _1449919)))], (35565 ^ _780205) ^ [] : [-(hAPP(_1449917, 35558 ^ [_1449913, _1449915, _1449917, _1449919]) = hAPP(_1449917, 35561 ^ [_1449913, _1449915, _1449917, _1449919]))], (35567 ^ _780205) ^ [] : [35558 ^ [_1449913, _1449915, _1449917, _1449919] = 35561 ^ [_1449913, _1449915, _1449917, _1449919]]], -(c_Fun_Oinj__on(_1449913, _1449915, _1449917, _1449919))], (35539 ^ _780205) ^ [_1449528, _1449530, _1449532, _1449534] : [c_Fun_Oinj__on(_1449528, _1449530, _1449532, _1449534), 35542 ^ _780205 : [(35543 ^ _780205) ^ [_1449636] : [hBOOL(hAPP(hAPP(c_member(_1449528), _1449636), _1449534)), 35546 ^ _780205 : [(35547 ^ _780205) ^ [_1449738] : [hBOOL(hAPP(hAPP(c_member(_1449528), _1449738), _1449534)), hAPP(_1449532, _1449636) = hAPP(_1449532, _1449738), -(_1449636 = _1449738)]]]]], (35571 ^ _780205) ^ [_1450305, _1450307] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1450305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1450307), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1450305, _1450307))], (35573 ^ _780205) ^ [_1450346] : [-(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)), _1450346)) = hAPP(c_Int_Onat, _1450346))], (35575 ^ _780205) ^ [_1450378, _1450380] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1450378), _1450380)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450380), _1450378)))], (35577 ^ _780205) ^ [_1450421, _1450423] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1450421), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1450423) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1450421, _1450423))], (35579 ^ _780205) ^ [_1450462, _1450464] : [-(c_Fun_Oinj__on(_1450462, _1450462, c_COMBI(_1450462), _1450464))], (35581 ^ _780205) ^ [_1450491, _1450493] : [-(hAPP(c_Set_Ovimage(_1450491, _1450491, c_COMBI(_1450491)), _1450493) = _1450493)], (35583 ^ _780205) ^ [_1450525, _1450527, _1450529, _1450531, _1450533, _1450535] : [c_Fun_Oinj__on(_1450525, _1450527, _1450529, _1450531), hAPP(_1450529, _1450533) = hAPP(_1450529, _1450535), hBOOL(hAPP(hAPP(c_member(_1450525), _1450533), _1450531)), hBOOL(hAPP(hAPP(c_member(_1450525), _1450535), _1450531)), -(_1450533 = _1450535)], (35601 ^ _780205) ^ [_1450834, _1450836, _1450838, _1450840, _1450842, _1450844] : [c_Fun_Oinj__on(_1450834, _1450836, _1450838, _1450840), hBOOL(hAPP(hAPP(c_member(_1450834), _1450842), _1450840)), hBOOL(hAPP(hAPP(c_member(_1450834), _1450844), _1450840)), 35612 ^ _780205 : [(35613 ^ _780205) ^ [] : [hAPP(_1450838, _1450842) = hAPP(_1450838, _1450844), -(_1450842 = _1450844)], (35619 ^ _780205) ^ [] : [_1450842 = _1450844, -(hAPP(_1450838, _1450842) = hAPP(_1450838, _1450844))]]], (35625 ^ _780205) ^ [_1451235, _1451237, _1451239, _1451241, _1451243, _1451245] : [c_Fun_Oinj__on(_1451235, _1451237, _1451239, _1451241), -(_1451243 = _1451245), hBOOL(hAPP(hAPP(c_member(_1451235), _1451243), _1451241)), hBOOL(hAPP(hAPP(c_member(_1451235), _1451245), _1451241)), hAPP(_1451239, _1451243) = hAPP(_1451239, _1451245)], (35643 ^ _780205) ^ [_1451548, _1451550, _1451552, _1451554, _1451556] : [c_Fun_Oinj__on(_1451548, _1451550, _1451552, _1451554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1451548, tc_HOL_Obool)), _1451556), _1451554)), -(c_Fun_Oinj__on(_1451548, _1451550, _1451552, _1451556))], (35653 ^ _780205) ^ [_1451717, _1451719, _1451721, _1451723, _1451725] : [c_Fun_Oinj__on(_1451717, _1451719, _1451721, c_Orderings_Otop__class_Otop(tc_fun(_1451717, tc_HOL_Obool))), 35656 ^ _780205 : [(35657 ^ _780205) ^ [] : [hAPP(_1451721, _1451723) = hAPP(_1451721, _1451725), -(_1451723 = _1451725)], (35663 ^ _780205) ^ [] : [_1451723 = _1451725, -(hAPP(_1451721, _1451723) = hAPP(_1451721, _1451725))]]], (35669 ^ _780205) ^ [_1451974, _1451976, _1451978, _1451980, _1451982] : [c_Fun_Oinj__on(_1451974, _1451976, _1451978, c_Orderings_Otop__class_Otop(tc_fun(_1451974, tc_HOL_Obool))), hAPP(_1451978, _1451980) = hAPP(_1451978, _1451982), -(_1451980 = _1451982)], (35679 ^ _780205) ^ [_1452141, _1452143, _1452145, _1452147, _1452149] : [c_Fun_Oinj__on(_1452141, _1452143, _1452145, _1452147), c_Fun_Oinj__on(_1452141, _1452143, _1452145, _1452149), -(c_Fun_Oinj__on(_1452141, _1452143, _1452145, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452141, tc_HOL_Obool)), _1452147), _1452149)))], (35689 ^ _780205) ^ [_1452316, _1452318, _1452320, _1452322, _1452324] : [c_Fun_Oinj__on(_1452316, _1452318, _1452320, _1452322), -(c_Fun_Oinj__on(_1452316, _1452318, _1452320, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1452316, tc_HOL_Obool)), _1452322), _1452324)))], (35695 ^ _780205) ^ [_1452429, _1452431, _1452433, _1452435] : [c_Fun_Oinj__on(_1452429, _1452431, _1452433, c_Orderings_Otop__class_Otop(tc_fun(_1452429, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1452429, tc_fun(_1452435, _1452431), hAPP(hAPP(c_COMBB(_1452431, tc_fun(_1452435, _1452431), _1452429), c_COMBK(_1452431, _1452435)), _1452433), c_Orderings_Otop__class_Otop(tc_fun(_1452429, tc_HOL_Obool))))], (35701 ^ _780205) ^ [_1452576, _1452578, _1452580, _1452582] : [c_Fun_Oinj__on(_1452576, _1452578, _1452580, c_Orderings_Otop__class_Otop(tc_fun(_1452576, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452576, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1452576, _1452578, _1452580), hAPP(hAPP(c_Set_Oinsert(_1452578), _1452582), c_Orderings_Obot__class_Obot(tc_fun(_1452578, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1452576), c_HOL_OThe(_1452576, hAPP(hAPP(c_COMBC(_1452576, _1452578, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1452578, tc_fun(_1452578, tc_HOL_Obool), _1452576), c_fequal), _1452580)), _1452582))), c_Orderings_Obot__class_Obot(tc_fun(_1452576, tc_HOL_Obool))))))], (35707 ^ _780205) ^ [_1452809, _1452811, _1452813, _1452815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452809, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452809, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35708 ^ [_1452809, _1452811, _1452813, _1452815])), _1452811)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452809, 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), 35708 ^ [_1452809, _1452811, _1452813, _1452815]), _1452813))), _1452815))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452809, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452809, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1452811)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452809, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1452815))))], (35714 ^ _780205) ^ [_1453139, _1453141, _1453143, _1453145] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1453139, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35715 ^ [_1453139, _1453141, _1453143, _1453145])), _1453141) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1453139, 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), 35715 ^ [_1453139, _1453141, _1453143, _1453145]), _1453143))), _1453145), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1453139, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1453141) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1453139, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1453145))], (35721 ^ _780205) ^ [_1453419, _1453421, _1453423, _1453425] : [-(c_HOL_OThe(tc_prod(_1453419, _1453421), hAPP(c_Product__Type_Oprod_Oprod__case(_1453419, _1453421, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1453419, tc_fun(_1453421, tc_HOL_Obool), tc_fun(_1453421, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1453421, tc_HOL_Obool), tc_fun(_1453421, tc_HOL_Obool)), _1453419), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1453421)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1453419), c_fconj), hAPP(c_fequal, _1453423)))), hAPP(c_fequal, _1453425)))) = hAPP(hAPP(c_Product__Type_OPair(_1453419, _1453421), _1453423), _1453425))], (35723 ^ _780205) ^ [_1453525, _1453527, _1453529] : [-(c_HOL_OThe(tc_prod(_1453525, _1453527), _1453529) = c_HOL_OThe(tc_prod(_1453525, _1453527), hAPP(c_Product__Type_Oprod_Oprod__case(_1453525, _1453527, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1453527, tc_prod(_1453525, _1453527)), tc_fun(_1453527, tc_HOL_Obool), _1453525), hAPP(c_COMBB(tc_prod(_1453525, _1453527), tc_HOL_Obool, _1453527), _1453529)), c_Product__Type_OPair(_1453525, _1453527)))))], (35725 ^ _780205) ^ [_1453603, _1453605, _1453607, _1453609, _1453611] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1453603, _1453605, _1453607), _1453609), _1453611) = c_HOL_OThe(_1453605, c_Finite__Set_Ofold__graph(_1453603, _1453605, _1453607, _1453609, _1453611)))], (35727 ^ _780205) ^ [_1453653, _1453655] : [-(c_Divides_Odivmod__nat(_1453653, _1453655) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1453653, _1453655)))], (35729 ^ _780205) ^ [_1453687, _1453689, _1453691] : [-(hAPP(c_Finite__Set_Ofold1(_1453687, _1453689), _1453691) = c_HOL_OThe(_1453687, c_Finite__Set_Ofold1Set(_1453687, _1453689, _1453691)))], (35731 ^ _780205) ^ [_1453727, _1453729, _1453731] : [-(c_HOL_OThe(tc_prod(_1453727, _1453729), hAPP(c_Product__Type_Oprod_Oprod__case(_1453727, _1453729, tc_HOL_Obool), _1453731)) = c_HOL_OThe(tc_prod(_1453727, _1453729), hAPP(hAPP(c_COMBS(tc_prod(_1453727, _1453729), _1453729, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1453727, tc_fun(_1453729, tc_HOL_Obool), tc_prod(_1453727, _1453729)), _1453731), c_Product__Type_Ofst(_1453727, _1453729))), c_Product__Type_Osnd(_1453727, _1453729))))], (35733 ^ _780205) ^ [_1453808, _1453810] : [-(c_Set_Othe__elem(_1453808, _1453810) = c_HOL_OThe(_1453808, hAPP(hAPP(c_COMBB(tc_fun(_1453808, tc_HOL_Obool), tc_HOL_Obool, _1453808), hAPP(c_fequal, _1453810)), hAPP(hAPP(c_COMBC(_1453808, tc_fun(_1453808, tc_HOL_Obool), tc_fun(_1453808, tc_HOL_Obool)), c_Set_Oinsert(_1453808)), c_Orderings_Obot__class_Obot(tc_fun(_1453808, tc_HOL_Obool))))))], (35735 ^ _780205) ^ [_1453890, _1453892, _1453894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1453890, tc_HOL_Obool)), _1453892), hAPP(hAPP(c_Set_Oinsert(_1453890), _1453894), c_Orderings_Obot__class_Obot(tc_fun(_1453890, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1453890, _1453894, _1453892) = _1453894)], (35741 ^ _780205) ^ [_1454017, _1454019, _1454021] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454017, tc_HOL_Obool)), _1454019), hAPP(hAPP(c_Set_Oinsert(_1454017), _1454021), c_Orderings_Obot__class_Obot(tc_fun(_1454017, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1454017, _1454021, _1454019) = c_HOL_OThe(_1454017, hAPP(hAPP(c_COMBC(_1454017, tc_fun(_1454017, tc_HOL_Obool), tc_HOL_Obool), c_member(_1454017)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1454017, tc_HOL_Obool)), _1454019), hAPP(hAPP(c_Set_Oinsert(_1454017), _1454021), c_Orderings_Obot__class_Obot(tc_fun(_1454017, tc_HOL_Obool)))))))], (35747 ^ _780205) ^ [_1454126, _1454128, _1454130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454126, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1454126, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35748 ^ [_1454126, _1454128, _1454130])), _1454128)), _1454130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454126, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1454126, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1454128)), _1454130)))], (35754 ^ _780205) ^ [] : [-(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))], (35756 ^ _780205) ^ [_1454370, _1454372, _1454374, _1454376, _1454378, _1454380, _1454382] : [c_Typedef_Otype__definition(_1454370, _1454372, _1454374, _1454376, _1454378), hBOOL(hAPP(hAPP(c_member(_1454372), _1454380), _1454378)), hBOOL(hAPP(hAPP(c_member(_1454372), _1454382), _1454378)), 35767 ^ _780205 : [(35768 ^ _780205) ^ [] : [hAPP(_1454376, _1454380) = hAPP(_1454376, _1454382), -(_1454380 = _1454382)], (35774 ^ _780205) ^ [] : [_1454380 = _1454382, -(hAPP(_1454376, _1454380) = hAPP(_1454376, _1454382))]]], (35780 ^ _780205) ^ [_1454783, _1454785, _1454787, _1454789, _1454791, _1454793] : [c_Typedef_Otype__definition(_1454783, _1454785, _1454787, _1454789, _1454791), hBOOL(hAPP(hAPP(c_member(_1454785), _1454793), _1454791)), -(hAPP(_1454787, hAPP(_1454789, _1454793)) = _1454793)], (35790 ^ _780205) ^ [_1454960, _1454962, _1454964, _1454966, _1454968, _1454970] : [c_Typedef_Otype__definition(_1454960, _1454962, _1454964, _1454966, _1454968), -(hBOOL(hAPP(hAPP(c_member(_1454962), hAPP(_1454964, _1454970)), _1454968)))], (35796 ^ _780205) ^ [_1455071, _1455073, _1455075, _1455077, _1455079, _1455081] : [c_Typedef_Otype__definition(_1455071, _1455073, _1455075, _1455077, _1455079), -(hAPP(_1455077, hAPP(_1455075, _1455081)) = _1455081)], (35802 ^ _780205) ^ [_1455174, _1455176, _1455178, _1455180, _1455182, _1455184, _1455186] : [c_Typedef_Otype__definition(_1455174, _1455176, _1455178, _1455180, _1455182), 35805 ^ _780205 : [(35806 ^ _780205) ^ [] : [hAPP(_1455178, _1455184) = hAPP(_1455178, _1455186), -(_1455184 = _1455186)], (35812 ^ _780205) ^ [] : [_1455184 = _1455186, -(hAPP(_1455178, _1455184) = hAPP(_1455178, _1455186))]]], (35818 ^ _780205) ^ [_1455447, _1455449, _1455451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1455447), _1455449)), -(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)), _1455447)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1455451), _1455449)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1455451), _1455447)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1455449), _1455447)))], (35824 ^ _780205) ^ [_1455599, _1455601, _1455603] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1455599), _1455601))), 35827 ^ _780205 : [(35828 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1455603), _1455601)), -(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)), _1455599)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1455603), _1455601)) = 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))))], (35834 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1455603), _1455601))), -(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)), _1455599)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1455603), _1455601)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (35840 ^ _780205) ^ [_1455868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1455868)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1455868) = 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, _1455868))))], (35846 ^ _780205) ^ [_1455971, _1455973] : [class_Orderings_Oorder(_1455971), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455971, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1455971), _1455973)), hAPP(c_SetInterval_Oord__class_OatLeast(_1455971), _1455973)) = hAPP(hAPP(c_Set_Oinsert(_1455971), _1455973), c_Orderings_Obot__class_Obot(tc_fun(_1455971, tc_HOL_Obool))))], (35852 ^ _780205) ^ [_1456114, _1456116, _1456118, _1456120, _1456122, _1456124] : [_1456114 = hAPP(_1456116, _1456118), hBOOL(hAPP(hAPP(c_member(_1456120), _1456118), _1456122)), -(hBOOL(hAPP(hAPP(c_member(_1456124), _1456114), hAPP(c_Set_Oimage(_1456120, _1456124, _1456116), _1456122))))], (35862 ^ _780205) ^ [_1456307, _1456309, _1456311, _1456313] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1456307), _1456309)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1456311), hAPP(c_Set_Oimage(_1456307, _1456311, _1456313), _1456309))))], (35868 ^ _780205) ^ [_1456418, _1456420, _1456422, _1456424, _1456426] : [-(hAPP(c_Set_Oimage(_1456418, _1456420, hAPP(hAPP(c_COMBB(_1456422, _1456420, _1456418), _1456424), _1456426)), c_Orderings_Otop__class_Otop(tc_fun(_1456418, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1456422, _1456420, _1456424), hAPP(c_Set_Oimage(_1456418, _1456422, _1456426), c_Orderings_Otop__class_Otop(tc_fun(_1456418, tc_HOL_Obool)))))], (35870 ^ _780205) ^ [_1456490, _1456492] : [class_Groups_Oordered__ab__group__add(_1456490), -(hAPP(c_Set_Oimage(_1456490, _1456490, c_Groups_Ouminus__class_Ouminus(_1456490)), hAPP(c_SetInterval_Oord__class_OatLeast(_1456490), _1456492)) = hAPP(c_SetInterval_Oord__class_OatMost(_1456490), hAPP(c_Groups_Ouminus__class_Ouminus(_1456490), _1456492)))], (35876 ^ _780205) ^ [_1456613, _1456615] : [class_Groups_Oordered__ab__group__add(_1456613), -(hAPP(c_Set_Oimage(_1456613, _1456613, c_Groups_Ouminus__class_Ouminus(_1456613)), hAPP(c_SetInterval_Oord__class_OatMost(_1456613), _1456615)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1456613), hAPP(c_Groups_Ouminus__class_Ouminus(_1456613), _1456615)))], (35882 ^ _780205) ^ [_1456736, _1456738, _1456740, _1456742, _1456744] : [-(hAPP(c_Set_Oimage(_1456736, _1456738, _1456740), hAPP(hAPP(c_Set_Oinsert(_1456736), _1456742), _1456744)) = hAPP(hAPP(c_Set_Oinsert(_1456738), hAPP(_1456740, _1456742)), hAPP(c_Set_Oimage(_1456736, _1456738, _1456740), _1456744)))], (35884 ^ _780205) ^ [_1456821, _1456823, _1456825, _1456827] : [c_Orderings_Obot__class_Obot(tc_fun(_1456821, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1456823, _1456821, _1456825), _1456827), -(_1456827 = c_Orderings_Obot__class_Obot(tc_fun(_1456823, tc_HOL_Obool)))], (35890 ^ _780205) ^ [_1456932, _1456934, _1456936, _1456938] : [_1456938 = c_Orderings_Obot__class_Obot(tc_fun(_1456934, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1456932, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1456934, _1456932, _1456936), _1456938))], (35896 ^ _780205) ^ [_1457049, _1457051, _1457053] : [-(hAPP(c_Set_Oimage(_1457049, _1457051, _1457053), c_Orderings_Obot__class_Obot(tc_fun(_1457049, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1457051, tc_HOL_Obool)))], (35898 ^ _780205) ^ [_1457114, _1457116, _1457118, _1457120] : [hAPP(c_Set_Oimage(_1457114, _1457116, _1457118), _1457120) = c_Orderings_Obot__class_Obot(tc_fun(_1457116, tc_HOL_Obool)), -(_1457120 = c_Orderings_Obot__class_Obot(tc_fun(_1457114, tc_HOL_Obool)))], (35904 ^ _780205) ^ [_1457225, _1457227, _1457229, _1457231] : [_1457231 = c_Orderings_Obot__class_Obot(tc_fun(_1457225, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1457225, _1457227, _1457229), _1457231) = c_Orderings_Obot__class_Obot(tc_fun(_1457227, tc_HOL_Obool)))], (35910 ^ _780205) ^ [_1457342, _1457344, _1457346] : [class_Orderings_Olinorder(_1457342), 35913 ^ _780205 : [(35914 ^ _780205) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1457342), _1457344) = hAPP(c_SetInterval_Oord__class_OatLeast(_1457342), _1457346), -(_1457344 = _1457346)], (35920 ^ _780205) ^ [] : [_1457344 = _1457346, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1457342), _1457344) = hAPP(c_SetInterval_Oord__class_OatLeast(_1457342), _1457346))]]], (35926 ^ _780205) ^ [_1457598, _1457600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1457598), _1457600)), -(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)), _1457598)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1457600))))], (35932 ^ _780205) ^ [_1457703, _1457705] : [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)), _1457703)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1457705))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1457703), _1457705)))], (35938 ^ _780205) ^ [_1457829, _1457831] : [_1457829 = _1457831, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1457829) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1457831))], (35944 ^ _780205) ^ [_1457914, _1457916] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1457914) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1457916), -(_1457914 = _1457916)], (35950 ^ _780205) ^ [_1458005, _1458007, _1458009, _1458011, _1458013] : [hAPP(c_Set_Oimage(_1458005, _1458007, _1458009), _1458011) = _1458013, -(hAPP(c_Set_Oimage(tc_fun(_1458005, tc_HOL_Obool), tc_fun(_1458007, tc_HOL_Obool), c_Set_Oimage(_1458005, _1458007, _1458009)), hAPP(c_Set_OPow(_1458005), _1458011)) = hAPP(c_Set_OPow(_1458007), _1458013))], (35956 ^ _780205) ^ [_1458156, _1458158, _1458160, _1458162, _1458164, _1458166] : [-(hAPP(c_Set_Oimage(_1458156, _1458158, _1458160), hAPP(c_Set_Oimage(_1458162, _1458156, _1458164), _1458166)) = hAPP(c_Set_Oimage(_1458162, _1458158, hAPP(hAPP(c_COMBB(_1458156, _1458158, _1458162), _1458160), _1458164)), _1458166))], (35958 ^ _780205) ^ [_1458220, _1458222, _1458224, _1458226, _1458228, _1458230] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458220, tc_fun(_1458222, tc_HOL_Obool)), _1458224), hAPP(hAPP(c_COMBB(_1458226, tc_fun(_1458222, tc_HOL_Obool), _1458220), _1458228), _1458230)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458226, tc_fun(_1458222, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1458220, _1458226, _1458230), _1458224)), _1458228))], (35960 ^ _780205) ^ [_1458297, _1458299, _1458301, _1458303, _1458305, _1458307] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458297, tc_fun(_1458299, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1458301, _1458297, _1458303), _1458305)), _1458307) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458301, tc_fun(_1458299, tc_HOL_Obool)), _1458305), hAPP(hAPP(c_COMBB(_1458297, tc_fun(_1458299, tc_HOL_Obool), _1458301), _1458307), _1458303)))], (35962 ^ _780205) ^ [_1458374, _1458376, _1458378, _1458380, _1458382, _1458384] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458374, tc_fun(_1458376, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1458378, _1458374, _1458380), _1458382)), _1458384) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458378, tc_fun(_1458376, tc_HOL_Obool)), _1458382), hAPP(hAPP(c_COMBB(_1458374, tc_fun(_1458376, tc_HOL_Obool), _1458378), _1458384), _1458380)))], (35964 ^ _780205) ^ [_1458451, _1458453, _1458455, _1458457, _1458459, _1458461] : [-(hAPP(c_Set_Oimage(_1458451, _1458453, _1458455), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458457, tc_fun(_1458451, tc_HOL_Obool)), _1458459), _1458461)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458457, tc_fun(_1458453, tc_HOL_Obool)), _1458459), hAPP(hAPP(c_COMBB(tc_fun(_1458451, tc_HOL_Obool), tc_fun(_1458453, tc_HOL_Obool), _1458457), c_Set_Oimage(_1458451, _1458453, _1458455)), _1458461)))], (35966 ^ _780205) ^ [_1458535, _1458537, _1458539, _1458541, _1458543, _1458545] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458535, tc_fun(_1458537, tc_HOL_Obool)), _1458539), hAPP(hAPP(c_COMBB(_1458541, tc_fun(_1458537, tc_HOL_Obool), _1458535), _1458543), _1458545)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458541, tc_fun(_1458537, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1458535, _1458541, _1458545), _1458539)), _1458543))], (35968 ^ _780205) ^ [_1458612, _1458614] : [-(hAPP(c_Set_Oimage(_1458612, _1458612, c_COMBI(_1458612)), _1458614) = _1458614)], (35970 ^ _780205) ^ [_1458646, _1458648, _1458650, _1458652, _1458654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458646, tc_HOL_Obool)), _1458648), _1458650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458652, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1458646, _1458652, _1458654), _1458648)), hAPP(c_Set_Oimage(_1458646, _1458652, _1458654), _1458650))))], (35976 ^ _780205) ^ [_1458821, _1458823, _1458825, _1458827, _1458829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458821, tc_HOL_Obool)), _1458823), hAPP(c_Set_Oimage(_1458825, _1458821, _1458827), _1458829))), 35980 ^ _780205 : [(35981 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458825, tc_HOL_Obool)), 35979 ^ [_1458821, _1458823, _1458825, _1458827, _1458829]), _1458829)))], (35983 ^ _780205) ^ [] : [-(_1458823 = hAPP(c_Set_Oimage(_1458825, _1458821, _1458827), 35979 ^ [_1458821, _1458823, _1458825, _1458827, _1458829]))]]], (35985 ^ _780205) ^ [_1459025, _1459027, _1459029, _1459031, _1459033] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459025, tc_HOL_Obool)), _1459027), hAPP(c_Set_Oimage(_1459029, _1459025, _1459031), _1459033)))), 35986 ^ _780205 : [(35987 ^ _780205) ^ [_1459105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459029, tc_HOL_Obool)), _1459105), _1459033)), _1459027 = hAPP(c_Set_Oimage(_1459029, _1459025, _1459031), _1459105)]]], (35995 ^ _780205) ^ [_1459270, _1459272, _1459274, _1459276, _1459278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1459270, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1459272, _1459270, _1459274), _1459276)), _1459278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1459270, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1459272, tc_HOL_Obool), tc_fun(_1459270, tc_HOL_Obool), c_Set_Oimage(_1459272, _1459270, _1459274)), hAPP(c_Set_OPow(_1459272), _1459276))), hAPP(c_Set_OPow(_1459270), _1459278))))], (36001 ^ _780205) ^ [_1459467, _1459469, _1459471, _1459473, _1459475] : [-(hAPP(c_Set_Oimage(_1459467, _1459469, _1459471), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459467, tc_HOL_Obool)), _1459473), _1459475)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459469, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1459467, _1459469, _1459471), _1459473)), hAPP(c_Set_Oimage(_1459467, _1459469, _1459471), _1459475)))], (36003 ^ _780205) ^ [_1459565, _1459567, _1459569, _1459571, _1459573] : [hBOOL(hAPP(hAPP(c_member(_1459565), _1459567), hAPP(c_Set_Oimage(_1459569, _1459565, _1459571), _1459573))), 36007 ^ _780205 : [(36008 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1459569), 36006 ^ [_1459565, _1459567, _1459569, _1459571, _1459573]), _1459573)))], (36010 ^ _780205) ^ [] : [-(_1459567 = hAPP(_1459571, 36006 ^ [_1459565, _1459567, _1459569, _1459571, _1459573]))]]], (36012 ^ _780205) ^ [_1459749, _1459751, _1459753, _1459755, _1459757] : [-(hBOOL(hAPP(hAPP(c_member(_1459749), _1459751), hAPP(c_Set_Oimage(_1459753, _1459749, _1459755), _1459757)))), 36013 ^ _780205 : [(36014 ^ _780205) ^ [_1459819] : [hBOOL(hAPP(hAPP(c_member(_1459753), _1459819), _1459757)), _1459751 = hAPP(_1459755, _1459819)]]], (36022 ^ _780205) ^ [_1459967, _1459969, _1459971, _1459973, _1459975] : [hBOOL(hAPP(hAPP(c_member(_1459967), _1459969), _1459971)), -(hBOOL(hAPP(hAPP(c_member(_1459973), hAPP(_1459975, _1459969)), hAPP(c_Set_Oimage(_1459967, _1459973, _1459975), _1459971))))], (36028 ^ _780205) ^ [_1460098, _1460100, _1460102, _1460104, _1460106, _1460108] : [hBOOL(hAPP(hAPP(c_member(_1460098), _1460100), _1460102)), _1460104 = hAPP(_1460106, _1460100), -(hBOOL(hAPP(hAPP(c_member(_1460108), _1460104), hAPP(c_Set_Oimage(_1460098, _1460108, _1460106), _1460102))))], (36038 ^ _780205) ^ [_1460291, _1460293, _1460295, _1460297, _1460299] : [hBOOL(hAPP(hAPP(c_member(_1460291), _1460293), _1460295)), -(hAPP(hAPP(c_Set_Oinsert(_1460297), hAPP(_1460299, _1460293)), hAPP(c_Set_Oimage(_1460291, _1460297, _1460299), _1460295)) = hAPP(c_Set_Oimage(_1460291, _1460297, _1460299), _1460295))], (36044 ^ _780205) ^ [_1460438, _1460440, _1460442, _1460444, _1460446] : [_1460438 = hAPP(_1460440, _1460442), -(hBOOL(hAPP(hAPP(c_member(_1460444), _1460438), hAPP(c_Set_Oimage(_1460446, _1460444, _1460440), c_Orderings_Otop__class_Otop(tc_fun(_1460446, tc_HOL_Obool))))))], (36050 ^ _780205) ^ [_1460565, _1460567, _1460569, _1460571] : [-(hBOOL(hAPP(hAPP(c_member(_1460565), hAPP(_1460567, _1460569)), hAPP(c_Set_Oimage(_1460571, _1460565, _1460567), c_Orderings_Otop__class_Otop(tc_fun(_1460571, tc_HOL_Obool))))))], (36052 ^ _780205) ^ [_1460616, _1460618, _1460620, _1460622, _1460624] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1460616), _1460618)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1460620, tc_HOL_Obool)), _1460622), hAPP(c_Set_Oimage(_1460616, _1460620, _1460624), _1460618))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1460620), _1460622)))], (36062 ^ _780205) ^ [_1460807, _1460809, _1460811, _1460813, _1460815] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1460807, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1460809, _1460807, _1460811), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460809, tc_HOL_Obool)), _1460813), _1460815))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460807, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1460809, _1460807, _1460811), _1460813)), hAPP(c_Set_Oimage(_1460809, _1460807, _1460811), _1460815)))))], (36064 ^ _780205) ^ [_1460891, _1460893, _1460895, _1460897] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1460891), hAPP(c_Set_Oimage(_1460893, _1460891, _1460895), _1460897))), c_Fun_Oinj__on(_1460893, _1460891, _1460895, _1460897), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1460893), _1460897)))], (36074 ^ _780205) ^ [_1461062, _1461064, _1461066, _1461068, _1461070] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1461062, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461062, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1461064, _1461062, _1461066), _1461068)), hAPP(c_Set_Oimage(_1461064, _1461062, _1461066), _1461070))), hAPP(c_Set_Oimage(_1461064, _1461062, _1461066), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461064, tc_HOL_Obool)), _1461068), _1461070)))))], (36076 ^ _780205) ^ [_1461146, _1461148, _1461150, _1461152, _1461154] : [c_Fun_Oinj__on(_1461146, _1461148, _1461150, c_Orderings_Otop__class_Otop(tc_fun(_1461146, tc_HOL_Obool))), 36079 ^ _780205 : [(36080 ^ _780205) ^ [] : [hAPP(c_Set_Oimage(_1461146, _1461148, _1461150), _1461152) = hAPP(c_Set_Oimage(_1461146, _1461148, _1461150), _1461154), -(_1461152 = _1461154)], (36086 ^ _780205) ^ [] : [_1461152 = _1461154, -(hAPP(c_Set_Oimage(_1461146, _1461148, _1461150), _1461152) = hAPP(c_Set_Oimage(_1461146, _1461148, _1461150), _1461154))]]], (36092 ^ _780205) ^ [_1461427, _1461429, _1461431, _1461433, _1461435] : [c_Fun_Oinj__on(_1461427, _1461429, _1461431, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461427, tc_HOL_Obool)), _1461433), _1461435)), 36095 ^ _780205 : [(36096 ^ _780205) ^ [] : [hAPP(c_Set_Oimage(_1461427, _1461429, _1461431), _1461433) = hAPP(c_Set_Oimage(_1461427, _1461429, _1461431), _1461435), -(_1461433 = _1461435)], (36102 ^ _780205) ^ [] : [_1461433 = _1461435, -(hAPP(c_Set_Oimage(_1461427, _1461429, _1461431), _1461433) = hAPP(c_Set_Oimage(_1461427, _1461429, _1461431), _1461435))]]], (36108 ^ _780205) ^ [_1461720, _1461722, _1461724] : [class_Groups_Oordered__ab__group__add(_1461720), -(hAPP(c_Set_Oimage(_1461720, _1461720, c_Groups_Ouminus__class_Ouminus(_1461720)), c_SetInterval_Oord__class_OatLeastAtMost(_1461720, _1461722, _1461724)) = c_SetInterval_Oord__class_OatLeastAtMost(_1461720, hAPP(c_Groups_Ouminus__class_Ouminus(_1461720), _1461724), hAPP(c_Groups_Ouminus__class_Ouminus(_1461720), _1461722)))], (36114 ^ _780205) ^ [_1461851, _1461853, _1461855, _1461857] : [c_Fun_Oinj__on(_1461851, _1461853, _1461855, _1461857), -(hAPP(c_Finite__Set_Ocard(_1461853), hAPP(c_Set_Oimage(_1461851, _1461853, _1461855), _1461857)) = hAPP(c_Finite__Set_Ocard(_1461851), _1461857))], (36120 ^ _780205) ^ [_1461970, _1461972, _1461974, _1461976] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1461970, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1461972, _1461970, _1461974), hAPP(c_Set_Ovimage(_1461972, _1461970, _1461974), _1461976))), _1461976)))], (36122 ^ _780205) ^ [_1462023, _1462025, _1462027, _1462029] : [hAPP(c_Set_Oimage(_1462023, _1462025, _1462027), c_Orderings_Otop__class_Otop(tc_fun(_1462023, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1462025, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1462023, _1462025, _1462027), hAPP(c_Set_Ovimage(_1462023, _1462025, _1462027), _1462029)) = _1462029)], (36128 ^ _780205) ^ [_1462166, _1462168] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1462166), _1462168)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1462166)), hAPP(c_Nat_OSuc, _1462168)))], (36130 ^ _780205) ^ [_1462212, _1462214, _1462216, _1462218, _1462220] : [c_Typedef_Otype__definition(_1462212, _1462214, _1462216, _1462218, _1462220), -(hAPP(c_Set_Oimage(_1462214, _1462212, _1462218), _1462220) = c_Orderings_Otop__class_Otop(tc_fun(_1462212, tc_HOL_Obool)))], (36136 ^ _780205) ^ [_1462325, _1462327, _1462329, _1462331, _1462333] : [c_Typedef_Otype__definition(_1462325, _1462327, _1462329, _1462331, _1462333), -(hAPP(c_Set_Oimage(_1462325, _1462327, _1462329), c_Orderings_Otop__class_Otop(tc_fun(_1462325, tc_HOL_Obool))) = _1462333)], (36142 ^ _780205) ^ [_1462438, _1462440] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1462438, _1462440)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1462438), hAPP(c_Nat_OSuc, _1462440)))], (36144 ^ _780205) ^ [_1462480, _1462482, _1462484] : [class_Groups_Oordered__ab__group__add(_1462480), -(hAPP(c_Set_Oimage(_1462480, _1462480, c_Groups_Ouminus__class_Ouminus(_1462480)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1462480, _1462482, _1462484)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1462480, hAPP(c_Groups_Ouminus__class_Ouminus(_1462480), _1462484), hAPP(c_Groups_Ouminus__class_Ouminus(_1462480), _1462482)))], (36150 ^ _780205) ^ [_1462611, _1462613, _1462615, _1462617, _1462619] : [c_Fun_Oinj__on(_1462611, _1462613, _1462615, _1462617), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1462611, tc_HOL_Obool)), _1462619), _1462617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1462613, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1462611, _1462613, _1462615), _1462619)), hAPP(c_Set_Oimage(_1462611, _1462613, _1462615), _1462617))))], (36160 ^ _780205) ^ [_1462839, _1462841, _1462843, _1462845] : [_1462839 = c_Orderings_Obot__class_Obot(tc_fun(_1462841, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1462841, _1462843, hAPP(c_COMBK(_1462843, _1462841), _1462845)), _1462839) = c_Orderings_Obot__class_Obot(tc_fun(_1462843, tc_HOL_Obool)))], (36166 ^ _780205) ^ [_1462960, _1462962, _1462964, _1462966] : [-(_1462960 = c_Orderings_Obot__class_Obot(tc_fun(_1462962, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1462962, _1462964, hAPP(c_COMBK(_1462964, _1462962), _1462966)), _1462960) = hAPP(hAPP(c_Set_Oinsert(_1462964), _1462966), c_Orderings_Obot__class_Obot(tc_fun(_1462964, tc_HOL_Obool))))], (36172 ^ _780205) ^ [_1463033, _1463035, _1463037, _1463039, _1463041] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1463033), hAPP(c_Set_Oimage(_1463035, _1463033, _1463037), c_Orderings_Otop__class_Otop(tc_fun(_1463035, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1463039), hAPP(c_Set_Oimage(_1463035, _1463039, hAPP(hAPP(c_COMBB(_1463033, _1463039, _1463035), _1463041), _1463037)), c_Orderings_Otop__class_Otop(tc_fun(_1463035, tc_HOL_Obool))))))], (36178 ^ _780205) ^ [_1463215, _1463217] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1463215), _1463217)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1463215)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1463217))))], (36184 ^ _780205) ^ [_1463320, _1463322] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1463320)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1463322))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1463320), _1463322)))], (36190 ^ _780205) ^ [_1463431, _1463433, _1463435] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1463431), _1463433), _1463435) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1463431), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1463431, tc_Int_Oint), _1463433), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1463435))), class_Groups_Ocomm__monoid__add(_1463431), class_Groups_Ocomm__monoid__mult(_1463431)], (36200 ^ _780205) ^ [_1463622, _1463624, _1463626] : [-(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)), _1463622)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1463624), _1463626)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1463624), _1463622)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1463626), _1463622)))], (36202 ^ _780205) ^ [_1463683, _1463685, _1463687] : [-(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)), _1463683)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1463685, _1463687)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1463685), _1463683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1463687), _1463683)))], (36204 ^ _780205) ^ [_1463755, _1463757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1463755), _1463757)), -(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)), _1463755)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1463757))))], (36210 ^ _780205) ^ [_1463860, _1463862] : [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)), _1463860)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1463862))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1463860), _1463862)))], (36216 ^ _780205) ^ [_1463971, _1463973, _1463975, _1463977] : [-(hAPP(c_Set_Oimage(_1463971, _1463973, _1463975), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1463971, tc_HOL_Obool), _1463977)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1463971, tc_HOL_Obool), tc_fun(_1463973, tc_HOL_Obool)), _1463977), c_Set_Oimage(_1463971, _1463973, _1463975)))], (36218 ^ _780205) ^ [_1464032, _1464034, _1464036, _1464038] : [c_Fun_Oinj__on(_1464032, _1464034, _1464036, c_Orderings_Otop__class_Otop(tc_fun(_1464032, tc_HOL_Obool))), 36221 ^ _780205 : [(36222 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1464034), _1464038), hAPP(c_Set_Oimage(_1464032, _1464034, _1464036), c_Orderings_Otop__class_Otop(tc_fun(_1464032, tc_HOL_Obool))))), 36226 ^ _780205 : [(36227 ^ _780205) ^ [] : [-(_1464038 = hAPP(_1464036, 36225 ^ [_1464032, _1464034, _1464036, _1464038]))], (36229 ^ _780205) ^ [_1464297] : [_1464038 = hAPP(_1464036, _1464297), -(_1464297 = 36225 ^ [_1464032, _1464034, _1464036, _1464038])]]], (36235 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1464034), _1464038), hAPP(c_Set_Oimage(_1464032, _1464034, _1464036), c_Orderings_Otop__class_Otop(tc_fun(_1464032, tc_HOL_Obool)))))), 36236 ^ _780205 : [(36237 ^ _780205) ^ [_1464435] : [_1464038 = hAPP(_1464036, _1464435), 36241 ^ _780205 : [(36242 ^ _780205) ^ [] : [-(_1464038 = hAPP(_1464036, 36240 ^ [_1464032, _1464034, _1464036, _1464038, _1464435]))], (36244 ^ _780205) ^ [] : [36240 ^ [_1464032, _1464034, _1464036, _1464038, _1464435] = _1464435]]]]]]], (36248 ^ _780205) ^ [_1464663, _1464665, _1464667, _1464669, _1464671] : [c_Fun_Oinj__on(_1464663, _1464665, _1464667, c_Orderings_Otop__class_Otop(tc_fun(_1464663, tc_HOL_Obool))), 36251 ^ _780205 : [(36252 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1464665), hAPP(_1464667, _1464669)), hAPP(c_Set_Oimage(_1464663, _1464665, _1464667), _1464671))), -(hBOOL(hAPP(hAPP(c_member(_1464663), _1464669), _1464671)))], (36258 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1464663), _1464669), _1464671)), -(hBOOL(hAPP(hAPP(c_member(_1464665), hAPP(_1464667, _1464669)), hAPP(c_Set_Oimage(_1464663, _1464665, _1464667), _1464671))))]]], (36264 ^ _780205) ^ [_1464973, _1464975, _1464977, _1464979] : [-(_1464973 = c_Orderings_Obot__class_Obot(tc_fun(_1464975, tc_HOL_Obool))), 36267 ^ _780205 : [(36279 ^ _780205) ^ [] : [36280 ^ _780205 : [(36281 ^ _780205) ^ [_1465306] : [hAPP(c_Set_Oimage(_1464977, _1464975, _1465306), _1464979) = _1464973]], 36283 ^ _780205 : [(36284 ^ _780205) ^ [] : [-(c_Fun_Oinj__on(_1464975, _1464977, 36282 ^ [_1464973, _1464975, _1464977, _1464979], _1464973))], (36286 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1464977, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1464975, _1464977, 36282 ^ [_1464973, _1464975, _1464977, _1464979]), _1464973)), _1464979)))]]], (36268 ^ _780205) ^ [] : [-(hAPP(c_Set_Oimage(_1464977, _1464975, 36275 ^ [_1464973, _1464975, _1464977, _1464979]), _1464979) = _1464973), 36269 ^ _780205 : [(36270 ^ _780205) ^ [_1465114] : [c_Fun_Oinj__on(_1464975, _1464977, _1465114, _1464973), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1464977, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1464975, _1464977, _1465114), _1464973)), _1464979))]]]]], (36288 ^ _780205) ^ [_1465431, _1465433, _1465435] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465431), _1465433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465431, tc_HOL_Obool)), _1465433), hAPP(c_Set_Oimage(_1465431, _1465431, _1465435), _1465433))), -(c_Fun_Oinj__on(_1465431, _1465431, _1465435, _1465433))], (36298 ^ _780205) ^ [_1465610, _1465612, _1465614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465610), _1465612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465610, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1465610, _1465610, _1465614), _1465612)), _1465612)), c_Fun_Oinj__on(_1465610, _1465610, _1465614, _1465612), -(hAPP(c_Set_Oimage(_1465610, _1465610, _1465614), _1465612) = _1465612)], (36312 ^ _780205) ^ [_1465857, _1465859] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465857), c_Orderings_Otop__class_Otop(tc_fun(_1465857, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1465857, _1465857, _1465859), c_Orderings_Otop__class_Otop(tc_fun(_1465857, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1465857, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1465857, _1465857, _1465859, c_Orderings_Otop__class_Otop(tc_fun(_1465857, tc_HOL_Obool))))], (36322 ^ _780205) ^ [_1466052, _1466054] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466052), c_Orderings_Otop__class_Otop(tc_fun(_1466052, tc_HOL_Obool)))), c_Fun_Oinj__on(_1466052, _1466052, _1466054, c_Orderings_Otop__class_Otop(tc_fun(_1466052, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1466052, _1466052, _1466054), c_Orderings_Otop__class_Otop(tc_fun(_1466052, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1466052, tc_HOL_Obool)))], (36332 ^ _780205) ^ [_1466247, _1466249, _1466251, _1466253] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466247), _1466249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1466251), hAPP(c_Set_Oimage(_1466247, _1466251, _1466253), _1466249))), hAPP(c_Finite__Set_Ocard(_1466247), _1466249))))], (36338 ^ _780205) ^ [_1466380, _1466382, _1466384, _1466386, _1466388] : [c_Fun_Oinj__on(_1466380, _1466382, _1466384, c_Orderings_Otop__class_Otop(tc_fun(_1466380, tc_HOL_Obool))), 36341 ^ _780205 : [(36342 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466382, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466380, _1466382, _1466384), _1466386)), hAPP(c_Set_Oimage(_1466380, _1466382, _1466384), _1466388))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466380, tc_HOL_Obool)), _1466386), _1466388)))], (36348 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466380, tc_HOL_Obool)), _1466386), _1466388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466382, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466380, _1466382, _1466384), _1466386)), hAPP(c_Set_Oimage(_1466380, _1466382, _1466384), _1466388))))]]], (36354 ^ _780205) ^ [_1466721, _1466723, _1466725, _1466727, _1466729, _1466731] : [c_Fun_Oinj__on(_1466721, _1466723, _1466725, _1466727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466721, tc_HOL_Obool)), _1466729), _1466727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466721, tc_HOL_Obool)), _1466731), _1466727)), -(hAPP(c_Set_Oimage(_1466721, _1466723, _1466725), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466721, tc_HOL_Obool)), _1466729), _1466731)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466723, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466721, _1466723, _1466725), _1466729)), hAPP(c_Set_Oimage(_1466721, _1466723, _1466725), _1466731)))], (36368 ^ _780205) ^ [_1467056, _1467058, _1467060, _1467062, _1467064] : [c_Fun_Oinj__on(_1467056, _1467058, _1467060, c_Orderings_Otop__class_Otop(tc_fun(_1467056, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1467056, _1467058, _1467060), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467056, tc_HOL_Obool)), _1467062), _1467064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467058, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1467056, _1467058, _1467060), _1467062)), hAPP(c_Set_Oimage(_1467056, _1467058, _1467060), _1467064)))], (36374 ^ _780205) ^ [_1467239, _1467241, _1467243, _1467245] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467239), _1467241)), hAPP(c_Finite__Set_Ocard(_1467243), hAPP(c_Set_Oimage(_1467239, _1467243, _1467245), _1467241)) = hAPP(c_Finite__Set_Ocard(_1467239), _1467241), -(c_Fun_Oinj__on(_1467239, _1467243, _1467245, _1467241))], (36384 ^ _780205) ^ [_1467422, _1467424, _1467426, _1467428] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467422), _1467424)), 36387 ^ _780205 : [(36388 ^ _780205) ^ [] : [c_Fun_Oinj__on(_1467422, _1467426, _1467428, _1467424), -(hAPP(c_Finite__Set_Ocard(_1467426), hAPP(c_Set_Oimage(_1467422, _1467426, _1467428), _1467424)) = hAPP(c_Finite__Set_Ocard(_1467422), _1467424))], (36394 ^ _780205) ^ [] : [hAPP(c_Finite__Set_Ocard(_1467426), hAPP(c_Set_Oimage(_1467422, _1467426, _1467428), _1467424)) = hAPP(c_Finite__Set_Ocard(_1467422), _1467424), -(c_Fun_Oinj__on(_1467422, _1467426, _1467428, _1467424))]]], (36400 ^ _780205) ^ [_1467706, _1467708, _1467710, _1467712, _1467714, _1467716] : [c_Fun_Oinj__on(_1467706, _1467708, _1467710, _1467712), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467706, tc_HOL_Obool)), _1467714), _1467712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467706, tc_HOL_Obool)), _1467716), _1467712)), -(hAPP(c_Set_Oimage(_1467706, _1467708, _1467710), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467706, tc_HOL_Obool)), _1467714), _1467716)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467708, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1467706, _1467708, _1467710), _1467714)), hAPP(c_Set_Oimage(_1467706, _1467708, _1467710), _1467716)))], (36414 ^ _780205) ^ [_1468041, _1468043, _1468045, _1468047, _1468049] : [c_Fun_Oinj__on(_1468041, _1468043, _1468045, c_Orderings_Otop__class_Otop(tc_fun(_1468041, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1468041, _1468043, _1468045), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468041, tc_HOL_Obool)), _1468047), _1468049)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468043, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468041, _1468043, _1468045), _1468047)), hAPP(c_Set_Oimage(_1468041, _1468043, _1468045), _1468049)))], (36420 ^ _780205) ^ [_1468224, _1468226, _1468228, _1468230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1468224), hAPP(c_Set_Oimage(_1468226, _1468224, _1468228), _1468230))), hAPP(c_Finite__Set_Ocard(_1468226), _1468230))), c_Fun_Oinj__on(_1468226, _1468224, _1468228, _1468230)], (36426 ^ _780205) ^ [_1468354, _1468356, _1468358, _1468360] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468354), hAPP(c_Set_Ovimage(_1468354, _1468356, _1468358), _1468360))), hAPP(c_Set_Oimage(_1468354, _1468356, _1468358), c_Orderings_Otop__class_Otop(tc_fun(_1468354, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1468356, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1468356), _1468360)))], (36436 ^ _780205) ^ [_1468555, _1468557, _1468559] : [class_Orderings_Oord(_1468555), 36439 ^ _780205 : [(36440 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1468555), _1468557), hAPP(c_SetInterval_Oord__class_OatLeast(_1468555), _1468559))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1468555), _1468559), _1468557)))], (36446 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1468555), _1468559), _1468557)), -(hBOOL(hAPP(hAPP(c_member(_1468555), _1468557), hAPP(c_SetInterval_Oord__class_OatLeast(_1468555), _1468559))))]]], (36452 ^ _780205) ^ [_1468823, _1468825, _1468827, _1468829] : [hAPP(c_Set_Oimage(_1468823, _1468825, _1468827), c_Orderings_Otop__class_Otop(tc_fun(_1468823, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1468825, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468825, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468825, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468823, _1468825, _1468827), _1468829))), hAPP(c_Set_Oimage(_1468823, _1468825, _1468827), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1468823, tc_HOL_Obool)), _1468829)))))], (36458 ^ _780205) ^ [_1469018, _1469020, _1469022, _1469024, _1469026] : [hAPP(c_Set_Oimage(_1469018, _1469020, _1469022), c_Orderings_Otop__class_Otop(tc_fun(_1469018, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1469020, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469018, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1469018, _1469020, _1469022), _1469024)), _1469026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469020, tc_HOL_Obool)), _1469024), hAPP(c_Set_Oimage(_1469018, _1469020, _1469022), _1469026))))], (36468 ^ _780205) ^ [_1469261, _1469263, _1469265, _1469267] : [-(hAPP(c_Set_Oimage(_1469261, _1469263, _1469265), hAPP(c_Set_Ovimage(_1469261, _1469263, _1469265), _1469267)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469263, tc_HOL_Obool)), _1469267), hAPP(c_Set_Oimage(_1469261, _1469263, _1469265), c_Orderings_Otop__class_Otop(tc_fun(_1469261, tc_HOL_Obool)))))], (36470 ^ _780205) ^ [_1469327, _1469329, _1469331, _1469333] : [c_Fun_Oinj__on(_1469327, _1469329, _1469331, c_Orderings_Otop__class_Otop(tc_fun(_1469327, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1469327, _1469329, _1469331), hAPP(c_Set_Oimage(_1469327, _1469329, _1469331), _1469333)) = _1469333)], (36476 ^ _780205) ^ [_1469450, _1469452, _1469454] : [class_Orderings_Oorder(_1469450), 36479 ^ _780205 : [(36480 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469450, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1469450), _1469452)), hAPP(c_SetInterval_Oord__class_OatLeast(_1469450), _1469454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1469450), _1469454), _1469452)))], (36486 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1469450), _1469454), _1469452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469450, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1469450), _1469452)), hAPP(c_SetInterval_Oord__class_OatLeast(_1469450), _1469454))))]]], (36492 ^ _780205) ^ [] : [-(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)))], (36494 ^ _780205) ^ [_1469760, _1469762, _1469764] : [class_Groups_Oordered__ab__group__add(_1469760), -(hAPP(c_Set_Oimage(_1469760, _1469760, c_Groups_Ouminus__class_Ouminus(_1469760)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1469760, _1469762, _1469764)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1469760, hAPP(c_Groups_Ouminus__class_Ouminus(_1469760), _1469764)), hAPP(c_Groups_Ouminus__class_Ouminus(_1469760), _1469762)))], (36500 ^ _780205) ^ [_1469895, _1469897, _1469899] : [class_Groups_Oordered__ab__group__add(_1469895), -(hAPP(c_Set_Oimage(_1469895, _1469895, c_Groups_Ouminus__class_Ouminus(_1469895)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1469895, _1469897), _1469899)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1469895, hAPP(c_Groups_Ouminus__class_Ouminus(_1469895), _1469899), hAPP(c_Groups_Ouminus__class_Ouminus(_1469895), _1469897)))], (36506 ^ _780205) ^ [_1470030, _1470032, _1470034, _1470036, _1470038] : [hBOOL(hAPP(hAPP(c_member(_1470030), _1470032), _1470034)), -(hAPP(c_Set_Oimage(_1470030, _1470036, hAPP(c_COMBK(_1470036, _1470030), _1470038)), _1470034) = hAPP(hAPP(c_Set_Oinsert(_1470036), _1470038), c_Orderings_Obot__class_Obot(tc_fun(_1470036, tc_HOL_Obool))))], (36512 ^ _780205) ^ [_1470179, _1470181, _1470183, _1470185] : [-(hAPP(c_Set_Oimage(_1470179, _1470181, _1470183), _1470185) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470179, tc_fun(_1470181, tc_HOL_Obool)), _1470185), hAPP(hAPP(c_COMBC(_1470179, tc_fun(_1470181, tc_HOL_Obool), tc_fun(_1470181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1470181, tc_fun(tc_fun(_1470181, tc_HOL_Obool), tc_fun(_1470181, tc_HOL_Obool)), _1470179), c_Set_Oinsert(_1470181)), _1470183)), c_Orderings_Obot__class_Obot(tc_fun(_1470181, tc_HOL_Obool)))))], (36514 ^ _780205) ^ [_1470269, _1470271, _1470273] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1470269), _1470271), _1470273) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1470269), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1470269, tc_Int_Oint), _1470271), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1470273))), class_Groups_Ocomm__monoid__add(_1470269), class_Groups_Ocomm__monoid__mult(_1470269)], (36524 ^ _780205) ^ [_1470460, _1470462] : [class_Orderings_Olinorder(_1470460), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1470460, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1470460), _1470462)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1470460), _1470462))], (36530 ^ _780205) ^ [_1470571, _1470573] : [class_Orderings_Olinorder(_1470571), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1470571, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1470571), _1470573)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1470571), _1470573))], (36536 ^ _780205) ^ [_1470694] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1470694)), -(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)), _1470694))))], (36542 ^ _780205) ^ [_1470779] : [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)), _1470779))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1470779)))], (36548 ^ _780205) ^ [_1470870] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1470870) = 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)), _1470870)))], (36550 ^ _780205) ^ [] : [-(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))))], (36552 ^ _780205) ^ [_1470920, _1470922, _1470924, _1470926, _1470928, _1470930] : [c_Fun_Oinj__on(_1470920, _1470922, _1470924, _1470926), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470922, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470920, _1470922, _1470924), _1470926)), _1470928)), c_Fun_Oinj__on(_1470922, _1470920, _1470930, _1470928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470920, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470922, _1470920, _1470930), _1470928)), _1470926)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470920), _1470926)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470922), _1470928)), -(hAPP(c_Finite__Set_Ocard(_1470920), _1470926) = hAPP(c_Finite__Set_Ocard(_1470922), _1470928))], (36578 ^ _780205) ^ [_1471417, _1471419, _1471421, _1471423] : [c_Fun_Oinj__on(_1471417, _1471419, _1471421, c_Orderings_Otop__class_Otop(tc_fun(_1471417, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471419, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471417, _1471419, _1471421), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1471417, tc_HOL_Obool)), _1471423))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1471419, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471417, _1471419, _1471421), _1471423)))))], (36584 ^ _780205) ^ [_1471592, _1471594, _1471596, _1471598, _1471600] : [c_Fun_Oinj__on(_1471592, _1471594, _1471596, c_Orderings_Otop__class_Otop(tc_fun(_1471592, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471594, tc_HOL_Obool)), _1471598), hAPP(c_Set_Oimage(_1471592, _1471594, _1471596), _1471600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471592, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1471592, _1471594, _1471596), _1471598)), _1471600)))], (36594 ^ _780205) ^ [_1471815, _1471817, _1471819, _1471821] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1471815), _1471817)), -(hAPP(c_Set_Oimage(_1471815, _1471819, _1471821), _1471817) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1471819, tc_HOL_Obool), _1471815, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1471819, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1471815, tc_fun(_1471819, tc_HOL_Obool), tc_fun(_1471819, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1471819, tc_fun(tc_fun(_1471819, tc_HOL_Obool), tc_fun(_1471819, tc_HOL_Obool)), _1471815), c_Set_Oinsert(_1471819)), _1471821)), c_Orderings_Obot__class_Obot(tc_fun(_1471819, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1471819, tc_HOL_Obool))), _1471817))], (36600 ^ _780205) ^ [_1472054] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1472054)) = 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), _1472054))))], (36602 ^ _780205) ^ [_1472092, _1472094, _1472096] : [class_Orderings_Olinorder(_1472092), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1472092), _1472094), _1472096)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1472092, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1472092, _1472094), _1472096)), hAPP(c_SetInterval_Oord__class_OatLeast(_1472092), _1472096)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1472092), _1472094))], (36612 ^ _780205) ^ [_1472291, _1472293, _1472295] : [class_Orderings_Oorder(_1472291), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472291, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1472291, _1472293), _1472295)), hAPP(c_SetInterval_Oord__class_OatLeast(_1472291), _1472295)) = c_Orderings_Obot__class_Obot(tc_fun(_1472291, tc_HOL_Obool)))], (36618 ^ _780205) ^ [_1472422, _1472424, _1472426, _1472428] : [class_Orderings_Olinorder(_1472422), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472422, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1472422, _1472424, _1472426)), hAPP(c_SetInterval_Oord__class_OatLeast(_1472422), _1472428)) = c_SetInterval_Oord__class_OatLeastAtMost(_1472422, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1472422), _1472424), _1472428), _1472426))], (36624 ^ _780205) ^ [_1472565, _1472567, _1472569, _1472571] : [class_Orderings_Olinorder(_1472565), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472565, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1472565), _1472567)), c_SetInterval_Oord__class_OatLeastAtMost(_1472565, _1472569, _1472571)) = c_SetInterval_Oord__class_OatLeastAtMost(_1472565, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1472565), _1472567), _1472569), _1472571))], (36630 ^ _780205) ^ [_1472732, _1472734, _1472736, _1472738, _1472740] : [c_Fun_Oinj__on(_1472732, _1472734, _1472736, hAPP(hAPP(c_Set_Oinsert(_1472732), _1472738), _1472740)), 36633 ^ _780205 : [(36634 ^ _780205) ^ [] : [-(c_Fun_Oinj__on(_1472732, _1472734, _1472736, _1472740))], (36636 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1472734), hAPP(_1472736, _1472738)), hAPP(c_Set_Oimage(_1472732, _1472734, _1472736), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472732, tc_HOL_Obool)), _1472740), hAPP(hAPP(c_Set_Oinsert(_1472732), _1472738), c_Orderings_Obot__class_Obot(tc_fun(_1472732, tc_HOL_Obool)))))))]]], (36638 ^ _780205) ^ [_1472951, _1472953, _1472955, _1472957, _1472959] : [-(c_Fun_Oinj__on(_1472951, _1472953, _1472955, hAPP(hAPP(c_Set_Oinsert(_1472951), _1472957), _1472959))), c_Fun_Oinj__on(_1472951, _1472953, _1472955, _1472959), -(hBOOL(hAPP(hAPP(c_member(_1472953), hAPP(_1472955, _1472957)), hAPP(c_Set_Oimage(_1472951, _1472953, _1472955), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472951, tc_HOL_Obool)), _1472959), hAPP(hAPP(c_Set_Oinsert(_1472951), _1472957), c_Orderings_Obot__class_Obot(tc_fun(_1472951, tc_HOL_Obool))))))))], (36648 ^ _780205) ^ [] : [-(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)))], (36650 ^ _780205) ^ [_1473245, _1473247, _1473249, _1473251, _1473253] : [c_Fun_Oinj__on(_1473245, _1473247, _1473249, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473245, tc_HOL_Obool)), _1473251), _1473253)), 36653 ^ _780205 : [(36654 ^ _780205) ^ [] : [-(c_Fun_Oinj__on(_1473245, _1473247, _1473249, _1473251))], (36656 ^ _780205) ^ [] : [-(c_Fun_Oinj__on(_1473245, _1473247, _1473249, _1473253))], (36658 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473247, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1473245, _1473247, _1473249), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1473245, tc_HOL_Obool)), _1473251), _1473253))), hAPP(c_Set_Oimage(_1473245, _1473247, _1473249), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1473245, tc_HOL_Obool)), _1473253), _1473251))) = c_Orderings_Obot__class_Obot(tc_fun(_1473247, tc_HOL_Obool)))]]], (36660 ^ _780205) ^ [_1473512, _1473514, _1473516, _1473518, _1473520] : [-(c_Fun_Oinj__on(_1473512, _1473514, _1473516, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473512, tc_HOL_Obool)), _1473518), _1473520))), c_Fun_Oinj__on(_1473512, _1473514, _1473516, _1473518), c_Fun_Oinj__on(_1473512, _1473514, _1473516, _1473520), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473514, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1473512, _1473514, _1473516), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1473512, tc_HOL_Obool)), _1473518), _1473520))), hAPP(c_Set_Oimage(_1473512, _1473514, _1473516), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1473512, tc_HOL_Obool)), _1473520), _1473518))) = c_Orderings_Obot__class_Obot(tc_fun(_1473514, tc_HOL_Obool))], (36674 ^ _780205) ^ [_1473851, _1473853, _1473855] : [class_Orderings_Oorder(_1473851), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473851, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1473851, _1473853, _1473855)), hAPP(c_SetInterval_Oord__class_OatLeast(_1473851), _1473855)) = c_Orderings_Obot__class_Obot(tc_fun(_1473851, tc_HOL_Obool)))], (36680 ^ _780205) ^ [_1473978, _1473980, _1473982, _1473984, _1473986] : [c_Fun_Oinj__on(_1473978, _1473980, _1473982, _1473984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473980, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1473978, _1473980, _1473982), _1473984)), _1473986)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473980), _1473986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1473978), _1473984)), hAPP(c_Finite__Set_Ocard(_1473980), _1473986))))], (36694 ^ _780205) ^ [_1474253, _1474255, _1474257, _1474259] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1474253), _1474255)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474257), _1474259)), 36701 ^ _780205 : [(36712 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1474253), _1474255)), hAPP(c_Finite__Set_Ocard(_1474257), _1474259))), 36716 ^ _780205 : [(36717 ^ _780205) ^ [] : [-(c_Fun_Oinj__on(_1474253, _1474257, 36715 ^ [_1474253, _1474255, _1474257, _1474259], _1474255))], (36719 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474257, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1474253, _1474257, 36715 ^ [_1474253, _1474255, _1474257, _1474259]), _1474255)), _1474259)))]]], (36702 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1474253), _1474255)), hAPP(c_Finite__Set_Ocard(_1474257), _1474259)))), 36703 ^ _780205 : [(36704 ^ _780205) ^ [_1474464] : [c_Fun_Oinj__on(_1474253, _1474257, _1474464, _1474255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474257, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1474253, _1474257, _1474464), _1474255)), _1474259))]]]]], (36721 ^ _780205) ^ [_1474780] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1474780)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1474780)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1474780), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (36723 ^ _780205) ^ [_1474824, _1474826] : [class_Groups_Olinordered__ab__group__add(_1474824), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474824), _1474826)), -(_1474826 = c_Orderings_Obot__class_Obot(tc_fun(_1474824, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1474824), c_Big__Operators_Olinorder__class_OMin(_1474824, _1474826)) = c_Big__Operators_Olinorder__class_OMax(_1474824, hAPP(c_Set_Oimage(_1474824, _1474824, c_Groups_Ouminus__class_Ouminus(_1474824)), _1474826)))], (36737 ^ _780205) ^ [_1475024, _1475026] : [class_Groups_Olinordered__ab__group__add(_1475024), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475024), _1475026)), -(_1475026 = c_Orderings_Obot__class_Obot(tc_fun(_1475024, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1475024), c_Big__Operators_Olinorder__class_OMax(_1475024, _1475026)) = c_Big__Operators_Olinorder__class_OMin(_1475024, hAPP(c_Set_Oimage(_1475024, _1475024, c_Groups_Ouminus__class_Ouminus(_1475024)), _1475026)))], (36751 ^ _780205) ^ [_1475224, _1475226] : [c_Nat__Transfer_Ois__nat(_1475224), c_Nat__Transfer_Ois__nat(_1475226), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1475224, _1475226) = 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, _1475224), hAPP(c_Int_Onat, _1475226))))], (36761 ^ _780205) ^ [_1475383, _1475385, _1475387, _1475389, _1475391, _1475393, _1475395, _1475397] : [c_Fun_Oinj__on(_1475383, _1475385, _1475387, _1475389), 36767 ^ _780205 : [(36768 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475391), 36766 ^ [_1475383, _1475385, _1475387, _1475389, _1475391, _1475393, _1475395, _1475397]), _1475393)))], (36770 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475383, tc_HOL_Obool)), hAPP(_1475395, 36766 ^ [_1475383, _1475385, _1475387, _1475389, _1475391, _1475393, _1475395, _1475397])), _1475389))]], hBOOL(hAPP(hAPP(c_member(_1475391), _1475397), _1475393)), -(hAPP(c_Set_Oimage(_1475383, _1475385, _1475387), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1475391, tc_fun(_1475383, tc_HOL_Obool)), _1475393), _1475395)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1475391, tc_fun(_1475385, tc_HOL_Obool)), _1475393), hAPP(hAPP(c_COMBB(tc_fun(_1475383, tc_HOL_Obool), tc_fun(_1475385, tc_HOL_Obool), _1475391), c_Set_Oimage(_1475383, _1475385, _1475387)), _1475395)))], (36778 ^ _780205) ^ [_1475872, _1475874, _1475876] : [class_Orderings_Olinorder(_1475872), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1475872), _1475874), _1475876)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1475872, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1475872, _1475874, _1475876)), hAPP(c_SetInterval_Oord__class_OatLeast(_1475872), _1475876)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1475872), _1475874))], (36788 ^ _780205) ^ [_1476088, _1476090, _1476092, _1476094, _1476096, _1476098] : [hBOOL(hAPP(hAPP(c_member(_1476088), _1476090), _1476092)), -(hAPP(c_Set_Oimage(_1476088, _1476094, c_Fun_Ofun__upd(_1476088, _1476094, _1476096, _1476090, _1476098)), _1476092) = hAPP(hAPP(c_Set_Oinsert(_1476094), _1476098), hAPP(c_Set_Oimage(_1476088, _1476094, _1476096), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1476088, tc_HOL_Obool)), _1476092), hAPP(hAPP(c_Set_Oinsert(_1476088), _1476090), c_Orderings_Obot__class_Obot(tc_fun(_1476088, tc_HOL_Obool)))))))], (36794 ^ _780205) ^ [_1476285, _1476287, _1476289, _1476291, _1476293, _1476295] : [-(hBOOL(hAPP(hAPP(c_member(_1476285), _1476287), _1476289))), -(hAPP(c_Set_Oimage(_1476285, _1476291, c_Fun_Ofun__upd(_1476285, _1476291, _1476293, _1476287, _1476295)), _1476289) = hAPP(c_Set_Oimage(_1476285, _1476291, _1476293), _1476289))], (36800 ^ _780205) ^ [_1476358, _1476360, _1476362, _1476364] : [-(c_Fun_Ofun__upd(_1476358, _1476360, _1476362, _1476364, hAPP(_1476362, _1476364)) = _1476362)], (36802 ^ _780205) ^ [_1476396, _1476398, _1476400, _1476402, _1476404, _1476406, _1476408] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1476396, _1476398)), hAPP(hAPP(c_Product__Type_OPair(_1476396, _1476398), _1476400), _1476402)), _1476404)), -(hBOOL(hAPP(hAPP(c_member(_1476406), hAPP(hAPP(_1476408, _1476400), _1476402)), hAPP(c_Set_Oimage(tc_prod(_1476396, _1476398), _1476406, hAPP(c_Product__Type_Oprod_Oprod__case(_1476396, _1476398, _1476406), _1476408)), _1476404))))], (36808 ^ _780205) ^ [_1476581] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1476581)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1476581))], (36810 ^ _780205) ^ [_1476629, _1476631, _1476633] : [hAPP(c_Set_Oimage(_1476631, tc_fun(_1476631, tc_HOL_Obool), _1476629), _1476633) = hAPP(c_Set_OPow(_1476631), _1476633)], (36812 ^ _780205) ^ [_1476671, _1476673, _1476675, _1476677, _1476679] : [hAPP(_1476671, _1476673) = _1476675, -(c_Fun_Ofun__upd(_1476677, _1476679, _1476671, _1476673, _1476675) = _1476671)], (36818 ^ _780205) ^ [_1476768, _1476770, _1476772, _1476774, _1476776, _1476778] : [-(_1476768 = _1476770), -(hAPP(c_Fun_Ofun__upd(_1476772, _1476774, _1476776, _1476770, _1476778), _1476768) = hAPP(_1476776, _1476768))], (36824 ^ _780205) ^ [_1476820, _1476822, _1476824, _1476826, _1476828, _1476830, _1476832] : [-(_1476820 = _1476822), -(c_Fun_Ofun__upd(_1476824, _1476826, c_Fun_Ofun__upd(_1476824, _1476826, _1476828, _1476820, _1476830), _1476822, _1476832) = c_Fun_Ofun__upd(_1476824, _1476826, c_Fun_Ofun__upd(_1476824, _1476826, _1476828, _1476822, _1476832), _1476820, _1476830))], (36830 ^ _780205) ^ [_1476911, _1476913, _1476915, _1476917, _1476919, _1476921] : [_1476911 = _1476913, -(hAPP(c_Fun_Ofun__upd(_1476915, _1476917, _1476919, _1476913, _1476921), _1476911) = _1476921)], (36836 ^ _780205) ^ [_1477008, _1477010, _1477012, _1477014, _1477016, _1477018] : [-(_1477008 = _1477010), -(hAPP(c_Fun_Ofun__upd(_1477012, _1477014, _1477016, _1477010, _1477018), _1477008) = hAPP(_1477016, _1477008))], (36842 ^ _780205) ^ [_1477066, _1477068, _1477070, _1477072, _1477074] : [-(hAPP(c_Fun_Ofun__upd(_1477066, _1477068, _1477070, _1477072, _1477074), _1477072) = _1477074)], (36844 ^ _780205) ^ [_1477106, _1477108, _1477110, _1477112, _1477114, _1477116] : [-(c_Fun_Ofun__upd(_1477106, _1477108, c_Fun_Ofun__upd(_1477106, _1477108, _1477110, _1477112, _1477114), _1477112, _1477116) = c_Fun_Ofun__upd(_1477106, _1477108, _1477110, _1477112, _1477116))], (36846 ^ _780205) ^ [_1477181, _1477183, _1477185, _1477187, _1477189] : [c_Fun_Ofun__upd(_1477181, _1477183, _1477185, _1477187, _1477189) = _1477185, -(hAPP(_1477185, _1477187) = _1477189)], (36852 ^ _780205) ^ [_1477278, _1477280, _1477282, _1477284, _1477286] : [hAPP(_1477282, _1477284) = _1477286, -(c_Fun_Ofun__upd(_1477278, _1477280, _1477282, _1477284, _1477286) = _1477282)], (36858 ^ _780205) ^ [_1477402, _1477404, _1477406, _1477408, _1477410, _1477412] : [_1477402 = _1477404, -(hAPP(c_Fun_Ofun__upd(_1477406, _1477408, _1477410, _1477404, _1477412), _1477402) = _1477412)], (36864 ^ _780205) ^ [_1477499, _1477501, _1477503, _1477505, _1477507, _1477509] : [-(_1477499 = _1477501), -(hAPP(c_Fun_Ofun__upd(_1477503, _1477505, _1477507, _1477501, _1477509), _1477499) = hAPP(_1477507, _1477499))], (36870 ^ _780205) ^ [_1477557, _1477559, _1477561] : [class_Orderings_Olinorder(_1477557), 36873 ^ _780205 : [(36874 ^ _780205) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1477557), _1477559) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1477557), _1477561), -(_1477559 = _1477561)], (36880 ^ _780205) ^ [] : [_1477559 = _1477561, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1477557), _1477559) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1477557), _1477561))]]], (36886 ^ _780205) ^ [_1477798, _1477800] : [-(hAPP(c_Relation_OField(_1477798), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1477798, _1477798), tc_HOL_Obool), _1477800)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1477798, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1477798, _1477798), tc_HOL_Obool), tc_fun(_1477798, tc_HOL_Obool), c_Relation_OField(_1477798)), _1477800)))], (36888 ^ _780205) ^ [_1477861, _1477863, _1477865, _1477867] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477861, tc_fun(_1477863, tc_HOL_Obool)), _1477865), _1477867) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1477863, tc_HOL_Obool), hAPP(c_Set_Oimage(_1477861, tc_fun(_1477863, tc_HOL_Obool), _1477867), _1477865)))], (36890 ^ _780205) ^ [_1477918, _1477920, _1477922, _1477924] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1477918, tc_HOL_Obool), hAPP(c_Set_Oimage(_1477920, tc_fun(_1477918, tc_HOL_Obool), _1477922), _1477924)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477920, tc_fun(_1477918, tc_HOL_Obool)), _1477924), _1477922))], (36892 ^ _780205) ^ [_1477975, _1477977, _1477979, _1477981] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1477975, tc_HOL_Obool), hAPP(c_Set_Oimage(_1477977, tc_fun(_1477975, tc_HOL_Obool), _1477979), _1477981)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477977, tc_fun(_1477975, tc_HOL_Obool)), _1477981), _1477979))], (36894 ^ _780205) ^ [_1478032, _1478034, _1478036, _1478038] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1478032, tc_fun(_1478034, tc_HOL_Obool)), _1478036), _1478038) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478034, tc_HOL_Obool), hAPP(c_Set_Oimage(_1478032, tc_fun(_1478034, tc_HOL_Obool), _1478038), _1478036)))], (36896 ^ _780205) ^ [_1478089, _1478091] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1478089), _1478091) = 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)), _1478089)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1478091))))], (36898 ^ _780205) ^ [_1478135] : [-(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)), _1478135)) = _1478135)], (36900 ^ _780205) ^ [_1478164, _1478166, _1478168] : [class_Orderings_Oord(_1478164), 36903 ^ _780205 : [(36904 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1478164), _1478166), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1478164), _1478168))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1478164), _1478168), _1478166)))], (36910 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1478164), _1478168), _1478166)), -(hBOOL(hAPP(hAPP(c_member(_1478164), _1478166), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1478164), _1478168))))]]], (36916 ^ _780205) ^ [_1478432, _1478434, _1478436] : [class_Orderings_Olinorder(_1478432), 36919 ^ _780205 : [(36920 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478432, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1478432), _1478434)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1478432), _1478436))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1478432), _1478436), _1478434)))], (36926 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1478432), _1478436), _1478434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478432, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1478432), _1478434)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1478432), _1478436))))]]], (36932 ^ _780205) ^ [_1478724, _1478726, _1478728, _1478730, _1478732] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478724, tc_fun(_1478726, tc_HOL_Obool)), _1478728), hAPP(hAPP(c_COMBS(_1478724, tc_fun(_1478726, tc_HOL_Obool), tc_fun(_1478726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478726, tc_HOL_Obool), tc_fun(tc_fun(_1478726, tc_HOL_Obool), tc_fun(_1478726, tc_HOL_Obool)), _1478724), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478726, tc_HOL_Obool))), _1478730)), _1478732)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478726, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1478726, tc_HOL_Obool), hAPP(c_Set_Oimage(_1478724, tc_fun(_1478726, tc_HOL_Obool), _1478730), _1478728))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1478726, tc_HOL_Obool), hAPP(c_Set_Oimage(_1478724, tc_fun(_1478726, tc_HOL_Obool), _1478732), _1478728))))], (36934 ^ _780205) ^ [_1478853, _1478855, _1478857, _1478859, _1478861] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1478853, tc_fun(_1478855, tc_HOL_Obool)), _1478857), hAPP(hAPP(c_COMBS(_1478853, tc_fun(_1478855, tc_HOL_Obool), tc_fun(_1478855, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478855, tc_HOL_Obool), tc_fun(tc_fun(_1478855, tc_HOL_Obool), tc_fun(_1478855, tc_HOL_Obool)), _1478853), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478855, tc_HOL_Obool))), _1478859)), _1478861)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478855, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478855, tc_HOL_Obool), hAPP(c_Set_Oimage(_1478853, tc_fun(_1478855, tc_HOL_Obool), _1478859), _1478857))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478855, tc_HOL_Obool), hAPP(c_Set_Oimage(_1478853, tc_fun(_1478855, tc_HOL_Obool), _1478861), _1478857))))], (36936 ^ _780205) ^ [_1478982, _1478984, _1478986] : [-(hAPP(c_Set_OPow(_1478982), hAPP(hAPP(c_Set_Oinsert(_1478982), _1478984), _1478986)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1478982, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1478982), _1478986)), hAPP(c_Set_Oimage(tc_fun(_1478982, tc_HOL_Obool), tc_fun(_1478982, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1478982), _1478984)), hAPP(c_Set_OPow(_1478982), _1478986))))], (36938 ^ _780205) ^ [_1479064, _1479066] : [class_Orderings_Olinorder(_1479064), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1479064, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1479064), _1479066)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1479064), _1479066))], (36944 ^ _780205) ^ [_1479175, _1479177] : [class_Orderings_Olinorder(_1479175), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1479175, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1479175), _1479177)) = hAPP(c_SetInterval_Oord__class_OatMost(_1479175), _1479177))], (36950 ^ _780205) ^ [] : [-(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))))], (36952 ^ _780205) ^ [] : [-(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)))], (36954 ^ _780205) ^ [_1479322, _1479324, _1479326, _1479328, _1479330, _1479332] : [c_Fun_Oinj__on(_1479322, _1479324, _1479326, _1479328), -(hBOOL(hAPP(hAPP(c_member(_1479324), _1479330), hAPP(c_Set_Oimage(_1479322, _1479324, _1479326), _1479328)))), -(c_Fun_Oinj__on(_1479322, _1479324, c_Fun_Ofun__upd(_1479322, _1479324, _1479326, _1479332, _1479330), _1479328))], (36964 ^ _780205) ^ [_1479470, _1479472] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1479470, _1479472) = 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), _1479470), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1479472))))], (36966 ^ _780205) ^ [_1479512, _1479514] : [-(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)), _1479512)), 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), _1479514), _1479512))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1479512), _1479514))], (36968 ^ _780205) ^ [_1479562, _1479564] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1479562), _1479564) = 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)), _1479562)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1479564))))], (36970 ^ _780205) ^ [_1479608, _1479610, _1479612] : [class_Orderings_Oorder(_1479608), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479608, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1479608, _1479610, _1479612)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1479608), _1479612)) = c_Orderings_Obot__class_Obot(tc_fun(_1479608, tc_HOL_Obool)))], (36976 ^ _780205) ^ [_1479735, _1479737, _1479739] : [class_Orderings_Olinorder(_1479735), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1479735), _1479737), _1479739)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1479735, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1479735, _1479737, _1479739)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1479735), _1479739)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1479735), _1479737))], (36986 ^ _780205) ^ [_1479930, _1479932] : [class_Groups_Oordered__ab__group__add(_1479930), -(hAPP(c_Set_Oimage(_1479930, _1479930, c_Groups_Ouminus__class_Ouminus(_1479930)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1479930), _1479932)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1479930), hAPP(c_Groups_Ouminus__class_Ouminus(_1479930), _1479932)))], (36992 ^ _780205) ^ [_1480053, _1480055] : [class_Groups_Oordered__ab__group__add(_1480053), -(hAPP(c_Set_Oimage(_1480053, _1480053, c_Groups_Ouminus__class_Ouminus(_1480053)), hAPP(c_SetInterval_Oord__class_OlessThan(_1480053), _1480055)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1480053), hAPP(c_Groups_Ouminus__class_Ouminus(_1480053), _1480055)))], (36998 ^ _780205) ^ [_1480176, _1480178, _1480180] : [class_Orderings_Oorder(_1480176), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1480176, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1480176, _1480178, _1480180)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1480176), _1480180)) = c_Orderings_Obot__class_Obot(tc_fun(_1480176, tc_HOL_Obool)))], (37004 ^ _780205) ^ [_1480303] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1480303)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1480303)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1480303)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (37006 ^ _780205) ^ [_1480350] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1480350) = 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), _1480350))))], (37008 ^ _780205) ^ [_1480386, _1480388] : [class_Orderings_Olinorder(_1480386), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480386, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1480386), _1480388), c_Orderings_Obot__class_Obot(tc_fun(_1480386, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1480386), _1480388)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1480386), _1480388))], (37014 ^ _780205) ^ [] : [-(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))))], (37016 ^ _780205) ^ [_1480547, _1480549, _1480551] : [class_Orderings_Olinorder(_1480547), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1480547), _1480549), _1480551)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480547, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1480547, _1480549, _1480551)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1480547), _1480551)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1480547), _1480549))], (37026 ^ _780205) ^ [_1480742, _1480744, _1480746] : [class_Groups_Ocomm__monoid__add(_1480742), class_Groups_Ocomm__monoid__mult(_1480742), c_Nat__Transfer_Onat__set(_1480744), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1480742), _1480746), _1480744) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1480742), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1480742, tc_Nat_Onat), _1480746), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1480744)))], (37040 ^ _780205) ^ [_1480987, _1480989, _1480991, _1480993, _1480995, _1480997, _1480999, _1481001, _1481003] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1480987), _1480989)), 37046 ^ _780205 : [(37047 ^ _780205) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1480991, _1480993, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1480991)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1480991), hAPP(_1480995, 37045 ^ [_1480987, _1480989, _1480991, _1480993, _1480995, _1480997, _1480999, _1481001, _1481003])), hAPP(_1480997, 37045 ^ [_1480987, _1480989, _1480991, _1480993, _1480995, _1480997, _1480999, _1481001, _1481003])), hAPP(_1480999, 37045 ^ [_1480987, _1480989, _1480991, _1480993, _1480995, _1480997, _1480999, _1481001, _1481003]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1480991), tc_HOL_Obool)))))], (37049 ^ _780205) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1480991, _1480993, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1480991)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1480991), hAPP(_1481001, 37045 ^ [_1480987, _1480989, _1480991, _1480993, _1480995, _1480997, _1480999, _1481001, _1481003])), hAPP(_1480997, 37045 ^ [_1480987, _1480989, _1480991, _1480993, _1480995, _1480997, _1480999, _1481001, _1481003])), hAPP(_1481003, 37045 ^ [_1480987, _1480989, _1480991, _1480993, _1480995, _1480997, _1480999, _1481001, _1481003]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1480991), tc_HOL_Obool))))]], c_Hoare__Mirabelle_Ohoare__derivs(_1480991, _1480993, hAPP(c_Set_Oimage(_1480987, tc_Hoare__Mirabelle_Otriple(_1480991), hAPP(hAPP(c_COMBS(_1480987, tc_fun(_1480991, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1480991)), hAPP(hAPP(c_COMBS(_1480987, tc_Com_Ocom, tc_fun(tc_fun(_1480991, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1480991))), hAPP(hAPP(c_COMBB(tc_fun(_1480991, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1480991, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1480991))), _1480987), c_Hoare__Mirabelle_Otriple_Otriple(_1480991)), _1480995)), _1480997)), _1480999)), _1480989)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1480991, _1480993, hAPP(c_Set_Oimage(_1480987, tc_Hoare__Mirabelle_Otriple(_1480991), hAPP(hAPP(c_COMBS(_1480987, tc_fun(_1480991, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1480991)), hAPP(hAPP(c_COMBS(_1480987, tc_Com_Ocom, tc_fun(tc_fun(_1480991, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1480991))), hAPP(hAPP(c_COMBB(tc_fun(_1480991, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1480991, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1480991))), _1480987), c_Hoare__Mirabelle_Otriple_Otriple(_1480991)), _1481001)), _1480997)), _1481003)), _1480989)))], (37057 ^ _780205) ^ [_1481876, _1481878, _1481880, _1481882, _1481884, _1481886] : [c_Fun_Oinj__on(_1481876, _1481878, _1481880, _1481882), hBOOL(hAPP(hAPP(c_member(_1481878), _1481884), hAPP(c_Set_Oimage(_1481876, _1481878, _1481880), _1481882))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481876, tc_HOL_Obool)), _1481882), _1481886)), -(hBOOL(hAPP(hAPP(c_member(_1481876), hAPP(c_Fun_Othe__inv__into(_1481876, _1481878, _1481882, _1481880), _1481884)), _1481886)))], (37071 ^ _780205) ^ [_1482163, _1482165] : [c_Nat__Transfer_Onat__set(_1482163), c_Nat__Transfer_Onat__set(_1482165), 37078 ^ _780205 : [(37079 ^ _780205) ^ [] : [_1482163 = _1482165, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1482163) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1482165))], (37085 ^ _780205) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1482163) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1482165), -(_1482163 = _1482165)]]], (37091 ^ _780205) ^ [_1482436, _1482438] : [c_Nat__Transfer_Onat__set(_1482436), c_Nat__Transfer_Onat__set(_1482438), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1482436), _1482438)))], (37101 ^ _780205) ^ [_1482571, _1482573] : [c_Nat__Transfer_Onat__set(_1482571), c_Nat__Transfer_Onat__set(_1482573), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1482571), _1482573)))], (37111 ^ _780205) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (37123 ^ _780205) ^ [_1482893] : [37125 ^ _780205 : [(37126 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 37124 ^ [_1482893]), _1482893)))], (37128 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37124 ^ [_1482893]))]], -(c_Nat__Transfer_Onat__set(_1482893))], (37113 ^ _780205) ^ [_1482736] : [c_Nat__Transfer_Onat__set(_1482736), 37116 ^ _780205 : [(37117 ^ _780205) ^ [_1482802] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1482802), _1482736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482802)))]]], (37132 ^ _780205) ^ [_1483041] : [-(c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1483041)))], (37134 ^ _780205) ^ [_1483066, _1483068] : [c_Nat__Transfer_Ois__nat(_1483066), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1483066, _1483068)))], (37140 ^ _780205) ^ [_1483147, _1483149] : [c_Nat__Transfer_Onat__set(_1483147), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1483149), _1483147)), -(c_Nat__Transfer_Ois__nat(_1483149))], (37150 ^ _780205) ^ [_1483282, _1483284, _1483286, _1483288, _1483290, _1483292] : [c_Fun_Oinj__on(_1483282, _1483284, _1483286, _1483288), hAPP(_1483286, _1483290) = _1483292, hBOOL(hAPP(hAPP(c_member(_1483282), _1483290), _1483288)), -(hAPP(c_Fun_Othe__inv__into(_1483282, _1483284, _1483288, _1483286), _1483292) = _1483290)], (37164 ^ _780205) ^ [_1483527, _1483529, _1483531, _1483533, _1483535] : [c_Fun_Oinj__on(_1483527, _1483529, _1483531, _1483533), hBOOL(hAPP(hAPP(c_member(_1483527), _1483535), _1483533)), -(hAPP(c_Fun_Othe__inv__into(_1483527, _1483529, _1483533, _1483531), hAPP(_1483531, _1483535)) = _1483535)], (37174 ^ _780205) ^ [_1483708, _1483710, _1483712, _1483714] : [c_Fun_Oinj__on(_1483708, _1483710, _1483712, _1483714), -(c_Fun_Oinj__on(_1483710, _1483708, c_Fun_Othe__inv__into(_1483708, _1483710, _1483714, _1483712), hAPP(c_Set_Oimage(_1483708, _1483710, _1483712), _1483714)))], (37180 ^ _780205) ^ [_1483821, _1483823, _1483825, _1483827] : [c_Fun_Oinj__on(_1483821, _1483823, _1483825, _1483827), -(hAPP(c_Set_Oimage(_1483823, _1483821, c_Fun_Othe__inv__into(_1483821, _1483823, _1483827, _1483825)), hAPP(c_Set_Oimage(_1483821, _1483823, _1483825), _1483827)) = _1483827)], (37186 ^ _780205) ^ [_1483944, _1483946, _1483948, _1483950] : [c_Fun_Oinj__on(_1483944, _1483946, _1483948, c_Orderings_Otop__class_Otop(tc_fun(_1483944, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1483944, _1483946, c_Orderings_Otop__class_Otop(tc_fun(_1483944, tc_HOL_Obool)), _1483948), hAPP(_1483948, _1483950)) = _1483950)], (37192 ^ _780205) ^ [_1484071, _1484073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484071)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1484071, _1484073)))], (37198 ^ _780205) ^ [_1484158, _1484160, _1484162, _1484164, _1484166] : [-(hAPP(c_Fun_Othe__inv__into(_1484158, _1484160, _1484162, _1484164), _1484166) = c_HOL_OThe(_1484158, hAPP(hAPP(c_COMBS(_1484158, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1484158), c_fconj), hAPP(hAPP(c_COMBC(_1484158, tc_fun(_1484158, tc_HOL_Obool), tc_HOL_Obool), c_member(_1484158)), _1484162))), hAPP(hAPP(c_COMBC(_1484158, _1484160, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1484160, tc_fun(_1484160, tc_HOL_Obool), _1484158), c_fequal), _1484164)), _1484166))))], (37200 ^ _780205) ^ [_1484258, _1484260] : [c_Nat__Transfer_Onat__set(_1484258), c_Nat__Transfer_Onat__set(_1484260), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1484258), _1484260) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1484258)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1484260))))], (37210 ^ _780205) ^ [_1484425] : [c_Nat__Transfer_Onat__set(_1484425), -(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), _1484425)) = _1484425)], (37216 ^ _780205) ^ [_1484510, _1484512] : [c_Nat__Transfer_Onat__set(_1484510), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1484512), _1484510)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484512)))], (37226 ^ _780205) ^ [_1484651] : [c_Nat__Transfer_Onat__set(_1484651), 37229 ^ _780205 : [(37230 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1484651)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1484651))))], (37236 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1484651))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1484651)))]]], (37242 ^ _780205) ^ [_1484871] : [c_Nat__Transfer_Onat__set(_1484871), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1484871) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1484871)))], (37248 ^ _780205) ^ [_1484962, _1484964, _1484966, _1484968, _1484970] : [c_Fun_Oinj__on(_1484962, _1484964, _1484966, _1484968), hBOOL(hAPP(hAPP(c_member(_1484964), _1484970), hAPP(c_Set_Oimage(_1484962, _1484964, _1484966), _1484968))), -(hAPP(_1484966, hAPP(c_Fun_Othe__inv__into(_1484962, _1484964, _1484968, _1484966), _1484970)) = _1484970)], (37258 ^ _780205) ^ [_1485157, _1485159] : [c_Nat__Transfer_Ois__nat(_1485157), c_Nat__Transfer_Onat__set(_1485159), 37265 ^ _780205 : [(37266 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1485157), _1485159)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1485157)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1485159))))], (37272 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1485157)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1485159))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1485157), _1485159)))]]], (37278 ^ _780205) ^ [_1485460, _1485462] : [c_Nat__Transfer_Onat__set(_1485460), c_Nat__Transfer_Onat__set(_1485462), 37285 ^ _780205 : [(37286 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1485460), _1485462)), -(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), _1485460)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1485462))))], (37292 ^ _780205) ^ [] : [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), _1485460)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1485462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1485460), _1485462)))]]], (37298 ^ _780205) ^ [_1485763, _1485765] : [c_Nat__Transfer_Onat__set(_1485763), c_Nat__Transfer_Onat__set(_1485765), 37305 ^ _780205 : [(37306 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1485763), _1485765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1485763)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1485765))))], (37312 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1485763)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1485765))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1485763), _1485765)))]]], (37318 ^ _780205) ^ [_1486066, _1486068, _1486070] : [class_Groups_Ocomm__monoid__add(_1486066), class_Groups_Ocomm__monoid__mult(_1486066), c_Nat__Transfer_Onat__set(_1486068), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1486066), _1486070), _1486068) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1486066), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1486066, tc_Nat_Onat), _1486070), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1486068)))], (37332 ^ _780205) ^ [_1486311, _1486313] : [c_Nat__Transfer_Onat__set(_1486311), c_Nat__Transfer_Onat__set(_1486313), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1486311), _1486313) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1486311)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1486313))))], (37342 ^ _780205) ^ [_1486478, _1486480, _1486482] : [class_Orderings_Olinorder(_1486478), hAPP(_1486480, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1486478), 37347 ^ [_1486478, _1486480, _1486482]), 37348 ^ [_1486478, _1486480, _1486482])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1486478), hAPP(_1486480, 37347 ^ [_1486478, _1486480, _1486482])), hAPP(_1486480, 37348 ^ [_1486478, _1486480, _1486482])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1486478), _1486482)), -(_1486482 = c_Orderings_Obot__class_Obot(tc_fun(_1486478, tc_HOL_Obool))), -(hAPP(_1486480, c_Big__Operators_Olattice_OSup__fin(_1486478, c_Orderings_Oord__class_Omax(_1486478), _1486482)) = c_Big__Operators_Olattice_OSup__fin(_1486478, c_Orderings_Oord__class_Omax(_1486478), hAPP(c_Set_Oimage(_1486478, _1486478, _1486480), _1486482)))], (37362 ^ _780205) ^ [_1486893, _1486895, _1486897] : [class_Orderings_Olinorder(_1486893), hAPP(_1486895, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1486893), 37367 ^ [_1486893, _1486895, _1486897]), 37368 ^ [_1486893, _1486895, _1486897])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1486893), hAPP(_1486895, 37367 ^ [_1486893, _1486895, _1486897])), hAPP(_1486895, 37368 ^ [_1486893, _1486895, _1486897])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1486893), _1486897)), -(_1486897 = c_Orderings_Obot__class_Obot(tc_fun(_1486893, tc_HOL_Obool))), -(hAPP(_1486895, c_Big__Operators_Olattice_OInf__fin(_1486893, c_Orderings_Oord__class_Omin(_1486893), _1486897)) = c_Big__Operators_Olattice_OInf__fin(_1486893, c_Orderings_Oord__class_Omin(_1486893), hAPP(c_Set_Oimage(_1486893, _1486893, _1486895), _1486897)))], (37382 ^ _780205) ^ [_1487308, _1487310, _1487312] : [class_Orderings_Olinorder(_1487308), hAPP(_1487310, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1487308), 37387 ^ [_1487308, _1487310, _1487312]), 37388 ^ [_1487308, _1487310, _1487312])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1487308), hAPP(_1487310, 37387 ^ [_1487308, _1487310, _1487312])), hAPP(_1487310, 37388 ^ [_1487308, _1487310, _1487312])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487308), _1487312)), -(_1487312 = c_Orderings_Obot__class_Obot(tc_fun(_1487308, tc_HOL_Obool))), -(hAPP(_1487310, c_Big__Operators_Olinorder__class_OMax(_1487308, _1487312)) = c_Big__Operators_Olinorder__class_OMax(_1487308, hAPP(c_Set_Oimage(_1487308, _1487308, _1487310), _1487312)))], (37402 ^ _780205) ^ [_1487711, _1487713, _1487715] : [class_Orderings_Olinorder(_1487711), hAPP(_1487713, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1487711), 37407 ^ [_1487711, _1487713, _1487715]), 37408 ^ [_1487711, _1487713, _1487715])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1487711), hAPP(_1487713, 37407 ^ [_1487711, _1487713, _1487715])), hAPP(_1487713, 37408 ^ [_1487711, _1487713, _1487715])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487711), _1487715)), -(_1487715 = c_Orderings_Obot__class_Obot(tc_fun(_1487711, tc_HOL_Obool))), -(hAPP(_1487713, c_Big__Operators_Olinorder__class_OMin(_1487711, _1487715)) = c_Big__Operators_Olinorder__class_OMin(_1487711, hAPP(c_Set_Oimage(_1487711, _1487711, _1487713), _1487715)))], (37422 ^ _780205) ^ [_1488114, _1488116, _1488118] : [class_Lattices_Olattice(_1488114), hAPP(_1488116, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1488114), 37427 ^ [_1488114, _1488116, _1488118]), 37428 ^ [_1488114, _1488116, _1488118])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1488114), hAPP(_1488116, 37427 ^ [_1488114, _1488116, _1488118])), hAPP(_1488116, 37428 ^ [_1488114, _1488116, _1488118])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488114), _1488118)), -(_1488118 = c_Orderings_Obot__class_Obot(tc_fun(_1488114, tc_HOL_Obool))), -(hAPP(_1488116, c_Big__Operators_Olattice__class_OInf__fin(_1488114, _1488118)) = c_Big__Operators_Olattice__class_OInf__fin(_1488114, hAPP(c_Set_Oimage(_1488114, _1488114, _1488116), _1488118)))], (37442 ^ _780205) ^ [_1488517, _1488519, _1488521] : [class_Lattices_Olattice(_1488517), hAPP(_1488519, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1488517), 37447 ^ [_1488517, _1488519, _1488521]), 37448 ^ [_1488517, _1488519, _1488521])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1488517), hAPP(_1488519, 37447 ^ [_1488517, _1488519, _1488521])), hAPP(_1488519, 37448 ^ [_1488517, _1488519, _1488521])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488517), _1488521)), -(_1488521 = c_Orderings_Obot__class_Obot(tc_fun(_1488517, tc_HOL_Obool))), -(hAPP(_1488519, c_Big__Operators_Olattice__class_OSup__fin(_1488517, _1488521)) = c_Big__Operators_Olattice__class_OSup__fin(_1488517, hAPP(c_Set_Oimage(_1488517, _1488517, _1488519), _1488521)))], (37462 ^ _780205) ^ [_1488920, _1488922, _1488924] : [class_Lattices_Oab__semigroup__idem__mult(_1488920), hAPP(_1488922, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1488920), 37467 ^ [_1488920, _1488922, _1488924]), 37468 ^ [_1488920, _1488922, _1488924])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1488920), hAPP(_1488922, 37467 ^ [_1488920, _1488922, _1488924])), hAPP(_1488922, 37468 ^ [_1488920, _1488922, _1488924])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488920), _1488924)), -(_1488924 = c_Orderings_Obot__class_Obot(tc_fun(_1488920, tc_HOL_Obool))), -(hAPP(_1488922, hAPP(c_Finite__Set_Ofold1(_1488920, c_Groups_Otimes__class_Otimes(_1488920)), _1488924)) = hAPP(c_Finite__Set_Ofold1(_1488920, c_Groups_Otimes__class_Otimes(_1488920)), hAPP(c_Set_Oimage(_1488920, _1488920, _1488922), _1488924)))], (37482 ^ _780205) ^ [_1489343, _1489345, _1489347, _1489349, _1489351] : [37485 ^ _780205 : [(37486 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1489343, 37483 ^ [_1489343, _1489345, _1489347, _1489349, _1489351]), 37484 ^ [_1489343, _1489345, _1489347, _1489349, _1489351])))], (37488 ^ _780205) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1489345, _1489347, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1489345)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1489345), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1489345), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 37484 ^ [_1489343, _1489345, _1489347, _1489349, _1489351]))), _1489349), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1489345), hAPP(_1489351, 37483 ^ [_1489343, _1489345, _1489347, _1489349, _1489351])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1489345), tc_HOL_Obool))))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1489345, _1489347, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1489345)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1489345), _1489343), _1489349), _1489351)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1489345), tc_HOL_Obool)))))], (37492 ^ _780205) ^ [_1489765, _1489767, _1489769, _1489771, _1489773] : [class_Groups_Ocomm__monoid__add(_1489765), class_Groups_Ocomm__monoid__mult(_1489765), _1489767 = _1489769, c_Nat__Transfer_Onat__set(_1489769), 37510 ^ _780205 : [(37511 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37509 ^ [_1489765, _1489767, _1489769, _1489771, _1489773])))], (37513 ^ _780205) ^ [] : [hAPP(_1489771, 37509 ^ [_1489765, _1489767, _1489769, _1489771, _1489773]) = hAPP(_1489773, 37509 ^ [_1489765, _1489767, _1489769, _1489771, _1489773])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1489765), _1489771), _1489767) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1489765), _1489773), _1489769))], (37517 ^ _780205) ^ [_1490228, _1490230, _1490232, _1490234, _1490236] : [class_Groups_Ocomm__monoid__add(_1490228), class_Groups_Ocomm__monoid__mult(_1490228), _1490230 = _1490232, c_Nat__Transfer_Onat__set(_1490232), 37535 ^ _780205 : [(37536 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37534 ^ [_1490228, _1490230, _1490232, _1490234, _1490236])))], (37538 ^ _780205) ^ [] : [hAPP(_1490234, 37534 ^ [_1490228, _1490230, _1490232, _1490234, _1490236]) = hAPP(_1490236, 37534 ^ [_1490228, _1490230, _1490232, _1490234, _1490236])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1490228), _1490234), _1490230) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1490228), _1490236), _1490232))], (37542 ^ _780205) ^ [_1490709, _1490711, _1490713] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1490709, hAPP(hAPP(c_COMBC(_1490709, tc_fun(tc_prod(_1490709, _1490709), tc_HOL_Obool), tc_fun(_1490709, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490709, tc_fun(tc_fun(tc_prod(_1490709, _1490709), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1490709, _1490709), tc_HOL_Obool), tc_fun(_1490709, tc_HOL_Obool)), _1490709), c_COMBC(_1490709, tc_fun(tc_prod(_1490709, _1490709), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490709, tc_prod(_1490709, _1490709)), tc_fun(_1490709, tc_fun(tc_fun(tc_prod(_1490709, _1490709), tc_HOL_Obool), tc_HOL_Obool)), _1490709), hAPP(c_COMBB(tc_prod(_1490709, _1490709), tc_fun(tc_fun(tc_prod(_1490709, _1490709), tc_HOL_Obool), tc_HOL_Obool), _1490709), c_member(tc_prod(_1490709, _1490709)))), c_Product__Type_OPair(_1490709, _1490709)))), _1490711)), _1490713)), -(hBOOL(hAPP(hAPP(c_member(_1490709), _1490713), c_Wellfounded_Oacc(_1490709, _1490711))))], (37548 ^ _780205) ^ [_1491050, _1491052, _1491054] : [hBOOL(hAPP(hAPP(c_member(_1491050), _1491054), c_Wellfounded_Oacc(_1491050, _1491052))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1491050, hAPP(hAPP(c_COMBC(_1491050, tc_fun(tc_prod(_1491050, _1491050), tc_HOL_Obool), tc_fun(_1491050, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491050, tc_fun(tc_fun(tc_prod(_1491050, _1491050), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1491050, _1491050), tc_HOL_Obool), tc_fun(_1491050, tc_HOL_Obool)), _1491050), c_COMBC(_1491050, tc_fun(tc_prod(_1491050, _1491050), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491050, tc_prod(_1491050, _1491050)), tc_fun(_1491050, tc_fun(tc_fun(tc_prod(_1491050, _1491050), tc_HOL_Obool), tc_HOL_Obool)), _1491050), hAPP(c_COMBB(tc_prod(_1491050, _1491050), tc_fun(tc_fun(tc_prod(_1491050, _1491050), tc_HOL_Obool), tc_HOL_Obool), _1491050), c_member(tc_prod(_1491050, _1491050)))), c_Product__Type_OPair(_1491050, _1491050)))), _1491052)), _1491054)))], (37554 ^ _780205) ^ [_1491418, _1491420, _1491422, _1491424] : [c_Wellfounded_Omax__extp(_1491418, _1491420, _1491422, _1491424), 37557 ^ _780205 : [(37558 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1491418), _1491422)))], (37560 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1491418), _1491424)))], (37562 ^ _780205) ^ [] : [_1491424 = c_Orderings_Obot__class_Obot(tc_fun(_1491418, tc_HOL_Obool))], (37564 ^ _780205) ^ [_1491634] : [hBOOL(hAPP(hAPP(c_member(_1491418), _1491634), _1491422)), 37568 ^ _780205 : [(37569 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491418), 37567 ^ [_1491418, _1491420, _1491422, _1491424, _1491634]), _1491424)))], (37571 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1491420, _1491634), 37567 ^ [_1491418, _1491420, _1491422, _1491424, _1491634])))]]]]], (37573 ^ _780205) ^ [_1491818, _1491820, _1491822, _1491824] : [-(c_Wellfounded_Omax__extp(_1491818, _1491820, _1491822, _1491824)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491818), _1491822)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491818), _1491824)), -(_1491824 = c_Orderings_Obot__class_Obot(tc_fun(_1491818, tc_HOL_Obool))), 37587 ^ _780205 : [(37588 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491818), 37586 ^ [_1491818, _1491820, _1491822, _1491824]), _1491822)))], (37590 ^ _780205) ^ [_1492163] : [hBOOL(hAPP(hAPP(c_member(_1491818), _1492163), _1491824)), hBOOL(hAPP(hAPP(_1491820, 37586 ^ [_1491818, _1491820, _1491822, _1491824]), _1492163))]]], (37598 ^ _780205) ^ [_1492331, _1492333, _1492335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1492331, _1492331), tc_HOL_Obool)), _1492333), _1492335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492331, tc_HOL_Obool)), c_Wellfounded_Oacc(_1492331, _1492335)), c_Wellfounded_Oacc(_1492331, _1492333))))], (37604 ^ _780205) ^ [_1492468, _1492470, _1492472, _1492474] : [hBOOL(hAPP(hAPP(c_member(_1492468), _1492470), c_Wellfounded_Oacc(_1492468, _1492472))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1492468, _1492468)), hAPP(hAPP(c_Product__Type_OPair(_1492468, _1492468), _1492474), _1492470)), _1492472)), -(hBOOL(hAPP(hAPP(c_member(_1492468), _1492474), c_Wellfounded_Oacc(_1492468, _1492472))))], (37624 ^ _780205) ^ [_1492954, _1492956, _1492958] : [37626 ^ _780205 : [(37627 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492954, _1492954)), hAPP(hAPP(c_Product__Type_OPair(_1492954, _1492954), 37625 ^ [_1492954, _1492956, _1492958]), _1492956)), _1492958)))], (37629 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1492954), 37625 ^ [_1492954, _1492956, _1492958]), c_Wellfounded_Oacc(_1492954, _1492958)))]], -(hBOOL(hAPP(hAPP(c_member(_1492954), _1492956), c_Wellfounded_Oacc(_1492954, _1492958))))], (37614 ^ _780205) ^ [_1492701, _1492703, _1492705] : [hBOOL(hAPP(hAPP(c_member(_1492701), _1492703), c_Wellfounded_Oacc(_1492701, _1492705))), 37617 ^ _780205 : [(37618 ^ _780205) ^ [_1492815] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492701, _1492701)), hAPP(hAPP(c_Product__Type_OPair(_1492701, _1492701), _1492815), _1492703)), _1492705)), -(hBOOL(hAPP(hAPP(c_member(_1492701), _1492815), c_Wellfounded_Oacc(_1492701, _1492705))))]]], (37633 ^ _780205) ^ [_1493193, _1493195, _1493197, _1493199] : [-(_1493193 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1493195, tc_HOL_Obool), tc_HOL_Obool))), 37639 ^ _780205 : [(37640 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1493195, tc_HOL_Obool)), 37638 ^ [_1493193, _1493195, _1493197, _1493199]), _1493193)))], (37642 ^ _780205) ^ [] : [c_Fun_Oinj__on(_1493195, _1493197, _1493199, 37638 ^ [_1493193, _1493195, _1493197, _1493199])]], -(c_Fun_Oinj__on(_1493195, _1493197, _1493199, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1493195, tc_HOL_Obool), _1493193)))], (37646 ^ _780205) ^ [_1493454, _1493456, _1493458, _1493460, _1493462, _1493464] : [-(hAPP(c_Set_Oimage(_1493454, tc_prod(_1493456, _1493458), hAPP(hAPP(c_COMBS(_1493454, _1493458, tc_prod(_1493456, _1493458)), hAPP(hAPP(c_COMBB(_1493456, tc_fun(_1493458, tc_prod(_1493456, _1493458)), _1493454), c_Product__Type_OPair(_1493456, _1493458)), _1493460)), _1493462)), _1493464) = hAPP(hAPP(c_Product__Type_OSigma(_1493456, _1493458), hAPP(c_Set_Oimage(_1493454, _1493456, _1493460), _1493464)), hAPP(hAPP(c_COMBB(tc_fun(_1493454, tc_HOL_Obool), tc_fun(_1493458, tc_HOL_Obool), _1493456), c_Set_Oimage(_1493454, _1493458, _1493462)), hAPP(hAPP(c_COMBC(_1493456, tc_fun(_1493454, tc_HOL_Obool), tc_fun(_1493454, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493454, tc_HOL_Obool), tc_fun(tc_fun(_1493454, tc_HOL_Obool), tc_fun(_1493454, tc_HOL_Obool)), _1493456), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493454, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1493456, tc_HOL_Obool), tc_fun(_1493454, tc_HOL_Obool), _1493456), c_Set_Ovimage(_1493454, _1493456, _1493460)), hAPP(hAPP(c_COMBC(_1493456, tc_fun(_1493456, tc_HOL_Obool), tc_fun(_1493456, tc_HOL_Obool)), c_Set_Oinsert(_1493456)), c_Orderings_Obot__class_Obot(tc_fun(_1493456, tc_HOL_Obool)))))), _1493464))))], (37648 ^ _780205) ^ [_1493651, _1493653, _1493655, _1493657, _1493659] : [c_Finite__Set_Ofolding__one__idem(_1493651, _1493653, _1493655), hAPP(_1493657, hAPP(hAPP(_1493653, 37653 ^ [_1493651, _1493653, _1493655, _1493657, _1493659]), 37654 ^ [_1493651, _1493653, _1493655, _1493657, _1493659])) = hAPP(hAPP(_1493653, hAPP(_1493657, 37653 ^ [_1493651, _1493653, _1493655, _1493657, _1493659])), hAPP(_1493657, 37654 ^ [_1493651, _1493653, _1493655, _1493657, _1493659])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493651), _1493659)), -(_1493659 = c_Orderings_Obot__class_Obot(tc_fun(_1493651, tc_HOL_Obool))), -(hAPP(_1493657, hAPP(_1493655, _1493659)) = hAPP(_1493655, hAPP(c_Set_Oimage(_1493651, _1493651, _1493657), _1493659)))], (37668 ^ _780205) ^ [_1494086, _1494088, _1494090, _1494092, _1494094, _1494096] : [hBOOL(hAPP(hAPP(c_member(_1494086), _1494088), _1494090)), hBOOL(hAPP(hAPP(c_member(_1494092), _1494094), hAPP(_1494096, _1494088))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494086, _1494092)), hAPP(hAPP(c_Product__Type_OPair(_1494086, _1494092), _1494088), _1494094)), hAPP(hAPP(c_Product__Type_OSigma(_1494086, _1494092), _1494090), _1494096))))], (37678 ^ _780205) ^ [_1494321, _1494323, _1494325, _1494327] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1494321, _1494323), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1494321, tc_HOL_Obool), _1494325)), _1494327) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1494321, tc_HOL_Obool), tc_fun(tc_prod(_1494321, _1494323), tc_HOL_Obool)), _1494325), hAPP(hAPP(c_COMBC(tc_fun(_1494321, tc_HOL_Obool), tc_fun(_1494321, tc_fun(_1494323, tc_HOL_Obool)), tc_fun(tc_prod(_1494321, _1494323), tc_HOL_Obool)), c_Product__Type_OSigma(_1494321, _1494323)), _1494327)))], (37680 ^ _780205) ^ [_1494411, _1494413, _1494415] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1494411, _1494413), c_Orderings_Obot__class_Obot(tc_fun(_1494411, tc_HOL_Obool))), _1494415) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1494411, _1494413), tc_HOL_Obool)))], (37682 ^ _780205) ^ [_1494460, _1494462, _1494464, _1494466, _1494468] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1494460, _1494462), _1494464), hAPP(hAPP(c_COMBS(_1494460, tc_fun(_1494462, tc_HOL_Obool), tc_fun(_1494462, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494462, tc_HOL_Obool), tc_fun(tc_fun(_1494462, tc_HOL_Obool), tc_fun(_1494462, tc_HOL_Obool)), _1494460), c_Groups_Ominus__class_Ominus(tc_fun(_1494462, tc_HOL_Obool))), _1494466)), _1494468)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1494460, _1494462), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1494460, _1494462), _1494464), _1494466)), hAPP(hAPP(c_Product__Type_OSigma(_1494460, _1494462), _1494464), _1494468)))], (37684 ^ _780205) ^ [_1494575, _1494577, _1494579, _1494581, _1494583] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1494575, _1494577), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494575, tc_HOL_Obool)), _1494579), _1494581)), hAPP(c_COMBK(tc_fun(_1494577, tc_HOL_Obool), _1494575), _1494583)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1494575, _1494577), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1494575, _1494577), _1494579), hAPP(c_COMBK(tc_fun(_1494577, tc_HOL_Obool), _1494575), _1494583))), hAPP(hAPP(c_Product__Type_OSigma(_1494575, _1494577), _1494581), hAPP(c_COMBK(tc_fun(_1494577, tc_HOL_Obool), _1494575), _1494583))))], (37686 ^ _780205) ^ [_1494685, _1494687, _1494689, _1494691, _1494693] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1494685, _1494687), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494685, tc_HOL_Obool)), _1494689), _1494691)), _1494693) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1494685, _1494687), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1494685, _1494687), _1494689), _1494693)), hAPP(hAPP(c_Product__Type_OSigma(_1494685, _1494687), _1494691), _1494693)))], (37688 ^ _780205) ^ [_1494768, _1494770, _1494772, _1494774, _1494776, _1494778] : [hBOOL(hAPP(hAPP(c_member(_1494768), _1494770), _1494772)), 37691 ^ _780205 : [(37692 ^ _780205) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1494774, _1494768), _1494776), hAPP(c_COMBK(tc_fun(_1494768, tc_HOL_Obool), _1494774), _1494772)) = hAPP(hAPP(c_Product__Type_OSigma(_1494774, _1494768), _1494778), hAPP(c_COMBK(tc_fun(_1494768, tc_HOL_Obool), _1494774), _1494772)), -(_1494776 = _1494778)], (37698 ^ _780205) ^ [] : [_1494776 = _1494778, -(hAPP(hAPP(c_Product__Type_OSigma(_1494774, _1494768), _1494776), hAPP(c_COMBK(tc_fun(_1494768, tc_HOL_Obool), _1494774), _1494772)) = hAPP(hAPP(c_Product__Type_OSigma(_1494774, _1494768), _1494778), hAPP(c_COMBK(tc_fun(_1494768, tc_HOL_Obool), _1494774), _1494772)))]]], (37704 ^ _780205) ^ [_1495121, _1495123, _1495125, _1495127] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1495121, _1495123)), hAPP(hAPP(c_Product__Type_OSigma(_1495121, _1495123), _1495125), hAPP(c_COMBK(tc_fun(_1495123, tc_HOL_Obool), _1495121), _1495127))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1495121), _1495125)), hAPP(c_Finite__Set_Ocard(_1495123), _1495127)))], (37706 ^ _780205) ^ [_1495192, _1495194, _1495196, _1495198, _1495200, _1495202] : [class_Groups_Ocomm__monoid__add(_1495192), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495194, _1495192), hAPP(hAPP(c_COMBC(_1495194, tc_fun(_1495196, tc_HOL_Obool), _1495192), hAPP(hAPP(c_COMBB(tc_fun(_1495196, _1495192), tc_fun(tc_fun(_1495196, tc_HOL_Obool), _1495192), _1495194), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495196, _1495192)), _1495198)), _1495200)), _1495202) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1495194, _1495196), _1495192), hAPP(c_Product__Type_Oprod_Oprod__case(_1495194, _1495196, _1495192), _1495198)), hAPP(hAPP(c_Product__Type_OSigma(_1495194, _1495196), _1495202), hAPP(c_COMBK(tc_fun(_1495196, tc_HOL_Obool), _1495194), _1495200))))], (37722 ^ _780205) ^ [_1495620, _1495622, _1495624, _1495626] : [37723 ^ _780205 : [(37724 ^ _780205) ^ [] : [_1495624 = c_Orderings_Obot__class_Obot(tc_fun(_1495620, tc_HOL_Obool))], (37726 ^ _780205) ^ [] : [_1495626 = c_Orderings_Obot__class_Obot(tc_fun(_1495622, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1495620, _1495622), _1495624), hAPP(c_COMBK(tc_fun(_1495622, tc_HOL_Obool), _1495620), _1495626)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1495620, _1495622), tc_HOL_Obool)))], (37712 ^ _780205) ^ [_1495458, _1495460, _1495462, _1495464] : [hAPP(hAPP(c_Product__Type_OSigma(_1495458, _1495460), _1495462), hAPP(c_COMBK(tc_fun(_1495460, tc_HOL_Obool), _1495458), _1495464)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1495458, _1495460), tc_HOL_Obool)), -(_1495462 = c_Orderings_Obot__class_Obot(tc_fun(_1495458, tc_HOL_Obool))), -(_1495464 = c_Orderings_Obot__class_Obot(tc_fun(_1495460, tc_HOL_Obool)))], (37730 ^ _780205) ^ [_1495813, _1495815, _1495817] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1495813, _1495815), _1495817), hAPP(c_COMBK(tc_fun(_1495815, tc_HOL_Obool), _1495813), c_Orderings_Obot__class_Obot(tc_fun(_1495815, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1495813, _1495815), tc_HOL_Obool)))], (37732 ^ _780205) ^ [_1495871, _1495873, _1495875] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1495871, _1495873), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1495871, _1495873), c_Orderings_Otop__class_Otop(tc_fun(_1495871, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1495873, tc_HOL_Obool), _1495871), _1495875))) = hAPP(hAPP(c_Product__Type_OSigma(_1495871, _1495873), c_Orderings_Otop__class_Otop(tc_fun(_1495871, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1495873, tc_HOL_Obool), _1495871), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1495873, tc_HOL_Obool)), _1495875))))], (37734 ^ _780205) ^ [_1495963, _1495965, _1495967] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1495963, _1495965), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1495963, _1495965), _1495967), hAPP(c_COMBK(tc_fun(_1495965, tc_HOL_Obool), _1495963), c_Orderings_Otop__class_Otop(tc_fun(_1495965, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1495963, _1495965), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1495963, tc_HOL_Obool)), _1495967)), hAPP(c_COMBK(tc_fun(_1495965, tc_HOL_Obool), _1495963), c_Orderings_Otop__class_Otop(tc_fun(_1495965, tc_HOL_Obool)))))], (37736 ^ _780205) ^ [_1496055, _1496057, _1496059, _1496061, _1496063, _1496065] : [class_Groups_Ocomm__monoid__mult(_1496055), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1496057, _1496055), hAPP(hAPP(c_COMBC(_1496057, tc_fun(_1496059, tc_HOL_Obool), _1496055), hAPP(hAPP(c_COMBB(tc_fun(_1496059, _1496055), tc_fun(tc_fun(_1496059, tc_HOL_Obool), _1496055), _1496057), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1496059, _1496055)), _1496061)), _1496063)), _1496065) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1496057, _1496059), _1496055), hAPP(c_Product__Type_Oprod_Oprod__case(_1496057, _1496059, _1496055), _1496061)), hAPP(hAPP(c_Product__Type_OSigma(_1496057, _1496059), _1496065), hAPP(c_COMBK(tc_fun(_1496059, tc_HOL_Obool), _1496057), _1496063))))], (37742 ^ _780205) ^ [_1496300, _1496302, _1496304, _1496306, _1496308] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1496300, _1496302), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496300, tc_HOL_Obool)), _1496304), _1496306)), _1496308) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1496300, _1496302), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1496300, _1496302), _1496304), _1496308)), hAPP(hAPP(c_Product__Type_OSigma(_1496300, _1496302), _1496306), _1496308)))], (37744 ^ _780205) ^ [_1496383, _1496385, _1496387, _1496389, _1496391] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1496383, _1496385), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496383, tc_HOL_Obool)), _1496387), _1496389)), hAPP(c_COMBK(tc_fun(_1496385, tc_HOL_Obool), _1496383), _1496391)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1496383, _1496385), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1496383, _1496385), _1496387), hAPP(c_COMBK(tc_fun(_1496385, tc_HOL_Obool), _1496383), _1496391))), hAPP(hAPP(c_Product__Type_OSigma(_1496383, _1496385), _1496389), hAPP(c_COMBK(tc_fun(_1496385, tc_HOL_Obool), _1496383), _1496391))))], (37746 ^ _780205) ^ [_1496493, _1496495, _1496497, _1496499, _1496501] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1496493, _1496495), _1496497), hAPP(hAPP(c_COMBS(_1496493, tc_fun(_1496495, tc_HOL_Obool), tc_fun(_1496495, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1496495, tc_HOL_Obool), tc_fun(tc_fun(_1496495, tc_HOL_Obool), tc_fun(_1496495, tc_HOL_Obool)), _1496493), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496495, tc_HOL_Obool))), _1496499)), _1496501)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1496493, _1496495), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1496493, _1496495), _1496497), _1496499)), hAPP(hAPP(c_Product__Type_OSigma(_1496493, _1496495), _1496497), _1496501)))], (37748 ^ _780205) ^ [_1496608, _1496610, _1496612, _1496614] : [-(hAPP(c_Set_Oimage(tc_prod(_1496608, _1496610), tc_prod(_1496610, _1496608), hAPP(c_Product__Type_Oprod_Oprod__case(_1496608, _1496610, tc_prod(_1496610, _1496608)), hAPP(c_COMBC(_1496610, _1496608, tc_prod(_1496610, _1496608)), c_Product__Type_OPair(_1496610, _1496608)))), hAPP(hAPP(c_Product__Type_OSigma(_1496608, _1496610), _1496612), hAPP(c_COMBK(tc_fun(_1496610, tc_HOL_Obool), _1496608), _1496614))) = hAPP(hAPP(c_Product__Type_OSigma(_1496610, _1496608), _1496614), hAPP(c_COMBK(tc_fun(_1496608, tc_HOL_Obool), _1496610), _1496612)))], (37750 ^ _780205) ^ [_1496709, _1496711, _1496713, _1496715] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496709), _1496711)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496713), _1496715)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1496709, _1496713)), hAPP(hAPP(c_Product__Type_OSigma(_1496709, _1496713), _1496711), hAPP(c_COMBK(tc_fun(_1496713, tc_HOL_Obool), _1496709), _1496715)))))], (37760 ^ _780205) ^ [_1496912, _1496914, _1496916] : [c_Equiv__Relations_Oequiv(_1496912, _1496914, _1496916), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1496912, _1496912), tc_HOL_Obool)), _1496916), hAPP(hAPP(c_Product__Type_OSigma(_1496912, _1496912), _1496914), hAPP(c_COMBK(tc_fun(_1496912, tc_HOL_Obool), _1496912), _1496914)))))], (37766 ^ _780205) ^ [_1497055, _1497057, _1497059, _1497061, _1497063] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497055, _1497057), _1497059), hAPP(hAPP(c_COMBS(_1497055, tc_fun(_1497057, tc_HOL_Obool), tc_fun(_1497057, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497057, tc_HOL_Obool), tc_fun(tc_fun(_1497057, tc_HOL_Obool), tc_fun(_1497057, tc_HOL_Obool)), _1497055), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1497057, tc_HOL_Obool))), _1497061)), _1497063)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1497055, _1497057), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1497055, _1497057), _1497059), _1497061)), hAPP(hAPP(c_Product__Type_OSigma(_1497055, _1497057), _1497059), _1497063)))], (37768 ^ _780205) ^ [_1497170, _1497172, _1497174, _1497176, _1497178] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497170, _1497172), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1497170, tc_HOL_Obool)), _1497174), _1497176)), hAPP(c_COMBK(tc_fun(_1497172, tc_HOL_Obool), _1497170), _1497178)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1497170, _1497172), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1497170, _1497172), _1497174), hAPP(c_COMBK(tc_fun(_1497172, tc_HOL_Obool), _1497170), _1497178))), hAPP(hAPP(c_Product__Type_OSigma(_1497170, _1497172), _1497176), hAPP(c_COMBK(tc_fun(_1497172, tc_HOL_Obool), _1497170), _1497178))))], (37770 ^ _780205) ^ [_1497280, _1497282, _1497284, _1497286, _1497288] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497280, _1497282), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1497280, tc_HOL_Obool)), _1497284), _1497286)), _1497288) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1497280, _1497282), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1497280, _1497282), _1497284), _1497288)), hAPP(hAPP(c_Product__Type_OSigma(_1497280, _1497282), _1497286), _1497288)))], (37772 ^ _780205) ^ [_1497363, _1497365] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1497363, _1497363), tc_HOL_Obool)), c_Relation_OId__on(_1497363, _1497365)), hAPP(hAPP(c_Product__Type_OSigma(_1497363, _1497363), _1497365), hAPP(c_COMBK(tc_fun(_1497363, tc_HOL_Obool), _1497363), _1497365)))))], (37774 ^ _780205) ^ [_1497422, _1497424] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497422, _1497424), c_Orderings_Otop__class_Otop(tc_fun(_1497422, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1497424, tc_HOL_Obool), _1497422), c_Orderings_Otop__class_Otop(tc_fun(_1497424, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1497422, _1497424), tc_HOL_Obool)))], (37776 ^ _780205) ^ [_1497483, _1497485, _1497487, _1497489, _1497491, _1497493] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1497483, _1497485)), hAPP(hAPP(c_Product__Type_OPair(_1497483, _1497485), _1497487), _1497489)), hAPP(hAPP(c_Product__Type_OSigma(_1497483, _1497485), _1497491), _1497493))), 37779 ^ _780205 : [(37780 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497483), _1497487), _1497491)))], (37782 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497485), _1497489), hAPP(_1497493, _1497487))))]]], (37784 ^ _780205) ^ [_1497688, _1497690, _1497692, _1497694, _1497696, _1497698] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1497688, _1497690)), hAPP(hAPP(c_Product__Type_OPair(_1497688, _1497690), _1497692), _1497694)), hAPP(hAPP(c_Product__Type_OSigma(_1497688, _1497690), _1497696), _1497698))), -(hBOOL(hAPP(hAPP(c_member(_1497690), _1497694), hAPP(_1497698, _1497692))))], (37790 ^ _780205) ^ [_1497849, _1497851, _1497853, _1497855, _1497857, _1497859] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1497849, _1497851)), hAPP(hAPP(c_Product__Type_OPair(_1497849, _1497851), _1497853), _1497855)), hAPP(hAPP(c_Product__Type_OSigma(_1497849, _1497851), _1497857), _1497859))), -(hBOOL(hAPP(hAPP(c_member(_1497849), _1497853), _1497857)))], (37796 ^ _780205) ^ [_1498031, _1498033, _1498035, _1498037, _1498039, _1498041] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1498031, _1498033)), hAPP(hAPP(c_Product__Type_OPair(_1498031, _1498033), _1498035), _1498037)), hAPP(hAPP(c_Product__Type_OSigma(_1498031, _1498033), _1498039), _1498041))), 37799 ^ _780205 : [(37800 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1498031), _1498035), _1498039)))], (37802 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1498033), _1498037), hAPP(_1498041, _1498035))))]]], (37804 ^ _780205) ^ [_1498228, _1498230, _1498232, _1498234, _1498236, _1498238] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1498228, _1498230)), hAPP(hAPP(c_Product__Type_OPair(_1498228, _1498230), _1498232), _1498234)), hAPP(hAPP(c_Product__Type_OSigma(_1498228, _1498230), _1498236), _1498238)))), hBOOL(hAPP(hAPP(c_member(_1498228), _1498232), _1498236)), hBOOL(hAPP(hAPP(c_member(_1498230), _1498234), hAPP(_1498238, _1498232)))], (37814 ^ _780205) ^ [_1498465, _1498467, _1498469, _1498471] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1498465, _1498467)), hAPP(hAPP(c_Product__Type_OSigma(_1498465, _1498467), hAPP(hAPP(c_Set_Oinsert(_1498465), _1498469), c_Orderings_Obot__class_Obot(tc_fun(_1498465, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1498467, tc_HOL_Obool), _1498465), _1498471))) = hAPP(c_Finite__Set_Ocard(_1498467), _1498471))], (37816 ^ _780205) ^ [_1498538, _1498540, _1498542, _1498544, _1498546, _1498548] : [hBOOL(hAPP(hAPP(c_member(_1498538), _1498540), _1498542)), 37819 ^ _780205 : [(37820 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1498544, _1498538), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1498544, _1498538), _1498546), hAPP(c_COMBK(tc_fun(_1498538, tc_HOL_Obool), _1498544), _1498542))), hAPP(hAPP(c_Product__Type_OSigma(_1498544, _1498538), _1498548), hAPP(c_COMBK(tc_fun(_1498538, tc_HOL_Obool), _1498544), _1498542)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498544, tc_HOL_Obool)), _1498546), _1498548)))], (37826 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498544, tc_HOL_Obool)), _1498546), _1498548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1498544, _1498538), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1498544, _1498538), _1498546), hAPP(c_COMBK(tc_fun(_1498538, tc_HOL_Obool), _1498544), _1498542))), hAPP(hAPP(c_Product__Type_OSigma(_1498544, _1498538), _1498548), hAPP(c_COMBK(tc_fun(_1498538, tc_HOL_Obool), _1498544), _1498542)))))]]], (37832 ^ _780205) ^ [_1498960, _1498962, _1498964, _1498966, _1498968, _1498970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1498960, _1498962), tc_HOL_Obool)), _1498964), hAPP(hAPP(c_Product__Type_OSigma(_1498960, _1498962), _1498966), hAPP(c_COMBK(tc_fun(_1498962, tc_HOL_Obool), _1498960), _1498968)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498962, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1498960, _1498962, _1498964), _1498970)), _1498968)))], (37838 ^ _780205) ^ [_1499141, _1499143, _1499145, _1499147] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1499141, _1499143)), hAPP(hAPP(c_Product__Type_OSigma(_1499141, _1499143), _1499145), hAPP(c_COMBK(tc_fun(_1499143, tc_HOL_Obool), _1499141), _1499147)))), -(_1499145 = c_Orderings_Obot__class_Obot(tc_fun(_1499141, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1499143), _1499147)))], (37848 ^ _780205) ^ [_1499305, _1499307, _1499309, _1499311] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1499305, _1499307)), hAPP(hAPP(c_Product__Type_OSigma(_1499305, _1499307), _1499309), hAPP(c_COMBK(tc_fun(_1499307, tc_HOL_Obool), _1499305), _1499311)))), -(_1499311 = c_Orderings_Obot__class_Obot(tc_fun(_1499307, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1499305), _1499309)))], (37858 ^ _780205) ^ [_1499484, _1499486, _1499488, _1499490] : [_1499484 = c_Orderings_Obot__class_Obot(tc_fun(_1499486, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1499488, _1499486), _1499488, c_Product__Type_Ofst(_1499488, _1499486)), hAPP(hAPP(c_Product__Type_OSigma(_1499488, _1499486), _1499490), hAPP(c_COMBK(tc_fun(_1499486, tc_HOL_Obool), _1499488), _1499484))) = c_Orderings_Obot__class_Obot(tc_fun(_1499488, tc_HOL_Obool)))], (37864 ^ _780205) ^ [_1499641, _1499643, _1499645, _1499647] : [-(_1499641 = c_Orderings_Obot__class_Obot(tc_fun(_1499643, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1499645, _1499643), _1499645, c_Product__Type_Ofst(_1499645, _1499643)), hAPP(hAPP(c_Product__Type_OSigma(_1499645, _1499643), _1499647), hAPP(c_COMBK(tc_fun(_1499643, tc_HOL_Obool), _1499645), _1499641))) = _1499647)], (37870 ^ _780205) ^ [_1499734, _1499736, _1499738, _1499740] : [_1499734 = c_Orderings_Obot__class_Obot(tc_fun(_1499736, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1499736, _1499738), _1499738, c_Product__Type_Osnd(_1499736, _1499738)), hAPP(hAPP(c_Product__Type_OSigma(_1499736, _1499738), _1499734), hAPP(c_COMBK(tc_fun(_1499738, tc_HOL_Obool), _1499736), _1499740))) = c_Orderings_Obot__class_Obot(tc_fun(_1499738, tc_HOL_Obool)))], (37876 ^ _780205) ^ [_1499891, _1499893, _1499895, _1499897] : [-(_1499891 = c_Orderings_Obot__class_Obot(tc_fun(_1499893, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1499893, _1499895), _1499895, c_Product__Type_Osnd(_1499893, _1499895)), hAPP(hAPP(c_Product__Type_OSigma(_1499893, _1499895), _1499891), hAPP(c_COMBK(tc_fun(_1499895, tc_HOL_Obool), _1499893), _1499897))) = _1499897)], (37882 ^ _780205) ^ [_1499969, _1499971, _1499973, _1499975, _1499977, _1499979] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1499969, _1499971), hAPP(hAPP(c_Set_Oinsert(_1499969), _1499973), _1499975)), hAPP(c_COMBK(tc_fun(_1499971, tc_HOL_Obool), _1499969), hAPP(hAPP(c_Set_Oinsert(_1499971), _1499977), _1499979))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1499969, _1499971)), hAPP(hAPP(c_Product__Type_OPair(_1499969, _1499971), _1499973), _1499977)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1499969, _1499971), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1499969, _1499971), _1499975), hAPP(c_COMBK(tc_fun(_1499971, tc_HOL_Obool), _1499969), hAPP(hAPP(c_Set_Oinsert(_1499971), _1499977), _1499979)))), hAPP(hAPP(c_Product__Type_OSigma(_1499969, _1499971), hAPP(hAPP(c_Set_Oinsert(_1499969), _1499973), _1499975)), hAPP(c_COMBK(tc_fun(_1499971, tc_HOL_Obool), _1499969), _1499979)))))], (37884 ^ _780205) ^ [_1500122, _1500124, _1500126, _1500128] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1500122), _1500124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1500122, _1500122), tc_HOL_Obool)), _1500126), hAPP(hAPP(c_Product__Type_OSigma(_1500122, _1500122), _1500124), hAPP(c_COMBK(tc_fun(_1500122, tc_HOL_Obool), _1500122), _1500124)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1500122, tc_HOL_Obool)), _1500128), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1500122), _1500124), _1500126))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1500122), _1500128)))], (37898 ^ _780205) ^ [_1500429, _1500431, _1500433, _1500435, _1500437, _1500439, _1500441, _1500443] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1500429, _1500431), tc_fun(tc_prod(_1500433, _1500435), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1500429, _1500431), _1500437), hAPP(c_COMBK(tc_fun(_1500431, tc_HOL_Obool), _1500429), _1500439))), hAPP(c_Product__Type_Oprod_Oprod__case(_1500429, _1500431, tc_fun(tc_prod(_1500433, _1500435), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1500429, tc_fun(_1500431, tc_fun(_1500433, tc_fun(_1500435, tc_HOL_Obool))), tc_fun(_1500431, tc_fun(tc_prod(_1500433, _1500435), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1500433, tc_fun(_1500435, tc_HOL_Obool)), tc_fun(tc_prod(_1500433, _1500435), tc_HOL_Obool)), tc_fun(tc_fun(_1500431, tc_fun(_1500433, tc_fun(_1500435, tc_HOL_Obool))), tc_fun(_1500431, tc_fun(tc_prod(_1500433, _1500435), tc_HOL_Obool))), _1500429), c_COMBB(tc_fun(_1500433, tc_fun(_1500435, tc_HOL_Obool)), tc_fun(tc_prod(_1500433, _1500435), tc_HOL_Obool), _1500431)), hAPP(hAPP(c_COMBB(tc_fun(_1500433, tc_HOL_Obool), tc_fun(tc_fun(_1500433, tc_fun(_1500435, tc_HOL_Obool)), tc_fun(tc_prod(_1500433, _1500435), tc_HOL_Obool)), _1500429), c_Product__Type_OSigma(_1500433, _1500435)), _1500441))), hAPP(hAPP(c_COMBB(tc_fun(_1500435, tc_HOL_Obool), tc_fun(_1500433, tc_fun(_1500435, tc_HOL_Obool)), _1500431), c_COMBK(tc_fun(_1500435, tc_HOL_Obool), _1500433)), _1500443)))) = hAPP(hAPP(c_Product__Type_OSigma(_1500433, _1500435), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500429, tc_fun(_1500433, tc_HOL_Obool)), _1500437), _1500441)), hAPP(c_COMBK(tc_fun(_1500435, tc_HOL_Obool), _1500433), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500431, tc_fun(_1500435, tc_HOL_Obool)), _1500439), _1500443))))], (37900 ^ _780205) ^ [_1500703, _1500705, _1500707, _1500709] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1500703, _1500705), _1500707), _1500709) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500703, tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool)), _1500707), hAPP(hAPP(c_COMBS(_1500703, tc_fun(_1500705, tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool)), tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500705, tc_HOL_Obool), tc_fun(tc_fun(_1500705, tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool)), tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool)), _1500703), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500705, tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool))), _1500709)), hAPP(hAPP(c_COMBC(_1500703, tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool), tc_fun(_1500705, tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1500705, tc_fun(tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool), tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool), tc_fun(_1500705, tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool))), _1500703), c_COMBC(_1500705, tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool), tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1500705, tc_prod(_1500703, _1500705)), tc_fun(_1500705, tc_fun(tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool), tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool))), _1500703), hAPP(c_COMBB(tc_prod(_1500703, _1500705), tc_fun(tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool), tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool)), _1500705), c_Set_Oinsert(tc_prod(_1500703, _1500705)))), c_Product__Type_OPair(_1500703, _1500705)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500703, _1500705), tc_HOL_Obool))))))], (37902 ^ _780205) ^ [_1500983, _1500985, _1500987] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1500983), _1500985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1500983, _1500983), tc_HOL_Obool)), _1500987), hAPP(hAPP(c_Product__Type_OSigma(_1500983, _1500983), _1500985), hAPP(c_COMBK(tc_fun(_1500983, tc_HOL_Obool), _1500983), _1500985)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1500983, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1500983), _1500985), _1500987))))], (37913 ^ _780205) ^ [_1501214, _1501216, _1501218, _1501220] : [-(c_Fun_Oinj__on(_1501214, tc_prod(_1501216, _1501214), 37911 ^ [_1501214, _1501216, _1501218, _1501220], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501216, tc_fun(_1501214, tc_HOL_Obool)), _1501218), _1501220)))], (37915 ^ _780205) ^ [_1501268, _1501270, _1501272, _1501274] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501270, _1501268), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1501268, tc_prod(_1501270, _1501268), 37911 ^ [_1501268, _1501270, _1501272, _1501274]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501270, tc_fun(_1501268, tc_HOL_Obool)), _1501272), _1501274))), hAPP(hAPP(c_Product__Type_OSigma(_1501270, _1501268), _1501272), _1501274))))], (37917 ^ _780205) ^ [_1501354, _1501356, _1501358, _1501360, _1501362, _1501364] : [class_Groups_Ocomm__monoid__mult(_1501354), hBOOL(hAPP(c_Finite__Set_Ofinite(_1501356), _1501358)), 37927 ^ _780205 : [(37928 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501356), 37926 ^ [_1501354, _1501356, _1501358, _1501360, _1501362, _1501364]), _1501358)))], (37930 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501360), hAPP(_1501362, 37926 ^ [_1501354, _1501356, _1501358, _1501360, _1501362, _1501364])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1501354, _1501356, c_Groups_Otimes__class_Otimes(_1501354)), hAPP(hAPP(c_COMBS(_1501356, tc_fun(_1501360, tc_HOL_Obool), _1501354), hAPP(hAPP(c_COMBC(_1501356, _1501354, tc_fun(tc_fun(_1501360, tc_HOL_Obool), _1501354)), hAPP(hAPP(c_COMBB(tc_fun(_1501360, _1501354), tc_fun(_1501354, tc_fun(tc_fun(_1501360, tc_HOL_Obool), _1501354)), _1501356), c_Finite__Set_Ofold__image(_1501354, _1501360, c_Groups_Otimes__class_Otimes(_1501354))), _1501364)), c_Groups_Oone__class_Oone(_1501354))), _1501362)), c_Groups_Oone__class_Oone(_1501354)), _1501358) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1501354, tc_prod(_1501356, _1501360), c_Groups_Otimes__class_Otimes(_1501354)), hAPP(c_Product__Type_Oprod_Oprod__case(_1501356, _1501360, _1501354), _1501364)), c_Groups_Oone__class_Oone(_1501354)), hAPP(hAPP(c_Product__Type_OSigma(_1501356, _1501360), _1501358), _1501362)))], (37934 ^ _780205) ^ [_1501911, _1501913, _1501915, _1501917] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501911), _1501913)), 37940 ^ _780205 : [(37941 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501911), 37939 ^ [_1501911, _1501913, _1501915, _1501917]), _1501913)))], (37943 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501915), hAPP(_1501917, 37939 ^ [_1501911, _1501913, _1501915, _1501917])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1501911, _1501915)), hAPP(hAPP(c_Product__Type_OSigma(_1501911, _1501915), _1501913), _1501917))))], (37947 ^ _780205) ^ [_1502198, _1502200, _1502202, _1502204, _1502206, _1502208] : [class_Groups_Ocomm__monoid__mult(_1502198), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502200), _1502202)), 37957 ^ _780205 : [(37958 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502200), 37956 ^ [_1502198, _1502200, _1502202, _1502204, _1502206, _1502208]), _1502202)))], (37960 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1502204), hAPP(_1502206, 37956 ^ [_1502198, _1502200, _1502202, _1502204, _1502206, _1502208])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1502200, _1502198), hAPP(hAPP(c_COMBS(_1502200, tc_fun(_1502204, tc_HOL_Obool), _1502198), hAPP(hAPP(c_COMBB(tc_fun(_1502204, _1502198), tc_fun(tc_fun(_1502204, tc_HOL_Obool), _1502198), _1502200), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1502204, _1502198)), _1502208)), _1502206)), _1502202) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1502200, _1502204), _1502198), hAPP(c_Product__Type_Oprod_Oprod__case(_1502200, _1502204, _1502198), _1502208)), hAPP(hAPP(c_Product__Type_OSigma(_1502200, _1502204), _1502202), _1502206)))], (37964 ^ _780205) ^ [_1502675, _1502677, _1502679, _1502681, _1502683, _1502685] : [class_Groups_Ocomm__monoid__add(_1502675), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502677), _1502679)), 37974 ^ _780205 : [(37975 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502677), 37973 ^ [_1502675, _1502677, _1502679, _1502681, _1502683, _1502685]), _1502679)))], (37977 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1502681), hAPP(_1502683, 37973 ^ [_1502675, _1502677, _1502679, _1502681, _1502683, _1502685])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1502677, _1502675), hAPP(hAPP(c_COMBS(_1502677, tc_fun(_1502681, tc_HOL_Obool), _1502675), hAPP(hAPP(c_COMBB(tc_fun(_1502681, _1502675), tc_fun(tc_fun(_1502681, tc_HOL_Obool), _1502675), _1502677), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1502681, _1502675)), _1502685)), _1502683)), _1502679) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1502677, _1502681), _1502675), hAPP(c_Product__Type_Oprod_Oprod__case(_1502677, _1502681, _1502675), _1502685)), hAPP(hAPP(c_Product__Type_OSigma(_1502677, _1502681), _1502679), _1502683)))], (37981 ^ _780205) ^ [_1503152, _1503154, _1503156, _1503158] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503152), _1503154)), 37987 ^ _780205 : [(37988 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503152), 37986 ^ [_1503152, _1503154, _1503156, _1503158]), _1503154)))], (37990 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503156), hAPP(_1503158, 37986 ^ [_1503152, _1503154, _1503156, _1503158])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1503152, _1503156)), hAPP(hAPP(c_Product__Type_OSigma(_1503152, _1503156), _1503154), _1503158)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503152, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1503156, tc_HOL_Obool), tc_Nat_Onat, _1503152), c_Finite__Set_Ocard(_1503156)), _1503158)), _1503154))], (37994 ^ _780205) ^ [_1503489, _1503491, _1503493, _1503495, _1503497] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1503489, _1503491)), _1503493), hAPP(hAPP(c_Product__Type_OSigma(_1503489, _1503491), _1503495), _1503497))), 37998 ^ _780205 : [(37999 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503489), 37997 ^ [_1503489, _1503491, _1503493, _1503495, _1503497]), _1503495)))], (38002 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503491), 38000 ^ [_1503489, _1503491, _1503493, _1503495, _1503497]), hAPP(_1503497, 37997 ^ [_1503489, _1503491, _1503493, _1503495, _1503497]))))], (38004 ^ _780205) ^ [] : [-(_1503493 = hAPP(hAPP(c_Product__Type_OPair(_1503489, _1503491), 37997 ^ [_1503489, _1503491, _1503493, _1503495, _1503497]), 38000 ^ [_1503489, _1503491, _1503493, _1503495, _1503497]))]]], (38006 ^ _780205) ^ [_1503791, _1503793, _1503795, _1503797, _1503799, _1503801] : [hAPP(c_Set_Oimage(_1503791, _1503793, _1503795), c_Orderings_Otop__class_Otop(tc_fun(_1503791, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1503793, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1503797, _1503799, _1503801), c_Orderings_Otop__class_Otop(tc_fun(_1503797, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1503799, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1503791, _1503797), tc_prod(_1503793, _1503799), c_Product__Type_Omap__pair(_1503791, _1503793, _1503797, _1503799, _1503795, _1503801)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1503791, _1503797), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1503793, _1503799), tc_HOL_Obool)))], (38016 ^ _780205) ^ [_1504076, _1504078, _1504080, _1504082, _1504084, _1504086, _1504088, _1504090] : [c_Fun_Oinj__on(_1504076, _1504078, _1504080, _1504082), c_Fun_Oinj__on(_1504084, _1504086, _1504088, _1504090), -(c_Fun_Oinj__on(tc_prod(_1504076, _1504084), tc_prod(_1504078, _1504086), c_Product__Type_Omap__pair(_1504076, _1504078, _1504084, _1504086, _1504080, _1504088), hAPP(hAPP(c_Product__Type_OSigma(_1504076, _1504084), _1504082), hAPP(c_COMBK(tc_fun(_1504084, tc_HOL_Obool), _1504076), _1504090))))], (38026 ^ _780205) ^ [_1504303, _1504305, _1504307, _1504309, _1504311, _1504313, _1504315, _1504317, _1504319] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504303, _1504305)), hAPP(hAPP(c_Product__Type_OPair(_1504303, _1504305), _1504307), _1504309)), _1504311)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504313, _1504315)), hAPP(hAPP(c_Product__Type_OPair(_1504313, _1504315), hAPP(_1504317, _1504307)), hAPP(_1504319, _1504309))), hAPP(c_Set_Oimage(tc_prod(_1504303, _1504305), tc_prod(_1504313, _1504315), c_Product__Type_Omap__pair(_1504303, _1504313, _1504305, _1504315, _1504317, _1504319)), _1504311))))], (38032 ^ _780205) ^ [_1504522, _1504524, _1504526, _1504528, _1504530, _1504532, _1504534] : [-(hAPP(c_Product__Type_Ofst(_1504522, _1504524), hAPP(c_Product__Type_Omap__pair(_1504526, _1504522, _1504528, _1504524, _1504530, _1504532), _1504534)) = hAPP(_1504530, hAPP(c_Product__Type_Ofst(_1504526, _1504528), _1504534)))], (38034 ^ _780205) ^ [_1504582, _1504584, _1504586, _1504588, _1504590, _1504592, _1504594, _1504596] : [-(hAPP(c_Product__Type_Omap__pair(_1504582, _1504584, _1504586, _1504588, _1504590, _1504592), hAPP(hAPP(c_Product__Type_OPair(_1504582, _1504586), _1504594), _1504596)) = hAPP(hAPP(c_Product__Type_OPair(_1504584, _1504588), hAPP(_1504590, _1504594)), hAPP(_1504592, _1504596)))], (38036 ^ _780205) ^ [_1504653, _1504655, _1504657] : [-(hAPP(c_Product__Type_Omap__pair(_1504653, _1504653, _1504655, _1504655, c_COMBI(_1504653), c_COMBI(_1504655)), _1504657) = _1504657)], (38038 ^ _780205) ^ [_1504694, _1504696, _1504698, _1504700, _1504702, _1504704, _1504706] : [-(hAPP(c_Product__Type_Osnd(_1504694, _1504696), hAPP(c_Product__Type_Omap__pair(_1504698, _1504694, _1504700, _1504696, _1504702, _1504704), _1504706)) = hAPP(_1504704, hAPP(c_Product__Type_Osnd(_1504698, _1504700), _1504706)))], (38040 ^ _780205) ^ [_1504754, _1504756, _1504758, _1504760, _1504762, _1504764] : [-(c_Product__Type_Omap__pair(_1504754, _1504756, _1504758, _1504760, _1504762, _1504764) = hAPP(c_Product__Type_Oprod_Oprod__case(_1504754, _1504758, tc_prod(_1504756, _1504760)), hAPP(hAPP(c_COMBC(_1504754, tc_fun(_1504758, _1504760), tc_fun(_1504758, tc_prod(_1504756, _1504760))), hAPP(hAPP(c_COMBB(tc_fun(_1504760, tc_prod(_1504756, _1504760)), tc_fun(tc_fun(_1504758, _1504760), tc_fun(_1504758, tc_prod(_1504756, _1504760))), _1504754), c_COMBB(_1504760, tc_prod(_1504756, _1504760), _1504758)), hAPP(hAPP(c_COMBB(_1504756, tc_fun(_1504760, tc_prod(_1504756, _1504760)), _1504754), c_Product__Type_OPair(_1504756, _1504760)), _1504762))), _1504764)))], (38042 ^ _780205) ^ [_1504877, _1504879, _1504881, _1504883, _1504885, _1504887, _1504889, _1504891, _1504893, _1504895] : [hAPP(c_Set_Oimage(_1504877, _1504879, _1504881), _1504883) = _1504885, hAPP(c_Set_Oimage(_1504887, _1504889, _1504891), _1504893) = _1504895, -(hAPP(c_Set_Oimage(tc_prod(_1504877, _1504887), tc_prod(_1504879, _1504889), c_Product__Type_Omap__pair(_1504877, _1504879, _1504887, _1504889, _1504881, _1504891)), hAPP(hAPP(c_Product__Type_OSigma(_1504877, _1504887), _1504883), hAPP(c_COMBK(tc_fun(_1504887, tc_HOL_Obool), _1504877), _1504893))) = hAPP(hAPP(c_Product__Type_OSigma(_1504879, _1504889), _1504885), hAPP(c_COMBK(tc_fun(_1504889, tc_HOL_Obool), _1504879), _1504895)))], (38052 ^ _780205) ^ [_1505178, _1505180, _1505182, _1505184, _1505186, _1505188, _1505190, _1505192] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1505178, _1505180)), _1505182), hAPP(c_Set_Oimage(tc_prod(_1505184, _1505186), tc_prod(_1505178, _1505180), c_Product__Type_Omap__pair(_1505184, _1505178, _1505186, _1505180, _1505188, _1505190)), _1505192))), 38057 ^ _780205 : [(38058 ^ _780205) ^ [] : [-(_1505182 = hAPP(hAPP(c_Product__Type_OPair(_1505178, _1505180), hAPP(_1505188, 38055 ^ [_1505178, _1505180, _1505182, _1505184, _1505186, _1505188, _1505190, _1505192])), hAPP(_1505190, 38056 ^ [_1505178, _1505180, _1505182, _1505184, _1505186, _1505188, _1505190, _1505192])))], (38060 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1505184, _1505186)), hAPP(hAPP(c_Product__Type_OPair(_1505184, _1505186), 38055 ^ [_1505178, _1505180, _1505182, _1505184, _1505186, _1505188, _1505190, _1505192]), 38056 ^ [_1505178, _1505180, _1505182, _1505184, _1505186, _1505188, _1505190, _1505192])), _1505192)))]]], (38062 ^ _780205) ^ [_1505529, _1505531, _1505533] : [c_Relation_Orefl__on(_1505529, _1505531, _1505533), 38065 ^ _780205 : [(38066 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1505529, _1505529), tc_HOL_Obool)), _1505533), hAPP(hAPP(c_Product__Type_OSigma(_1505529, _1505529), _1505531), hAPP(c_COMBK(tc_fun(_1505529, tc_HOL_Obool), _1505529), _1505531)))))], (38068 ^ _780205) ^ [_1505711] : [hBOOL(hAPP(hAPP(c_member(_1505529), _1505711), _1505531)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1505529, _1505529)), hAPP(hAPP(c_Product__Type_OPair(_1505529, _1505529), _1505711), _1505711)), _1505533)))]]], (38074 ^ _780205) ^ [_1505846, _1505848, _1505850] : [-(c_Relation_Orefl__on(_1505846, _1505848, _1505850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1505846, _1505846), tc_HOL_Obool)), _1505850), hAPP(hAPP(c_Product__Type_OSigma(_1505846, _1505846), _1505848), hAPP(c_COMBK(tc_fun(_1505846, tc_HOL_Obool), _1505846), _1505848)))), 38080 ^ _780205 : [(38081 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1505846), 38079 ^ [_1505846, _1505848, _1505850]), _1505848)))], (38083 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1505846, _1505846)), hAPP(hAPP(c_Product__Type_OPair(_1505846, _1505846), 38079 ^ [_1505846, _1505848, _1505850]), 38079 ^ [_1505846, _1505848, _1505850])), _1505850))]]], (38087 ^ _780205) ^ [_1506195] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1506195), c_Int_OInteg)), -(_1506195 = hAPP(c_Int_ORep__Integ, 38090 ^ [_1506195]))], (38094 ^ _780205) ^ [_1506300, _1506302] : [-(c_Relation_Orefl__on(_1506300, _1506302, c_Relation_OId__on(_1506300, _1506302)))], (38096 ^ _780205) ^ [_1506329] : [-(c_Relation_Orefl__on(_1506329, c_Orderings_Obot__class_Obot(tc_fun(_1506329, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1506329, _1506329), tc_HOL_Obool))))], (38098 ^ _780205) ^ [_1506366, _1506368, _1506370, _1506372, _1506374] : [c_Relation_Orefl__on(_1506366, _1506368, _1506370), c_Relation_Orefl__on(_1506366, _1506372, _1506374), -(c_Relation_Orefl__on(_1506366, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1506366, tc_HOL_Obool)), _1506368), _1506372), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1506366, _1506366), tc_HOL_Obool)), _1506370), _1506374)))], (38108 ^ _780205) ^ [_1506563, _1506565, _1506567, _1506569, _1506571] : [c_Relation_Orefl__on(_1506563, _1506565, _1506567), c_Relation_Orefl__on(_1506563, _1506569, _1506571), -(c_Relation_Orefl__on(_1506563, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506563, tc_HOL_Obool)), _1506565), _1506569), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1506563, _1506563), tc_HOL_Obool)), _1506567), _1506571)))], (38118 ^ _780205) ^ [_1506760, _1506762, _1506764, _1506766] : [c_Relation_Orefl__on(_1506760, _1506762, _1506764), hBOOL(hAPP(hAPP(c_member(_1506760), _1506766), _1506762)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1506760, _1506760)), hAPP(hAPP(c_Product__Type_OPair(_1506760, _1506760), _1506766), _1506766)), _1506764)))], (38128 ^ _780205) ^ [_1506951, _1506953, _1506955, _1506957, _1506959] : [c_Relation_Orefl__on(_1506951, _1506953, _1506955), hBOOL(hAPP(hAPP(c_member(tc_prod(_1506951, _1506951)), hAPP(hAPP(c_Product__Type_OPair(_1506951, _1506951), _1506957), _1506959)), _1506955)), -(hBOOL(hAPP(hAPP(c_member(_1506951), _1506957), _1506953)))], (38138 ^ _780205) ^ [_1507146, _1507148, _1507150, _1507152, _1507154] : [c_Relation_Orefl__on(_1507146, _1507148, _1507150), hBOOL(hAPP(hAPP(c_member(tc_prod(_1507146, _1507146)), hAPP(hAPP(c_Product__Type_OPair(_1507146, _1507146), _1507152), _1507154)), _1507150)), -(hBOOL(hAPP(hAPP(c_member(_1507146), _1507154), _1507148)))], (38148 ^ _780205) ^ [_1507341, _1507343, _1507345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507341, _1507341), tc_HOL_Obool)), _1507343), hAPP(hAPP(c_Product__Type_OSigma(_1507341, _1507341), _1507345), hAPP(c_COMBK(tc_fun(_1507341, tc_HOL_Obool), _1507341), _1507345)))), 38154 ^ _780205 : [(38155 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1507341), 38153 ^ [_1507341, _1507343, _1507345]), _1507345)))], (38157 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1507341, _1507341)), hAPP(hAPP(c_Product__Type_OPair(_1507341, _1507341), 38153 ^ [_1507341, _1507343, _1507345]), 38153 ^ [_1507341, _1507343, _1507345])), _1507343))]], -(c_Relation_Orefl__on(_1507341, _1507345, _1507343))], (38161 ^ _780205) ^ [_1507688, _1507690] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1507688), c_Int_OInteg)), hBOOL(hAPP(_1507690, hAPP(c_Int_ORep__Integ, 38166 ^ [_1507688, _1507690]))), -(hBOOL(hAPP(_1507690, _1507688)))], (38172 ^ _780205) ^ [_1507869, _1507871, _1507873, _1507875, _1507877, _1507879] : [-(_1507869 = c_Orderings_Obot__class_Obot(tc_fun(_1507871, tc_HOL_Obool))), 38178 ^ _780205 : [(38179 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1507871), 38177 ^ [_1507869, _1507871, _1507873, _1507875, _1507877, _1507879]), _1507869)))], (38181 ^ _780205) ^ [] : [c_Fun_Oinj__on(_1507873, _1507875, _1507877, hAPP(_1507879, 38177 ^ [_1507869, _1507871, _1507873, _1507875, _1507877, _1507879]))]], -(c_Fun_Oinj__on(_1507873, _1507875, _1507877, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1507871, tc_fun(_1507873, tc_HOL_Obool)), _1507869), _1507879)))], (38185 ^ _780205) ^ [_1508161, _1508163] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1508161)), -(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)), _1508161))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1508163))))) = 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)), _1508161))), 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, _1508163))))))], (38191 ^ _780205) ^ [_1508338, _1508340] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1508338)), 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)), _1508338))), 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, _1508340))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (38197 ^ _780205) ^ [_1508464, _1508466] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1508464))), -(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)), _1508464))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1508466)))) = 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)), _1508464))), 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, _1508466))))))], (38203 ^ _780205) ^ [_1508547, _1508549, _1508551] : [hBOOL(hAPP(_1508547, _1508549)), -(hBOOL(hAPP(hAPP(c_member(_1508551), _1508549), hAPP(c_Set_OCollect(_1508551), _1508547))))], (38209 ^ _780205) ^ [_1508654, _1508656, _1508658] : [38210 ^ _780205 : [(38211 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1508654), hAPP(c_Set_OCollect(_1508654), _1508656)))], (38213 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1508654), hAPP(c_Set_OCollect(_1508654), _1508658)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1508654), hAPP(c_Set_OCollect(_1508654), hAPP(hAPP(c_COMBS(_1508654, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508654), c_fconj), _1508656)), _1508658)))))], (38217 ^ _780205) ^ [_1508865] : [-(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)), _1508865)))))], (38219 ^ _780205) ^ [_1508896] : [-(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)), _1508896)))))], (38221 ^ _780205) ^ [_1508927, _1508929, _1508931, _1508933] : [-(hAPP(c_Set_OCollect(tc_prod(_1508927, _1508929)), hAPP(c_Product__Type_Oprod_Oprod__case(_1508927, _1508929, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1508927, tc_fun(_1508929, tc_HOL_Obool), tc_fun(_1508929, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1508929, tc_HOL_Obool), tc_fun(_1508929, tc_HOL_Obool)), _1508927), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1508929)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508927), c_fconj), _1508931))), _1508933))) = hAPP(hAPP(c_Product__Type_OSigma(_1508927, _1508929), hAPP(c_Set_OCollect(_1508927), _1508931)), hAPP(c_COMBK(tc_fun(_1508929, tc_HOL_Obool), _1508927), hAPP(c_Set_OCollect(_1508929), _1508933))))], (38223 ^ _780205) ^ [_1509048, _1509050, _1509052, _1509054] : [-(hAPP(c_Set_OCollect(tc_prod(_1509048, _1509050)), hAPP(c_Product__Type_Oprod_Oprod__case(_1509048, _1509050, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1509048, tc_fun(_1509050, tc_HOL_Obool), tc_fun(_1509050, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1509050, tc_HOL_Obool), tc_fun(_1509050, tc_HOL_Obool)), _1509048), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1509050)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509048), c_fconj), _1509052))), _1509054))) = hAPP(hAPP(c_Product__Type_OSigma(_1509048, _1509050), hAPP(c_Set_OCollect(_1509048), _1509052)), hAPP(hAPP(c_COMBB(tc_fun(_1509050, tc_HOL_Obool), tc_fun(_1509050, tc_HOL_Obool), _1509048), c_Set_OCollect(_1509050)), _1509054)))], (38225 ^ _780205) ^ [_1509173, _1509175] : [-(hAPP(c_Set_OCollect(_1509173), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1509173), c_fNot), _1509175)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1509173, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1509173), _1509175)))], (38227 ^ _780205) ^ [_1509226, _1509228, _1509230] : [-(hAPP(c_Set_OCollect(_1509226), hAPP(hAPP(c_COMBS(_1509226, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509226), c_fconj), _1509228)), _1509230)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509226, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1509226), _1509228)), hAPP(c_Set_OCollect(_1509226), _1509230)))], (38229 ^ _780205) ^ [_1509299, _1509301, _1509303] : [-(hAPP(c_Set_OCollect(_1509299), hAPP(hAPP(c_COMBS(_1509299, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509299), c_fdisj), _1509301)), _1509303)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1509299, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1509299), _1509301)), hAPP(c_Set_OCollect(_1509299), _1509303)))], (38231 ^ _780205) ^ [_1509390, _1509392, _1509394] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1509390), hAPP(c_Set_OCollect(_1509390), hAPP(hAPP(c_COMBS(_1509390, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509390), c_fdisj), _1509392)), _1509394)))), 38234 ^ _780205 : [(38235 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1509390), hAPP(c_Set_OCollect(_1509390), _1509392))))], (38237 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1509390), hAPP(c_Set_OCollect(_1509390), _1509394))))]]], (38239 ^ _780205) ^ [_1509585, _1509587, _1509589] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1509585), hAPP(c_Set_OCollect(_1509585), hAPP(hAPP(c_COMBS(_1509585, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509585), c_fdisj), _1509587)), _1509589))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509585), hAPP(c_Set_OCollect(_1509585), _1509587))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509585), hAPP(c_Set_OCollect(_1509585), _1509589)))], (38249 ^ _780205) ^ [_1509814, _1509816, _1509818, _1509820] : [-(hAPP(c_Set_Ovimage(_1509814, _1509816, _1509818), hAPP(c_Set_OCollect(_1509816), _1509820)) = hAPP(c_Set_OCollect(_1509814), hAPP(hAPP(c_COMBB(_1509816, tc_HOL_Obool, _1509814), _1509820), _1509818)))], (38251 ^ _780205) ^ [_1509870, _1509872] : [-(hAPP(c_Set_OCollect(_1509870), _1509872) = _1509872)], (38253 ^ _780205) ^ [_1509900] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1509900, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1509900), hAPP(c_COMBK(tc_HOL_Obool, _1509900), c_fFalse)))], (38255 ^ _780205) ^ [_1509954, _1509956] : [hAPP(c_Set_OCollect(_1509954), _1509956) = c_Orderings_Obot__class_Obot(tc_fun(_1509954, tc_HOL_Obool)), 38258 ^ _780205 : [(38259 ^ _780205) ^ [_1510039] : [hBOOL(hAPP(_1509956, _1510039))]]], (38261 ^ _780205) ^ [_1510062, _1510064] : [-(hBOOL(hAPP(_1510064, 38262 ^ [_1510062, _1510064]))), -(hAPP(c_Set_OCollect(_1510062), _1510064) = c_Orderings_Obot__class_Obot(tc_fun(_1510062, tc_HOL_Obool)))], (38268 ^ _780205) ^ [_1510134, _1510136] : [c_Orderings_Obot__class_Obot(tc_fun(_1510134, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1510134), _1510136), 38271 ^ _780205 : [(38272 ^ _780205) ^ [_1510219] : [hBOOL(hAPP(_1510136, _1510219))]]], (38274 ^ _780205) ^ [_1510242, _1510244] : [-(hBOOL(hAPP(_1510244, 38275 ^ [_1510242, _1510244]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1510242, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1510242), _1510244))], (38281 ^ _780205) ^ [_1510299, _1510301, _1510303] : [-(hAPP(hAPP(c_Set_Oinsert(_1510299), _1510301), hAPP(c_Set_OCollect(_1510299), _1510303)) = hAPP(c_Set_OCollect(_1510299), hAPP(hAPP(c_COMBS(_1510299, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510299), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1510299), c_fNot), hAPP(hAPP(c_COMBC(_1510299, _1510299, tc_HOL_Obool), c_fequal), _1510301)))), _1510303)))], (38283 ^ _780205) ^ [_1510384] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1510384, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1510384), hAPP(c_COMBK(tc_HOL_Obool, _1510384), c_fTrue)))], (38285 ^ _780205) ^ [_1510423, _1510425, _1510427] : [hBOOL(hAPP(hAPP(c_member(_1510423), _1510425), hAPP(c_Set_OCollect(_1510423), _1510427))), -(hBOOL(hAPP(_1510427, _1510425)))], (38291 ^ _780205) ^ [_1510530, _1510532, _1510534] : [hBOOL(hAPP(hAPP(c_member(_1510530), _1510532), hAPP(c_Set_OCollect(_1510530), _1510534))), -(hBOOL(hAPP(_1510534, _1510532)))], (38297 ^ _780205) ^ [_1510655, _1510657, _1510659] : [hBOOL(hAPP(hAPP(c_member(_1510655), _1510657), hAPP(c_Set_OCollect(_1510655), _1510659))), -(hBOOL(hAPP(_1510659, _1510657)))], (38303 ^ _780205) ^ [_1510758, _1510760, _1510762] : [hBOOL(hAPP(_1510762, _1510760)), -(hBOOL(hAPP(hAPP(c_member(_1510758), _1510760), hAPP(c_Set_OCollect(_1510758), _1510762))))], (38309 ^ _780205) ^ [_1510867, _1510869] : [-(hAPP(c_Set_OCollect(_1510867), hAPP(hAPP(c_COMBC(_1510867, tc_fun(_1510867, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510867)), _1510869)) = _1510869)], (38311 ^ _780205) ^ [_1510912, _1510914, _1510916] : [-(hAPP(hAPP(c_Set_Oinsert(_1510912), _1510914), _1510916) = hAPP(c_Set_OCollect(_1510912), hAPP(hAPP(c_COMBS(_1510912, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510912), c_fdisj), hAPP(hAPP(c_COMBC(_1510912, _1510912, tc_HOL_Obool), c_fequal), _1510914))), hAPP(hAPP(c_COMBC(_1510912, tc_fun(_1510912, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510912)), _1510916))))], (38313 ^ _780205) ^ [_1510997, _1510999, _1511001] : [-(hAPP(hAPP(c_Set_Oinsert(_1510997), _1510999), _1511001) = hAPP(c_Set_OCollect(_1510997), hAPP(hAPP(c_COMBS(_1510997, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510997), c_fdisj), hAPP(hAPP(c_COMBC(_1510997, _1510997, tc_HOL_Obool), c_fequal), _1510999))), hAPP(hAPP(c_COMBC(_1510997, tc_fun(_1510997, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510997)), _1511001))))], (38315 ^ _780205) ^ [_1511082, _1511084, _1511086] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1511082, tc_HOL_Obool)), _1511084), _1511086) = hAPP(c_Set_OCollect(_1511082), hAPP(hAPP(c_COMBS(_1511082, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511082), c_fdisj), hAPP(hAPP(c_COMBC(_1511082, tc_fun(_1511082, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511082)), _1511084))), hAPP(hAPP(c_COMBC(_1511082, tc_fun(_1511082, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511082)), _1511086))))], (38317 ^ _780205) ^ [_1511196, _1511198, _1511200, _1511202] : [hBOOL(hAPP(hAPP(c_member(_1511196), _1511198), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511196, tc_HOL_Obool)), _1511200), hAPP(c_Set_OCollect(_1511196), _1511202)))), 38320 ^ _780205 : [(38321 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1511196), _1511198), _1511200)))], (38323 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1511202, _1511198)))]]], (38325 ^ _780205) ^ [_1511363, _1511365, _1511367, _1511369] : [-(hBOOL(hAPP(hAPP(c_member(_1511363), _1511365), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511363, tc_HOL_Obool)), _1511367), hAPP(c_Set_OCollect(_1511363), _1511369))))), hBOOL(hAPP(hAPP(c_member(_1511363), _1511365), _1511367)), hBOOL(hAPP(_1511369, _1511365))], (38335 ^ _780205) ^ [_1511566, _1511568, _1511570] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511566, tc_HOL_Obool)), _1511568), _1511570) = hAPP(c_Set_OCollect(_1511566), hAPP(hAPP(c_COMBS(_1511566, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511566), c_fconj), hAPP(hAPP(c_COMBC(_1511566, tc_fun(_1511566, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511566)), _1511568))), hAPP(hAPP(c_COMBC(_1511566, tc_fun(_1511566, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511566)), _1511570))))], (38337 ^ _780205) ^ [_1511671, _1511673, _1511675] : [hBOOL(hAPP(_1511671, _1511673)), -(hAPP(c_Set_OCollect(_1511675), hAPP(hAPP(c_COMBS(_1511675, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511675), c_fconj), hAPP(hAPP(c_COMBC(_1511675, _1511675, tc_HOL_Obool), c_fequal), _1511673))), _1511671)) = hAPP(hAPP(c_Set_Oinsert(_1511675), _1511673), c_Orderings_Obot__class_Obot(tc_fun(_1511675, tc_HOL_Obool))))], (38343 ^ _780205) ^ [_1511844, _1511846, _1511848] : [-(hBOOL(hAPP(_1511844, _1511846))), -(hAPP(c_Set_OCollect(_1511848), hAPP(hAPP(c_COMBS(_1511848, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511848), c_fconj), hAPP(hAPP(c_COMBC(_1511848, _1511848, tc_HOL_Obool), c_fequal), _1511846))), _1511844)) = c_Orderings_Obot__class_Obot(tc_fun(_1511848, tc_HOL_Obool)))], (38349 ^ _780205) ^ [_1511938, _1511940, _1511942] : [hBOOL(hAPP(_1511938, _1511940)), -(hAPP(c_Set_OCollect(_1511942), hAPP(hAPP(c_COMBS(_1511942, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511942), c_fconj), hAPP(c_fequal, _1511940))), _1511938)) = hAPP(hAPP(c_Set_Oinsert(_1511942), _1511940), c_Orderings_Obot__class_Obot(tc_fun(_1511942, tc_HOL_Obool))))], (38355 ^ _780205) ^ [_1512097, _1512099, _1512101] : [-(hBOOL(hAPP(_1512097, _1512099))), -(hAPP(c_Set_OCollect(_1512101), hAPP(hAPP(c_COMBS(_1512101, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512101), c_fconj), hAPP(c_fequal, _1512099))), _1512097)) = c_Orderings_Obot__class_Obot(tc_fun(_1512101, tc_HOL_Obool)))], (38361 ^ _780205) ^ [_1512172, _1512174] : [-(hAPP(c_Set_OCollect(_1512172), hAPP(hAPP(c_COMBC(_1512172, _1512172, tc_HOL_Obool), c_fequal), _1512174)) = hAPP(hAPP(c_Set_Oinsert(_1512172), _1512174), c_Orderings_Obot__class_Obot(tc_fun(_1512172, tc_HOL_Obool))))], (38363 ^ _780205) ^ [_1512225, _1512227] : [-(hAPP(c_Set_OCollect(_1512225), hAPP(c_fequal, _1512227)) = hAPP(hAPP(c_Set_Oinsert(_1512225), _1512227), c_Orderings_Obot__class_Obot(tc_fun(_1512225, tc_HOL_Obool))))], (38365 ^ _780205) ^ [_1512271, _1512273, _1512275] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1512271, tc_HOL_Obool)), _1512273), _1512275) = hAPP(c_Set_OCollect(_1512271), hAPP(hAPP(c_COMBS(_1512271, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512271), c_fconj), hAPP(hAPP(c_COMBC(_1512271, tc_fun(_1512271, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512271)), _1512273))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1512271), c_fNot), hAPP(hAPP(c_COMBC(_1512271, tc_fun(_1512271, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512271)), _1512275)))))], (38367 ^ _780205) ^ [_1512374, _1512376] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512374), hAPP(c_Set_OCollect(_1512374), _1512376))), 38370 ^ _780205 : [(38371 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512374), hAPP(c_Set_OCollect(_1512374), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1512374), c_fNot), _1512376)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512374), c_Orderings_Otop__class_Otop(tc_fun(_1512374, tc_HOL_Obool)))))], (38377 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512374), c_Orderings_Otop__class_Otop(tc_fun(_1512374, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512374), hAPP(c_Set_OCollect(_1512374), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1512374), c_fNot), _1512376)))))]]], (38383 ^ _780205) ^ [_1512683, _1512685, _1512687] : [-(hAPP(hAPP(c_Set_Oinsert(_1512683), _1512685), _1512687) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1512683, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1512683), hAPP(hAPP(c_COMBC(_1512683, _1512683, tc_HOL_Obool), c_fequal), _1512685))), _1512687))], (38385 ^ _780205) ^ [_1512744, _1512746] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1512744, tc_HOL_Obool)), _1512746) = hAPP(c_Set_OCollect(_1512744), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1512744), c_fNot), hAPP(hAPP(c_COMBC(_1512744, tc_fun(_1512744, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512744)), _1512746))))], (38387 ^ _780205) ^ [_1512807, _1512809, _1512811, _1512813] : [-(hAPP(c_Set_Ovimage(_1512807, _1512809, _1512811), _1512813) = hAPP(c_Set_OCollect(_1512807), hAPP(hAPP(c_COMBC(_1512807, tc_fun(_1512809, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1512809, tc_fun(tc_fun(_1512809, tc_HOL_Obool), tc_HOL_Obool), _1512807), c_member(_1512809)), _1512811)), _1512813)))], (38389 ^ _780205) ^ [_1512879, _1512881, _1512883] : [-(hAPP(c_Set_OCollect(_1512879), hAPP(hAPP(c_COMBS(_1512879, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512879), c_fimplies), _1512881)), _1512883)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1512879, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1512879, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1512879), _1512881))), hAPP(c_Set_OCollect(_1512879), _1512883)))], (38391 ^ _780205) ^ [_1512960, _1512962] : [-(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), _1512960)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1512962))))))], (38393 ^ _780205) ^ [_1513002, _1513004, _1513006, _1513008, _1513010, _1513012, _1513014] : [class_Groups_Ocomm__monoid__add(_1513002), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513004), _1513006)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513008), _1513010)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513004, _1513002), hAPP(hAPP(c_COMBS(_1513004, tc_fun(_1513008, tc_HOL_Obool), _1513002), hAPP(hAPP(c_COMBB(tc_fun(_1513008, _1513002), tc_fun(tc_fun(_1513008, tc_HOL_Obool), _1513002), _1513004), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513008, _1513002)), _1513012)), hAPP(hAPP(c_COMBB(tc_fun(_1513008, tc_HOL_Obool), tc_fun(_1513008, tc_HOL_Obool), _1513004), c_Set_OCollect(_1513008)), hAPP(hAPP(c_COMBB(tc_fun(_1513008, tc_HOL_Obool), tc_fun(_1513008, tc_HOL_Obool), _1513004), hAPP(c_COMBS(_1513008, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513008), c_fconj), hAPP(hAPP(c_COMBC(_1513008, tc_fun(_1513008, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513008)), _1513010)))), _1513014)))), _1513006) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513008, _1513002), hAPP(hAPP(c_COMBS(_1513008, tc_fun(_1513004, tc_HOL_Obool), _1513002), hAPP(hAPP(c_COMBB(tc_fun(_1513004, _1513002), tc_fun(tc_fun(_1513004, tc_HOL_Obool), _1513002), _1513008), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513004, _1513002)), hAPP(c_COMBC(_1513004, _1513008, _1513002), _1513012))), hAPP(hAPP(c_COMBB(tc_fun(_1513004, tc_HOL_Obool), tc_fun(_1513004, tc_HOL_Obool), _1513008), c_Set_OCollect(_1513004)), hAPP(hAPP(c_COMBB(tc_fun(_1513004, tc_HOL_Obool), tc_fun(_1513004, tc_HOL_Obool), _1513008), hAPP(c_COMBS(_1513004, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513004), c_fconj), hAPP(hAPP(c_COMBC(_1513004, tc_fun(_1513004, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513004)), _1513006)))), hAPP(c_COMBC(_1513004, _1513008, tc_HOL_Obool), _1513014))))), _1513010))], (38407 ^ _780205) ^ [_1513695, _1513697, _1513699, _1513701, _1513703, _1513705] : [-(hAPP(c_Set_Oimage(_1513695, _1513697, hAPP(hAPP(c_COMBS(_1513695, _1513697, _1513697), hAPP(hAPP(c_COMBS(_1513695, _1513697, tc_fun(_1513697, _1513697)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1513697, tc_fun(_1513697, _1513697)), _1513695), c_If(_1513697)), _1513699)), _1513701)), _1513703)), _1513705) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1513697, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1513695, _1513697, _1513701), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1513695, tc_HOL_Obool)), _1513705), hAPP(c_Set_OCollect(_1513695), _1513699)))), hAPP(c_Set_Oimage(_1513695, _1513697, _1513703), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1513695, tc_HOL_Obool)), _1513705), hAPP(c_Set_OCollect(_1513695), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1513695), c_fNot), _1513699))))))], (38409 ^ _780205) ^ [_1513843, _1513845, _1513847, _1513849] : [_1513843 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1513845, _1513847), 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)), _1513849))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1513845), _1513843)))], (38415 ^ _780205) ^ [_1513958, _1513960, _1513962, _1513964, _1513966] : [class_Groups_Ocomm__monoid__add(_1513958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513960), _1513962)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513960, _1513958), _1513964), hAPP(c_Set_OCollect(_1513960), hAPP(hAPP(c_COMBS(_1513960, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513960), c_fconj), hAPP(hAPP(c_COMBC(_1513960, tc_fun(_1513960, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513960)), _1513962))), hAPP(hAPP(c_COMBC(_1513960, tc_fun(_1513960, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513960)), _1513966)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513960, _1513958), hAPP(hAPP(c_COMBC(_1513960, _1513958, _1513958), hAPP(hAPP(c_COMBS(_1513960, _1513958, tc_fun(_1513958, _1513958)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1513958, tc_fun(_1513958, _1513958)), _1513960), c_If(_1513958)), hAPP(hAPP(c_COMBC(_1513960, tc_fun(_1513960, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513960)), _1513966))), _1513964)), c_Groups_Ozero__class_Ozero(_1513958))), _1513962))], (38425 ^ _780205) ^ [_1514367, _1514369, _1514371, _1514373, _1514375, _1514377] : [class_Groups_Ocomm__monoid__add(_1514367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514369), _1514371)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514369, _1514367), _1514373), _1514371) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514375, _1514367), hAPP(hAPP(c_COMBB(tc_fun(_1514369, tc_HOL_Obool), _1514367, _1514375), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514369, _1514367), _1514373)), hAPP(hAPP(c_COMBB(tc_fun(_1514369, tc_HOL_Obool), tc_fun(_1514369, tc_HOL_Obool), _1514375), c_Set_OCollect(_1514369)), hAPP(hAPP(c_COMBB(tc_fun(_1514369, tc_HOL_Obool), tc_fun(_1514369, tc_HOL_Obool), _1514375), hAPP(c_COMBS(_1514369, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1514369), c_fconj), hAPP(hAPP(c_COMBC(_1514369, tc_fun(_1514369, tc_HOL_Obool), tc_HOL_Obool), c_member(_1514369)), _1514371)))), hAPP(c_COMBC(_1514369, _1514375, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1514375, tc_fun(_1514375, tc_HOL_Obool), _1514369), c_fequal), _1514377)))))), hAPP(c_Set_Oimage(_1514369, _1514375, _1514377), _1514371)))], (38435 ^ _780205) ^ [_1514778, _1514780, _1514782, _1514784] : [-(hAPP(c_Relation_OImage(_1514778, _1514780, _1514782), hAPP(hAPP(c_Set_Oinsert(_1514778), _1514784), c_Orderings_Obot__class_Obot(tc_fun(_1514778, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1514780), hAPP(hAPP(c_COMBC(_1514780, tc_fun(tc_prod(_1514778, _1514780), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1514778, _1514780), tc_fun(tc_fun(tc_prod(_1514778, _1514780), tc_HOL_Obool), tc_HOL_Obool), _1514780), c_member(tc_prod(_1514778, _1514780))), hAPP(c_Product__Type_OPair(_1514778, _1514780), _1514784))), _1514782)))], (38437 ^ _780205) ^ [_1514881, _1514883, _1514885, _1514887, _1514889, _1514891] : [class_Groups_Ocomm__monoid__add(_1514881), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514883), _1514885)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514883, _1514881), hAPP(hAPP(c_COMBS(_1514883, _1514881, _1514881), hAPP(hAPP(c_COMBS(_1514883, _1514881, tc_fun(_1514881, _1514881)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1514881, tc_fun(_1514881, _1514881)), _1514883), c_If(_1514881)), _1514887)), _1514889)), _1514891)), _1514885) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1514881), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514883, _1514881), _1514889), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1514883, tc_HOL_Obool)), _1514885), hAPP(c_Set_OCollect(_1514883), _1514887)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514883, _1514881), _1514891), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1514883, tc_HOL_Obool)), _1514885), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1514883, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1514883), _1514887))))))], (38447 ^ _780205) ^ [_1515264, _1515266, _1515268, _1515270, _1515272, _1515274] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515264), _1515266)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515268), _1515270)), 38457 ^ _780205 : [(38458 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515268), 38456 ^ [_1515264, _1515266, _1515268, _1515270, _1515272, _1515274]), _1515270)))], (38460 ^ _780205) ^ [] : [hAPP(c_Finite__Set_Ocard(_1515264), hAPP(c_Set_OCollect(_1515264), hAPP(hAPP(c_COMBS(_1515264, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515264), c_fconj), hAPP(hAPP(c_COMBC(_1515264, tc_fun(_1515264, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515264)), _1515266))), hAPP(hAPP(c_COMBC(_1515264, _1515268, tc_HOL_Obool), _1515272), 38456 ^ [_1515264, _1515266, _1515268, _1515270, _1515272, _1515274])))) = _1515274]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1515264, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1515268, tc_HOL_Obool), tc_Nat_Onat, _1515264), c_Finite__Set_Ocard(_1515268)), hAPP(hAPP(c_COMBB(tc_fun(_1515268, tc_HOL_Obool), tc_fun(_1515268, tc_HOL_Obool), _1515264), c_Set_OCollect(_1515268)), hAPP(hAPP(c_COMBB(tc_fun(_1515268, tc_HOL_Obool), tc_fun(_1515268, tc_HOL_Obool), _1515264), hAPP(c_COMBS(_1515268, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515268), c_fconj), hAPP(hAPP(c_COMBC(_1515268, tc_fun(_1515268, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515268)), _1515270)))), _1515272)))), _1515266) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1515274), hAPP(c_Finite__Set_Ocard(_1515268), _1515270)))], (38464 ^ _780205) ^ [_1515954, _1515956, _1515958] : [class_Orderings_Olinorder(_1515954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515954), _1515956)), -(_1515956 = c_Orderings_Obot__class_Obot(tc_fun(_1515954, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515954), _1515958)), -(_1515958 = c_Orderings_Obot__class_Obot(tc_fun(_1515954, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1515954), c_Big__Operators_Olattice_OSup__fin(_1515954, c_Orderings_Oord__class_Omax(_1515954), _1515956)), c_Big__Operators_Olattice_OSup__fin(_1515954, c_Orderings_Oord__class_Omax(_1515954), _1515958)) = c_Big__Operators_Olattice_OSup__fin(_1515954, c_Orderings_Oord__class_Omax(_1515954), hAPP(c_Set_OCollect(_1515954), hAPP(hAPP(c_COMBB(tc_fun(_1515954, tc_HOL_Obool), tc_HOL_Obool, _1515954), c_HOL_OEx(_1515954)), hAPP(hAPP(c_COMBB(tc_fun(_1515954, tc_fun(_1515954, tc_HOL_Obool)), tc_fun(_1515954, tc_HOL_Obool), _1515954), hAPP(c_COMBB(tc_fun(_1515954, tc_HOL_Obool), tc_HOL_Obool, _1515954), c_HOL_OEx(_1515954))), hAPP(hAPP(c_COMBC(_1515954, tc_fun(_1515954, tc_fun(_1515954, tc_HOL_Obool)), tc_fun(_1515954, tc_fun(_1515954, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1515954, tc_fun(tc_fun(_1515954, tc_HOL_Obool), tc_fun(_1515954, tc_HOL_Obool))), tc_fun(tc_fun(_1515954, tc_fun(_1515954, tc_HOL_Obool)), tc_fun(_1515954, tc_fun(_1515954, tc_HOL_Obool))), _1515954), c_COMBS(_1515954, tc_fun(_1515954, tc_HOL_Obool), tc_fun(_1515954, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1515954, tc_fun(_1515954, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1515954, tc_fun(tc_fun(_1515954, tc_HOL_Obool), tc_fun(_1515954, tc_HOL_Obool))), _1515954), hAPP(c_COMBB(tc_fun(_1515954, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1515954, tc_HOL_Obool), tc_fun(_1515954, tc_HOL_Obool)), _1515954), c_COMBS(_1515954, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1515954, tc_fun(_1515954, tc_HOL_Obool)), tc_fun(_1515954, tc_fun(_1515954, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1515954), hAPP(c_COMBB(tc_fun(_1515954, tc_HOL_Obool), tc_fun(_1515954, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1515954), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515954), c_fconj))), hAPP(hAPP(c_COMBC(_1515954, tc_fun(_1515954, tc_fun(_1515954, _1515954)), tc_fun(_1515954, tc_fun(_1515954, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1515954, _1515954), tc_fun(_1515954, tc_HOL_Obool)), tc_fun(tc_fun(_1515954, tc_fun(_1515954, _1515954)), tc_fun(_1515954, tc_fun(_1515954, tc_HOL_Obool))), _1515954), c_COMBB(tc_fun(_1515954, _1515954), tc_fun(_1515954, tc_HOL_Obool), _1515954)), hAPP(hAPP(c_COMBB(tc_fun(_1515954, tc_HOL_Obool), tc_fun(tc_fun(_1515954, _1515954), tc_fun(_1515954, tc_HOL_Obool)), _1515954), c_COMBB(_1515954, tc_HOL_Obool, _1515954)), c_fequal))), c_Orderings_Oord__class_Omin(_1515954)))))), hAPP(hAPP(c_COMBC(_1515954, tc_fun(_1515954, tc_HOL_Obool), tc_fun(_1515954, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1515954, tc_HOL_Obool), tc_fun(_1515954, tc_HOL_Obool)), _1515954), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1515954)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515954), c_fconj), hAPP(hAPP(c_COMBC(_1515954, tc_fun(_1515954, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515954)), _1515956)))), hAPP(hAPP(c_COMBC(_1515954, tc_fun(_1515954, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515954)), _1515958))))))))], (38486 ^ _780205) ^ [_1517071, _1517073, _1517075] : [class_Orderings_Olinorder(_1517071), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517071), _1517073)), -(_1517073 = c_Orderings_Obot__class_Obot(tc_fun(_1517071, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1517071), _1517075), c_Big__Operators_Olattice_OSup__fin(_1517071, c_Orderings_Oord__class_Omax(_1517071), _1517073)) = c_Big__Operators_Olattice_OSup__fin(_1517071, c_Orderings_Oord__class_Omax(_1517071), hAPP(c_Set_OCollect(_1517071), hAPP(hAPP(c_COMBB(tc_fun(_1517071, tc_HOL_Obool), tc_HOL_Obool, _1517071), c_HOL_OEx(_1517071)), hAPP(hAPP(c_COMBC(_1517071, tc_fun(_1517071, tc_HOL_Obool), tc_fun(_1517071, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517071, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1517071, tc_HOL_Obool), tc_fun(_1517071, tc_HOL_Obool)), _1517071), c_COMBS(_1517071, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517071, tc_HOL_Obool), tc_fun(_1517071, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1517071), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1517071), c_fconj)), hAPP(hAPP(c_COMBC(_1517071, tc_fun(_1517071, _1517071), tc_fun(_1517071, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517071, tc_HOL_Obool), tc_fun(tc_fun(_1517071, _1517071), tc_fun(_1517071, tc_HOL_Obool)), _1517071), c_COMBB(_1517071, tc_HOL_Obool, _1517071)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1517071), _1517075))))), hAPP(hAPP(c_COMBC(_1517071, tc_fun(_1517071, tc_HOL_Obool), tc_HOL_Obool), c_member(_1517071)), _1517073))))))], (38500 ^ _780205) ^ [_1517569, _1517571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1517569), _1517571)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1517569, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1517569, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1517569, tc_HOL_Obool), tc_fun(_1517569, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1517569, tc_HOL_Obool))), _1517571)))))], (38506 ^ _780205) ^ [_1517726, _1517728] : [-(hAPP(c_Set_OPow(_1517726), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1517726, tc_HOL_Obool)), _1517728)) = hAPP(c_Set_OCollect(tc_fun(_1517726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1517726, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1517726, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1517726, tc_HOL_Obool), tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1517726, tc_HOL_Obool)), c_COMBS(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1517726, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1517726, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1517726, tc_HOL_Obool), tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_fun(_1517726, tc_HOL_Obool)), tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_fun(_1517726, tc_HOL_Obool)), tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1517726, tc_HOL_Obool)), c_COMBB(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1517726, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1517726, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1517726, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1517726, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1517726, tc_HOL_Obool)), _1517728)), c_Set_OPow(_1517726))))))], (38508 ^ _780205) ^ [_1518006, _1518008] : [-(hAPP(c_Set_OPow(_1518006), _1518008) = hAPP(c_Set_OCollect(tc_fun(_1518006, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1518006, tc_HOL_Obool), tc_fun(_1518006, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1518006, tc_HOL_Obool))), _1518008)))], (38510 ^ _780205) ^ [_1518065, _1518067, _1518069, _1518071] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518065), hAPP(c_Set_OCollect(_1518065), _1518067))), 38513 ^ _780205 : [(38524 ^ _780205) ^ [] : [38526 ^ _780205 : [(38527 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1518067, 38525 ^ [_1518065, _1518067, _1518069, _1518071])))], (38529 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518069), hAPP(c_Set_OCollect(_1518069), hAPP(hAPP(c_COMBC(_1518069, _1518065, tc_HOL_Obool), _1518071), 38525 ^ [_1518065, _1518067, _1518069, _1518071]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1518069), hAPP(c_Set_OCollect(_1518069), hAPP(hAPP(c_COMBB(tc_fun(_1518065, tc_HOL_Obool), tc_HOL_Obool, _1518069), c_HOL_OEx(_1518065)), hAPP(hAPP(c_COMBB(tc_fun(_1518065, tc_HOL_Obool), tc_fun(_1518065, tc_HOL_Obool), _1518069), hAPP(c_COMBS(_1518065, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518065), c_fconj), _1518067))), _1518071))))))], (38514 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518069), hAPP(c_Set_OCollect(_1518069), hAPP(hAPP(c_COMBB(tc_fun(_1518065, tc_HOL_Obool), tc_HOL_Obool, _1518069), c_HOL_OEx(_1518065)), hAPP(hAPP(c_COMBB(tc_fun(_1518065, tc_HOL_Obool), tc_fun(_1518065, tc_HOL_Obool), _1518069), hAPP(c_COMBS(_1518065, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518065), c_fconj), _1518067))), _1518071))))), 38517 ^ _780205 : [(38518 ^ _780205) ^ [_1518348] : [hBOOL(hAPP(_1518067, _1518348)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1518069), hAPP(c_Set_OCollect(_1518069), hAPP(hAPP(c_COMBC(_1518069, _1518065, tc_HOL_Obool), _1518071), _1518348)))))]]]]], (38533 ^ _780205) ^ [_1518713, _1518715, _1518717, _1518719] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518713), hAPP(c_Set_OCollect(_1518713), _1518715))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1518717), hAPP(c_Set_OCollect(_1518717), hAPP(hAPP(c_COMBB(tc_fun(_1518713, tc_HOL_Obool), tc_HOL_Obool, _1518717), c_HOL_OEx(_1518713)), hAPP(hAPP(c_COMBC(_1518717, tc_fun(_1518713, tc_HOL_Obool), tc_fun(_1518713, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518713, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1518713, tc_HOL_Obool), tc_fun(_1518713, tc_HOL_Obool)), _1518717), c_COMBS(_1518713, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518713, tc_HOL_Obool), tc_fun(_1518713, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1518717), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518713), c_fconj)), hAPP(hAPP(c_COMBC(_1518717, tc_fun(_1518713, _1518717), tc_fun(_1518713, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518717, tc_HOL_Obool), tc_fun(tc_fun(_1518713, _1518717), tc_fun(_1518713, tc_HOL_Obool)), _1518717), c_COMBB(_1518717, tc_HOL_Obool, _1518713)), c_fequal)), _1518719)))), _1518715))))))], (38539 ^ _780205) ^ [_1519074, _1519076] : [-(c_Fun_Oinj__on(tc_fun(_1519074, _1519076), tc_fun(tc_prod(_1519074, _1519076), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1519074, _1519076), tc_HOL_Obool), tc_fun(tc_prod(_1519074, _1519076), tc_HOL_Obool), tc_fun(_1519074, _1519076)), c_Set_OCollect(tc_prod(_1519074, _1519076))), hAPP(hAPP(c_COMBB(tc_fun(_1519074, tc_fun(_1519076, tc_HOL_Obool)), tc_fun(tc_prod(_1519074, _1519076), tc_HOL_Obool), tc_fun(_1519074, _1519076)), c_Product__Type_Oprod_Oprod__case(_1519074, _1519076, tc_HOL_Obool)), hAPP(c_COMBB(_1519076, tc_fun(_1519076, tc_HOL_Obool), _1519074), hAPP(c_COMBC(_1519076, _1519076, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1519074, _1519076), tc_HOL_Obool))))], (38541 ^ _780205) ^ [_1519194] : [-(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)))), _1519194))))], (38543 ^ _780205) ^ [_1519222] : [-(c_Wellfounded_Ofinite__psubset(_1519222) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1519222, tc_HOL_Obool), tc_fun(_1519222, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1519222, tc_HOL_Obool), tc_fun(_1519222, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1519222, tc_HOL_Obool), tc_fun(tc_fun(_1519222, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1519222, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1519222, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1519222, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1519222, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1519222, tc_HOL_Obool)), c_COMBS(tc_fun(_1519222, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1519222, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1519222, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1519222, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1519222, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1519222, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1519222)))))], (38545 ^ _780205) ^ [_1519382, _1519384, _1519386, _1519388] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1519382, _1519384), _1519386), _1519388) = hAPP(c_Set_OCollect(tc_prod(_1519384, _1519384)), hAPP(c_Product__Type_Oprod_Oprod__case(_1519384, _1519384, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1519384, tc_fun(tc_prod(_1519382, _1519382), tc_HOL_Obool), tc_fun(_1519384, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519384, tc_fun(tc_fun(tc_prod(_1519382, _1519382), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1519382, _1519382), tc_HOL_Obool), tc_fun(_1519384, tc_HOL_Obool)), _1519384), c_COMBC(_1519384, tc_fun(tc_prod(_1519382, _1519382), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519384, tc_prod(_1519382, _1519382)), tc_fun(_1519384, tc_fun(tc_fun(tc_prod(_1519382, _1519382), tc_HOL_Obool), tc_HOL_Obool)), _1519384), hAPP(c_COMBB(tc_prod(_1519382, _1519382), tc_fun(tc_fun(tc_prod(_1519382, _1519382), tc_HOL_Obool), tc_HOL_Obool), _1519384), c_member(tc_prod(_1519382, _1519382)))), hAPP(hAPP(c_COMBC(_1519384, tc_fun(_1519384, _1519382), tc_fun(_1519384, tc_prod(_1519382, _1519382))), hAPP(hAPP(c_COMBB(tc_fun(_1519382, tc_prod(_1519382, _1519382)), tc_fun(tc_fun(_1519384, _1519382), tc_fun(_1519384, tc_prod(_1519382, _1519382))), _1519384), c_COMBB(_1519382, tc_prod(_1519382, _1519382), _1519384)), hAPP(hAPP(c_COMBB(_1519382, tc_fun(_1519382, tc_prod(_1519382, _1519382)), _1519384), c_Product__Type_OPair(_1519382, _1519382)), _1519388))), _1519388)))), _1519386))))], (38547 ^ _780205) ^ [_1519623] : [-(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)))), _1519623)) = 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), _1519623), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (38549 ^ _780205) ^ [_1519664] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1519664) = 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), _1519664), c_Int_Onat)))))], (38551 ^ _780205) ^ [_1519705, _1519707, _1519709] : [class_Groups_Olinordered__ab__semigroup__add(_1519705), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519705), _1519707)), -(_1519707 = c_Orderings_Obot__class_Obot(tc_fun(_1519705, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1519705), _1519709), c_Big__Operators_Olinorder__class_OMin(_1519705, _1519707)) = c_Big__Operators_Olinorder__class_OMin(_1519705, hAPP(c_Set_OCollect(_1519705), hAPP(hAPP(c_COMBB(tc_fun(_1519705, tc_HOL_Obool), tc_HOL_Obool, _1519705), c_HOL_OEx(_1519705)), hAPP(hAPP(c_COMBC(_1519705, tc_fun(_1519705, tc_HOL_Obool), tc_fun(_1519705, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519705, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1519705, tc_HOL_Obool), tc_fun(_1519705, tc_HOL_Obool)), _1519705), c_COMBS(_1519705, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519705, tc_HOL_Obool), tc_fun(_1519705, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1519705), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519705), c_fconj)), hAPP(hAPP(c_COMBC(_1519705, tc_fun(_1519705, _1519705), tc_fun(_1519705, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519705, tc_HOL_Obool), tc_fun(tc_fun(_1519705, _1519705), tc_fun(_1519705, tc_HOL_Obool)), _1519705), c_COMBB(_1519705, tc_HOL_Obool, _1519705)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1519705), _1519709))))), hAPP(hAPP(c_COMBC(_1519705, tc_fun(_1519705, tc_HOL_Obool), tc_HOL_Obool), c_member(_1519705)), _1519707))))))], (38565 ^ _780205) ^ [_1520191, _1520193, _1520195] : [class_Groups_Olinordered__ab__semigroup__add(_1520191), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520191), _1520193)), -(_1520193 = c_Orderings_Obot__class_Obot(tc_fun(_1520191, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1520191), _1520195), c_Big__Operators_Olinorder__class_OMax(_1520191, _1520193)) = c_Big__Operators_Olinorder__class_OMax(_1520191, hAPP(c_Set_OCollect(_1520191), hAPP(hAPP(c_COMBB(tc_fun(_1520191, tc_HOL_Obool), tc_HOL_Obool, _1520191), c_HOL_OEx(_1520191)), hAPP(hAPP(c_COMBC(_1520191, tc_fun(_1520191, tc_HOL_Obool), tc_fun(_1520191, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520191, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1520191, tc_HOL_Obool), tc_fun(_1520191, tc_HOL_Obool)), _1520191), c_COMBS(_1520191, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520191, tc_HOL_Obool), tc_fun(_1520191, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1520191), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520191), c_fconj)), hAPP(hAPP(c_COMBC(_1520191, tc_fun(_1520191, _1520191), tc_fun(_1520191, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520191, tc_HOL_Obool), tc_fun(tc_fun(_1520191, _1520191), tc_fun(_1520191, tc_HOL_Obool)), _1520191), c_COMBB(_1520191, tc_HOL_Obool, _1520191)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1520191), _1520195))))), hAPP(hAPP(c_COMBC(_1520191, tc_fun(_1520191, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520191)), _1520193))))))], (38579 ^ _780205) ^ [_1520677, _1520679, _1520681] : [class_Lattices_Odistrib__lattice(_1520677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520677), _1520679)), -(_1520679 = c_Orderings_Obot__class_Obot(tc_fun(_1520677, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520677), _1520681)), -(_1520681 = c_Orderings_Obot__class_Obot(tc_fun(_1520677, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1520677), c_Big__Operators_Olattice__class_OInf__fin(_1520677, _1520679)), c_Big__Operators_Olattice__class_OInf__fin(_1520677, _1520681)) = c_Big__Operators_Olattice__class_OInf__fin(_1520677, hAPP(c_Set_OCollect(_1520677), hAPP(hAPP(c_COMBB(tc_fun(_1520677, tc_HOL_Obool), tc_HOL_Obool, _1520677), c_HOL_OEx(_1520677)), hAPP(hAPP(c_COMBB(tc_fun(_1520677, tc_fun(_1520677, tc_HOL_Obool)), tc_fun(_1520677, tc_HOL_Obool), _1520677), hAPP(c_COMBB(tc_fun(_1520677, tc_HOL_Obool), tc_HOL_Obool, _1520677), c_HOL_OEx(_1520677))), hAPP(hAPP(c_COMBC(_1520677, tc_fun(_1520677, tc_fun(_1520677, tc_HOL_Obool)), tc_fun(_1520677, tc_fun(_1520677, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1520677, tc_fun(tc_fun(_1520677, tc_HOL_Obool), tc_fun(_1520677, tc_HOL_Obool))), tc_fun(tc_fun(_1520677, tc_fun(_1520677, tc_HOL_Obool)), tc_fun(_1520677, tc_fun(_1520677, tc_HOL_Obool))), _1520677), c_COMBS(_1520677, tc_fun(_1520677, tc_HOL_Obool), tc_fun(_1520677, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1520677, tc_fun(_1520677, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1520677, tc_fun(tc_fun(_1520677, tc_HOL_Obool), tc_fun(_1520677, tc_HOL_Obool))), _1520677), hAPP(c_COMBB(tc_fun(_1520677, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1520677, tc_HOL_Obool), tc_fun(_1520677, tc_HOL_Obool)), _1520677), c_COMBS(_1520677, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1520677, tc_fun(_1520677, tc_HOL_Obool)), tc_fun(_1520677, tc_fun(_1520677, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1520677), hAPP(c_COMBB(tc_fun(_1520677, tc_HOL_Obool), tc_fun(_1520677, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1520677), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520677), c_fconj))), hAPP(hAPP(c_COMBC(_1520677, tc_fun(_1520677, tc_fun(_1520677, _1520677)), tc_fun(_1520677, tc_fun(_1520677, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1520677, _1520677), tc_fun(_1520677, tc_HOL_Obool)), tc_fun(tc_fun(_1520677, tc_fun(_1520677, _1520677)), tc_fun(_1520677, tc_fun(_1520677, tc_HOL_Obool))), _1520677), c_COMBB(tc_fun(_1520677, _1520677), tc_fun(_1520677, tc_HOL_Obool), _1520677)), hAPP(hAPP(c_COMBB(tc_fun(_1520677, tc_HOL_Obool), tc_fun(tc_fun(_1520677, _1520677), tc_fun(_1520677, tc_HOL_Obool)), _1520677), c_COMBB(_1520677, tc_HOL_Obool, _1520677)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1520677)))))), hAPP(hAPP(c_COMBC(_1520677, tc_fun(_1520677, tc_HOL_Obool), tc_fun(_1520677, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1520677, tc_HOL_Obool), tc_fun(_1520677, tc_HOL_Obool)), _1520677), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1520677)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520677), c_fconj), hAPP(hAPP(c_COMBC(_1520677, tc_fun(_1520677, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520677)), _1520679)))), hAPP(hAPP(c_COMBC(_1520677, tc_fun(_1520677, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520677)), _1520681))))))))], (38601 ^ _780205) ^ [_1521776, _1521778, _1521780] : [class_Lattices_Odistrib__lattice(_1521776), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521776), _1521778)), -(_1521778 = c_Orderings_Obot__class_Obot(tc_fun(_1521776, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1521776), _1521780), c_Big__Operators_Olattice__class_OInf__fin(_1521776, _1521778)) = c_Big__Operators_Olattice__class_OInf__fin(_1521776, hAPP(c_Set_OCollect(_1521776), hAPP(hAPP(c_COMBB(tc_fun(_1521776, tc_HOL_Obool), tc_HOL_Obool, _1521776), c_HOL_OEx(_1521776)), hAPP(hAPP(c_COMBC(_1521776, tc_fun(_1521776, tc_HOL_Obool), tc_fun(_1521776, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1521776, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1521776, tc_HOL_Obool), tc_fun(_1521776, tc_HOL_Obool)), _1521776), c_COMBS(_1521776, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1521776, tc_HOL_Obool), tc_fun(_1521776, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1521776), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521776), c_fconj)), hAPP(hAPP(c_COMBC(_1521776, tc_fun(_1521776, _1521776), tc_fun(_1521776, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1521776, tc_HOL_Obool), tc_fun(tc_fun(_1521776, _1521776), tc_fun(_1521776, tc_HOL_Obool)), _1521776), c_COMBB(_1521776, tc_HOL_Obool, _1521776)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1521776), _1521780))))), hAPP(hAPP(c_COMBC(_1521776, tc_fun(_1521776, tc_HOL_Obool), tc_HOL_Obool), c_member(_1521776)), _1521778))))))], (38615 ^ _780205) ^ [_1522262, _1522264, _1522266] : [class_Lattices_Odistrib__lattice(_1522262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522262), _1522264)), -(_1522264 = c_Orderings_Obot__class_Obot(tc_fun(_1522262, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522262), _1522266)), -(_1522266 = c_Orderings_Obot__class_Obot(tc_fun(_1522262, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1522262), c_Big__Operators_Olattice__class_OSup__fin(_1522262, _1522264)), c_Big__Operators_Olattice__class_OSup__fin(_1522262, _1522266)) = c_Big__Operators_Olattice__class_OSup__fin(_1522262, hAPP(c_Set_OCollect(_1522262), hAPP(hAPP(c_COMBB(tc_fun(_1522262, tc_HOL_Obool), tc_HOL_Obool, _1522262), c_HOL_OEx(_1522262)), hAPP(hAPP(c_COMBB(tc_fun(_1522262, tc_fun(_1522262, tc_HOL_Obool)), tc_fun(_1522262, tc_HOL_Obool), _1522262), hAPP(c_COMBB(tc_fun(_1522262, tc_HOL_Obool), tc_HOL_Obool, _1522262), c_HOL_OEx(_1522262))), hAPP(hAPP(c_COMBC(_1522262, tc_fun(_1522262, tc_fun(_1522262, tc_HOL_Obool)), tc_fun(_1522262, tc_fun(_1522262, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1522262, tc_fun(tc_fun(_1522262, tc_HOL_Obool), tc_fun(_1522262, tc_HOL_Obool))), tc_fun(tc_fun(_1522262, tc_fun(_1522262, tc_HOL_Obool)), tc_fun(_1522262, tc_fun(_1522262, tc_HOL_Obool))), _1522262), c_COMBS(_1522262, tc_fun(_1522262, tc_HOL_Obool), tc_fun(_1522262, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1522262, tc_fun(_1522262, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1522262, tc_fun(tc_fun(_1522262, tc_HOL_Obool), tc_fun(_1522262, tc_HOL_Obool))), _1522262), hAPP(c_COMBB(tc_fun(_1522262, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1522262, tc_HOL_Obool), tc_fun(_1522262, tc_HOL_Obool)), _1522262), c_COMBS(_1522262, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1522262, tc_fun(_1522262, tc_HOL_Obool)), tc_fun(_1522262, tc_fun(_1522262, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1522262), hAPP(c_COMBB(tc_fun(_1522262, tc_HOL_Obool), tc_fun(_1522262, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1522262), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522262), c_fconj))), hAPP(hAPP(c_COMBC(_1522262, tc_fun(_1522262, tc_fun(_1522262, _1522262)), tc_fun(_1522262, tc_fun(_1522262, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1522262, _1522262), tc_fun(_1522262, tc_HOL_Obool)), tc_fun(tc_fun(_1522262, tc_fun(_1522262, _1522262)), tc_fun(_1522262, tc_fun(_1522262, tc_HOL_Obool))), _1522262), c_COMBB(tc_fun(_1522262, _1522262), tc_fun(_1522262, tc_HOL_Obool), _1522262)), hAPP(hAPP(c_COMBB(tc_fun(_1522262, tc_HOL_Obool), tc_fun(tc_fun(_1522262, _1522262), tc_fun(_1522262, tc_HOL_Obool)), _1522262), c_COMBB(_1522262, tc_HOL_Obool, _1522262)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1522262)))))), hAPP(hAPP(c_COMBC(_1522262, tc_fun(_1522262, tc_HOL_Obool), tc_fun(_1522262, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1522262, tc_HOL_Obool), tc_fun(_1522262, tc_HOL_Obool)), _1522262), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1522262)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522262), c_fconj), hAPP(hAPP(c_COMBC(_1522262, tc_fun(_1522262, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522262)), _1522264)))), hAPP(hAPP(c_COMBC(_1522262, tc_fun(_1522262, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522262)), _1522266))))))))], (38637 ^ _780205) ^ [_1523361, _1523363, _1523365] : [class_Lattices_Odistrib__lattice(_1523361), hBOOL(hAPP(c_Finite__Set_Ofinite(_1523361), _1523363)), -(_1523363 = c_Orderings_Obot__class_Obot(tc_fun(_1523361, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1523361), _1523365), c_Big__Operators_Olattice__class_OSup__fin(_1523361, _1523363)) = c_Big__Operators_Olattice__class_OSup__fin(_1523361, hAPP(c_Set_OCollect(_1523361), hAPP(hAPP(c_COMBB(tc_fun(_1523361, tc_HOL_Obool), tc_HOL_Obool, _1523361), c_HOL_OEx(_1523361)), hAPP(hAPP(c_COMBC(_1523361, tc_fun(_1523361, tc_HOL_Obool), tc_fun(_1523361, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523361, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1523361, tc_HOL_Obool), tc_fun(_1523361, tc_HOL_Obool)), _1523361), c_COMBS(_1523361, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523361, tc_HOL_Obool), tc_fun(_1523361, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1523361), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523361), c_fconj)), hAPP(hAPP(c_COMBC(_1523361, tc_fun(_1523361, _1523361), tc_fun(_1523361, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523361, tc_HOL_Obool), tc_fun(tc_fun(_1523361, _1523361), tc_fun(_1523361, tc_HOL_Obool)), _1523361), c_COMBB(_1523361, tc_HOL_Obool, _1523361)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1523361), _1523365))))), hAPP(hAPP(c_COMBC(_1523361, tc_fun(_1523361, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523361)), _1523363))))))], (38651 ^ _780205) ^ [_1523847, _1523849, _1523851] : [class_Orderings_Olinorder(_1523847), hBOOL(hAPP(c_Finite__Set_Ofinite(_1523847), _1523849)), -(_1523849 = c_Orderings_Obot__class_Obot(tc_fun(_1523847, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1523847), _1523851), c_Big__Operators_Olattice_OInf__fin(_1523847, c_Orderings_Oord__class_Omin(_1523847), _1523849)) = c_Big__Operators_Olattice_OInf__fin(_1523847, c_Orderings_Oord__class_Omin(_1523847), hAPP(c_Set_OCollect(_1523847), hAPP(hAPP(c_COMBB(tc_fun(_1523847, tc_HOL_Obool), tc_HOL_Obool, _1523847), c_HOL_OEx(_1523847)), hAPP(hAPP(c_COMBC(_1523847, tc_fun(_1523847, tc_HOL_Obool), tc_fun(_1523847, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523847, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1523847, tc_HOL_Obool), tc_fun(_1523847, tc_HOL_Obool)), _1523847), c_COMBS(_1523847, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523847, tc_HOL_Obool), tc_fun(_1523847, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1523847), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523847), c_fconj)), hAPP(hAPP(c_COMBC(_1523847, tc_fun(_1523847, _1523847), tc_fun(_1523847, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523847, tc_HOL_Obool), tc_fun(tc_fun(_1523847, _1523847), tc_fun(_1523847, tc_HOL_Obool)), _1523847), c_COMBB(_1523847, tc_HOL_Obool, _1523847)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1523847), _1523851))))), hAPP(hAPP(c_COMBC(_1523847, tc_fun(_1523847, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523847)), _1523849))))))], (38665 ^ _780205) ^ [_1524345, _1524347, _1524349] : [class_Orderings_Olinorder(_1524345), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524345), _1524347)), -(_1524347 = c_Orderings_Obot__class_Obot(tc_fun(_1524345, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524345), _1524349)), -(_1524349 = c_Orderings_Obot__class_Obot(tc_fun(_1524345, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1524345), c_Big__Operators_Olattice_OInf__fin(_1524345, c_Orderings_Oord__class_Omin(_1524345), _1524347)), c_Big__Operators_Olattice_OInf__fin(_1524345, c_Orderings_Oord__class_Omin(_1524345), _1524349)) = c_Big__Operators_Olattice_OInf__fin(_1524345, c_Orderings_Oord__class_Omin(_1524345), hAPP(c_Set_OCollect(_1524345), hAPP(hAPP(c_COMBB(tc_fun(_1524345, tc_HOL_Obool), tc_HOL_Obool, _1524345), c_HOL_OEx(_1524345)), hAPP(hAPP(c_COMBB(tc_fun(_1524345, tc_fun(_1524345, tc_HOL_Obool)), tc_fun(_1524345, tc_HOL_Obool), _1524345), hAPP(c_COMBB(tc_fun(_1524345, tc_HOL_Obool), tc_HOL_Obool, _1524345), c_HOL_OEx(_1524345))), hAPP(hAPP(c_COMBC(_1524345, tc_fun(_1524345, tc_fun(_1524345, tc_HOL_Obool)), tc_fun(_1524345, tc_fun(_1524345, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1524345, tc_fun(tc_fun(_1524345, tc_HOL_Obool), tc_fun(_1524345, tc_HOL_Obool))), tc_fun(tc_fun(_1524345, tc_fun(_1524345, tc_HOL_Obool)), tc_fun(_1524345, tc_fun(_1524345, tc_HOL_Obool))), _1524345), c_COMBS(_1524345, tc_fun(_1524345, tc_HOL_Obool), tc_fun(_1524345, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1524345, tc_fun(_1524345, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1524345, tc_fun(tc_fun(_1524345, tc_HOL_Obool), tc_fun(_1524345, tc_HOL_Obool))), _1524345), hAPP(c_COMBB(tc_fun(_1524345, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1524345, tc_HOL_Obool), tc_fun(_1524345, tc_HOL_Obool)), _1524345), c_COMBS(_1524345, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1524345, tc_fun(_1524345, tc_HOL_Obool)), tc_fun(_1524345, tc_fun(_1524345, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1524345), hAPP(c_COMBB(tc_fun(_1524345, tc_HOL_Obool), tc_fun(_1524345, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1524345), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524345), c_fconj))), hAPP(hAPP(c_COMBC(_1524345, tc_fun(_1524345, tc_fun(_1524345, _1524345)), tc_fun(_1524345, tc_fun(_1524345, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1524345, _1524345), tc_fun(_1524345, tc_HOL_Obool)), tc_fun(tc_fun(_1524345, tc_fun(_1524345, _1524345)), tc_fun(_1524345, tc_fun(_1524345, tc_HOL_Obool))), _1524345), c_COMBB(tc_fun(_1524345, _1524345), tc_fun(_1524345, tc_HOL_Obool), _1524345)), hAPP(hAPP(c_COMBB(tc_fun(_1524345, tc_HOL_Obool), tc_fun(tc_fun(_1524345, _1524345), tc_fun(_1524345, tc_HOL_Obool)), _1524345), c_COMBB(_1524345, tc_HOL_Obool, _1524345)), c_fequal))), c_Orderings_Oord__class_Omax(_1524345)))))), hAPP(hAPP(c_COMBC(_1524345, tc_fun(_1524345, tc_HOL_Obool), tc_fun(_1524345, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1524345, tc_HOL_Obool), tc_fun(_1524345, tc_HOL_Obool)), _1524345), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1524345)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524345), c_fconj), hAPP(hAPP(c_COMBC(_1524345, tc_fun(_1524345, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524345)), _1524347)))), hAPP(hAPP(c_COMBC(_1524345, tc_fun(_1524345, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524345)), _1524349))))))))], (38687 ^ _780205) ^ [_1525462, _1525464, _1525466, _1525468] : [-(c_Nitpick_Oprod(_1525462, _1525464, _1525466, _1525468) = hAPP(c_Set_OCollect(tc_prod(_1525462, _1525464)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525462, _1525464, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1525462, tc_fun(_1525464, tc_HOL_Obool), tc_fun(_1525464, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1525464, tc_HOL_Obool), tc_fun(_1525464, tc_HOL_Obool)), _1525462), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1525464)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525462), c_fconj), hAPP(hAPP(c_COMBC(_1525462, tc_fun(_1525462, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525462)), _1525466)))), hAPP(hAPP(c_COMBC(_1525464, tc_fun(_1525464, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525464)), _1525468)))))], (38689 ^ _780205) ^ [_1525590] : [-(c_Int_Oint__ge__less__than(_1525590) = 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), _1525590)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (38691 ^ _780205) ^ [_1525636] : [-(c_Int_Oint__ge__less__than2(_1525636) = 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), _1525636)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (38693 ^ _780205) ^ [_1525697, _1525699] : [c_Predicate_Oreflp(_1525697, _1525699), -(c_Relation_Orefl__on(_1525697, c_Orderings_Otop__class_Otop(tc_fun(_1525697, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1525697, _1525697)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525697, _1525697, tc_HOL_Obool), _1525699))))], (38699 ^ _780205) ^ [_1525812, _1525814] : [c_Relation_Orefl__on(_1525812, c_Orderings_Otop__class_Otop(tc_fun(_1525812, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1525812, _1525812)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525812, _1525812, tc_HOL_Obool), _1525814))), -(c_Predicate_Oreflp(_1525812, _1525814))], (38705 ^ _780205) ^ [_1525933, _1525935, _1525937, _1525939, _1525941, _1525943, _1525945] : [class_Rings_Osemiring__0(_1525933), c_Fun_Oinj__on(tc_prod(_1525935, _1525937), _1525933, hAPP(c_Product__Type_Oprod_Oprod__case(_1525935, _1525937, _1525933), hAPP(hAPP(c_COMBC(_1525935, tc_fun(_1525937, _1525933), tc_fun(_1525937, _1525933)), hAPP(hAPP(c_COMBB(tc_fun(_1525933, _1525933), tc_fun(tc_fun(_1525937, _1525933), tc_fun(_1525937, _1525933)), _1525935), c_COMBB(_1525933, _1525933, _1525937)), hAPP(hAPP(c_COMBB(_1525933, tc_fun(_1525933, _1525933), _1525935), c_Groups_Otimes__class_Otimes(_1525933)), _1525939))), _1525941)), hAPP(hAPP(c_Product__Type_OSigma(_1525935, _1525937), _1525943), hAPP(c_COMBK(tc_fun(_1525937, tc_HOL_Obool), _1525935), _1525945))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1525933), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525935, _1525933), _1525939), _1525943)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525937, _1525933), _1525941), _1525945)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525933, _1525933), c_Fun_Oid(_1525933)), hAPP(c_Set_OCollect(_1525933), hAPP(hAPP(c_COMBB(tc_fun(_1525935, tc_HOL_Obool), tc_HOL_Obool, _1525933), c_HOL_OEx(_1525935)), hAPP(hAPP(c_COMBB(tc_fun(_1525935, tc_fun(_1525937, tc_HOL_Obool)), tc_fun(_1525935, tc_HOL_Obool), _1525933), hAPP(c_COMBB(tc_fun(_1525937, tc_HOL_Obool), tc_HOL_Obool, _1525935), c_HOL_OEx(_1525937))), hAPP(hAPP(c_COMBC(_1525933, tc_fun(_1525935, tc_fun(_1525937, tc_HOL_Obool)), tc_fun(_1525935, tc_fun(_1525937, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1525935, tc_fun(tc_fun(_1525937, tc_HOL_Obool), tc_fun(_1525937, tc_HOL_Obool))), tc_fun(tc_fun(_1525935, tc_fun(_1525937, tc_HOL_Obool)), tc_fun(_1525935, tc_fun(_1525937, tc_HOL_Obool))), _1525933), c_COMBS(_1525935, tc_fun(_1525937, tc_HOL_Obool), tc_fun(_1525937, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1525935, tc_fun(_1525937, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1525935, tc_fun(tc_fun(_1525937, tc_HOL_Obool), tc_fun(_1525937, tc_HOL_Obool))), _1525933), hAPP(c_COMBB(tc_fun(_1525937, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1525937, tc_HOL_Obool), tc_fun(_1525937, tc_HOL_Obool)), _1525935), c_COMBS(_1525937, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1525935, tc_fun(_1525937, tc_HOL_Obool)), tc_fun(_1525935, tc_fun(_1525937, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1525933), hAPP(c_COMBB(tc_fun(_1525937, tc_HOL_Obool), tc_fun(_1525937, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1525935), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525937), c_fconj))), hAPP(hAPP(c_COMBC(_1525933, tc_fun(_1525935, tc_fun(_1525937, _1525933)), tc_fun(_1525935, tc_fun(_1525937, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1525937, _1525933), tc_fun(_1525937, tc_HOL_Obool)), tc_fun(tc_fun(_1525935, tc_fun(_1525937, _1525933)), tc_fun(_1525935, tc_fun(_1525937, tc_HOL_Obool))), _1525933), c_COMBB(tc_fun(_1525937, _1525933), tc_fun(_1525937, tc_HOL_Obool), _1525935)), hAPP(hAPP(c_COMBB(tc_fun(_1525933, tc_HOL_Obool), tc_fun(tc_fun(_1525937, _1525933), tc_fun(_1525937, tc_HOL_Obool)), _1525933), c_COMBB(_1525933, tc_HOL_Obool, _1525937)), c_fequal))), hAPP(hAPP(c_COMBC(_1525935, tc_fun(_1525937, _1525933), tc_fun(_1525937, _1525933)), hAPP(hAPP(c_COMBB(tc_fun(_1525933, _1525933), tc_fun(tc_fun(_1525937, _1525933), tc_fun(_1525937, _1525933)), _1525935), c_COMBB(_1525933, _1525933, _1525937)), hAPP(hAPP(c_COMBB(_1525933, tc_fun(_1525933, _1525933), _1525935), c_Groups_Otimes__class_Otimes(_1525933)), _1525939))), _1525941)))))), hAPP(hAPP(c_COMBC(_1525935, tc_fun(_1525937, tc_HOL_Obool), tc_fun(_1525937, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1525937, tc_HOL_Obool), tc_fun(_1525937, tc_HOL_Obool)), _1525935), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1525937)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525935), c_fconj), hAPP(hAPP(c_COMBC(_1525935, tc_fun(_1525935, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525935)), _1525943)))), hAPP(hAPP(c_COMBC(_1525937, tc_fun(_1525937, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525937)), _1525945))))))))], (38715 ^ _780205) ^ [_1527210, _1527212, _1527214, _1527216, _1527218, _1527220] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527210), _1527212)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1527214), _1527216)), 38725 ^ _780205 : [(38726 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527214), 38724 ^ [_1527210, _1527212, _1527214, _1527216, _1527218, _1527220]), _1527216)))], (38728 ^ _780205) ^ [] : [hAPP(c_Finite__Set_Ocard(_1527210), hAPP(c_Set_OCollect(_1527210), hAPP(hAPP(c_COMBS(_1527210, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527210), c_fconj), hAPP(hAPP(c_COMBC(_1527210, tc_fun(_1527210, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527210)), _1527212))), hAPP(hAPP(c_COMBC(_1527210, _1527214, tc_HOL_Obool), _1527218), 38724 ^ [_1527210, _1527212, _1527214, _1527216, _1527218, _1527220])))) = hAPP(_1527220, 38724 ^ [_1527210, _1527212, _1527214, _1527216, _1527218, _1527220])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527210, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1527214, tc_HOL_Obool), tc_Nat_Onat, _1527210), c_Finite__Set_Ocard(_1527214)), hAPP(hAPP(c_COMBB(tc_fun(_1527214, tc_HOL_Obool), tc_fun(_1527214, tc_HOL_Obool), _1527210), c_Set_OCollect(_1527214)), hAPP(hAPP(c_COMBB(tc_fun(_1527214, tc_HOL_Obool), tc_fun(_1527214, tc_HOL_Obool), _1527210), hAPP(c_COMBS(_1527214, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527214), c_fconj), hAPP(hAPP(c_COMBC(_1527214, tc_fun(_1527214, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527214)), _1527216)))), _1527218)))), _1527212) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527214, tc_Nat_Onat), _1527220), _1527216))], (38732 ^ _780205) ^ [_1527920, _1527922] : [-(c_Fun_Oinj__on(_1527920, _1527920, c_Fun_Oid(_1527920), _1527922))], (38734 ^ _780205) ^ [_1527949, _1527951] : [-(c_Product__Type_Oapsnd(_1527949, _1527949, _1527951, c_Fun_Oid(_1527949)) = c_Fun_Oid(tc_prod(_1527951, _1527949)))], (38736 ^ _780205) ^ [_1527986, _1527988, _1527990] : [c_Predicate_Oreflp(_1527986, _1527988), -(hBOOL(hAPP(hAPP(_1527988, _1527990), _1527990)))], (38742 ^ _780205) ^ [_1528075, _1528077] : [-(c_Product__Type_Oapfst(_1528075, _1528075, _1528077, c_Fun_Oid(_1528075)) = c_Fun_Oid(tc_prod(_1528075, _1528077)))], (38744 ^ _780205) ^ [_1528112, _1528114] : [-(hAPP(c_Fun_Oid(_1528112), _1528114) = _1528114)], (38746 ^ _780205) ^ [_1528142, _1528144] : [-(hAPP(c_Fun_Oid(_1528142), _1528144) = _1528144)], (38748 ^ _780205) ^ [_1528172, _1528174] : [-(hAPP(c_Set_Ovimage(_1528172, _1528172, c_Fun_Oid(_1528172)), _1528174) = _1528174)], (38750 ^ _780205) ^ [_1528206, _1528208] : [-(c_Product__Type_Omap__pair(_1528206, _1528206, _1528208, _1528208, c_COMBI(_1528206), c_COMBI(_1528208)) = c_Fun_Oid(tc_prod(_1528206, _1528208)))], (38752 ^ _780205) ^ [_1528247, _1528249] : [-(c_Product__Type_Omap__pair(_1528247, _1528247, _1528249, _1528249, c_Fun_Oid(_1528247), c_Fun_Oid(_1528249)) = c_Fun_Oid(tc_prod(_1528247, _1528249)))], (38754 ^ _780205) ^ [_1528288, _1528290] : [-(hAPP(c_Set_Oimage(_1528288, _1528288, c_Fun_Oid(_1528288)), _1528290) = _1528290)], (38756 ^ _780205) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (38758 ^ _780205) ^ [_1528340] : [-(hAPP(c_Set_Oimage(_1528340, _1528340, c_Fun_Oid(_1528340)), c_Orderings_Otop__class_Otop(tc_fun(_1528340, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1528340, tc_HOL_Obool)))], (38760 ^ _780205) ^ [_1528382, _1528384, _1528386, _1528388] : [-(c_Product__Type_Oapsnd(_1528382, _1528384, _1528386, _1528388) = c_Product__Type_Omap__pair(_1528386, _1528386, _1528382, _1528384, c_Fun_Oid(_1528386), _1528388))], (38762 ^ _780205) ^ [_1528425, _1528427, _1528429, _1528431] : [-(c_Product__Type_Oapfst(_1528425, _1528427, _1528429, _1528431) = c_Product__Type_Omap__pair(_1528425, _1528427, _1528429, _1528429, _1528431, c_Fun_Oid(_1528429)))], (38764 ^ _780205) ^ [_1528468, _1528470] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1528468, _1528470, tc_prod(_1528468, _1528470)), c_Product__Type_OPair(_1528468, _1528470)) = c_Fun_Oid(tc_prod(_1528468, _1528470)))], (38766 ^ _780205) ^ [_1528511, _1528513, _1528515, _1528517] : [class_Groups_Ocomm__monoid__add(_1528511), c_Fun_Oinj__on(_1528513, _1528511, _1528515, _1528517), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1528513, _1528511), _1528515), _1528517) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1528511, _1528511), c_Fun_Oid(_1528511)), hAPP(c_Set_Oimage(_1528513, _1528511, _1528515), _1528517)))], (38776 ^ _780205) ^ [_1528704, _1528706, _1528708, _1528710] : [class_Groups_Ocomm__monoid__mult(_1528704), c_Fun_Oinj__on(_1528706, _1528704, _1528708, _1528710), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1528706, _1528704), _1528708), _1528710) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1528704, _1528704), c_Fun_Oid(_1528704)), hAPP(c_Set_Oimage(_1528706, _1528704, _1528708), _1528710)))], (38786 ^ _780205) ^ [_1528912, _1528914] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1528912), _1528914)), -(_1528914 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1528912, 38790 ^ [_1528912, _1528914]), 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)), 38789 ^ [_1528912, _1528914]))))], (38794 ^ _780205) ^ [_1529043, _1529045] : [38795 ^ _780205 : [(38796 ^ _780205) ^ [_1529107, _1529109] : [_1529045 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1529043, _1529107), 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)), _1529109)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1529043), _1529045)))], (38800 ^ _780205) ^ [_1529179, _1529181, _1529183, _1529185, _1529187] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1529179, _1529181, _1529183), _1529185), _1529187) = hAPP(c_Set_OCollect(tc_prod(_1529179, _1529183)), hAPP(c_Product__Type_Oprod_Oprod__case(_1529179, _1529183, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1529183, tc_fun(_1529181, tc_HOL_Obool)), tc_fun(_1529183, tc_HOL_Obool), _1529179), hAPP(c_COMBB(tc_fun(_1529181, tc_HOL_Obool), tc_HOL_Obool, _1529183), c_HOL_OEx(_1529181))), hAPP(hAPP(c_COMBC(_1529179, tc_fun(_1529183, tc_fun(_1529181, tc_HOL_Obool)), tc_fun(_1529183, tc_fun(_1529181, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1529181, tc_HOL_Obool), tc_fun(_1529181, tc_HOL_Obool)), tc_fun(tc_fun(_1529183, tc_fun(_1529181, tc_HOL_Obool)), tc_fun(_1529183, tc_fun(_1529181, tc_HOL_Obool))), _1529179), c_COMBB(tc_fun(_1529181, tc_HOL_Obool), tc_fun(_1529181, tc_HOL_Obool), _1529183)), hAPP(hAPP(c_COMBB(tc_fun(_1529181, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1529181, tc_HOL_Obool), tc_fun(_1529181, tc_HOL_Obool)), _1529179), c_COMBS(_1529181, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529181, tc_HOL_Obool), tc_fun(_1529181, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1529179), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529181), c_fconj)), hAPP(hAPP(c_COMBC(_1529179, tc_fun(tc_prod(_1529179, _1529181), tc_HOL_Obool), tc_fun(_1529181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529181, tc_fun(tc_fun(tc_prod(_1529179, _1529181), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529179, _1529181), tc_HOL_Obool), tc_fun(_1529181, tc_HOL_Obool)), _1529179), c_COMBC(_1529181, tc_fun(tc_prod(_1529179, _1529181), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529181, tc_prod(_1529179, _1529181)), tc_fun(_1529181, tc_fun(tc_fun(tc_prod(_1529179, _1529181), tc_HOL_Obool), tc_HOL_Obool)), _1529179), hAPP(c_COMBB(tc_prod(_1529179, _1529181), tc_fun(tc_fun(tc_prod(_1529179, _1529181), tc_HOL_Obool), tc_HOL_Obool), _1529181), c_member(tc_prod(_1529179, _1529181)))), c_Product__Type_OPair(_1529179, _1529181)))), _1529185))))), hAPP(hAPP(c_COMBC(_1529183, tc_fun(tc_prod(_1529181, _1529183), tc_HOL_Obool), tc_fun(_1529181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529181, tc_fun(tc_fun(tc_prod(_1529181, _1529183), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529181, _1529183), tc_HOL_Obool), tc_fun(_1529181, tc_HOL_Obool)), _1529183), c_COMBC(_1529181, tc_fun(tc_prod(_1529181, _1529183), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529181, tc_prod(_1529181, _1529183)), tc_fun(_1529181, tc_fun(tc_fun(tc_prod(_1529181, _1529183), tc_HOL_Obool), tc_HOL_Obool)), _1529183), hAPP(c_COMBB(tc_prod(_1529181, _1529183), tc_fun(tc_fun(tc_prod(_1529181, _1529183), tc_HOL_Obool), tc_HOL_Obool), _1529181), c_member(tc_prod(_1529181, _1529183)))), hAPP(c_COMBC(_1529181, _1529183, tc_prod(_1529181, _1529183)), c_Product__Type_OPair(_1529181, _1529183))))), _1529187))))))], (38802 ^ _780205) ^ [_1529627, _1529629, _1529631] : [-(hAPP(c_Relation_ORange(_1529627, _1529629), hAPP(c_Set_OCollect(tc_prod(_1529627, _1529629)), hAPP(c_Product__Type_Oprod_Oprod__case(_1529627, _1529629, tc_HOL_Obool), _1529631))) = hAPP(c_Set_OCollect(_1529629), hAPP(hAPP(c_COMBB(tc_fun(_1529627, tc_HOL_Obool), tc_HOL_Obool, _1529629), c_HOL_OEx(_1529627)), hAPP(c_COMBC(_1529627, _1529629, tc_HOL_Obool), _1529631))))], (38804 ^ _780205) ^ [_1529702, _1529704, _1529706, _1529708, _1529710, _1529712, _1529714, _1529716] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529702, _1529704)), hAPP(hAPP(c_Product__Type_OPair(_1529702, _1529704), _1529706), _1529708)), _1529710)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1529704, _1529712)), hAPP(hAPP(c_Product__Type_OPair(_1529704, _1529712), _1529708), _1529714)), _1529716)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1529702, _1529712)), hAPP(hAPP(c_Product__Type_OPair(_1529702, _1529712), _1529706), _1529714)), hAPP(hAPP(c_Relation_Orel__comp(_1529702, _1529704, _1529712), _1529710), _1529716))))], (38814 ^ _780205) ^ [_1529989, _1529991, _1529993, _1529995, _1529997] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529989, _1529991)), hAPP(hAPP(c_Product__Type_OPair(_1529989, _1529991), _1529993), _1529995)), _1529997)), -(hBOOL(hAPP(hAPP(c_member(_1529991), _1529995), hAPP(c_Relation_ORange(_1529989, _1529991), _1529997))))], (38820 ^ _780205) ^ [_1530136, _1530138, _1530140, _1530142, _1530144, _1530146, _1530148] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530136, _1530138, _1530140), _1530142), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530144, tc_fun(tc_prod(_1530138, _1530140), tc_HOL_Obool)), _1530146), _1530148)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530144, tc_fun(tc_prod(_1530136, _1530140), tc_HOL_Obool)), _1530146), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1530138, _1530140), tc_HOL_Obool), tc_fun(tc_prod(_1530136, _1530140), tc_HOL_Obool), _1530144), hAPP(c_Relation_Orel__comp(_1530136, _1530138, _1530140), _1530142)), _1530148)))], (38822 ^ _780205) ^ [_1530240, _1530242, _1530244, _1530246, _1530248, _1530250, _1530252] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530240, _1530242, _1530244), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530246, tc_fun(tc_prod(_1530240, _1530242), tc_HOL_Obool)), _1530248), _1530250)), _1530252) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530246, tc_fun(tc_prod(_1530240, _1530244), tc_HOL_Obool)), _1530248), hAPP(hAPP(c_COMBC(_1530246, tc_fun(tc_prod(_1530242, _1530244), tc_HOL_Obool), tc_fun(tc_prod(_1530240, _1530244), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1530240, _1530242), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1530242, _1530244), tc_HOL_Obool), tc_fun(tc_prod(_1530240, _1530244), tc_HOL_Obool)), _1530246), c_Relation_Orel__comp(_1530240, _1530242, _1530244)), _1530250)), _1530252)))], (38824 ^ _780205) ^ [_1530372, _1530374, _1530376, _1530378, _1530380, _1530382] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530372, _1530374, _1530376), _1530378), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530374, _1530376), tc_HOL_Obool)), _1530380), _1530382)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530372, _1530376), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530372, _1530374, _1530376), _1530378), _1530380)), hAPP(hAPP(c_Relation_Orel__comp(_1530372, _1530374, _1530376), _1530378), _1530382)))], (38826 ^ _780205) ^ [_1530463, _1530465, _1530467, _1530469, _1530471, _1530473] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530463, _1530465, _1530467), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530463, _1530465), tc_HOL_Obool)), _1530469), _1530471)), _1530473) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530463, _1530467), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530463, _1530465, _1530467), _1530469), _1530473)), hAPP(hAPP(c_Relation_Orel__comp(_1530463, _1530465, _1530467), _1530471), _1530473)))], (38828 ^ _780205) ^ [_1530554, _1530556, _1530558, _1530560, _1530562, _1530564, _1530566] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530554, _1530556, _1530558), hAPP(hAPP(c_Relation_Orel__comp(_1530554, _1530560, _1530556), _1530562), _1530564)), _1530566) = hAPP(hAPP(c_Relation_Orel__comp(_1530554, _1530560, _1530558), _1530562), hAPP(hAPP(c_Relation_Orel__comp(_1530560, _1530556, _1530558), _1530564), _1530566)))], (38830 ^ _780205) ^ [_1530629, _1530631, _1530633, _1530635] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530629, _1530631, _1530633), _1530635), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530631, _1530633), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530629, _1530633), tc_HOL_Obool)))], (38832 ^ _780205) ^ [_1530684, _1530686, _1530688, _1530690] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530684, _1530686, _1530688), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530684, _1530686), tc_HOL_Obool))), _1530690) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530684, _1530688), tc_HOL_Obool)))], (38834 ^ _780205) ^ [_1530739, _1530741] : [-(hAPP(c_Relation_ORange(_1530739, _1530739), c_Relation_OId__on(_1530739, _1530741)) = _1530741)], (38836 ^ _780205) ^ [_1530773, _1530775, _1530777, _1530779, _1530781, _1530783, _1530785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530773, _1530775), tc_HOL_Obool)), _1530777), _1530779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530775, _1530781), tc_HOL_Obool)), _1530783), _1530785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530773, _1530781), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530773, _1530775, _1530781), _1530777), _1530783)), hAPP(hAPP(c_Relation_Orel__comp(_1530773, _1530775, _1530781), _1530779), _1530785))))], (38846 ^ _780205) ^ [_1531040, _1531042, _1531044, _1531046] : [hAPP(hAPP(c_Relation_Orel__comp(_1531040, _1531040, _1531040), _1531042), _1531044) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531040, _1531040), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531040, _1531040, _1531040), _1531042), _1531046) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531040, _1531040), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1531040, _1531040, _1531040), _1531042), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531040, _1531040), tc_HOL_Obool)), _1531044), _1531046)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531040, _1531040), tc_HOL_Obool)))], (38856 ^ _780205) ^ [_1531313, _1531315, _1531317, _1531319] : [hAPP(hAPP(c_Relation_Orel__comp(_1531313, _1531313, _1531313), _1531315), _1531317) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531313, _1531313), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531313, _1531313, _1531313), _1531319), _1531317) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531313, _1531313), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1531313, _1531313, _1531313), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531313, _1531313), tc_HOL_Obool)), _1531315), _1531319)), _1531317) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531313, _1531313), tc_HOL_Obool)))], (38866 ^ _780205) ^ [_1531586, _1531588, _1531590] : [-(hAPP(c_Relation_ORange(_1531586, _1531588), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1531586, _1531588), tc_HOL_Obool), _1531590)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1531586, _1531588), tc_HOL_Obool), tc_fun(_1531588, tc_HOL_Obool)), _1531590), c_Relation_ORange(_1531586, _1531588)))], (38868 ^ _780205) ^ [_1531667, _1531669, _1531671] : [hAPP(c_Relation_ORange(_1531667, _1531669), _1531671) = c_Orderings_Obot__class_Obot(tc_fun(_1531669, tc_HOL_Obool)), -(_1531671 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531667, _1531669), tc_HOL_Obool)))], (38874 ^ _780205) ^ [_1531780, _1531782, _1531784] : [_1531784 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531780, _1531782), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1531780, _1531782), _1531784) = c_Orderings_Obot__class_Obot(tc_fun(_1531782, tc_HOL_Obool)))], (38880 ^ _780205) ^ [_1531899, _1531901] : [-(hAPP(c_Relation_ORange(_1531899, _1531901), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531899, _1531901), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1531901, tc_HOL_Obool)))], (38882 ^ _780205) ^ [_1531943, _1531945, _1531947, _1531949, _1531951, _1531953, _1531955, _1531957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531943, _1531945), tc_HOL_Obool)), _1531947), hAPP(hAPP(c_Product__Type_OSigma(_1531943, _1531945), _1531949), hAPP(c_COMBK(tc_fun(_1531945, tc_HOL_Obool), _1531943), _1531951)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531945, _1531953), tc_HOL_Obool)), _1531955), hAPP(hAPP(c_Product__Type_OSigma(_1531945, _1531953), _1531951), hAPP(c_COMBK(tc_fun(_1531953, tc_HOL_Obool), _1531945), _1531957)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531943, _1531953), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531943, _1531945, _1531953), _1531947), _1531955)), hAPP(hAPP(c_Product__Type_OSigma(_1531943, _1531953), _1531949), hAPP(c_COMBK(tc_fun(_1531953, tc_HOL_Obool), _1531943), _1531957)))))], (38892 ^ _780205) ^ [_1532302, _1532304, _1532306, _1532308] : [-(hAPP(c_Relation_ORange(_1532302, _1532304), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1532302, _1532304), tc_HOL_Obool)), _1532306), _1532308)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1532304, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1532302, _1532304), _1532306)), hAPP(c_Relation_ORange(_1532302, _1532304), _1532308)))], (38894 ^ _780205) ^ [_1532374, _1532376, _1532378] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1532374, _1532376)), _1532378)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1532376), hAPP(c_Relation_ORange(_1532374, _1532376), _1532378))))], (38900 ^ _780205) ^ [_1532487, _1532489, _1532491] : [-(hAPP(c_Set_Oimage(tc_prod(_1532487, _1532489), _1532489, c_Product__Type_Osnd(_1532487, _1532489)), _1532491) = hAPP(c_Relation_ORange(_1532487, _1532489), _1532491))], (38902 ^ _780205) ^ [_1532554, _1532556, _1532558, _1532560] : [hBOOL(hAPP(hAPP(c_member(_1532554), _1532556), hAPP(c_Relation_ORange(_1532558, _1532554), _1532560))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532558, _1532554)), hAPP(hAPP(c_Product__Type_OPair(_1532558, _1532554), 38905 ^ [_1532554, _1532556, _1532558, _1532560]), _1532556)), _1532560)))], (38909 ^ _780205) ^ [_1532711, _1532713, _1532715, _1532717] : [38910 ^ _780205 : [(38911 ^ _780205) ^ [_1532786] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532715, _1532711)), hAPP(hAPP(c_Product__Type_OPair(_1532715, _1532711), _1532786), _1532713)), _1532717))]], -(hBOOL(hAPP(hAPP(c_member(_1532711), _1532713), hAPP(c_Relation_ORange(_1532715, _1532711), _1532717))))], (38915 ^ _780205) ^ [_1532871, _1532873, _1532875, _1532877, _1532879] : [-(hAPP(c_Relation_ORange(_1532871, _1532873), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1532871, _1532873)), hAPP(hAPP(c_Product__Type_OPair(_1532871, _1532873), _1532875), _1532877)), _1532879)) = hAPP(hAPP(c_Set_Oinsert(_1532873), _1532877), hAPP(c_Relation_ORange(_1532871, _1532873), _1532879)))], (38917 ^ _780205) ^ [_1532942, _1532944, _1532946, _1532948] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1532942, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1532944, _1532942), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1532944, _1532942), tc_HOL_Obool)), _1532946), _1532948))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1532942, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1532944, _1532942), _1532946)), hAPP(c_Relation_ORange(_1532944, _1532942), _1532948)))))], (38919 ^ _780205) ^ [_1533024, _1533026, _1533028, _1533030] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533024, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1533024, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1533026, _1533024), _1533028)), hAPP(c_Relation_ORange(_1533026, _1533024), _1533030))), hAPP(c_Relation_ORange(_1533026, _1533024), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1533026, _1533024), tc_HOL_Obool)), _1533028), _1533030)))))], (38921 ^ _780205) ^ [_1533106, _1533108, _1533110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533106, _1533106), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1533106, _1533106, _1533106), _1533108), _1533110)), _1533108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1533106, tc_HOL_Obool), tc_fun(_1533106, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1533106, tc_HOL_Obool), tc_fun(_1533106, tc_HOL_Obool), tc_fun(_1533106, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1533106, _1533108)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1533106, tc_HOL_Obool), tc_fun(_1533106, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1533106, _1533110)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1533106, tc_HOL_Obool), tc_fun(_1533106, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1533106, tc_HOL_Obool), tc_fun(_1533106, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1533106, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1533106, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1533106, tc_HOL_Obool), tc_fun(_1533106, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1533106, _1533108))))], (38927 ^ _780205) ^ [_1533477, _1533479, _1533481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533477, _1533477), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1533477, _1533477, _1533477), _1533479), _1533481)), _1533479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1533477, tc_HOL_Obool), tc_fun(_1533477, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1533477, tc_HOL_Obool), tc_fun(_1533477, tc_HOL_Obool), tc_fun(_1533477, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1533477, _1533479)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1533477, tc_HOL_Obool), tc_fun(_1533477, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1533477, _1533481)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1533477, tc_HOL_Obool), tc_fun(_1533477, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1533477, tc_HOL_Obool), tc_fun(_1533477, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1533477, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1533477, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1533477, tc_HOL_Obool), tc_fun(_1533477, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1533477, _1533479))))], (38933 ^ _780205) ^ [_1533869, _1533871, _1533873, _1533875] : [hBOOL(hAPP(c_Predicate_ORangeP(_1533869, _1533871, hAPP(hAPP(c_COMBC(_1533869, tc_fun(tc_prod(_1533869, _1533871), tc_HOL_Obool), tc_fun(_1533871, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533871, tc_fun(tc_fun(tc_prod(_1533869, _1533871), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1533869, _1533871), tc_HOL_Obool), tc_fun(_1533871, tc_HOL_Obool)), _1533869), c_COMBC(_1533871, tc_fun(tc_prod(_1533869, _1533871), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533871, tc_prod(_1533869, _1533871)), tc_fun(_1533871, tc_fun(tc_fun(tc_prod(_1533869, _1533871), tc_HOL_Obool), tc_HOL_Obool)), _1533869), hAPP(c_COMBB(tc_prod(_1533869, _1533871), tc_fun(tc_fun(tc_prod(_1533869, _1533871), tc_HOL_Obool), tc_HOL_Obool), _1533871), c_member(tc_prod(_1533869, _1533871)))), c_Product__Type_OPair(_1533869, _1533871)))), _1533873)), _1533875)), -(hBOOL(hAPP(hAPP(c_member(_1533871), _1533875), hAPP(c_Relation_ORange(_1533869, _1533871), _1533873))))], (38939 ^ _780205) ^ [_1534220, _1534222, _1534224, _1534226] : [hBOOL(hAPP(hAPP(c_member(_1534222), _1534226), hAPP(c_Relation_ORange(_1534220, _1534222), _1534224))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1534220, _1534222, hAPP(hAPP(c_COMBC(_1534220, tc_fun(tc_prod(_1534220, _1534222), tc_HOL_Obool), tc_fun(_1534222, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534222, tc_fun(tc_fun(tc_prod(_1534220, _1534222), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534220, _1534222), tc_HOL_Obool), tc_fun(_1534222, tc_HOL_Obool)), _1534220), c_COMBC(_1534222, tc_fun(tc_prod(_1534220, _1534222), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534222, tc_prod(_1534220, _1534222)), tc_fun(_1534222, tc_fun(tc_fun(tc_prod(_1534220, _1534222), tc_HOL_Obool), tc_HOL_Obool)), _1534220), hAPP(c_COMBB(tc_prod(_1534220, _1534222), tc_fun(tc_fun(tc_prod(_1534220, _1534222), tc_HOL_Obool), tc_HOL_Obool), _1534222), c_member(tc_prod(_1534220, _1534222)))), c_Product__Type_OPair(_1534220, _1534222)))), _1534224)), _1534226)))], (38945 ^ _780205) ^ [_1534577, _1534579, _1534581, _1534583] : [hBOOL(hAPP(hAPP(c_member(_1534577), _1534579), hAPP(c_Relation_ORange(_1534581, _1534577), _1534583))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534581, _1534577)), hAPP(hAPP(c_Product__Type_OPair(_1534581, _1534577), 38948 ^ [_1534577, _1534579, _1534581, _1534583]), _1534579)), _1534583)))], (38952 ^ _780205) ^ [_1534772, _1534774, _1534776, _1534778, _1534780, _1534782, _1534784] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1534772, _1534774, _1534776, hAPP(hAPP(c_COMBC(_1534772, tc_fun(tc_prod(_1534772, _1534774), tc_HOL_Obool), tc_fun(_1534774, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534774, tc_fun(tc_fun(tc_prod(_1534772, _1534774), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534772, _1534774), tc_HOL_Obool), tc_fun(_1534774, tc_HOL_Obool)), _1534772), c_COMBC(_1534774, tc_fun(tc_prod(_1534772, _1534774), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534774, tc_prod(_1534772, _1534774)), tc_fun(_1534774, tc_fun(tc_fun(tc_prod(_1534772, _1534774), tc_HOL_Obool), tc_HOL_Obool)), _1534772), hAPP(c_COMBB(tc_prod(_1534772, _1534774), tc_fun(tc_fun(tc_prod(_1534772, _1534774), tc_HOL_Obool), tc_HOL_Obool), _1534774), c_member(tc_prod(_1534772, _1534774)))), c_Product__Type_OPair(_1534772, _1534774)))), _1534778), hAPP(hAPP(c_COMBC(_1534774, tc_fun(tc_prod(_1534774, _1534776), tc_HOL_Obool), tc_fun(_1534776, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534776, tc_fun(tc_fun(tc_prod(_1534774, _1534776), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534774, _1534776), tc_HOL_Obool), tc_fun(_1534776, tc_HOL_Obool)), _1534774), c_COMBC(_1534776, tc_fun(tc_prod(_1534774, _1534776), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534776, tc_prod(_1534774, _1534776)), tc_fun(_1534776, tc_fun(tc_fun(tc_prod(_1534774, _1534776), tc_HOL_Obool), tc_HOL_Obool)), _1534774), hAPP(c_COMBB(tc_prod(_1534774, _1534776), tc_fun(tc_fun(tc_prod(_1534774, _1534776), tc_HOL_Obool), tc_HOL_Obool), _1534776), c_member(tc_prod(_1534774, _1534776)))), c_Product__Type_OPair(_1534774, _1534776)))), _1534780)), _1534782), _1534784)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534772, _1534776)), hAPP(hAPP(c_Product__Type_OPair(_1534772, _1534776), _1534782), _1534784)), hAPP(hAPP(c_Relation_Orel__comp(_1534772, _1534774, _1534776), _1534778), _1534780))))], (38958 ^ _780205) ^ [_1535407, _1535409, _1535411, _1535413, _1535415, _1535417, _1535419] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1535407, _1535411)), hAPP(hAPP(c_Product__Type_OPair(_1535407, _1535411), _1535417), _1535419)), hAPP(hAPP(c_Relation_Orel__comp(_1535407, _1535409, _1535411), _1535413), _1535415))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1535407, _1535409, _1535411, hAPP(hAPP(c_COMBC(_1535407, tc_fun(tc_prod(_1535407, _1535409), tc_HOL_Obool), tc_fun(_1535409, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535409, tc_fun(tc_fun(tc_prod(_1535407, _1535409), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1535407, _1535409), tc_HOL_Obool), tc_fun(_1535409, tc_HOL_Obool)), _1535407), c_COMBC(_1535409, tc_fun(tc_prod(_1535407, _1535409), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535409, tc_prod(_1535407, _1535409)), tc_fun(_1535409, tc_fun(tc_fun(tc_prod(_1535407, _1535409), tc_HOL_Obool), tc_HOL_Obool)), _1535407), hAPP(c_COMBB(tc_prod(_1535407, _1535409), tc_fun(tc_fun(tc_prod(_1535407, _1535409), tc_HOL_Obool), tc_HOL_Obool), _1535409), c_member(tc_prod(_1535407, _1535409)))), c_Product__Type_OPair(_1535407, _1535409)))), _1535413), hAPP(hAPP(c_COMBC(_1535409, tc_fun(tc_prod(_1535409, _1535411), tc_HOL_Obool), tc_fun(_1535411, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535411, tc_fun(tc_fun(tc_prod(_1535409, _1535411), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1535409, _1535411), tc_HOL_Obool), tc_fun(_1535411, tc_HOL_Obool)), _1535409), c_COMBC(_1535411, tc_fun(tc_prod(_1535409, _1535411), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535411, tc_prod(_1535409, _1535411)), tc_fun(_1535411, tc_fun(tc_fun(tc_prod(_1535409, _1535411), tc_HOL_Obool), tc_HOL_Obool)), _1535409), hAPP(c_COMBB(tc_prod(_1535409, _1535411), tc_fun(tc_fun(tc_prod(_1535409, _1535411), tc_HOL_Obool), tc_HOL_Obool), _1535411), c_member(tc_prod(_1535409, _1535411)))), c_Product__Type_OPair(_1535409, _1535411)))), _1535415)), _1535417), _1535419)))], (38964 ^ _780205) ^ [_1536048, _1536050, _1536052, _1536054, _1536056, _1536058, _1536060, _1536062] : [hBOOL(hAPP(hAPP(_1536048, _1536050), _1536052)), hBOOL(hAPP(hAPP(_1536054, _1536052), _1536056)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1536058, _1536060, _1536062, _1536048, _1536054), _1536050), _1536056)))], (38974 ^ _780205) ^ [_1536243, _1536245, _1536247, _1536249, _1536251] : [hBOOL(hAPP(hAPP(_1536243, _1536245), _1536247)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1536249, _1536251, _1536243), _1536247)))], (38980 ^ _780205) ^ [_1536369, _1536371, _1536373, _1536375] : [hBOOL(hAPP(c_Predicate_ORangeP(_1536369, _1536371, _1536373), _1536375)), -(hBOOL(hAPP(hAPP(_1536373, 38983 ^ [_1536369, _1536371, _1536373, _1536375]), _1536375)))], (38987 ^ _780205) ^ [_1536484, _1536486, _1536488, _1536490] : [38988 ^ _780205 : [(38989 ^ _780205) ^ [_1536538] : [hBOOL(hAPP(hAPP(_1536488, _1536538), _1536490))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1536484, _1536486, _1536488), _1536490)))], (38993 ^ _780205) ^ [_1536632, _1536634, _1536636, _1536638, _1536640, _1536642, _1536644] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1536632, _1536634, _1536636, _1536638, _1536640), _1536642), _1536644)), 38997 ^ _780205 : [(38998 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1536638, _1536642), 38996 ^ [_1536632, _1536634, _1536636, _1536638, _1536640, _1536642, _1536644])))], (39000 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1536640, 38996 ^ [_1536632, _1536634, _1536636, _1536638, _1536640, _1536642, _1536644]), _1536644)))]]], (39002 ^ _780205) ^ [_1536822, _1536824, _1536826, _1536828, _1536830, _1536832, _1536834] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1536822, _1536824, _1536826, _1536828, _1536830), _1536832), _1536834))), 39003 ^ _780205 : [(39004 ^ _780205) ^ [_1536893] : [hBOOL(hAPP(hAPP(_1536828, _1536832), _1536893)), hBOOL(hAPP(hAPP(_1536830, _1536893), _1536834))]]], (39012 ^ _780205) ^ [_1537042, _1537044, _1537046] : [c_Wellfounded_Owf(_1537042, _1537044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537042, _1537042), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1537042, _1537042, _1537042), _1537044), _1537046)), _1537044)), -(c_FunDef_Oreduction__pair(_1537042, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1537042, _1537042), tc_HOL_Obool), tc_fun(tc_prod(_1537042, _1537042), tc_HOL_Obool)), _1537044), _1537046)))], (39022 ^ _780205) ^ [_1537263, _1537265, _1537267] : [-(hAPP(c_Relation_ODomain(_1537263, _1537265), hAPP(c_Set_OCollect(tc_prod(_1537263, _1537265)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537263, _1537265, tc_HOL_Obool), _1537267))) = hAPP(c_Set_OCollect(_1537263), hAPP(hAPP(c_COMBB(tc_fun(_1537265, tc_HOL_Obool), tc_HOL_Obool, _1537263), c_HOL_OEx(_1537265)), _1537267)))], (39024 ^ _780205) ^ [_1537331, _1537333] : [-(c_HOL_OThe(_1537331, hAPP(hAPP(c_COMBC(_1537331, _1537331, tc_HOL_Obool), c_fequal), _1537333)) = _1537333)], (39026 ^ _780205) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (39028 ^ _780205) ^ [_1537387] : [-(c_Wellfounded_Owf(_1537387, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1537387, _1537387), tc_HOL_Obool))))], (39030 ^ _780205) ^ [_1537418, _1537420, _1537422, _1537424] : [c_Wellfounded_Owf(_1537418, _1537420), -(c_Wellfounded_Owf(_1537422, hAPP(hAPP(c_Relation_Oinv__image(_1537418, _1537422), _1537420), _1537424)))], (39036 ^ _780205) ^ [_1537517, _1537519, _1537521, _1537523] : [c_Wellfounded_Owf(_1537517, _1537519), c_Wellfounded_Owf(_1537521, _1537523), -(c_Wellfounded_Owf(tc_prod(_1537517, _1537521), c_Wellfounded_Olex__prod(_1537517, _1537521, _1537519, _1537523)))], (39046 ^ _780205) ^ [_1537670, _1537672] : [-(c_Wellfounded_Owf(_1537670, hAPP(c_Wellfounded_Omeasure(_1537670), _1537672)))], (39048 ^ _780205) ^ [_1537700, _1537702, _1537704, _1537706, _1537708] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537700, _1537702)), hAPP(hAPP(c_Product__Type_OPair(_1537700, _1537702), _1537704), _1537706)), _1537708)), -(hBOOL(hAPP(hAPP(c_member(_1537700), _1537704), hAPP(c_Relation_ODomain(_1537700, _1537702), _1537708))))], (39054 ^ _780205) ^ [_1537862, _1537864] : [c_Wellfounded_Owf(_1537862, _1537864), -(c_Wellfounded_Owf(_1537862, hAPP(hAPP(c_Relation_Orel__comp(_1537862, _1537862, _1537862), _1537864), _1537864)))], (39060 ^ _780205) ^ [_1537955, _1537957] : [c_Wellfounded_Owf(_1537955, hAPP(hAPP(c_Relation_Orel__comp(_1537955, _1537955, _1537955), _1537957), _1537957)), -(c_Wellfounded_Owf(_1537955, _1537957))], (39066 ^ _780205) ^ [_1538054, _1538056, _1538058] : [c_Wellfounded_Owf(_1538054, _1538056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1538054, _1538054), tc_HOL_Obool)), _1538058), _1538056)), -(c_Wellfounded_Owf(_1538054, _1538058))], (39076 ^ _780205) ^ [_1538213, _1538215] : [c_Wellfounded_Owf(_1538213, _1538215), -(c_Wellfounded_Owf(tc_fun(_1538213, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1538213, _1538215)))], (39082 ^ _780205) ^ [_1538302, _1538304, _1538306] : [c_Wellfounded_Owf(_1538302, _1538304), -(c_Wellfounded_Owf(_1538302, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538302, _1538302), tc_HOL_Obool)), _1538306), _1538304)))], (39088 ^ _780205) ^ [_1538409, _1538411, _1538413] : [c_Wellfounded_Owf(_1538409, _1538411), -(c_Wellfounded_Owf(_1538409, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538409, _1538409), tc_HOL_Obool)), _1538411), _1538413)))], (39094 ^ _780205) ^ [_1538516, _1538518] : [c_Wellfounded_Owf(_1538516, _1538518), -(c_Wellfounded_Owf(tc_fun(_1538516, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1538516, _1538518)))], (39100 ^ _780205) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (39102 ^ _780205) ^ [_1538623, _1538625] : [-(hAPP(c_Relation_ODomain(_1538623, _1538623), c_Relation_OId__on(_1538623, _1538625)) = _1538625)], (39104 ^ _780205) ^ [_1538657] : [-(c_Wellfounded_Owf(tc_fun(_1538657, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1538657)))], (39106 ^ _780205) ^ [_1538685, _1538687, _1538689] : [c_Wellfounded_Owf(_1538685, _1538687), -(c_Wellfounded_Owf(_1538685, c_Wellfounded_Omlex__prod(_1538685, _1538689, _1538687)))], (39112 ^ _780205) ^ [] : [-(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)))))], (39114 ^ _780205) ^ [_1538790, _1538792, _1538794] : [c_Wellfounded_Owf(_1538790, _1538792), hBOOL(hAPP(hAPP(c_member(tc_prod(_1538790, _1538790)), hAPP(hAPP(c_Product__Type_OPair(_1538790, _1538790), _1538794), _1538794)), _1538792))], (39120 ^ _780205) ^ [_1538908, _1538910, _1538912, _1538914] : [c_Wellfounded_Owf(_1538908, _1538910), hBOOL(hAPP(hAPP(c_member(tc_prod(_1538908, _1538908)), hAPP(hAPP(c_Product__Type_OPair(_1538908, _1538908), _1538912), _1538914)), _1538910)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1538908, _1538908)), hAPP(hAPP(c_Product__Type_OPair(_1538908, _1538908), _1538914), _1538912)), _1538910))], (39130 ^ _780205) ^ [_1539122, _1539124, _1539126, _1539128] : [c_Wellfounded_Owf(_1539122, _1539124), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539122, _1539122)), hAPP(hAPP(c_Product__Type_OPair(_1539122, _1539122), _1539126), _1539128)), _1539124)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539122, _1539122)), hAPP(hAPP(c_Product__Type_OPair(_1539122, _1539122), _1539128), _1539126)), _1539124))], (39140 ^ _780205) ^ [_1539336, _1539338, _1539340] : [c_Wellfounded_Owf(_1539336, _1539338), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539336, _1539336)), hAPP(hAPP(c_Product__Type_OPair(_1539336, _1539336), _1539340), _1539340)), _1539338))], (39146 ^ _780205) ^ [_1539454] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1539454)))], (39148 ^ _780205) ^ [_1539479] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1539479)))], (39150 ^ _780205) ^ [_1539504, _1539506, _1539508] : [c_Wellfounded_Owf(_1539504, _1539506), c_Wellfounded_Owf(_1539504, _1539508), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1539504, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1539504, _1539504), _1539506)), hAPP(c_Relation_ORange(_1539504, _1539504), _1539508)) = c_Orderings_Obot__class_Obot(tc_fun(_1539504, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1539504, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1539504, _1539504), tc_HOL_Obool)), _1539506), _1539508)))], (39164 ^ _780205) ^ [_1539775, _1539777, _1539779] : [c_Wellfounded_Owf(_1539775, _1539777), -(hBOOL(hAPP(hAPP(c_member(_1539775), _1539779), c_Wellfounded_Oacc(_1539775, _1539777))))], (39170 ^ _780205) ^ [_1539889, _1539891] : [c_Wellfounded_Owf(_1539889, _1539891), 39173 ^ _780205 : [(39174 ^ _780205) ^ [_1539958] : [-(hBOOL(hAPP(hAPP(c_member(_1539889), _1539958), c_Wellfounded_Oacc(_1539889, _1539891))))]]], (39176 ^ _780205) ^ [_1539991, _1539993] : [hBOOL(hAPP(hAPP(c_member(_1539991), 39177 ^ [_1539991, _1539993]), c_Wellfounded_Oacc(_1539991, _1539993))), -(c_Wellfounded_Owf(_1539991, _1539993))], (39183 ^ _780205) ^ [_1540124, _1540126] : [hAPP(hAPP(c_Relation_Orel__comp(_1540124, _1540124, _1540124), _1540126), _1540126) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1540124, _1540124), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1540124, _1540126))], (39189 ^ _780205) ^ [_1540255, _1540257, _1540259] : [c_Wellfounded_Owf(_1540255, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540255, _1540255), tc_HOL_Obool)), _1540257), _1540259)), -(c_Wellfounded_Owf(_1540255, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540255, _1540255), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540255, _1540255), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1540255, _1540255, _1540255), _1540257), _1540257)), hAPP(hAPP(c_Relation_Orel__comp(_1540255, _1540255, _1540255), _1540259), _1540257))), _1540259)))], (39195 ^ _780205) ^ [_1540454, _1540456, _1540458] : [c_Wellfounded_Owf(_1540454, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540454, _1540454), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540454, _1540454), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1540454, _1540454, _1540454), _1540456), _1540456)), hAPP(hAPP(c_Relation_Orel__comp(_1540454, _1540454, _1540454), _1540458), _1540456))), _1540458)), -(c_Wellfounded_Owf(_1540454, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540454, _1540454), tc_HOL_Obool)), _1540456), _1540458)))], (39201 ^ _780205) ^ [_1540677, _1540679, _1540681] : [hAPP(c_Relation_ODomain(_1540677, _1540679), _1540681) = c_Orderings_Obot__class_Obot(tc_fun(_1540677, tc_HOL_Obool)), -(_1540681 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1540677, _1540679), tc_HOL_Obool)))], (39207 ^ _780205) ^ [_1540790, _1540792, _1540794] : [_1540794 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1540790, _1540792), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1540790, _1540792), _1540794) = c_Orderings_Obot__class_Obot(tc_fun(_1540790, tc_HOL_Obool)))], (39213 ^ _780205) ^ [_1540909, _1540911] : [-(hAPP(c_Relation_ODomain(_1540909, _1540911), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1540909, _1540911), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1540909, tc_HOL_Obool)))], (39215 ^ _780205) ^ [_1540953, _1540955, _1540957, _1540959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1540953, _1540955), tc_HOL_Obool)), _1540957), _1540959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1540953, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1540953, _1540955), _1540957)), hAPP(c_Relation_ODomain(_1540953, _1540955), _1540959))))], (39221 ^ _780205) ^ [_1541104, _1541106, _1541108, _1541110] : [-(hAPP(c_Relation_ODomain(_1541104, _1541106), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1541104, _1541106), tc_HOL_Obool)), _1541108), _1541110)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1541104, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1541104, _1541106), _1541108)), hAPP(c_Relation_ODomain(_1541104, _1541106), _1541110)))], (39223 ^ _780205) ^ [_1541176, _1541178, _1541180] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1541176, _1541178)), _1541180)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1541176), hAPP(c_Relation_ODomain(_1541176, _1541178), _1541180))))], (39229 ^ _780205) ^ [_1541289, _1541291, _1541293] : [-(hAPP(c_Set_Oimage(tc_prod(_1541289, _1541291), _1541289, c_Product__Type_Ofst(_1541289, _1541291)), _1541293) = hAPP(c_Relation_ODomain(_1541289, _1541291), _1541293))], (39231 ^ _780205) ^ [_1541350, _1541352] : [c_Wellfounded_Owf(_1541350, _1541352), 39235 ^ _780205 : [(39236 ^ _780205) ^ [_1541486] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1541350, _1541350)), hAPP(hAPP(c_Product__Type_OPair(_1541350, _1541350), hAPP(_1541486, hAPP(c_Nat_OSuc, 39234 ^ [_1541350, _1541352, _1541486]))), hAPP(_1541486, 39234 ^ [_1541350, _1541352, _1541486]))), _1541352))]]], (39238 ^ _780205) ^ [_1541553, _1541555] : [39240 ^ _780205 : [(39241 ^ _780205) ^ [_1541578] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1541553, _1541553)), hAPP(hAPP(c_Product__Type_OPair(_1541553, _1541553), hAPP(39239 ^ [_1541553, _1541555], hAPP(c_Nat_OSuc, _1541578))), hAPP(39239 ^ [_1541553, _1541555], _1541578))), _1541555)))]], -(c_Wellfounded_Owf(_1541553, _1541555))], (39245 ^ _780205) ^ [_1541654, _1541656, _1541658] : [c_Wellfounded_Owf(_1541654, _1541656), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1541654, tc_HOL_Obool)), _1541658), hAPP(c_Relation_OImage(_1541654, _1541654, _1541656), _1541658))), -(_1541658 = c_Orderings_Obot__class_Obot(tc_fun(_1541654, tc_HOL_Obool)))], (39255 ^ _780205) ^ [_1541831, _1541833, _1541835] : [c_Wellfounded_Owf(_1541831, _1541833), c_Wellfounded_Owf(_1541831, _1541835), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541831, _1541831), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541831, _1541831, _1541831), _1541833), _1541835)), _1541833)), -(c_Wellfounded_Owf(_1541831, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1541831, _1541831), tc_HOL_Obool)), _1541833), _1541835)))], (39269 ^ _780205) ^ [_1542113, _1542115, _1542117, _1542119] : [hBOOL(hAPP(hAPP(c_member(_1542113), _1542115), hAPP(c_Relation_ODomain(_1542113, _1542117), _1542119))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542113, _1542117)), hAPP(hAPP(c_Product__Type_OPair(_1542113, _1542117), _1542115), 39272 ^ [_1542113, _1542115, _1542117, _1542119])), _1542119)))], (39276 ^ _780205) ^ [_1542270, _1542272, _1542274, _1542276] : [39277 ^ _780205 : [(39278 ^ _780205) ^ [_1542345] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542270, _1542274)), hAPP(hAPP(c_Product__Type_OPair(_1542270, _1542274), _1542272), _1542345)), _1542276))]], -(hBOOL(hAPP(hAPP(c_member(_1542270), _1542272), hAPP(c_Relation_ODomain(_1542270, _1542274), _1542276))))], (39282 ^ _780205) ^ [_1542430] : [class_Orderings_Owellorder(_1542430), -(c_Wellfounded_Owf(_1542430, hAPP(c_Set_OCollect(tc_prod(_1542430, _1542430)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542430, _1542430, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1542430)))))], (39288 ^ _780205) ^ [_1542537, _1542539, _1542541, _1542543, _1542545] : [-(hAPP(c_Relation_ODomain(_1542537, _1542539), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1542537, _1542539)), hAPP(hAPP(c_Product__Type_OPair(_1542537, _1542539), _1542541), _1542543)), _1542545)) = hAPP(hAPP(c_Set_Oinsert(_1542537), _1542541), hAPP(c_Relation_ODomain(_1542537, _1542539), _1542545)))], (39290 ^ _780205) ^ [_1542623, _1542625] : [c_FunDef_Oreduction__pair(_1542623, _1542625), 39293 ^ _780205 : [(39294 ^ _780205) ^ [] : [-(c_Wellfounded_Owf(_1542623, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1542623, _1542623), tc_HOL_Obool), tc_fun(tc_prod(_1542623, _1542623), tc_HOL_Obool)), _1542625)))], (39296 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542623, _1542623), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1542623, _1542623, _1542623), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1542623, _1542623), tc_HOL_Obool), tc_fun(tc_prod(_1542623, _1542623), tc_HOL_Obool)), _1542625)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1542623, _1542623), tc_HOL_Obool), tc_fun(tc_prod(_1542623, _1542623), tc_HOL_Obool)), _1542625))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1542623, _1542623), tc_HOL_Obool), tc_fun(tc_prod(_1542623, _1542623), tc_HOL_Obool)), _1542625))))]]], (39298 ^ _780205) ^ [_1542912, _1542914] : [-(c_FunDef_Oreduction__pair(_1542912, _1542914)), c_Wellfounded_Owf(_1542912, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1542912, _1542912), tc_HOL_Obool), tc_fun(tc_prod(_1542912, _1542912), tc_HOL_Obool)), _1542914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542912, _1542912), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1542912, _1542912, _1542912), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1542912, _1542912), tc_HOL_Obool), tc_fun(tc_prod(_1542912, _1542912), tc_HOL_Obool)), _1542914)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1542912, _1542912), tc_HOL_Obool), tc_fun(tc_prod(_1542912, _1542912), tc_HOL_Obool)), _1542914))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1542912, _1542912), tc_HOL_Obool), tc_fun(tc_prod(_1542912, _1542912), tc_HOL_Obool)), _1542914)))], (39308 ^ _780205) ^ [_1543233, _1543235, _1543237, _1543239] : [c_FunDef_Oreduction__pair(_1543233, _1543235), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1543233, _1543233), tc_HOL_Obool)), _1543237), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1543233, _1543233), tc_HOL_Obool), tc_fun(tc_prod(_1543233, _1543233), tc_HOL_Obool)), _1543235))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1543233, _1543233), tc_HOL_Obool)), _1543239), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1543233, _1543233), tc_HOL_Obool), tc_fun(tc_prod(_1543233, _1543233), tc_HOL_Obool)), _1543235))), c_Wellfounded_Owf(_1543233, _1543239), -(c_Wellfounded_Owf(_1543233, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543233, _1543233), tc_HOL_Obool)), _1543237), _1543239)))], (39326 ^ _780205) ^ [_1543634, _1543636, _1543638, _1543640] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1543634, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1543634, _1543636), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1543634, _1543636), tc_HOL_Obool)), _1543638), _1543640))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543634, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1543634, _1543636), _1543638)), hAPP(c_Relation_ODomain(_1543634, _1543636), _1543640)))))], (39328 ^ _780205) ^ [_1543716, _1543718, _1543720, _1543722] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1543716, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1543716, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1543716, _1543718), _1543720)), hAPP(c_Relation_ODomain(_1543716, _1543718), _1543722))), hAPP(c_Relation_ODomain(_1543716, _1543718), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1543716, _1543718), tc_HOL_Obool)), _1543720), _1543722)))))], (39330 ^ _780205) ^ [_1543798, _1543800] : [-(hAPP(c_Relation_OField(_1543798), _1543800) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1543798, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1543798, _1543798), _1543800)), hAPP(c_Relation_ORange(_1543798, _1543798), _1543800)))], (39332 ^ _780205) ^ [_1543851, _1543853, _1543855, _1543857] : [c_Wellfounded_Owf(_1543851, _1543853), c_Fun_Oinj__on(_1543851, _1543855, _1543857, c_Orderings_Otop__class_Otop(tc_fun(_1543851, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1543855, hAPP(c_Set_Oimage(tc_prod(_1543851, _1543851), tc_prod(_1543855, _1543855), c_Product__Type_Omap__pair(_1543851, _1543855, _1543851, _1543855, _1543857, _1543857)), _1543853)))], (39342 ^ _780205) ^ [_1544042, _1544044, _1544046] : [-(hAPP(c_Relation_ODomain(_1544042, _1544044), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1544042, _1544044), tc_HOL_Obool), _1544046)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1544042, _1544044), tc_HOL_Obool), tc_fun(_1544042, tc_HOL_Obool)), _1544046), c_Relation_ODomain(_1544042, _1544044)))], (39344 ^ _780205) ^ [_1544105, _1544107] : [-(c_HOL_OThe(_1544105, hAPP(c_fequal, _1544107)) = _1544107)], (39346 ^ _780205) ^ [_1544157, _1544159, _1544161, _1544163] : [hBOOL(hAPP(c_Predicate_ODomainP(_1544157, _1544159, hAPP(hAPP(c_COMBC(_1544157, tc_fun(tc_prod(_1544157, _1544159), tc_HOL_Obool), tc_fun(_1544159, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544159, tc_fun(tc_fun(tc_prod(_1544157, _1544159), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1544157, _1544159), tc_HOL_Obool), tc_fun(_1544159, tc_HOL_Obool)), _1544157), c_COMBC(_1544159, tc_fun(tc_prod(_1544157, _1544159), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544159, tc_prod(_1544157, _1544159)), tc_fun(_1544159, tc_fun(tc_fun(tc_prod(_1544157, _1544159), tc_HOL_Obool), tc_HOL_Obool)), _1544157), hAPP(c_COMBB(tc_prod(_1544157, _1544159), tc_fun(tc_fun(tc_prod(_1544157, _1544159), tc_HOL_Obool), tc_HOL_Obool), _1544159), c_member(tc_prod(_1544157, _1544159)))), c_Product__Type_OPair(_1544157, _1544159)))), _1544161)), _1544163)), -(hBOOL(hAPP(hAPP(c_member(_1544157), _1544163), hAPP(c_Relation_ODomain(_1544157, _1544159), _1544161))))], (39352 ^ _780205) ^ [_1544508, _1544510, _1544512, _1544514] : [hBOOL(hAPP(hAPP(c_member(_1544508), _1544514), hAPP(c_Relation_ODomain(_1544508, _1544510), _1544512))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1544508, _1544510, hAPP(hAPP(c_COMBC(_1544508, tc_fun(tc_prod(_1544508, _1544510), tc_HOL_Obool), tc_fun(_1544510, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544510, tc_fun(tc_fun(tc_prod(_1544508, _1544510), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1544508, _1544510), tc_HOL_Obool), tc_fun(_1544510, tc_HOL_Obool)), _1544508), c_COMBC(_1544510, tc_fun(tc_prod(_1544508, _1544510), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544510, tc_prod(_1544508, _1544510)), tc_fun(_1544510, tc_fun(tc_fun(tc_prod(_1544508, _1544510), tc_HOL_Obool), tc_HOL_Obool)), _1544508), hAPP(c_COMBB(tc_prod(_1544508, _1544510), tc_fun(tc_fun(tc_prod(_1544508, _1544510), tc_HOL_Obool), tc_HOL_Obool), _1544510), c_member(tc_prod(_1544508, _1544510)))), c_Product__Type_OPair(_1544508, _1544510)))), _1544512)), _1544514)))], (39358 ^ _780205) ^ [_1544865, _1544867] : [c_Wellfounded_Owf(_1544865, _1544867), -(c_Wellfounded_Owf(tc_List_Olist(_1544865), c_List_Olenlex(_1544865, _1544867)))], (39364 ^ _780205) ^ [_1544952, _1544954, _1544956, _1544958] : [hBOOL(hAPP(hAPP(c_member(_1544952), _1544954), hAPP(c_Relation_ODomain(_1544952, _1544956), _1544958))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544952, _1544956)), hAPP(hAPP(c_Product__Type_OPair(_1544952, _1544956), _1544954), 39367 ^ [_1544952, _1544954, _1544956, _1544958])), _1544958)))], (39371 ^ _780205) ^ [_1545117, _1545119, _1545121, _1545123, _1545125] : [hBOOL(hAPP(hAPP(_1545117, _1545119), _1545121)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1545123, _1545125, _1545117), _1545119)))], (39377 ^ _780205) ^ [_1545243, _1545245, _1545247, _1545249] : [hBOOL(hAPP(c_Predicate_ODomainP(_1545243, _1545245, _1545247), _1545249)), -(hBOOL(hAPP(hAPP(_1545247, _1545249), 39380 ^ [_1545243, _1545245, _1545247, _1545249])))], (39384 ^ _780205) ^ [_1545358, _1545360, _1545362, _1545364] : [39385 ^ _780205 : [(39386 ^ _780205) ^ [_1545412] : [hBOOL(hAPP(hAPP(_1545362, _1545364), _1545412))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1545358, _1545360, _1545362), _1545364)))], (39390 ^ _780205) ^ [] : [-(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))))], (39392 ^ _780205) ^ [_1545494, _1545496] : [c_Wellfounded_Owf(_1545494, _1545496), -(c_Wellfounded_Owf(tc_List_Olist(_1545494), c_List_Olex(_1545494, _1545496)))], (39398 ^ _780205) ^ [_1545581, _1545583, _1545585] : [c_Wellfounded_Owf(_1545581, _1545583), -(c_Wellfounded_Owf(tc_List_Olist(_1545581), hAPP(c_List_Olexn(_1545581, _1545583), _1545585)))], (39404 ^ _780205) ^ [_1545676, _1545678] : [-(c_List_Olex(_1545676, _1545678) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1545676), tc_List_Olist(_1545676)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1545676, _1545678)))], (39406 ^ _780205) ^ [_1545726, _1545728] : [-(hAPP(c_List_Olexn(_1545726, _1545728), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1545726), tc_List_Olist(_1545726)), tc_HOL_Obool)))], (39408 ^ _780205) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (39410 ^ _780205) ^ [_1545787, _1545789, _1545791, _1545793] : [39412 ^ _780205 : [(39413 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1545787, 39411 ^ [_1545787, _1545789, _1545791, _1545793])))], (39415 ^ _780205) ^ [] : [c_Wellfounded_Owf(_1545789, hAPP(_1545791, 39411 ^ [_1545787, _1545789, _1545791, _1545793]))]], -(c_Wellfounded_Owf(tc_prod(_1545793, _1545789), c_Recdef_Osame__fst(_1545793, _1545789, _1545787, _1545791)))], (39419 ^ _780205) ^ [_1545972, _1545974, _1545976, _1545978] : [39421 ^ _780205 : [(39422 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1545972, 39420 ^ [_1545972, _1545974, _1545976, _1545978])))], (39424 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1545974, hAPP(_1545976, 39420 ^ [_1545972, _1545974, _1545976, _1545978]))), hAPP(_1545974, 39420 ^ [_1545972, _1545974, _1545976, _1545978])))]], -(c_Wellfounded_Owf(_1545978, hAPP(c_Set_OCollect(tc_prod(_1545978, _1545978)), hAPP(c_Product__Type_Oprod_Oprod__case(_1545978, _1545978, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1545978, tc_HOL_Obool), tc_fun(_1545978, tc_HOL_Obool), _1545978), hAPP(c_COMBS(_1545978, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545978), c_fconj), _1545972))), hAPP(hAPP(c_COMBC(_1545978, tc_fun(_1545978, _1545978), tc_fun(_1545978, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545978, tc_HOL_Obool), tc_fun(tc_fun(_1545978, _1545978), tc_fun(_1545978, tc_HOL_Obool)), _1545978), c_COMBB(_1545978, tc_HOL_Obool, _1545978)), c_fequal)), _1545976))))))], (39428 ^ _780205) ^ [_1546380, _1546382] : [c_Wellfounded_OwfP(_1546380, _1546382), -(c_Wellfounded_Owf(_1546380, hAPP(c_Set_OCollect(tc_prod(_1546380, _1546380)), hAPP(c_Product__Type_Oprod_Oprod__case(_1546380, _1546380, tc_HOL_Obool), _1546382))))], (39434 ^ _780205) ^ [_1546483, _1546485] : [c_Wellfounded_Owf(_1546483, hAPP(c_Set_OCollect(tc_prod(_1546483, _1546483)), hAPP(c_Product__Type_Oprod_Oprod__case(_1546483, _1546483, tc_HOL_Obool), _1546485))), -(c_Wellfounded_OwfP(_1546483, _1546485))], (39440 ^ _780205) ^ [_1546592] : [-(c_Wellfounded_OwfP(_1546592, hAPP(c_COMBK(tc_fun(_1546592, tc_HOL_Obool), _1546592), hAPP(c_COMBK(tc_HOL_Obool, _1546592), c_fFalse))))], (39442 ^ _780205) ^ [_1546630, _1546632, _1546634] : [c_Wellfounded_OwfP(_1546630, _1546632), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1546630, _1546632), _1546634)))], (39448 ^ _780205) ^ [_1546734, _1546736] : [c_Wellfounded_OwfP(_1546734, _1546736), 39451 ^ _780205 : [(39452 ^ _780205) ^ [_1546798] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1546734, _1546736), _1546798)))]]], (39454 ^ _780205) ^ [_1546826, _1546828] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1546826, _1546828), 39455 ^ [_1546826, _1546828])), -(c_Wellfounded_OwfP(_1546826, _1546828))], (39461 ^ _780205) ^ [_1546944, _1546946, _1546948] : [c_Wellfounded_OwfP(_1546944, _1546946), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1546944, tc_fun(_1546944, tc_HOL_Obool))), _1546948), _1546946)), -(c_Wellfounded_OwfP(_1546944, _1546948))], (39471 ^ _780205) ^ [_1547103, _1547105] : [c_Wellfounded_Owf(_1547103, _1547105), -(c_Wellfounded_OwfP(_1547103, c_FunDef_Oin__rel(_1547103, _1547103, _1547105)))], (39477 ^ _780205) ^ [_1547203, _1547205] : [c_Wellfounded_OwfP(_1547203, hAPP(hAPP(c_COMBC(_1547203, tc_fun(tc_prod(_1547203, _1547203), tc_HOL_Obool), tc_fun(_1547203, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547203, tc_fun(tc_fun(tc_prod(_1547203, _1547203), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1547203, _1547203), tc_HOL_Obool), tc_fun(_1547203, tc_HOL_Obool)), _1547203), c_COMBC(_1547203, tc_fun(tc_prod(_1547203, _1547203), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547203, tc_prod(_1547203, _1547203)), tc_fun(_1547203, tc_fun(tc_fun(tc_prod(_1547203, _1547203), tc_HOL_Obool), tc_HOL_Obool)), _1547203), hAPP(c_COMBB(tc_prod(_1547203, _1547203), tc_fun(tc_fun(tc_prod(_1547203, _1547203), tc_HOL_Obool), tc_HOL_Obool), _1547203), c_member(tc_prod(_1547203, _1547203)))), c_Product__Type_OPair(_1547203, _1547203)))), _1547205)), -(c_Wellfounded_Owf(_1547203, _1547205))], (39483 ^ _780205) ^ [_1547512, _1547514] : [c_Wellfounded_Owf(_1547512, _1547514), -(c_Wellfounded_OwfP(_1547512, hAPP(hAPP(c_COMBC(_1547512, tc_fun(tc_prod(_1547512, _1547512), tc_HOL_Obool), tc_fun(_1547512, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547512, tc_fun(tc_fun(tc_prod(_1547512, _1547512), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1547512, _1547512), tc_HOL_Obool), tc_fun(_1547512, tc_HOL_Obool)), _1547512), c_COMBC(_1547512, tc_fun(tc_prod(_1547512, _1547512), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547512, tc_prod(_1547512, _1547512)), tc_fun(_1547512, tc_fun(tc_fun(tc_prod(_1547512, _1547512), tc_HOL_Obool), tc_HOL_Obool)), _1547512), hAPP(c_COMBB(tc_prod(_1547512, _1547512), tc_fun(tc_fun(tc_prod(_1547512, _1547512), tc_HOL_Obool), tc_HOL_Obool), _1547512), c_member(tc_prod(_1547512, _1547512)))), c_Product__Type_OPair(_1547512, _1547512)))), _1547514)))], (39489 ^ _780205) ^ [_1547827, _1547829] : [c_Wellfounded_OwfP(_1547827, _1547829), -(c_Wellfounded_Oacyclic(_1547827, hAPP(c_Set_OCollect(tc_prod(_1547827, _1547827)), hAPP(c_Product__Type_Oprod_Oprod__case(_1547827, _1547827, tc_HOL_Obool), _1547829))))], (39495 ^ _780205) ^ [_1547933, _1547935, _1547937, _1547939] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1547933), _1547935))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547937), hAPP(c_Set_Oimage(_1547933, _1547937, _1547939), _1547935))), 39503 ^ _780205 : [(39504 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547933), 39502 ^ [_1547933, _1547935, _1547937, _1547939]), _1547935)))], (39506 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1547933), hAPP(c_Set_OCollect(_1547933), hAPP(hAPP(c_COMBS(_1547933, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547933), c_fconj), hAPP(hAPP(c_COMBC(_1547933, tc_fun(_1547933, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547933)), _1547935))), hAPP(hAPP(c_COMBC(_1547933, _1547937, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1547937, tc_fun(_1547937, tc_HOL_Obool), _1547933), c_fequal), _1547939)), hAPP(_1547939, 39502 ^ [_1547933, _1547935, _1547937, _1547939]))))))]]], (39524 ^ _780205) ^ [_1549035, _1549037, _1549039] : [-(c_Relation_Orefl__on(_1549035, _1549037, _1549039)), 39528 ^ _780205 : [(39529 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549035, _1549035)), 39527 ^ [_1549035, _1549037, _1549039]), _1549039)))], (39531 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1549035, _1549035, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1549035, tc_fun(_1549035, tc_HOL_Obool), tc_fun(_1549035, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1549035, tc_HOL_Obool), tc_fun(_1549035, tc_HOL_Obool)), _1549035), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1549035)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549035), c_fconj), hAPP(hAPP(c_COMBC(_1549035, tc_fun(_1549035, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549035)), _1549037)))), hAPP(hAPP(c_COMBC(_1549035, tc_fun(_1549035, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549035)), _1549037))), 39527 ^ [_1549035, _1549037, _1549039]))]], 39533 ^ _780205 : [(39534 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549035), 39532 ^ [_1549035, _1549037, _1549039]), _1549037)))], (39536 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549035, _1549035)), hAPP(hAPP(c_Product__Type_OPair(_1549035, _1549035), 39532 ^ [_1549035, _1549037, _1549039]), 39532 ^ [_1549035, _1549037, _1549039])), _1549039))]]], (39508 ^ _780205) ^ [_1548416, _1548418, _1548420] : [c_Relation_Orefl__on(_1548416, _1548418, _1548420), 39511 ^ _780205 : [(39512 ^ _780205) ^ [_1548627] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548416, _1548416)), _1548627), _1548420)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1548416, _1548416, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1548416, tc_fun(_1548416, tc_HOL_Obool), tc_fun(_1548416, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1548416, tc_HOL_Obool), tc_fun(_1548416, tc_HOL_Obool)), _1548416), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1548416)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548416), c_fconj), hAPP(hAPP(c_COMBC(_1548416, tc_fun(_1548416, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548416)), _1548418)))), hAPP(hAPP(c_COMBC(_1548416, tc_fun(_1548416, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548416)), _1548418))), _1548627)))], (39518 ^ _780205) ^ [_1548900] : [hBOOL(hAPP(hAPP(c_member(_1548416), _1548900), _1548418)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548416, _1548416)), hAPP(hAPP(c_Product__Type_OPair(_1548416, _1548416), _1548900), _1548900)), _1548420)))]]], (39540 ^ _780205) ^ [_1549676, _1549678, _1549680] : [hBOOL(hAPP(hAPP(c_member(_1549678), _1549676), c_Orderings_Obot__class_Obot(tc_fun(_1549678, tc_HOL_Obool)))), -(hBOOL(hAPP(_1549680, _1549676)))], (39546 ^ _780205) ^ [_1549783, _1549785] : [c_Wellfounded_Owf(_1549783, _1549785), -(c_Wellfounded_Oacyclic(_1549783, _1549785))], (39552 ^ _780205) ^ [_1549860, _1549862, _1549864] : [c_Wellfounded_Oacyclic(_1549860, _1549862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1549860, _1549860), tc_HOL_Obool)), _1549864), _1549862)), -(c_Wellfounded_Oacyclic(_1549860, _1549864))], (39572 ^ _780205) ^ [_1550220, _1550222, _1550224] : [39574 ^ _780205 : [(39575 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550220), 39573 ^ [_1550220, _1550222, _1550224]), _1550224)))], (39577 ^ _780205) ^ [] : [hBOOL(hAPP(_1550222, 39573 ^ [_1550220, _1550222, _1550224]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1550220, _1550222), _1550224)))], (39562 ^ _780205) ^ [_1550037, _1550039, _1550041] : [hBOOL(hAPP(c_Predicate_OPowp(_1550037, _1550039), _1550041)), 39565 ^ _780205 : [(39566 ^ _780205) ^ [_1550121] : [hBOOL(hAPP(hAPP(c_member(_1550037), _1550121), _1550041)), -(hBOOL(hAPP(_1550039, _1550121)))]]], (39581 ^ _780205) ^ [_1550400] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1550400, tc_HOL_Obool) = c_Set_OBall(_1550400))], (39583 ^ _780205) ^ [_1550428, _1550430, _1550432, _1550434] : [-(hAPP(c_Set_OCollect(_1550428), hAPP(hAPP(c_COMBB(tc_fun(_1550430, tc_HOL_Obool), tc_HOL_Obool, _1550428), c_HOL_OAll(_1550430)), hAPP(hAPP(c_COMBB(tc_fun(_1550430, tc_HOL_Obool), tc_fun(_1550430, tc_HOL_Obool), _1550428), hAPP(c_COMBS(_1550430, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550430), c_fimplies), hAPP(hAPP(c_COMBC(_1550430, tc_fun(_1550430, tc_HOL_Obool), tc_HOL_Obool), c_member(_1550430)), _1550432)))), _1550434))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1550430, tc_fun(_1550428, tc_HOL_Obool)), _1550432), hAPP(hAPP(c_COMBB(tc_fun(_1550428, tc_HOL_Obool), tc_fun(_1550428, tc_HOL_Obool), _1550430), c_Set_OCollect(_1550428)), hAPP(c_COMBC(_1550428, _1550430, tc_HOL_Obool), _1550434))))], (39595 ^ _780205) ^ [_1550959, _1550961, _1550963, _1550965] : [39597 ^ _780205 : [(39598 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1550959, _1550959)), 39596 ^ [_1550959, _1550961, _1550963, _1550965]), _1550963)))], (39600 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550959, _1550959, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1550959, tc_fun(_1550959, _1550961), tc_fun(_1550959, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550961, tc_HOL_Obool), tc_fun(tc_fun(_1550959, _1550961), tc_fun(_1550959, tc_HOL_Obool)), _1550959), c_COMBB(_1550961, tc_HOL_Obool, _1550959)), hAPP(hAPP(c_COMBB(_1550961, tc_fun(_1550961, tc_HOL_Obool), _1550959), c_fequal), _1550965))), _1550965)), 39596 ^ [_1550959, _1550961, _1550963, _1550965]))]], -(c_Equiv__Relations_Ocongruent(_1550959, _1550961, _1550963, _1550965))], (39585 ^ _780205) ^ [_1550583, _1550585, _1550587, _1550589] : [c_Equiv__Relations_Ocongruent(_1550583, _1550585, _1550587, _1550589), 39588 ^ _780205 : [(39589 ^ _780205) ^ [_1550728] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1550583, _1550583)), _1550728), _1550587)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550583, _1550583, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1550583, tc_fun(_1550583, _1550585), tc_fun(_1550583, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550585, tc_HOL_Obool), tc_fun(tc_fun(_1550583, _1550585), tc_fun(_1550583, tc_HOL_Obool)), _1550583), c_COMBB(_1550585, tc_HOL_Obool, _1550583)), hAPP(hAPP(c_COMBB(_1550585, tc_fun(_1550585, tc_HOL_Obool), _1550583), c_fequal), _1550589))), _1550589)), _1550728)))]]], (39604 ^ _780205) ^ [_1551334, _1551336, _1551338, _1551340] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1551334, tc_fun(_1551336, tc_HOL_Obool)), _1551338), _1551340) = hAPP(c_Set_OCollect(_1551336), hAPP(hAPP(c_COMBB(tc_fun(_1551334, tc_HOL_Obool), tc_HOL_Obool, _1551336), c_HOL_OAll(_1551334)), hAPP(hAPP(c_COMBB(tc_fun(_1551334, tc_HOL_Obool), tc_fun(_1551334, tc_HOL_Obool), _1551336), hAPP(c_COMBS(_1551334, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551334), c_fimplies), hAPP(hAPP(c_COMBC(_1551334, tc_fun(_1551334, tc_HOL_Obool), tc_HOL_Obool), c_member(_1551334)), _1551338)))), hAPP(hAPP(c_COMBC(_1551336, tc_fun(_1551334, tc_fun(_1551336, tc_HOL_Obool)), tc_fun(_1551334, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1551336, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1551334, tc_fun(_1551336, tc_HOL_Obool)), tc_fun(_1551334, tc_HOL_Obool)), _1551336), c_COMBB(tc_fun(_1551336, tc_HOL_Obool), tc_HOL_Obool, _1551334)), c_member(_1551336))), _1551340)))))], (39606 ^ _780205) ^ [_1551499, _1551501] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1551499, _1551499)), _1551501)), 39609 ^ _780205 : [(39610 ^ _780205) ^ [] : [c_Wellfounded_Owf(_1551499, _1551501), -(c_Wellfounded_Oacyclic(_1551499, _1551501))], (39616 ^ _780205) ^ [] : [c_Wellfounded_Oacyclic(_1551499, _1551501), -(c_Wellfounded_Owf(_1551499, _1551501))]]], (39622 ^ _780205) ^ [_1551720, _1551722] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1551720, _1551720)), _1551722)), c_Wellfounded_Oacyclic(_1551720, _1551722), -(c_Wellfounded_Owf(_1551720, _1551722))], (39632 ^ _780205) ^ [_1551863, _1551865] : [class_Complete__Lattice_Ocomplete__lattice(_1551863), -(c_Complete__Lattice_OSup__class_OSup(_1551863, _1551865) = c_Complete__Lattice_OInf__class_OInf(_1551863, hAPP(c_Set_OCollect(_1551863), hAPP(hAPP(c_COMBB(tc_fun(_1551863, tc_HOL_Obool), tc_HOL_Obool, _1551863), c_HOL_OAll(_1551863)), hAPP(hAPP(c_COMBB(tc_fun(_1551863, tc_HOL_Obool), tc_fun(_1551863, tc_HOL_Obool), _1551863), hAPP(c_COMBS(_1551863, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551863), c_fimplies), hAPP(hAPP(c_COMBC(_1551863, tc_fun(_1551863, tc_HOL_Obool), tc_HOL_Obool), c_member(_1551863)), _1551865)))), hAPP(c_COMBC(_1551863, _1551863, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1551863)))))))], (39638 ^ _780205) ^ [_1552104, _1552106] : [class_Complete__Lattice_Ocomplete__lattice(_1552104), -(c_Complete__Lattice_OInf__class_OInf(_1552104, _1552106) = c_Complete__Lattice_OSup__class_OSup(_1552104, hAPP(c_Set_OCollect(_1552104), hAPP(hAPP(c_COMBB(tc_fun(_1552104, tc_HOL_Obool), tc_HOL_Obool, _1552104), c_HOL_OAll(_1552104)), hAPP(hAPP(c_COMBB(tc_fun(_1552104, tc_HOL_Obool), tc_fun(_1552104, tc_HOL_Obool), _1552104), hAPP(c_COMBS(_1552104, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1552104), c_fimplies), hAPP(hAPP(c_COMBC(_1552104, tc_fun(_1552104, tc_HOL_Obool), tc_HOL_Obool), c_member(_1552104)), _1552106)))), c_Orderings_Oord__class_Oless__eq(_1552104))))))], (39644 ^ _780205) ^ [_1552346, _1552348] : [c_Nitpick_Owf_H(_1552346, _1552348), 39647 ^ _780205 : [(39648 ^ _780205) ^ [] : [-(c_Wellfounded_Oacyclic(_1552346, _1552348))], (39650 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1552346, _1552346)), _1552348))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (39656 ^ _780205) ^ [_1552466, _1552468] : [-(c_Nitpick_Owf_H(_1552466, _1552468)), c_Wellfounded_Oacyclic(_1552466, _1552468), 39661 ^ _780205 : [(39662 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1552466, _1552466)), _1552468))], (39664 ^ _780205) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (39669 ^ _780205) ^ [_1552641] : [-(_1552641 = hAPP(c_Int_OAbs__Integ, 39667 ^ [_1552641]))], (39671 ^ _780205) ^ [_1552669] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39667 ^ [_1552669]), c_Int_OInteg)))], (39673 ^ _780205) ^ [_1552704, _1552706] : [39675 ^ _780205 : [(39676 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39674 ^ [_1552704, _1552706]), c_Int_OInteg)))], (39678 ^ _780205) ^ [] : [hBOOL(hAPP(_1552704, hAPP(c_Int_OAbs__Integ, 39674 ^ [_1552704, _1552706])))]], -(hBOOL(hAPP(_1552704, _1552706)))], (39682 ^ _780205) ^ [_1552873, _1552875] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1552873, tc_HOL_Obool), _1552875) = hAPP(c_Set_OCollect(_1552873), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1552873, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1552873), c_HOL_OAll(tc_fun(_1552873, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1552873, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1552873, tc_HOL_Obool), tc_HOL_Obool), _1552873), hAPP(c_COMBS(tc_fun(_1552873, 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(_1552873, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1552873, tc_HOL_Obool), tc_fun(tc_fun(_1552873, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1552873, tc_HOL_Obool))), _1552875)))), c_member(_1552873)))))], (39684 ^ _780205) ^ [_1553001, _1553003, _1553005, _1553007] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1553001), _1553003)), 39690 ^ _780205 : [(39691 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553001), 39689 ^ [_1553001, _1553003, _1553005, _1553007]), _1553003)))], (39693 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1553005), hAPP(_1553007, 39689 ^ [_1553001, _1553003, _1553005, _1553007])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1553005), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1553001, tc_fun(_1553005, tc_HOL_Obool)), _1553003), _1553007))))], (39697 ^ _780205) ^ [_1553288, _1553290] : [39699 ^ _780205 : [(39700 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 39698 ^ [_1553288, _1553290]), _1553288)))], (39702 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1553290), 39698 ^ [_1553288, _1553290]))]], -(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)), _1553290), _1553288))], (39706 ^ _780205) ^ [_1553463, _1553465, _1553467] : [c_Wellfounded_OwfP(_1553463, hAPP(_1553465, 39707 ^ [_1553463, _1553465, _1553467])), 39714 ^ _780205 : [(39715 ^ _780205) ^ [] : [hAPP(_1553465, 39712 ^ [_1553463, _1553465, _1553467]) = hAPP(_1553465, 39713 ^ [_1553463, _1553465, _1553467])], (39717 ^ _780205) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1553463, tc_HOL_Obool)), c_Predicate_ODomainP(_1553463, _1553463, hAPP(_1553465, 39712 ^ [_1553463, _1553465, _1553467]))), c_Predicate_ORangeP(_1553463, _1553463, hAPP(_1553465, 39713 ^ [_1553463, _1553465, _1553467]))) = c_Orderings_Obot__class_Obot(tc_fun(_1553463, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1553463, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1553467, tc_fun(_1553463, tc_fun(_1553463, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1553467, tc_HOL_Obool))), _1553465)))], (39721 ^ _780205) ^ [_1553903, _1553905, _1553907, _1553909, _1553911, _1553913] : [39724 ^ _780205 : [(39725 ^ _780205) ^ [] : [-(_1553903 = hAPP(hAPP(c_Product__Type_OPair(_1553905, _1553907), 39722 ^ [_1553903, _1553905, _1553907, _1553909, _1553911, _1553913]), 39723 ^ [_1553903, _1553905, _1553907, _1553909, _1553911, _1553913]))], (39727 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1553909), _1553911), hAPP(hAPP(_1553913, 39722 ^ [_1553903, _1553905, _1553907, _1553909, _1553911, _1553913]), 39723 ^ [_1553903, _1553905, _1553907, _1553909, _1553911, _1553913])))]], -(hBOOL(hAPP(hAPP(c_member(_1553909), _1553911), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1553905, _1553907, tc_fun(_1553909, tc_HOL_Obool)), _1553913), _1553903))))], (39731 ^ _780205) ^ [_1554228, _1554230, _1554232, _1554234, _1554236, _1554238] : [hBOOL(hAPP(hAPP(c_member(_1554228), _1554230), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1554232, _1554234, tc_fun(_1554228, tc_HOL_Obool)), _1554236), _1554238))), 39736 ^ _780205 : [(39737 ^ _780205) ^ [] : [-(_1554238 = hAPP(hAPP(c_Product__Type_OPair(_1554232, _1554234), 39734 ^ [_1554228, _1554230, _1554232, _1554234, _1554236, _1554238]), 39735 ^ [_1554228, _1554230, _1554232, _1554234, _1554236, _1554238]))], (39739 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554228), _1554230), hAPP(hAPP(_1554236, 39734 ^ [_1554228, _1554230, _1554232, _1554234, _1554236, _1554238]), 39735 ^ [_1554228, _1554230, _1554232, _1554234, _1554236, _1554238]))))]]], (39741 ^ _780205) ^ [_1554497, _1554499, _1554501, _1554503, _1554505, _1554507] : [-(hAPP(c_Set_Ovimage(_1554497, tc_prod(_1554499, _1554501), _1554503), hAPP(hAPP(c_Product__Type_OSigma(_1554499, _1554501), _1554505), hAPP(c_COMBK(tc_fun(_1554501, tc_HOL_Obool), _1554499), _1554507))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1554497, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1554497, _1554499, hAPP(c_Fun_Ocomp(tc_prod(_1554499, _1554501), _1554499, _1554497, c_Product__Type_Ofst(_1554499, _1554501)), _1554503)), _1554505)), hAPP(c_Set_Ovimage(_1554497, _1554501, hAPP(c_Fun_Ocomp(tc_prod(_1554499, _1554501), _1554501, _1554497, c_Product__Type_Osnd(_1554499, _1554501)), _1554503)), _1554507)))], (39743 ^ _780205) ^ [_1554611, _1554613, _1554615, _1554617, _1554619, _1554621, _1554623] : [hAPP(c_Fun_Ocomp(_1554611, _1554613, _1554615, _1554617), _1554619) = hAPP(c_Fun_Ocomp(_1554613, _1554613, _1554615, c_Fun_Oid(_1554613)), _1554621), -(hAPP(_1554617, hAPP(_1554619, _1554623)) = hAPP(_1554621, _1554623))], (39749 ^ _780205) ^ [_1554752, _1554754, _1554756] : [-(hAPP(c_Fun_Ocomp(_1554752, _1554752, _1554754, c_Fun_Oid(_1554752)), _1554756) = _1554756)], (39751 ^ _780205) ^ [_1554789, _1554791, _1554793] : [-(hAPP(c_Fun_Ocomp(_1554789, _1554791, _1554789, _1554793), c_Fun_Oid(_1554789)) = _1554793)], (39753 ^ _780205) ^ [_1554826, _1554828, _1554830, _1554832, _1554834, _1554836, _1554838] : [-(hAPP(c_Fun_Ocomp(_1554826, _1554828, _1554830, _1554832), c_Fun_Ofun__upd(_1554830, _1554826, _1554834, _1554836, _1554838)) = c_Fun_Ofun__upd(_1554830, _1554828, hAPP(c_Fun_Ocomp(_1554826, _1554828, _1554830, _1554832), _1554834), _1554836, hAPP(_1554832, _1554838)))], (39755 ^ _780205) ^ [_1554892, _1554894, _1554896, _1554898, _1554900, _1554902, _1554904] : [-(hAPP(c_Product__Type_Oapsnd(_1554892, _1554894, _1554896, _1554898), hAPP(c_Product__Type_Oapsnd(_1554900, _1554892, _1554896, _1554902), _1554904)) = hAPP(c_Product__Type_Oapsnd(_1554900, _1554894, _1554896, hAPP(c_Fun_Ocomp(_1554892, _1554894, _1554900, _1554898), _1554902)), _1554904))], (39757 ^ _780205) ^ [_1554959, _1554961, _1554963, _1554965, _1554967] : [c_Finite__Set_Ofun__left__comm(_1554959, _1554961, _1554963), -(hAPP(c_Fun_Ocomp(_1554961, _1554961, _1554961, hAPP(_1554963, _1554965)), hAPP(_1554963, _1554967)) = hAPP(c_Fun_Ocomp(_1554961, _1554961, _1554961, hAPP(_1554963, _1554967)), hAPP(_1554963, _1554965)))], (39763 ^ _780205) ^ [_1555100, _1555102, _1555104, _1555106, _1555108, _1555110, _1555112, _1555114, _1555116, _1555118, _1555120] : [hAPP(_1555100, hAPP(_1555102, _1555104)) = hAPP(_1555106, hAPP(_1555108, _1555110)), -(hAPP(hAPP(c_Fun_Ocomp(_1555112, _1555114, _1555116, _1555100), _1555102), _1555104) = hAPP(hAPP(c_Fun_Ocomp(_1555118, _1555114, _1555120, _1555106), _1555108), _1555110))], (39769 ^ _780205) ^ [_1555263, _1555265, _1555267, _1555269] : [c_Finite__Set_Ofun__left__comm__idem(_1555263, _1555265, _1555267), -(hAPP(c_Fun_Ocomp(_1555265, _1555265, _1555265, hAPP(_1555267, _1555269)), hAPP(_1555267, _1555269)) = hAPP(_1555267, _1555269))], (39775 ^ _780205) ^ [_1555380, _1555382, _1555384, _1555386, _1555388, _1555390, _1555392] : [hAPP(c_Fun_Ocomp(_1555380, _1555382, _1555384, _1555386), _1555388) = _1555390, -(hAPP(_1555386, hAPP(_1555388, _1555392)) = hAPP(_1555390, _1555392))], (39781 ^ _780205) ^ [_1555501, _1555503, _1555505, _1555507, _1555509, _1555511] : [-(hAPP(hAPP(c_Fun_Ocomp(_1555501, _1555503, _1555505, hAPP(c_COMBK(_1555503, _1555501), _1555507)), _1555509), _1555511) = _1555507)], (39783 ^ _780205) ^ [_1555551, _1555553, _1555555, _1555557, _1555559, _1555561, _1555563] : [-(hAPP(c_Product__Type_Oapfst(_1555551, _1555553, _1555555, _1555557), hAPP(c_Product__Type_Oapfst(_1555559, _1555551, _1555555, _1555561), _1555563)) = hAPP(c_Product__Type_Oapfst(_1555559, _1555553, _1555555, hAPP(c_Fun_Ocomp(_1555551, _1555553, _1555559, _1555557), _1555561)), _1555563))], (39785 ^ _780205) ^ [_1555618, _1555620, _1555622, _1555624, _1555626, _1555628] : [-(hAPP(hAPP(c_Fun_Ocomp(_1555618, _1555620, _1555622, _1555624), _1555626), _1555628) = hAPP(_1555624, hAPP(_1555626, _1555628)))], (39787 ^ _780205) ^ [_1555668, _1555670, _1555672, _1555674, _1555676, _1555678] : [-(hAPP(c_Set_Ovimage(_1555668, _1555670, hAPP(c_Fun_Ocomp(_1555672, _1555670, _1555668, _1555674), _1555676)), _1555678) = hAPP(c_Set_Ovimage(_1555668, _1555672, _1555676), hAPP(c_Set_Ovimage(_1555672, _1555670, _1555674), _1555678)))], (39789 ^ _780205) ^ [_1555730, _1555732, _1555734, _1555736, _1555738, _1555740, _1555742] : [-(hAPP(c_Fun_Ocomp(_1555730, _1555732, _1555734, _1555736), hAPP(c_Fun_Ocomp(_1555738, _1555730, _1555734, _1555740), _1555742)) = hAPP(c_Fun_Ocomp(_1555738, _1555732, _1555734, hAPP(c_Fun_Ocomp(_1555730, _1555732, _1555738, _1555736), _1555740)), _1555742))], (39791 ^ _780205) ^ [_1555797, _1555799, _1555801, _1555803, _1555805, _1555807] : [-(hAPP(hAPP(c_Fun_Ocomp(_1555797, _1555799, _1555801, _1555803), _1555805), _1555807) = hAPP(_1555803, hAPP(_1555805, _1555807)))], (39793 ^ _780205) ^ [_1555847, _1555849, _1555851, _1555853, _1555855, _1555857, _1555859, _1555861, _1555863] : [hAPP(c_Fun_Ocomp(_1555847, _1555849, _1555851, _1555853), _1555855) = hAPP(c_Fun_Ocomp(_1555857, _1555849, _1555851, _1555859), _1555861), -(hAPP(_1555853, hAPP(_1555855, _1555863)) = hAPP(_1555859, hAPP(_1555861, _1555863)))], (39799 ^ _780205) ^ [_1555994, _1555996, _1555998, _1556000, _1556002, _1556004, _1556006, _1556008] : [hAPP(c_Fun_Ocomp(_1555994, _1555996, _1555998, _1556000), _1556002) = hAPP(c_Fun_Ocomp(_1556004, _1555996, _1555998, _1556006), _1556008), 39802 ^ _780205 : [(39803 ^ _780205) ^ [_1556109] : [-(hAPP(_1556000, hAPP(_1556002, _1556109)) = hAPP(_1556006, hAPP(_1556008, _1556109)))]]], (39805 ^ _780205) ^ [_1556148, _1556150, _1556152, _1556154, _1556156, _1556158, _1556160, _1556162, _1556164, _1556166, _1556168] : [-(hAPP(c_Product__Type_Omap__pair(_1556148, _1556150, _1556152, _1556154, _1556156, _1556158), hAPP(c_Product__Type_Omap__pair(_1556160, _1556148, _1556162, _1556152, _1556164, _1556166), _1556168)) = hAPP(c_Product__Type_Omap__pair(_1556160, _1556150, _1556162, _1556154, hAPP(c_Fun_Ocomp(_1556148, _1556150, _1556160, _1556156), _1556164), hAPP(c_Fun_Ocomp(_1556152, _1556154, _1556162, _1556158), _1556166)), _1556168))], (39807 ^ _780205) ^ [_1556237, _1556239, _1556241, _1556243, _1556245, _1556247, _1556249, _1556251, _1556253, _1556255] : [-(c_Product__Type_Omap__pair(_1556237, _1556239, _1556241, _1556243, hAPP(c_Fun_Ocomp(_1556245, _1556239, _1556237, _1556247), _1556249), hAPP(c_Fun_Ocomp(_1556251, _1556243, _1556241, _1556253), _1556255)) = hAPP(c_Fun_Ocomp(tc_prod(_1556245, _1556251), tc_prod(_1556239, _1556243), tc_prod(_1556237, _1556241), c_Product__Type_Omap__pair(_1556245, _1556239, _1556251, _1556243, _1556247, _1556253)), c_Product__Type_Omap__pair(_1556237, _1556245, _1556241, _1556251, _1556249, _1556255)))], (39809 ^ _780205) ^ [_1556332, _1556334, _1556336, _1556338, _1556340, _1556342, _1556344, _1556346, _1556348, _1556350] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1556332, _1556334), tc_prod(_1556336, _1556338), tc_prod(_1556340, _1556342), c_Product__Type_Omap__pair(_1556332, _1556336, _1556334, _1556338, _1556344, _1556346)), c_Product__Type_Omap__pair(_1556340, _1556332, _1556342, _1556334, _1556348, _1556350)) = c_Product__Type_Omap__pair(_1556340, _1556336, _1556342, _1556338, hAPP(c_Fun_Ocomp(_1556332, _1556336, _1556340, _1556344), _1556348), hAPP(c_Fun_Ocomp(_1556334, _1556338, _1556342, _1556346), _1556350)))], (39811 ^ _780205) ^ [_1556427, _1556429, _1556431, _1556433, _1556435, _1556437] : [-(hAPP(c_Set_Oimage(_1556427, _1556429, hAPP(c_Fun_Ocomp(_1556431, _1556429, _1556427, _1556433), _1556435)), _1556437) = hAPP(c_Set_Oimage(_1556431, _1556429, _1556433), hAPP(c_Set_Oimage(_1556427, _1556431, _1556435), _1556437)))], (39813 ^ _780205) ^ [_1556489, _1556491, _1556493, _1556495, _1556497] : [hAPP(c_Set_Oimage(_1556489, _1556491, _1556493), c_Orderings_Otop__class_Otop(tc_fun(_1556489, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1556491, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1556491, _1556495, _1556497), c_Orderings_Otop__class_Otop(tc_fun(_1556491, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1556495, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1556489, _1556495, hAPP(c_Fun_Ocomp(_1556491, _1556495, _1556489, _1556497), _1556493)), c_Orderings_Otop__class_Otop(tc_fun(_1556489, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1556495, tc_HOL_Obool)))], (39823 ^ _780205) ^ [_1556748, _1556750, _1556752, _1556754, _1556756, _1556758] : [c_Fun_Oinj__on(_1556748, _1556750, hAPP(c_Fun_Ocomp(_1556752, _1556750, _1556748, _1556754), _1556756), _1556758), -(c_Fun_Oinj__on(_1556748, _1556752, _1556756, _1556758))], (39829 ^ _780205) ^ [_1556857, _1556859, _1556861, _1556863, _1556865] : [c_Fun_Oinj__on(_1556857, _1556859, _1556861, c_Orderings_Otop__class_Otop(tc_fun(_1556857, tc_HOL_Obool))), c_Fun_Oinj__on(_1556863, _1556857, _1556865, c_Orderings_Otop__class_Otop(tc_fun(_1556863, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1556863, _1556859, hAPP(c_Fun_Ocomp(_1556857, _1556859, _1556863, _1556861), _1556865), c_Orderings_Otop__class_Otop(tc_fun(_1556863, tc_HOL_Obool))))], (39839 ^ _780205) ^ [_1557056, _1557058, _1557060, _1557062, _1557064, _1557066] : [c_Fun_Oinj__on(_1557056, _1557058, _1557060, _1557062), 39842 ^ _780205 : [(39843 ^ _780205) ^ [] : [c_Fun_Oinj__on(_1557058, _1557064, _1557066, hAPP(c_Set_Oimage(_1557056, _1557058, _1557060), _1557062)), -(c_Fun_Oinj__on(_1557056, _1557064, hAPP(c_Fun_Ocomp(_1557058, _1557064, _1557056, _1557066), _1557060), _1557062))], (39849 ^ _780205) ^ [] : [c_Fun_Oinj__on(_1557056, _1557064, hAPP(c_Fun_Ocomp(_1557058, _1557064, _1557056, _1557066), _1557060), _1557062), -(c_Fun_Oinj__on(_1557058, _1557064, _1557066, hAPP(c_Set_Oimage(_1557056, _1557058, _1557060), _1557062)))]]], (39855 ^ _780205) ^ [_1557348, _1557350, _1557352, _1557354, _1557356, _1557358] : [c_Fun_Oinj__on(_1557348, _1557350, _1557352, _1557354), c_Fun_Oinj__on(_1557350, _1557356, _1557358, hAPP(c_Set_Oimage(_1557348, _1557350, _1557352), _1557354)), -(c_Fun_Oinj__on(_1557348, _1557356, hAPP(c_Fun_Ocomp(_1557350, _1557356, _1557348, _1557358), _1557352), _1557354))], (39865 ^ _780205) ^ [_1557535, _1557537, _1557539, _1557541, _1557543, _1557545] : [c_Fun_Oinj__on(_1557535, _1557537, hAPP(c_Fun_Ocomp(_1557539, _1557537, _1557535, _1557541), _1557543), _1557545), -(c_Fun_Oinj__on(_1557539, _1557537, _1557541, hAPP(c_Set_Oimage(_1557535, _1557539, _1557543), _1557545)))], (39871 ^ _780205) ^ [_1557658, _1557660, _1557662, _1557664, _1557666, _1557668] : [class_Groups_Ocomm__monoid__add(_1557658), c_Fun_Oinj__on(_1557660, _1557662, _1557664, _1557666), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557662, _1557658), _1557668), hAPP(c_Set_Oimage(_1557660, _1557662, _1557664), _1557666)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557660, _1557658), hAPP(c_Fun_Ocomp(_1557662, _1557658, _1557660, _1557668), _1557664)), _1557666))], (39881 ^ _780205) ^ [_1557871, _1557873, _1557875, _1557877, _1557879, _1557881] : [class_Groups_Ocomm__monoid__mult(_1557871), c_Fun_Oinj__on(_1557873, _1557875, _1557877, _1557879), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1557875, _1557871), _1557881), hAPP(c_Set_Oimage(_1557873, _1557875, _1557877), _1557879)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1557873, _1557871), hAPP(c_Fun_Ocomp(_1557875, _1557871, _1557873, _1557881), _1557877)), _1557879))], (39891 ^ _780205) ^ [_1558084, _1558086, _1558088, _1558090, _1558092, _1558094, _1558096, _1558098] : [class_Groups_Ocomm__monoid__mult(_1558084), c_Fun_Oinj__on(_1558086, _1558088, _1558090, _1558092), _1558094 = hAPP(c_Set_Oimage(_1558086, _1558088, _1558090), _1558092), _1558096 = hAPP(c_Fun_Ocomp(_1558088, _1558084, _1558086, _1558098), _1558090), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1558088, _1558084), _1558098), _1558094) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1558086, _1558084), _1558096), _1558092))], (39909 ^ _780205) ^ [_1558433, _1558435, _1558437, _1558439, _1558441] : [class_Groups_Ocomm__monoid__add(_1558433), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558435), _1558437)), c_Fun_Oinj__on(_1558435, _1558435, _1558439, _1558437), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558435, _1558433), _1558441), hAPP(c_Set_Oimage(_1558435, _1558435, _1558439), _1558437)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558435, _1558433), hAPP(c_Fun_Ocomp(_1558435, _1558433, _1558435, _1558441), _1558439)), _1558437))], (39923 ^ _780205) ^ [_1558708, _1558710, _1558712, _1558714, _1558716] : [class_Groups_Ocomm__monoid__mult(_1558708), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558710), _1558712)), c_Fun_Oinj__on(_1558710, _1558710, _1558714, _1558712), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1558710, _1558708), _1558716), hAPP(c_Set_Oimage(_1558710, _1558710, _1558714), _1558712)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1558710, _1558708), hAPP(c_Fun_Ocomp(_1558710, _1558708, _1558710, _1558716), _1558714)), _1558712))], (39937 ^ _780205) ^ [_1558983, _1558985, _1558987, _1558989, _1558991, _1558993, _1558995] : [c_Fun_Oinj__on(_1558983, _1558985, _1558987, hAPP(c_Set_Oimage(_1558989, _1558983, _1558991), _1558993)), c_Fun_Oinj__on(_1558989, _1558983, _1558991, _1558993), hBOOL(hAPP(hAPP(c_member(_1558985), _1558995), hAPP(c_Set_Oimage(_1558983, _1558985, _1558987), hAPP(c_Set_Oimage(_1558989, _1558983, _1558991), _1558993)))), -(hAPP(c_Fun_Othe__inv__into(_1558989, _1558985, _1558993, hAPP(c_Fun_Ocomp(_1558983, _1558985, _1558989, _1558987), _1558991)), _1558995) = hAPP(hAPP(c_Fun_Ocomp(_1558983, _1558989, _1558985, c_Fun_Othe__inv__into(_1558989, _1558983, _1558993, _1558991)), c_Fun_Othe__inv__into(_1558983, _1558985, hAPP(c_Set_Oimage(_1558989, _1558983, _1558991), _1558993), _1558987)), _1558995))], (39951 ^ _780205) ^ [_1559346, _1559348, _1559350, _1559352, _1559354, _1559356, _1559358] : [class_Groups_Oab__semigroup__mult(_1559346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559348), _1559350)), c_Fun_Oinj__on(_1559348, _1559352, _1559354, _1559350), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1559346, _1559352, c_Groups_Otimes__class_Otimes(_1559346)), _1559356), _1559358), hAPP(c_Set_Oimage(_1559348, _1559352, _1559354), _1559350)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1559346, _1559348, c_Groups_Otimes__class_Otimes(_1559346)), hAPP(c_Fun_Ocomp(_1559352, _1559346, _1559348, _1559356), _1559354)), _1559358), _1559350))], (39965 ^ _780205) ^ [_1559657, _1559659, _1559661, _1559663, _1559665, _1559667] : [c_Finite__Set_Ofolding(_1559657, _1559659, _1559661, _1559663), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559657), _1559665)), hBOOL(hAPP(hAPP(c_member(_1559657), _1559667), _1559665)), -(hAPP(_1559663, _1559665) = hAPP(c_Fun_Ocomp(_1559659, _1559659, _1559659, hAPP(_1559663, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1559657, tc_HOL_Obool)), _1559665), hAPP(hAPP(c_Set_Oinsert(_1559657), _1559667), c_Orderings_Obot__class_Obot(tc_fun(_1559657, tc_HOL_Obool)))))), hAPP(_1559661, _1559667)))], (39979 ^ _780205) ^ [_1559970, _1559972, _1559974, _1559976, _1559978, _1559980, _1559982, _1559984] : [c_Finite__Set_Ofolding__image(_1559970, _1559972, _1559974, _1559976, _1559978), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559972), _1559980)), c_Fun_Oinj__on(_1559972, _1559972, _1559982, _1559980), -(hAPP(hAPP(_1559978, _1559984), hAPP(c_Set_Oimage(_1559972, _1559972, _1559982), _1559980)) = hAPP(hAPP(_1559978, hAPP(c_Fun_Ocomp(_1559972, _1559970, _1559972, _1559984), _1559982)), _1559980))], (39993 ^ _780205) ^ [_1560259, _1560261, _1560263, _1560265, _1560267, _1560269] : [c_Finite__Set_Ofolding(_1560259, _1560261, _1560263, _1560265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560259), _1560267)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560259), _1560269)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1560259, tc_HOL_Obool)), _1560267), _1560269) = c_Orderings_Obot__class_Obot(tc_fun(_1560259, tc_HOL_Obool)), -(hAPP(_1560265, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1560259, tc_HOL_Obool)), _1560267), _1560269)) = hAPP(c_Fun_Ocomp(_1560261, _1560261, _1560261, hAPP(_1560265, _1560267)), hAPP(_1560265, _1560269)))], (40011 ^ _780205) ^ [_1560632, _1560634, _1560636, _1560638, _1560640, _1560642, _1560644, _1560646, _1560648, _1560650, _1560652] : [c_Finite__Set_Ofolding(_1560632, _1560634, _1560636, _1560638), -(hAPP(c_Fun_Ocomp(_1560640, _1560642, _1560644, _1560646), hAPP(c_Fun_Ocomp(_1560648, _1560640, _1560644, _1560650), _1560652)) = hAPP(c_Fun_Ocomp(_1560648, _1560642, _1560644, hAPP(c_Fun_Ocomp(_1560640, _1560642, _1560648, _1560646), _1560650)), _1560652))], (40017 ^ _780205) ^ [_1560795, _1560797, _1560799, _1560801, _1560803, _1560805] : [c_Finite__Set_Ofolding(_1560795, _1560797, _1560799, _1560801), -(hAPP(c_Fun_Ocomp(_1560797, _1560797, _1560797, hAPP(_1560799, _1560803)), hAPP(_1560799, _1560805)) = hAPP(c_Fun_Ocomp(_1560797, _1560797, _1560797, hAPP(_1560799, _1560805)), hAPP(_1560799, _1560803)))], (40023 ^ _780205) ^ [_1560940, _1560942, _1560944, _1560946, _1560948, _1560950, _1560952, _1560954] : [c_Finite__Set_Ofolding(_1560940, _1560942, _1560944, _1560946), -(hAPP(c_Fun_Ocomp(_1560942, _1560942, _1560948, hAPP(_1560944, _1560950)), hAPP(c_Fun_Ocomp(_1560942, _1560942, _1560948, hAPP(_1560944, _1560952)), _1560954)) = hAPP(c_Fun_Ocomp(_1560942, _1560942, _1560948, hAPP(_1560944, _1560952)), hAPP(c_Fun_Ocomp(_1560942, _1560942, _1560948, hAPP(_1560944, _1560950)), _1560954)))], (40029 ^ _780205) ^ [_1561121, _1561123, _1561125, _1561127, _1561129, _1561131] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1561121, _1561123), _1561121, tc_prod(_1561125, _1561127), c_Product__Type_Ofst(_1561121, _1561123)), c_Product__Type_Omap__pair(_1561125, _1561121, _1561127, _1561123, _1561129, _1561131)) = hAPP(c_Fun_Ocomp(_1561125, _1561121, tc_prod(_1561125, _1561127), _1561129), c_Product__Type_Ofst(_1561125, _1561127)))], (40031 ^ _780205) ^ [_1561192, _1561194, _1561196, _1561198, _1561200, _1561202] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1561192, tc_fun(_1561194, tc_HOL_Obool)), _1561196), hAPP(c_Fun_Ocomp(_1561198, tc_fun(_1561194, tc_HOL_Obool), _1561192, _1561200), _1561202)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1561198, tc_fun(_1561194, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1561192, _1561198, _1561202), _1561196)), _1561200))], (40033 ^ _780205) ^ [_1561267, _1561269, _1561271, _1561273, _1561275, _1561277] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1561267, _1561269), _1561269, tc_prod(_1561271, _1561273), c_Product__Type_Osnd(_1561267, _1561269)), c_Product__Type_Omap__pair(_1561271, _1561267, _1561273, _1561269, _1561275, _1561277)) = hAPP(c_Fun_Ocomp(_1561273, _1561269, tc_prod(_1561271, _1561273), _1561277), c_Product__Type_Osnd(_1561271, _1561273)))], (40035 ^ _780205) ^ [_1561338, _1561340, _1561342, _1561344, _1561346, _1561348, _1561350, _1561352] : [c_Finite__Set_Ofolding__image(_1561338, _1561340, _1561342, _1561344, _1561346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561340), _1561348)), -(hAPP(hAPP(_1561346, hAPP(hAPP(c_COMBS(_1561340, _1561338, _1561338), hAPP(hAPP(c_COMBB(_1561338, tc_fun(_1561338, _1561338), _1561340), _1561342), _1561350)), _1561352)), _1561348) = hAPP(hAPP(_1561342, hAPP(hAPP(_1561346, _1561350), _1561348)), hAPP(hAPP(_1561346, _1561352), _1561348)))], (40045 ^ _780205) ^ [_1561599, _1561601, _1561603, _1561605, _1561607, _1561609, _1561611] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1561599, _1561601, _1561603), hAPP(c_Fun_Ocomp(_1561605, tc_fun(_1561601, _1561603), _1561599, _1561607), _1561609)), _1561611) = hAPP(hAPP(_1561607, hAPP(_1561609, hAPP(c_Product__Type_Ofst(_1561599, _1561601), _1561611))), hAPP(c_Product__Type_Osnd(_1561599, _1561601), _1561611)))], (40047 ^ _780205) ^ [_1561676, _1561678, _1561680, _1561682, _1561684, _1561686] : [c_Finite__Set_Ofolding(_1561676, _1561678, _1561680, _1561682), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561676), _1561684)), -(hAPP(c_Fun_Ocomp(_1561678, _1561678, _1561678, hAPP(_1561680, _1561686)), hAPP(_1561682, _1561684)) = hAPP(c_Fun_Ocomp(_1561678, _1561678, _1561678, hAPP(_1561682, _1561684)), hAPP(_1561680, _1561686)))], (40057 ^ _780205) ^ [_1561889, _1561891, _1561893, _1561895, _1561897, _1561899, _1561901, _1561903] : [c_Finite__Set_Ofolding(_1561889, _1561891, _1561893, _1561895), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561889), _1561897)), -(hAPP(c_Fun_Ocomp(_1561891, _1561891, _1561899, hAPP(_1561893, _1561901)), hAPP(c_Fun_Ocomp(_1561891, _1561891, _1561899, hAPP(_1561895, _1561897)), _1561903)) = hAPP(c_Fun_Ocomp(_1561891, _1561891, _1561899, hAPP(_1561895, _1561897)), hAPP(c_Fun_Ocomp(_1561891, _1561891, _1561899, hAPP(_1561893, _1561901)), _1561903)))], (40067 ^ _780205) ^ [_1562142, _1562144, _1562146, _1562148, _1562150, _1562152] : [c_Finite__Set_Ofolding(_1562142, _1562144, _1562146, _1562148), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562142), _1562150)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562142), _1562152)), -(hAPP(c_Fun_Ocomp(_1562144, _1562144, _1562144, hAPP(_1562148, _1562152)), hAPP(_1562148, _1562150)) = hAPP(c_Fun_Ocomp(_1562144, _1562144, _1562144, hAPP(_1562148, _1562150)), hAPP(_1562148, _1562152)))], (40081 ^ _780205) ^ [_1562423, _1562425, _1562427, _1562429, _1562431, _1562433, _1562435, _1562437] : [c_Finite__Set_Ofolding(_1562423, _1562425, _1562427, _1562429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562423), _1562431)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562423), _1562433)), -(hAPP(c_Fun_Ocomp(_1562425, _1562425, _1562435, hAPP(_1562429, _1562433)), hAPP(c_Fun_Ocomp(_1562425, _1562425, _1562435, hAPP(_1562429, _1562431)), _1562437)) = hAPP(c_Fun_Ocomp(_1562425, _1562425, _1562435, hAPP(_1562429, _1562431)), hAPP(c_Fun_Ocomp(_1562425, _1562425, _1562435, hAPP(_1562429, _1562433)), _1562437)))], (40095 ^ _780205) ^ [_1562748, _1562750, _1562752, _1562754] : [c_Finite__Set_Ofolding(_1562748, _1562750, _1562752, _1562754), -(hAPP(_1562754, c_Orderings_Obot__class_Obot(tc_fun(_1562748, tc_HOL_Obool))) = c_Fun_Oid(_1562750))], (40101 ^ _780205) ^ [_1562853, _1562855, _1562857, _1562859, _1562861, _1562863] : [c_Finite__Set_Ofolding(_1562853, _1562855, _1562857, _1562859), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562853), _1562861)), -(hAPP(hAPP(_1562859, _1562861), _1562863) = hAPP(hAPP(c_Finite__Set_Ofold(_1562853, _1562855, _1562857), _1562863), _1562861))], (40111 ^ _780205) ^ [_1563042, _1563044, _1563046, _1563048, _1563050, _1563052, _1563054] : [c_Finite__Set_Ofolding__image(_1563042, _1563044, _1563046, _1563048, _1563050), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563044), _1563052)), -(hAPP(hAPP(_1563050, _1563054), _1563052) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1563042, _1563044, _1563046), _1563054), _1563048), _1563052))], (40121 ^ _780205) ^ [_1563243, _1563245, _1563247, _1563249, _1563251, _1563253] : [c_Finite__Set_Ofolding(_1563243, _1563245, _1563247, _1563249), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563243), _1563251)), -(hBOOL(hAPP(hAPP(c_member(_1563243), _1563253), _1563251))), -(hAPP(_1563249, hAPP(hAPP(c_Set_Oinsert(_1563243), _1563253), _1563251)) = hAPP(c_Fun_Ocomp(_1563245, _1563245, _1563245, hAPP(_1563249, _1563251)), hAPP(_1563247, _1563253)))], (40135 ^ _780205) ^ [_1563479, _1563481, _1563483, _1563485, _1563487, _1563489] : [c_Finite__Set_Ofolding(_1563479, _1563481, _1563483, _1563485), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563479), _1563487)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563479), _1563489)), -(hAPP(c_Fun_Ocomp(_1563481, _1563481, _1563481, hAPP(_1563485, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1563479, tc_HOL_Obool)), _1563487), _1563489))), hAPP(_1563485, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1563479, tc_HOL_Obool)), _1563487), _1563489))) = hAPP(c_Fun_Ocomp(_1563481, _1563481, _1563481, hAPP(_1563485, _1563487)), hAPP(_1563485, _1563489)))], (40149 ^ _780205) ^ [_1563804, _1563806, _1563808, _1563810, _1563812, _1563814] : [c_Finite__Set_Ofolding(_1563804, _1563806, _1563808, _1563810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563804), _1563812)), -(hAPP(_1563810, hAPP(hAPP(c_Set_Oinsert(_1563804), _1563814), _1563812)) = hAPP(c_Fun_Ocomp(_1563806, _1563806, _1563806, hAPP(_1563810, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1563804, tc_HOL_Obool)), _1563812), hAPP(hAPP(c_Set_Oinsert(_1563804), _1563814), c_Orderings_Obot__class_Obot(tc_fun(_1563804, tc_HOL_Obool)))))), hAPP(_1563808, _1563814)))], (40159 ^ _780205) ^ [_1564059, _1564061, _1564063, _1564065, _1564067] : [c_Hoare__Mirabelle_Ohoare__valids(_1564059, _1564061, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1564059)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1564059), c_Hoare__Mirabelle_Opeek__and(_1564059, _1564063, _1564065)), _1564067), _1564063)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1564059), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__valids(_1564059, _1564061, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1564059)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1564059), _1564063), c_Com_Ocom_OWhile(_1564065, _1564067)), c_Hoare__Mirabelle_Opeek__and(_1564059, _1564063, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1564065)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1564059), tc_HOL_Obool)))))], (40165 ^ _780205) ^ [_1564286, _1564288, _1564290, _1564292, _1564294, _1564296, _1564298] : [c_Hoare__Mirabelle_Ohoare__derivs(_1564286, _1564288, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1564286)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1564286), c_Hoare__Mirabelle_Opeek__and(_1564286, _1564290, _1564292)), _1564294), _1564296)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1564286), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1564286, _1564288, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1564286)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1564286), c_Hoare__Mirabelle_Opeek__and(_1564286, _1564290, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1564292))), _1564298), _1564296)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1564286), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1564286, _1564288, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1564286)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1564286), _1564290), c_Com_Ocom_OCond(_1564292, _1564294, _1564298)), _1564296)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1564286), tc_HOL_Obool)))))], (40175 ^ _780205) ^ [_1564639, _1564641, _1564643, _1564645, _1564647] : [c_Hoare__Mirabelle_Ohoare__derivs(_1564639, _1564641, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1564639)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1564639), c_Hoare__Mirabelle_Opeek__and(_1564639, _1564643, _1564645)), _1564647), _1564643)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1564639), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1564639, _1564641, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1564639)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1564639), _1564643), c_Com_Ocom_OWhile(_1564645, _1564647)), c_Hoare__Mirabelle_Opeek__and(_1564639, _1564643, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1564645)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1564639), tc_HOL_Obool)))))], (40181 ^ _780205) ^ [_1564890, _1564892, _1564894, _1564896, _1564898] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1564890, _1564892, _1564894), _1564896), _1564898)), 40184 ^ _780205 : [(40185 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1564892, _1564896), _1564898)))], (40187 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1564894, _1564898)))]]], (40189 ^ _780205) ^ [_1565027, _1565029, _1565031, _1565033, _1565035] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1565027, _1565029, _1565031), _1565033), _1565035))), hBOOL(hAPP(hAPP(_1565029, _1565033), _1565035)), hBOOL(hAPP(_1565031, _1565035))], (40199 ^ _780205) ^ [_1565202, _1565204, _1565206, _1565208, _1565210, _1565212] : [class_Groups_Ocomm__monoid__add(_1565202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565204), _1565206)), 40209 ^ _780205 : [(40210 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565204), 40208 ^ [_1565202, _1565204, _1565206, _1565208, _1565210, _1565212]), _1565206)))], (40213 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565204), 40211 ^ [_1565202, _1565204, _1565206, _1565208, _1565210, _1565212]), _1565206)))], (40215 ^ _780205) ^ [] : [40208 ^ [_1565202, _1565204, _1565206, _1565208, _1565210, _1565212] = 40211 ^ [_1565202, _1565204, _1565206, _1565208, _1565210, _1565212]], (40217 ^ _780205) ^ [] : [-(hAPP(_1565208, 40208 ^ [_1565202, _1565204, _1565206, _1565208, _1565210, _1565212]) = hAPP(_1565208, 40211 ^ [_1565202, _1565204, _1565206, _1565208, _1565210, _1565212]))], (40219 ^ _780205) ^ [] : [hAPP(_1565210, hAPP(_1565208, 40208 ^ [_1565202, _1565204, _1565206, _1565208, _1565210, _1565212])) = c_Groups_Ozero__class_Ozero(_1565202)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565212, _1565202), _1565210), hAPP(c_Set_Oimage(_1565204, _1565212, _1565208), _1565206)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1565204, _1565202), hAPP(c_Fun_Ocomp(_1565212, _1565202, _1565204, _1565210), _1565208)), _1565206))], (40223 ^ _780205) ^ [_1565939, _1565941, _1565943, _1565945, _1565947, _1565949] : [c_Finite__Set_Ofolding__idem(_1565939, _1565941, _1565943, _1565945), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565939), _1565947)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565939), _1565949)), -(hAPP(_1565945, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565939, tc_HOL_Obool)), _1565947), _1565949)) = hAPP(c_Fun_Ocomp(_1565941, _1565941, _1565941, hAPP(_1565945, _1565947)), hAPP(_1565945, _1565949)))], (40237 ^ _780205) ^ [_1566220, _1566222, _1566224, _1566226, _1566228, _1566230] : [c_Finite__Set_Ofolding__idem(_1566220, _1566222, _1566224, _1566226), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566220), _1566228)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1566220, tc_HOL_Obool)), _1566230), _1566228)), -(hAPP(c_Fun_Ocomp(_1566222, _1566222, _1566222, hAPP(_1566226, _1566228)), hAPP(_1566226, _1566230)) = hAPP(_1566226, _1566228))], (40251 ^ _780205) ^ [_1566491, _1566493, _1566495, _1566497, _1566499, _1566501, _1566503] : [c_Finite__Set_Ofolding__idem(_1566491, _1566493, _1566495, _1566497), -(hAPP(c_Fun_Ocomp(_1566493, _1566493, _1566499, hAPP(_1566495, _1566501)), hAPP(c_Fun_Ocomp(_1566493, _1566493, _1566499, hAPP(_1566495, _1566501)), _1566503)) = hAPP(c_Fun_Ocomp(_1566493, _1566493, _1566499, hAPP(_1566495, _1566501)), _1566503))], (40257 ^ _780205) ^ [_1566648, _1566650, _1566652, _1566654, _1566656] : [c_Finite__Set_Ofolding__idem(_1566648, _1566650, _1566652, _1566654), -(hAPP(c_Fun_Ocomp(_1566650, _1566650, _1566650, hAPP(_1566652, _1566656)), hAPP(_1566652, _1566656)) = hAPP(_1566652, _1566656))], (40263 ^ _780205) ^ [_1566769, _1566771, _1566773, _1566775, _1566777, _1566779] : [c_Finite__Set_Ofolding__idem(_1566769, _1566771, _1566773, _1566775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566769), _1566777)), hBOOL(hAPP(hAPP(c_member(_1566769), _1566779), _1566777)), -(hAPP(c_Fun_Ocomp(_1566771, _1566771, _1566771, hAPP(_1566775, _1566777)), hAPP(_1566773, _1566779)) = hAPP(_1566775, _1566777))], (40277 ^ _780205) ^ [_1567034, _1567036, _1567038, _1567040, _1567042, _1567044] : [c_Finite__Set_Ofolding__idem(_1567034, _1567036, _1567038, _1567040), hBOOL(hAPP(c_Finite__Set_Ofinite(_1567034), _1567042)), -(hAPP(_1567040, hAPP(hAPP(c_Set_Oinsert(_1567034), _1567044), _1567042)) = hAPP(c_Fun_Ocomp(_1567036, _1567036, _1567036, hAPP(_1567040, _1567042)), hAPP(_1567038, _1567044)))], (40287 ^ _780205) ^ [_1567241, _1567243, _1567245, _1567247, _1567249, _1567251, _1567253, _1567255] : [class_Groups_Ocomm__monoid__mult(_1567241), c_Fun_Oinj__on(_1567243, _1567245, _1567247, _1567249), _1567251 = hAPP(c_Set_Oimage(_1567243, _1567245, _1567247), _1567249), 40301 ^ _780205 : [(40302 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567243), 40300 ^ [_1567241, _1567243, _1567245, _1567247, _1567249, _1567251, _1567253, _1567255]), _1567249)))], (40304 ^ _780205) ^ [] : [hAPP(_1567253, 40300 ^ [_1567241, _1567243, _1567245, _1567247, _1567249, _1567251, _1567253, _1567255]) = hAPP(hAPP(c_Fun_Ocomp(_1567245, _1567241, _1567243, _1567255), _1567247), 40300 ^ [_1567241, _1567243, _1567245, _1567247, _1567249, _1567251, _1567253, _1567255])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1567245, _1567241), _1567255), _1567251) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1567243, _1567241), _1567253), _1567249))], (40308 ^ _780205) ^ [_1567749, _1567751, _1567753] : [-(c_Hilbert__Choice_OEps(tc_prod(_1567749, _1567751), hAPP(c_Product__Type_Oprod_Oprod__case(_1567749, _1567751, tc_HOL_Obool), _1567753)) = c_Hilbert__Choice_OEps(tc_prod(_1567749, _1567751), hAPP(hAPP(c_COMBS(tc_prod(_1567749, _1567751), _1567751, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1567749, tc_fun(_1567751, tc_HOL_Obool), tc_prod(_1567749, _1567751)), _1567753), c_Product__Type_Ofst(_1567749, _1567751))), c_Product__Type_Osnd(_1567749, _1567751))))], (40310 ^ _780205) ^ [_1567830, _1567832] : [40312 ^ _780205 : [(40313 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567830, tc_HOL_Obool)), 40311 ^ [_1567830, _1567832]), hAPP(c_Relation_OImage(_1567830, _1567830, _1567832), 40311 ^ [_1567830, _1567832]))))], (40315 ^ _780205) ^ [] : [40311 ^ [_1567830, _1567832] = c_Orderings_Obot__class_Obot(tc_fun(_1567830, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1567830, _1567832))], (40319 ^ _780205) ^ [_1568027, _1568029, _1568031] : [40320 ^ _780205 : [(40321 ^ _780205) ^ [_1568081] : [hBOOL(hAPP(_1568027, _1568081))]], _1568029 = c_Hilbert__Choice_OEps(_1568031, _1568027), -(hBOOL(hAPP(_1568027, _1568029)))], (40329 ^ _780205) ^ [_1568187, _1568189] : [40330 ^ _780205 : [(40331 ^ _780205) ^ [_1568233] : [hBOOL(hAPP(_1568187, _1568233))]], -(hBOOL(hAPP(_1568187, c_Hilbert__Choice_OEps(_1568189, _1568187))))], (40335 ^ _780205) ^ [_1568291, _1568293, _1568295] : [hBOOL(hAPP(_1568291, _1568293)), -(hBOOL(hAPP(_1568291, c_Hilbert__Choice_OEps(_1568295, _1568291))))], (40341 ^ _780205) ^ [_1568384, _1568386] : [-(c_Hilbert__Choice_OEps(_1568384, hAPP(c_fequal, _1568386)) = _1568386)], (40343 ^ _780205) ^ [_1568415, _1568417] : [-(c_Hilbert__Choice_OEps(_1568415, hAPP(hAPP(c_COMBC(_1568415, _1568415, tc_HOL_Obool), c_fequal), _1568417)) = _1568417)], (40345 ^ _780205) ^ [_1568468, _1568470] : [hBOOL(hAPP(_1568468, c_Hilbert__Choice_OEps(_1568470, _1568468))), -(hBOOL(hAPP(_1568468, 40348 ^ [_1568468, _1568470])))], (40352 ^ _780205) ^ [_1568567, _1568569] : [40353 ^ _780205 : [(40354 ^ _780205) ^ [_1568613] : [hBOOL(hAPP(_1568567, _1568613))]], -(hBOOL(hAPP(_1568567, c_Hilbert__Choice_OEps(_1568569, _1568567))))], (40358 ^ _780205) ^ [_1568673, _1568675] : [40359 ^ _780205 : [(40360 ^ _780205) ^ [_1568719] : [hBOOL(hAPP(_1568673, _1568719))]], -(hBOOL(hAPP(_1568673, c_Hilbert__Choice_OEps(_1568675, _1568673))))], (40364 ^ _780205) ^ [_1568777, _1568779, _1568781] : [-(c_Hilbert__Choice_OEps(tc_prod(_1568777, _1568779), _1568781) = c_Hilbert__Choice_OEps(tc_prod(_1568777, _1568779), hAPP(c_Product__Type_Oprod_Oprod__case(_1568777, _1568779, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1568779, tc_prod(_1568777, _1568779)), tc_fun(_1568779, tc_HOL_Obool), _1568777), hAPP(c_COMBB(tc_prod(_1568777, _1568779), tc_HOL_Obool, _1568779), _1568781)), c_Product__Type_OPair(_1568777, _1568779)))))], (40366 ^ _780205) ^ [_1568855, _1568857, _1568859, _1568861] : [-(c_Hilbert__Choice_OEps(tc_prod(_1568855, _1568857), hAPP(c_Product__Type_Oprod_Oprod__case(_1568855, _1568857, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1568855, tc_fun(_1568857, tc_HOL_Obool), tc_fun(_1568857, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1568857, tc_HOL_Obool), tc_fun(_1568857, tc_HOL_Obool)), _1568855), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1568857)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1568855), c_fconj), hAPP(c_fequal, _1568859)))), hAPP(c_fequal, _1568861)))) = hAPP(hAPP(c_Product__Type_OPair(_1568855, _1568857), _1568859), _1568861))], (40368 ^ _780205) ^ [_1568961, _1568963, _1568965, _1568967, _1568969, _1568971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1568961, tc_HOL_Obool)), _1568963), _1568965)), 40374 ^ _780205 : [(40375 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568961), 40373 ^ [_1568961, _1568963, _1568965, _1568967, _1568969, _1568971]), _1568963)))], (40377 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1568967, tc_HOL_Obool)), hAPP(_1568969, 40373 ^ [_1568961, _1568963, _1568965, _1568967, _1568969, _1568971])), hAPP(_1568971, 40373 ^ [_1568961, _1568963, _1568965, _1568967, _1568969, _1568971])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568961, _1568967), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1568961, _1568967), _1568963), _1568969)), hAPP(hAPP(c_Product__Type_OSigma(_1568961, _1568967), _1568965), _1568971))))], (40381 ^ _780205) ^ [_1569352, _1569354, _1569356] : [40383 ^ _780205 : [(40384 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569352, _1569352)), hAPP(hAPP(c_Product__Type_OPair(_1569352, _1569352), 40382 ^ [_1569352, _1569354, _1569356]), _1569354)), _1569356)))], (40386 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1569352), 40382 ^ [_1569352, _1569354, _1569356]), c_Wellfounded_Oacc(_1569352, _1569356)))]], -(hBOOL(hAPP(hAPP(c_member(_1569352), _1569354), c_Wellfounded_Oacc(_1569352, _1569356))))], (40390 ^ _780205) ^ [_1569589, _1569591, _1569593] : [-(hBOOL(hAPP(hAPP(c_member(_1569589), _1569591), c_Wellfounded_Oacc(_1569589, _1569593)))), 40394 ^ _780205 : [(40395 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569589, _1569589)), hAPP(hAPP(c_Product__Type_OPair(_1569589, _1569589), 40393 ^ [_1569589, _1569591, _1569593]), _1569591)), _1569593)))], (40397 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1569589), 40393 ^ [_1569589, _1569591, _1569593]), c_Wellfounded_Oacc(_1569589, _1569593)))]]], (40399 ^ _780205) ^ [_1569837, _1569839, _1569841, _1569843] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1569837, tc_HOL_Obool), tc_fun(_1569837, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1569837, tc_HOL_Obool), tc_fun(_1569837, tc_HOL_Obool)), _1569839), _1569841)), c_Wellfounded_Omax__ext(_1569837, _1569843))), 40402 ^ _780205 : [(40403 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1569837), _1569839)))], (40405 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1569837), _1569841)))], (40407 ^ _780205) ^ [] : [_1569841 = c_Orderings_Obot__class_Obot(tc_fun(_1569837, tc_HOL_Obool))], (40409 ^ _780205) ^ [_1570131] : [hBOOL(hAPP(hAPP(c_member(_1569837), _1570131), _1569839)), 40413 ^ _780205 : [(40414 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1569837), 40412 ^ [_1569837, _1569839, _1569841, _1569843, _1570131]), _1569841)))], (40416 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569837, _1569837)), hAPP(hAPP(c_Product__Type_OPair(_1569837, _1569837), _1570131), 40412 ^ [_1569837, _1569839, _1569841, _1569843, _1570131])), _1569843)))]]]]], (40418 ^ _780205) ^ [_1570343, _1570345, _1570347, _1570349] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1570343, tc_HOL_Obool), tc_fun(_1570343, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1570343, tc_HOL_Obool), tc_fun(_1570343, tc_HOL_Obool)), _1570345), _1570347)), c_Wellfounded_Omax__ext(_1570343, _1570349)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570343), _1570345)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570343), _1570347)), -(_1570347 = c_Orderings_Obot__class_Obot(tc_fun(_1570343, tc_HOL_Obool))), 40432 ^ _780205 : [(40433 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1570343), 40431 ^ [_1570343, _1570345, _1570347, _1570349]), _1570345)))], (40435 ^ _780205) ^ [_1570748] : [hBOOL(hAPP(hAPP(c_member(_1570343), _1570748), _1570347)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570343, _1570343)), hAPP(hAPP(c_Product__Type_OPair(_1570343, _1570343), 40431 ^ [_1570343, _1570345, _1570347, _1570349]), _1570748)), _1570349))]]], (40443 ^ _780205) ^ [_1570976, _1570978, _1570980, _1570982] : [class_Orderings_Olinorder(_1570976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570976), _1570978)), 40453 ^ _780205 : [(40454 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1570976), 40452 ^ [_1570976, _1570978, _1570980, _1570982]), _1570978)))], (40456 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1570976), 40452 ^ [_1570976, _1570978, _1570980, _1570982]), _1570980))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1570976), hAPP(hAPP(c_Finite__Set_Ofold(_1570976, _1570976, c_Orderings_Oord__class_Omax(_1570976)), _1570982), _1570978)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1570976), _1570980), _1570982))))], (40460 ^ _780205) ^ [_1571340, _1571342, _1571344] : [class_Orderings_Olinorder(_1571340), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571340), _1571342)), 40470 ^ _780205 : [(40471 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1571340), 40469 ^ [_1571340, _1571342, _1571344]), _1571342)))], (40473 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1571340), 40469 ^ [_1571340, _1571342, _1571344]), _1571344))]], hBOOL(hAPP(hAPP(c_member(_1571340), _1571344), _1571342)), -(c_Big__Operators_Olinorder__class_OMax(_1571340, _1571342) = _1571344)], (40481 ^ _780205) ^ [_1571712, _1571714, _1571716] : [c_Wellfounded_Owf(_1571712, _1571714), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571712, _1571712)), hAPP(hAPP(c_Product__Type_OPair(_1571712, _1571712), hAPP(_1571716, hAPP(c_Nat_OSuc, 40484 ^ [_1571712, _1571714, _1571716]))), hAPP(_1571716, 40484 ^ [_1571712, _1571714, _1571716]))), _1571714))], (40488 ^ _780205) ^ [_1571931, _1571933, _1571935, _1571937, _1571939] : [_1571931 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1571933, _1571935, _1571931, _1571937), _1571939) = hAPP(c_Product__Type_OPair(_1571933, _1571935), _1571939))], (40494 ^ _780205) ^ [_1572036, _1572038, _1572040, _1572042, _1572044] : [-(_1572036 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1572038, _1572040, _1572036, _1572042), _1572044) = hAPP(hAPP(c_Product__Type_Oscomp(_1572040, _1572038, _1572040, tc_prod(_1572038, _1572040)), hAPP(_1572042, _1572044)), c_Random_Oiterate(_1572038, _1572040, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1572036), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1572042)))], (40500 ^ _780205) ^ [_1572116, _1572118, _1572120, _1572122, _1572124, _1572126, _1572128, _1572130] : [class_Groups_Ocomm__monoid__add(_1572116), c_Fun_Oinj__on(_1572118, _1572120, _1572122, _1572124), _1572126 = hAPP(c_Set_Oimage(_1572118, _1572120, _1572122), _1572124), 40514 ^ _780205 : [(40515 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1572118), 40513 ^ [_1572116, _1572118, _1572120, _1572122, _1572124, _1572126, _1572128, _1572130]), _1572124)))], (40517 ^ _780205) ^ [] : [hAPP(_1572128, 40513 ^ [_1572116, _1572118, _1572120, _1572122, _1572124, _1572126, _1572128, _1572130]) = hAPP(_1572130, hAPP(_1572122, 40513 ^ [_1572116, _1572118, _1572120, _1572122, _1572124, _1572126, _1572128, _1572130]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1572120, _1572116), _1572130), _1572126) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1572118, _1572116), _1572128), _1572124))], (40521 ^ _780205) ^ [_1572608, _1572610, _1572612, _1572614, _1572616] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1572608, _1572610, _1572608, _1572612), hAPP(c_Product__Type_OPair(_1572610, _1572608), _1572614)), _1572616) = hAPP(_1572616, _1572614))], (40523 ^ _780205) ^ [_1572659, _1572661, _1572663, _1572665, _1572667, _1572669, _1572671, _1572673, _1572675] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1572659, _1572661, _1572663, _1572665), hAPP(hAPP(c_Product__Type_Oscomp(_1572659, _1572667, _1572669, tc_prod(_1572661, _1572663)), _1572671), _1572673)), _1572675) = hAPP(hAPP(c_Product__Type_Oscomp(_1572659, _1572667, _1572669, _1572665), _1572671), hAPP(hAPP(c_COMBC(_1572667, tc_fun(_1572661, tc_fun(_1572663, _1572665)), tc_fun(_1572669, _1572665)), hAPP(hAPP(c_COMBB(tc_fun(_1572669, tc_prod(_1572661, _1572663)), tc_fun(tc_fun(_1572661, tc_fun(_1572663, _1572665)), tc_fun(_1572669, _1572665)), _1572667), c_Product__Type_Oscomp(_1572669, _1572661, _1572663, _1572665)), _1572673)), _1572675)))], (40525 ^ _780205) ^ [_1572786, _1572788, _1572790, _1572792] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1572786, _1572788, _1572790, tc_prod(_1572788, _1572790)), _1572792), c_Product__Type_OPair(_1572788, _1572790)) = _1572792)], (40527 ^ _780205) ^ [_1572832, _1572834, _1572836, _1572838, _1572840, _1572842, _1572844] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1572832, _1572834, _1572836, _1572838), _1572840), _1572842), _1572844) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1572834, _1572836, _1572838), _1572842), hAPP(_1572840, _1572844)))], (40529 ^ _780205) ^ [_1572894, _1572896, _1572898, _1572900, _1572902, _1572904, _1572906] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1572894, _1572896, _1572898, _1572900), _1572902), _1572904), _1572906) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1572896, _1572898, _1572900), _1572904), hAPP(_1572902, _1572906)))], (40531 ^ _780205) ^ [_1572956, _1572958, _1572960, _1572962, _1572964, _1572966, _1572968] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1572956, _1572958, _1572960, _1572962), _1572964), _1572966), _1572968) = hAPP(hAPP(_1572966, hAPP(c_Product__Type_Ofst(_1572958, _1572960), hAPP(_1572964, _1572968))), hAPP(c_Product__Type_Osnd(_1572958, _1572960), hAPP(_1572964, _1572968))))], (40533 ^ _780205) ^ [_1573029, _1573031, _1573033, _1573035, _1573037, _1573039, _1573041, _1573043] : [class_Groups_Ocomm__monoid__add(_1573029), class_Orderings_Oord(_1573031), _1573033 = _1573035, _1573037 = _1573039, 40551 ^ _780205 : [(40552 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1573031), _1573035), 40550 ^ [_1573029, _1573031, _1573033, _1573035, _1573037, _1573039, _1573041, _1573043])))], (40554 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1573031), 40550 ^ [_1573029, _1573031, _1573033, _1573035, _1573037, _1573039, _1573041, _1573043]), _1573039)))], (40556 ^ _780205) ^ [] : [hAPP(_1573041, 40550 ^ [_1573029, _1573031, _1573033, _1573035, _1573037, _1573039, _1573041, _1573043]) = hAPP(_1573043, 40550 ^ [_1573029, _1573031, _1573033, _1573035, _1573037, _1573039, _1573041, _1573043])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1573031, _1573029), _1573041), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1573031, _1573033), _1573037)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1573031, _1573029), _1573043), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1573031, _1573035), _1573039)))], (40560 ^ _780205) ^ [_1573673, _1573675] : [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), _1573673), _1573675)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1573673), _1573675)))], (40566 ^ _780205) ^ [_1573778, _1573780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1573778), _1573780)), -(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), _1573778), _1573780)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (40572 ^ _780205) ^ [_1573889, _1573891] : [c_Wellfounded_Owf(_1573889, _1573891), -(c_Wellfounded_Owf(_1573889, c_Transitive__Closure_Otrancl(_1573889, _1573891)))], (40578 ^ _780205) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (40580 ^ _780205) ^ [_1574005, _1574007] : [c_Wellfounded_Oacyclic(_1574005, _1574007), 40583 ^ _780205 : [(40584 ^ _780205) ^ [_1574090] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574005, _1574005)), hAPP(hAPP(c_Product__Type_OPair(_1574005, _1574005), _1574090), _1574090)), c_Transitive__Closure_Otrancl(_1574005, _1574007)))]]], (40586 ^ _780205) ^ [_1574133, _1574135] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574133, _1574133)), hAPP(hAPP(c_Product__Type_OPair(_1574133, _1574133), 40587 ^ [_1574133, _1574135]), 40587 ^ [_1574133, _1574135])), c_Transitive__Closure_Otrancl(_1574133, _1574135)))), -(c_Wellfounded_Oacyclic(_1574133, _1574135))], (40593 ^ _780205) ^ [_1574207, _1574209, _1574211, _1574213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574207, _1574207)), hAPP(hAPP(c_Product__Type_OPair(_1574207, _1574207), _1574209), _1574211)), _1574213)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574207, _1574207)), hAPP(hAPP(c_Product__Type_OPair(_1574207, _1574207), _1574209), _1574211)), c_Transitive__Closure_Otrancl(_1574207, _1574213))))], (40599 ^ _780205) ^ [_1574370, _1574372] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574370, _1574370), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1574370, _1574372)), hAPP(hAPP(c_Product__Type_OSigma(_1574370, _1574370), hAPP(c_Relation_OField(_1574370), _1574372)), hAPP(c_COMBK(tc_fun(_1574370, tc_HOL_Obool), _1574370), hAPP(c_Relation_OField(_1574370), _1574372))))))], (40601 ^ _780205) ^ [_1574439, _1574441, _1574443] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574439, _1574439)), _1574441), _1574443)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574439, _1574439)), _1574441), c_Transitive__Closure_Otrancl(_1574439, _1574443))))], (40607 ^ _780205) ^ [_1574564] : [-(c_Transitive__Closure_Otrancl(_1574564, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1574564, _1574564), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1574564, _1574564), tc_HOL_Obool)))], (40609 ^ _780205) ^ [_1574606, _1574608] : [-(hAPP(c_Relation_ODomain(_1574606, _1574606), c_Transitive__Closure_Otrancl(_1574606, _1574608)) = hAPP(c_Relation_ODomain(_1574606, _1574606), _1574608))], (40611 ^ _780205) ^ [_1574646, _1574648] : [-(hAPP(c_Relation_ORange(_1574646, _1574646), c_Transitive__Closure_Otrancl(_1574646, _1574648)) = hAPP(c_Relation_ORange(_1574646, _1574646), _1574648))], (40613 ^ _780205) ^ [_1574701, _1574703] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1574701, _1574701)), c_Transitive__Closure_Otrancl(_1574701, _1574703))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1574701, _1574701)), _1574703)))], (40619 ^ _780205) ^ [_1574808, _1574810] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1574808, _1574808)), _1574810)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1574808, _1574808)), c_Transitive__Closure_Otrancl(_1574808, _1574810))))], (40625 ^ _780205) ^ [_1574921, _1574923, _1574925, _1574927, _1574929] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574921, _1574921)), hAPP(hAPP(c_Product__Type_OPair(_1574921, _1574921), _1574923), _1574925)), _1574927)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574921, _1574921)), hAPP(hAPP(c_Product__Type_OPair(_1574921, _1574921), _1574925), _1574929)), _1574927)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574921, _1574921)), hAPP(hAPP(c_Product__Type_OPair(_1574921, _1574921), _1574923), _1574929)), c_Transitive__Closure_Otrancl(_1574921, _1574927))))], (40635 ^ _780205) ^ [_1575182, _1575184, _1575186, _1575188, _1575190] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575182, _1575182)), hAPP(hAPP(c_Product__Type_OPair(_1575182, _1575182), _1575184), _1575186)), _1575188)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575182, _1575182)), hAPP(hAPP(c_Product__Type_OPair(_1575182, _1575182), _1575186), _1575190)), c_Transitive__Closure_Otrancl(_1575182, _1575188))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575182, _1575182)), hAPP(hAPP(c_Product__Type_OPair(_1575182, _1575182), _1575184), _1575190)), c_Transitive__Closure_Otrancl(_1575182, _1575188))))], (40645 ^ _780205) ^ [_1575449, _1575451, _1575453, _1575455, _1575457] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575449, _1575449)), hAPP(hAPP(c_Product__Type_OPair(_1575449, _1575449), _1575451), _1575453)), c_Transitive__Closure_Otrancl(_1575449, _1575455))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575449, _1575449)), hAPP(hAPP(c_Product__Type_OPair(_1575449, _1575449), _1575453), _1575457)), _1575455)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575449, _1575449)), hAPP(hAPP(c_Product__Type_OPair(_1575449, _1575449), _1575451), _1575457)), c_Transitive__Closure_Otrancl(_1575449, _1575455))))], (40655 ^ _780205) ^ [_1575716, _1575718, _1575720, _1575722, _1575724] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575716, _1575716)), hAPP(hAPP(c_Product__Type_OPair(_1575716, _1575716), _1575718), _1575720)), c_Transitive__Closure_Otrancl(_1575716, _1575722))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575716, _1575716)), hAPP(hAPP(c_Product__Type_OPair(_1575716, _1575716), _1575720), _1575724)), c_Transitive__Closure_Otrancl(_1575716, _1575722))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575716, _1575716)), hAPP(hAPP(c_Product__Type_OPair(_1575716, _1575716), _1575718), _1575724)), c_Transitive__Closure_Otrancl(_1575716, _1575722))))], (40665 ^ _780205) ^ [_1575989, _1575991, _1575993, _1575995] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575989, _1575989)), _1575991), c_Transitive__Closure_Otrancl(_1575989, _1575993))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575989, _1575989), tc_HOL_Obool)), _1575993), _1575995)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575989, _1575989)), _1575991), c_Transitive__Closure_Otrancl(_1575989, _1575995))))], (40675 ^ _780205) ^ [_1576204, _1576206] : [-(c_Transitive__Closure_Otrancl(_1576204, _1576206) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1576204, _1576204), tc_HOL_Obool)), _1576206), hAPP(hAPP(c_Relation_Orel__comp(_1576204, _1576204, _1576204), c_Transitive__Closure_Otrancl(_1576204, _1576206)), _1576206)))], (40677 ^ _780205) ^ [_1576259, _1576261, _1576263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1576259, _1576259), tc_HOL_Obool)), _1576261), hAPP(hAPP(c_Product__Type_OSigma(_1576259, _1576259), _1576263), hAPP(c_COMBK(tc_fun(_1576259, tc_HOL_Obool), _1576259), _1576263)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1576259, _1576259), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1576259, _1576261)), hAPP(hAPP(c_Product__Type_OSigma(_1576259, _1576259), _1576263), hAPP(c_COMBK(tc_fun(_1576259, tc_HOL_Obool), _1576259), _1576263)))))], (40683 ^ _780205) ^ [_1576468, _1576470, _1576472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1576468, _1576468), tc_HOL_Obool)), _1576470), _1576472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1576468, _1576468), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1576468, _1576468, _1576468), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1576468, _1576468), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1576468, _1576470)), _1576472)), _1576470)), _1576472)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1576468, _1576468), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1576468, _1576470)), _1576472)))], (40693 ^ _780205) ^ [_1576739, _1576741, _1576743, _1576745] : [-(c_Transitive__Closure_Otrancl(_1576739, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1576739, _1576739)), hAPP(hAPP(c_Product__Type_OPair(_1576739, _1576739), _1576741), _1576743)), _1576745)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1576739, _1576739), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1576739, _1576745)), hAPP(c_Set_OCollect(tc_prod(_1576739, _1576739)), hAPP(c_Product__Type_Oprod_Oprod__case(_1576739, _1576739, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1576739, tc_fun(_1576739, tc_HOL_Obool), tc_fun(_1576739, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1576739, tc_HOL_Obool), tc_fun(_1576739, tc_HOL_Obool)), _1576739), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1576739)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1576739), c_fconj), hAPP(hAPP(c_COMBC(_1576739, tc_fun(tc_prod(_1576739, _1576739), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1576739, _1576739), tc_fun(tc_fun(tc_prod(_1576739, _1576739), tc_HOL_Obool), tc_HOL_Obool), _1576739), c_member(tc_prod(_1576739, _1576739))), hAPP(hAPP(c_COMBC(_1576739, _1576739, tc_prod(_1576739, _1576739)), c_Product__Type_OPair(_1576739, _1576739)), _1576741))), c_Transitive__Closure_Ortrancl(_1576739, _1576745))))), hAPP(hAPP(c_COMBC(_1576739, tc_fun(tc_prod(_1576739, _1576739), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1576739, _1576739), tc_fun(tc_fun(tc_prod(_1576739, _1576739), tc_HOL_Obool), tc_HOL_Obool), _1576739), c_member(tc_prod(_1576739, _1576739))), hAPP(c_Product__Type_OPair(_1576739, _1576739), _1576743))), c_Transitive__Closure_Ortrancl(_1576739, _1576745)))))))], (40695 ^ _780205) ^ [_1577007, _1577009, _1577011, _1577013] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1577007, tc_fun(_1577007, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1577007, tc_fun(tc_prod(_1577007, _1577007), tc_HOL_Obool), tc_fun(_1577007, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577007, tc_fun(tc_fun(tc_prod(_1577007, _1577007), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1577007, _1577007), tc_HOL_Obool), tc_fun(_1577007, tc_HOL_Obool)), _1577007), c_COMBC(_1577007, tc_fun(tc_prod(_1577007, _1577007), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577007, tc_prod(_1577007, _1577007)), tc_fun(_1577007, tc_fun(tc_fun(tc_prod(_1577007, _1577007), tc_HOL_Obool), tc_HOL_Obool)), _1577007), hAPP(c_COMBB(tc_prod(_1577007, _1577007), tc_fun(tc_fun(tc_prod(_1577007, _1577007), tc_HOL_Obool), tc_HOL_Obool), _1577007), c_member(tc_prod(_1577007, _1577007)))), c_Product__Type_OPair(_1577007, _1577007)))), _1577009)), c_fequal), _1577011), _1577013)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577007, _1577007)), hAPP(hAPP(c_Product__Type_OPair(_1577007, _1577007), _1577011), _1577013)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1577007, _1577007), tc_HOL_Obool)), _1577009), c_Relation_OId(_1577007)))))], (40701 ^ _780205) ^ [_1577428, _1577430, _1577432, _1577434] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577428, _1577428)), hAPP(hAPP(c_Product__Type_OPair(_1577428, _1577428), _1577432), _1577434)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1577428, _1577428), tc_HOL_Obool)), _1577430), c_Relation_OId(_1577428)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1577428, tc_fun(_1577428, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1577428, tc_fun(tc_prod(_1577428, _1577428), tc_HOL_Obool), tc_fun(_1577428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577428, tc_fun(tc_fun(tc_prod(_1577428, _1577428), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1577428, _1577428), tc_HOL_Obool), tc_fun(_1577428, tc_HOL_Obool)), _1577428), c_COMBC(_1577428, tc_fun(tc_prod(_1577428, _1577428), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577428, tc_prod(_1577428, _1577428)), tc_fun(_1577428, tc_fun(tc_fun(tc_prod(_1577428, _1577428), tc_HOL_Obool), tc_HOL_Obool)), _1577428), hAPP(c_COMBB(tc_prod(_1577428, _1577428), tc_fun(tc_fun(tc_prod(_1577428, _1577428), tc_HOL_Obool), tc_HOL_Obool), _1577428), c_member(tc_prod(_1577428, _1577428)))), c_Product__Type_OPair(_1577428, _1577428)))), _1577430)), c_fequal), _1577432), _1577434)))], (40707 ^ _780205) ^ [_1577855, _1577857, _1577859] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577855, _1577855)), _1577857), _1577859)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577855, _1577855)), _1577857), c_Transitive__Closure_Ortrancl(_1577855, _1577859))))], (40713 ^ _780205) ^ [_1577980, _1577982, _1577984] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577980, _1577980)), hAPP(hAPP(c_Product__Type_OPair(_1577980, _1577980), _1577982), _1577982)), c_Transitive__Closure_Ortrancl(_1577980, _1577984))))], (40715 ^ _780205) ^ [_1578029, _1578031] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578029, _1578029)), hAPP(hAPP(c_Product__Type_OPair(_1578029, _1578029), _1578031), _1578031)), c_Relation_OId(_1578029))))], (40717 ^ _780205) ^ [_1578075, _1578077, _1578079, _1578081] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578075, _1578075)), hAPP(hAPP(c_Product__Type_OPair(_1578075, _1578075), _1578077), _1578079)), c_Transitive__Closure_Otrancl(_1578075, _1578081))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578075, _1578075)), hAPP(hAPP(c_Product__Type_OPair(_1578075, _1578075), _1578077), _1578079)), c_Transitive__Closure_Ortrancl(_1578075, _1578081))))], (40723 ^ _780205) ^ [_1578244, _1578246] : [-(c_Transitive__Closure_Otrancl(_1578244, _1578246) = hAPP(hAPP(c_Relation_Orel__comp(_1578244, _1578244, _1578244), _1578246), c_Transitive__Closure_Ortrancl(_1578244, _1578246)))], (40725 ^ _780205) ^ [_1578285, _1578287] : [-(c_Transitive__Closure_Otrancl(_1578285, _1578287) = hAPP(hAPP(c_Relation_Orel__comp(_1578285, _1578285, _1578285), c_Transitive__Closure_Ortrancl(_1578285, _1578287)), _1578287))], (40727 ^ _780205) ^ [_1578326, _1578328] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1578326, _1578326), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1578326, _1578328)), c_Relation_OId(_1578326)) = c_Transitive__Closure_Ortrancl(_1578326, _1578328))], (40729 ^ _780205) ^ [_1578373, _1578375] : [-(c_Transitive__Closure_Otrancl(_1578373, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1578373, _1578373), tc_HOL_Obool)), _1578375), c_Relation_OId(_1578373))) = c_Transitive__Closure_Ortrancl(_1578373, _1578375))], (40731 ^ _780205) ^ [_1578420, _1578422] : [-(c_Transitive__Closure_Otrancl(_1578420, c_Transitive__Closure_Ortrancl(_1578420, _1578422)) = c_Transitive__Closure_Ortrancl(_1578420, _1578422))], (40733 ^ _780205) ^ [_1578454, _1578456] : [-(c_Transitive__Closure_Ortrancl(_1578454, c_Transitive__Closure_Otrancl(_1578454, _1578456)) = c_Transitive__Closure_Ortrancl(_1578454, _1578456))], (40735 ^ _780205) ^ [_1578488, _1578490] : [-(hAPP(c_Relation_ODomain(_1578488, _1578488), c_Transitive__Closure_Ortrancl(_1578488, _1578490)) = c_Orderings_Otop__class_Otop(tc_fun(_1578488, tc_HOL_Obool)))], (40737 ^ _780205) ^ [_1578527, _1578529] : [-(hAPP(c_Relation_ORange(_1578527, _1578527), c_Transitive__Closure_Ortrancl(_1578527, _1578529)) = c_Orderings_Otop__class_Otop(tc_fun(_1578527, tc_HOL_Obool)))], (40739 ^ _780205) ^ [_1578566, _1578568] : [-(c_Relation_Orefl__on(_1578566, c_Orderings_Otop__class_Otop(tc_fun(_1578566, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1578566, _1578568)))], (40741 ^ _780205) ^ [_1578600, _1578602, _1578604, _1578606, _1578608] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578600, _1578600)), hAPP(hAPP(c_Product__Type_OPair(_1578600, _1578600), _1578602), _1578604)), _1578606)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578600, _1578600)), hAPP(hAPP(c_Product__Type_OPair(_1578600, _1578600), _1578604), _1578608)), c_Transitive__Closure_Ortrancl(_1578600, _1578606))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578600, _1578600)), hAPP(hAPP(c_Product__Type_OPair(_1578600, _1578600), _1578602), _1578608)), c_Transitive__Closure_Ortrancl(_1578600, _1578606))))], (40751 ^ _780205) ^ [_1578867, _1578869, _1578871, _1578873, _1578875] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578867, _1578867)), hAPP(hAPP(c_Product__Type_OPair(_1578867, _1578867), _1578869), _1578871)), c_Transitive__Closure_Ortrancl(_1578867, _1578873))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578867, _1578867)), hAPP(hAPP(c_Product__Type_OPair(_1578867, _1578867), _1578871), _1578875)), _1578873)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578867, _1578867)), hAPP(hAPP(c_Product__Type_OPair(_1578867, _1578867), _1578869), _1578875)), c_Transitive__Closure_Ortrancl(_1578867, _1578873))))], (40761 ^ _780205) ^ [_1579134, _1579136, _1579138, _1579140, _1579142] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579134, _1579134)), hAPP(hAPP(c_Product__Type_OPair(_1579134, _1579134), _1579136), _1579138)), c_Transitive__Closure_Ortrancl(_1579134, _1579140))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1579134, _1579134)), hAPP(hAPP(c_Product__Type_OPair(_1579134, _1579134), _1579138), _1579142)), c_Transitive__Closure_Ortrancl(_1579134, _1579140))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579134, _1579134)), hAPP(hAPP(c_Product__Type_OPair(_1579134, _1579134), _1579136), _1579142)), c_Transitive__Closure_Ortrancl(_1579134, _1579140))))], (40771 ^ _780205) ^ [_1579407, _1579409] : [-(c_Transitive__Closure_Ortrancl(_1579407, c_Transitive__Closure_Ortrancl(_1579407, _1579409)) = c_Transitive__Closure_Ortrancl(_1579407, _1579409))], (40773 ^ _780205) ^ [_1579441, _1579443] : [-(c_Transitive__Closure_Ortrancl(_1579441, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1579441, _1579441), tc_HOL_Obool)), _1579443), c_Relation_OId(_1579441))) = c_Transitive__Closure_Ortrancl(_1579441, _1579443))], (40775 ^ _780205) ^ [_1579488, _1579490, _1579492, _1579494] : [40776 ^ _780205 : [(40777 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579488, _1579488)), _1579490), c_Transitive__Closure_Ortrancl(_1579488, _1579492)))], (40779 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579488, _1579488)), _1579490), c_Transitive__Closure_Ortrancl(_1579488, _1579494)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579488, _1579488)), _1579490), c_Transitive__Closure_Ortrancl(_1579488, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1579488, _1579488), tc_HOL_Obool)), _1579492), _1579494)))))], (40783 ^ _780205) ^ [_1579713, _1579715, _1579717] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1579713, _1579713), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1579713, _1579713), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1579713, _1579715)), c_Transitive__Closure_Ortrancl(_1579713, _1579717))), c_Transitive__Closure_Ortrancl(_1579713, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1579713, _1579713), tc_HOL_Obool)), _1579715), _1579717)))))], (40785 ^ _780205) ^ [_1579790, _1579792] : [-(c_Transitive__Closure_Ortrancl(_1579790, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1579790, _1579790), tc_HOL_Obool)), _1579792), c_Relation_OId(_1579790))) = c_Transitive__Closure_Ortrancl(_1579790, _1579792))], (40787 ^ _780205) ^ [_1579837, _1579839, _1579841] : [-(c_Transitive__Closure_Ortrancl(_1579837, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1579837, _1579837), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1579837, _1579839)), c_Transitive__Closure_Ortrancl(_1579837, _1579841))) = c_Transitive__Closure_Ortrancl(_1579837, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1579837, _1579837), tc_HOL_Obool)), _1579839), _1579841)))], (40789 ^ _780205) ^ [_1579904, _1579906] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1579904, _1579904), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1579904, _1579906)), c_Relation_OId(_1579904)) = c_Transitive__Closure_Ortrancl(_1579904, _1579906))], (40791 ^ _780205) ^ [_1579951, _1579953, _1579955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579951, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579951, _1579951, _1579953), _1579955)), _1579955)), -(hAPP(c_Relation_OImage(_1579951, _1579951, c_Transitive__Closure_Ortrancl(_1579951, _1579953)), _1579955) = _1579955)], (40797 ^ _780205) ^ [_1580084, _1580086, _1580088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580084, _1580084), tc_HOL_Obool)), _1580086), _1580088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580084, _1580084), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1580084, _1580086)), c_Transitive__Closure_Ortrancl(_1580084, _1580088))))], (40803 ^ _780205) ^ [_1580227, _1580229, _1580231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580227, _1580227), tc_HOL_Obool)), _1580229), _1580231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580227, _1580227), tc_HOL_Obool)), _1580231), c_Transitive__Closure_Ortrancl(_1580227, _1580229))), -(c_Transitive__Closure_Ortrancl(_1580227, _1580231) = c_Transitive__Closure_Ortrancl(_1580227, _1580229))], (40813 ^ _780205) ^ [_1580430, _1580432, _1580434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580430, _1580430), tc_HOL_Obool)), _1580432), c_Transitive__Closure_Ortrancl(_1580430, _1580434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580430, _1580430), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1580430, _1580432)), c_Transitive__Closure_Ortrancl(_1580430, _1580434))))], (40819 ^ _780205) ^ [_1580579, _1580581] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1580579, _1580579, _1580579), c_Transitive__Closure_Ortrancl(_1580579, _1580581)), c_Transitive__Closure_Ortrancl(_1580579, _1580581)) = c_Transitive__Closure_Ortrancl(_1580579, _1580581))], (40821 ^ _780205) ^ [_1580623, _1580625] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1580623, _1580623, _1580623), _1580625), c_Transitive__Closure_Ortrancl(_1580623, _1580625)) = hAPP(hAPP(c_Relation_Orel__comp(_1580623, _1580623, _1580623), c_Transitive__Closure_Ortrancl(_1580623, _1580625)), _1580625))], (40823 ^ _780205) ^ [_1580674, _1580676] : [-(c_Transitive__Closure_Ortrancl(_1580674, _1580676) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1580674, _1580674), tc_HOL_Obool)), c_Relation_OId(_1580674)), hAPP(hAPP(c_Relation_Orel__comp(_1580674, _1580674, _1580674), c_Transitive__Closure_Ortrancl(_1580674, _1580676)), _1580676)))], (40825 ^ _780205) ^ [_1580731, _1580733, _1580735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580731, _1580731), tc_HOL_Obool)), c_Relation_OId(_1580731)), _1580733)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580731, _1580731), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1580731, _1580731, _1580731), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1580731, _1580731), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1580731, _1580735)), _1580733)), _1580735)), _1580733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580731, _1580731), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1580731, _1580735)), _1580733)))], (40835 ^ _780205) ^ [_1581006] : [-(c_Transitive__Closure_Ortrancl(_1581006, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1581006, _1581006), tc_HOL_Obool))) = c_Relation_OId(_1581006))], (40837 ^ _780205) ^ [_1581042, _1581044, _1581046] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1581042, _1581044, _1581044), _1581046), c_Relation_OId(_1581044)) = _1581046)], (40839 ^ _780205) ^ [_1581081, _1581083, _1581085] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1581081, _1581081, _1581083), c_Relation_OId(_1581081)), _1581085) = _1581085)], (40841 ^ _780205) ^ [_1581120, _1581122] : [-(hAPP(c_Relation_OImage(_1581120, _1581120, c_Relation_OId(_1581120)), _1581122) = _1581122)], (40843 ^ _780205) ^ [_1581172, _1581174, _1581176] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581172, _1581172)), hAPP(hAPP(c_Product__Type_OPair(_1581172, _1581172), _1581174), _1581176)), c_Relation_OId(_1581172))), -(_1581174 = _1581176)], (40849 ^ _780205) ^ [_1581289, _1581291, _1581293] : [_1581291 = _1581293, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581289, _1581289)), hAPP(hAPP(c_Product__Type_OPair(_1581289, _1581289), _1581291), _1581293)), c_Relation_OId(_1581289))))], (40855 ^ _780205) ^ [_1581433, _1581435, _1581437, _1581439] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581433, _1581433)), hAPP(hAPP(c_Product__Type_OPair(_1581433, _1581433), _1581435), _1581437)), c_Transitive__Closure_Ortrancl(_1581433, _1581439))), -(_1581435 = _1581437), 40862 ^ _780205 : [(40863 ^ _780205) ^ [] : [_1581435 = _1581437], (40865 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581433, _1581433)), hAPP(hAPP(c_Product__Type_OPair(_1581433, _1581433), _1581435), _1581437)), c_Transitive__Closure_Otrancl(_1581433, _1581439))))]]], (40867 ^ _780205) ^ [_1581691, _1581693, _1581695, _1581697] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581691, _1581691)), hAPP(hAPP(c_Product__Type_OPair(_1581691, _1581691), _1581693), _1581695)), c_Transitive__Closure_Ortrancl(_1581691, _1581697)))), 40868 ^ _780205 : [(40869 ^ _780205) ^ [] : [_1581693 = _1581695], (40871 ^ _780205) ^ [] : [-(_1581693 = _1581695), hBOOL(hAPP(hAPP(c_member(tc_prod(_1581691, _1581691)), hAPP(hAPP(c_Product__Type_OPair(_1581691, _1581691), _1581693), _1581695)), c_Transitive__Closure_Otrancl(_1581691, _1581697)))]]], (40879 ^ _780205) ^ [_1581957, _1581959, _1581961, _1581963, _1581965] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581957, _1581957)), hAPP(hAPP(c_Product__Type_OPair(_1581957, _1581957), _1581959), _1581961)), _1581963)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1581957, _1581957)), hAPP(hAPP(c_Product__Type_OPair(_1581957, _1581957), _1581961), _1581965)), c_Transitive__Closure_Ortrancl(_1581957, _1581963))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581957, _1581957)), hAPP(hAPP(c_Product__Type_OPair(_1581957, _1581957), _1581959), _1581965)), c_Transitive__Closure_Otrancl(_1581957, _1581963))))], (40889 ^ _780205) ^ [_1582224, _1582226, _1582228, _1582230] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582224, _1582224)), hAPP(hAPP(c_Product__Type_OPair(_1582224, _1582224), _1582226), _1582228)), c_Transitive__Closure_Ortrancl(_1582224, _1582230))), -(_1582226 = _1582228), 40896 ^ _780205 : [(40897 ^ _780205) ^ [] : [_1582226 = _1582228], (40899 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582224, _1582224)), hAPP(hAPP(c_Product__Type_OPair(_1582224, _1582224), _1582226), _1582228)), c_Transitive__Closure_Otrancl(_1582224, _1582230))))]]], (40901 ^ _780205) ^ [_1582486, _1582488, _1582490, _1582492, _1582494] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582486, _1582486)), hAPP(hAPP(c_Product__Type_OPair(_1582486, _1582486), _1582488), _1582490)), c_Transitive__Closure_Ortrancl(_1582486, _1582492))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1582486, _1582486)), hAPP(hAPP(c_Product__Type_OPair(_1582486, _1582486), _1582490), _1582494)), _1582492)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582486, _1582486)), hAPP(hAPP(c_Product__Type_OPair(_1582486, _1582486), _1582488), _1582494)), c_Transitive__Closure_Otrancl(_1582486, _1582492))))], (40911 ^ _780205) ^ [_1582753, _1582755, _1582757, _1582759, _1582761] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582753, _1582753)), hAPP(hAPP(c_Product__Type_OPair(_1582753, _1582753), _1582755), _1582757)), c_Transitive__Closure_Otrancl(_1582753, _1582759))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1582753, _1582753)), hAPP(hAPP(c_Product__Type_OPair(_1582753, _1582753), _1582757), _1582761)), c_Transitive__Closure_Ortrancl(_1582753, _1582759))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582753, _1582753)), hAPP(hAPP(c_Product__Type_OPair(_1582753, _1582753), _1582755), _1582761)), c_Transitive__Closure_Otrancl(_1582753, _1582759))))], (40921 ^ _780205) ^ [_1583026, _1583028, _1583030, _1583032, _1583034] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583026, _1583026)), hAPP(hAPP(c_Product__Type_OPair(_1583026, _1583026), _1583028), _1583030)), c_Transitive__Closure_Ortrancl(_1583026, _1583032))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583026, _1583026)), hAPP(hAPP(c_Product__Type_OPair(_1583026, _1583026), _1583030), _1583034)), c_Transitive__Closure_Otrancl(_1583026, _1583032))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583026, _1583026)), hAPP(hAPP(c_Product__Type_OPair(_1583026, _1583026), _1583028), _1583034)), c_Transitive__Closure_Otrancl(_1583026, _1583032))))], (40931 ^ _780205) ^ [_1583299] : [-(hAPP(c_Relation_ODomain(_1583299, _1583299), c_Relation_OId(_1583299)) = c_Orderings_Otop__class_Otop(tc_fun(_1583299, tc_HOL_Obool)))], (40933 ^ _780205) ^ [_1583335] : [-(hAPP(c_Relation_ORange(_1583335, _1583335), c_Relation_OId(_1583335)) = c_Orderings_Otop__class_Otop(tc_fun(_1583335, tc_HOL_Obool)))], (40935 ^ _780205) ^ [_1583371] : [-(c_Relation_Orefl__on(_1583371, c_Orderings_Otop__class_Otop(tc_fun(_1583371, tc_HOL_Obool)), c_Relation_OId(_1583371)))], (40937 ^ _780205) ^ [] : [-(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))))], (40939 ^ _780205) ^ [_1583419, _1583421, _1583423, _1583425] : [-(hBOOL(hAPP(hAPP(c_member(_1583419), _1583421), hAPP(c_Relation_ODomain(_1583419, _1583419), _1583423)))), 40942 ^ _780205 : [(40943 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583419, _1583419)), hAPP(hAPP(c_Product__Type_OPair(_1583419, _1583419), _1583421), _1583425)), c_Transitive__Closure_Ortrancl(_1583419, _1583423))), -(_1583421 = _1583425)], (40949 ^ _780205) ^ [] : [_1583421 = _1583425, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583419, _1583419)), hAPP(hAPP(c_Product__Type_OPair(_1583419, _1583419), _1583421), _1583425)), c_Transitive__Closure_Ortrancl(_1583419, _1583423))))]]], (40955 ^ _780205) ^ [_1583715, _1583717, _1583719, _1583721] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583715, _1583715)), hAPP(hAPP(c_Product__Type_OPair(_1583715, _1583715), _1583717), _1583719)), c_Transitive__Closure_Ortrancl(_1583715, _1583721))), hBOOL(hAPP(hAPP(c_member(_1583715), _1583719), c_Wellfounded_Oacc(_1583715, _1583721))), -(hBOOL(hAPP(hAPP(c_member(_1583715), _1583717), c_Wellfounded_Oacc(_1583715, _1583721))))], (40965 ^ _780205) ^ [_1583936, _1583938, _1583940, _1583942] : [hBOOL(hAPP(hAPP(c_member(_1583936), _1583938), c_Wellfounded_Oacc(_1583936, _1583940))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583936, _1583936)), hAPP(hAPP(c_Product__Type_OPair(_1583936, _1583936), _1583942), _1583938)), c_Transitive__Closure_Ortrancl(_1583936, _1583940))), -(hBOOL(hAPP(hAPP(c_member(_1583936), _1583942), c_Wellfounded_Oacc(_1583936, _1583940))))], (40975 ^ _780205) ^ [_1584178, _1584180, _1584182, _1584184] : [c_Wellfounded_Owf(_1584178, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1584178, _1584178)), hAPP(hAPP(c_Product__Type_OPair(_1584178, _1584178), _1584180), _1584182)), _1584184)), 40978 ^ _780205 : [(40979 ^ _780205) ^ [] : [-(c_Wellfounded_Owf(_1584178, _1584184))], (40981 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584178, _1584178)), hAPP(hAPP(c_Product__Type_OPair(_1584178, _1584178), _1584182), _1584180)), c_Transitive__Closure_Ortrancl(_1584178, _1584184)))]]], (40983 ^ _780205) ^ [_1584373, _1584375, _1584377, _1584379] : [-(c_Wellfounded_Owf(_1584373, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1584373, _1584373)), hAPP(hAPP(c_Product__Type_OPair(_1584373, _1584373), _1584375), _1584377)), _1584379))), c_Wellfounded_Owf(_1584373, _1584379), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584373, _1584373)), hAPP(hAPP(c_Product__Type_OPair(_1584373, _1584373), _1584377), _1584375)), c_Transitive__Closure_Ortrancl(_1584373, _1584379))))], (40993 ^ _780205) ^ [_1584620, _1584622, _1584624, _1584626] : [c_Wellfounded_Oacyclic(_1584620, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1584620, _1584620)), hAPP(hAPP(c_Product__Type_OPair(_1584620, _1584620), _1584622), _1584624)), _1584626)), 40996 ^ _780205 : [(40997 ^ _780205) ^ [] : [-(c_Wellfounded_Oacyclic(_1584620, _1584626))], (40999 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584620, _1584620)), hAPP(hAPP(c_Product__Type_OPair(_1584620, _1584620), _1584624), _1584622)), c_Transitive__Closure_Ortrancl(_1584620, _1584626)))]]], (41001 ^ _780205) ^ [_1584815, _1584817, _1584819, _1584821] : [-(c_Wellfounded_Oacyclic(_1584815, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1584815, _1584815)), hAPP(hAPP(c_Product__Type_OPair(_1584815, _1584815), _1584817), _1584819)), _1584821))), c_Wellfounded_Oacyclic(_1584815, _1584821), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584815, _1584815)), hAPP(hAPP(c_Product__Type_OPair(_1584815, _1584815), _1584819), _1584817)), c_Transitive__Closure_Ortrancl(_1584815, _1584821))))], (41011 ^ _780205) ^ [_1585041, _1585043] : [-(c_Relation_Orefl__on(_1585041, c_Orderings_Otop__class_Otop(tc_fun(_1585041, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585041, _1585041), tc_HOL_Obool)), _1585043), c_Relation_OId(_1585041))))], (41013 ^ _780205) ^ [_1585088] : [-(c_Relation_OId(_1585088) = hAPP(c_Set_OCollect(tc_prod(_1585088, _1585088)), hAPP(hAPP(c_COMBB(tc_fun(_1585088, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1585088, _1585088)), c_HOL_OEx(_1585088)), hAPP(hAPP(c_COMBC(tc_prod(_1585088, _1585088), tc_fun(_1585088, tc_prod(_1585088, _1585088)), tc_fun(_1585088, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1585088, _1585088), tc_HOL_Obool), tc_fun(tc_fun(_1585088, tc_prod(_1585088, _1585088)), tc_fun(_1585088, tc_HOL_Obool)), tc_prod(_1585088, _1585088)), c_COMBB(tc_prod(_1585088, _1585088), tc_HOL_Obool, _1585088)), c_fequal)), hAPP(hAPP(c_COMBS(_1585088, _1585088, tc_prod(_1585088, _1585088)), c_Product__Type_OPair(_1585088, _1585088)), c_COMBI(_1585088))))))], (41015 ^ _780205) ^ [_1585217, _1585219] : [-(c_Relation_Oirrefl(_1585217, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1585217, _1585217), tc_HOL_Obool)), _1585219), c_Relation_OId(_1585217))))], (41017 ^ _780205) ^ [_1585273, _1585275] : [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), _1585273), _1585275)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1585273), _1585275)))], (41023 ^ _780205) ^ [_1585378, _1585380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1585378), _1585380)), -(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), _1585378), _1585380)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (41029 ^ _780205) ^ [_1585489, _1585491, _1585493, _1585495, _1585497] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585489, _1585489)), hAPP(hAPP(c_Product__Type_OPair(_1585489, _1585489), _1585491), _1585493)), c_Transitive__Closure_Ortrancl(_1585489, _1585495))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585489, _1585489), tc_HOL_Obool)), _1585495), hAPP(hAPP(c_Product__Type_OSigma(_1585489, _1585489), _1585497), hAPP(c_COMBK(tc_fun(_1585489, tc_HOL_Obool), _1585489), _1585497)))), -(_1585491 = _1585493), -(hBOOL(hAPP(hAPP(c_member(_1585489), _1585491), _1585497)))], (41043 ^ _780205) ^ [_1585763, _1585765, _1585767] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1585763, _1585763), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1585763, _1585763), _1585765)), c_Transitive__Closure_Ortrancl(_1585763, _1585765)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1585763, _1585763), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585763, _1585763)), hAPP(hAPP(c_Product__Type_OPair(_1585763, _1585763), _1585767), _1585767)), c_Transitive__Closure_Otrancl(_1585763, _1585765)))], (41049 ^ _780205) ^ [_1585949, _1585951, _1585953, _1585955, _1585957] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585949, _1585949)), hAPP(hAPP(c_Product__Type_OPair(_1585949, _1585949), hAPP(_1585951, hAPP(c_Nat_OSuc, 41050 ^ [_1585949, _1585951, _1585953, _1585955, _1585957]))), hAPP(_1585951, 41050 ^ [_1585949, _1585951, _1585953, _1585955, _1585957]))), c_Transitive__Closure_Ortrancl(_1585949, _1585953))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585949, _1585949)), hAPP(hAPP(c_Product__Type_OPair(_1585949, _1585949), hAPP(_1585951, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1585955), _1585957))), hAPP(_1585951, _1585955))), c_Transitive__Closure_Ortrancl(_1585949, _1585953))))], (41056 ^ _780205) ^ [_1586242, _1586244] : [-(c_Transitive__Closure_Ortrancl(_1586242, hAPP(c_Relation_Oconverse(_1586242, _1586242), _1586244)) = hAPP(c_Relation_Oconverse(_1586242, _1586242), c_Transitive__Closure_Ortrancl(_1586242, _1586244)))], (41058 ^ _780205) ^ [_1586285] : [-(hAPP(c_Relation_Oconverse(_1586285, _1586285), c_Relation_OId(_1586285)) = c_Relation_OId(_1586285))], (41060 ^ _780205) ^ [_1586333, _1586335] : [c_Wellfounded_Oacyclic(_1586333, hAPP(c_Relation_Oconverse(_1586333, _1586333), _1586335)), -(c_Wellfounded_Oacyclic(_1586333, _1586335))], (41066 ^ _780205) ^ [_1586418, _1586420] : [c_Wellfounded_Oacyclic(_1586418, _1586420), -(c_Wellfounded_Oacyclic(_1586418, hAPP(c_Relation_Oconverse(_1586418, _1586418), _1586420)))], (41072 ^ _780205) ^ [_1586527, _1586529, _1586531] : [c_Relation_Orefl__on(_1586527, _1586529, hAPP(c_Relation_Oconverse(_1586527, _1586527), _1586531)), -(c_Relation_Orefl__on(_1586527, _1586529, _1586531))], (41078 ^ _780205) ^ [_1586618, _1586620, _1586622] : [c_Relation_Orefl__on(_1586618, _1586620, _1586622), -(c_Relation_Orefl__on(_1586618, _1586620, hAPP(c_Relation_Oconverse(_1586618, _1586618), _1586622)))], (41084 ^ _780205) ^ [_1586715, _1586717] : [-(hAPP(c_Relation_Oconverse(_1586715, _1586715), c_Relation_OId__on(_1586715, _1586717)) = c_Relation_OId__on(_1586715, _1586717))], (41086 ^ _780205) ^ [_1586752, _1586754] : [-(hAPP(c_Relation_OField(_1586752), hAPP(c_Relation_Oconverse(_1586752, _1586752), _1586754)) = hAPP(c_Relation_OField(_1586752), _1586754))], (41088 ^ _780205) ^ [_1586793, _1586795, _1586797] : [-(hAPP(c_Relation_Oconverse(_1586793, _1586795), hAPP(c_Relation_Oconverse(_1586795, _1586793), _1586797)) = _1586797)], (41090 ^ _780205) ^ [_1586832, _1586834, _1586836, _1586838] : [-(hAPP(c_Relation_Oconverse(_1586832, _1586832), hAPP(hAPP(c_Relation_Oinv__image(_1586834, _1586832), _1586836), _1586838)) = hAPP(hAPP(c_Relation_Oinv__image(_1586834, _1586832), hAPP(c_Relation_Oconverse(_1586834, _1586834), _1586836)), _1586838))], (41092 ^ _780205) ^ [_1586909, _1586911, _1586913] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1586909, _1586911)), hAPP(c_Relation_Oconverse(_1586911, _1586909), _1586913))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1586911, _1586909)), _1586913)))], (41098 ^ _780205) ^ [_1587024, _1587026, _1587028] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1587026, _1587024)), _1587028)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1587024, _1587026)), hAPP(c_Relation_Oconverse(_1587026, _1587024), _1587028))))], (41104 ^ _780205) ^ [_1587145, _1587147, _1587149, _1587151] : [-(hAPP(c_Relation_Oconverse(_1587145, _1587147), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1587145, _1587147), tc_HOL_Obool)), _1587149), _1587151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1587147, _1587145), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1587145, _1587147), _1587149)), hAPP(c_Relation_Oconverse(_1587145, _1587147), _1587151)))], (41106 ^ _780205) ^ [_1587220, _1587222, _1587224, _1587226] : [-(hAPP(c_Relation_Oconverse(_1587220, _1587222), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587220, _1587222), tc_HOL_Obool)), _1587224), _1587226)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587222, _1587220), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1587220, _1587222), _1587224)), hAPP(c_Relation_Oconverse(_1587220, _1587222), _1587226)))], (41108 ^ _780205) ^ [_1587295, _1587297, _1587299, _1587301, _1587303] : [-(hAPP(c_Relation_Oconverse(_1587295, _1587297), hAPP(hAPP(c_Relation_Orel__comp(_1587295, _1587299, _1587297), _1587301), _1587303)) = hAPP(hAPP(c_Relation_Orel__comp(_1587297, _1587299, _1587295), hAPP(c_Relation_Oconverse(_1587299, _1587297), _1587303)), hAPP(c_Relation_Oconverse(_1587295, _1587299), _1587301)))], (41110 ^ _780205) ^ [_1587364, _1587366, _1587368, _1587370, _1587372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587364, _1587366)), hAPP(hAPP(c_Product__Type_OPair(_1587364, _1587366), _1587368), _1587370)), hAPP(c_Relation_Oconverse(_1587366, _1587364), _1587372))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587366, _1587364)), hAPP(hAPP(c_Product__Type_OPair(_1587366, _1587364), _1587370), _1587368)), _1587372)))], (41116 ^ _780205) ^ [_1587535, _1587537, _1587539, _1587541, _1587543] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587535, _1587537)), hAPP(hAPP(c_Product__Type_OPair(_1587535, _1587537), _1587539), _1587541)), _1587543)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587537, _1587535)), hAPP(hAPP(c_Product__Type_OPair(_1587537, _1587535), _1587541), _1587539)), hAPP(c_Relation_Oconverse(_1587535, _1587537), _1587543))))], (41122 ^ _780205) ^ [_1587730, _1587732, _1587734, _1587736, _1587738] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587730, _1587732)), hAPP(hAPP(c_Product__Type_OPair(_1587730, _1587732), _1587734), _1587736)), hAPP(c_Relation_Oconverse(_1587732, _1587730), _1587738))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587732, _1587730)), hAPP(hAPP(c_Product__Type_OPair(_1587732, _1587730), _1587736), _1587734)), _1587738)))], (41128 ^ _780205) ^ [_1587897, _1587899, _1587901, _1587903, _1587905] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587899, _1587897)), hAPP(hAPP(c_Product__Type_OPair(_1587899, _1587897), _1587903), _1587901)), _1587905)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587897, _1587899)), hAPP(hAPP(c_Product__Type_OPair(_1587897, _1587899), _1587901), _1587903)), hAPP(c_Relation_Oconverse(_1587899, _1587897), _1587905))))], (41134 ^ _780205) ^ [_1588070, _1588072, _1588074, _1588076, _1588078] : [-(hAPP(c_Relation_Oconverse(_1588070, _1588072), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1588074, tc_fun(tc_prod(_1588070, _1588072), tc_HOL_Obool)), _1588076), _1588078)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1588074, tc_fun(tc_prod(_1588072, _1588070), tc_HOL_Obool)), _1588076), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1588070, _1588072), tc_HOL_Obool), tc_fun(tc_prod(_1588072, _1588070), tc_HOL_Obool), _1588074), c_Relation_Oconverse(_1588070, _1588072)), _1588078)))], (41136 ^ _780205) ^ [_1588162, _1588164, _1588166, _1588168, _1588170] : [-(hAPP(c_Relation_Oconverse(_1588162, _1588164), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1588166, tc_fun(tc_prod(_1588162, _1588164), tc_HOL_Obool)), _1588168), _1588170)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1588166, tc_fun(tc_prod(_1588164, _1588162), tc_HOL_Obool)), _1588168), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1588162, _1588164), tc_HOL_Obool), tc_fun(tc_prod(_1588164, _1588162), tc_HOL_Obool), _1588166), c_Relation_Oconverse(_1588162, _1588164)), _1588170)))], (41138 ^ _780205) ^ [_1588254, _1588256] : [-(c_Transitive__Closure_Otrancl(_1588254, hAPP(c_Relation_Oconverse(_1588254, _1588254), _1588256)) = hAPP(c_Relation_Oconverse(_1588254, _1588254), c_Transitive__Closure_Otrancl(_1588254, _1588256)))], (41140 ^ _780205) ^ [_1588297, _1588299] : [c_Wellfounded_Owf(_1588297, hAPP(c_Relation_Oconverse(_1588297, _1588297), _1588299)), -(c_Wellfounded_Owf(_1588297, hAPP(c_Relation_Oconverse(_1588297, _1588297), c_Transitive__Closure_Otrancl(_1588297, _1588299))))], (41146 ^ _780205) ^ [_1588404, _1588406, _1588408] : [c_Equiv__Relations_Oequiv(_1588404, _1588406, _1588408), -(hAPP(hAPP(c_Relation_Orel__comp(_1588404, _1588404, _1588404), hAPP(c_Relation_Oconverse(_1588404, _1588404), _1588408)), _1588408) = _1588408)], (41152 ^ _780205) ^ [_1588517, _1588519, _1588521] : [-(hAPP(c_Relation_ORange(_1588517, _1588519), _1588521) = hAPP(c_Relation_ODomain(_1588519, _1588517), hAPP(c_Relation_Oconverse(_1588517, _1588519), _1588521)))], (41154 ^ _780205) ^ [_1588562, _1588564, _1588566] : [-(hAPP(c_Relation_ODomain(_1588562, _1588564), hAPP(c_Relation_Oconverse(_1588564, _1588562), _1588566)) = hAPP(c_Relation_ORange(_1588564, _1588562), _1588566))], (41156 ^ _780205) ^ [_1588607, _1588609, _1588611] : [-(hAPP(c_Relation_ORange(_1588607, _1588609), hAPP(c_Relation_Oconverse(_1588609, _1588607), _1588611)) = hAPP(c_Relation_ODomain(_1588609, _1588607), _1588611))], (41158 ^ _780205) ^ [_1588652, _1588654, _1588656, _1588658] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588652, _1588652)), hAPP(hAPP(c_Product__Type_OPair(_1588652, _1588652), _1588654), _1588656)), c_Transitive__Closure_Ortrancl(_1588652, hAPP(c_Relation_Oconverse(_1588652, _1588652), _1588658)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588652, _1588652)), hAPP(hAPP(c_Product__Type_OPair(_1588652, _1588652), _1588656), _1588654)), c_Transitive__Closure_Ortrancl(_1588652, _1588658))))], (41164 ^ _780205) ^ [_1588833, _1588835, _1588837, _1588839] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588833, _1588833)), hAPP(hAPP(c_Product__Type_OPair(_1588833, _1588833), _1588835), _1588837)), c_Transitive__Closure_Ortrancl(_1588833, _1588839))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588833, _1588833)), hAPP(hAPP(c_Product__Type_OPair(_1588833, _1588833), _1588837), _1588835)), c_Transitive__Closure_Ortrancl(_1588833, hAPP(c_Relation_Oconverse(_1588833, _1588833), _1588839)))))], (41170 ^ _780205) ^ [_1589014, _1589016, _1589018, _1589020] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589014, _1589014)), hAPP(hAPP(c_Product__Type_OPair(_1589014, _1589014), _1589016), _1589018)), c_Transitive__Closure_Otrancl(_1589014, hAPP(c_Relation_Oconverse(_1589014, _1589014), _1589020)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589014, _1589014)), hAPP(hAPP(c_Product__Type_OPair(_1589014, _1589014), _1589016), _1589018)), hAPP(c_Relation_Oconverse(_1589014, _1589014), c_Transitive__Closure_Otrancl(_1589014, _1589020)))))], (41176 ^ _780205) ^ [_1589207, _1589209, _1589211, _1589213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589207, _1589207)), hAPP(hAPP(c_Product__Type_OPair(_1589207, _1589207), _1589209), _1589211)), hAPP(c_Relation_Oconverse(_1589207, _1589207), c_Transitive__Closure_Otrancl(_1589207, _1589213)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589207, _1589207)), hAPP(hAPP(c_Product__Type_OPair(_1589207, _1589207), _1589209), _1589211)), c_Transitive__Closure_Otrancl(_1589207, hAPP(c_Relation_Oconverse(_1589207, _1589207), _1589213)))))], (41182 ^ _780205) ^ [_1589424, _1589426, _1589428, _1589430, _1589432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1589424, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1589426, _1589424, _1589428), _1589430)), _1589432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1589426, tc_HOL_Obool)), _1589430), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1589426, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1589424, _1589426, hAPP(c_Relation_Oconverse(_1589426, _1589424), _1589428)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1589424, tc_HOL_Obool)), _1589432))))))], (41188 ^ _780205) ^ [_1589615, _1589617, _1589619, _1589621, _1589623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1589617, tc_HOL_Obool)), _1589621), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1589617, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1589615, _1589617, hAPP(c_Relation_Oconverse(_1589617, _1589615), _1589619)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1589615, tc_HOL_Obool)), _1589623))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1589615, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1589617, _1589615, _1589619), _1589621)), _1589623)))], (41194 ^ _780205) ^ [_1589812, _1589814, _1589816] : [c_Relation_Orefl__on(_1589812, _1589814, _1589816), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1589812, _1589812), tc_HOL_Obool)), _1589816), hAPP(hAPP(c_Relation_Orel__comp(_1589812, _1589812, _1589812), hAPP(c_Relation_Oconverse(_1589812, _1589812), _1589816)), _1589816))))], (41200 ^ _780205) ^ [_1589951, _1589953, _1589955] : [hAPP(hAPP(c_Relation_Orel__comp(_1589951, _1589951, _1589951), hAPP(c_Relation_Oconverse(_1589951, _1589951), _1589953)), _1589953) = _1589953, hAPP(c_Relation_ODomain(_1589951, _1589951), _1589953) = _1589955, -(c_Equiv__Relations_Oequiv(_1589951, _1589955, _1589953))], (41210 ^ _780205) ^ [_1590130, _1590132] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1590130, _1590130)), _1590132)), c_Wellfounded_Oacyclic(_1590130, _1590132), -(c_Wellfounded_Owf(_1590130, hAPP(c_Relation_Oconverse(_1590130, _1590130), _1590132)))], (41220 ^ _780205) ^ [_1590285, _1590287, _1590289] : [-(hAPP(c_Relation_Oconverse(_1590285, _1590287), _1590289) = hAPP(c_Set_OCollect(tc_prod(_1590287, _1590285)), hAPP(c_Product__Type_Oprod_Oprod__case(_1590287, _1590285, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1590287, tc_fun(tc_prod(_1590285, _1590287), tc_HOL_Obool), tc_fun(_1590285, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1590285, tc_fun(tc_fun(tc_prod(_1590285, _1590287), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1590285, _1590287), tc_HOL_Obool), tc_fun(_1590285, tc_HOL_Obool)), _1590287), c_COMBC(_1590285, tc_fun(tc_prod(_1590285, _1590287), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1590285, tc_prod(_1590285, _1590287)), tc_fun(_1590285, tc_fun(tc_fun(tc_prod(_1590285, _1590287), tc_HOL_Obool), tc_HOL_Obool)), _1590287), hAPP(c_COMBB(tc_prod(_1590285, _1590287), tc_fun(tc_fun(tc_prod(_1590285, _1590287), tc_HOL_Obool), tc_HOL_Obool), _1590285), c_member(tc_prod(_1590285, _1590287)))), hAPP(c_COMBC(_1590285, _1590287, tc_prod(_1590285, _1590287)), c_Product__Type_OPair(_1590285, _1590287))))), _1590289))))], (41222 ^ _780205) ^ [_1590461, _1590463, _1590465, _1590467, _1590469, _1590471] : [c_Relation_Osingle__valued(_1590461, _1590463, hAPP(c_Relation_Oconverse(_1590463, _1590461), _1590465)), -(_1590467 = c_Orderings_Obot__class_Obot(tc_fun(_1590469, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1590463, _1590461, _1590465), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590469, tc_fun(_1590463, tc_HOL_Obool)), _1590467), _1590471)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1590469, tc_fun(_1590461, tc_HOL_Obool)), _1590467), hAPP(hAPP(c_COMBB(tc_fun(_1590463, tc_HOL_Obool), tc_fun(_1590461, tc_HOL_Obool), _1590469), c_Relation_OImage(_1590463, _1590461, _1590465)), _1590471)))], (41232 ^ _780205) ^ [_1590705, _1590707, _1590709] : [c_Relation_Ototal__on(_1590705, _1590707, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1590705, _1590705), tc_HOL_Obool)), _1590709), c_Relation_OId(_1590705))), -(c_Relation_Ototal__on(_1590705, _1590707, _1590709))], (41238 ^ _780205) ^ [_1590816, _1590818, _1590820] : [c_Relation_Ototal__on(_1590816, _1590818, _1590820), -(c_Relation_Ototal__on(_1590816, _1590818, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1590816, _1590816), tc_HOL_Obool)), _1590820), c_Relation_OId(_1590816))))], (41244 ^ _780205) ^ [_1590933] : [-(c_Relation_Osingle__valued(_1590933, _1590933, c_Relation_OId(_1590933)))], (41246 ^ _780205) ^ [_1590959, _1590961, _1590963, _1590965, _1590967] : [c_Relation_Osingle__valued(_1590959, _1590961, _1590963), c_Relation_Osingle__valued(_1590961, _1590965, _1590967), -(c_Relation_Osingle__valued(_1590959, _1590965, hAPP(hAPP(c_Relation_Orel__comp(_1590959, _1590961, _1590965), _1590963), _1590967)))], (41256 ^ _780205) ^ [_1591126, _1591128, _1591130, _1591132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1591126, _1591128), tc_HOL_Obool)), _1591130), _1591132)), c_Relation_Osingle__valued(_1591126, _1591128, _1591132), -(c_Relation_Osingle__valued(_1591126, _1591128, _1591130))], (41266 ^ _780205) ^ [_1591293, _1591295] : [-(c_Relation_Osingle__valued(_1591293, _1591293, c_Relation_OId__on(_1591293, _1591295)))], (41268 ^ _780205) ^ [_1591322, _1591324] : [-(c_Relation_Ototal__on(_1591322, c_Orderings_Obot__class_Obot(tc_fun(_1591322, tc_HOL_Obool)), _1591324))], (41270 ^ _780205) ^ [_1591371, _1591373, _1591375] : [c_Relation_Ototal__on(_1591371, _1591373, hAPP(c_Relation_Oconverse(_1591371, _1591371), _1591375)), -(c_Relation_Ototal__on(_1591371, _1591373, _1591375))], (41276 ^ _780205) ^ [_1591462, _1591464, _1591466] : [c_Relation_Ototal__on(_1591462, _1591464, _1591466), -(c_Relation_Ototal__on(_1591462, _1591464, hAPP(c_Relation_Oconverse(_1591462, _1591462), _1591466)))], (41282 ^ _780205) ^ [_1591559, _1591561, _1591563, _1591565, _1591567, _1591569] : [c_Relation_Osingle__valued(_1591559, _1591561, _1591563), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591559, _1591561)), hAPP(hAPP(c_Product__Type_OPair(_1591559, _1591561), _1591565), _1591567)), _1591563)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591559, _1591561)), hAPP(hAPP(c_Product__Type_OPair(_1591559, _1591561), _1591565), _1591569)), _1591563)), -(_1591567 = _1591569)], (41310 ^ _780205) ^ [_1592234, _1592236, _1592238] : [41313 ^ _780205 : [(41314 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592234, _1592236)), hAPP(hAPP(c_Product__Type_OPair(_1592234, _1592236), 41311 ^ [_1592234, _1592236, _1592238]), 41312 ^ [_1592234, _1592236, _1592238])), _1592238)))], (41317 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592234, _1592236)), hAPP(hAPP(c_Product__Type_OPair(_1592234, _1592236), 41311 ^ [_1592234, _1592236, _1592238]), 41315 ^ [_1592234, _1592236, _1592238])), _1592238)))], (41319 ^ _780205) ^ [] : [41312 ^ [_1592234, _1592236, _1592238] = 41315 ^ [_1592234, _1592236, _1592238]]], -(c_Relation_Osingle__valued(_1592234, _1592236, _1592238))], (41296 ^ _780205) ^ [_1591860, _1591862, _1591864] : [c_Relation_Osingle__valued(_1591860, _1591862, _1591864), 41299 ^ _780205 : [(41300 ^ _780205) ^ [_1591981, _1591983] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591860, _1591862)), hAPP(hAPP(c_Product__Type_OPair(_1591860, _1591862), _1591983), _1591981)), _1591864)), 41303 ^ _780205 : [(41304 ^ _780205) ^ [_1592107] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591860, _1591862)), hAPP(hAPP(c_Product__Type_OPair(_1591860, _1591862), _1591983), _1592107)), _1591864)), -(_1591981 = _1592107)]]]]], (41345 ^ _780205) ^ [_1593111, _1593113, _1593115] : [41347 ^ _780205 : [(41348 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1593111), 41346 ^ [_1593111, _1593113, _1593115]), _1593113)))], (41351 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1593111), 41349 ^ [_1593111, _1593113, _1593115]), _1593113)))], (41353 ^ _780205) ^ [] : [41346 ^ [_1593111, _1593113, _1593115] = 41349 ^ [_1593111, _1593113, _1593115]], (41355 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593111, _1593111)), hAPP(hAPP(c_Product__Type_OPair(_1593111, _1593111), 41346 ^ [_1593111, _1593113, _1593115]), 41349 ^ [_1593111, _1593113, _1593115])), _1593115))], (41357 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593111, _1593111)), hAPP(hAPP(c_Product__Type_OPair(_1593111, _1593111), 41349 ^ [_1593111, _1593113, _1593115]), 41346 ^ [_1593111, _1593113, _1593115])), _1593115))]], -(c_Relation_Ototal__on(_1593111, _1593113, _1593115))], (41323 ^ _780205) ^ [_1592622, _1592624, _1592626] : [c_Relation_Ototal__on(_1592622, _1592624, _1592626), 41326 ^ _780205 : [(41327 ^ _780205) ^ [_1592766] : [hBOOL(hAPP(hAPP(c_member(_1592622), _1592766), _1592624)), 41330 ^ _780205 : [(41331 ^ _780205) ^ [_1592906] : [hBOOL(hAPP(hAPP(c_member(_1592622), _1592906), _1592624)), -(_1592766 = _1592906), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592622, _1592622)), hAPP(hAPP(c_Product__Type_OPair(_1592622, _1592622), _1592766), _1592906)), _1592626))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592622, _1592622)), hAPP(hAPP(c_Product__Type_OPair(_1592622, _1592622), _1592906), _1592766)), _1592626)))]]]]], (41361 ^ _780205) ^ [_1593693, _1593695, _1593697, _1593699, _1593701] : [c_Relation_Osingle__valued(_1593693, _1593693, _1593695), hBOOL(hAPP(hAPP(c_member(tc_prod(_1593693, _1593693)), hAPP(hAPP(c_Product__Type_OPair(_1593693, _1593693), _1593697), _1593699)), c_Transitive__Closure_Ortrancl(_1593693, _1593695))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1593693, _1593693)), hAPP(hAPP(c_Product__Type_OPair(_1593693, _1593693), _1593697), _1593701)), c_Transitive__Closure_Ortrancl(_1593693, _1593695))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593693, _1593693)), hAPP(hAPP(c_Product__Type_OPair(_1593693, _1593693), _1593699), _1593701)), c_Transitive__Closure_Ortrancl(_1593693, _1593695)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593693, _1593693)), hAPP(hAPP(c_Product__Type_OPair(_1593693, _1593693), _1593701), _1593699)), c_Transitive__Closure_Ortrancl(_1593693, _1593695))))], (41379 ^ _780205) ^ [_1594083, _1594085, _1594087, _1594089, _1594091] : [c_Relation_Osingle__valued(_1594083, _1594085, hAPP(c_Relation_Oconverse(_1594085, _1594083), _1594087)), -(hAPP(c_Relation_OImage(_1594085, _1594083, _1594087), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1594085, tc_HOL_Obool)), _1594089), _1594091)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1594083, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1594085, _1594083, _1594087), _1594089)), hAPP(c_Relation_OImage(_1594085, _1594083, _1594087), _1594091)))], (41385 ^ _780205) ^ [_1594266, _1594268, _1594270] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594266, _1594266)), _1594268), c_Transitive__Closure_Ortrancl(_1594266, _1594270))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594266, _1594266)), _1594268), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1594266, _1594266), 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(_1594266, _1594266), tc_HOL_Obool), tc_fun(tc_prod(_1594266, _1594266), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1594266, _1594266), tc_HOL_Obool)), _1594270)))))], (41391 ^ _780205) ^ [_1594473, _1594475] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594473, _1594473)), hAPP(hAPP(c_Product__Type_OPair(_1594473, _1594473), 41392 ^ [_1594473, _1594475]), 41392 ^ [_1594473, _1594475])), c_Transitive__Closure_Otrancl(_1594473, _1594475)))), -(c_Wellfounded_Oacyclic(_1594473, _1594475))], (41398 ^ _780205) ^ [_1594545, _1594547, _1594549] : [c_Relation_Osingle__valued(_1594545, _1594545, _1594547), -(c_Relation_Osingle__valued(_1594545, _1594545, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594545, _1594545), tc_HOL_Obool), _1594549), _1594547)))], (41404 ^ _780205) ^ [_1594652, _1594654, _1594656, _1594658] : [-(hAPP(_1594652, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1594654, _1594654), _1594656), _1594652), _1594658)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1594654, _1594654), _1594656), _1594652), hAPP(_1594652, _1594658)))], (41406 ^ _780205) ^ [_1594711, _1594713, _1594715, _1594717] : [-(hAPP(hAPP(c_Nat_Ocompow(_1594711, _1594711), _1594713), hAPP(hAPP(c_Nat_Ocompow(_1594711, _1594711), _1594715), _1594717)) = hAPP(hAPP(c_Nat_Ocompow(_1594711, _1594711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1594715), _1594713)), _1594717))], (41408 ^ _780205) ^ [_1594773, _1594775, _1594777] : [c_Wellfounded_Owf(_1594773, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594773, _1594773), tc_HOL_Obool), _1594775), _1594777)), -(c_Wellfounded_Owf(_1594773, _1594777))], (41414 ^ _780205) ^ [_1594876, _1594878, _1594880, _1594882] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1594876, _1594878), tc_fun(_1594876, _1594878)), _1594880), c_Fun_Ocomp(_1594878, _1594878, _1594876, _1594882)) = c_Fun_Ocomp(_1594878, _1594878, _1594876, hAPP(hAPP(c_Nat_Ocompow(_1594878, _1594878), _1594880), _1594882)))], (41416 ^ _780205) ^ [_1594939, _1594941, _1594943] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1594939, _1594939, _1594939), _1594941), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594939, _1594939), tc_HOL_Obool), _1594943), _1594941)) = hAPP(hAPP(c_Relation_Orel__comp(_1594939, _1594939, _1594939), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594939, _1594939), tc_HOL_Obool), _1594943), _1594941)), _1594941))], (41418 ^ _780205) ^ [_1595010, _1595012] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595010, _1595010), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1595012) = _1595012)], (41420 ^ _780205) ^ [_1595065, _1595067, _1595069] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595065, _1595065)), _1595067), c_Transitive__Closure_Ortrancl(_1595065, _1595069))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595065, _1595065)), _1595067), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595065, _1595065), tc_HOL_Obool), 41423 ^ [_1595065, _1595067, _1595069]), _1595069))))], (41427 ^ _780205) ^ [_1595224, _1595226, _1595228] : [41428 ^ _780205 : [(41429 ^ _780205) ^ [_1595300] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595224, _1595224)), _1595226), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595224, _1595224), tc_HOL_Obool), _1595300), _1595228)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595224, _1595224)), _1595226), c_Transitive__Closure_Ortrancl(_1595224, _1595228))))], (41433 ^ _780205) ^ [_1595388, _1595390, _1595392, _1595394] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595388, _1595388)), _1595390), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595388, _1595388), tc_HOL_Obool), _1595392), _1595394))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595388, _1595388)), _1595390), c_Transitive__Closure_Ortrancl(_1595388, _1595394))))], (41439 ^ _780205) ^ [_1595539, _1595541, _1595543] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595539, _1595539), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1595541)), _1595543) = hAPP(hAPP(c_Relation_Orel__comp(_1595539, _1595539, _1595539), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595539, _1595539), tc_HOL_Obool), _1595541), _1595543)), _1595543))], (41441 ^ _780205) ^ [_1595603, _1595605, _1595607, _1595609] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595603, _1595603), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1595605), _1595607)), _1595609) = hAPP(hAPP(c_Relation_Orel__comp(_1595603, _1595603, _1595603), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595603, _1595603), tc_HOL_Obool), _1595605), _1595609)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595603, _1595603), tc_HOL_Obool), _1595607), _1595609)))], (41443 ^ _780205) ^ [_1595684, _1595686] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595684, _1595684), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1595686) = c_Relation_OId(_1595684))], (41445 ^ _780205) ^ [_1595723, _1595725, _1595727] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595723, _1595723)), hAPP(hAPP(c_Product__Type_OPair(_1595723, _1595723), _1595725), _1595725)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595723, _1595723), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1595727))))], (41447 ^ _780205) ^ [_1595781, _1595783, _1595785, _1595787] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595781, _1595781)), hAPP(hAPP(c_Product__Type_OPair(_1595781, _1595781), _1595783), _1595785)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595781, _1595781), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1595787))), -(_1595783 = _1595785)], (41453 ^ _780205) ^ [_1595924, _1595926, _1595928, _1595930, _1595932, _1595934] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595924, _1595924)), hAPP(hAPP(c_Product__Type_OPair(_1595924, _1595924), _1595926), _1595928)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595924, _1595924), tc_HOL_Obool), _1595930), _1595932))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1595924, _1595924)), hAPP(hAPP(c_Product__Type_OPair(_1595924, _1595924), _1595928), _1595934)), _1595932)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595924, _1595924)), hAPP(hAPP(c_Product__Type_OPair(_1595924, _1595924), _1595926), _1595934)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595924, _1595924), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1595930)), _1595932))))], (41463 ^ _780205) ^ [_1596237, _1596239, _1596241, _1596243, _1596245, _1596247] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596237, _1596237)), hAPP(hAPP(c_Product__Type_OPair(_1596237, _1596237), _1596239), _1596241)), _1596243)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1596237, _1596237)), hAPP(hAPP(c_Product__Type_OPair(_1596237, _1596237), _1596241), _1596245)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1596237, _1596237), tc_HOL_Obool), _1596247), _1596243))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596237, _1596237)), hAPP(hAPP(c_Product__Type_OPair(_1596237, _1596237), _1596239), _1596245)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1596237, _1596237), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1596247)), _1596243))))], (41473 ^ _780205) ^ [_1596550, _1596552, _1596554] : [-(hAPP(hAPP(c_Nat_Ocompow(_1596550, _1596550), hAPP(c_Nat_OSuc, _1596552)), _1596554) = hAPP(c_Fun_Ocomp(_1596550, _1596550, _1596550, _1596554), hAPP(hAPP(c_Nat_Ocompow(_1596550, _1596550), _1596552), _1596554)))], (41475 ^ _780205) ^ [_1596606, _1596608, _1596610, _1596612] : [-(hAPP(hAPP(c_Nat_Ocompow(_1596606, _1596606), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1596608), _1596610)), _1596612) = hAPP(c_Fun_Ocomp(_1596606, _1596606, _1596606, hAPP(hAPP(c_Nat_Ocompow(_1596606, _1596606), _1596608), _1596612)), hAPP(hAPP(c_Nat_Ocompow(_1596606, _1596606), _1596610), _1596612)))], (41477 ^ _780205) ^ [_1596676, _1596678] : [-(hAPP(hAPP(c_Nat_Ocompow(_1596676, _1596676), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1596678) = c_Fun_Oid(_1596676))], (41479 ^ _780205) ^ [_1596730, _1596732, _1596734] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596730, _1596730)), _1596732), c_Transitive__Closure_Otrancl(_1596730, _1596734))), 41483 ^ _780205 : [(41484 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41482 ^ [_1596730, _1596732, _1596734])))], (41486 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596730, _1596730)), _1596732), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1596730, _1596730), tc_HOL_Obool), 41482 ^ [_1596730, _1596732, _1596734]), _1596734))))]]], (41488 ^ _780205) ^ [_1596928, _1596930, _1596932] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596928, _1596928)), _1596930), c_Transitive__Closure_Otrancl(_1596928, _1596932)))), 41489 ^ _780205 : [(41490 ^ _780205) ^ [_1597007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1597007)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1596928, _1596928)), _1596930), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1596928, _1596928), tc_HOL_Obool), _1597007), _1596932)))]]], (41498 ^ _780205) ^ [_1597178, _1597180] : [-(c_Transitive__Closure_Ortrancl(_1597178, _1597180) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1597178, _1597178), 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(_1597178, _1597178), tc_HOL_Obool), tc_fun(tc_prod(_1597178, _1597178), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1597178, _1597178), tc_HOL_Obool)), _1597180)))], (41500 ^ _780205) ^ [_1597249] : [-(c_Nat_Ofunpow(_1597249) = c_Nat_Ocompow(_1597249, _1597249))], (41502 ^ _780205) ^ [_1597277, _1597279, _1597281, _1597283, _1597285] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597277, _1597277)), hAPP(hAPP(c_Product__Type_OPair(_1597277, _1597277), _1597279), _1597281)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1597277, _1597277), tc_HOL_Obool), _1597283), _1597285))), 41507 ^ _780205 : [(41508 ^ _780205) ^ [] : [-(_1597283 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41510 ^ _780205) ^ [] : [-(_1597279 = _1597281)]], 41513 ^ _780205 : [(41514 ^ _780205) ^ [] : [-(_1597283 = hAPP(c_Nat_OSuc, 41512 ^ [_1597277, _1597279, _1597281, _1597283, _1597285]))], (41516 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597277, _1597277)), hAPP(hAPP(c_Product__Type_OPair(_1597277, _1597277), _1597279), 41511 ^ [_1597277, _1597279, _1597281, _1597283, _1597285])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1597277, _1597277), tc_HOL_Obool), 41512 ^ [_1597277, _1597279, _1597281, _1597283, _1597285]), _1597285))))], (41518 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597277, _1597277)), hAPP(hAPP(c_Product__Type_OPair(_1597277, _1597277), 41511 ^ [_1597277, _1597279, _1597281, _1597283, _1597285]), _1597281)), _1597285)))]]], (41520 ^ _780205) ^ [_1597719, _1597721, _1597723, _1597725, _1597727] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597719, _1597719)), hAPP(hAPP(c_Product__Type_OPair(_1597719, _1597719), _1597721), _1597723)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1597719, _1597719), tc_HOL_Obool), _1597725), _1597727))), 41525 ^ _780205 : [(41526 ^ _780205) ^ [] : [-(_1597725 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41528 ^ _780205) ^ [] : [-(_1597721 = _1597723)]], 41531 ^ _780205 : [(41532 ^ _780205) ^ [] : [-(_1597725 = hAPP(c_Nat_OSuc, 41530 ^ [_1597719, _1597721, _1597723, _1597725, _1597727]))], (41534 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597719, _1597719)), hAPP(hAPP(c_Product__Type_OPair(_1597719, _1597719), _1597721), 41529 ^ [_1597719, _1597721, _1597723, _1597725, _1597727])), _1597727)))], (41536 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597719, _1597719)), hAPP(hAPP(c_Product__Type_OPair(_1597719, _1597719), 41529 ^ [_1597719, _1597721, _1597723, _1597725, _1597727]), _1597723)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1597719, _1597719), tc_HOL_Obool), 41530 ^ [_1597719, _1597721, _1597723, _1597725, _1597727]), _1597727))))]]], (41538 ^ _780205) ^ [_1598161, _1598163, _1598165, _1598167, _1598169] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1598161, _1598161)), hAPP(hAPP(c_Product__Type_OPair(_1598161, _1598161), _1598163), _1598165)), c_Transitive__Closure_Ortrancl(_1598161, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1598161, _1598161), tc_HOL_Obool)), _1598167), _1598169)))), 41544 ^ _780205 : [(41545 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598161, _1598161)), hAPP(hAPP(c_Product__Type_OPair(_1598161, _1598161), _1598163), 41543 ^ [_1598161, _1598163, _1598165, _1598167, _1598169])), c_Transitive__Closure_Ortrancl(_1598161, _1598167))))], (41548 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598161, _1598161)), hAPP(hAPP(c_Product__Type_OPair(_1598161, _1598161), 41543 ^ [_1598161, _1598163, _1598165, _1598167, _1598169]), 41546 ^ [_1598161, _1598163, _1598165, _1598167, _1598169])), _1598169)))], (41550 ^ _780205) ^ [] : [41543 ^ [_1598161, _1598163, _1598165, _1598167, _1598169] = 41546 ^ [_1598161, _1598163, _1598165, _1598167, _1598169]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598161, _1598161)), hAPP(hAPP(c_Product__Type_OPair(_1598161, _1598161), _1598163), _1598165)), c_Transitive__Closure_Ortrancl(_1598161, _1598167))))], (41554 ^ _780205) ^ [_1598720, _1598722, _1598724, _1598726, _1598728] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1598720, _1598720)), hAPP(hAPP(c_Product__Type_OPair(_1598720, _1598720), _1598722), _1598724)), c_Transitive__Closure_Ortrancl(_1598720, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1598720, _1598720), tc_HOL_Obool)), _1598726), _1598728)))), 41560 ^ _780205 : [(41561 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598720, _1598720)), hAPP(hAPP(c_Product__Type_OPair(_1598720, _1598720), 41559 ^ [_1598720, _1598722, _1598724, _1598726, _1598728]), _1598724)), c_Transitive__Closure_Ortrancl(_1598720, _1598726))))], (41564 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598720, _1598720)), hAPP(hAPP(c_Product__Type_OPair(_1598720, _1598720), 41562 ^ [_1598720, _1598722, _1598724, _1598726, _1598728]), 41559 ^ [_1598720, _1598722, _1598724, _1598726, _1598728])), _1598728)))], (41566 ^ _780205) ^ [] : [41562 ^ [_1598720, _1598722, _1598724, _1598726, _1598728] = 41559 ^ [_1598720, _1598722, _1598724, _1598726, _1598728]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598720, _1598720)), hAPP(hAPP(c_Product__Type_OPair(_1598720, _1598720), _1598722), _1598724)), c_Transitive__Closure_Ortrancl(_1598720, _1598726))))], (41570 ^ _780205) ^ [_1599279, _1599281, _1599283, _1599285, _1599287] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599279, _1599279)), hAPP(hAPP(c_Product__Type_OPair(_1599279, _1599279), _1599281), _1599283)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1599279, _1599279), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1599285)), _1599287))), 41574 ^ _780205 : [(41575 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599279, _1599279)), hAPP(hAPP(c_Product__Type_OPair(_1599279, _1599279), _1599281), 41573 ^ [_1599279, _1599281, _1599283, _1599285, _1599287])), _1599287)))], (41577 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599279, _1599279)), hAPP(hAPP(c_Product__Type_OPair(_1599279, _1599279), 41573 ^ [_1599279, _1599281, _1599283, _1599285, _1599287]), _1599283)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1599279, _1599279), tc_HOL_Obool), _1599285), _1599287))))]]], (41579 ^ _780205) ^ [_1599587, _1599589, _1599591, _1599593, _1599595] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599587, _1599587)), hAPP(hAPP(c_Product__Type_OPair(_1599587, _1599587), _1599589), _1599591)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1599587, _1599587), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1599593)), _1599595))), 41583 ^ _780205 : [(41584 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599587, _1599587)), hAPP(hAPP(c_Product__Type_OPair(_1599587, _1599587), _1599589), 41582 ^ [_1599587, _1599589, _1599591, _1599593, _1599595])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1599587, _1599587), tc_HOL_Obool), _1599593), _1599595))))], (41586 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599587, _1599587)), hAPP(hAPP(c_Product__Type_OPair(_1599587, _1599587), 41582 ^ [_1599587, _1599589, _1599591, _1599593, _1599595]), _1599591)), _1599595)))]]], (41588 ^ _780205) ^ [_1599899, _1599901, _1599903, _1599905, _1599907] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599899, _1599899)), hAPP(hAPP(c_Product__Type_OPair(_1599899, _1599899), _1599901), _1599903)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1599899, _1599899), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1599905)), _1599907))), 41592 ^ _780205 : [(41593 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599899, _1599899)), hAPP(hAPP(c_Product__Type_OPair(_1599899, _1599899), _1599901), 41591 ^ [_1599899, _1599901, _1599903, _1599905, _1599907])), _1599907)))], (41595 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599899, _1599899)), hAPP(hAPP(c_Product__Type_OPair(_1599899, _1599899), 41591 ^ [_1599899, _1599901, _1599903, _1599905, _1599907]), _1599903)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1599899, _1599899), tc_HOL_Obool), _1599905), _1599907))))]]], (41597 ^ _780205) ^ [_1600211, _1600213, _1600215, _1600217] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600211, _1600211)), hAPP(hAPP(c_Product__Type_OPair(_1600211, _1600211), _1600213), _1600215)), c_Transitive__Closure_Otrancl(_1600211, _1600217))), 41601 ^ _780205 : [(41602 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600211, _1600211)), hAPP(hAPP(c_Product__Type_OPair(_1600211, _1600211), _1600213), 41600 ^ [_1600211, _1600213, _1600215, _1600217])), _1600217)))], (41604 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600211, _1600211)), hAPP(hAPP(c_Product__Type_OPair(_1600211, _1600211), 41600 ^ [_1600211, _1600213, _1600215, _1600217]), _1600215)), c_Transitive__Closure_Ortrancl(_1600211, _1600217))))]]], (41606 ^ _780205) ^ [_1600471, _1600473, _1600475, _1600477] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600471, _1600471)), hAPP(hAPP(c_Product__Type_OPair(_1600471, _1600471), _1600473), _1600475)), c_Transitive__Closure_Otrancl(_1600471, _1600477))), 41610 ^ _780205 : [(41611 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600471, _1600471)), hAPP(hAPP(c_Product__Type_OPair(_1600471, _1600471), _1600473), 41609 ^ [_1600471, _1600473, _1600475, _1600477])), c_Transitive__Closure_Ortrancl(_1600471, _1600477))))], (41613 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600471, _1600471)), hAPP(hAPP(c_Product__Type_OPair(_1600471, _1600471), 41609 ^ [_1600471, _1600473, _1600475, _1600477]), _1600475)), _1600477)))]]], (41615 ^ _780205) ^ [_1600731, _1600733] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600731, _1600731)), _1600733), c_Relation_OId(_1600731))), -(_1600733 = hAPP(hAPP(c_Product__Type_OPair(_1600731, _1600731), 41618 ^ [_1600731, _1600733]), 41618 ^ [_1600731, _1600733]))], (41639 ^ _780205) ^ [_1601407, _1601409] : [-(c_Wellfounded_Owf(_1601407, _1601409)), 41642 ^ _780205 : [(41643 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601407), 41641 ^ [_1601407, _1601409]), 41640 ^ [_1601407, _1601409])))], (41645 ^ _780205) ^ [_1601627] : [hBOOL(hAPP(hAPP(c_member(_1601407), _1601627), 41640 ^ [_1601407, _1601409])), 41649 ^ _780205 : [(41650 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601407, _1601407)), hAPP(hAPP(c_Product__Type_OPair(_1601407, _1601407), 41648 ^ [_1601407, _1601409, _1601627]), _1601627)), _1601409)))], (41652 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601407), 41648 ^ [_1601407, _1601409, _1601627]), 41640 ^ [_1601407, _1601409])))]]]]], (41622 ^ _780205) ^ [_1600888, _1600890] : [c_Wellfounded_Owf(_1600888, _1600890), 41625 ^ _780205 : [(41626 ^ _780205) ^ [_1601020] : [41627 ^ _780205 : [(41628 ^ _780205) ^ [_1601125] : [hBOOL(hAPP(hAPP(c_member(_1600888), _1601125), _1601020))]], 41630 ^ _780205 : [(41631 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1600888), 41629 ^ [_1600888, _1600890, _1601020]), _1601020)))], (41633 ^ _780205) ^ [_1601247] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600888, _1600888)), hAPP(hAPP(c_Product__Type_OPair(_1600888, _1600888), _1601247), 41629 ^ [_1600888, _1600890, _1601020])), _1600890)), hBOOL(hAPP(hAPP(c_member(_1600888), _1601247), _1601020))]]]]], (41656 ^ _780205) ^ [_1601883, _1601885] : [-(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)))), _1601883)) = 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)))), _1601885))), 41658 ^ _780205 : [(41659 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41657 ^ [_1601883, _1601885])))], (41661 ^ _780205) ^ [] : [41662 ^ _780205 : [(41663 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1601883, 41657 ^ [_1601883, _1601885])))], (41665 ^ _780205) ^ [] : [hBOOL(hAPP(_1601885, 41657 ^ [_1601883, _1601885]))]], 41666 ^ _780205 : [(41667 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1601885, 41657 ^ [_1601883, _1601885])))], (41669 ^ _780205) ^ [] : [hBOOL(hAPP(_1601883, 41657 ^ [_1601883, _1601885]))]]]]], (41673 ^ _780205) ^ [_1602204, _1602206, _1602208, _1602210, _1602212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1602204, tc_HOL_Obool)), _1602206), _1602208)), 41679 ^ _780205 : [(41680 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602204), 41678 ^ [_1602204, _1602206, _1602208, _1602210, _1602212]), _1602206)))], (41682 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1602210, 41678 ^ [_1602204, _1602206, _1602208, _1602210, _1602212])))], (41684 ^ _780205) ^ [] : [hBOOL(hAPP(_1602212, 41678 ^ [_1602204, _1602206, _1602208, _1602210, _1602212]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1602204, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602204, tc_HOL_Obool)), _1602206), hAPP(c_Set_OCollect(_1602204), _1602210))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602204, tc_HOL_Obool)), _1602208), hAPP(c_Set_OCollect(_1602204), _1602212)))))], (41688 ^ _780205) ^ [_1602604, _1602606, _1602608, _1602610, _1602612, _1602614] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602604, _1602606)), _1602608), hAPP(hAPP(c_Relation_Orel__comp(_1602604, _1602610, _1602606), _1602612), _1602614))), 41694 ^ _780205 : [(41695 ^ _780205) ^ [] : [-(_1602608 = hAPP(hAPP(c_Product__Type_OPair(_1602604, _1602606), 41691 ^ [_1602604, _1602606, _1602608, _1602610, _1602612, _1602614]), 41693 ^ [_1602604, _1602606, _1602608, _1602610, _1602612, _1602614]))], (41697 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602604, _1602610)), hAPP(hAPP(c_Product__Type_OPair(_1602604, _1602610), 41691 ^ [_1602604, _1602606, _1602608, _1602610, _1602612, _1602614]), 41692 ^ [_1602604, _1602606, _1602608, _1602610, _1602612, _1602614])), _1602612)))], (41699 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602610, _1602606)), hAPP(hAPP(c_Product__Type_OPair(_1602610, _1602606), 41692 ^ [_1602604, _1602606, _1602608, _1602610, _1602612, _1602614]), 41693 ^ [_1602604, _1602606, _1602608, _1602610, _1602612, _1602614])), _1602614)))]]], (41701 ^ _780205) ^ [_1602982, _1602984, _1602986, _1602988] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602982, _1602984)), _1602986), hAPP(c_Relation_Oconverse(_1602984, _1602982), _1602988))), 41706 ^ _780205 : [(41707 ^ _780205) ^ [] : [-(_1602986 = hAPP(hAPP(c_Product__Type_OPair(_1602982, _1602984), 41705 ^ [_1602982, _1602984, _1602986, _1602988]), 41704 ^ [_1602982, _1602984, _1602986, _1602988]))], (41709 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602984, _1602982)), hAPP(hAPP(c_Product__Type_OPair(_1602984, _1602982), 41704 ^ [_1602982, _1602984, _1602986, _1602988]), 41705 ^ [_1602982, _1602984, _1602986, _1602988])), _1602988)))]]], (41711 ^ _780205) ^ [_1603235, _1603237, _1603239] : [-(c_Nitpick_Oplus__frac(_1603235, _1603237, _1603239) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1603235), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1603235), _1603237), hAPP(c_Nitpick_Odenom(_1603235), _1603239))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1603235), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1603235), tc_Int_Oint), c_Nitpick_Ofrac(_1603235)), 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(_1603235), _1603237))), 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(_1603235), _1603237))))), 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(_1603235), _1603239))), 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(_1603235), _1603239)))))), c_COMBI(tc_Int_Oint))))], (41713 ^ _780205) ^ [_1603366, _1603368, _1603370] : [-(c_Product__Type_Ointernal__split(_1603366, _1603368, _1603370) = c_Product__Type_Oprod_Oprod__case(_1603366, _1603368, _1603370))], (41715 ^ _780205) ^ [_1603401, _1603403, _1603405, _1603407, _1603409, _1603411] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1603401, _1603403, _1603405), _1603407), hAPP(hAPP(c_Product__Type_OPair(_1603401, _1603403), _1603409), _1603411)) = hAPP(hAPP(_1603407, _1603409), _1603411))], (41717 ^ _780205) ^ [_1603459, _1603461, _1603463] : [-(c_Nitpick_Otimes__frac(_1603459, _1603461, _1603463) = hAPP(hAPP(c_Nitpick_Ofrac(_1603459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1603459), _1603461)), hAPP(c_Nitpick_Onum(_1603459), _1603463))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1603459), _1603461)), hAPP(c_Nitpick_Odenom(_1603459), _1603463))))], (41719 ^ _780205) ^ [_1603530, _1603532, _1603534] : [-(c_Nitpick_Oof__frac(_1603532, _1603530, _1603534) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1603530), hAPP(c_Int_Oring__1__class_Oof__int(_1603530), hAPP(c_Nitpick_Onum(_1603532), _1603534))), hAPP(c_Int_Oring__1__class_Oof__int(_1603530), hAPP(c_Nitpick_Odenom(_1603532), _1603534)))), class_Rings_Oinverse(_1603530), class_Rings_Oring__1(_1603530)], (41729 ^ _780205) ^ [_1603723, _1603725] : [-(c_Nitpick_Oinverse__frac(_1603723, _1603725) = hAPP(hAPP(c_Nitpick_Ofrac(_1603723), hAPP(c_Nitpick_Odenom(_1603723), _1603725)), hAPP(c_Nitpick_Onum(_1603723), _1603725)))], (41731 ^ _780205) ^ [_1603769, _1603771] : [-(c_Nitpick_Ouminus__frac(_1603769, _1603771) = c_Nitpick_OAbs__Frac(_1603769, 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(_1603769), _1603771))), hAPP(c_Nitpick_Odenom(_1603769), _1603771))))], (41733 ^ _780205) ^ [_1603837, _1603839, _1603841] : [c_Nitpick_Oless__frac(_1603837, _1603839, _1603841), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1603837), c_Nitpick_Oplus__frac(_1603837, _1603839, c_Nitpick_Ouminus__frac(_1603837, _1603841)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41739 ^ _780205) ^ [_1603948, _1603950, _1603952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1603948), c_Nitpick_Oplus__frac(_1603948, _1603950, c_Nitpick_Ouminus__frac(_1603948, _1603952)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1603948, _1603950, _1603952))], (41745 ^ _780205) ^ [_1604083, _1604085, _1604087] : [c_Nitpick_Oless__eq__frac(_1604083, _1604085, _1604087), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1604083), c_Nitpick_Oplus__frac(_1604083, _1604085, c_Nitpick_Ouminus__frac(_1604083, _1604087)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41751 ^ _780205) ^ [_1604194, _1604196, _1604198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1604194), c_Nitpick_Oplus__frac(_1604194, _1604196, c_Nitpick_Ouminus__frac(_1604194, _1604198)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1604194, _1604196, _1604198))], (41757 ^ _780205) ^ [_1604311] : [-(c_Nitpick_Odenom(_1604311) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1604311, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1604311)))], (41759 ^ _780205) ^ [_1604346] : [-(c_Nitpick_Onum(_1604346) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1604346, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1604346)))], (41761 ^ _780205) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41763 ^ _780205) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41765 ^ _780205) ^ [_1604417, _1604419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41766 ^ [_1604417, _1604419]), hAPP(_1604417, 41766 ^ [_1604417, _1604419]))), -(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)), _1604417)), _1604419)))))], (41772 ^ _780205) ^ [_1604577, _1604579] : [-(c_List_Olenlex(_1604577, _1604579) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1604577)), tc_List_Olist(_1604577)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1604577), c_Wellfounded_Oless__than, c_List_Olex(_1604577, _1604579))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1604577), tc_List_Olist(_1604577), tc_prod(tc_Nat_Onat, tc_List_Olist(_1604577))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1604577), tc_prod(tc_Nat_Onat, tc_List_Olist(_1604577))), tc_List_Olist(_1604577)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1604577))), c_Nat_Osize__class_Osize(tc_List_Olist(_1604577)))), c_COMBI(tc_List_Olist(_1604577)))))], (41774 ^ _780205) ^ [_1604684, _1604686, _1604688] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604684)), _1604686) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604684)), _1604688)), _1604686 = _1604688], (41780 ^ _780205) ^ [_1604776, _1604778, _1604780, _1604782, _1604784] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604776), tc_List_Olist(_1604776))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604776), tc_List_Olist(_1604776)), _1604778), _1604780)), hAPP(c_List_Olexn(_1604776, _1604782), _1604784))), 41783 ^ _780205 : [(41784 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604776)), _1604778) = _1604784)], (41786 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604776)), _1604780) = _1604784)]]], (41788 ^ _780205) ^ [_1604979, _1604981] : [-(c_List_Olenlex(_1604979, _1604981) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1604979), tc_List_Olist(_1604979))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1604979), tc_List_Olist(_1604979), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1604979), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1604979), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool)), tc_List_Olist(_1604979)), c_COMBS(tc_List_Olist(_1604979), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604979), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1604979)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1604979)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1604979), tc_fun(tc_List_Olist(_1604979), tc_Nat_Onat), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1604979), tc_Nat_Onat), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool)), tc_List_Olist(_1604979)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1604979))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1604979)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1604979))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1604979)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1604979), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1604979), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool)), tc_List_Olist(_1604979)), c_COMBS(tc_List_Olist(_1604979), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604979), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1604979)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1604979)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1604979), tc_fun(tc_List_Olist(_1604979), tc_Nat_Onat), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1604979), tc_Nat_Onat), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool)), tc_List_Olist(_1604979)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1604979))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1604979)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1604979))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1604979)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1604979), tc_fun(tc_prod(tc_List_Olist(_1604979), tc_List_Olist(_1604979)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1604979), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1604979), tc_List_Olist(_1604979)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1604979), tc_List_Olist(_1604979)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604979), tc_HOL_Obool)), tc_List_Olist(_1604979)), c_COMBC(tc_List_Olist(_1604979), tc_fun(tc_prod(tc_List_Olist(_1604979), tc_List_Olist(_1604979)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1604979), tc_prod(tc_List_Olist(_1604979), tc_List_Olist(_1604979))), tc_fun(tc_List_Olist(_1604979), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1604979), tc_List_Olist(_1604979)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1604979)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1604979), tc_List_Olist(_1604979)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1604979), tc_List_Olist(_1604979)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1604979)), c_member(tc_prod(tc_List_Olist(_1604979), tc_List_Olist(_1604979))))), c_Product__Type_OPair(tc_List_Olist(_1604979), tc_List_Olist(_1604979))))), c_List_Olex(_1604979, _1604981)))))))], (41790 ^ _780205) ^ [_1605535, _1605537, _1605539] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605535)), c_List_Osublist(_1605535, _1605537, _1605539)) = 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(_1605535)), _1605537)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1605539)))))], (41792 ^ _780205) ^ [_1605601, _1605603, _1605605] : [-(hAPP(c_List_Olexn(_1605601, _1605603), hAPP(c_Nat_OSuc, _1605605)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1605601), tc_List_Olist(_1605601)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1605601, tc_List_Olist(_1605601)), tc_prod(_1605601, tc_List_Olist(_1605601))), tc_prod(tc_List_Olist(_1605601), tc_List_Olist(_1605601)), c_Product__Type_Omap__pair(tc_prod(_1605601, tc_List_Olist(_1605601)), tc_List_Olist(_1605601), tc_prod(_1605601, tc_List_Olist(_1605601)), tc_List_Olist(_1605601), hAPP(c_Product__Type_Oprod_Oprod__case(_1605601, tc_List_Olist(_1605601), tc_List_Olist(_1605601)), c_List_Olist_OCons(_1605601)), hAPP(c_Product__Type_Oprod_Oprod__case(_1605601, tc_List_Olist(_1605601), tc_List_Olist(_1605601)), c_List_Olist_OCons(_1605601)))), c_Wellfounded_Olex__prod(_1605601, tc_List_Olist(_1605601), _1605603, hAPP(c_List_Olexn(_1605601, _1605603), _1605605)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1605601), tc_List_Olist(_1605601))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1605601), tc_List_Olist(_1605601), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1605601), tc_fun(tc_List_Olist(_1605601), tc_HOL_Obool), tc_fun(tc_List_Olist(_1605601), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1605601), tc_HOL_Obool), tc_fun(tc_List_Olist(_1605601), tc_HOL_Obool)), tc_List_Olist(_1605601)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1605601))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1605601)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1605601), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1605601)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1605601)))), hAPP(c_Nat_OSuc, _1605605))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1605601), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1605601)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1605601)))), hAPP(c_Nat_OSuc, _1605605)))))))], (41794 ^ _780205) ^ [_1605892, _1605894, _1605896, _1605898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605892)), _1605894)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605892)), _1605896))), _1605894 = hAPP(hAPP(c_List_Olist_OCons(_1605892), _1605898), _1605896)], (41800 ^ _780205) ^ [_1606043, _1606045, _1606047] : [_1606043 = hAPP(hAPP(c_List_Olist_OCons(_1606045), _1606047), _1606043)], (41802 ^ _780205) ^ [_1606093, _1606095, _1606097] : [hAPP(hAPP(c_List_Olist_OCons(_1606093), _1606095), _1606097) = _1606097], (41804 ^ _780205) ^ [_1606152, _1606154, _1606156, _1606158, _1606160] : [hAPP(hAPP(c_List_Olist_OCons(_1606152), _1606154), _1606156) = hAPP(hAPP(c_List_Olist_OCons(_1606152), _1606158), _1606160), 41807 ^ _780205 : [(41808 ^ _780205) ^ [] : [-(_1606154 = _1606158)], (41810 ^ _780205) ^ [] : [-(_1606156 = _1606160)]]], (41812 ^ _780205) ^ [_1606289, _1606291, _1606293, _1606295, _1606297] : [-(hAPP(hAPP(c_List_Olist_OCons(_1606289), _1606291), _1606293) = hAPP(hAPP(c_List_Olist_OCons(_1606289), _1606295), _1606297)), _1606291 = _1606295, _1606293 = _1606297], (41822 ^ _780205) ^ [_1606464, _1606466, _1606468] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606464)), hAPP(hAPP(c_List_Olist_OCons(_1606464), _1606466), _1606468)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606464)), _1606468)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41824 ^ _780205) ^ [_1606546, _1606548, _1606550, _1606552, _1606554, _1606556] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606546), tc_List_Olist(_1606546))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606546), tc_List_Olist(_1606546)), hAPP(hAPP(c_List_Olist_OCons(_1606546), _1606548), _1606550)), hAPP(hAPP(c_List_Olist_OCons(_1606546), _1606552), _1606554))), c_List_Olex(_1606546, _1606556))), 41829 ^ _780205 : [(41830 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606546, _1606546)), hAPP(hAPP(c_Product__Type_OPair(_1606546, _1606546), _1606548), _1606552)), _1606556)))], (41832 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606546)), _1606550) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606546)), _1606554))]], 41833 ^ _780205 : [(41834 ^ _780205) ^ [] : [-(_1606548 = _1606552)], (41836 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606546), tc_List_Olist(_1606546))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606546), tc_List_Olist(_1606546)), _1606550), _1606554)), c_List_Olex(_1606546, _1606556))))]]], (41838 ^ _780205) ^ [_1606944, _1606946, _1606948, _1606950, _1606952, _1606954] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606944), tc_List_Olist(_1606944))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606944), tc_List_Olist(_1606944)), hAPP(hAPP(c_List_Olist_OCons(_1606944), _1606946), _1606948)), hAPP(hAPP(c_List_Olist_OCons(_1606944), _1606950), _1606952))), c_List_Olex(_1606944, _1606954)))), 41839 ^ _780205 : [(41840 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606944, _1606944)), hAPP(hAPP(c_Product__Type_OPair(_1606944, _1606944), _1606946), _1606950)), _1606954)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606944)), _1606948) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606944)), _1606952)], (41846 ^ _780205) ^ [] : [_1606946 = _1606950, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606944), tc_List_Olist(_1606944))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606944), tc_List_Olist(_1606944)), _1606948), _1606952)), c_List_Olex(_1606944, _1606954)))]]], (41854 ^ _780205) ^ [_1607400, _1607402, _1607404] : [-(c_List_Oset__Cons(_1607400, _1607402, _1607404) = hAPP(c_Set_OCollect(tc_List_Olist(_1607400)), hAPP(hAPP(c_COMBB(tc_fun(_1607400, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1607400)), c_HOL_OEx(_1607400)), hAPP(hAPP(c_COMBB(tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool)), tc_fun(_1607400, tc_HOL_Obool), tc_List_Olist(_1607400)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), tc_HOL_Obool, _1607400), c_HOL_OEx(tc_List_Olist(_1607400)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1607400), tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool)), tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1607400, tc_fun(tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool))), tc_fun(tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool)), tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool))), tc_List_Olist(_1607400)), c_COMBS(_1607400, tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1607400, tc_fun(tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool))), tc_List_Olist(_1607400)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1607400), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool)), _1607400), c_COMBS(tc_List_Olist(_1607400), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool)), tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1607400)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1607400), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1607400), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1607400)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1607400), tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_List_Olist(_1607400))), tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1607400), tc_List_Olist(_1607400)), tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool)), tc_fun(tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_List_Olist(_1607400))), tc_fun(_1607400, tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool))), tc_List_Olist(_1607400)), c_COMBB(tc_fun(tc_List_Olist(_1607400), tc_List_Olist(_1607400)), tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), _1607400)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1607400), tc_List_Olist(_1607400)), tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool)), tc_List_Olist(_1607400)), c_COMBB(tc_List_Olist(_1607400), tc_HOL_Obool, tc_List_Olist(_1607400))), c_fequal))), c_List_Olist_OCons(_1607400)))))), hAPP(hAPP(c_COMBC(_1607400, tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool)), _1607400), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1607400))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1607400), c_fconj), hAPP(hAPP(c_COMBC(_1607400, tc_fun(_1607400, tc_HOL_Obool), tc_HOL_Obool), c_member(_1607400)), _1607402)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1607400), tc_fun(tc_List_Olist(_1607400), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1607400))), _1607404)))))))], (41856 ^ _780205) ^ [_1607950, _1607952, _1607954, _1607956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1607950), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1607952), _1607954))), -(hAPP(c_Random_Opick(_1607952, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1607952)), _1607954), _1607956)), _1607950) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1607952), _1607954))], (41862 ^ _780205) ^ [_1608093, _1608095, _1608097, _1608099] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1608093), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1608095), _1608097)))), -(hAPP(c_Random_Opick(_1608095, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1608095)), _1608097), _1608099)), _1608093) = hAPP(c_Random_Opick(_1608095, _1608099), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1608093), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1608095), _1608097))))], (41868 ^ _780205) ^ [_1608181, _1608183, _1608185] : [-(c_Random_Oselect__weight(_1608181, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1608181)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1608181), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1608183)), _1608185)) = c_Random_Oselect__weight(_1608181, _1608185))], (41870 ^ _780205) ^ [_1608261, _1608263, _1608265, _1608267, _1608269, _1608271] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608261), tc_List_Olist(_1608261))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608261), tc_List_Olist(_1608261)), hAPP(hAPP(c_List_Olist_OCons(_1608261), _1608263), _1608265)), hAPP(hAPP(c_List_Olist_OCons(_1608261), _1608267), _1608269))), c_List_Olexord(_1608261, _1608271))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608261, _1608261)), hAPP(hAPP(c_Product__Type_OPair(_1608261, _1608261), _1608263), _1608267)), _1608271))), 41877 ^ _780205 : [(41878 ^ _780205) ^ [] : [-(_1608263 = _1608267)], (41880 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608261), tc_List_Olist(_1608261))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608261), tc_List_Olist(_1608261)), _1608265), _1608269)), c_List_Olexord(_1608261, _1608271))))]]], (41882 ^ _780205) ^ [_1608588, _1608590, _1608592, _1608594, _1608596, _1608598] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608588), tc_List_Olist(_1608588))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608588), tc_List_Olist(_1608588)), hAPP(hAPP(c_List_Olist_OCons(_1608588), _1608590), _1608592)), hAPP(hAPP(c_List_Olist_OCons(_1608588), _1608594), _1608596))), c_List_Olexord(_1608588, _1608598)))), 41883 ^ _780205 : [(41884 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608588, _1608588)), hAPP(hAPP(c_Product__Type_OPair(_1608588, _1608588), _1608590), _1608594)), _1608598))], (41886 ^ _780205) ^ [] : [_1608590 = _1608594, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608588), tc_List_Olist(_1608588))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608588), tc_List_Olist(_1608588)), _1608592), _1608596)), c_List_Olexord(_1608588, _1608598)))]]], (41894 ^ _780205) ^ [_1608982, _1608984, _1608986, _1608988] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608982), tc_List_Olist(_1608982))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608982), tc_List_Olist(_1608982)), _1608984), _1608986)), c_List_Olex(_1608982, _1608988))), 41897 ^ _780205 : [(41898 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608982), tc_List_Olist(_1608982))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608982), tc_List_Olist(_1608982)), _1608984), _1608986)), c_List_Olexord(_1608982, _1608988))))], (41900 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608982)), _1608984) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608982)), _1608986))]]], (41902 ^ _780205) ^ [_1609233, _1609235, _1609237, _1609239] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609233), tc_List_Olist(_1609233))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609233), tc_List_Olist(_1609233)), _1609235), _1609237)), c_List_Olex(_1609233, _1609239)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609233), tc_List_Olist(_1609233))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609233), tc_List_Olist(_1609233)), _1609235), _1609237)), c_List_Olexord(_1609233, _1609239))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609233)), _1609235) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609233)), _1609237)], (41912 ^ _780205) ^ [_1609520, _1609522, _1609524, _1609526, _1609528, _1609530] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609520, _1609520)), hAPP(hAPP(c_Product__Type_OPair(_1609520, _1609520), _1609522), _1609524)), c_Transitive__Closure_Ortrancl(_1609520, _1609526))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609520), tc_List_Olist(_1609520))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609520), tc_List_Olist(_1609520)), _1609528), _1609530)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1609520), c_List_Olistrel1(_1609520, _1609526)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609520), tc_List_Olist(_1609520))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609520), tc_List_Olist(_1609520)), hAPP(hAPP(c_List_Olist_OCons(_1609520), _1609522), _1609528)), hAPP(hAPP(c_List_Olist_OCons(_1609520), _1609524), _1609530))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1609520), c_List_Olistrel1(_1609520, _1609526)))))], (41922 ^ _780205) ^ [_1609881, _1609883, _1609885, _1609887] : [-(c_List_Olist_Olist__size(_1609881, _1609883, hAPP(hAPP(c_List_Olist_OCons(_1609881), _1609885), _1609887)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1609883, _1609885)), c_List_Olist_Olist__size(_1609881, _1609883, _1609887))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41924 ^ _780205) ^ [_1609941, _1609943, _1609945, _1609947] : [hBOOL(hAPP(hAPP(c_member(_1609941), _1609943), c_Wellfounded_Oacc(_1609941, _1609945))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1609941)), _1609947), c_Wellfounded_Oacc(tc_List_Olist(_1609941), c_List_Olistrel1(_1609941, _1609945)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1609941)), hAPP(hAPP(c_List_Olist_OCons(_1609941), _1609943), _1609947)), c_Wellfounded_Oacc(tc_List_Olist(_1609941), c_List_Olistrel1(_1609941, _1609945)))))], (41934 ^ _780205) ^ [_1610182, _1610184] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1610182), tc_List_Olist(_1610182)), tc_HOL_Obool)), c_List_Olistrel1(_1610182, c_Transitive__Closure_Ortrancl(_1610182, _1610184))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1610182), c_List_Olistrel1(_1610182, _1610184)))))], (41936 ^ _780205) ^ [_1610238, _1610240] : [-(c_List_Olistrel1(_1610238, hAPP(c_Relation_Oconverse(_1610238, _1610238), _1610240)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1610238), tc_List_Olist(_1610238)), c_List_Olistrel1(_1610238, _1610240)))], (41938 ^ _780205) ^ [_1610285, _1610287, _1610289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1610285, _1610285), tc_HOL_Obool)), _1610287), _1610289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1610285), tc_List_Olist(_1610285)), tc_HOL_Obool)), c_List_Olistrel1(_1610285, _1610287)), c_List_Olistrel1(_1610285, _1610289))))], (41944 ^ _780205) ^ [_1610436, _1610438, _1610440, _1610442, _1610444] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610436), tc_List_Olist(_1610436))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610436), tc_List_Olist(_1610436)), _1610438), _1610440)), c_List_Olistrel1(_1610436, _1610442))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610436), tc_List_Olist(_1610436))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610436), tc_List_Olist(_1610436)), hAPP(hAPP(c_List_Olist_OCons(_1610436), _1610444), _1610438)), hAPP(hAPP(c_List_Olist_OCons(_1610436), _1610444), _1610440))), c_List_Olistrel1(_1610436, _1610442))))], (41950 ^ _780205) ^ [_1610671, _1610673, _1610675, _1610677, _1610679] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610671), tc_List_Olist(_1610671))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610671), tc_List_Olist(_1610671)), _1610673), _1610675)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1610671), c_List_Olistrel1(_1610671, _1610677)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610671), tc_List_Olist(_1610671))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610671), tc_List_Olist(_1610671)), hAPP(hAPP(c_List_Olist_OCons(_1610671), _1610679), _1610673)), hAPP(hAPP(c_List_Olist_OCons(_1610671), _1610679), _1610675))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1610671), c_List_Olistrel1(_1610671, _1610677)))))], (41956 ^ _780205) ^ [_1610926, _1610928, _1610930, _1610932] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610926), tc_List_Olist(_1610926))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610926), tc_List_Olist(_1610926)), _1610928), _1610930)), c_List_Olistrel1(_1610926, _1610932))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610926)), _1610928) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610926)), _1610930))], (41962 ^ _780205) ^ [_1611095, _1611097, _1611099, _1611101] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611095), tc_List_Olist(_1611095))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611095), tc_List_Olist(_1611095)), _1611097), _1611099)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1611095), c_List_Olistrel1(_1611095, _1611101)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611095)), _1611097) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611095)), _1611099))], (41968 ^ _780205) ^ [_1611295, _1611297, _1611299, _1611301] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611295), tc_List_Olist(_1611295))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611295), tc_List_Olist(_1611295)), _1611297), _1611299)), c_List_Olistrel1(_1611295, hAPP(c_Relation_Oconverse(_1611295, _1611295), _1611301)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611295), tc_List_Olist(_1611295))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611295), tc_List_Olist(_1611295)), _1611297), _1611299)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1611295), tc_List_Olist(_1611295)), c_List_Olistrel1(_1611295, _1611301)))))], (41974 ^ _780205) ^ [_1611524, _1611526, _1611528, _1611530] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611524), tc_List_Olist(_1611524))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611524), tc_List_Olist(_1611524)), _1611526), _1611528)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1611524), tc_List_Olist(_1611524)), c_List_Olistrel1(_1611524, _1611530)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611524), tc_List_Olist(_1611524))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611524), tc_List_Olist(_1611524)), _1611526), _1611528)), c_List_Olistrel1(_1611524, hAPP(c_Relation_Oconverse(_1611524, _1611524), _1611530)))))], (41980 ^ _780205) ^ [_1611759, _1611761, _1611763, _1611765, _1611767] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611759, _1611759)), hAPP(hAPP(c_Product__Type_OPair(_1611759, _1611759), _1611761), _1611763)), _1611765)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611759), tc_List_Olist(_1611759))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611759), tc_List_Olist(_1611759)), hAPP(hAPP(c_List_Olist_OCons(_1611759), _1611761), _1611767)), hAPP(hAPP(c_List_Olist_OCons(_1611759), _1611763), _1611767))), c_List_Olistrel1(_1611759, _1611765))))], (41986 ^ _780205) ^ [_1611999, _1612001, _1612003, _1612005, _1612007, _1612009] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611999), tc_List_Olist(_1611999))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611999), tc_List_Olist(_1611999)), hAPP(hAPP(c_List_Olist_OCons(_1611999), _1612001), _1612003)), hAPP(hAPP(c_List_Olist_OCons(_1611999), _1612005), _1612007))), c_List_Olistrel1(_1611999, _1612009))), 41991 ^ _780205 : [(41992 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611999, _1611999)), hAPP(hAPP(c_Product__Type_OPair(_1611999, _1611999), _1612001), _1612005)), _1612009)))], (41994 ^ _780205) ^ [] : [-(_1612003 = _1612007)]], 41995 ^ _780205 : [(41996 ^ _780205) ^ [] : [-(_1612001 = _1612005)], (41998 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611999), tc_List_Olist(_1611999))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611999), tc_List_Olist(_1611999)), _1612003), _1612007)), c_List_Olistrel1(_1611999, _1612009))))]]], (42000 ^ _780205) ^ [_1612369, _1612371, _1612373, _1612375, _1612377, _1612379] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612369), tc_List_Olist(_1612369))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612369), tc_List_Olist(_1612369)), hAPP(hAPP(c_List_Olist_OCons(_1612369), _1612371), _1612373)), hAPP(hAPP(c_List_Olist_OCons(_1612369), _1612375), _1612377))), c_List_Olistrel1(_1612369, _1612379)))), 42001 ^ _780205 : [(42002 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612369, _1612369)), hAPP(hAPP(c_Product__Type_OPair(_1612369, _1612369), _1612371), _1612375)), _1612379)), _1612373 = _1612377], (42008 ^ _780205) ^ [] : [_1612371 = _1612375, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612369), tc_List_Olist(_1612369))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612369), tc_List_Olist(_1612369)), _1612373), _1612377)), c_List_Olistrel1(_1612369, _1612379)))]]], (42016 ^ _780205) ^ [_1612797, _1612799, _1612801, _1612803] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1612797), tc_List_Olist(_1612797), c_List_Olistrel(_1612797, _1612799)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1612797)), hAPP(hAPP(c_List_Olist_OCons(_1612797), _1612801), _1612803)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1612797), tc_HOL_Obool)))) = c_List_Oset__Cons(_1612797, hAPP(c_Relation_OImage(_1612797, _1612797, _1612799), hAPP(hAPP(c_Set_Oinsert(_1612797), _1612801), c_Orderings_Obot__class_Obot(tc_fun(_1612797, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1612797), tc_List_Olist(_1612797), c_List_Olistrel(_1612797, _1612799)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1612797)), _1612803), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1612797), tc_HOL_Obool))))))], (42018 ^ _780205) ^ [_1612919, _1612921, _1612923] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612919, _1612919)), hAPP(hAPP(c_Product__Type_OPair(_1612919, _1612919), 42019 ^ [_1612919, _1612921, _1612923]), 42019 ^ [_1612919, _1612921, _1612923])), _1612921))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612919), tc_List_Olist(_1612919))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612919), tc_List_Olist(_1612919)), _1612923), _1612923)), c_List_Olexord(_1612919, _1612921)))], (42025 ^ _780205) ^ [_1613094, _1613096, _1613098] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613094), tc_List_Olist(_1613094))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613094), tc_List_Olist(_1613094)), _1613096), _1613096)), c_List_Olistrel(_1613094, c_Transitive__Closure_Ortrancl(_1613094, _1613098)))))], (42027 ^ _780205) ^ [_1613154, _1613156, _1613158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1613154, _1613154), tc_HOL_Obool)), _1613156), _1613158)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1613154), tc_List_Olist(_1613154)), tc_HOL_Obool)), c_List_Olistrel(_1613154, _1613156)), c_List_Olistrel(_1613154, _1613158))))], (42033 ^ _780205) ^ [_1613305, _1613307] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1613305), tc_List_Olist(_1613305)), tc_HOL_Obool)), c_List_Olistrel(_1613305, _1613307)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1613305), c_List_Olistrel1(_1613305, _1613307)))))], (42035 ^ _780205) ^ [_1613358, _1613360, _1613362, _1613364] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613358), tc_List_Olist(_1613358))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613358), tc_List_Olist(_1613358)), _1613360), _1613362)), c_List_Olistrel(_1613358, _1613364))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613358)), _1613360) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613358)), _1613362))], (42041 ^ _780205) ^ [_1613527, _1613529, _1613531, _1613533, _1613535] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613527), tc_List_Olist(_1613527))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613527), tc_List_Olist(_1613527)), _1613529), _1613531)), c_List_Olistrel(_1613527, c_Transitive__Closure_Ortrancl(_1613527, _1613533)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613527), tc_List_Olist(_1613527))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613527), tc_List_Olist(_1613527)), _1613531), _1613535)), c_List_Olistrel(_1613527, c_Transitive__Closure_Ortrancl(_1613527, _1613533)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613527), tc_List_Olist(_1613527))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613527), tc_List_Olist(_1613527)), _1613529), _1613535)), c_List_Olistrel(_1613527, c_Transitive__Closure_Ortrancl(_1613527, _1613533)))))], (42051 ^ _780205) ^ [_1613866, _1613868] : [-(c_List_Olistrel(_1613866, c_Transitive__Closure_Ortrancl(_1613866, _1613868)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1613866), c_List_Olistrel1(_1613866, _1613868)))], (42053 ^ _780205) ^ [_1613905, _1613907, _1613909, _1613911] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613905), tc_List_Olist(_1613905))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613905), tc_List_Olist(_1613905)), _1613907), _1613909)), c_List_Olistrel1(_1613905, _1613911))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613905), tc_List_Olist(_1613905))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613905), tc_List_Olist(_1613905)), _1613907), _1613909)), c_List_Olistrel(_1613905, c_Transitive__Closure_Ortrancl(_1613905, _1613911)))))], (42059 ^ _780205) ^ [_1614112, _1614114, _1614116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1614112, _1614112), tc_HOL_Obool)), _1614114), _1614116)), c_Relation_Orefl__on(_1614112, c_Orderings_Otop__class_Otop(tc_fun(_1614112, tc_HOL_Obool)), _1614116), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1614112), tc_List_Olist(_1614112)), tc_HOL_Obool)), c_List_Olistrel1(_1614112, _1614114)), c_List_Olistrel(_1614112, _1614116))))], (42069 ^ _780205) ^ [_1614329, _1614331, _1614333, _1614335] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614329), tc_List_Olist(_1614329))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614329), tc_List_Olist(_1614329)), _1614331), _1614333)), c_List_Olistrel(_1614329, _1614335))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614329), tc_List_Olist(_1614329))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614329), tc_List_Olist(_1614329)), _1614331), _1614333)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1614329), c_List_Olistrel1(_1614329, _1614335)))))], (42075 ^ _780205) ^ [_1614540, _1614542, _1614544, _1614546, _1614548, _1614550] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614540, _1614540)), hAPP(hAPP(c_Product__Type_OPair(_1614540, _1614540), _1614542), _1614544)), _1614546)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614540), tc_List_Olist(_1614540))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614540), tc_List_Olist(_1614540)), _1614548), _1614550)), c_List_Olistrel(_1614540, _1614546))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614540), tc_List_Olist(_1614540))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614540), tc_List_Olist(_1614540)), hAPP(hAPP(c_List_Olist_OCons(_1614540), _1614542), _1614548)), hAPP(hAPP(c_List_Olist_OCons(_1614540), _1614544), _1614550))), c_List_Olistrel(_1614540, _1614546))))], (42085 ^ _780205) ^ [_1614896, _1614898, _1614900, _1614902] : [c_List_Olistrelp(_1614896, hAPP(hAPP(c_COMBC(_1614896, tc_fun(tc_prod(_1614896, _1614896), tc_HOL_Obool), tc_fun(_1614896, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614896, tc_fun(tc_fun(tc_prod(_1614896, _1614896), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1614896, _1614896), tc_HOL_Obool), tc_fun(_1614896, tc_HOL_Obool)), _1614896), c_COMBC(_1614896, tc_fun(tc_prod(_1614896, _1614896), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614896, tc_prod(_1614896, _1614896)), tc_fun(_1614896, tc_fun(tc_fun(tc_prod(_1614896, _1614896), tc_HOL_Obool), tc_HOL_Obool)), _1614896), hAPP(c_COMBB(tc_prod(_1614896, _1614896), tc_fun(tc_fun(tc_prod(_1614896, _1614896), tc_HOL_Obool), tc_HOL_Obool), _1614896), c_member(tc_prod(_1614896, _1614896)))), c_Product__Type_OPair(_1614896, _1614896)))), _1614898), _1614900, _1614902), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614896), tc_List_Olist(_1614896))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614896), tc_List_Olist(_1614896)), _1614900), _1614902)), c_List_Olistrel(_1614896, _1614898))))], (42091 ^ _780205) ^ [_1615273, _1615275, _1615277, _1615279] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615273), tc_List_Olist(_1615273))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615273), tc_List_Olist(_1615273)), _1615277), _1615279)), c_List_Olistrel(_1615273, _1615275))), -(c_List_Olistrelp(_1615273, hAPP(hAPP(c_COMBC(_1615273, tc_fun(tc_prod(_1615273, _1615273), tc_HOL_Obool), tc_fun(_1615273, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615273, tc_fun(tc_fun(tc_prod(_1615273, _1615273), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1615273, _1615273), tc_HOL_Obool), tc_fun(_1615273, tc_HOL_Obool)), _1615273), c_COMBC(_1615273, tc_fun(tc_prod(_1615273, _1615273), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615273, tc_prod(_1615273, _1615273)), tc_fun(_1615273, tc_fun(tc_fun(tc_prod(_1615273, _1615273), tc_HOL_Obool), tc_HOL_Obool)), _1615273), hAPP(c_COMBB(tc_prod(_1615273, _1615273), tc_fun(tc_fun(tc_prod(_1615273, _1615273), tc_HOL_Obool), tc_HOL_Obool), _1615273), c_member(tc_prod(_1615273, _1615273)))), c_Product__Type_OPair(_1615273, _1615273)))), _1615275), _1615277, _1615279))], (42097 ^ _780205) ^ [_1615656, _1615658, _1615660, _1615662, _1615664] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615656), tc_List_Olist(_1615656))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615656), tc_List_Olist(_1615656)), _1615658), hAPP(hAPP(c_List_Olist_OCons(_1615656), _1615660), _1615662))), c_List_Olistrel(_1615656, _1615664))), 42102 ^ _780205 : [(42103 ^ _780205) ^ [] : [-(_1615658 = hAPP(hAPP(c_List_Olist_OCons(_1615656), 42100 ^ [_1615656, _1615658, _1615660, _1615662, _1615664]), 42101 ^ [_1615656, _1615658, _1615660, _1615662, _1615664]))], (42105 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615656, _1615656)), hAPP(hAPP(c_Product__Type_OPair(_1615656, _1615656), 42100 ^ [_1615656, _1615658, _1615660, _1615662, _1615664]), _1615660)), _1615664)))], (42107 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615656), tc_List_Olist(_1615656))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615656), tc_List_Olist(_1615656)), 42101 ^ [_1615656, _1615658, _1615660, _1615662, _1615664]), _1615662)), c_List_Olistrel(_1615656, _1615664))))]]], (42109 ^ _780205) ^ [_1616045, _1616047, _1616049, _1616051, _1616053, _1616055] : [hBOOL(hAPP(hAPP(_1616045, _1616047), _1616049)), c_List_Olistrelp(_1616051, _1616045, _1616053, _1616055), -(c_List_Olistrelp(_1616051, _1616045, hAPP(hAPP(c_List_Olist_OCons(_1616051), _1616047), _1616053), hAPP(hAPP(c_List_Olist_OCons(_1616051), _1616049), _1616055)))], (42119 ^ _780205) ^ [_1616267, _1616269, _1616271, _1616273, _1616275, _1616277] : [c_List_Olistrelp(_1616267, _1616269, hAPP(hAPP(c_List_Olist_OCons(_1616267), _1616271), _1616273), hAPP(hAPP(c_List_Olist_OCons(_1616267), _1616275), _1616277)), 42122 ^ _780205 : [(42123 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1616269, _1616271), _1616275)))], (42125 ^ _780205) ^ [] : [-(c_List_Olistrelp(_1616267, _1616269, _1616273, _1616277))]]], (42127 ^ _780205) ^ [_1616424, _1616426, _1616428, _1616430, _1616432, _1616434] : [-(c_List_Olistrelp(_1616424, _1616426, hAPP(hAPP(c_List_Olist_OCons(_1616424), _1616428), _1616430), hAPP(hAPP(c_List_Olist_OCons(_1616424), _1616432), _1616434))), hBOOL(hAPP(hAPP(_1616426, _1616428), _1616432)), c_List_Olistrelp(_1616424, _1616426, _1616430, _1616434)], (42137 ^ _780205) ^ [_1616621, _1616623, _1616625, _1616627, _1616629] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616621), tc_List_Olist(_1616621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616621), tc_List_Olist(_1616621)), hAPP(hAPP(c_List_Olist_OCons(_1616621), _1616623), _1616625)), _1616627)), c_List_Olistrel(_1616621, _1616629))), 42142 ^ _780205 : [(42143 ^ _780205) ^ [] : [-(_1616627 = hAPP(hAPP(c_List_Olist_OCons(_1616621), 42140 ^ [_1616621, _1616623, _1616625, _1616627, _1616629]), 42141 ^ [_1616621, _1616623, _1616625, _1616627, _1616629]))], (42145 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616621, _1616621)), hAPP(hAPP(c_Product__Type_OPair(_1616621, _1616621), _1616623), 42140 ^ [_1616621, _1616623, _1616625, _1616627, _1616629])), _1616629)))], (42147 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616621), tc_List_Olist(_1616621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616621), tc_List_Olist(_1616621)), _1616625), 42141 ^ [_1616621, _1616623, _1616625, _1616627, _1616629])), c_List_Olistrel(_1616621, _1616629))))]]], (42149 ^ _780205) ^ [_1617010, _1617012, _1617014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1617010, _1617010), tc_HOL_Obool)), _1617012), hAPP(hAPP(c_Product__Type_OSigma(_1617010, _1617010), _1617014), hAPP(c_COMBK(tc_fun(_1617010, tc_HOL_Obool), _1617010), _1617014)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1617010), tc_List_Olist(_1617010)), tc_HOL_Obool)), c_List_Olistrel(_1617010, _1617012)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1617010), tc_List_Olist(_1617010)), c_List_Olists(_1617010, _1617014)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1617010), tc_HOL_Obool), tc_List_Olist(_1617010)), c_List_Olists(_1617010, _1617014))))))], (42155 ^ _780205) ^ [_1617255] : [-(c_List_Olists(_1617255, c_Orderings_Otop__class_Otop(tc_fun(_1617255, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1617255), tc_HOL_Obool)))], (42157 ^ _780205) ^ [_1617293, _1617295, _1617297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1617293, tc_HOL_Obool)), _1617295), _1617297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1617293), tc_HOL_Obool)), c_List_Olists(_1617293, _1617295)), c_List_Olists(_1617293, _1617297))))], (42163 ^ _780205) ^ [_1617428, _1617430, _1617432] : [c_Equiv__Relations_Oequiv(_1617428, _1617430, _1617432), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1617428), c_List_Olists(_1617428, _1617430), c_List_Olistrel(_1617428, _1617432)))], (42169 ^ _780205) ^ [_1617527, _1617529, _1617531] : [c_Relation_Orefl__on(_1617527, _1617529, _1617531), -(c_Relation_Orefl__on(tc_List_Olist(_1617527), c_List_Olists(_1617527, _1617529), c_List_Olistrel(_1617527, _1617531)))], (42175 ^ _780205) ^ [_1617647, _1617649, _1617651, _1617653] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1617647)), hAPP(hAPP(c_List_Olist_OCons(_1617647), _1617649), _1617651)), c_List_Olists(_1617647, _1617653))), 42178 ^ _780205 : [(42179 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617647), _1617649), _1617653)))], (42181 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1617647)), _1617651), c_List_Olists(_1617647, _1617653))))]]], (42183 ^ _780205) ^ [_1617828, _1617830, _1617832, _1617834] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1617828)), hAPP(hAPP(c_List_Olist_OCons(_1617828), _1617830), _1617832)), c_List_Olists(_1617828, _1617834)))), hBOOL(hAPP(hAPP(c_member(_1617828), _1617830), _1617834)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1617828)), _1617832), c_List_Olists(_1617828, _1617834)))], (42193 ^ _780205) ^ [_1618045, _1618047, _1618049] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1618045)), _1618047), c_Wellfounded_Oacc(tc_List_Olist(_1618045), c_List_Olistrel1(_1618045, _1618049)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1618045)), _1618047), c_List_Olists(_1618045, c_Wellfounded_Oacc(_1618045, _1618049)))))], (42199 ^ _780205) ^ [_1618188, _1618190, _1618192] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1618188)), _1618190), c_List_Olists(_1618188, c_Wellfounded_Oacc(_1618188, _1618192)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1618188)), _1618190), c_Wellfounded_Oacc(tc_List_Olist(_1618188), c_List_Olistrel1(_1618188, _1618192)))))], (42205 ^ _780205) ^ [_1618352, _1618354, _1618356, _1618358] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618352), tc_List_Olist(_1618352))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618352), tc_List_Olist(_1618352)), _1618354), _1618356)), c_List_Olistrel(_1618352, _1618358))), 42208 ^ _780205 : [(42209 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618352)), _1618354) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618352)), _1618356))], (42211 ^ _780205) ^ [_1618581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618581), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618352)), _1618354))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618352, _1618352)), hAPP(hAPP(c_Product__Type_OPair(_1618352, _1618352), hAPP(hAPP(c_List_Onth(_1618352), _1618354), _1618581)), hAPP(hAPP(c_List_Onth(_1618352), _1618356), _1618581))), _1618358)))]]], (42217 ^ _780205) ^ [_1618760, _1618762, _1618764, _1618766] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618760), tc_List_Olist(_1618760))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618760), tc_List_Olist(_1618760)), _1618762), _1618764)), c_List_Olistrel(_1618760, _1618766)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618760)), _1618762) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618760)), _1618764), 42223 ^ _780205 : [(42224 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42222 ^ [_1618760, _1618762, _1618764, _1618766]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618760)), _1618762))))], (42226 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618760, _1618760)), hAPP(hAPP(c_Product__Type_OPair(_1618760, _1618760), hAPP(hAPP(c_List_Onth(_1618760), _1618762), 42222 ^ [_1618760, _1618762, _1618764, _1618766])), hAPP(hAPP(c_List_Onth(_1618760), _1618764), 42222 ^ [_1618760, _1618762, _1618764, _1618766]))), _1618766))]]], (42230 ^ _780205) ^ [_1619204, _1619206, _1619208, _1619210] : [42233 ^ _780205 : [(42234 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619204, _1619204)), hAPP(hAPP(c_Product__Type_OPair(_1619204, _1619204), 42231 ^ [_1619204, _1619206, _1619208, _1619210]), 42232 ^ [_1619204, _1619206, _1619208, _1619210])), _1619206))], (42236 ^ _780205) ^ [] : [42231 ^ [_1619204, _1619206, _1619208, _1619210] = 42232 ^ [_1619204, _1619206, _1619208, _1619210]], (42238 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619204, _1619204)), hAPP(hAPP(c_Product__Type_OPair(_1619204, _1619204), 42232 ^ [_1619204, _1619206, _1619208, _1619210]), 42231 ^ [_1619204, _1619206, _1619208, _1619210])), _1619206))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619204), tc_List_Olist(_1619204))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619204), tc_List_Olist(_1619204)), _1619208), _1619210)), c_List_Olexord(_1619204, _1619206)))), -(_1619208 = _1619210), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619204), tc_List_Olist(_1619204))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619204), tc_List_Olist(_1619204)), _1619210), _1619208)), c_List_Olexord(_1619204, _1619206))))], (42250 ^ _780205) ^ [_1619760] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1619760)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1619760), tc_HOL_Obool))))], (42252 ^ _780205) ^ [_1619814, _1619816, _1619818] : [_1619814 = _1619816, 42255 ^ _780205 : [(42256 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619818)), _1619814) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619818)), _1619816))], (42258 ^ _780205) ^ [_1619962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619962), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619818)), _1619814))), -(hAPP(hAPP(c_List_Onth(_1619818), _1619814), _1619962) = hAPP(hAPP(c_List_Onth(_1619818), _1619816), _1619962))]]], (42264 ^ _780205) ^ [_1620101, _1620103, _1620105] : [-(_1620101 = _1620103), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620105)), _1620101) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620105)), _1620103), 42270 ^ _780205 : [(42271 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42269 ^ [_1620101, _1620103, _1620105]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620105)), _1620101))))], (42273 ^ _780205) ^ [] : [hAPP(hAPP(c_List_Onth(_1620105), _1620101), 42269 ^ [_1620101, _1620103, _1620105]) = hAPP(hAPP(c_List_Onth(_1620105), _1620103), 42269 ^ [_1620101, _1620103, _1620105])]]], (42277 ^ _780205) ^ [_1620416, _1620418, _1620420] : [-(hAPP(hAPP(c_List_Onth(_1620416), hAPP(hAPP(c_List_Olist_OCons(_1620416), _1620418), _1620420)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1620418)], (42279 ^ _780205) ^ [_1620459, _1620461, _1620463, _1620465] : [-(hAPP(hAPP(c_List_Onth(_1620459), hAPP(hAPP(c_List_Olist_OCons(_1620459), _1620461), _1620463)), hAPP(c_Nat_OSuc, _1620465)) = hAPP(hAPP(c_List_Onth(_1620459), _1620463), _1620465))], (42281 ^ _780205) ^ [_1620515, _1620517, _1620519, _1620521] : [-(hAPP(hAPP(c_List_Onth(_1620515), hAPP(hAPP(c_List_Olist_OCons(_1620515), _1620517), _1620519)), _1620521) = c_Nat_Onat_Onat__case(_1620515, _1620517, hAPP(c_List_Onth(_1620515), _1620519), _1620521))], (42283 ^ _780205) ^ [_1620585, _1620587, _1620589, _1620591] : [_1620585 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1620587), hAPP(hAPP(c_List_Olist_OCons(_1620587), _1620589), _1620591)), _1620585) = _1620589)], (42289 ^ _780205) ^ [_1620692, _1620694, _1620696, _1620698] : [-(_1620692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1620694), hAPP(hAPP(c_List_Olist_OCons(_1620694), _1620696), _1620698)), _1620692) = hAPP(hAPP(c_List_Onth(_1620694), _1620698), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1620692), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (42295 ^ _780205) ^ [_1620779, _1620781, _1620783, _1620785] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1620779) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1620781), hAPP(hAPP(c_List_Olist_OCons(_1620781), _1620783), _1620785)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1620779)) = _1620783)], (42301 ^ _780205) ^ [_1620898, _1620900, _1620902, _1620904] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1620898) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1620900), hAPP(hAPP(c_List_Olist_OCons(_1620900), _1620902), _1620904)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1620898)) = hAPP(hAPP(c_List_Onth(_1620900), _1620904), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1620898)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (42307 ^ _780205) ^ [_1621000, _1621002, _1621004, _1621006] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621000), tc_List_Olist(_1621000))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621000), tc_List_Olist(_1621000)), _1621002), _1621004)), c_List_Olexord(_1621000, _1621006))), 42312 ^ _780205 : [(42313 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621000)), _1621002)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621000)), _1621004))))], (42315 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1621000), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621000)), _1621002)), _1621004) = _1621002)]], 42317 ^ _780205 : [(42318 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42316 ^ [_1621000, _1621002, _1621004, _1621006]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621000)), _1621002)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621000)), _1621004)))))], (42320 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1621000), 42316 ^ [_1621000, _1621002, _1621004, _1621006]), _1621002) = hAPP(hAPP(c_List_Otake(_1621000), 42316 ^ [_1621000, _1621002, _1621004, _1621006]), _1621004))], (42322 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621000, _1621000)), hAPP(hAPP(c_Product__Type_OPair(_1621000, _1621000), hAPP(hAPP(c_List_Onth(_1621000), _1621002), 42316 ^ [_1621000, _1621002, _1621004, _1621006])), hAPP(hAPP(c_List_Onth(_1621000), _1621004), 42316 ^ [_1621000, _1621002, _1621004, _1621006]))), _1621006)))]]], (42324 ^ _780205) ^ [_1621540, _1621542, _1621544, _1621546] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621540), tc_List_Olist(_1621540))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621540), tc_List_Olist(_1621540)), _1621542), _1621544)), c_List_Olexord(_1621540, _1621546)))), 42325 ^ _780205 : [(42326 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621540)), _1621542)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621540)), _1621544))), hAPP(hAPP(c_List_Otake(_1621540), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621540)), _1621542)), _1621544) = _1621542], (42332 ^ _780205) ^ [_1621847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1621847), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621540)), _1621542)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621540)), _1621544)))), hAPP(hAPP(c_List_Otake(_1621540), _1621847), _1621542) = hAPP(hAPP(c_List_Otake(_1621540), _1621847), _1621544), hBOOL(hAPP(hAPP(c_member(tc_prod(_1621540, _1621540)), hAPP(hAPP(c_Product__Type_OPair(_1621540, _1621540), hAPP(hAPP(c_List_Onth(_1621540), _1621542), _1621847)), hAPP(hAPP(c_List_Onth(_1621540), _1621544), _1621847))), _1621546))]]], (42344 ^ _780205) ^ [_1622201, _1622203, _1622205] : [-(hAPP(c_List_Oset(_1622201), c_List_Osublist(_1622201, _1622203, _1622205)) = hAPP(c_Set_OCollect(_1622201), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1622201), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1622201, 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)), _1622201), 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)), _1622201), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1622201, tc_fun(tc_Nat_Onat, _1622201), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1622201, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1622201), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1622201), c_COMBB(_1622201, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1622201), _1622203))))), 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(_1622201)), _1622203)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1622205))))))], (42346 ^ _780205) ^ [_1622345, _1622347] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1622345), hAPP(c_List_Oset(_1622345), _1622347))))], (42348 ^ _780205) ^ [_1622379, _1622381, _1622383] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622379, tc_HOL_Obool)), hAPP(c_List_Oset(_1622379), _1622381)), hAPP(c_List_Oset(_1622379), hAPP(hAPP(c_List_Olist_OCons(_1622379), _1622383), _1622381)))))], (42350 ^ _780205) ^ [_1622434, _1622436, _1622438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622434)), _1622436)), _1622438)), -(hAPP(hAPP(c_List_Otake(_1622434), _1622438), _1622436) = _1622436)], (42356 ^ _780205) ^ [_1622553, _1622555, _1622557] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622553, tc_HOL_Obool)), hAPP(c_List_Oset(_1622553), hAPP(hAPP(c_List_Otake(_1622553), _1622555), _1622557))), hAPP(c_List_Oset(_1622553), _1622557))))], (42358 ^ _780205) ^ [_1622608, _1622610, _1622612, _1622614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1622608), _1622610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622612, tc_HOL_Obool)), hAPP(c_List_Oset(_1622612), hAPP(hAPP(c_List_Otake(_1622612), _1622608), _1622614))), hAPP(c_List_Oset(_1622612), hAPP(hAPP(c_List_Otake(_1622612), _1622610), _1622614)))))], (42364 ^ _780205) ^ [_1622771, _1622773, _1622775] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622771, tc_HOL_Obool)), hAPP(c_List_Oset(_1622771), c_List_Osublist(_1622771, _1622773, _1622775))), hAPP(c_List_Oset(_1622771), _1622773))))], (42366 ^ _780205) ^ [_1622822, _1622824, _1622826, _1622828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622822), _1622824)), -(hAPP(hAPP(c_List_Onth(_1622826), hAPP(hAPP(c_List_Otake(_1622826), _1622824), _1622828)), _1622822) = hAPP(hAPP(c_List_Onth(_1622826), _1622828), _1622822))], (42372 ^ _780205) ^ [_1622960, _1622962, _1622964, _1622966] : [-(hBOOL(hAPP(hAPP(c_member(_1622960), _1622962), hAPP(c_List_Oset(_1622960), _1622964)))), hBOOL(hAPP(hAPP(c_member(_1622960), _1622962), hAPP(c_List_Oset(_1622960), c_List_Osublist(_1622960, _1622964, _1622966))))], (42378 ^ _780205) ^ [_1623084, _1623086, _1623088, _1623090] : [hBOOL(hAPP(hAPP(c_member(_1623084), _1623086), hAPP(c_List_Oset(_1623084), hAPP(hAPP(c_List_Otake(_1623084), _1623088), _1623090)))), -(hBOOL(hAPP(hAPP(c_member(_1623084), _1623086), hAPP(c_List_Oset(_1623084), _1623090))))], (42384 ^ _780205) ^ [_1623229, _1623231, _1623233, _1623235] : [hBOOL(hAPP(hAPP(c_member(_1623229), _1623231), hAPP(c_List_Oset(_1623229), c_List_Osublist(_1623229, _1623233, _1623235)))), -(hBOOL(hAPP(hAPP(c_member(_1623229), _1623231), hAPP(c_List_Oset(_1623229), _1623233))))], (42390 ^ _780205) ^ [_1623366, _1623368, _1623370, _1623372] : [hBOOL(hAPP(hAPP(c_member(_1623366), _1623368), hAPP(c_List_Oset(_1623366), hAPP(hAPP(c_List_Olist_OCons(_1623366), _1623370), _1623372)))), -(_1623368 = _1623370), -(hBOOL(hAPP(hAPP(c_member(_1623366), _1623368), hAPP(c_List_Oset(_1623366), _1623372))))], (42400 ^ _780205) ^ [_1623524, _1623526, _1623528, _1623530] : [-(hAPP(hAPP(c_List_Otake(_1623524), hAPP(c_Nat_OSuc, _1623526)), hAPP(hAPP(c_List_Olist_OCons(_1623524), _1623528), _1623530)) = hAPP(hAPP(c_List_Olist_OCons(_1623524), _1623528), hAPP(hAPP(c_List_Otake(_1623524), _1623526), _1623530)))], (42402 ^ _780205) ^ [_1623588, _1623590, _1623592] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623588)), hAPP(hAPP(c_List_Otake(_1623588), _1623590), _1623592)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623588)), _1623592)), _1623590))], (42404 ^ _780205) ^ [_1623643, _1623645, _1623647, _1623649] : [-(hAPP(hAPP(c_List_Otake(_1623643), _1623645), hAPP(hAPP(c_List_Otake(_1623643), _1623647), _1623649)) = hAPP(hAPP(c_List_Otake(_1623643), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1623645), _1623647)), _1623649))], (42406 ^ _780205) ^ [_1623702, _1623704, _1623706] : [-(hAPP(c_List_Oset(_1623702), hAPP(hAPP(c_List_Olist_OCons(_1623702), _1623704), _1623706)) = hAPP(hAPP(c_Set_Oinsert(_1623702), _1623704), hAPP(c_List_Oset(_1623702), _1623706)))], (42408 ^ _780205) ^ [_1623755, _1623757, _1623759] : [-(c_List_Osublist(_1623755, _1623757, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1623759)) = hAPP(hAPP(c_List_Otake(_1623755), _1623759), _1623757))], (42410 ^ _780205) ^ [_1623797, _1623799] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1623797), hAPP(c_List_Oset(_1623797), _1623799))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623797)), _1623799))))], (42412 ^ _780205) ^ [_1623862, _1623864, _1623866] : [42414 ^ _780205 : [(42415 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623862), 42413 ^ [_1623862, _1623864, _1623866]), hAPP(c_List_Oset(_1623862), _1623864))))], (42417 ^ _780205) ^ [] : [hBOOL(hAPP(_1623866, 42413 ^ [_1623862, _1623864, _1623866]))]], 42418 ^ _780205 : [(42419 ^ _780205) ^ [_1624046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624046), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623862)), _1623864))), -(hBOOL(hAPP(_1623866, hAPP(hAPP(c_List_Onth(_1623862), _1623864), _1624046))))]]], (42425 ^ _780205) ^ [_1624173, _1624175, _1624177] : [42427 ^ _780205 : [(42428 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42426 ^ [_1624173, _1624175, _1624177]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624173)), _1624175))))], (42430 ^ _780205) ^ [] : [hBOOL(hAPP(_1624177, hAPP(hAPP(c_List_Onth(_1624173), _1624175), 42426 ^ [_1624173, _1624175, _1624177])))]], 42431 ^ _780205 : [(42432 ^ _780205) ^ [_1624375] : [hBOOL(hAPP(hAPP(c_member(_1624173), _1624375), hAPP(c_List_Oset(_1624173), _1624175))), -(hBOOL(hAPP(_1624177, _1624375)))]]], (42438 ^ _780205) ^ [_1624492, _1624494, _1624496, _1624498, _1624500] : [hBOOL(hAPP(hAPP(c_member(_1624492), _1624494), hAPP(c_List_Oset(_1624492), _1624496))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624498), hAPP(_1624500, _1624494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624498), c_List_Olist_Olist__size(_1624492, _1624500, _1624496))))], (42448 ^ _780205) ^ [_1624691, _1624693, _1624695, _1624697, _1624699] : [hBOOL(hAPP(hAPP(c_member(_1624691), _1624693), hAPP(c_List_Oset(_1624691), _1624695))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1624697), hAPP(_1624699, _1624693))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1624697), c_List_Olist_Olist__size(_1624691, _1624699, _1624695))))], (42468 ^ _780205) ^ [_1625135, _1625137, _1625139] : [42470 ^ _780205 : [(42471 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625135), 42469 ^ [_1625135, _1625137, _1625139]), hAPP(c_List_Oset(_1625135), _1625137))))], (42473 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1625135), 42469 ^ [_1625135, _1625137, _1625139]), _1625139))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1625135)), _1625137), c_List_Olists(_1625135, _1625139))))], (42458 ^ _780205) ^ [_1624908, _1624910, _1624912] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1624908)), _1624910), c_List_Olists(_1624908, _1624912))), 42461 ^ _780205 : [(42462 ^ _780205) ^ [_1625016] : [hBOOL(hAPP(hAPP(c_member(_1624908), _1625016), hAPP(c_List_Oset(_1624908), _1624910))), -(hBOOL(hAPP(hAPP(c_member(_1624908), _1625016), _1624912)))]]], (42477 ^ _780205) ^ [_1625355, _1625357, _1625359] : [hBOOL(hAPP(hAPP(c_member(_1625355), _1625357), hAPP(c_List_Oset(_1625355), _1625359))), -(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(_1625355)), _1625359))))], (42483 ^ _780205) ^ [_1625494, _1625496, _1625498] : [hBOOL(hAPP(hAPP(c_member(_1625494), _1625496), hAPP(c_List_Oset(_1625494), _1625498))), 42487 ^ _780205 : [(42488 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42486 ^ [_1625494, _1625496, _1625498]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625494)), _1625498))))], (42490 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1625494), _1625498), 42486 ^ [_1625494, _1625496, _1625498]) = _1625496)]]], (42492 ^ _780205) ^ [_1625682, _1625684, _1625686] : [-(hBOOL(hAPP(hAPP(c_member(_1625682), _1625684), hAPP(c_List_Oset(_1625682), _1625686)))), 42493 ^ _780205 : [(42494 ^ _780205) ^ [_1625756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625756), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625682)), _1625686))), hAPP(hAPP(c_List_Onth(_1625682), _1625686), _1625756) = _1625684]]], (42502 ^ _780205) ^ [_1625918, _1625920, _1625922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625918), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625920)), _1625922))), -(hBOOL(hAPP(hAPP(c_member(_1625920), hAPP(hAPP(c_List_Onth(_1625920), _1625922), _1625918)), hAPP(c_List_Oset(_1625920), _1625922))))], (42508 ^ _780205) ^ [_1626061, _1626063] : [-(c_List_Olists(_1626061, _1626063) = hAPP(c_Set_OCollect(tc_List_Olist(_1626061)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1626061), tc_fun(_1626061, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1626061, tc_HOL_Obool), tc_fun(tc_fun(_1626061, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1626061)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1626061, tc_HOL_Obool))), c_List_Oset(_1626061))), _1626063)))], (42510 ^ _780205) ^ [_1626139, _1626141] : [-(hAPP(c_List_Oset(_1626139), _1626141) = hAPP(c_Set_OCollect(_1626139), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1626139), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1626139, 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)), _1626139), 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)), _1626139), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1626139, tc_fun(tc_Nat_Onat, _1626139), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1626139, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1626139), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1626139), c_COMBB(_1626139, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1626139), _1626141))))), 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(_1626139)), _1626141))))))], (42512 ^ _780205) ^ [_1626265, _1626267, _1626269] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1626265), _1626267)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1626265)), hAPP(c_Set_OCollect(tc_List_Olist(_1626265)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1626265), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1626265)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1626265), tc_fun(_1626265, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1626265, tc_HOL_Obool), tc_fun(tc_fun(_1626265, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1626265)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1626265, tc_HOL_Obool))), c_List_Oset(_1626265))), _1626267))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1626265), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1626265)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1626265)))), _1626269))))))], (42518 ^ _780205) ^ [_1626568, _1626570, _1626572] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1626568), _1626570)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1626568)), hAPP(c_Set_OCollect(tc_List_Olist(_1626568)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1626568), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1626568)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1626568), tc_fun(_1626568, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1626568, tc_HOL_Obool), tc_fun(tc_fun(_1626568, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1626568)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1626568, tc_HOL_Obool))), c_List_Oset(_1626568))), _1626570))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1626568), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1626568)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1626568)))), _1626572))))))], (42524 ^ _780205) ^ [_1626892, _1626894, _1626896, _1626898] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1626892), tc_List_Olist(_1626892))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626892), tc_List_Olist(_1626892)), _1626894), _1626896)), c_List_Olistrel(_1626892, _1626898))), 42527 ^ _780205 : [(42528 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626892)), _1626894) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626892)), _1626896))], (42530 ^ _780205) ^ [_1627228] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1626892, _1626892)), _1627228), hAPP(c_List_Oset(tc_prod(_1626892, _1626892)), hAPP(hAPP(c_List_Ozip(_1626892, _1626892), _1626894), _1626896)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1626892, _1626892, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1626892, tc_fun(tc_prod(_1626892, _1626892), tc_HOL_Obool), tc_fun(_1626892, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1626892, tc_fun(tc_fun(tc_prod(_1626892, _1626892), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1626892, _1626892), tc_HOL_Obool), tc_fun(_1626892, tc_HOL_Obool)), _1626892), c_COMBC(_1626892, tc_fun(tc_prod(_1626892, _1626892), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1626892, tc_prod(_1626892, _1626892)), tc_fun(_1626892, tc_fun(tc_fun(tc_prod(_1626892, _1626892), tc_HOL_Obool), tc_HOL_Obool)), _1626892), hAPP(c_COMBB(tc_prod(_1626892, _1626892), tc_fun(tc_fun(tc_prod(_1626892, _1626892), tc_HOL_Obool), tc_HOL_Obool), _1626892), c_member(tc_prod(_1626892, _1626892)))), c_Product__Type_OPair(_1626892, _1626892)))), _1626898)), _1627228)))]]], (42536 ^ _780205) ^ [_1627621, _1627623, _1627625, _1627627] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627621), tc_List_Olist(_1627621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627621), tc_List_Olist(_1627621)), _1627623), _1627625)), c_List_Olistrel(_1627621, _1627627)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627621)), _1627623) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627621)), _1627625), 42542 ^ _780205 : [(42543 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1627621, _1627621)), 42541 ^ [_1627621, _1627623, _1627625, _1627627]), hAPP(c_List_Oset(tc_prod(_1627621, _1627621)), hAPP(hAPP(c_List_Ozip(_1627621, _1627621), _1627623), _1627625)))))], (42545 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1627621, _1627621, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1627621, tc_fun(tc_prod(_1627621, _1627621), tc_HOL_Obool), tc_fun(_1627621, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1627621, tc_fun(tc_fun(tc_prod(_1627621, _1627621), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1627621, _1627621), tc_HOL_Obool), tc_fun(_1627621, tc_HOL_Obool)), _1627621), c_COMBC(_1627621, tc_fun(tc_prod(_1627621, _1627621), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1627621, tc_prod(_1627621, _1627621)), tc_fun(_1627621, tc_fun(tc_fun(tc_prod(_1627621, _1627621), tc_HOL_Obool), tc_HOL_Obool)), _1627621), hAPP(c_COMBB(tc_prod(_1627621, _1627621), tc_fun(tc_fun(tc_prod(_1627621, _1627621), tc_HOL_Obool), tc_HOL_Obool), _1627621), c_member(tc_prod(_1627621, _1627621)))), c_Product__Type_OPair(_1627621, _1627621)))), _1627627)), 42541 ^ [_1627621, _1627623, _1627625, _1627627]))]]], (42549 ^ _780205) ^ [_1628359, _1628361, _1628363, _1628365] : [-(hAPP(c_List_Oset(tc_prod(_1628359, _1628361)), hAPP(hAPP(c_List_Ozip(_1628359, _1628361), _1628363), _1628365)) = hAPP(c_Set_OCollect(tc_prod(_1628359, _1628361)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1628359, _1628361)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1628359, _1628361), 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(_1628359, _1628361)), 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(_1628359, _1628361)), 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(_1628359, _1628361), tc_fun(tc_Nat_Onat, tc_prod(_1628359, _1628361)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1628359, _1628361), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1628359, _1628361)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1628359, _1628361)), c_COMBB(tc_prod(_1628359, _1628361), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1628361, tc_prod(_1628359, _1628361)), hAPP(hAPP(c_COMBB(_1628359, tc_fun(_1628361, tc_prod(_1628359, _1628361)), tc_Nat_Onat), c_Product__Type_OPair(_1628359, _1628361)), hAPP(c_List_Onth(_1628359), _1628363))), hAPP(c_List_Onth(_1628361), _1628365)))))), 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(_1628359)), _1628363)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628361)), _1628365)))))))], (42551 ^ _780205) ^ [_1628584, _1628586, _1628588, _1628590, _1628592] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1628584, _1628586)), _1628588), hAPP(hAPP(c_List_Ozip(_1628584, _1628586), _1628590), _1628592)) = hAPP(hAPP(c_List_Ozip(_1628584, _1628586), hAPP(hAPP(c_List_Otake(_1628584), _1628588), _1628590)), hAPP(hAPP(c_List_Otake(_1628586), _1628588), _1628592)))], (42553 ^ _780205) ^ [_1628660, _1628662, _1628664, _1628666] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1628660, _1628662))), hAPP(hAPP(c_List_Ozip(_1628660, _1628662), _1628664), _1628666)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628660)), _1628664)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628662)), _1628666)))], (42555 ^ _780205) ^ [_1628728, _1628730, _1628732, _1628734, _1628736, _1628738] : [-(hAPP(hAPP(c_List_Ozip(_1628728, _1628730), hAPP(hAPP(c_List_Olist_OCons(_1628728), _1628732), _1628734)), hAPP(hAPP(c_List_Olist_OCons(_1628730), _1628736), _1628738)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1628728, _1628730)), hAPP(hAPP(c_Product__Type_OPair(_1628728, _1628730), _1628732), _1628736)), hAPP(hAPP(c_List_Ozip(_1628728, _1628730), _1628734), _1628738)))], (42557 ^ _780205) ^ [_1628833, _1628835, _1628837] : [_1628833 = _1628835, 42560 ^ _780205 : [(42561 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628837)), _1628833) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628837)), _1628835))], (42563 ^ _780205) ^ [_1628989] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1628837, _1628837)), _1628989), hAPP(c_List_Oset(tc_prod(_1628837, _1628837)), hAPP(hAPP(c_List_Ozip(_1628837, _1628837), _1628833), _1628835)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1628837, _1628837, tc_HOL_Obool), c_fequal), _1628989)))]]], (42569 ^ _780205) ^ [_1629144, _1629146, _1629148] : [-(_1629144 = _1629146), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629148)), _1629144) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629148)), _1629146), 42575 ^ _780205 : [(42576 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629148, _1629148)), 42574 ^ [_1629144, _1629146, _1629148]), hAPP(c_List_Oset(tc_prod(_1629148, _1629148)), hAPP(hAPP(c_List_Ozip(_1629148, _1629148), _1629144), _1629146)))))], (42578 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1629148, _1629148, tc_HOL_Obool), c_fequal), 42574 ^ [_1629144, _1629146, _1629148]))]]], (42582 ^ _780205) ^ [_1629479, _1629481, _1629483, _1629485] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629479, _1629479)), hAPP(hAPP(c_Product__Type_OPair(_1629479, _1629479), _1629481), _1629483)), hAPP(c_List_Oset(tc_prod(_1629479, _1629479)), hAPP(hAPP(c_List_Ozip(_1629479, _1629479), _1629485), _1629485)))), 42585 ^ _780205 : [(42586 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1629479), _1629481), hAPP(c_List_Oset(_1629479), _1629485))))], (42588 ^ _780205) ^ [] : [-(_1629481 = _1629483)]]], (42590 ^ _780205) ^ [_1629678, _1629680, _1629682, _1629684] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629678, _1629678)), hAPP(hAPP(c_Product__Type_OPair(_1629678, _1629678), _1629680), _1629682)), hAPP(c_List_Oset(tc_prod(_1629678, _1629678)), hAPP(hAPP(c_List_Ozip(_1629678, _1629678), _1629684), _1629684))))), hBOOL(hAPP(hAPP(c_member(_1629678), _1629680), hAPP(c_List_Oset(_1629678), _1629684))), _1629680 = _1629682], (42600 ^ _780205) ^ [_1629913, _1629915, _1629917, _1629919, _1629921, _1629923] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629913, _1629915)), hAPP(hAPP(c_Product__Type_OPair(_1629913, _1629915), _1629917), _1629919)), hAPP(c_List_Oset(tc_prod(_1629913, _1629915)), hAPP(hAPP(c_List_Ozip(_1629913, _1629915), _1629921), _1629923)))), -(hBOOL(hAPP(hAPP(c_member(_1629913), _1629917), hAPP(c_List_Oset(_1629913), _1629921))))], (42606 ^ _780205) ^ [_1630094, _1630096, _1630098, _1630100, _1630102, _1630104] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630094, _1630096)), hAPP(hAPP(c_Product__Type_OPair(_1630094, _1630096), _1630098), _1630100)), hAPP(c_List_Oset(tc_prod(_1630094, _1630096)), hAPP(hAPP(c_List_Ozip(_1630094, _1630096), _1630102), _1630104)))), -(hBOOL(hAPP(hAPP(c_member(_1630096), _1630100), hAPP(c_List_Oset(_1630096), _1630104))))], (42612 ^ _780205) ^ [_1630275, _1630277, _1630279, _1630281, _1630283, _1630285] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630275, _1630277)), hAPP(hAPP(c_Product__Type_OPair(_1630275, _1630277), _1630279), _1630281)), hAPP(c_List_Oset(tc_prod(_1630275, _1630277)), hAPP(hAPP(c_List_Ozip(_1630275, _1630277), _1630283), _1630285)))), 42615 ^ _780205 : [(42616 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1630275), _1630279), hAPP(c_List_Oset(_1630275), _1630283))))], (42618 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1630277), _1630281), hAPP(c_List_Oset(_1630277), _1630285))))]]], (42620 ^ _780205) ^ [_1630510, _1630512, _1630514, _1630516, _1630518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630510), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630512)), _1630514))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630510), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630516)), _1630518))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1630512, _1630516)), hAPP(hAPP(c_List_Ozip(_1630512, _1630516), _1630514), _1630518)), _1630510) = hAPP(hAPP(c_Product__Type_OPair(_1630512, _1630516), hAPP(hAPP(c_List_Onth(_1630512), _1630514), _1630510)), hAPP(hAPP(c_List_Onth(_1630516), _1630518), _1630510)))], (42630 ^ _780205) ^ [_1630789, _1630791] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1630789, _1630791) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1630789), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1630791), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42632 ^ _780205) ^ [_1630836, _1630838] : [class_Groups_Ocomm__monoid__add(_1630836), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1630836), _1630838) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1630836), hAPP(c_List_Onth(_1630836), _1630838)), 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(_1630836)), _1630838))))], (42638 ^ _780205) ^ [_1630969, _1630971] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1630969, _1630971)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1630969, _1630971))], (42640 ^ _780205) ^ [_1631004, _1631006] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1631004, _1631006) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1631004, _1631006)))], (42652 ^ _780205) ^ [_1631219] : [42654 ^ _780205 : [(42655 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42653 ^ [_1631219]), hAPP(c_List_Oset(tc_Nat_Onat), _1631219))))], (42657 ^ _780205) ^ [] : [42653 ^ [_1631219] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1631219) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42642 ^ _780205) ^ [_1631051] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1631051) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42645 ^ _780205 : [(42646 ^ _780205) ^ [_1631126] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1631126), hAPP(c_List_Oset(tc_Nat_Onat), _1631051))), -(_1631126 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42661 ^ _780205) ^ [_1631375, _1631377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631375), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1631377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1631377), _1631375)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1631377))))], (42667 ^ _780205) ^ [_1631496, _1631498, _1631500] : [class_Groups_Omonoid__add(_1631496), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1631496), hAPP(hAPP(c_List_Olist_OCons(_1631496), _1631498), _1631500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1631496), _1631498), hAPP(c_List_Omonoid__add__class_Olistsum(_1631496), _1631500)))], (42673 ^ _780205) ^ [_1631625, _1631627] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1631625), _1631627) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1631625, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1631627), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42675 ^ _780205) ^ [_1631668, _1631670] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1631668, _1631670) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1631668), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1631670)))], (42677 ^ _780205) ^ [_1631721] : [c_List_Onat__list(_1631721), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1631721)))], (42683 ^ _780205) ^ [_1631794] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1631794)), -(c_List_Onat__list(_1631794))], (42689 ^ _780205) ^ [_1631873, _1631875, _1631877, _1631879] : [42691 ^ _780205 : [(42692 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1631873), 42690 ^ [_1631873, _1631875, _1631877, _1631879]), hAPP(c_List_Oset(_1631873), _1631875))))], (42694 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1631877, 42690 ^ [_1631873, _1631875, _1631877, _1631879])), hAPP(_1631879, 42690 ^ [_1631873, _1631875, _1631877, _1631879])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1631873, _1631877, _1631875)), c_List_Olist_Olist__size(_1631873, _1631879, _1631875))))], (42698 ^ _780205) ^ [_1632123, _1632125, _1632127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632123), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1632125))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1632125), _1632123), _1632127)) = 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), _1632125)), _1632127)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1632125), _1632123)))], (42704 ^ _780205) ^ [_1632284, _1632286, _1632288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1632284), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632286)), _1632288))), -(c_List_Obutlast(_1632286, hAPP(hAPP(c_List_Otake(_1632286), _1632284), _1632288)) = hAPP(hAPP(c_List_Otake(_1632286), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1632284), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1632288))], (42710 ^ _780205) ^ [_1632437, _1632439, _1632441, _1632443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632437)), _1632439)), _1632441)), -(hAPP(hAPP(c_List_Olist__update(_1632437, _1632439), _1632441), _1632443) = _1632439)], (42716 ^ _780205) ^ [_1632556, _1632558, _1632560, _1632562, _1632564] : [-(_1632556 = _1632558), -(hAPP(hAPP(c_List_Onth(_1632560), hAPP(hAPP(c_List_Olist__update(_1632560, _1632562), _1632556), _1632564)), _1632558) = hAPP(hAPP(c_List_Onth(_1632560), _1632562), _1632558))], (42722 ^ _780205) ^ [_1632623, _1632625, _1632627] : [-(hAPP(hAPP(c_List_Olist__update(_1632623, _1632625), _1632627), hAPP(hAPP(c_List_Onth(_1632623), _1632625), _1632627)) = _1632625)], (42724 ^ _780205) ^ [_1632682, _1632684, _1632686, _1632688] : [_1632682 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632684)), _1632686)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1632684, hAPP(hAPP(c_List_Olist__update(_1632684, _1632686), _1632682), _1632688)) = c_List_Obutlast(_1632684, _1632686))], (42730 ^ _780205) ^ [_1632813, _1632815, _1632817, _1632819] : [-(_1632813 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632815)), _1632817)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1632815, hAPP(hAPP(c_List_Olist__update(_1632815, _1632817), _1632813), _1632819)) = hAPP(hAPP(c_List_Olist__update(_1632815, c_List_Obutlast(_1632815, _1632817)), _1632813), _1632819))], (42736 ^ _780205) ^ [_1632892, _1632894, _1632896, _1632898] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632892)), hAPP(hAPP(c_List_Olist__update(_1632892, _1632894), _1632896), _1632898)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632892)), _1632894))], (42738 ^ _780205) ^ [_1632944, _1632946, _1632948, _1632950, _1632952, _1632954, _1632956] : [-(hAPP(hAPP(c_List_Ozip(_1632944, _1632946), hAPP(hAPP(c_List_Olist__update(_1632944, _1632948), _1632950), _1632952)), hAPP(hAPP(c_List_Olist__update(_1632946, _1632954), _1632950), _1632956)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1632944, _1632946), hAPP(hAPP(c_List_Ozip(_1632944, _1632946), _1632948), _1632954)), _1632950), hAPP(hAPP(c_Product__Type_OPair(_1632944, _1632946), _1632952), _1632956)))], (42740 ^ _780205) ^ [_1633036, _1633038, _1633040, _1633042, _1633044, _1633046] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1633036, _1633038), hAPP(hAPP(c_List_Ozip(_1633036, _1633038), _1633040), _1633042)), _1633044), _1633046) = hAPP(hAPP(c_List_Ozip(_1633036, _1633038), hAPP(hAPP(c_List_Olist__update(_1633036, _1633040), _1633044), hAPP(c_Product__Type_Ofst(_1633036, _1633038), _1633046))), hAPP(hAPP(c_List_Olist__update(_1633038, _1633042), _1633044), hAPP(c_Product__Type_Osnd(_1633036, _1633038), _1633046))))], (42742 ^ _780205) ^ [_1633129, _1633131, _1633133, _1633135, _1633137] : [-(hAPP(hAPP(c_List_Olist__update(_1633129, hAPP(hAPP(c_List_Olist__update(_1633129, _1633131), _1633133), _1633135)), _1633133), _1633137) = hAPP(hAPP(c_List_Olist__update(_1633129, _1633131), _1633133), _1633137))], (42744 ^ _780205) ^ [_1633183, _1633185, _1633187, _1633189, _1633191, _1633193] : [-(_1633183 = _1633185), -(hAPP(hAPP(c_List_Olist__update(_1633187, hAPP(hAPP(c_List_Olist__update(_1633187, _1633189), _1633183), _1633191)), _1633185), _1633193) = hAPP(hAPP(c_List_Olist__update(_1633187, hAPP(hAPP(c_List_Olist__update(_1633187, _1633189), _1633185), _1633193)), _1633183), _1633191))], (42750 ^ _780205) ^ [_1633263, _1633265, _1633267, _1633269] : [-(hAPP(hAPP(c_List_Olist__update(_1633263, hAPP(hAPP(c_List_Olist_OCons(_1633263), _1633265), _1633267)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1633269) = hAPP(hAPP(c_List_Olist_OCons(_1633263), _1633269), _1633267))], (42752 ^ _780205) ^ [_1633317, _1633319, _1633321, _1633323, _1633325] : [-(hAPP(hAPP(c_List_Olist__update(_1633317, hAPP(hAPP(c_List_Olist_OCons(_1633317), _1633319), _1633321)), hAPP(c_Nat_OSuc, _1633323)), _1633325) = hAPP(hAPP(c_List_Olist_OCons(_1633317), _1633319), hAPP(hAPP(c_List_Olist__update(_1633317, _1633321), _1633323), _1633325)))], (42754 ^ _780205) ^ [_1633385, _1633387, _1633389, _1633391, _1633393] : [-(hAPP(hAPP(c_List_Olist__update(_1633385, hAPP(hAPP(c_List_Olist_OCons(_1633385), _1633387), _1633389)), _1633391), _1633393) = c_Nat_Onat_Onat__case(tc_List_Olist(_1633385), hAPP(hAPP(c_List_Olist_OCons(_1633385), _1633393), _1633389), hAPP(hAPP(c_COMBB(tc_List_Olist(_1633385), tc_List_Olist(_1633385), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1633385), _1633387)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1633385, tc_List_Olist(_1633385)), c_List_Olist__update(_1633385, _1633389)), _1633393)), _1633391))], (42756 ^ _780205) ^ [_1633482, _1633484, _1633486] : [hBOOL(hAPP(hAPP(c_member(_1633482), _1633484), hAPP(c_List_Oset(_1633482), c_List_Obutlast(_1633482, _1633486)))), -(hBOOL(hAPP(hAPP(c_member(_1633482), _1633484), hAPP(c_List_Oset(_1633482), _1633486))))], (42762 ^ _780205) ^ [_1633615, _1633617, _1633619, _1633621, _1633623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1633615, tc_HOL_Obool)), hAPP(c_List_Oset(_1633615), _1633617)), _1633619)), hBOOL(hAPP(hAPP(c_member(_1633615), _1633621), _1633619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1633615, tc_HOL_Obool)), hAPP(c_List_Oset(_1633615), hAPP(hAPP(c_List_Olist__update(_1633615, _1633617), _1633623), _1633621))), _1633619)))], (42772 ^ _780205) ^ [_1633848, _1633850, _1633852, _1633854] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1633848, tc_HOL_Obool)), hAPP(c_List_Oset(_1633848), hAPP(hAPP(c_List_Olist__update(_1633848, _1633850), _1633852), _1633854))), hAPP(hAPP(c_Set_Oinsert(_1633848), _1633854), hAPP(c_List_Oset(_1633848), _1633850)))))], (42774 ^ _780205) ^ [_1633914, _1633916, _1633918, _1633920, _1633922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1633914), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633916)), _1633918))), 42777 ^ _780205 : [(42778 ^ _780205) ^ [] : [_1633914 = _1633920, -(hAPP(hAPP(c_List_Onth(_1633916), hAPP(hAPP(c_List_Olist__update(_1633916, _1633918), _1633914), _1633922)), _1633920) = _1633922)], (42784 ^ _780205) ^ [] : [-(_1633914 = _1633920), -(hAPP(hAPP(c_List_Onth(_1633916), hAPP(hAPP(c_List_Olist__update(_1633916, _1633918), _1633914), _1633922)), _1633920) = hAPP(hAPP(c_List_Onth(_1633916), _1633918), _1633920))]]], (42790 ^ _780205) ^ [_1634210, _1634212, _1634214, _1634216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634210), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634212)), _1634214))), 42793 ^ _780205 : [(42794 ^ _780205) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1634212, _1634214), _1634210), _1634216) = _1634214, -(hAPP(hAPP(c_List_Onth(_1634212), _1634214), _1634210) = _1634216)], (42800 ^ _780205) ^ [] : [hAPP(hAPP(c_List_Onth(_1634212), _1634214), _1634210) = _1634216, -(hAPP(hAPP(c_List_Olist__update(_1634212, _1634214), _1634210), _1634216) = _1634214)]]], (42806 ^ _780205) ^ [_1634504, _1634506, _1634508, _1634510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634504), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634506)), _1634508))), -(hAPP(hAPP(c_List_Onth(_1634506), hAPP(hAPP(c_List_Olist__update(_1634506, _1634508), _1634504), _1634510)), _1634504) = _1634510)], (42812 ^ _780205) ^ [_1634643, _1634645, _1634647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634643), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634645)), _1634647))), -(hAPP(hAPP(c_List_Otake(_1634645), _1634643), c_List_Obutlast(_1634645, _1634647)) = hAPP(hAPP(c_List_Otake(_1634645), _1634643), _1634647))], (42818 ^ _780205) ^ [_1634784, _1634786] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634784)), c_List_Obutlast(_1634784, _1634786)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634784)), _1634786)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42820 ^ _780205) ^ [_1634832, _1634834, _1634836, _1634838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634832), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634834)), _1634836))), -(hBOOL(hAPP(hAPP(c_member(_1634834), _1634838), hAPP(c_List_Oset(_1634834), hAPP(hAPP(c_List_Olist__update(_1634834, _1634836), _1634832), _1634838)))))], (42826 ^ _780205) ^ [_1634979, _1634981] : [-(c_List_Obutlast(_1634979, _1634981) = hAPP(hAPP(c_List_Otake(_1634979), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634979)), _1634981)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1634981))], (42828 ^ _780205) ^ [_1635049, _1635051, _1635053, _1635055] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635049), tc_List_Olist(_1635049))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635049), tc_List_Olist(_1635049)), _1635051), _1635053)), c_List_Olistrel1(_1635049, _1635055))), 42833 ^ _780205 : [(42834 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635049, _1635049)), hAPP(hAPP(c_Product__Type_OPair(_1635049, _1635049), hAPP(hAPP(c_List_Onth(_1635049), _1635051), 42832 ^ [_1635049, _1635051, _1635053, _1635055])), 42831 ^ [_1635049, _1635051, _1635053, _1635055])), _1635055)))], (42836 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42832 ^ [_1635049, _1635051, _1635053, _1635055]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635049)), _1635051))))], (42838 ^ _780205) ^ [] : [-(_1635053 = hAPP(hAPP(c_List_Olist__update(_1635049, _1635051), 42832 ^ [_1635049, _1635051, _1635053, _1635055]), 42831 ^ [_1635049, _1635051, _1635053, _1635055]))]]], (42840 ^ _780205) ^ [_1635397, _1635399, _1635401, _1635403] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635397), tc_List_Olist(_1635397))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635397), tc_List_Olist(_1635397)), _1635399), _1635401)), c_List_Olistrel1(_1635397, _1635403)))), 42841 ^ _780205 : [(42842 ^ _780205) ^ [_1635530, _1635532] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635397, _1635397)), hAPP(hAPP(c_Product__Type_OPair(_1635397, _1635397), hAPP(hAPP(c_List_Onth(_1635397), _1635399), _1635530)), _1635532)), _1635403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1635530), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635397)), _1635399))), _1635401 = hAPP(hAPP(c_List_Olist__update(_1635397, _1635399), _1635530), _1635532)]]], (42854 ^ _780205) ^ [_1635830, _1635832, _1635834, _1635836] : [hBOOL(hAPP(c_List_Odistinct(_1635830), _1635832)), -(hBOOL(hAPP(hAPP(c_member(_1635830), _1635834), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1635830, tc_HOL_Obool)), hAPP(c_List_Oset(_1635830), _1635832)), hAPP(hAPP(c_Set_Oinsert(_1635830), hAPP(hAPP(c_List_Onth(_1635830), _1635832), _1635836)), c_Orderings_Obot__class_Obot(tc_fun(_1635830, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1635830), hAPP(hAPP(c_List_Olist__update(_1635830, _1635832), _1635836), _1635834))))], (42864 ^ _780205) ^ [_1636048, _1636050] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1636048, _1636050))))], (42866 ^ _780205) ^ [_1636078, _1636080, _1636082] : [hBOOL(hAPP(c_List_Odistinct(_1636078), _1636080)), -(hBOOL(hAPP(c_List_Odistinct(_1636078), hAPP(hAPP(c_List_Otake(_1636078), _1636082), _1636080))))], (42872 ^ _780205) ^ [_1636189, _1636191, _1636193] : [hBOOL(hAPP(c_List_Odistinct(_1636189), _1636191)), -(hBOOL(hAPP(c_List_Odistinct(_1636189), c_List_Osublist(_1636189, _1636191, _1636193))))], (42878 ^ _780205) ^ [_1636292, _1636294, _1636296, _1636298] : [hBOOL(hAPP(c_List_Odistinct(_1636292), _1636294)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1636292, _1636296)), hAPP(hAPP(c_List_Ozip(_1636292, _1636296), _1636294), _1636298))))], (42884 ^ _780205) ^ [_1636413, _1636415, _1636417, _1636419] : [hBOOL(hAPP(c_List_Odistinct(_1636413), _1636415)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1636417, _1636413)), hAPP(hAPP(c_List_Ozip(_1636417, _1636413), _1636419), _1636415))))], (42890 ^ _780205) ^ [_1636552, _1636554, _1636556] : [hBOOL(hAPP(c_List_Odistinct(_1636552), hAPP(hAPP(c_List_Olist_OCons(_1636552), _1636554), _1636556))), 42893 ^ _780205 : [(42894 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1636552), _1636554), hAPP(c_List_Oset(_1636552), _1636556)))], (42896 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1636552), _1636556)))]]], (42898 ^ _780205) ^ [_1636719, _1636721, _1636723] : [-(hBOOL(hAPP(c_List_Odistinct(_1636719), hAPP(hAPP(c_List_Olist_OCons(_1636719), _1636721), _1636723)))), -(hBOOL(hAPP(hAPP(c_member(_1636719), _1636721), hAPP(c_List_Oset(_1636719), _1636723)))), hBOOL(hAPP(c_List_Odistinct(_1636719), _1636723))], (42908 ^ _780205) ^ [_1636913, _1636915] : [hBOOL(hAPP(c_List_Odistinct(_1636913), _1636915)), -(hAPP(c_Finite__Set_Ocard(_1636913), hAPP(c_List_Oset(_1636913), _1636915)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636913)), _1636915))], (42914 ^ _780205) ^ [_1637032, _1637034] : [hAPP(c_Finite__Set_Ocard(_1637032), hAPP(c_List_Oset(_1637032), _1637034)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637032)), _1637034), -(hBOOL(hAPP(c_List_Odistinct(_1637032), _1637034)))], (42938 ^ _780205) ^ [_1637626, _1637628] : [42940 ^ _780205 : [(42941 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42939 ^ [_1637626, _1637628]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637626)), _1637628))))], (42944 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42942 ^ [_1637626, _1637628]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637626)), _1637628))))], (42946 ^ _780205) ^ [] : [42939 ^ [_1637626, _1637628] = 42942 ^ [_1637626, _1637628]], (42948 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1637626), _1637628), 42939 ^ [_1637626, _1637628]) = hAPP(hAPP(c_List_Onth(_1637626), _1637628), 42942 ^ [_1637626, _1637628]))]], -(hBOOL(hAPP(c_List_Odistinct(_1637626), _1637628)))], (42920 ^ _780205) ^ [_1637166, _1637168] : [hBOOL(hAPP(c_List_Odistinct(_1637166), _1637168)), 42923 ^ _780205 : [(42924 ^ _780205) ^ [_1637298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1637298), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637166)), _1637168))), 42927 ^ _780205 : [(42928 ^ _780205) ^ [_1637425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1637425), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637166)), _1637168))), -(_1637298 = _1637425), hAPP(hAPP(c_List_Onth(_1637166), _1637168), _1637298) = hAPP(hAPP(c_List_Onth(_1637166), _1637168), _1637425)]]]]], (42952 ^ _780205) ^ [_1638058, _1638060, _1638062, _1638064] : [hBOOL(hAPP(c_List_Odistinct(_1638058), _1638060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1638062), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638058)), _1638060))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1638064), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638058)), _1638060))), 42963 ^ _780205 : [(42964 ^ _780205) ^ [] : [hAPP(hAPP(c_List_Onth(_1638058), _1638060), _1638062) = hAPP(hAPP(c_List_Onth(_1638058), _1638060), _1638064), -(_1638062 = _1638064)], (42970 ^ _780205) ^ [] : [_1638062 = _1638064, -(hAPP(hAPP(c_List_Onth(_1638058), _1638060), _1638062) = hAPP(hAPP(c_List_Onth(_1638058), _1638060), _1638064))]]], (42976 ^ _780205) ^ [_1638493, _1638495] : [class_Groups_Ocomm__monoid__add(_1638493), hBOOL(hAPP(c_List_Odistinct(_1638493), _1638495)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1638493), _1638495) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1638493, _1638493), c_COMBI(_1638493)), hAPP(c_List_Oset(_1638493), _1638495)))], (42986 ^ _780205) ^ [_1638679, _1638681] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1638679), _1638681)), -(c_Nitpick_Ocard_H(_1638679, _1638681) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638679)), c_Hilbert__Choice_OEps(tc_List_Olist(_1638679), hAPP(hAPP(c_COMBS(tc_List_Olist(_1638679), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1638679)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1638679), tc_fun(_1638679, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1638679, tc_HOL_Obool), tc_fun(tc_fun(_1638679, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1638679)), c_fequal), c_List_Oset(_1638679))), _1638681))), c_List_Odistinct(_1638679)))))], (42992 ^ _780205) ^ [_1638916, _1638918] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1638916), _1638918))), -(c_Nitpick_Ocard_H(_1638916, _1638918) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42998 ^ _780205) ^ [_1638961, _1638963, _1638965, _1638967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1638961), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638963)), _1638965))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1638961), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638963)), _1638967))), 43008 ^ _780205 : [(43009 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43007 ^ [_1638961, _1638963, _1638965, _1638967]), _1638961)))], (43011 ^ _780205) ^ [] : [hAPP(hAPP(c_List_Onth(_1638963), _1638965), 43007 ^ [_1638961, _1638963, _1638965, _1638967]) = hAPP(hAPP(c_List_Onth(_1638963), _1638967), 43007 ^ [_1638961, _1638963, _1638965, _1638967])]], -(hAPP(hAPP(c_List_Otake(_1638963), _1638961), _1638965) = hAPP(hAPP(c_List_Otake(_1638963), _1638961), _1638967))], (43015 ^ _780205) ^ [_1639378, _1639380, _1639382] : [hBOOL(hAPP(c_List_Odistinct(_1639378), _1639380)), -(hAPP(c_List_Oset(_1639378), c_List_Oremove1(_1639378, _1639382, _1639380)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1639378, tc_HOL_Obool)), hAPP(c_List_Oset(_1639378), _1639380)), hAPP(hAPP(c_Set_Oinsert(_1639378), _1639382), c_Orderings_Obot__class_Obot(tc_fun(_1639378, tc_HOL_Obool)))))], (43021 ^ _780205) ^ [_1639556, _1639558, _1639560, _1639562] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1639556) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1639558), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1639556)), hAPP(hAPP(c_List_Olist_OCons(_1639558), _1639560), _1639562)) = c_List_Olist_ONil(_1639558))], (43027 ^ _780205) ^ [_1639679, _1639681, _1639683, _1639685] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1639679) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1639681), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1639679)), hAPP(hAPP(c_List_Olist_OCons(_1639681), _1639683), _1639685)) = hAPP(hAPP(c_List_Olist_OCons(_1639681), _1639683), hAPP(hAPP(c_List_Otake(_1639681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1639679)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1639685)))], (43033 ^ _780205) ^ [_1639768, _1639770] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1639768)), c_List_Olist_ONil(_1639768)), c_List_Olists(_1639768, _1639770))))], (43035 ^ _780205) ^ [_1639807, _1639809, _1639811] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639807), tc_List_Olist(_1639807))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639807), tc_List_Olist(_1639807)), c_List_Olist_ONil(_1639807)), _1639809)), c_List_Olistrel(_1639807, _1639811))), -(_1639809 = c_List_Olist_ONil(_1639807))], (43041 ^ _780205) ^ [_1639954, _1639956, _1639958] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639954), tc_List_Olist(_1639954))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639954), tc_List_Olist(_1639954)), _1639956), c_List_Olist_ONil(_1639954))), c_List_Olistrel(_1639954, _1639958))), -(_1639956 = c_List_Olist_ONil(_1639954))], (43047 ^ _780205) ^ [_1640100, _1640102] : [-(_1640100 = c_List_Olist_ONil(_1640102)), hBOOL(hAPP(c_List_Odistinct(_1640102), _1640100)), -(hBOOL(hAPP(c_List_Odistinct(_1640102), c_List_Obutlast(_1640102, _1640100))))], (43057 ^ _780205) ^ [_1640251, _1640253, _1640255] : [hBOOL(hAPP(c_List_Odistinct(_1640251), _1640253)), -(hBOOL(hAPP(c_List_Odistinct(_1640251), c_List_Oremove1(_1640251, _1640255, _1640253))))], (43063 ^ _780205) ^ [_1640354] : [-(hBOOL(hAPP(c_List_Odistinct(_1640354), c_List_Olist_ONil(_1640354))))], (43065 ^ _780205) ^ [_1640383] : [-(c_List_Obutlast(_1640383, c_List_Olist_ONil(_1640383)) = c_List_Olist_ONil(_1640383))], (43067 ^ _780205) ^ [_1640425, _1640427, _1640429] : [_1640425 = c_List_Olist_ONil(_1640427), -(c_List_Obutlast(_1640427, hAPP(hAPP(c_List_Olist_OCons(_1640427), _1640429), _1640425)) = c_List_Olist_ONil(_1640427))], (43073 ^ _780205) ^ [_1640528, _1640530, _1640532] : [-(_1640528 = c_List_Olist_ONil(_1640530)), -(c_List_Obutlast(_1640530, hAPP(hAPP(c_List_Olist_OCons(_1640530), _1640532), _1640528)) = hAPP(hAPP(c_List_Olist_OCons(_1640530), _1640532), c_List_Obutlast(_1640530, _1640528)))], (43079 ^ _780205) ^ [_1640607, _1640609, _1640611] : [c_List_Olist_ONil(_1640607) = hAPP(hAPP(c_List_Olist_OCons(_1640607), _1640609), _1640611)], (43081 ^ _780205) ^ [_1640659, _1640661, _1640663] : [hAPP(hAPP(c_List_Olist_OCons(_1640659), _1640661), _1640663) = c_List_Olist_ONil(_1640659)], (43083 ^ _780205) ^ [_1640711, _1640713, _1640715, _1640717] : [_1640711 = _1640713, -(c_List_Oremove1(_1640715, _1640711, hAPP(hAPP(c_List_Olist_OCons(_1640715), _1640713), _1640717)) = _1640717)], (43089 ^ _780205) ^ [_1640810, _1640812, _1640814, _1640816] : [-(_1640810 = _1640812), -(c_List_Oremove1(_1640814, _1640810, hAPP(hAPP(c_List_Olist_OCons(_1640814), _1640812), _1640816)) = hAPP(hAPP(c_List_Olist_OCons(_1640814), _1640812), c_List_Oremove1(_1640814, _1640810, _1640816)))], (43095 ^ _780205) ^ [_1640876, _1640878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1640876), _1640878)), -(c_List_Oupto(_1640878, _1640876) = c_List_Olist_ONil(tc_Int_Oint))], (43111 ^ _780205) ^ [_1641099, _1641101, _1641103] : [43112 ^ _780205 : [(43113 ^ _780205) ^ [] : [_1641101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43115 ^ _780205) ^ [] : [_1641103 = c_List_Olist_ONil(_1641099)]], -(hAPP(hAPP(c_List_Otake(_1641099), _1641101), _1641103) = c_List_Olist_ONil(_1641099))], (43101 ^ _780205) ^ [_1640987, _1640989, _1640991] : [hAPP(hAPP(c_List_Otake(_1640987), _1640989), _1640991) = c_List_Olist_ONil(_1640987), -(_1640989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1640991 = c_List_Olist_ONil(_1640987))], (43119 ^ _780205) ^ [_1641242, _1641244] : [-(hAPP(hAPP(c_List_Otake(_1641242), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1641244) = c_List_Olist_ONil(_1641242))], (43121 ^ _780205) ^ [_1641277, _1641279] : [-(hAPP(hAPP(c_List_Otake(_1641277), _1641279), c_List_Olist_ONil(_1641277)) = c_List_Olist_ONil(_1641277))], (43123 ^ _780205) ^ [_1641314, _1641316] : [-(c_List_Osublist(_1641314, c_List_Olist_ONil(_1641314), _1641316) = c_List_Olist_ONil(_1641314))], (43125 ^ _780205) ^ [_1641347, _1641349, _1641351, _1641353] : [-(c_List_Oremove1(_1641347, _1641349, c_List_Oremove1(_1641347, _1641351, _1641353)) = c_List_Oremove1(_1641347, _1641351, c_List_Oremove1(_1641347, _1641349, _1641353)))], (43127 ^ _780205) ^ [_1641392, _1641394] : [-(c_List_Oremove1(_1641392, _1641394, c_List_Olist_ONil(_1641392)) = c_List_Olist_ONil(_1641392))], (43129 ^ _780205) ^ [_1641425, _1641427] : [-(c_List_Olistrelp(_1641425, _1641427, c_List_Olist_ONil(_1641425), c_List_Olist_ONil(_1641425)))], (43131 ^ _780205) ^ [_1641456, _1641458] : [-(c_List_Olistrelp(_1641456, _1641458, c_List_Olist_ONil(_1641456), c_List_Olist_ONil(_1641456)))], (43133 ^ _780205) ^ [_1641487, _1641489, _1641491] : [-(hAPP(hAPP(c_List_Ozip(_1641487, _1641489), c_List_Olist_ONil(_1641487)), _1641491) = c_List_Olist_ONil(tc_prod(_1641487, _1641489)))], (43135 ^ _780205) ^ [_1641530, _1641532, _1641534] : [-(hAPP(hAPP(c_List_Ozip(_1641530, _1641532), _1641534), c_List_Olist_ONil(_1641532)) = c_List_Olist_ONil(tc_prod(_1641530, _1641532)))], (43137 ^ _780205) ^ [_1641573, _1641575] : [-(c_List_Olist_Olist__size(_1641573, _1641575, c_List_Olist_ONil(_1641573)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43139 ^ _780205) ^ [_1641604] : [class_Groups_Omonoid__add(_1641604), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1641604), c_List_Olist_ONil(_1641604)) = c_Groups_Ozero__class_Ozero(_1641604))], (43145 ^ _780205) ^ [_1641695] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641695)), c_List_Olist_ONil(_1641695)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43147 ^ _780205) ^ [_1641742, _1641744] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641742)), _1641744) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1641744 = c_List_Olist_ONil(_1641742))], (43153 ^ _780205) ^ [_1641833, _1641835] : [_1641835 = c_List_Olist_ONil(_1641833), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641833)), _1641835) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43159 ^ _780205) ^ [_1641945, _1641947] : [hAPP(c_List_Oset(_1641945), _1641947) = c_Orderings_Obot__class_Obot(tc_fun(_1641945, tc_HOL_Obool)), -(_1641947 = c_List_Olist_ONil(_1641945))], (43165 ^ _780205) ^ [_1642042, _1642044] : [_1642044 = c_List_Olist_ONil(_1642042), -(hAPP(c_List_Oset(_1642042), _1642044) = c_Orderings_Obot__class_Obot(tc_fun(_1642042, tc_HOL_Obool)))], (43171 ^ _780205) ^ [_1642160, _1642162] : [c_Orderings_Obot__class_Obot(tc_fun(_1642160, tc_HOL_Obool)) = hAPP(c_List_Oset(_1642160), _1642162), -(_1642162 = c_List_Olist_ONil(_1642160))], (43177 ^ _780205) ^ [_1642257, _1642259] : [_1642259 = c_List_Olist_ONil(_1642257), -(c_Orderings_Obot__class_Obot(tc_fun(_1642257, tc_HOL_Obool)) = hAPP(c_List_Oset(_1642257), _1642259))], (43183 ^ _780205) ^ [_1642360] : [-(hAPP(c_List_Oset(_1642360), c_List_Olist_ONil(_1642360)) = c_Orderings_Obot__class_Obot(tc_fun(_1642360, tc_HOL_Obool)))], (43185 ^ _780205) ^ [_1642395, _1642397, _1642399] : [-(hAPP(hAPP(c_List_Olist__update(_1642395, c_List_Olist_ONil(_1642395)), _1642397), _1642399) = c_List_Olist_ONil(_1642395))], (43187 ^ _780205) ^ [_1642435, _1642437, _1642439] : [-(hAPP(hAPP(c_List_Olist__update(_1642435, c_List_Olist_ONil(_1642435)), _1642437), _1642439) = c_List_Olist_ONil(_1642435))], (43189 ^ _780205) ^ [_1642496, _1642498, _1642500, _1642502] : [hAPP(hAPP(c_List_Olist__update(_1642496, _1642498), _1642500), _1642502) = c_List_Olist_ONil(_1642496), -(_1642498 = c_List_Olist_ONil(_1642496))], (43195 ^ _780205) ^ [_1642599, _1642601, _1642603, _1642605] : [_1642601 = c_List_Olist_ONil(_1642599), -(hAPP(hAPP(c_List_Olist__update(_1642599, _1642601), _1642603), _1642605) = c_List_Olist_ONil(_1642599))], (43201 ^ _780205) ^ [_1642704, _1642706, _1642708] : [-(hBOOL(hAPP(hAPP(c_member(_1642704), _1642706), hAPP(c_List_Oset(_1642704), _1642708)))), -(c_List_Oremove1(_1642704, _1642706, _1642708) = _1642708)], (43207 ^ _780205) ^ [_1642757, _1642759, _1642761, _1642763] : [-(hBOOL(hAPP(hAPP(c_member(_1642757), _1642759), hAPP(c_List_Oset(_1642757), _1642761)))), hBOOL(hAPP(hAPP(c_member(_1642757), _1642759), hAPP(c_List_Oset(_1642757), c_List_Oremove1(_1642757, _1642763, _1642761))))], (43213 ^ _780205) ^ [_1642880, _1642882, _1642884, _1642886] : [-(_1642880 = _1642882), 43216 ^ _780205 : [(43217 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642884), _1642880), hAPP(c_List_Oset(_1642884), c_List_Oremove1(_1642884, _1642882, _1642886)))), -(hBOOL(hAPP(hAPP(c_member(_1642884), _1642880), hAPP(c_List_Oset(_1642884), _1642886))))], (43223 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642884), _1642880), hAPP(c_List_Oset(_1642884), _1642886))), -(hBOOL(hAPP(hAPP(c_member(_1642884), _1642880), hAPP(c_List_Oset(_1642884), c_List_Oremove1(_1642884, _1642882, _1642886)))))]]], (43229 ^ _780205) ^ [_1643181, _1643183] : [-(c_List_Osublist(_1643181, _1643183, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1643181))], (43231 ^ _780205) ^ [_1643212, _1643214, _1643216] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1643212, tc_HOL_Obool)), hAPP(c_List_Oset(_1643212), c_List_Oremove1(_1643212, _1643214, _1643216))), hAPP(c_List_Oset(_1643212), _1643216))))], (43233 ^ _780205) ^ [_1643278, _1643280] : [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(_1643278)), _1643280))), _1643280 = c_List_Olist_ONil(_1643278)], (43239 ^ _780205) ^ [_1643372, _1643374] : [-(_1643374 = c_List_Olist_ONil(_1643372)), -(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(_1643372)), _1643374))))], (43245 ^ _780205) ^ [_1643421, _1643423, _1643425] : [-(hAPP(hAPP(c_List_Otake(_1643421), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1643421), _1643423), _1643425)) = hAPP(hAPP(c_List_Olist_OCons(_1643421), _1643423), c_List_Olist_ONil(_1643421)))], (43247 ^ _780205) ^ [_1643489, _1643491, _1643493] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643489), tc_List_Olist(_1643489))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643489), tc_List_Olist(_1643489)), c_List_Olist_ONil(_1643489)), _1643491)), c_List_Olistrel1(_1643489, _1643493)))], (43249 ^ _780205) ^ [_1643563, _1643565, _1643567] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643563), tc_List_Olist(_1643563))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643563), tc_List_Olist(_1643563)), _1643565), c_List_Olist_ONil(_1643563))), c_List_Olistrel1(_1643563, _1643567)))], (43251 ^ _780205) ^ [_1643622, _1643624] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643622), tc_List_Olist(_1643622))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643622), tc_List_Olist(_1643622)), c_List_Olist_ONil(_1643622)), c_List_Olist_ONil(_1643622))), c_List_Olistrel(_1643622, _1643624))))], (43253 ^ _780205) ^ [_1643696, _1643698, _1643700] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643696), tc_List_Olist(_1643696))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643696), tc_List_Olist(_1643696)), _1643698), c_List_Olist_ONil(_1643696))), c_List_Olexord(_1643696, _1643700)))], (43255 ^ _780205) ^ [_1643770, _1643772, _1643774] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643770), tc_List_Olist(_1643770))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643770), tc_List_Olist(_1643770)), c_List_Olist_ONil(_1643770)), _1643772)), c_List_Olex(_1643770, _1643774)))], (43257 ^ _780205) ^ [_1643844, _1643846, _1643848] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643844), tc_List_Olist(_1643844))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643844), tc_List_Olist(_1643844)), _1643846), c_List_Olist_ONil(_1643844))), c_List_Olex(_1643844, _1643848)))], (43259 ^ _780205) ^ [_1643903, _1643905, _1643907, _1643909] : [-(hAPP(hAPP(c_List_Otake(_1643903), _1643905), hAPP(hAPP(c_List_Olist_OCons(_1643903), _1643907), _1643909)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1643903), c_List_Olist_ONil(_1643903), hAPP(hAPP(c_COMBB(tc_List_Olist(_1643903), tc_List_Olist(_1643903), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1643903), _1643907)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1643903), tc_List_Olist(_1643903)), c_List_Otake(_1643903)), _1643909)), _1643905))], (43261 ^ _780205) ^ [_1644001, _1644003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1644001), _1644003)), -(c_List_Oupto(_1644001, _1644003) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1644001), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1644001), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1644003)))], (43267 ^ _780205) ^ [_1644118, _1644120] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1644118), _1644120))), -(c_List_Oupto(_1644118, _1644120) = c_List_Olist_ONil(tc_Int_Oint))], (43273 ^ _780205) ^ [_1644176, _1644178, _1644180] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1644176)), -(c_List_Osublist(_1644178, hAPP(hAPP(c_List_Olist_OCons(_1644178), _1644180), c_List_Olist_ONil(_1644178)), _1644176) = hAPP(hAPP(c_List_Olist_OCons(_1644178), _1644180), c_List_Olist_ONil(_1644178)))], (43279 ^ _780205) ^ [_1644301, _1644303, _1644305] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1644301))), -(c_List_Osublist(_1644303, hAPP(hAPP(c_List_Olist_OCons(_1644303), _1644305), c_List_Olist_ONil(_1644303)), _1644301) = c_List_Olist_ONil(_1644303))], (43285 ^ _780205) ^ [_1644359] : [-(c_List_Olists(_1644359, c_Orderings_Obot__class_Obot(tc_fun(_1644359, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1644359)), c_List_Olist_ONil(_1644359)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1644359), tc_HOL_Obool))))], (43287 ^ _780205) ^ [_1644424, _1644426, _1644428, _1644430] : [_1644424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1644426), _1644424), hAPP(hAPP(c_List_Olist_OCons(_1644426), _1644428), _1644430)) = c_List_Olist_ONil(_1644426))], (43293 ^ _780205) ^ [_1644535, _1644537, _1644539, _1644541] : [-(_1644535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1644537), _1644535), hAPP(hAPP(c_List_Olist_OCons(_1644537), _1644539), _1644541)) = hAPP(hAPP(c_List_Olist_OCons(_1644537), _1644539), hAPP(hAPP(c_List_Otake(_1644537), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644535), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1644541)))], (43299 ^ _780205) ^ [_1644624, _1644626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644624)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644626))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644624), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644626)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644624)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644624)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644626))))], (43305 ^ _780205) ^ [_1644783, _1644785] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644783)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644785)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644783), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1644785)) = c_List_Olist_ONil(tc_Int_Oint))], (43311 ^ _780205) ^ [_1644841, _1644843] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1644841), tc_List_Olist(_1644841), c_List_Olistrel(_1644841, _1644843)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1644841)), c_List_Olist_ONil(_1644841)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1644841), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1644841)), c_List_Olist_ONil(_1644841)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1644841), tc_HOL_Obool))))], (43313 ^ _780205) ^ [_1644918, _1644920] : [-(c_List_Oset__Cons(_1644918, _1644920, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1644918)), c_List_Olist_ONil(_1644918)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1644918), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1644918, tc_List_Olist(_1644918), hAPP(hAPP(c_COMBC(_1644918, tc_List_Olist(_1644918), tc_List_Olist(_1644918)), c_List_Olist_OCons(_1644918)), c_List_Olist_ONil(_1644918))), _1644920))], (43315 ^ _780205) ^ [_1645005, _1645007, _1645009] : [hBOOL(hAPP(hAPP(c_member(_1645005), _1645007), hAPP(c_List_Oset(_1645005), _1645009))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645005)), c_List_Oremove1(_1645005, _1645007, _1645009)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645005)), _1645009)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43321 ^ _780205) ^ [_1645150, _1645152, _1645154] : [-(hBOOL(hAPP(hAPP(c_member(_1645150), _1645152), hAPP(c_List_Oset(_1645150), _1645154)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645150)), c_List_Oremove1(_1645150, _1645152, _1645154)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645150)), _1645154))], (43327 ^ _780205) ^ [_1645220, _1645222] : [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), _1645220), _1645222))), 43330 ^ _780205 : [(43331 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1645220), _1645222)), -(c_List_Oupto(_1645220, _1645222) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1645220), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1645220), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1645222)))], (43337 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1645220), _1645222))), -(c_List_Oupto(_1645220, _1645222) = c_List_Olist_ONil(tc_Int_Oint))]]], (43343 ^ _780205) ^ [_1645470, _1645472, _1645474] : [-(_1645470 = c_List_Olist_ONil(_1645472)), -(hBOOL(hAPP(hAPP(c_member(_1645472), hAPP(c_Product__Type_Ofst(_1645472, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1645472, _1645470), _1645474))), hAPP(c_List_Oset(_1645472), _1645470))))], (43349 ^ _780205) ^ [_1645534] : [-(c_List_Olistset(_1645534, c_List_Olist_ONil(tc_fun(_1645534, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1645534)), c_List_Olist_ONil(_1645534)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1645534), tc_HOL_Obool))))], (43351 ^ _780205) ^ [_1645584, _1645586, _1645588, _1645590, _1645592] : [-(hAPP(hAPP(c_List_Ozip(_1645584, _1645586), hAPP(hAPP(c_List_Olist_OCons(_1645584), _1645588), _1645590)), _1645592) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1645584, _1645586)), _1645586, c_List_Olist_ONil(tc_prod(_1645584, _1645586)), hAPP(hAPP(c_COMBC(_1645586, tc_fun(tc_List_Olist(_1645586), tc_List_Olist(tc_prod(_1645584, _1645586))), tc_fun(tc_List_Olist(_1645586), tc_List_Olist(tc_prod(_1645584, _1645586)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1645584, _1645586)), tc_List_Olist(tc_prod(_1645584, _1645586))), tc_fun(tc_fun(tc_List_Olist(_1645586), tc_List_Olist(tc_prod(_1645584, _1645586))), tc_fun(tc_List_Olist(_1645586), tc_List_Olist(tc_prod(_1645584, _1645586)))), _1645586), c_COMBB(tc_List_Olist(tc_prod(_1645584, _1645586)), tc_List_Olist(tc_prod(_1645584, _1645586)), tc_List_Olist(_1645586))), hAPP(hAPP(c_COMBB(tc_prod(_1645584, _1645586), tc_fun(tc_List_Olist(tc_prod(_1645584, _1645586)), tc_List_Olist(tc_prod(_1645584, _1645586))), _1645586), c_List_Olist_OCons(tc_prod(_1645584, _1645586))), hAPP(c_Product__Type_OPair(_1645584, _1645586), _1645588)))), hAPP(c_List_Ozip(_1645584, _1645586), _1645590))), _1645592))], (43353 ^ _780205) ^ [_1645785, _1645787, _1645789, _1645791, _1645793, _1645795] : [-(hAPP(c_List_Olist_Olist__case(_1645785, _1645787, _1645789, _1645791), hAPP(hAPP(c_List_Olist_OCons(_1645787), _1645793), _1645795)) = hAPP(hAPP(_1645791, _1645793), _1645795))], (43355 ^ _780205) ^ [_1645840, _1645842, _1645844, _1645846] : [-(hAPP(c_List_Olist_Olist__case(_1645840, _1645842, _1645844, _1645846), c_List_Olist_ONil(_1645842)) = _1645844)], (43357 ^ _780205) ^ [_1645879, _1645881, _1645883] : [-(c_List_Olistset(_1645879, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1645879, tc_HOL_Obool)), _1645881), _1645883)) = c_List_Oset__Cons(_1645879, _1645881, c_List_Olistset(_1645879, _1645883)))], (43359 ^ _780205) ^ [_1645927, _1645929, _1645931, _1645933, _1645935] : [-(hAPP(hAPP(c_List_Ozip(_1645927, _1645929), _1645931), hAPP(hAPP(c_List_Olist_OCons(_1645929), _1645933), _1645935)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1645927, _1645929)), _1645927, c_List_Olist_ONil(tc_prod(_1645927, _1645929)), hAPP(hAPP(c_COMBC(_1645927, tc_fun(tc_List_Olist(_1645927), tc_List_Olist(tc_prod(_1645927, _1645929))), tc_fun(tc_List_Olist(_1645927), tc_List_Olist(tc_prod(_1645927, _1645929)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1645927, _1645929)), tc_List_Olist(tc_prod(_1645927, _1645929))), tc_fun(tc_fun(tc_List_Olist(_1645927), tc_List_Olist(tc_prod(_1645927, _1645929))), tc_fun(tc_List_Olist(_1645927), tc_List_Olist(tc_prod(_1645927, _1645929)))), _1645927), c_COMBB(tc_List_Olist(tc_prod(_1645927, _1645929)), tc_List_Olist(tc_prod(_1645927, _1645929)), tc_List_Olist(_1645927))), hAPP(hAPP(c_COMBB(tc_prod(_1645927, _1645929), tc_fun(tc_List_Olist(tc_prod(_1645927, _1645929)), tc_List_Olist(tc_prod(_1645927, _1645929))), _1645927), c_List_Olist_OCons(tc_prod(_1645927, _1645929))), hAPP(hAPP(c_COMBC(_1645927, _1645929, tc_prod(_1645927, _1645929)), c_Product__Type_OPair(_1645927, _1645929)), _1645933)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1645927), tc_List_Olist(_1645929), tc_List_Olist(tc_prod(_1645927, _1645929))), c_List_Ozip(_1645927, _1645929)), _1645935))), _1645931))], (43361 ^ _780205) ^ [_1646154, _1646156, _1646158] : [class_Orderings_Olinorder(_1646154), hBOOL(hAPP(c_Finite__Set_Ofinite(_1646154), _1646156)), -(c_List_Olinorder__class_Osorted__list__of__set(_1646154, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1646154, tc_HOL_Obool)), _1646156), hAPP(hAPP(c_Set_Oinsert(_1646154), _1646158), c_Orderings_Obot__class_Obot(tc_fun(_1646154, tc_HOL_Obool))))) = c_List_Oremove1(_1646154, _1646158, c_List_Olinorder__class_Osorted__list__of__set(_1646154, _1646156)))], (43371 ^ _780205) ^ [_1646361, _1646363, _1646365] : [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), _1646361), _1646363))), -(hBOOL(hAPP(hAPP(_1646365, _1646361), _1646363))), 43378 ^ _780205 : [(43379 ^ _780205) ^ [] : [-(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), 43376 ^ [_1646361, _1646363, _1646365]), 43377 ^ [_1646361, _1646363, _1646365]))))], (43387 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1646365, 43376 ^ [_1646361, _1646363, _1646365]), 43377 ^ [_1646361, _1646363, _1646365]))], (43381 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 43376 ^ [_1646361, _1646363, _1646365]), 43377 ^ [_1646361, _1646363, _1646365])), -(hBOOL(hAPP(hAPP(_1646365, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43376 ^ [_1646361, _1646363, _1646365]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 43377 ^ [_1646361, _1646363, _1646365])))]]], (43391 ^ _780205) ^ [_1646852] : [class_Orderings_Olinorder(_1646852), -(c_List_Olinorder__class_Osorted__list__of__set(_1646852, c_Orderings_Obot__class_Obot(tc_fun(_1646852, tc_HOL_Obool))) = c_List_Olist_ONil(_1646852))], (43397 ^ _780205) ^ [_1646963, _1646965, _1646967, _1646969, _1646971] : [_1646963 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1646965, _1646967, _1646969), _1646963), _1646971) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646967), _1646965), c_List_Olist_ONil(_1646967)), _1646971))], (43403 ^ _780205) ^ [_1647086, _1647088, _1647090, _1647092, _1647094] : [-(_1647086 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1647088, _1647090, _1647092), _1647086), _1647094) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1647090), _1647088), tc_prod(_1647090, _1647088), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647090), _1647088), c_List_Olist_ONil(_1647090)), _1647094), hAPP(c_Product__Type_Oprod_Oprod__case(_1647090, _1647088, tc_prod(tc_List_Olist(_1647090), _1647088)), hAPP(hAPP(c_COMBC(_1647090, tc_fun(_1647088, tc_prod(tc_List_Olist(_1647090), _1647088)), tc_fun(_1647088, tc_prod(tc_List_Olist(_1647090), _1647088))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1647090), _1647088), tc_prod(tc_List_Olist(_1647090), _1647088)), tc_fun(tc_fun(_1647088, tc_prod(tc_List_Olist(_1647090), _1647088)), tc_fun(_1647088, tc_prod(tc_List_Olist(_1647090), _1647088))), _1647090), c_COMBB(tc_prod(tc_List_Olist(_1647090), _1647088), tc_prod(tc_List_Olist(_1647090), _1647088), _1647088)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1647090), tc_fun(_1647088, tc_prod(tc_List_Olist(_1647090), _1647088))), tc_fun(tc_prod(tc_List_Olist(_1647090), _1647088), tc_prod(tc_List_Olist(_1647090), _1647088)), _1647090), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1647090), _1647088, tc_prod(tc_List_Olist(_1647090), _1647088))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1647090), tc_List_Olist(_1647090)), tc_fun(tc_List_Olist(_1647090), tc_fun(_1647088, tc_prod(tc_List_Olist(_1647090), _1647088))), _1647090), hAPP(c_COMBB(tc_List_Olist(_1647090), tc_fun(_1647088, tc_prod(tc_List_Olist(_1647090), _1647088)), tc_List_Olist(_1647090)), c_Product__Type_OPair(tc_List_Olist(_1647090), _1647088))), c_List_Olist_OCons(_1647090))))), hAPP(c_Lazy__Sequence_Oanamorph(_1647088, _1647090, _1647092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1647086), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1647092, _1647094)))], (43409 ^ _780205) ^ [_1647380, _1647382, _1647384, _1647386] : [-(c_List_Osublist(_1647380, hAPP(hAPP(c_List_Olist_OCons(_1647380), _1647382), _1647384), _1647386) = hAPP(hAPP(c_List_Oappend(_1647380), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1647380)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1647386)), hAPP(hAPP(c_List_Olist_OCons(_1647380), _1647382), c_List_Olist_ONil(_1647380))), c_List_Olist_ONil(_1647380))), c_List_Osublist(_1647380, _1647384, 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)), _1647386)))))], (43411 ^ _780205) ^ [_1647491, _1647493, _1647495, _1647497, _1647499] : [hAPP(hAPP(c_List_Oappend(_1647491), _1647493), _1647495) = hAPP(hAPP(c_List_Olist_OCons(_1647491), _1647497), _1647499), 43416 ^ _780205 : [(43417 ^ _780205) ^ [] : [-(_1647493 = c_List_Olist_ONil(_1647491))], (43419 ^ _780205) ^ [] : [-(_1647495 = hAPP(hAPP(c_List_Olist_OCons(_1647491), _1647497), _1647499))]], 43421 ^ _780205 : [(43422 ^ _780205) ^ [] : [-(_1647493 = hAPP(hAPP(c_List_Olist_OCons(_1647491), _1647497), 43420 ^ [_1647491, _1647493, _1647495, _1647497, _1647499]))], (43424 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1647491), 43420 ^ [_1647491, _1647493, _1647495, _1647497, _1647499]), _1647495) = _1647499)]]], (43426 ^ _780205) ^ [_1647784, _1647786, _1647788, _1647790, _1647792] : [-(hAPP(hAPP(c_List_Oappend(_1647784), _1647786), _1647788) = hAPP(hAPP(c_List_Olist_OCons(_1647784), _1647790), _1647792)), 43427 ^ _780205 : [(43428 ^ _780205) ^ [] : [_1647786 = c_List_Olist_ONil(_1647784), _1647788 = hAPP(hAPP(c_List_Olist_OCons(_1647784), _1647790), _1647792)], (43434 ^ _780205) ^ [_1647967] : [_1647786 = hAPP(hAPP(c_List_Olist_OCons(_1647784), _1647790), _1647967), hAPP(hAPP(c_List_Oappend(_1647784), _1647967), _1647788) = _1647792]]], (43442 ^ _780205) ^ [_1648155, _1648157, _1648159, _1648161, _1648163] : [hAPP(hAPP(c_List_Olist_OCons(_1648155), _1648157), _1648159) = hAPP(hAPP(c_List_Oappend(_1648155), _1648161), _1648163), 43447 ^ _780205 : [(43448 ^ _780205) ^ [] : [-(_1648161 = c_List_Olist_ONil(_1648155))], (43450 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1648155), _1648157), _1648159) = _1648163)]], 43452 ^ _780205 : [(43453 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1648155), _1648157), 43451 ^ [_1648155, _1648157, _1648159, _1648161, _1648163]) = _1648161)], (43455 ^ _780205) ^ [] : [-(_1648159 = hAPP(hAPP(c_List_Oappend(_1648155), 43451 ^ [_1648155, _1648157, _1648159, _1648161, _1648163]), _1648163))]]], (43457 ^ _780205) ^ [_1648448, _1648450, _1648452, _1648454, _1648456] : [-(hAPP(hAPP(c_List_Olist_OCons(_1648448), _1648450), _1648452) = hAPP(hAPP(c_List_Oappend(_1648448), _1648454), _1648456)), 43458 ^ _780205 : [(43459 ^ _780205) ^ [] : [_1648454 = c_List_Olist_ONil(_1648448), hAPP(hAPP(c_List_Olist_OCons(_1648448), _1648450), _1648452) = _1648456], (43465 ^ _780205) ^ [_1648631] : [hAPP(hAPP(c_List_Olist_OCons(_1648448), _1648450), _1648631) = _1648454, _1648452 = hAPP(hAPP(c_List_Oappend(_1648448), _1648631), _1648456)]]], (43473 ^ _780205) ^ [_1648819, _1648821, _1648823, _1648825, _1648827] : [hAPP(hAPP(c_List_Oappend(_1648819), _1648821), hAPP(hAPP(c_List_Olist_OCons(_1648819), _1648823), c_List_Olist_ONil(_1648819))) = hAPP(hAPP(c_List_Oappend(_1648819), _1648825), hAPP(hAPP(c_List_Olist_OCons(_1648819), _1648827), c_List_Olist_ONil(_1648819))), 43476 ^ _780205 : [(43477 ^ _780205) ^ [] : [-(_1648821 = _1648825)], (43479 ^ _780205) ^ [] : [-(_1648823 = _1648827)]]], (43481 ^ _780205) ^ [_1648996, _1648998, _1649000, _1649002, _1649004] : [-(hAPP(hAPP(c_List_Oappend(_1648996), _1648998), hAPP(hAPP(c_List_Olist_OCons(_1648996), _1649000), c_List_Olist_ONil(_1648996))) = hAPP(hAPP(c_List_Oappend(_1648996), _1649002), hAPP(hAPP(c_List_Olist_OCons(_1648996), _1649004), c_List_Olist_ONil(_1648996)))), _1648998 = _1649002, _1649000 = _1649004], (43491 ^ _780205) ^ [_1649211, _1649213, _1649215, _1649217] : [-(hAPP(hAPP(c_List_Oappend(_1649211), hAPP(hAPP(c_List_Olist_OCons(_1649211), _1649213), _1649215)), _1649217) = hAPP(hAPP(c_List_Olist_OCons(_1649211), _1649213), hAPP(hAPP(c_List_Oappend(_1649211), _1649215), _1649217)))], (43493 ^ _780205) ^ [_1649272, _1649274, _1649276, _1649278, _1649280, _1649282] : [hAPP(hAPP(c_List_Olist_OCons(_1649272), _1649274), _1649276) = _1649278, _1649280 = hAPP(hAPP(c_List_Oappend(_1649272), _1649276), _1649282), -(hAPP(hAPP(c_List_Olist_OCons(_1649272), _1649274), _1649280) = hAPP(hAPP(c_List_Oappend(_1649272), _1649278), _1649282))], (43503 ^ _780205) ^ [_1649502, _1649504, _1649506, _1649508] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649502)), hAPP(hAPP(c_List_Oappend(_1649502), _1649504), _1649506)), c_List_Olists(_1649502, _1649508))), 43506 ^ _780205 : [(43507 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649502)), _1649504), c_List_Olists(_1649502, _1649508))))], (43509 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649502)), _1649506), c_List_Olists(_1649502, _1649508))))]]], (43511 ^ _780205) ^ [_1649693, _1649695, _1649697, _1649699] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649693)), hAPP(hAPP(c_List_Oappend(_1649693), _1649695), _1649697)), c_List_Olists(_1649693, _1649699)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649693)), _1649695), c_List_Olists(_1649693, _1649699))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649693)), _1649697), c_List_Olists(_1649693, _1649699)))], (43521 ^ _780205) ^ [_1649920, _1649922, _1649924, _1649926, _1649928, _1649930] : [hAPP(hAPP(c_List_Oappend(_1649920), _1649922), _1649924) = _1649926, _1649928 = hAPP(hAPP(c_List_Oappend(_1649920), _1649924), _1649930), -(hAPP(hAPP(c_List_Oappend(_1649920), _1649922), _1649928) = hAPP(hAPP(c_List_Oappend(_1649920), _1649926), _1649930))], (43531 ^ _780205) ^ [_1650150, _1650152, _1650154, _1650156] : [hAPP(hAPP(c_List_Oappend(_1650150), _1650152), _1650154) = hAPP(hAPP(c_List_Oappend(_1650150), _1650156), _1650154), -(_1650152 = _1650156)], (43537 ^ _780205) ^ [_1650259, _1650261, _1650263, _1650265] : [_1650261 = _1650265, -(hAPP(hAPP(c_List_Oappend(_1650259), _1650261), _1650263) = hAPP(hAPP(c_List_Oappend(_1650259), _1650265), _1650263))], (43543 ^ _780205) ^ [_1650395, _1650397, _1650399, _1650401] : [hAPP(hAPP(c_List_Oappend(_1650395), _1650397), _1650399) = hAPP(hAPP(c_List_Oappend(_1650395), _1650397), _1650401), -(_1650399 = _1650401)], (43549 ^ _780205) ^ [_1650504, _1650506, _1650508, _1650510] : [_1650508 = _1650510, -(hAPP(hAPP(c_List_Oappend(_1650504), _1650506), _1650508) = hAPP(hAPP(c_List_Oappend(_1650504), _1650506), _1650510))], (43555 ^ _780205) ^ [_1650643, _1650645, _1650647, _1650649, _1650651] : [hAPP(hAPP(c_List_Oappend(_1650643), _1650645), _1650647) = hAPP(hAPP(c_List_Oappend(_1650643), _1650649), _1650651), 43561 ^ _780205 : [(43562 ^ _780205) ^ [] : [-(_1650645 = hAPP(hAPP(c_List_Oappend(_1650643), _1650649), 43558 ^ [_1650643, _1650645, _1650647, _1650649, _1650651]))], (43564 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1650643), 43558 ^ [_1650643, _1650645, _1650647, _1650649, _1650651]), _1650647) = _1650651)]], 43565 ^ _780205 : [(43566 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1650643), _1650645), 43558 ^ [_1650643, _1650645, _1650647, _1650649, _1650651]) = _1650649)], (43568 ^ _780205) ^ [] : [-(_1650647 = hAPP(hAPP(c_List_Oappend(_1650643), 43558 ^ [_1650643, _1650645, _1650647, _1650649, _1650651]), _1650651))]]], (43570 ^ _780205) ^ [_1650974, _1650976, _1650978, _1650980, _1650982] : [-(hAPP(hAPP(c_List_Oappend(_1650974), _1650976), _1650978) = hAPP(hAPP(c_List_Oappend(_1650974), _1650980), _1650982)), 43571 ^ _780205 : [(43572 ^ _780205) ^ [_1651086] : [_1650976 = hAPP(hAPP(c_List_Oappend(_1650974), _1650980), _1651086), hAPP(hAPP(c_List_Oappend(_1650974), _1651086), _1650978) = _1650982], (43578 ^ _780205) ^ [_1651198] : [hAPP(hAPP(c_List_Oappend(_1650974), _1650976), _1651198) = _1650980, _1650978 = hAPP(hAPP(c_List_Oappend(_1650974), _1651198), _1650982)]]], (43586 ^ _780205) ^ [_1651362, _1651364, _1651366, _1651368] : [-(hAPP(hAPP(c_List_Oappend(_1651362), hAPP(hAPP(c_List_Oappend(_1651362), _1651364), _1651366)), _1651368) = hAPP(hAPP(c_List_Oappend(_1651362), _1651364), hAPP(hAPP(c_List_Oappend(_1651362), _1651366), _1651368)))], (43588 ^ _780205) ^ [_1651423, _1651425, _1651427] : [class_Groups_Omonoid__add(_1651423), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1651423), hAPP(hAPP(c_List_Oappend(_1651423), _1651425), _1651427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1651423), hAPP(c_List_Omonoid__add__class_Olistsum(_1651423), _1651425)), hAPP(c_List_Omonoid__add__class_Olistsum(_1651423), _1651427)))], (43594 ^ _780205) ^ [_1651562, _1651564, _1651566] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651562)), hAPP(hAPP(c_List_Oappend(_1651562), _1651564), _1651566)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651562)), _1651564)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651562)), _1651566)))], (43596 ^ _780205) ^ [_1651624, _1651626, _1651628, _1651630, _1651632, _1651634] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651624)), _1651626) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651628)), _1651630), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651624)), _1651632) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651628)), _1651634), -(hAPP(hAPP(c_List_Ozip(_1651624, _1651628), hAPP(hAPP(c_List_Oappend(_1651624), _1651626), _1651632)), hAPP(hAPP(c_List_Oappend(_1651628), _1651630), _1651634)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1651624, _1651628)), hAPP(hAPP(c_List_Ozip(_1651624, _1651628), _1651626), _1651630)), hAPP(hAPP(c_List_Ozip(_1651624, _1651628), _1651632), _1651634)))], (43606 ^ _780205) ^ [_1651933, _1651935, _1651937] : [-(hAPP(c_List_Oset(_1651933), hAPP(hAPP(c_List_Oappend(_1651933), _1651935), _1651937)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1651933, tc_HOL_Obool)), hAPP(c_List_Oset(_1651933), _1651935)), hAPP(c_List_Oset(_1651933), _1651937)))], (43608 ^ _780205) ^ [_1651994, _1651996] : [-(hAPP(hAPP(c_List_Oappend(_1651994), c_List_Olist_ONil(_1651994)), _1651996) = _1651996)], (43610 ^ _780205) ^ [_1652047, _1652049, _1652051] : [c_List_Olist_ONil(_1652047) = hAPP(hAPP(c_List_Oappend(_1652047), _1652049), _1652051), 43613 ^ _780205 : [(43614 ^ _780205) ^ [] : [-(_1652049 = c_List_Olist_ONil(_1652047))], (43616 ^ _780205) ^ [] : [-(_1652051 = c_List_Olist_ONil(_1652047))]]], (43618 ^ _780205) ^ [_1652176, _1652178, _1652180] : [-(c_List_Olist_ONil(_1652176) = hAPP(hAPP(c_List_Oappend(_1652176), _1652178), _1652180)), _1652178 = c_List_Olist_ONil(_1652176), _1652180 = c_List_Olist_ONil(_1652176)], (43628 ^ _780205) ^ [_1652339, _1652341] : [-(hAPP(hAPP(c_List_Oappend(_1652339), _1652341), c_List_Olist_ONil(_1652339)) = _1652341)], (43630 ^ _780205) ^ [_1652392, _1652394, _1652396] : [_1652392 = hAPP(hAPP(c_List_Oappend(_1652394), _1652392), _1652396), -(_1652396 = c_List_Olist_ONil(_1652394))], (43636 ^ _780205) ^ [_1652487, _1652489, _1652491] : [_1652491 = c_List_Olist_ONil(_1652489), -(_1652487 = hAPP(hAPP(c_List_Oappend(_1652489), _1652487), _1652491))], (43642 ^ _780205) ^ [_1652606, _1652608, _1652610] : [_1652606 = hAPP(hAPP(c_List_Oappend(_1652608), _1652610), _1652606), -(_1652610 = c_List_Olist_ONil(_1652608))], (43648 ^ _780205) ^ [_1652701, _1652703, _1652705] : [_1652705 = c_List_Olist_ONil(_1652703), -(_1652701 = hAPP(hAPP(c_List_Oappend(_1652703), _1652705), _1652701))], (43654 ^ _780205) ^ [_1652820, _1652822, _1652824] : [hAPP(hAPP(c_List_Oappend(_1652820), _1652822), _1652824) = c_List_Olist_ONil(_1652820), 43657 ^ _780205 : [(43658 ^ _780205) ^ [] : [-(_1652822 = c_List_Olist_ONil(_1652820))], (43660 ^ _780205) ^ [] : [-(_1652824 = c_List_Olist_ONil(_1652820))]]], (43662 ^ _780205) ^ [_1652949, _1652951, _1652953] : [-(hAPP(hAPP(c_List_Oappend(_1652949), _1652951), _1652953) = c_List_Olist_ONil(_1652949)), _1652951 = c_List_Olist_ONil(_1652949), _1652953 = c_List_Olist_ONil(_1652949)], (43672 ^ _780205) ^ [_1653130, _1653132, _1653134] : [hAPP(hAPP(c_List_Oappend(_1653130), _1653132), _1653134) = _1653132, -(_1653134 = c_List_Olist_ONil(_1653130))], (43678 ^ _780205) ^ [_1653225, _1653227, _1653229] : [_1653229 = c_List_Olist_ONil(_1653225), -(hAPP(hAPP(c_List_Oappend(_1653225), _1653227), _1653229) = _1653227)], (43684 ^ _780205) ^ [_1653344, _1653346, _1653348] : [hAPP(hAPP(c_List_Oappend(_1653344), _1653346), _1653348) = _1653348, -(_1653346 = c_List_Olist_ONil(_1653344))], (43690 ^ _780205) ^ [_1653439, _1653441, _1653443] : [_1653441 = c_List_Olist_ONil(_1653439), -(hAPP(hAPP(c_List_Oappend(_1653439), _1653441), _1653443) = _1653443)], (43696 ^ _780205) ^ [_1653540, _1653542, _1653544] : [_1653540 = _1653542, -(_1653540 = hAPP(hAPP(c_List_Oappend(_1653544), c_List_Olist_ONil(_1653544)), _1653542))], (43702 ^ _780205) ^ [_1653651, _1653653, _1653655] : [_1653651 = c_List_Olist_ONil(_1653653), -(c_List_Obutlast(_1653653, hAPP(hAPP(c_List_Oappend(_1653653), _1653655), _1653651)) = c_List_Obutlast(_1653653, _1653655))], (43708 ^ _780205) ^ [_1653756, _1653758, _1653760] : [-(_1653756 = c_List_Olist_ONil(_1653758)), -(c_List_Obutlast(_1653758, hAPP(hAPP(c_List_Oappend(_1653758), _1653760), _1653756)) = hAPP(hAPP(c_List_Oappend(_1653758), _1653760), c_List_Obutlast(_1653758, _1653756)))], (43714 ^ _780205) ^ [_1653820, _1653822, _1653824, _1653826] : [-(hAPP(hAPP(c_List_Onth(_1653820), hAPP(hAPP(c_List_Oappend(_1653820), _1653822), hAPP(hAPP(c_List_Olist_OCons(_1653820), _1653824), _1653826))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653820)), _1653822)) = _1653824)], (43716 ^ _780205) ^ [_1653880, _1653882, _1653884, _1653886] : [-(hAPP(hAPP(c_List_Onth(_1653880), hAPP(hAPP(c_List_Oappend(_1653880), _1653882), _1653884)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653880)), _1653882)), _1653886)) = hAPP(hAPP(c_List_Onth(_1653880), _1653884), _1653886))], (43718 ^ _780205) ^ [_1653946, _1653948, _1653950, _1653952] : [-(hAPP(hAPP(c_List_Otake(_1653946), _1653948), hAPP(hAPP(c_List_Oappend(_1653946), _1653950), _1653952)) = hAPP(hAPP(c_List_Oappend(_1653946), hAPP(hAPP(c_List_Otake(_1653946), _1653948), _1653950)), hAPP(hAPP(c_List_Otake(_1653946), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1653948), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653946)), _1653950))), _1653952)))], (43720 ^ _780205) ^ [_1654028, _1654030, _1654032, _1654034, _1654036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1654028), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654030)), _1654032))), -(hAPP(hAPP(c_List_Olist__update(_1654030, hAPP(hAPP(c_List_Oappend(_1654030), _1654032), _1654034)), _1654028), _1654036) = hAPP(hAPP(c_List_Oappend(_1654030), hAPP(hAPP(c_List_Olist__update(_1654030, _1654032), _1654028), _1654036)), _1654034))], (43726 ^ _780205) ^ [_1654203, _1654205, _1654207, _1654209, _1654211] : [-(hAPP(hAPP(c_List_Olist__update(_1654203, hAPP(hAPP(c_List_Oappend(_1654203), _1654205), hAPP(hAPP(c_List_Olist_OCons(_1654203), _1654207), _1654209))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654203)), _1654205)), _1654211) = hAPP(hAPP(c_List_Oappend(_1654203), _1654205), hAPP(hAPP(c_List_Olist_OCons(_1654203), _1654211), _1654209)))], (43728 ^ _780205) ^ [_1654297, _1654299, _1654301, _1654303] : [hBOOL(hAPP(hAPP(c_member(_1654297), _1654299), hAPP(c_List_Oset(_1654297), _1654301))), -(c_List_Oremove1(_1654297, _1654299, hAPP(hAPP(c_List_Oappend(_1654297), _1654301), _1654303)) = hAPP(hAPP(c_List_Oappend(_1654297), c_List_Oremove1(_1654297, _1654299, _1654301)), _1654303))], (43734 ^ _780205) ^ [_1654444, _1654446, _1654448, _1654450] : [-(hBOOL(hAPP(hAPP(c_member(_1654444), _1654446), hAPP(c_List_Oset(_1654444), _1654448)))), -(c_List_Oremove1(_1654444, _1654446, hAPP(hAPP(c_List_Oappend(_1654444), _1654448), _1654450)) = hAPP(hAPP(c_List_Oappend(_1654444), _1654448), c_List_Oremove1(_1654444, _1654446, _1654450)))], (43740 ^ _780205) ^ [_1654522, _1654524, _1654526, _1654528] : [43741 ^ _780205 : [(43742 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1654522), _1654524), hAPP(c_List_Oset(_1654522), c_List_Obutlast(_1654522, _1654526))))], (43744 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1654522), _1654524), hAPP(c_List_Oset(_1654522), c_List_Obutlast(_1654522, _1654528))))]], -(hBOOL(hAPP(hAPP(c_member(_1654522), _1654524), hAPP(c_List_Oset(_1654522), c_List_Obutlast(_1654522, hAPP(hAPP(c_List_Oappend(_1654522), _1654526), _1654528))))))], (43748 ^ _780205) ^ [_1654747, _1654749, _1654751] : [-(c_List_Obutlast(_1654747, hAPP(hAPP(c_List_Oappend(_1654747), _1654749), hAPP(hAPP(c_List_Olist_OCons(_1654747), _1654751), c_List_Olist_ONil(_1654747)))) = _1654749)], (43750 ^ _780205) ^ [_1654795, _1654797, _1654799, _1654801, _1654803, _1654805] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654795), tc_List_Olist(_1654795))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654795), tc_List_Olist(_1654795)), hAPP(hAPP(c_List_Oappend(_1654795), _1654797), _1654803)), hAPP(hAPP(c_List_Oappend(_1654795), _1654799), _1654805))), c_List_Olistrel1(_1654795, _1654801)))), 43751 ^ _780205 : [(43752 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654795), tc_List_Olist(_1654795))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654795), tc_List_Olist(_1654795)), _1654797), _1654799)), c_List_Olistrel1(_1654795, _1654801))), _1654803 = _1654805], (43758 ^ _780205) ^ [] : [_1654797 = _1654799, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654795), tc_List_Olist(_1654795))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654795), tc_List_Olist(_1654795)), _1654803), _1654805)), c_List_Olistrel1(_1654795, _1654801)))]]], (43766 ^ _780205) ^ [_1655243, _1655245, _1655247, _1655249, _1655251] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655243), tc_List_Olist(_1655243))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655243), tc_List_Olist(_1655243)), _1655245), _1655247)), c_List_Olexord(_1655243, _1655249))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655243), tc_List_Olist(_1655243))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655243), tc_List_Olist(_1655243)), hAPP(hAPP(c_List_Oappend(_1655243), _1655251), _1655245)), hAPP(hAPP(c_List_Oappend(_1655243), _1655251), _1655247))), c_List_Olexord(_1655243, _1655249))))], (43772 ^ _780205) ^ [_1655496, _1655498, _1655500] : [hBOOL(hAPP(c_List_Odistinct(_1655496), hAPP(hAPP(c_List_Oappend(_1655496), _1655498), _1655500))), 43775 ^ _780205 : [(43776 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1655496), _1655498)))], (43778 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1655496), _1655500)))], (43780 ^ _780205) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1655496, tc_HOL_Obool)), hAPP(c_List_Oset(_1655496), _1655498)), hAPP(c_List_Oset(_1655496), _1655500)) = c_Orderings_Obot__class_Obot(tc_fun(_1655496, tc_HOL_Obool)))]]], (43782 ^ _780205) ^ [_1655713, _1655715, _1655717] : [-(hBOOL(hAPP(c_List_Odistinct(_1655713), hAPP(hAPP(c_List_Oappend(_1655713), _1655715), _1655717)))), hBOOL(hAPP(c_List_Odistinct(_1655713), _1655715)), hBOOL(hAPP(c_List_Odistinct(_1655713), _1655717)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1655713, tc_HOL_Obool)), hAPP(c_List_Oset(_1655713), _1655715)), hAPP(c_List_Oset(_1655713), _1655717)) = c_Orderings_Obot__class_Obot(tc_fun(_1655713, tc_HOL_Obool))], (43796 ^ _780205) ^ [_1656009, _1656011, _1656013, _1656015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656009), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656011)), _1656013))), -(hAPP(hAPP(c_List_Onth(_1656011), hAPP(hAPP(c_List_Oappend(_1656011), _1656013), _1656015)), _1656009) = hAPP(hAPP(c_List_Onth(_1656011), _1656013), _1656009))], (43802 ^ _780205) ^ [_1656156, _1656158, _1656160, _1656162] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656156), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656158)), _1656160)))), -(hAPP(hAPP(c_List_Onth(_1656158), hAPP(hAPP(c_List_Oappend(_1656158), _1656160), _1656162)), _1656156) = hAPP(hAPP(c_List_Onth(_1656158), _1656162), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1656156), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656158)), _1656160))))], (43808 ^ _780205) ^ [_1656265, _1656267, _1656269, _1656271, _1656273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656265), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656267)), _1656269))), -(hAPP(hAPP(c_List_Olist__update(_1656267, hAPP(hAPP(c_List_Oappend(_1656267), _1656269), _1656271)), _1656265), _1656273) = hAPP(hAPP(c_List_Oappend(_1656267), hAPP(hAPP(c_List_Olist__update(_1656267, _1656269), _1656265), _1656273)), _1656271))], (43814 ^ _780205) ^ [_1656434, _1656436, _1656438, _1656440, _1656442] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656434), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656436)), _1656438)))), -(hAPP(hAPP(c_List_Olist__update(_1656436, hAPP(hAPP(c_List_Oappend(_1656436), _1656438), _1656440)), _1656434), _1656442) = hAPP(hAPP(c_List_Oappend(_1656436), _1656438), hAPP(hAPP(c_List_Olist__update(_1656436, _1656440), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1656434), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656436)), _1656438))), _1656442)))], (43820 ^ _780205) ^ [_1656537, _1656539, _1656541, _1656543] : [-(c_List_Osublist(_1656537, hAPP(hAPP(c_List_Oappend(_1656537), _1656539), _1656541), _1656543) = hAPP(hAPP(c_List_Oappend(_1656537), c_List_Osublist(_1656537, _1656539, _1656543)), c_List_Osublist(_1656537, _1656541, 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(_1656537)), _1656539)))), _1656543)))))], (43822 ^ _780205) ^ [_1656616, _1656618, _1656620, _1656622, _1656624, _1656626, _1656628, _1656630] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656616, _1656616)), hAPP(hAPP(c_Product__Type_OPair(_1656616, _1656616), _1656618), _1656620)), _1656622)), _1656624 = hAPP(hAPP(c_List_Oappend(_1656616), _1656626), hAPP(hAPP(c_List_Olist_OCons(_1656616), _1656618), _1656628)), _1656630 = hAPP(hAPP(c_List_Oappend(_1656616), _1656626), hAPP(hAPP(c_List_Olist_OCons(_1656616), _1656620), _1656628)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656616), tc_List_Olist(_1656616))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656616), tc_List_Olist(_1656616)), _1656624), _1656630)), c_List_Olistrel1(_1656616, _1656622))))], (43836 ^ _780205) ^ [_1656995, _1656997, _1656999, _1657001, _1657003, _1657005, _1657007] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656995, _1656995)), hAPP(hAPP(c_Product__Type_OPair(_1656995, _1656995), _1656997), _1656999)), _1657001)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656995), tc_List_Olist(_1656995))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656995), tc_List_Olist(_1656995)), hAPP(hAPP(c_List_Oappend(_1656995), _1657003), hAPP(hAPP(c_List_Olist_OCons(_1656995), _1656997), _1657005))), hAPP(hAPP(c_List_Oappend(_1656995), _1657003), hAPP(hAPP(c_List_Olist_OCons(_1656995), _1656999), _1657007)))), c_List_Olexord(_1656995, _1657001))))], (43842 ^ _780205) ^ [_1657244, _1657246, _1657248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657244), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657246)), _1657248))), -(hAPP(hAPP(c_List_Otake(_1657246), hAPP(c_Nat_OSuc, _1657244)), _1657248) = hAPP(hAPP(c_List_Oappend(_1657246), hAPP(hAPP(c_List_Otake(_1657246), _1657244), _1657248)), hAPP(hAPP(c_List_Olist_OCons(_1657246), hAPP(hAPP(c_List_Onth(_1657246), _1657248), _1657244)), c_List_Olist_ONil(_1657246))))], (43848 ^ _780205) ^ [_1657464, _1657466, _1657468, _1657470, _1657472, _1657474] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657464), tc_List_Olist(_1657464))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657464), tc_List_Olist(_1657464)), hAPP(hAPP(c_List_Oappend(_1657464), _1657466), hAPP(hAPP(c_List_Olist_OCons(_1657464), _1657468), c_List_Olist_ONil(_1657464)))), hAPP(hAPP(c_List_Oappend(_1657464), _1657470), hAPP(hAPP(c_List_Olist_OCons(_1657464), _1657472), c_List_Olist_ONil(_1657464))))), c_List_Olistrel1(_1657464, _1657474))), 43853 ^ _780205 : [(43854 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657464), tc_List_Olist(_1657464))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657464), tc_List_Olist(_1657464)), _1657466), _1657470)), c_List_Olistrel1(_1657464, _1657474))))], (43856 ^ _780205) ^ [] : [-(_1657468 = _1657472)]], 43857 ^ _780205 : [(43858 ^ _780205) ^ [] : [-(_1657466 = _1657470)], (43860 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1657464, _1657464)), hAPP(hAPP(c_Product__Type_OPair(_1657464, _1657464), _1657468), _1657472)), _1657474)))]]], (43862 ^ _780205) ^ [_1657874, _1657876, _1657878, _1657880, _1657882, _1657884] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657874), tc_List_Olist(_1657874))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657874), tc_List_Olist(_1657874)), hAPP(hAPP(c_List_Oappend(_1657874), _1657876), hAPP(hAPP(c_List_Olist_OCons(_1657874), _1657878), c_List_Olist_ONil(_1657874)))), hAPP(hAPP(c_List_Oappend(_1657874), _1657880), hAPP(hAPP(c_List_Olist_OCons(_1657874), _1657882), c_List_Olist_ONil(_1657874))))), c_List_Olistrel1(_1657874, _1657884)))), 43863 ^ _780205 : [(43864 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657874), tc_List_Olist(_1657874))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657874), tc_List_Olist(_1657874)), _1657876), _1657880)), c_List_Olistrel1(_1657874, _1657884))), _1657878 = _1657882], (43870 ^ _780205) ^ [] : [_1657876 = _1657880, hBOOL(hAPP(hAPP(c_member(tc_prod(_1657874, _1657874)), hAPP(hAPP(c_Product__Type_OPair(_1657874, _1657874), _1657878), _1657882)), _1657884))]]], (43878 ^ _780205) ^ [_1658342, _1658344, _1658346, _1658348] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658342), tc_List_Olist(_1658342))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658342), tc_List_Olist(_1658342)), _1658344), _1658346)), c_List_Olistrel1(_1658342, _1658348))), 43883 ^ _780205 : [(43884 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1658342, _1658342)), hAPP(hAPP(c_Product__Type_OPair(_1658342, _1658342), 43881 ^ [_1658342, _1658344, _1658346, _1658348]), 43882 ^ [_1658342, _1658344, _1658346, _1658348])), _1658348)))], (43888 ^ _780205) ^ [] : [-(_1658344 = hAPP(hAPP(c_List_Oappend(_1658342), 43885 ^ [_1658342, _1658344, _1658346, _1658348]), hAPP(hAPP(c_List_Olist_OCons(_1658342), 43881 ^ [_1658342, _1658344, _1658346, _1658348]), 43886 ^ [_1658342, _1658344, _1658346, _1658348])))], (43890 ^ _780205) ^ [] : [-(_1658346 = hAPP(hAPP(c_List_Oappend(_1658342), 43885 ^ [_1658342, _1658344, _1658346, _1658348]), hAPP(hAPP(c_List_Olist_OCons(_1658342), 43882 ^ [_1658342, _1658344, _1658346, _1658348]), 43886 ^ [_1658342, _1658344, _1658346, _1658348])))]]], (43892 ^ _780205) ^ [_1658747, _1658749, _1658751, _1658753, _1658755] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658747), tc_List_Olist(_1658747))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658747), tc_List_Olist(_1658747)), hAPP(hAPP(c_List_Oappend(_1658747), _1658749), _1658751)), hAPP(hAPP(c_List_Oappend(_1658747), _1658749), _1658753))), c_List_Olexord(_1658747, _1658755))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1658747, _1658747)), hAPP(hAPP(c_Product__Type_OPair(_1658747, _1658747), 43897 ^ [_1658747, _1658749, _1658751, _1658753, _1658755]), 43897 ^ [_1658747, _1658749, _1658751, _1658753, _1658755])), _1658755))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658747), tc_List_Olist(_1658747))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658747), tc_List_Olist(_1658747)), _1658751), _1658753)), c_List_Olexord(_1658747, _1658755))))], (43903 ^ _780205) ^ [_1659066, _1659068] : [-(hAPP(c_List_Orotate1(_1659066), _1659068) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1659066), _1659066, c_List_Olist_ONil(_1659066), hAPP(hAPP(c_COMBB(tc_List_Olist(_1659066), tc_fun(tc_List_Olist(_1659066), tc_List_Olist(_1659066)), _1659066), hAPP(c_COMBC(tc_List_Olist(_1659066), tc_List_Olist(_1659066), tc_List_Olist(_1659066)), c_List_Oappend(_1659066))), hAPP(hAPP(c_COMBC(_1659066, tc_List_Olist(_1659066), tc_List_Olist(_1659066)), c_List_Olist_OCons(_1659066)), c_List_Olist_ONil(_1659066)))), _1659068))], (43905 ^ _780205) ^ [_1659160, _1659162, _1659164, _1659166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659160), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659162)), _1659164))), -(hAPP(hAPP(c_List_Olist__update(_1659162, _1659164), _1659160), _1659166) = hAPP(hAPP(c_List_Oappend(_1659162), hAPP(hAPP(c_List_Otake(_1659162), _1659160), _1659164)), hAPP(hAPP(c_List_Olist_OCons(_1659162), _1659166), hAPP(hAPP(c_List_Odrop(_1659162), hAPP(c_Nat_OSuc, _1659160)), _1659164))))], (43911 ^ _780205) ^ [_1659353, _1659355, _1659357] : [-(hAPP(hAPP(c_List_Oappend(_1659353), hAPP(hAPP(c_List_Otake(_1659353), _1659355), _1659357)), hAPP(hAPP(c_List_Odrop(_1659353), _1659355), _1659357)) = _1659357)], (43913 ^ _780205) ^ [_1659404, _1659406, _1659408] : [-(hAPP(hAPP(c_List_Odrop(_1659404), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1659404), _1659406), _1659408)) = _1659408)], (43915 ^ _780205) ^ [_1659447, _1659449, _1659451, _1659453] : [-(hAPP(hAPP(c_List_Odrop(_1659447), hAPP(c_Nat_OSuc, _1659449)), hAPP(hAPP(c_List_Olist_OCons(_1659447), _1659451), _1659453)) = hAPP(hAPP(c_List_Odrop(_1659447), _1659449), _1659453))], (43917 ^ _780205) ^ [_1659503, _1659505, _1659507, _1659509, _1659511] : [hAPP(hAPP(c_List_Odrop(_1659503), _1659505), _1659507) = hAPP(hAPP(c_List_Olist_OCons(_1659503), _1659509), _1659511), -(hAPP(hAPP(c_List_Onth(_1659503), _1659507), _1659505) = _1659509)], (43923 ^ _780205) ^ [_1659634, _1659636, _1659638] : [hBOOL(hAPP(c_List_Odistinct(_1659634), _1659636)), -(hBOOL(hAPP(c_List_Odistinct(_1659634), hAPP(hAPP(c_List_Odrop(_1659634), _1659638), _1659636))))], (43929 ^ _780205) ^ [_1659760, _1659762] : [hBOOL(hAPP(c_List_Odistinct(_1659760), hAPP(c_List_Orotate1(_1659760), _1659762))), -(hBOOL(hAPP(c_List_Odistinct(_1659760), _1659762)))], (43935 ^ _780205) ^ [_1659859, _1659861] : [hBOOL(hAPP(c_List_Odistinct(_1659859), _1659861)), -(hBOOL(hAPP(c_List_Odistinct(_1659859), hAPP(c_List_Orotate1(_1659859), _1659861))))], (43941 ^ _780205) ^ [_1659964, _1659966, _1659968] : [-(c_List_Obutlast(_1659964, hAPP(hAPP(c_List_Odrop(_1659964), _1659966), _1659968)) = hAPP(hAPP(c_List_Odrop(_1659964), _1659966), c_List_Obutlast(_1659964, _1659968)))], (43943 ^ _780205) ^ [_1660013, _1660015, _1660017] : [-(hAPP(hAPP(c_List_Odrop(_1660013), _1660015), c_List_Obutlast(_1660013, _1660017)) = c_List_Obutlast(_1660013, hAPP(hAPP(c_List_Odrop(_1660013), _1660015), _1660017)))], (43945 ^ _780205) ^ [_1660062, _1660064, _1660066, _1660068] : [-(hAPP(hAPP(c_List_Odrop(_1660062), _1660064), hAPP(hAPP(c_List_Otake(_1660062), _1660066), _1660068)) = hAPP(hAPP(c_List_Otake(_1660062), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1660066), _1660064)), hAPP(hAPP(c_List_Odrop(_1660062), _1660064), _1660068)))], (43947 ^ _780205) ^ [_1660129, _1660131, _1660133, _1660135] : [-(hAPP(hAPP(c_List_Otake(_1660129), _1660131), hAPP(hAPP(c_List_Odrop(_1660129), _1660133), _1660135)) = hAPP(hAPP(c_List_Odrop(_1660129), _1660133), hAPP(hAPP(c_List_Otake(_1660129), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1660131), _1660133)), _1660135)))], (43949 ^ _780205) ^ [_1660196, _1660198, _1660200, _1660202] : [-(hAPP(hAPP(c_List_Odrop(_1660196), _1660198), hAPP(hAPP(c_List_Odrop(_1660196), _1660200), _1660202)) = hAPP(hAPP(c_List_Odrop(_1660196), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1660198), _1660200)), _1660202))], (43951 ^ _780205) ^ [_1660255, _1660257] : [-(hAPP(hAPP(c_List_Odrop(_1660255), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1660257) = _1660257)], (43953 ^ _780205) ^ [_1660288, _1660290, _1660292, _1660294, _1660296] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1660288, _1660290)), _1660292), hAPP(hAPP(c_List_Ozip(_1660288, _1660290), _1660294), _1660296)) = hAPP(hAPP(c_List_Ozip(_1660288, _1660290), hAPP(hAPP(c_List_Odrop(_1660288), _1660292), _1660294)), hAPP(hAPP(c_List_Odrop(_1660290), _1660292), _1660296)))], (43955 ^ _780205) ^ [_1660364, _1660366] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660364)), hAPP(c_List_Orotate1(_1660364), _1660366)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660364)), _1660366))], (43957 ^ _780205) ^ [_1660408, _1660410, _1660412] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660408)), hAPP(hAPP(c_List_Odrop(_1660408), _1660410), _1660412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660408)), _1660412)), _1660410))], (43959 ^ _780205) ^ [_1660463, _1660465] : [-(hAPP(c_List_Oset(_1660463), hAPP(c_List_Orotate1(_1660463), _1660465)) = hAPP(c_List_Oset(_1660463), _1660465))], (43961 ^ _780205) ^ [_1660503, _1660505, _1660507, _1660509] : [hBOOL(hAPP(hAPP(c_member(_1660503), _1660505), hAPP(c_List_Oset(_1660503), hAPP(hAPP(c_List_Odrop(_1660503), _1660507), _1660509)))), -(hBOOL(hAPP(hAPP(c_member(_1660503), _1660505), hAPP(c_List_Oset(_1660503), _1660509))))], (43967 ^ _780205) ^ [_1660648, _1660650, _1660652] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660648, tc_HOL_Obool)), hAPP(c_List_Oset(_1660648), hAPP(hAPP(c_List_Odrop(_1660648), _1660650), _1660652))), hAPP(c_List_Oset(_1660648), _1660652))))], (43969 ^ _780205) ^ [_1660703, _1660705] : [-(hAPP(hAPP(c_List_Odrop(_1660703), _1660705), c_List_Olist_ONil(_1660703)) = c_List_Olist_ONil(_1660703))], (43971 ^ _780205) ^ [_1660755, _1660757] : [hAPP(c_List_Orotate1(_1660755), _1660757) = c_List_Olist_ONil(_1660755), -(_1660757 = c_List_Olist_ONil(_1660755))], (43977 ^ _780205) ^ [_1660846, _1660848] : [_1660848 = c_List_Olist_ONil(_1660846), -(hAPP(c_List_Orotate1(_1660846), _1660848) = c_List_Olist_ONil(_1660846))], (43983 ^ _780205) ^ [_1660943, _1660945, _1660947, _1660949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1660943), _1660945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660947, tc_HOL_Obool)), hAPP(c_List_Oset(_1660947), hAPP(hAPP(c_List_Odrop(_1660947), _1660945), _1660949))), hAPP(c_List_Oset(_1660947), hAPP(hAPP(c_List_Odrop(_1660947), _1660943), _1660949)))))], (43989 ^ _780205) ^ [_1661106, _1661108, _1661110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661106)), _1661108)), _1661110)), -(hAPP(hAPP(c_List_Odrop(_1661106), _1661110), _1661108) = c_List_Olist_ONil(_1661106))], (43995 ^ _780205) ^ [_1661247, _1661249, _1661251] : [hAPP(hAPP(c_List_Odrop(_1661247), _1661249), _1661251) = c_List_Olist_ONil(_1661247), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661247)), _1661251)), _1661249)))], (44001 ^ _780205) ^ [_1661366, _1661368, _1661370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661366)), _1661370)), _1661368)), -(hAPP(hAPP(c_List_Odrop(_1661366), _1661368), _1661370) = c_List_Olist_ONil(_1661366))], (44007 ^ _780205) ^ [_1661491, _1661493, _1661495, _1661497] : [-(hAPP(hAPP(c_List_Odrop(_1661491), _1661493), hAPP(hAPP(c_List_Oappend(_1661491), _1661495), _1661497)) = hAPP(hAPP(c_List_Oappend(_1661491), hAPP(hAPP(c_List_Odrop(_1661491), _1661493), _1661495)), hAPP(hAPP(c_List_Odrop(_1661491), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1661493), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661491)), _1661495))), _1661497)))], (44009 ^ _780205) ^ [_1661594, _1661596, _1661598, _1661600] : [hAPP(hAPP(c_List_Oappend(_1661594), _1661596), _1661598) = _1661600, 44012 ^ _780205 : [(44013 ^ _780205) ^ [] : [-(_1661596 = hAPP(hAPP(c_List_Otake(_1661594), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661594)), _1661596)), _1661600))], (44015 ^ _780205) ^ [] : [-(_1661598 = hAPP(hAPP(c_List_Odrop(_1661594), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661594)), _1661596)), _1661600))]]], (44017 ^ _780205) ^ [_1661773, _1661775, _1661777, _1661779] : [-(hAPP(hAPP(c_List_Oappend(_1661773), _1661775), _1661777) = _1661779), _1661775 = hAPP(hAPP(c_List_Otake(_1661773), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661773)), _1661775)), _1661779), _1661777 = hAPP(hAPP(c_List_Odrop(_1661773), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661773)), _1661775)), _1661779)], (44027 ^ _780205) ^ [_1661988, _1661990, _1661992, _1661994] : [-(hAPP(hAPP(c_List_Odrop(_1661988), _1661990), hAPP(hAPP(c_List_Olist_OCons(_1661988), _1661992), _1661994)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1661988), hAPP(hAPP(c_List_Olist_OCons(_1661988), _1661992), _1661994), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1661988), tc_List_Olist(_1661988)), c_List_Odrop(_1661988)), _1661994), _1661990))], (44029 ^ _780205) ^ [_1662079, _1662081, _1662083, _1662085] : [_1662079 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1662081), _1662079), hAPP(hAPP(c_List_Olist_OCons(_1662081), _1662083), _1662085)) = hAPP(hAPP(c_List_Olist_OCons(_1662081), _1662083), _1662085))], (44035 ^ _780205) ^ [_1662202, _1662204, _1662206, _1662208] : [-(_1662202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1662204), _1662202), hAPP(hAPP(c_List_Olist_OCons(_1662204), _1662206), _1662208)) = hAPP(hAPP(c_List_Odrop(_1662204), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1662202), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1662208))], (44041 ^ _780205) ^ [_1662274, _1662276, _1662278, _1662280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1662274), _1662276)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662278)), _1662280))), -(hAPP(hAPP(c_List_Onth(_1662278), hAPP(hAPP(c_List_Odrop(_1662278), _1662274), _1662280)), _1662276) = hAPP(hAPP(c_List_Onth(_1662278), _1662280), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1662274), _1662276)))], (44047 ^ _780205) ^ [_1662475, _1662477, _1662479, _1662481, _1662483] : [hAPP(hAPP(c_List_Oappend(_1662475), _1662477), _1662479) = hAPP(hAPP(c_List_Oappend(_1662475), _1662481), _1662483), 44050 ^ _780205 : [(44051 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662475)), _1662477)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662475)), _1662481))), 44054 ^ _780205 : [(44055 ^ _780205) ^ [] : [-(_1662477 = hAPP(hAPP(c_List_Otake(_1662475), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662475)), _1662477)), _1662481))], (44057 ^ _780205) ^ [] : [-(_1662479 = hAPP(hAPP(c_List_Oappend(_1662475), hAPP(hAPP(c_List_Odrop(_1662475), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662475)), _1662477)), _1662481)), _1662483))]]], (44059 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662475)), _1662477)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662475)), _1662481)))), 44062 ^ _780205 : [(44063 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1662475), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662475)), _1662481)), _1662477) = _1662481)], (44065 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1662475), hAPP(hAPP(c_List_Odrop(_1662475), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662475)), _1662481)), _1662477)), _1662479) = _1662483)]]]]], (44067 ^ _780205) ^ [_1662988, _1662990, _1662992, _1662994, _1662996] : [-(hAPP(hAPP(c_List_Oappend(_1662988), _1662990), _1662992) = hAPP(hAPP(c_List_Oappend(_1662988), _1662994), _1662996)), 44070 ^ _780205 : [(44071 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662988)), _1662990)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662988)), _1662994))))], (44073 ^ _780205) ^ [] : [_1662990 = hAPP(hAPP(c_List_Otake(_1662988), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662988)), _1662990)), _1662994), _1662992 = hAPP(hAPP(c_List_Oappend(_1662988), hAPP(hAPP(c_List_Odrop(_1662988), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662988)), _1662990)), _1662994)), _1662996)]], 44078 ^ _780205 : [(44079 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662988)), _1662990)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662988)), _1662994)))], (44081 ^ _780205) ^ [] : [hAPP(hAPP(c_List_Otake(_1662988), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662988)), _1662994)), _1662990) = _1662994, hAPP(hAPP(c_List_Oappend(_1662988), hAPP(hAPP(c_List_Odrop(_1662988), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662988)), _1662994)), _1662990)), _1662992) = _1662996]]], (44089 ^ _780205) ^ [_1663576, _1663578, _1663580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663576), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663578)), _1663580))), -(hAPP(hAPP(c_List_Olist_OCons(_1663578), hAPP(hAPP(c_List_Onth(_1663578), _1663580), _1663576)), hAPP(hAPP(c_List_Odrop(_1663578), hAPP(c_Nat_OSuc, _1663576)), _1663580)) = hAPP(hAPP(c_List_Odrop(_1663578), _1663576), _1663580))], (44095 ^ _780205) ^ [_1663747, _1663749, _1663751, _1663753] : [-(hAPP(c_List_Orotate1(_1663747), c_List_Olist_ONil(_1663747)) = c_List_Olist_ONil(_1663747))], (44097 ^ _780205) ^ [_1663782, _1663784, _1663786, _1663788] : [-(hAPP(c_List_Orotate1(_1663784), hAPP(hAPP(c_List_Olist_OCons(_1663784), _1663786), _1663788)) = hAPP(hAPP(c_List_Oappend(_1663784), _1663788), hAPP(hAPP(c_List_Olist_OCons(_1663784), _1663786), c_List_Olist_ONil(_1663784))))], (44099 ^ _780205) ^ [_1663859, _1663861, _1663863, _1663865] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1663859) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1663861), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1663859)), hAPP(hAPP(c_List_Olist_OCons(_1663861), _1663863), _1663865)) = hAPP(hAPP(c_List_Olist_OCons(_1663861), _1663863), _1663865))], (44105 ^ _780205) ^ [_1663994, _1663996, _1663998, _1664000] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1663994) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1663996), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1663994)), hAPP(hAPP(c_List_Olist_OCons(_1663996), _1663998), _1664000)) = hAPP(hAPP(c_List_Odrop(_1663996), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1663994)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1664000))], (44111 ^ _780205) ^ [_1664075, _1664077, _1664079, _1664081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1664075), _1664077)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664079)), _1664081))), -(hAPP(hAPP(c_List_Otake(_1664079), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1664075), _1664077)), _1664081) = hAPP(hAPP(c_List_Oappend(_1664079), hAPP(hAPP(c_List_Otake(_1664079), _1664075), _1664081)), hAPP(hAPP(c_List_Otake(_1664079), _1664077), hAPP(hAPP(c_List_Odrop(_1664079), _1664075), _1664081))))], (44117 ^ _780205) ^ [_1664284, _1664286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664284)), _1664286)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1664284), _1664286) = _1664286)], (44123 ^ _780205) ^ [_1664395, _1664397, _1664399, _1664401, _1664403] : [-(hAPP(hAPP(c_List_Ozip(_1664395, _1664397), _1664399), hAPP(hAPP(c_List_Oappend(_1664397), _1664401), _1664403)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1664395, _1664397)), hAPP(hAPP(c_List_Ozip(_1664395, _1664397), hAPP(hAPP(c_List_Otake(_1664395), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664397)), _1664401)), _1664399)), _1664401)), hAPP(hAPP(c_List_Ozip(_1664395, _1664397), hAPP(hAPP(c_List_Odrop(_1664395), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664397)), _1664401)), _1664399)), _1664403)))], (44125 ^ _780205) ^ [_1664502, _1664504, _1664506, _1664508, _1664510] : [-(hAPP(hAPP(c_List_Ozip(_1664502, _1664504), hAPP(hAPP(c_List_Oappend(_1664502), _1664506), _1664508)), _1664510) = hAPP(hAPP(c_List_Oappend(tc_prod(_1664502, _1664504)), hAPP(hAPP(c_List_Ozip(_1664502, _1664504), _1664506), hAPP(hAPP(c_List_Otake(_1664504), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664502)), _1664506)), _1664510))), hAPP(hAPP(c_List_Ozip(_1664502, _1664504), _1664508), hAPP(hAPP(c_List_Odrop(_1664504), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664502)), _1664506)), _1664510))))], (44127 ^ _780205) ^ [_1664609, _1664611, _1664613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1664609), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664611)), _1664613))), -(_1664613 = hAPP(hAPP(c_List_Oappend(_1664611), hAPP(hAPP(c_List_Otake(_1664611), _1664609), _1664613)), hAPP(hAPP(c_List_Olist_OCons(_1664611), hAPP(hAPP(c_List_Onth(_1664611), _1664613), _1664609)), hAPP(hAPP(c_List_Odrop(_1664611), hAPP(c_Nat_OSuc, _1664609)), _1664613))))], (44133 ^ _780205) ^ [_1664798, _1664800, _1664802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1664798), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664800)), _1664802))), -(hAPP(hAPP(c_List_Oappend(_1664800), hAPP(hAPP(c_List_Otake(_1664800), _1664798), _1664802)), hAPP(hAPP(c_List_Olist_OCons(_1664800), hAPP(c_List_Ohd(_1664800), hAPP(hAPP(c_List_Odrop(_1664800), _1664798), _1664802))), c_List_Olist_ONil(_1664800))) = hAPP(hAPP(c_List_Otake(_1664800), hAPP(c_Nat_OSuc, _1664798)), _1664802))], (44139 ^ _780205) ^ [_1665000, _1665002, _1665004] : [-(_1665000 = c_List_Olist_ONil(_1665002)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665004), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665002)), _1665000))), -(hAPP(c_List_Ohd(_1665002), hAPP(hAPP(c_List_Odrop(_1665002), _1665004), _1665000)) = hAPP(hAPP(c_List_Onth(_1665002), _1665000), _1665004))], (44149 ^ _780205) ^ [_1665199, _1665201, _1665203] : [-(hAPP(c_List_Ohd(_1665199), hAPP(hAPP(c_List_Olist_OCons(_1665199), _1665201), _1665203)) = _1665201)], (44151 ^ _780205) ^ [_1665235, _1665237, _1665239] : [-(_1665235 = c_List_Olist_ONil(_1665237)), -(hAPP(c_List_Ohd(_1665237), hAPP(hAPP(c_List_Oappend(_1665237), _1665235), _1665239)) = hAPP(c_List_Ohd(_1665237), _1665235))], (44157 ^ _780205) ^ [_1665305, _1665307, _1665309] : [_1665305 = c_List_Olist_ONil(_1665307), -(hAPP(c_List_Ohd(_1665307), hAPP(hAPP(c_List_Oappend(_1665307), _1665305), _1665309)) = hAPP(c_List_Ohd(_1665307), _1665309))], (44163 ^ _780205) ^ [_1665418, _1665420, _1665422] : [-(_1665418 = c_List_Olist_ONil(_1665420)), -(hAPP(c_List_Ohd(_1665420), hAPP(hAPP(c_List_Oappend(_1665420), _1665418), _1665422)) = hAPP(c_List_Ohd(_1665420), _1665418))], (44169 ^ _780205) ^ [_1665474, _1665476] : [-(_1665474 = c_List_Olist_ONil(_1665476)), -(hBOOL(hAPP(hAPP(c_member(_1665476), hAPP(c_List_Ohd(_1665476), _1665474)), hAPP(c_List_Oset(_1665476), _1665474))))], (44175 ^ _780205) ^ [_1665525, _1665527] : [-(_1665525 = c_List_Olist_ONil(_1665527)), -(hAPP(c_List_Ohd(_1665527), _1665525) = hAPP(hAPP(c_List_Onth(_1665527), _1665525), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44181 ^ _780205) ^ [_1665572, _1665574] : [-(_1665572 = c_List_Olist_ONil(_1665574)), -(hAPP(c_List_Orotate1(_1665574), _1665572) = hAPP(hAPP(c_List_Oappend(_1665574), hAPP(c_List_Otl(_1665574), _1665572)), hAPP(hAPP(c_List_Olist_OCons(_1665574), hAPP(c_List_Ohd(_1665574), _1665572)), c_List_Olist_ONil(_1665574))))], (44187 ^ _780205) ^ [_1665639, _1665641, _1665643] : [-(_1665639 = c_List_Olist_ONil(_1665641)), -(hAPP(c_List_Ohd(_1665641), hAPP(c_List_Orotate(_1665641, _1665643), _1665639)) = hAPP(hAPP(c_List_Onth(_1665641), _1665639), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1665643, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665641)), _1665639))))], (44193 ^ _780205) ^ [_1665709, _1665711, _1665713] : [-(hAPP(hAPP(c_List_Odrop(_1665709), _1665711), hAPP(c_List_Otl(_1665709), _1665713)) = hAPP(c_List_Otl(_1665709), hAPP(hAPP(c_List_Odrop(_1665709), _1665711), _1665713)))], (44195 ^ _780205) ^ [_1665762, _1665764, _1665766] : [-(hAPP(c_List_Otl(_1665762), hAPP(hAPP(c_List_Odrop(_1665762), _1665764), _1665766)) = hAPP(hAPP(c_List_Odrop(_1665762), _1665764), hAPP(c_List_Otl(_1665762), _1665766)))], (44197 ^ _780205) ^ [_1665815, _1665817, _1665819] : [-(hAPP(c_List_Otl(_1665815), hAPP(hAPP(c_List_Olist_OCons(_1665815), _1665817), _1665819)) = _1665819)], (44199 ^ _780205) ^ [_1665855, _1665857] : [hBOOL(hAPP(c_List_Odistinct(_1665855), _1665857)), -(hBOOL(hAPP(c_List_Odistinct(_1665855), hAPP(c_List_Otl(_1665855), _1665857))))], (44205 ^ _780205) ^ [_1665976, _1665978, _1665980] : [hBOOL(hAPP(c_List_Odistinct(_1665976), hAPP(c_List_Orotate(_1665976, _1665978), _1665980))), -(hBOOL(hAPP(c_List_Odistinct(_1665976), _1665980)))], (44211 ^ _780205) ^ [_1666079, _1666081, _1666083] : [hBOOL(hAPP(c_List_Odistinct(_1666079), _1666083)), -(hBOOL(hAPP(c_List_Odistinct(_1666079), hAPP(c_List_Orotate(_1666079, _1666081), _1666083))))], (44217 ^ _780205) ^ [_1666188, _1666190, _1666192, _1666194] : [-(hAPP(c_List_Orotate(_1666188, _1666190), hAPP(c_List_Orotate(_1666188, _1666192), _1666194)) = hAPP(c_List_Orotate(_1666188, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666190), _1666192)), _1666194))], (44219 ^ _780205) ^ [_1666241] : [-(c_List_Orotate(_1666241, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1666241)))], (44221 ^ _780205) ^ [_1666271, _1666273, _1666275] : [-(c_List_Orotate(_1666271, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666273), _1666275)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1666271), tc_List_Olist(_1666271), tc_List_Olist(_1666271), c_List_Orotate(_1666271, _1666273)), c_List_Orotate(_1666271, _1666275)))], (44223 ^ _780205) ^ [_1666327, _1666329, _1666331] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666327)), hAPP(c_List_Orotate(_1666327, _1666329), _1666331)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666327)), _1666331))], (44225 ^ _780205) ^ [_1666374, _1666376, _1666378] : [-(hAPP(c_List_Oset(_1666374), hAPP(c_List_Orotate(_1666374, _1666376), _1666378)) = hAPP(c_List_Oset(_1666374), _1666378))], (44227 ^ _780205) ^ [_1666417] : [-(hAPP(c_List_Otl(_1666417), c_List_Olist_ONil(_1666417)) = c_List_Olist_ONil(_1666417))], (44229 ^ _780205) ^ [_1666467, _1666469, _1666471] : [hAPP(c_List_Orotate(_1666467, _1666469), _1666471) = c_List_Olist_ONil(_1666467), -(_1666471 = c_List_Olist_ONil(_1666467))], (44235 ^ _780205) ^ [_1666562, _1666564, _1666566] : [_1666566 = c_List_Olist_ONil(_1666562), -(hAPP(c_List_Orotate(_1666562, _1666564), _1666566) = c_List_Olist_ONil(_1666562))], (44241 ^ _780205) ^ [_1666663, _1666665] : [-(c_List_Orotate(_1666663, _1666665) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1666663), tc_List_Olist(_1666663)), _1666665), c_List_Orotate1(_1666663)))], (44243 ^ _780205) ^ [_1666706, _1666708, _1666710] : [-(hAPP(c_List_Orotate1(_1666706), hAPP(c_List_Orotate(_1666706, _1666708), _1666710)) = hAPP(c_List_Orotate(_1666706, _1666708), hAPP(c_List_Orotate1(_1666706), _1666710)))], (44245 ^ _780205) ^ [_1666751, _1666753, _1666755] : [-(_1666751 = c_List_Olist_ONil(_1666753)), -(hAPP(c_List_Otl(_1666753), hAPP(hAPP(c_List_Oappend(_1666753), _1666751), _1666755)) = hAPP(hAPP(c_List_Oappend(_1666753), hAPP(c_List_Otl(_1666753), _1666751)), _1666755))], (44251 ^ _780205) ^ [_1666817, _1666819, _1666821] : [-(hAPP(hAPP(c_List_Otake(_1666817), _1666819), hAPP(c_List_Otl(_1666817), _1666821)) = hAPP(c_List_Otl(_1666817), hAPP(hAPP(c_List_Otake(_1666817), hAPP(c_Nat_OSuc, _1666819)), _1666821)))], (44253 ^ _780205) ^ [_1666873, _1666875, _1666877] : [-(hAPP(c_List_Orotate(_1666873, _1666875), _1666877) = hAPP(c_List_Orotate(_1666873, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1666875, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666873)), _1666877))), _1666877))], (44255 ^ _780205) ^ [_1666923, _1666925, _1666927] : [-(hAPP(hAPP(c_List_Odrop(_1666923), hAPP(c_Nat_OSuc, _1666925)), _1666927) = hAPP(hAPP(c_List_Odrop(_1666923), _1666925), hAPP(c_List_Otl(_1666923), _1666927)))], (44257 ^ _780205) ^ [_1666974, _1666976, _1666978] : [-(hAPP(c_List_Orotate(_1666974, hAPP(c_Nat_OSuc, _1666976)), _1666978) = hAPP(c_List_Orotate1(_1666974), hAPP(c_List_Orotate(_1666974, _1666976), _1666978)))], (44259 ^ _780205) ^ [_1667021, _1667023, _1667025] : [-(hAPP(c_List_Otl(_1667021), hAPP(hAPP(c_List_Oappend(_1667021), _1667023), _1667025)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1667021), _1667021, hAPP(c_List_Otl(_1667021), _1667025), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1667021), tc_List_Olist(_1667021)), _1667021), hAPP(hAPP(c_COMBC(tc_List_Olist(_1667021), tc_List_Olist(_1667021), tc_List_Olist(_1667021)), c_List_Oappend(_1667021)), _1667025))), _1667023))], (44261 ^ _780205) ^ [_1667107, _1667109, _1667111] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1667107, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667109)), _1667111)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1667109, _1667107), _1667111) = _1667111)], (44267 ^ _780205) ^ [_1667220, _1667222, _1667224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667220)), _1667222)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1667220, _1667224), _1667222) = _1667222)], (44273 ^ _780205) ^ [_1667335, _1667337] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667335)), hAPP(c_List_Otl(_1667335), _1667337)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667335)), _1667337)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44275 ^ _780205) ^ [_1667385, _1667387, _1667389] : [-(hAPP(c_List_Otl(_1667385), hAPP(hAPP(c_List_Otake(_1667385), _1667387), _1667389)) = hAPP(hAPP(c_List_Otake(_1667385), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1667387), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1667385), _1667389)))], (44277 ^ _780205) ^ [_1667440, _1667442, _1667444] : [-(_1667440 = c_List_Olist_ONil(_1667442)), -(hAPP(hAPP(c_List_Otake(_1667442), hAPP(c_Nat_OSuc, _1667444)), _1667440) = hAPP(hAPP(c_List_Olist_OCons(_1667442), hAPP(c_List_Ohd(_1667442), _1667440)), hAPP(hAPP(c_List_Otake(_1667442), _1667444), hAPP(c_List_Otl(_1667442), _1667440))))], (44283 ^ _780205) ^ [_1667517, _1667519, _1667521] : [-(hAPP(c_List_Orotate(_1667517, _1667519), _1667521) = hAPP(hAPP(c_List_Oappend(_1667517), hAPP(hAPP(c_List_Odrop(_1667517), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1667519, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667517)), _1667521))), _1667521)), hAPP(hAPP(c_List_Otake(_1667517), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1667519, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667517)), _1667521))), _1667521)))], (44285 ^ _780205) ^ [_1667596, _1667598] : [class_Lattices_Oab__semigroup__idem__mult(_1667596), -(_1667598 = c_List_Olist_ONil(_1667596)), -(hAPP(c_Finite__Set_Ofold1(_1667596, c_Groups_Otimes__class_Otimes(_1667596)), hAPP(c_List_Oset(_1667596), _1667598)) = hAPP(c_List_Ofoldl(_1667596, _1667596, c_Groups_Otimes__class_Otimes(_1667596), hAPP(c_List_Ohd(_1667596), _1667598)), hAPP(c_List_Otl(_1667596), _1667598)))], (44295 ^ _780205) ^ [_1667756, _1667758, _1667760, _1667762] : [44296 ^ _780205 : [(44297 ^ _780205) ^ [_1667853, _1667855] : [_1667756 = hAPP(hAPP(c_List_Olist_OCons(_1667758), _1667855), _1667853)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667758), tc_List_Olist(_1667758))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667758), tc_List_Olist(_1667758)), _1667760), hAPP(hAPP(c_List_Oappend(_1667758), _1667760), _1667756))), c_List_Olexord(_1667758, _1667762))))], (44301 ^ _780205) ^ [_1667952, _1667954, _1667956, _1667958] : [-(hAPP(c_List_Ofoldl(_1667952, _1667954, _1667956, _1667958), c_List_Olist_ONil(_1667954)) = _1667958)], (44303 ^ _780205) ^ [_1667991, _1667993, _1667995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667991), _1667993)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667991), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1667993), _1667995))))], (44309 ^ _780205) ^ [_1668106, _1668108, _1668110, _1668112] : [class_Groups_Osemigroup__add(_1668106), -(hAPP(c_List_Ofoldl(_1668106, _1668106, c_Groups_Oplus__class_Oplus(_1668106), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1668106), _1668108), _1668110)), _1668112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1668106), _1668108), hAPP(c_List_Ofoldl(_1668106, _1668106, c_Groups_Oplus__class_Oplus(_1668106), _1668110), _1668112)))], (44315 ^ _780205) ^ [_1668257, _1668259, _1668261] : [class_Groups_Omonoid__add(_1668257), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1668257), _1668259), hAPP(c_List_Ofoldl(_1668257, _1668257, c_Groups_Oplus__class_Oplus(_1668257), c_Groups_Ozero__class_Ozero(_1668257)), _1668261)) = hAPP(c_List_Ofoldl(_1668257, _1668257, c_Groups_Oplus__class_Oplus(_1668257), _1668259), _1668261))], (44321 ^ _780205) ^ [_1668394, _1668396, _1668398, _1668400, _1668402, _1668404] : [-(hAPP(c_List_Ofoldl(_1668394, _1668396, _1668398, _1668400), hAPP(hAPP(c_List_Olist_OCons(_1668396), _1668402), _1668404)) = hAPP(c_List_Ofoldl(_1668394, _1668396, _1668398, hAPP(hAPP(_1668398, _1668400), _1668402)), _1668404))], (44323 ^ _780205) ^ [_1668457, _1668459, _1668461, _1668463, _1668465, _1668467] : [-(hAPP(c_List_Ofoldl(_1668457, _1668459, _1668461, _1668463), hAPP(hAPP(c_List_Oappend(_1668459), _1668465), _1668467)) = hAPP(c_List_Ofoldl(_1668457, _1668459, _1668461, hAPP(c_List_Ofoldl(_1668457, _1668459, _1668461, _1668463), _1668465)), _1668467))], (44325 ^ _780205) ^ [_1668522] : [class_Groups_Omonoid__add(_1668522), -(c_List_Omonoid__add__class_Olistsum(_1668522) = c_List_Ofoldl(_1668522, _1668522, c_Groups_Oplus__class_Oplus(_1668522), c_Groups_Ozero__class_Ozero(_1668522)))], (44331 ^ _780205) ^ [_1668632, _1668634] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1668632), _1668634) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44334 ^ _780205 : [(44335 ^ _780205) ^ [] : [-(_1668632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44337 ^ _780205) ^ [_1668746] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1668746), hAPP(c_List_Oset(tc_Nat_Onat), _1668634))), -(_1668746 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44343 ^ _780205) ^ [_1668843, _1668845] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1668843), _1668845) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1668843 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44349 ^ _780205 : [(44350 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 44348 ^ [_1668843, _1668845]), hAPP(c_List_Oset(tc_Nat_Onat), _1668845))))], (44352 ^ _780205) ^ [] : [44348 ^ [_1668843, _1668845] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (44356 ^ _780205) ^ [_1669069, _1669071, _1669073, _1669075, _1669077] : [c_Finite__Set_Ofun__left__comm__idem(_1669069, _1669071, _1669073), -(hAPP(hAPP(c_Finite__Set_Ofold(_1669069, _1669071, _1669073), _1669075), hAPP(c_List_Oset(_1669069), _1669077)) = hAPP(c_List_Ofoldl(_1669071, _1669069, hAPP(c_COMBC(_1669069, _1669071, _1669071), _1669073), _1669075), _1669077))], (44362 ^ _780205) ^ [_1669214, _1669216] : [class_Complete__Lattice_Ocomplete__lattice(_1669214), -(c_Complete__Lattice_OSup__class_OSup(_1669214, hAPP(c_List_Oset(_1669214), _1669216)) = hAPP(c_List_Ofoldl(_1669214, _1669214, c_Lattices_Osemilattice__sup__class_Osup(_1669214), c_Orderings_Obot__class_Obot(_1669214)), _1669216))], (44368 ^ _780205) ^ [_1669329, _1669331] : [class_Complete__Lattice_Ocomplete__lattice(_1669329), -(c_Complete__Lattice_OInf__class_OInf(_1669329, hAPP(c_List_Oset(_1669329), _1669331)) = hAPP(c_List_Ofoldl(_1669329, _1669329, c_Lattices_Osemilattice__inf__class_Oinf(_1669329), c_Orderings_Otop__class_Otop(_1669329)), _1669331))], (44374 ^ _780205) ^ [_1669444, _1669446, _1669448] : [class_Lattices_Olattice(_1669444), -(c_Big__Operators_Olattice__class_OSup__fin(_1669444, hAPP(c_List_Oset(_1669444), hAPP(hAPP(c_List_Olist_OCons(_1669444), _1669446), _1669448))) = hAPP(c_List_Ofoldl(_1669444, _1669444, c_Lattices_Osemilattice__sup__class_Osup(_1669444), _1669446), _1669448))], (44380 ^ _780205) ^ [_1669573, _1669575, _1669577] : [class_Lattices_Olattice(_1669573), -(c_Big__Operators_Olattice__class_OInf__fin(_1669573, hAPP(c_List_Oset(_1669573), hAPP(hAPP(c_List_Olist_OCons(_1669573), _1669575), _1669577))) = hAPP(c_List_Ofoldl(_1669573, _1669573, c_Lattices_Osemilattice__inf__class_Oinf(_1669573), _1669575), _1669577))], (44386 ^ _780205) ^ [_1669702, _1669704, _1669706] : [class_Orderings_Olinorder(_1669702), -(c_Big__Operators_Olinorder__class_OMin(_1669702, hAPP(c_List_Oset(_1669702), hAPP(hAPP(c_List_Olist_OCons(_1669702), _1669704), _1669706))) = hAPP(c_List_Ofoldl(_1669702, _1669702, c_Orderings_Oord__class_Omin(_1669702), _1669704), _1669706))], (44392 ^ _780205) ^ [_1669831, _1669833, _1669835] : [class_Orderings_Olinorder(_1669831), -(c_Big__Operators_Olinorder__class_OMax(_1669831, hAPP(c_List_Oset(_1669831), hAPP(hAPP(c_List_Olist_OCons(_1669831), _1669833), _1669835))) = hAPP(c_List_Ofoldl(_1669831, _1669831, c_Orderings_Oord__class_Omax(_1669831), _1669833), _1669835))], (44398 ^ _780205) ^ [_1669960, _1669962, _1669964] : [class_Orderings_Olinorder(_1669960), -(c_Big__Operators_Olattice_OInf__fin(_1669960, c_Orderings_Oord__class_Omin(_1669960), hAPP(c_List_Oset(_1669960), hAPP(hAPP(c_List_Olist_OCons(_1669960), _1669962), _1669964))) = hAPP(c_List_Ofoldl(_1669960, _1669960, c_Orderings_Oord__class_Omin(_1669960), _1669962), _1669964))], (44404 ^ _780205) ^ [_1670095, _1670097, _1670099] : [class_Orderings_Olinorder(_1670095), -(c_Big__Operators_Olattice_OSup__fin(_1670095, c_Orderings_Oord__class_Omax(_1670095), hAPP(c_List_Oset(_1670095), hAPP(hAPP(c_List_Olist_OCons(_1670095), _1670097), _1670099))) = hAPP(c_List_Ofoldl(_1670095, _1670095, c_Orderings_Oord__class_Omax(_1670095), _1670097), _1670099))], (44410 ^ _780205) ^ [_1670230, _1670232, _1670234, _1670236] : [class_Complete__Lattice_Ocomplete__lattice(_1670230), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1670232, _1670230), hAPP(c_List_Oset(_1670232), _1670234)), _1670236) = hAPP(c_List_Ofoldl(_1670230, _1670232, hAPP(c_COMBC(_1670232, _1670230, _1670230), hAPP(hAPP(c_COMBB(_1670230, tc_fun(_1670230, _1670230), _1670232), c_Lattices_Osemilattice__sup__class_Osup(_1670230)), _1670236)), c_Orderings_Obot__class_Obot(_1670230)), _1670234))], (44416 ^ _780205) ^ [_1670401, _1670403, _1670405, _1670407] : [class_Complete__Lattice_Ocomplete__lattice(_1670401), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670403, _1670401), hAPP(c_List_Oset(_1670403), _1670405)), _1670407) = hAPP(c_List_Ofoldl(_1670401, _1670403, hAPP(c_COMBC(_1670403, _1670401, _1670401), hAPP(hAPP(c_COMBB(_1670401, tc_fun(_1670401, _1670401), _1670403), c_Lattices_Osemilattice__inf__class_Oinf(_1670401)), _1670407)), c_Orderings_Otop__class_Otop(_1670401)), _1670405))], (44422 ^ _780205) ^ [_1670572, _1670574] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1670572), hAPP(c_List_Oset(tc_Nat_Onat), _1670574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1670572), 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)), _1670574))))], (44428 ^ _780205) ^ [_1670681, _1670683, _1670685] : [class_Orderings_Olinorder(_1670681), hBOOL(hAPP(c_Finite__Set_Ofinite(_1670681), _1670683)), -(c_List_Olinorder__class_Osorted__list__of__set(_1670681, hAPP(hAPP(c_Set_Oinsert(_1670681), _1670685), _1670683)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1670681, _1670681, c_COMBI(_1670681)), _1670685), c_List_Olinorder__class_Osorted__list__of__set(_1670681, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1670681, tc_HOL_Obool)), _1670683), hAPP(hAPP(c_Set_Oinsert(_1670681), _1670685), c_Orderings_Obot__class_Obot(tc_fun(_1670681, tc_HOL_Obool)))))))], (44438 ^ _780205) ^ [_1670938, _1670940, _1670942] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1670938), tc_List_Olist(_1670938))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1670938), tc_List_Olist(_1670938)), c_List_Olist_ONil(_1670938)), _1670940)), c_List_Olexord(_1670938, _1670942))), -(_1670940 = hAPP(hAPP(c_List_Olist_OCons(_1670938), 44441 ^ [_1670938, _1670940, _1670942]), 44442 ^ [_1670938, _1670940, _1670942]))], (44446 ^ _780205) ^ [_1671121, _1671123, _1671125] : [44447 ^ _780205 : [(44448 ^ _780205) ^ [_1671210, _1671212] : [_1671123 = hAPP(hAPP(c_List_Olist_OCons(_1671121), _1671212), _1671210)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671121), tc_List_Olist(_1671121))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671121), tc_List_Olist(_1671121)), c_List_Olist_ONil(_1671121)), _1671123)), c_List_Olexord(_1671121, _1671125))))], (44452 ^ _780205) ^ [_1671305, _1671307, _1671309, _1671311] : [class_Orderings_Olinorder(_1671305), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1671307, _1671305, _1671309), _1671311), c_List_Olist_ONil(_1671307)) = hAPP(hAPP(c_List_Olist_OCons(_1671307), _1671311), c_List_Olist_ONil(_1671307)))], (44458 ^ _780205) ^ [_1671428, _1671430, _1671432, _1671434, _1671436, _1671438] : [class_Orderings_Olinorder(_1671428), 44461 ^ _780205 : [(44462 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1671428), hAPP(_1671430, _1671432)), hAPP(_1671430, _1671434))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1671436, _1671428, _1671430), _1671432), hAPP(hAPP(c_List_Olist_OCons(_1671436), _1671434), _1671438)) = hAPP(hAPP(c_List_Olist_OCons(_1671436), _1671432), hAPP(hAPP(c_List_Olist_OCons(_1671436), _1671434), _1671438)))], (44468 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1671428), hAPP(_1671430, _1671432)), hAPP(_1671430, _1671434)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1671436, _1671428, _1671430), _1671432), hAPP(hAPP(c_List_Olist_OCons(_1671436), _1671434), _1671438)) = hAPP(hAPP(c_List_Olist_OCons(_1671436), _1671434), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1671436, _1671428, _1671430), _1671432), _1671438)))]]], (44474 ^ _780205) ^ [_1671810, _1671812, _1671814, _1671816, _1671818] : [class_Orderings_Olinorder(_1671810), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671812)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1671812, _1671810, _1671814), _1671816), _1671818)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671812)), _1671818)))], (44480 ^ _780205) ^ [_1671945, _1671947, _1671949, _1671951, _1671953, _1671955] : [class_Orderings_Olinorder(_1671945), -(hAPP(_1671947, _1671949) = hAPP(_1671947, _1671951)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1671953, _1671945, _1671947), _1671951), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1671953, _1671945, _1671947), _1671949), _1671955)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1671953, _1671945, _1671947), _1671949), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1671953, _1671945, _1671947), _1671951), _1671955)))], (44490 ^ _780205) ^ [_1672135, _1672137, _1672139, _1672141] : [class_Orderings_Olinorder(_1672135), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1672135, _1672135, c_COMBI(_1672135)), _1672137), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1672135, _1672135, c_COMBI(_1672135)), _1672139), _1672141)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1672135, _1672135, c_COMBI(_1672135)), _1672139), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1672135, _1672135, c_COMBI(_1672135)), _1672137), _1672141)))], (44496 ^ _780205) ^ [_1672310] : [class_Orderings_Olinorder(_1672310), -(c_Finite__Set_Ofun__left__comm(_1672310, tc_List_Olist(_1672310), c_List_Olinorder__class_Oinsort__key(_1672310, _1672310, c_COMBI(_1672310))))], (44502 ^ _780205) ^ [_1672401, _1672403, _1672405, _1672407, _1672409] : [class_Orderings_Olinorder(_1672401), -(hAPP(c_List_Oset(_1672403), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1672403, _1672401, _1672405), _1672407), _1672409)) = hAPP(hAPP(c_Set_Oinsert(_1672403), _1672407), hAPP(c_List_Oset(_1672403), _1672409)))], (44508 ^ _780205) ^ [_1672538, _1672540, _1672542] : [class_Orderings_Olinorder(_1672538), -(c_List_Oremove1(_1672538, _1672540, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1672538, _1672538, c_COMBI(_1672538)), _1672540), _1672542)) = _1672542)], (44514 ^ _780205) ^ [_1672647, _1672649, _1672651, _1672653, _1672655] : [class_Orderings_Olinorder(_1672647), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1672649, _1672647, _1672651), _1672653), _1672655) = c_List_Olist_ONil(_1672649)], (44520 ^ _780205) ^ [_1672753, _1672755, _1672757, _1672759, _1672761] : [class_Orderings_Olinorder(_1672753), 44523 ^ _780205 : [(44524 ^ _780205) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1672755), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1672755, _1672753, _1672757), _1672759), _1672761))), 44527 ^ _780205 : [(44528 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1672755), _1672759), hAPP(c_List_Oset(_1672755), _1672761)))], (44530 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1672755), _1672761)))]]], (44532 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1672755), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1672755, _1672753, _1672757), _1672759), _1672761)))), -(hBOOL(hAPP(hAPP(c_member(_1672755), _1672759), hAPP(c_List_Oset(_1672755), _1672761)))), hBOOL(hAPP(c_List_Odistinct(_1672755), _1672761))]]], (44542 ^ _780205) ^ [_1673155, _1673157, _1673159, _1673161, _1673163] : [class_Orderings_Olinorder(_1673155), -(hBOOL(hAPP(hAPP(c_member(_1673155), hAPP(_1673157, _1673159)), hAPP(c_Set_Oimage(_1673161, _1673155, _1673157), hAPP(c_List_Oset(_1673161), _1673163))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1673161, _1673155, _1673157, _1673159, _1673163) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1673161, _1673155, _1673157), _1673159), _1673163))], (44552 ^ _780205) ^ [_1673327, _1673329, _1673331] : [class_Orderings_Olinorder(_1673327), -(hBOOL(hAPP(hAPP(c_member(_1673327), _1673329), hAPP(c_List_Oset(_1673327), _1673331)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1673327, _1673327, c_COMBI(_1673327), _1673329, _1673331) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1673327, _1673327, c_COMBI(_1673327)), _1673329), _1673331))], (44562 ^ _780205) ^ [_1673483, _1673485, _1673487, _1673489, _1673491] : [class_Orderings_Olinorder(_1673483), hBOOL(hAPP(c_List_Odistinct(_1673485), _1673487)), -(hBOOL(hAPP(c_List_Odistinct(_1673485), c_List_Olinorder__class_Oinsort__insert__key(_1673485, _1673483, _1673489, _1673491, _1673487))))], (44572 ^ _780205) ^ [_1673650, _1673652, _1673654] : [class_Orderings_Olinorder(_1673650), hBOOL(hAPP(hAPP(c_member(_1673650), _1673652), hAPP(c_List_Oset(_1673650), _1673654))), -(c_List_Olinorder__class_Oinsort__insert__key(_1673650, _1673650, c_COMBI(_1673650), _1673652, _1673654) = _1673654)], (44582 ^ _780205) ^ [_1673821, _1673823, _1673825] : [class_Orderings_Olinorder(_1673821), -(hAPP(c_List_Oset(_1673821), c_List_Olinorder__class_Oinsort__insert__key(_1673821, _1673821, c_COMBI(_1673821), _1673823, _1673825)) = hAPP(hAPP(c_Set_Oinsert(_1673821), _1673823), hAPP(c_List_Oset(_1673821), _1673825)))], (44588 ^ _780205) ^ [_1673950, _1673952, _1673954, _1673956, _1673958] : [class_Orderings_Olinorder(_1673950), hBOOL(hAPP(hAPP(c_member(_1673950), hAPP(_1673952, _1673954)), hAPP(c_Set_Oimage(_1673956, _1673950, _1673952), hAPP(c_List_Oset(_1673956), _1673958)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1673956, _1673950, _1673952, _1673954, _1673958) = _1673958)], (44598 ^ _780205) ^ [_1674144, _1674146, _1674148, _1674150] : [-(_1674144 = c_List_Olist_ONil(_1674146)), 44601 ^ _780205 : [(44602 ^ _780205) ^ [] : [_1674148 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674146)), _1674144)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1674146, hAPP(hAPP(c_List_Olist__update(_1674146, _1674144), _1674148), _1674150)) = _1674150)], (44608 ^ _780205) ^ [] : [-(_1674148 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674146)), _1674144)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1674146, hAPP(hAPP(c_List_Olist__update(_1674146, _1674144), _1674148), _1674150)) = c_List_Olast(_1674146, _1674144))]]], (44614 ^ _780205) ^ [_1674430, _1674432] : [-(_1674430 = c_List_Olist_ONil(_1674432)), -(c_List_Olast(_1674432, _1674430) = hAPP(hAPP(c_List_Onth(_1674432), _1674430), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674432)), _1674430)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (44620 ^ _780205) ^ [_1674504, _1674506, _1674508] : [_1674504 = c_List_Olist_ONil(_1674506), -(c_List_Olast(_1674506, hAPP(hAPP(c_List_Olist_OCons(_1674506), _1674508), _1674504)) = _1674508)], (44626 ^ _780205) ^ [_1674603, _1674605, _1674607] : [-(_1674603 = c_List_Olist_ONil(_1674605)), -(c_List_Olast(_1674605, hAPP(hAPP(c_List_Olist_OCons(_1674605), _1674607), _1674603)) = c_List_Olast(_1674605, _1674603))], (44632 ^ _780205) ^ [_1674655, _1674657, _1674659] : [-(_1674655 = c_List_Olist_ONil(_1674657)), -(c_List_Olast(_1674657, hAPP(hAPP(c_List_Olist_OCons(_1674657), _1674659), _1674655)) = c_List_Olast(_1674657, _1674655))], (44638 ^ _780205) ^ [_1674709, _1674711, _1674713] : [_1674709 = c_List_Olist_ONil(_1674711), -(c_List_Olast(_1674711, hAPP(hAPP(c_List_Olist_OCons(_1674711), _1674713), _1674709)) = _1674713)], (44644 ^ _780205) ^ [_1674826, _1674828, _1674830] : [_1674826 = c_List_Olist_ONil(_1674828), -(c_List_Olast(_1674828, hAPP(hAPP(c_List_Oappend(_1674828), _1674830), _1674826)) = c_List_Olast(_1674828, _1674830))], (44650 ^ _780205) ^ [_1674931, _1674933, _1674935] : [-(_1674931 = c_List_Olist_ONil(_1674933)), -(c_List_Olast(_1674933, hAPP(hAPP(c_List_Oappend(_1674933), _1674935), _1674931)) = c_List_Olast(_1674933, _1674931))], (44656 ^ _780205) ^ [_1674983, _1674985, _1674987] : [-(_1674983 = c_List_Olist_ONil(_1674985)), -(c_List_Olast(_1674985, hAPP(hAPP(c_List_Oappend(_1674985), _1674987), _1674983)) = c_List_Olast(_1674985, _1674983))], (44662 ^ _780205) ^ [_1675037, _1675039, _1675041] : [_1675037 = c_List_Olist_ONil(_1675039), -(c_List_Olast(_1675039, hAPP(hAPP(c_List_Oappend(_1675039), _1675041), _1675037)) = c_List_Olast(_1675039, _1675041))], (44668 ^ _780205) ^ [_1675144, _1675146] : [-(_1675144 = c_List_Olist_ONil(_1675146)), -(hBOOL(hAPP(hAPP(c_member(_1675146), c_List_Olast(_1675146, _1675144)), hAPP(c_List_Oset(_1675146), _1675144))))], (44674 ^ _780205) ^ [_1675197, _1675199, _1675201] : [-(c_List_Olast(_1675197, hAPP(hAPP(c_List_Oappend(_1675197), _1675199), hAPP(hAPP(c_List_Olist_OCons(_1675197), _1675201), c_List_Olist_ONil(_1675197)))) = _1675201)], (44676 ^ _780205) ^ [_1675245, _1675247, _1675249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1675245), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675247)), _1675249))), -(c_List_Olast(_1675247, hAPP(hAPP(c_List_Odrop(_1675247), _1675245), _1675249)) = c_List_Olast(_1675247, _1675249))], (44682 ^ _780205) ^ [_1675372, _1675374] : [-(_1675372 = c_List_Olist_ONil(_1675374)), -(hAPP(hAPP(c_List_Oappend(_1675374), c_List_Obutlast(_1675374, _1675372)), hAPP(hAPP(c_List_Olist_OCons(_1675374), c_List_Olast(_1675374, _1675372)), c_List_Olist_ONil(_1675374))) = _1675372)], (44688 ^ _780205) ^ [_1675455, _1675457, _1675459, _1675461] : [hAPP(hAPP(c_List_Oappend(_1675455), _1675457), hAPP(hAPP(c_List_Olist_OCons(_1675455), _1675459), c_List_Olist_ONil(_1675455))) = _1675461, 44691 ^ _780205 : [(44692 ^ _780205) ^ [] : [_1675461 = c_List_Olist_ONil(_1675455)], (44694 ^ _780205) ^ [] : [-(c_List_Obutlast(_1675455, _1675461) = _1675457)], (44696 ^ _780205) ^ [] : [-(c_List_Olast(_1675455, _1675461) = _1675459)]]], (44698 ^ _780205) ^ [_1675644, _1675646, _1675648, _1675650] : [-(hAPP(hAPP(c_List_Oappend(_1675644), _1675646), hAPP(hAPP(c_List_Olist_OCons(_1675644), _1675648), c_List_Olist_ONil(_1675644))) = _1675650), -(_1675650 = c_List_Olist_ONil(_1675644)), c_List_Obutlast(_1675644, _1675650) = _1675646, c_List_Olast(_1675644, _1675650) = _1675648], (44712 ^ _780205) ^ [_1675912, _1675914, _1675916] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1675912)), _1675914), c_List_Olists(_1675912, _1675916))), -(_1675914 = c_List_Olist_ONil(_1675912)), 44721 ^ _780205 : [(44722 ^ _780205) ^ [] : [-(_1675914 = hAPP(hAPP(c_List_Olist_OCons(_1675912), 44719 ^ [_1675912, _1675914, _1675916]), 44720 ^ [_1675912, _1675914, _1675916]))], (44724 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1675912), 44719 ^ [_1675912, _1675914, _1675916]), _1675916)))], (44726 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1675912)), 44720 ^ [_1675912, _1675914, _1675916]), c_List_Olists(_1675912, _1675916))))]]], (44728 ^ _780205) ^ [_1676195, _1676197, _1676199] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1676195)), _1676197), c_List_Olists(_1676195, _1676199)))), 44729 ^ _780205 : [(44730 ^ _780205) ^ [] : [_1676197 = c_List_Olist_ONil(_1676195)], (44732 ^ _780205) ^ [_1676323, _1676325] : [_1676197 = hAPP(hAPP(c_List_Olist_OCons(_1676195), _1676325), _1676323), hBOOL(hAPP(hAPP(c_member(_1676195), _1676325), _1676199)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1676195)), _1676323), c_List_Olists(_1676195, _1676199)))]]], (44744 ^ _780205) ^ [_1676557, _1676559] : [-(_1676557 = c_List_Olist_ONil(_1676559)), -(c_Random_Oselect__weight(_1676559, hAPP(hAPP(c_List_Omap(_1676559, tc_prod(tc_Code__Numeral_Ocode__numeral, _1676559)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1676559), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1676557)) = c_Random_Oselect(_1676559, _1676557))], (44750 ^ _780205) ^ [_1676619, _1676621, _1676623] : [c_Fun_Oinj__on(_1676619, _1676621, _1676623, c_Orderings_Otop__class_Otop(tc_fun(_1676619, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1676619), tc_List_Olist(_1676621), hAPP(c_List_Omap(_1676619, _1676621), _1676623), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1676619), tc_HOL_Obool))))], (44756 ^ _780205) ^ [_1676746, _1676748, _1676750, _1676752] : [-(_1676746 = c_List_Olist_ONil(_1676748)), -(c_List_Olast(_1676750, hAPP(hAPP(c_List_Omap(_1676748, _1676750), _1676752), _1676746)) = hAPP(_1676752, c_List_Olast(_1676748, _1676746)))], (44762 ^ _780205) ^ [_1676806, _1676808, _1676810, _1676812, _1676814, _1676816, _1676818] : [-(hAPP(c_List_Ofoldl(_1676806, _1676808, _1676810, _1676812), hAPP(hAPP(c_List_Omap(_1676814, _1676808), _1676816), _1676818)) = hAPP(c_List_Ofoldl(_1676806, _1676814, hAPP(hAPP(c_COMBC(_1676806, tc_fun(_1676814, _1676808), tc_fun(_1676814, _1676806)), hAPP(hAPP(c_COMBB(tc_fun(_1676808, _1676806), tc_fun(tc_fun(_1676814, _1676808), tc_fun(_1676814, _1676806)), _1676806), c_COMBB(_1676808, _1676806, _1676814)), _1676810)), _1676816), _1676812), _1676818))], (44764 ^ _780205) ^ [_1676908, _1676910, _1676912, _1676914, _1676916] : [-(hAPP(c_List_Orotate(_1676908, _1676910), hAPP(hAPP(c_List_Omap(_1676912, _1676908), _1676914), _1676916)) = hAPP(hAPP(c_List_Omap(_1676912, _1676908), _1676914), hAPP(c_List_Orotate(_1676912, _1676910), _1676916)))], (44766 ^ _780205) ^ [_1676969, _1676971, _1676973, _1676975] : [-(hAPP(hAPP(c_List_Omap(_1676969, _1676971), _1676973), hAPP(c_List_Otl(_1676969), _1676975)) = hAPP(c_List_Otl(_1676971), hAPP(hAPP(c_List_Omap(_1676969, _1676971), _1676973), _1676975)))], (44768 ^ _780205) ^ [_1677026, _1677028, _1677030, _1677032, _1677034, _1677036] : [-(hAPP(hAPP(c_List_Ozip(_1677026, _1677028), _1677030), hAPP(hAPP(c_List_Omap(_1677032, _1677028), _1677034), _1677036)) = hAPP(hAPP(c_List_Omap(tc_prod(_1677026, _1677032), tc_prod(_1677026, _1677028)), hAPP(c_Product__Type_Oprod_Oprod__case(_1677026, _1677032, tc_prod(_1677026, _1677028)), hAPP(hAPP(c_COMBC(_1677026, tc_fun(_1677032, _1677028), tc_fun(_1677032, tc_prod(_1677026, _1677028))), hAPP(hAPP(c_COMBB(tc_fun(_1677028, tc_prod(_1677026, _1677028)), tc_fun(tc_fun(_1677032, _1677028), tc_fun(_1677032, tc_prod(_1677026, _1677028))), _1677026), c_COMBB(_1677028, tc_prod(_1677026, _1677028), _1677032)), c_Product__Type_OPair(_1677026, _1677028))), _1677034))), hAPP(hAPP(c_List_Ozip(_1677026, _1677032), _1677030), _1677036)))], (44770 ^ _780205) ^ [_1677168, _1677170, _1677172, _1677174, _1677176, _1677178, _1677180, _1677182] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1677168, _1677170), _1677172), _1677174), hAPP(hAPP(c_List_Ozip(_1677168, _1677170), _1677176), hAPP(hAPP(c_List_Omap(_1677178, _1677170), _1677180), _1677182))) = hAPP(hAPP(c_List_Omap(tc_prod(_1677168, _1677178), _1677172), hAPP(c_Product__Type_Oprod_Oprod__case(_1677168, _1677178, _1677172), hAPP(hAPP(c_COMBB(tc_fun(_1677178, tc_prod(_1677168, _1677170)), tc_fun(_1677178, _1677172), _1677168), hAPP(c_COMBB(tc_prod(_1677168, _1677170), _1677172, _1677178), _1677174)), hAPP(hAPP(c_COMBC(_1677168, tc_fun(_1677178, _1677170), tc_fun(_1677178, tc_prod(_1677168, _1677170))), hAPP(hAPP(c_COMBB(tc_fun(_1677170, tc_prod(_1677168, _1677170)), tc_fun(tc_fun(_1677178, _1677170), tc_fun(_1677178, tc_prod(_1677168, _1677170))), _1677168), c_COMBB(_1677170, tc_prod(_1677168, _1677170), _1677178)), c_Product__Type_OPair(_1677168, _1677170))), _1677180)))), hAPP(hAPP(c_List_Ozip(_1677168, _1677178), _1677176), _1677182)))], (44772 ^ _780205) ^ [_1677349, _1677351, _1677353, _1677355, _1677357, _1677359, _1677361, _1677363] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1677349, _1677351), _1677353), _1677355), hAPP(hAPP(c_List_Ozip(_1677349, _1677351), hAPP(hAPP(c_List_Omap(_1677357, _1677349), _1677359), _1677361)), _1677363)) = hAPP(hAPP(c_List_Omap(tc_prod(_1677357, _1677351), _1677353), hAPP(c_Product__Type_Oprod_Oprod__case(_1677357, _1677351, _1677353), hAPP(hAPP(c_COMBB(tc_fun(_1677351, tc_prod(_1677349, _1677351)), tc_fun(_1677351, _1677353), _1677357), hAPP(c_COMBB(tc_prod(_1677349, _1677351), _1677353, _1677351), _1677355)), hAPP(hAPP(c_COMBB(_1677349, tc_fun(_1677351, tc_prod(_1677349, _1677351)), _1677357), c_Product__Type_OPair(_1677349, _1677351)), _1677359)))), hAPP(hAPP(c_List_Ozip(_1677357, _1677351), _1677361), _1677363)))], (44774 ^ _780205) ^ [_1677492, _1677494, _1677496, _1677498, _1677500, _1677502] : [-(hAPP(hAPP(c_List_Ozip(_1677492, _1677494), hAPP(hAPP(c_List_Omap(_1677496, _1677492), _1677498), _1677500)), _1677502) = hAPP(hAPP(c_List_Omap(tc_prod(_1677496, _1677494), tc_prod(_1677492, _1677494)), hAPP(c_Product__Type_Oprod_Oprod__case(_1677496, _1677494, tc_prod(_1677492, _1677494)), hAPP(hAPP(c_COMBB(_1677492, tc_fun(_1677494, tc_prod(_1677492, _1677494)), _1677496), c_Product__Type_OPair(_1677492, _1677494)), _1677498))), hAPP(hAPP(c_List_Ozip(_1677496, _1677494), _1677500), _1677502)))], (44776 ^ _780205) ^ [_1677596, _1677598, _1677600, _1677602, _1677604, _1677606, _1677608, _1677610] : [-(hAPP(hAPP(c_List_Ozip(_1677596, _1677598), hAPP(hAPP(c_List_Omap(_1677600, _1677596), _1677602), _1677604)), hAPP(hAPP(c_List_Omap(_1677606, _1677598), _1677608), _1677610)) = hAPP(hAPP(c_List_Omap(tc_prod(_1677600, _1677606), tc_prod(_1677596, _1677598)), hAPP(c_Product__Type_Oprod_Oprod__case(_1677600, _1677606, tc_prod(_1677596, _1677598)), hAPP(hAPP(c_COMBC(_1677600, tc_fun(_1677606, _1677598), tc_fun(_1677606, tc_prod(_1677596, _1677598))), hAPP(hAPP(c_COMBB(tc_fun(_1677598, tc_prod(_1677596, _1677598)), tc_fun(tc_fun(_1677606, _1677598), tc_fun(_1677606, tc_prod(_1677596, _1677598))), _1677600), c_COMBB(_1677598, tc_prod(_1677596, _1677598), _1677606)), hAPP(hAPP(c_COMBB(_1677596, tc_fun(_1677598, tc_prod(_1677596, _1677598)), _1677600), c_Product__Type_OPair(_1677596, _1677598)), _1677602))), _1677608))), hAPP(hAPP(c_List_Ozip(_1677600, _1677606), _1677604), _1677610)))], (44778 ^ _780205) ^ [_1677767, _1677769] : [-(hAPP(hAPP(c_List_Ozip(_1677767, _1677767), _1677769), _1677769) = hAPP(hAPP(c_List_Omap(_1677767, tc_prod(_1677767, _1677767)), hAPP(hAPP(c_COMBS(_1677767, _1677767, tc_prod(_1677767, _1677767)), c_Product__Type_OPair(_1677767, _1677767)), c_COMBI(_1677767))), _1677769))], (44780 ^ _780205) ^ [_1677852, _1677854, _1677856, _1677858] : [hAPP(hAPP(c_List_Omap(_1677852, _1677854), _1677856), _1677858) = c_List_Olist_ONil(_1677854), -(_1677858 = c_List_Olist_ONil(_1677852))], (44786 ^ _780205) ^ [_1677955, _1677957, _1677959, _1677961] : [_1677961 = c_List_Olist_ONil(_1677955), -(hAPP(hAPP(c_List_Omap(_1677955, _1677957), _1677959), _1677961) = c_List_Olist_ONil(_1677957))], (44792 ^ _780205) ^ [_1678064, _1678066, _1678068] : [-(hAPP(hAPP(c_List_Omap(_1678064, _1678066), _1678068), c_List_Olist_ONil(_1678064)) = c_List_Olist_ONil(_1678066))], (44794 ^ _780205) ^ [_1678125, _1678127, _1678129, _1678131] : [c_List_Olist_ONil(_1678125) = hAPP(hAPP(c_List_Omap(_1678127, _1678125), _1678129), _1678131), -(_1678131 = c_List_Olist_ONil(_1678127))], (44800 ^ _780205) ^ [_1678228, _1678230, _1678232, _1678234] : [_1678234 = c_List_Olist_ONil(_1678230), -(c_List_Olist_ONil(_1678228) = hAPP(hAPP(c_List_Omap(_1678230, _1678228), _1678232), _1678234))], (44806 ^ _780205) ^ [_1678337, _1678339, _1678341, _1678343, _1678345, _1678347] : [-(hAPP(hAPP(c_List_Omap(_1678337, _1678339), _1678341), hAPP(hAPP(c_List_Olist__update(_1678337, _1678343), _1678345), _1678347)) = hAPP(hAPP(c_List_Olist__update(_1678339, hAPP(hAPP(c_List_Omap(_1678337, _1678339), _1678341), _1678343)), _1678345), hAPP(_1678341, _1678347)))], (44818 ^ _780205) ^ [_1678677, _1678679, _1678681, _1678683, _1678685] : [44820 ^ _780205 : [(44821 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678677), 44819 ^ [_1678677, _1678679, _1678681, _1678683, _1678685]), hAPP(c_List_Oset(_1678677), _1678683))))], (44823 ^ _780205) ^ [] : [hAPP(_1678681, 44819 ^ [_1678677, _1678679, _1678681, _1678683, _1678685]) = hAPP(_1678685, 44819 ^ [_1678677, _1678679, _1678681, _1678683, _1678685])]], -(hAPP(hAPP(c_List_Omap(_1678677, _1678679), _1678681), _1678683) = hAPP(hAPP(c_List_Omap(_1678677, _1678679), _1678685), _1678683))], (44808 ^ _780205) ^ [_1678433, _1678435, _1678437, _1678439, _1678441] : [hAPP(hAPP(c_List_Omap(_1678433, _1678435), _1678437), _1678439) = hAPP(hAPP(c_List_Omap(_1678433, _1678435), _1678441), _1678439), 44811 ^ _780205 : [(44812 ^ _780205) ^ [_1678556] : [hBOOL(hAPP(hAPP(c_member(_1678433), _1678556), hAPP(c_List_Oset(_1678433), _1678439))), -(hAPP(_1678437, _1678556) = hAPP(_1678441, _1678556))]]], (44827 ^ _780205) ^ [_1678934, _1678936, _1678938, _1678940, _1678942, _1678944, _1678946] : [hAPP(hAPP(c_List_Omap(_1678934, _1678936), _1678938), _1678940) = hAPP(hAPP(c_List_Omap(_1678942, _1678936), _1678944), _1678946), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678934)), _1678940) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678942)), _1678946))], (44833 ^ _780205) ^ [_1679085, _1679087, _1679089, _1679091] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679085)), hAPP(hAPP(c_List_Omap(_1679087, _1679085), _1679089), _1679091)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679087)), _1679091))], (44835 ^ _780205) ^ [_1679137, _1679139, _1679141, _1679143, _1679145] : [class_Rings_Osemiring__0(_1679137), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1679137), hAPP(hAPP(c_List_Omap(_1679139, _1679137), hAPP(hAPP(c_COMBC(_1679139, _1679137, _1679137), hAPP(hAPP(c_COMBB(_1679137, tc_fun(_1679137, _1679137), _1679139), c_Groups_Otimes__class_Otimes(_1679137)), _1679141)), _1679143)), _1679145)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1679137), hAPP(c_List_Omonoid__add__class_Olistsum(_1679137), hAPP(hAPP(c_List_Omap(_1679139, _1679137), _1679141), _1679145))), _1679143))], (44841 ^ _780205) ^ [_1679340, _1679342, _1679344, _1679346, _1679348] : [class_Rings_Osemiring__0(_1679340), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1679340), hAPP(hAPP(c_List_Omap(_1679342, _1679340), hAPP(hAPP(c_COMBB(_1679340, _1679340, _1679342), hAPP(c_Groups_Otimes__class_Otimes(_1679340), _1679344)), _1679346)), _1679348)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1679340), _1679344), hAPP(c_List_Omonoid__add__class_Olistsum(_1679340), hAPP(hAPP(c_List_Omap(_1679342, _1679340), _1679346), _1679348))))], (44847 ^ _780205) ^ [_1679523, _1679525, _1679527] : [class_Groups_Omonoid__add(_1679523), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1679523), hAPP(hAPP(c_List_Omap(_1679525, _1679523), hAPP(c_COMBK(_1679523, _1679525), c_Groups_Ozero__class_Ozero(_1679523))), _1679527)) = c_Groups_Ozero__class_Ozero(_1679523))], (44853 ^ _780205) ^ [_1679648, _1679650, _1679652, _1679654, _1679656] : [class_Groups_Ocomm__monoid__add(_1679648), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1679648), hAPP(hAPP(c_List_Omap(_1679650, _1679648), hAPP(hAPP(c_COMBS(_1679650, _1679648, _1679648), hAPP(hAPP(c_COMBB(_1679648, tc_fun(_1679648, _1679648), _1679650), c_Groups_Oplus__class_Oplus(_1679648)), _1679652)), _1679654)), _1679656)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1679648), hAPP(c_List_Omonoid__add__class_Olistsum(_1679648), hAPP(hAPP(c_List_Omap(_1679650, _1679648), _1679652), _1679656))), hAPP(c_List_Omonoid__add__class_Olistsum(_1679648), hAPP(hAPP(c_List_Omap(_1679650, _1679648), _1679654), _1679656))))], (44859 ^ _780205) ^ [_1679879, _1679881, _1679883, _1679885, _1679887] : [class_Groups_Oab__group__add(_1679879), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1679879), hAPP(hAPP(c_List_Omap(_1679881, _1679879), hAPP(hAPP(c_COMBS(_1679881, _1679879, _1679879), hAPP(hAPP(c_COMBB(_1679879, tc_fun(_1679879, _1679879), _1679881), c_Groups_Ominus__class_Ominus(_1679879)), _1679883)), _1679885)), _1679887)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1679879), hAPP(c_List_Omonoid__add__class_Olistsum(_1679879), hAPP(hAPP(c_List_Omap(_1679881, _1679879), _1679883), _1679887))), hAPP(c_List_Omonoid__add__class_Olistsum(_1679879), hAPP(hAPP(c_List_Omap(_1679881, _1679879), _1679885), _1679887))))], (44865 ^ _780205) ^ [_1680110, _1680112, _1680114, _1680116, _1680118] : [c_Fun_Oinj__on(_1680110, _1680112, _1680114, c_Orderings_Otop__class_Otop(tc_fun(_1680110, tc_HOL_Obool))), 44868 ^ _780205 : [(44869 ^ _780205) ^ [] : [hAPP(hAPP(c_List_Omap(_1680110, _1680112), _1680114), _1680116) = hAPP(hAPP(c_List_Omap(_1680110, _1680112), _1680114), _1680118), -(_1680116 = _1680118)], (44875 ^ _780205) ^ [] : [_1680116 = _1680118, -(hAPP(hAPP(c_List_Omap(_1680110, _1680112), _1680114), _1680116) = hAPP(hAPP(c_List_Omap(_1680110, _1680112), _1680114), _1680118))]]], (44881 ^ _780205) ^ [_1680403, _1680405, _1680407, _1680409, _1680411] : [hAPP(hAPP(c_List_Omap(_1680403, _1680405), _1680407), _1680409) = hAPP(hAPP(c_List_Omap(_1680403, _1680405), _1680407), _1680411), c_Fun_Oinj__on(_1680403, _1680405, _1680407, c_Orderings_Otop__class_Otop(tc_fun(_1680403, tc_HOL_Obool))), -(_1680409 = _1680411)], (44891 ^ _780205) ^ [_1680594, _1680596] : [-(hAPP(hAPP(c_List_Omap(_1680594, _1680594), c_COMBI(_1680594)), _1680596) = _1680596)], (44893 ^ _780205) ^ [_1680630, _1680632, _1680634, _1680636, _1680638] : [-(hAPP(hAPP(c_List_Otake(_1680630), _1680632), hAPP(hAPP(c_List_Omap(_1680634, _1680630), _1680636), _1680638)) = hAPP(hAPP(c_List_Omap(_1680634, _1680630), _1680636), hAPP(hAPP(c_List_Otake(_1680634), _1680632), _1680638)))], (44895 ^ _780205) ^ [_1680695, _1680697, _1680699, _1680701] : [-(hAPP(hAPP(c_List_Omap(_1680695, _1680697), _1680699), c_List_Obutlast(_1680695, _1680701)) = c_List_Obutlast(_1680697, hAPP(hAPP(c_List_Omap(_1680695, _1680697), _1680699), _1680701)))], (44897 ^ _780205) ^ [_1680748, _1680750, _1680752, _1680754] : [-(hAPP(c_List_Oset(_1680748), hAPP(hAPP(c_List_Omap(_1680750, _1680748), _1680752), _1680754)) = hAPP(c_Set_Oimage(_1680750, _1680748, _1680752), hAPP(c_List_Oset(_1680750), _1680754)))], (44899 ^ _780205) ^ [_1680803, _1680805, _1680807, _1680809, _1680811] : [-(hAPP(hAPP(c_List_Omap(_1680803, _1680805), _1680807), hAPP(hAPP(c_List_Olist_OCons(_1680803), _1680809), _1680811)) = hAPP(hAPP(c_List_Olist_OCons(_1680805), hAPP(_1680807, _1680809)), hAPP(hAPP(c_List_Omap(_1680803, _1680805), _1680807), _1680811)))], (44901 ^ _780205) ^ [_1680871, _1680873, _1680875, _1680877, _1680879] : [-(hAPP(hAPP(c_List_Omap(_1680871, _1680873), _1680875), hAPP(hAPP(c_List_Oappend(_1680871), _1680877), _1680879)) = hAPP(hAPP(c_List_Oappend(_1680873), hAPP(hAPP(c_List_Omap(_1680871, _1680873), _1680875), _1680877)), hAPP(hAPP(c_List_Omap(_1680871, _1680873), _1680875), _1680879)))], (44903 ^ _780205) ^ [_1680941, _1680943, _1680945, _1680947] : [-(_1680941 = c_List_Olist_ONil(_1680943)), -(hAPP(c_List_Ohd(_1680945), hAPP(hAPP(c_List_Omap(_1680943, _1680945), _1680947), _1680941)) = hAPP(_1680947, hAPP(c_List_Ohd(_1680943), _1680941)))], (44909 ^ _780205) ^ [_1681005, _1681007, _1681009, _1681011, _1681013] : [-(hAPP(hAPP(c_List_Odrop(_1681005), _1681007), hAPP(hAPP(c_List_Omap(_1681009, _1681005), _1681011), _1681013)) = hAPP(hAPP(c_List_Omap(_1681009, _1681005), _1681011), hAPP(hAPP(c_List_Odrop(_1681009), _1681007), _1681013)))], (44911 ^ _780205) ^ [_1681070] : [-(hAPP(c_List_Omap(_1681070, _1681070), c_Fun_Oid(_1681070)) = c_Fun_Oid(tc_List_Olist(_1681070)))], (44913 ^ _780205) ^ [_1681105] : [-(hAPP(c_List_Omap(_1681105, _1681105), c_COMBI(_1681105)) = c_Fun_Oid(tc_List_Olist(_1681105)))], (44915 ^ _780205) ^ [_1681140, _1681142, _1681144, _1681146, _1681148] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1681140), tc_List_Olist(_1681142), tc_List_Olist(_1681144), hAPP(c_List_Omap(_1681140, _1681142), _1681146)), hAPP(c_List_Omap(_1681144, _1681140), _1681148)) = hAPP(c_List_Omap(_1681144, _1681142), hAPP(c_Fun_Ocomp(_1681140, _1681142, _1681144, _1681146), _1681148)))], (44917 ^ _780205) ^ [_1681211, _1681213, _1681215, _1681217, _1681219] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1681211), tc_List_Olist(_1681213), tc_List_Olist(_1681215), hAPP(c_List_Omap(_1681211, _1681213), _1681217)), hAPP(c_List_Omap(_1681215, _1681211), _1681219)) = hAPP(c_List_Omap(_1681215, _1681213), hAPP(c_Fun_Ocomp(_1681211, _1681213, _1681215, _1681217), _1681219)))], (44919 ^ _780205) ^ [_1681282, _1681284, _1681286, _1681288, _1681290, _1681292] : [-(hAPP(hAPP(c_List_Omap(_1681282, _1681284), _1681286), hAPP(hAPP(c_List_Omap(_1681288, _1681282), _1681290), _1681292)) = hAPP(hAPP(c_List_Omap(_1681288, _1681284), hAPP(c_Fun_Ocomp(_1681282, _1681284, _1681288, _1681286), _1681290)), _1681292))], (44921 ^ _780205) ^ [_1681350, _1681352, _1681354, _1681356, _1681358, _1681360] : [-(hAPP(hAPP(c_List_Omap(_1681350, _1681352), _1681354), hAPP(hAPP(c_List_Omap(_1681356, _1681350), _1681358), _1681360)) = hAPP(hAPP(c_List_Omap(_1681356, _1681352), hAPP(c_Fun_Ocomp(_1681350, _1681352, _1681356, _1681354), _1681358)), _1681360))], (44923 ^ _780205) ^ [_1681418, _1681420, _1681422, _1681424, _1681426] : [-(c_List_Olist_Olist__size(_1681418, _1681420, hAPP(hAPP(c_List_Omap(_1681422, _1681418), _1681424), _1681426)) = c_List_Olist_Olist__size(_1681422, hAPP(c_Fun_Ocomp(_1681418, tc_Nat_Onat, _1681422, _1681420), _1681424), _1681426))], (44925 ^ _780205) ^ [_1681474, _1681476, _1681478, _1681480, _1681482] : [hAPP(hAPP(c_List_Omap(_1681474, _1681476), _1681478), _1681480) = hAPP(hAPP(c_List_Omap(_1681474, _1681476), _1681478), _1681482), c_Fun_Oinj__on(_1681474, _1681476, _1681478, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1681474, tc_HOL_Obool)), hAPP(c_List_Oset(_1681474), _1681480)), hAPP(c_List_Oset(_1681474), _1681482))), -(_1681480 = _1681482)], (44935 ^ _780205) ^ [_1681697, _1681699, _1681701, _1681703, _1681705] : [c_Fun_Oinj__on(_1681697, _1681699, _1681701, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1681697, tc_HOL_Obool)), hAPP(c_List_Oset(_1681697), _1681703)), hAPP(c_List_Oset(_1681697), _1681705))), 44938 ^ _780205 : [(44939 ^ _780205) ^ [] : [hAPP(hAPP(c_List_Omap(_1681697, _1681699), _1681701), _1681703) = hAPP(hAPP(c_List_Omap(_1681697, _1681699), _1681701), _1681705), -(_1681703 = _1681705)], (44945 ^ _780205) ^ [] : [_1681703 = _1681705, -(hAPP(hAPP(c_List_Omap(_1681697, _1681699), _1681701), _1681703) = hAPP(hAPP(c_List_Omap(_1681697, _1681699), _1681701), _1681705))]]], (44951 ^ _780205) ^ [_1682022, _1682024, _1682026, _1682028, _1682030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682022), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682024)), _1682026))), -(hAPP(hAPP(c_List_Onth(_1682028), hAPP(hAPP(c_List_Omap(_1682024, _1682028), _1682030), _1682026)), _1682022) = hAPP(_1682030, hAPP(hAPP(c_List_Onth(_1682024), _1682026), _1682022)))], (44957 ^ _780205) ^ [_1682181, _1682183, _1682185, _1682187, _1682189, _1682191] : [-(hBOOL(hAPP(hAPP(c_member(_1682181), _1682183), hAPP(c_List_Oset(_1682181), _1682185)))), -(hAPP(hAPP(c_List_Omap(_1682181, _1682187), c_Fun_Ofun__upd(_1682181, _1682187, _1682189, _1682183, _1682191)), _1682185) = hAPP(hAPP(c_List_Omap(_1682181, _1682187), _1682189), _1682185))], (44963 ^ _780205) ^ [_1682282, _1682284, _1682286, _1682288] : [hBOOL(hAPP(c_List_Odistinct(_1682282), hAPP(hAPP(c_List_Omap(_1682284, _1682282), _1682286), _1682288))), 44966 ^ _780205 : [(44967 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1682284), _1682288)))], (44969 ^ _780205) ^ [] : [-(c_Fun_Oinj__on(_1682284, _1682282, _1682286, hAPP(c_List_Oset(_1682284), _1682288)))]]], (44971 ^ _780205) ^ [_1682433, _1682435, _1682437, _1682439] : [-(hBOOL(hAPP(c_List_Odistinct(_1682433), hAPP(hAPP(c_List_Omap(_1682435, _1682433), _1682437), _1682439)))), hBOOL(hAPP(c_List_Odistinct(_1682435), _1682439)), c_Fun_Oinj__on(_1682435, _1682433, _1682437, hAPP(c_List_Oset(_1682435), _1682439))], (44981 ^ _780205) ^ [_1682620, _1682622] : [class_Groups_Oordered__ab__group__add__abs(_1682620), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1682620), hAPP(c_Groups_Oabs__class_Oabs(_1682620), hAPP(c_List_Omonoid__add__class_Olistsum(_1682620), _1682622))), hAPP(c_List_Omonoid__add__class_Olistsum(_1682620), hAPP(hAPP(c_List_Omap(_1682620, _1682620), c_Groups_Oabs__class_Oabs(_1682620)), _1682622)))))], (44987 ^ _780205) ^ [_1682761, _1682763, _1682765, _1682767] : [class_Groups_Oab__group__add(_1682761), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1682761), hAPP(c_List_Omonoid__add__class_Olistsum(_1682761), hAPP(hAPP(c_List_Omap(_1682763, _1682761), _1682765), _1682767))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1682761), hAPP(hAPP(c_List_Omap(_1682763, _1682761), hAPP(c_Fun_Ocomp(_1682761, _1682761, _1682763, c_Groups_Ouminus__class_Ouminus(_1682761)), _1682765)), _1682767)))], (44993 ^ _780205) ^ [_1682926, _1682928, _1682930, _1682932] : [c_Fun_Oinj__on(_1682926, _1682928, _1682930, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1682926, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1682926), tc_fun(_1682926, tc_HOL_Obool), c_List_Oset(_1682926)), _1682932))), -(c_Fun_Oinj__on(tc_List_Olist(_1682926), tc_List_Olist(_1682928), hAPP(c_List_Omap(_1682926, _1682928), _1682930), _1682932))], (44999 ^ _780205) ^ [_1683075, _1683077, _1683079] : [c_Fun_Oinj__on(tc_List_Olist(_1683075), tc_List_Olist(_1683077), hAPP(c_List_Omap(_1683075, _1683077), _1683079), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1683075), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1683075, _1683077, _1683079, c_Orderings_Otop__class_Otop(tc_fun(_1683075, tc_HOL_Obool))))], (45005 ^ _780205) ^ [_1683224, _1683226, _1683228] : [c_Fun_Oinj__on(tc_List_Olist(_1683224), tc_List_Olist(_1683226), hAPP(c_List_Omap(_1683224, _1683226), _1683228), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1683224), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1683224, _1683226, _1683228, c_Orderings_Otop__class_Otop(tc_fun(_1683224, tc_HOL_Obool))))], (45011 ^ _780205) ^ [_1683351, _1683353, _1683355] : [c_Fun_Oinj__on(_1683351, _1683353, _1683355, c_Orderings_Otop__class_Otop(tc_fun(_1683351, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1683351), tc_List_Olist(_1683353), hAPP(c_List_Omap(_1683351, _1683353), _1683355), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1683351), tc_HOL_Obool))))], (45017 ^ _780205) ^ [_1683484, _1683486, _1683488, _1683490] : [class_Groups_Ocomm__monoid__add(_1683484), hBOOL(hAPP(c_List_Odistinct(_1683486), _1683488)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1683484), hAPP(hAPP(c_List_Omap(_1683486, _1683484), _1683490), _1683488)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1683486, _1683484), _1683490), hAPP(c_List_Oset(_1683486), _1683488)))], (45027 ^ _780205) ^ [_1683683, _1683685, _1683687, _1683689] : [class_Rings_Osemiring__1(_1683683), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1683683), hAPP(hAPP(c_List_Omap(_1683685, _1683683), hAPP(c_COMBK(_1683683, _1683685), _1683687)), _1683689)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1683683), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1683683), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683685)), _1683689))), _1683687))], (45033 ^ _780205) ^ [_1683842, _1683844, _1683846, _1683848, _1683850] : [class_Groups_Ocomm__monoid__add(_1683842), hBOOL(hAPP(hAPP(c_member(_1683844), _1683846), hAPP(c_List_Oset(_1683844), _1683848))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1683842), hAPP(hAPP(c_List_Omap(_1683844, _1683842), _1683850), _1683848)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1683842), hAPP(_1683850, _1683846)), hAPP(c_List_Omonoid__add__class_Olistsum(_1683842), hAPP(hAPP(c_List_Omap(_1683844, _1683842), _1683850), c_List_Oremove1(_1683844, _1683846, _1683848)))))], (45043 ^ _780205) ^ [_1684091, _1684093, _1684095, _1684097] : [class_Groups_Ocomm__monoid__add(_1684091), 45046 ^ _780205 : [(45047 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1684093), _1684095)), -(c_Nitpick_Osetsum_H(_1684093, _1684091, _1684097, _1684095) = hAPP(c_List_Omonoid__add__class_Olistsum(_1684091), hAPP(hAPP(c_List_Omap(_1684093, _1684091), _1684097), c_Hilbert__Choice_OEps(tc_List_Olist(_1684093), hAPP(hAPP(c_COMBS(tc_List_Olist(_1684093), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1684093)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1684093), tc_fun(_1684093, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1684093, tc_HOL_Obool), tc_fun(tc_fun(_1684093, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1684093)), c_fequal), c_List_Oset(_1684093))), _1684095))), c_List_Odistinct(_1684093))))))], (45053 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1684093), _1684095))), -(c_Nitpick_Osetsum_H(_1684093, _1684091, _1684097, _1684095) = c_Groups_Ozero__class_Ozero(_1684091))]]], (45059 ^ _780205) ^ [_1684479, _1684481, _1684483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684479), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684481)), _1684483))), -(hAPP(c_Random_Opick(_1684481, hAPP(hAPP(c_List_Omap(_1684481, tc_prod(tc_Code__Numeral_Ocode__numeral, _1684481)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1684481), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1684483)), hAPP(c_Code__Numeral_Oof__nat, _1684479)) = hAPP(hAPP(c_List_Onth(_1684481), _1684483), _1684479))], (45065 ^ _780205) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45067 ^ _780205) ^ [_1684670, _1684672] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1684670)), hAPP(c_Code__Numeral_Oof__nat, _1684672)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1684670), _1684672)))], (45069 ^ _780205) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (45071 ^ _780205) ^ [_1684749, _1684751] : [hAPP(c_Code__Numeral_Oof__nat, _1684749) = hAPP(c_Code__Numeral_Oof__nat, _1684751), -(_1684749 = _1684751)], (45077 ^ _780205) ^ [_1684834, _1684836] : [_1684834 = _1684836, -(hAPP(c_Code__Numeral_Oof__nat, _1684834) = hAPP(c_Code__Numeral_Oof__nat, _1684836))], (45083 ^ _780205) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45085 ^ _780205) ^ [_1684958, _1684960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1684958)), hAPP(c_Code__Numeral_Oof__nat, _1684960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684958), _1684960)))], (45091 ^ _780205) ^ [_1685063, _1685065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685063), _1685065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1685063)), hAPP(c_Code__Numeral_Oof__nat, _1685065))))], (45097 ^ _780205) ^ [_1685174, _1685176] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1685174), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1685176), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 45104 ^ _780205 : [(45105 ^ _780205) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1685174) = hAPP(c_Code__Numeral_Oof__nat, _1685176), -(_1685174 = _1685176)], (45111 ^ _780205) ^ [] : [_1685174 = _1685176, -(hAPP(c_Code__Numeral_Oof__nat, _1685174) = hAPP(c_Code__Numeral_Oof__nat, _1685176))]]], (45117 ^ _780205) ^ [_1685471, _1685473, _1685475, _1685477] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685471)), _1685473) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685475)), _1685477), -(hAPP(hAPP(c_List_Omap(tc_prod(_1685471, _1685475), _1685471), c_Product__Type_Ofst(_1685471, _1685475)), hAPP(hAPP(c_List_Ozip(_1685471, _1685475), _1685473), _1685477)) = _1685473)], (45123 ^ _780205) ^ [_1685628, _1685630, _1685632, _1685634] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685628)), _1685630) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685632)), _1685634), -(hAPP(hAPP(c_List_Omap(tc_prod(_1685628, _1685632), _1685632), c_Product__Type_Osnd(_1685628, _1685632)), hAPP(hAPP(c_List_Ozip(_1685628, _1685632), _1685630), _1685634)) = _1685634)], (45129 ^ _780205) ^ [] : [-(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))], (45131 ^ _780205) ^ [_1685803, _1685805, _1685807] : [-(hAPP(hAPP(c_List_Ozip(_1685803, _1685805), hAPP(hAPP(c_List_Omap(tc_prod(_1685803, _1685805), _1685803), c_Product__Type_Ofst(_1685803, _1685805)), _1685807)), hAPP(hAPP(c_List_Omap(tc_prod(_1685803, _1685805), _1685805), c_Product__Type_Osnd(_1685803, _1685805)), _1685807)) = _1685807)], (45133 ^ _780205) ^ [_1685869, _1685871] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1685869)), hAPP(c_Code__Numeral_Oof__nat, _1685871)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1685869), _1685871)))], (45135 ^ _780205) ^ [_1685930, _1685932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1685930)), hAPP(c_Code__Numeral_Oof__nat, _1685932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1685930), _1685932)))], (45141 ^ _780205) ^ [_1686035, _1686037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1686035), _1686037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1686035)), hAPP(c_Code__Numeral_Oof__nat, _1686037))))], (45147 ^ _780205) ^ [_1686146, _1686148] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1686146)), hAPP(c_Code__Numeral_Oof__nat, _1686148)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1686146), _1686148)))], (45149 ^ _780205) ^ [_1686192, _1686194, _1686196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1686192), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1686194), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1686194)), _1686196)))), -(hBOOL(hAPP(hAPP(c_member(_1686194), hAPP(c_Random_Opick(_1686194, _1686196), _1686192)), hAPP(c_List_Oset(_1686194), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1686194), _1686194), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1686194)), _1686196)))))], (45155 ^ _780205) ^ [_1686383, _1686385, _1686387, _1686389, _1686391] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686383)), _1686385) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686387)), _1686389), 45158 ^ _780205 : [(45159 ^ _780205) ^ [] : [hAPP(hAPP(c_List_Ozip(_1686383, _1686387), _1686385), _1686389) = _1686391, 45162 ^ _780205 : [(45163 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1686383, _1686387), _1686383), c_Product__Type_Ofst(_1686383, _1686387)), _1686391) = _1686385)], (45165 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1686383, _1686387), _1686387), c_Product__Type_Osnd(_1686383, _1686387)), _1686391) = _1686389)]]], (45167 ^ _780205) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1686383, _1686387), _1686385), _1686389) = _1686391), hAPP(hAPP(c_List_Omap(tc_prod(_1686383, _1686387), _1686383), c_Product__Type_Ofst(_1686383, _1686387)), _1686391) = _1686385, hAPP(hAPP(c_List_Omap(tc_prod(_1686383, _1686387), _1686387), c_Product__Type_Osnd(_1686383, _1686387)), _1686391) = _1686389]]], (45177 ^ _780205) ^ [_1686831, _1686833, _1686835] : [-(c_List_Olist_Olist__size(_1686831, _1686833, _1686835) = 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(_1686831, tc_Nat_Onat), _1686833), _1686835))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686831)), _1686835)))], (45179 ^ _780205) ^ [_1686893] : [-(_1686893 = 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)), _1686893)))], (45185 ^ _780205) ^ [_1686925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1686925)), _1686925 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45191 ^ _780205) ^ [_1687007, _1687009, _1687011, _1687013] : [class_Groups_Ocomm__monoid__add(_1687007), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687007), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1687007), _1687009), c_List_Oupto(_1687011, _1687013))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1687007), _1687009), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1687011, _1687013))))], (45197 ^ _780205) ^ [_1687150, _1687152, _1687154, _1687156] : [class_Groups_Ocomm__monoid__add(_1687150), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1687150), _1687152), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1687154, _1687156))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1687150), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1687150), _1687152), c_List_Oupto(_1687154, _1687156))))], (45203 ^ _780205) ^ [_1687293, _1687295, _1687297] : [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, _1687293), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1687293)), _1687295)))), -(hBOOL(hAPP(hAPP(c_member(_1687293), hAPP(c_Product__Type_Ofst(_1687293, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1687293, _1687295), _1687297))), hAPP(c_List_Oset(_1687293), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1687293), _1687293), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1687293)), _1687295)))))], (45209 ^ _780205) ^ [_1687490, _1687492] : [-(c_Random_Oselect__weight(_1687490, _1687492) = 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(_1687490, 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, _1687490), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1687490)), _1687492)))), hAPP(hAPP(c_COMBB(_1687490, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1687490, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1687490, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1687490, _1687492))))], (45211 ^ _780205) ^ [_1687574, _1687576] : [-(c_Random_Oselect(_1687574, _1687576) = 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(_1687574, 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(_1687574)), _1687576)))), hAPP(hAPP(c_COMBB(_1687574, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1687574, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1687574, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1687574, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1687574), _1687576)), c_Code__Numeral_Onat__of))))], (45213 ^ _780205) ^ [_1687662, _1687664, _1687666, _1687668, _1687670] : [class_Groups_Omonoid__add(_1687662), class_Groups_Oordered__ab__semigroup__add(_1687662), 45223 ^ _780205 : [(45224 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1687664), 45222 ^ [_1687662, _1687664, _1687666, _1687668, _1687670]), hAPP(c_List_Oset(_1687664), _1687666))))], (45226 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1687662), hAPP(_1687668, 45222 ^ [_1687662, _1687664, _1687666, _1687668, _1687670])), hAPP(_1687670, 45222 ^ [_1687662, _1687664, _1687666, _1687668, _1687670])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1687662), hAPP(c_List_Omonoid__add__class_Olistsum(_1687662), hAPP(hAPP(c_List_Omap(_1687664, _1687662), _1687668), _1687666))), hAPP(c_List_Omonoid__add__class_Olistsum(_1687662), hAPP(hAPP(c_List_Omap(_1687664, _1687662), _1687670), _1687666)))))], (45230 ^ _780205) ^ [_1688086] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1688086)) = _1688086)], (45232 ^ _780205) ^ [_1688115] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1688115)) = _1688115)], (45234 ^ _780205) ^ [_1688144] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1688144)) = _1688144)], (45236 ^ _780205) ^ [_1688173, _1688175] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1688173), _1688175) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1688173)), hAPP(c_Code__Numeral_Onat__of, _1688175))))], (45238 ^ _780205) ^ [_1688234, _1688236] : [hAPP(c_Code__Numeral_Onat__of, _1688234) = hAPP(c_Code__Numeral_Onat__of, _1688236), -(_1688234 = _1688236)], (45244 ^ _780205) ^ [_1688319, _1688321] : [_1688319 = _1688321, -(hAPP(c_Code__Numeral_Onat__of, _1688319) = hAPP(c_Code__Numeral_Onat__of, _1688321))], (45250 ^ _780205) ^ [_1688425, _1688427] : [hAPP(c_Code__Numeral_Onat__of, _1688425) = hAPP(c_Code__Numeral_Onat__of, _1688427), -(_1688425 = _1688427)], (45256 ^ _780205) ^ [_1688510, _1688512] : [_1688510 = _1688512, -(hAPP(c_Code__Numeral_Onat__of, _1688510) = hAPP(c_Code__Numeral_Onat__of, _1688512))], (45262 ^ _780205) ^ [] : [-(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))))], (45264 ^ _780205) ^ [_1688634, _1688636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1688634), _1688636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1688634)), hAPP(c_Code__Numeral_Onat__of, _1688636))))], (45270 ^ _780205) ^ [_1688739, _1688741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1688739)), hAPP(c_Code__Numeral_Onat__of, _1688741))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1688739), _1688741)))], (45276 ^ _780205) ^ [_1688850] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1688850)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (45278 ^ _780205) ^ [_1688881] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1688881)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1688881))], (45280 ^ _780205) ^ [] : [-(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))], (45282 ^ _780205) ^ [_1688946, _1688948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1688946), _1688948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1688946)), hAPP(c_Code__Numeral_Onat__of, _1688948))))], (45288 ^ _780205) ^ [_1689051, _1689053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1689051)), hAPP(c_Code__Numeral_Onat__of, _1689053))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1689051), _1689053)))], (45294 ^ _780205) ^ [_1689162] : [-(hAPP(c_Code__Numeral_Onat__of, _1689162) = c_Code__Numeral_Onat__of__aux(_1689162, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45296 ^ _780205) ^ [_1689191, _1689193] : [-(c_Code__Numeral_Onat__of__aux(_1689191, _1689193) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1689191)), _1689193))], (45298 ^ _780205) ^ [_1689228] : [-(c_Code__Numeral_OSuc__code__numeral(_1689228) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1689228))))], (45300 ^ _780205) ^ [_1689262, _1689264] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1689262), _1689264) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1689262)), hAPP(c_Code__Numeral_Onat__of, _1689264))))], (45302 ^ _780205) ^ [_1689308] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1689308), 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, _1689308)) = _1689308)], (45308 ^ _780205) ^ [_1689405, _1689407] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1689405), _1689407) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1689405)), hAPP(c_Code__Numeral_Onat__of, _1689407))))], (45310 ^ _780205) ^ [_1689451, _1689453] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1689451), _1689453) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1689451)), hAPP(c_Code__Numeral_Onat__of, _1689453))))], (45312 ^ _780205) ^ [_1689497, _1689499] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1689497, _1689499) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1689497), hAPP(c_Code__Numeral_Onat__of, _1689499))))], (45314 ^ _780205) ^ [_1689535] : [-(_1689535 = 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, _1689535)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1689535))))], (45320 ^ _780205) ^ [_1689586, _1689588] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1689586), _1689588) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1689586, 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)))), _1689588))))], (45322 ^ _780205) ^ [_1689624, _1689626, _1689628, _1689630, _1689632] : [c_List_Opartition(_1689624, _1689626, _1689628) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689624), tc_List_Olist(_1689624)), _1689630), _1689632), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1689624, tc_HOL_Obool)), hAPP(c_List_Oset(_1689624), _1689630)), hAPP(c_List_Oset(_1689624), _1689632)) = hAPP(c_List_Oset(_1689624), _1689628))], (45328 ^ _780205) ^ [_1689793, _1689795, _1689797, _1689799, _1689801] : [c_List_Opartition(_1689793, _1689795, _1689797) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689793), tc_List_Olist(_1689793)), _1689799), _1689801), 45331 ^ _780205 : [(45332 ^ _780205) ^ [_1689946] : [hBOOL(hAPP(hAPP(c_member(_1689793), _1689946), hAPP(c_List_Oset(_1689793), _1689799))), -(hBOOL(hAPP(_1689795, _1689946)))], (45338 ^ _780205) ^ [_1690055] : [hBOOL(hAPP(hAPP(c_member(_1689793), _1690055), hAPP(c_List_Oset(_1689793), _1689801))), hBOOL(hAPP(_1689795, _1690055))]]], (45344 ^ _780205) ^ [_1690175, _1690177] : [-(c_List_Opartition(_1690175, _1690177, c_List_Olist_ONil(_1690175)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690175), tc_List_Olist(_1690175)), c_List_Olist_ONil(_1690175)), c_List_Olist_ONil(_1690175)))], (45346 ^ _780205) ^ [_1690223, _1690225, _1690227, _1690229] : [-(c_List_Opartition(_1690223, _1690225, hAPP(hAPP(c_List_Olist_OCons(_1690223), _1690227), _1690229)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1690223), tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1690223), tc_fun(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223))), tc_fun(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690223), tc_fun(tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)))), tc_fun(tc_fun(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223))), tc_fun(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)))), tc_List_Olist(_1690223)), c_COMBS(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223))), tc_fun(tc_List_Olist(_1690223), tc_fun(tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)))), tc_List_Olist(_1690223)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)), tc_fun(tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223))), tc_List_Olist(_1690223)), hAPP(c_If(tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223))), hAPP(_1690225, _1690227)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1690223), tc_fun(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223))), tc_List_Olist(_1690223)), c_Product__Type_OPair(tc_List_Olist(_1690223), tc_List_Olist(_1690223))), hAPP(c_List_Olist_OCons(_1690223), _1690227))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690223), tc_fun(tc_List_Olist(_1690223), tc_List_Olist(_1690223)), tc_fun(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223))), tc_fun(tc_fun(tc_List_Olist(_1690223), tc_List_Olist(_1690223)), tc_fun(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)))), tc_List_Olist(_1690223)), c_COMBB(tc_List_Olist(_1690223), tc_prod(tc_List_Olist(_1690223), tc_List_Olist(_1690223)), tc_List_Olist(_1690223))), c_Product__Type_OPair(tc_List_Olist(_1690223), tc_List_Olist(_1690223)))), hAPP(c_List_Olist_OCons(_1690223), _1690227)))), c_List_Opartition(_1690223, _1690225, _1690229)))], (45348 ^ _780205) ^ [_1690642, _1690644, _1690646, _1690648] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1690642)), _1690644), c_List_Olists(_1690642, _1690646))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1690642)), _1690644), c_List_Olists(_1690642, _1690648))), -(hBOOL(hAPP(c_List_Olistsp(_1690642, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1690642, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1690642, tc_fun(_1690642, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690642)), _1690646)), hAPP(hAPP(c_COMBC(_1690642, tc_fun(_1690642, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690642)), _1690648))), _1690644)))], (45358 ^ _780205) ^ [_1690919, _1690921, _1690923] : [-(c_List_Olistsp(_1690919, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1690919, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1690919, tc_fun(_1690919, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690919)), _1690921)), hAPP(hAPP(c_COMBC(_1690919, tc_fun(_1690919, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690919)), _1690923))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1690919), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690919), tc_fun(tc_List_Olist(_1690919), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1690919))), c_List_Olists(_1690919, _1690921))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690919), tc_fun(tc_List_Olist(_1690919), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1690919))), c_List_Olists(_1690919, _1690923))))], (45360 ^ _780205) ^ [_1691051, _1691053] : [-(hBOOL(hAPP(c_List_Olistsp(_1691051, _1691053), c_List_Olist_ONil(_1691051))))], (45362 ^ _780205) ^ [_1691083, _1691085] : [-(hBOOL(hAPP(c_List_Olistsp(_1691083, _1691085), c_List_Olist_ONil(_1691083))))], (45374 ^ _780205) ^ [_1691331, _1691333, _1691335] : [45376 ^ _780205 : [(45377 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1691331), 45375 ^ [_1691331, _1691333, _1691335]), hAPP(c_List_Oset(_1691331), _1691335))))], (45379 ^ _780205) ^ [] : [hBOOL(hAPP(_1691333, 45375 ^ [_1691331, _1691333, _1691335]))]], -(hBOOL(hAPP(c_List_Olistsp(_1691331, _1691333), _1691335)))], (45364 ^ _780205) ^ [_1691133, _1691135, _1691137] : [hBOOL(hAPP(c_List_Olistsp(_1691133, _1691135), _1691137)), 45367 ^ _780205 : [(45368 ^ _780205) ^ [_1691222] : [hBOOL(hAPP(hAPP(c_member(_1691133), _1691222), hAPP(c_List_Oset(_1691133), _1691137))), -(hBOOL(hAPP(_1691135, _1691222)))]]], (45383 ^ _780205) ^ [_1691542, _1691544, _1691546, _1691548] : [hBOOL(hAPP(c_List_Olistsp(_1691542, hAPP(hAPP(c_COMBS(_1691542, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1691542), c_fconj), _1691544)), _1691546)), _1691548)), 45386 ^ _780205 : [(45387 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1691542, _1691544), _1691548)))], (45389 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1691542, _1691546), _1691548)))]]], (45391 ^ _780205) ^ [_1691715, _1691717, _1691719, _1691721] : [-(hBOOL(hAPP(c_List_Olistsp(_1691715, hAPP(hAPP(c_COMBS(_1691715, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1691715), c_fconj), _1691717)), _1691719)), _1691721))), hBOOL(hAPP(c_List_Olistsp(_1691715, _1691717), _1691721)), hBOOL(hAPP(c_List_Olistsp(_1691715, _1691719), _1691721))], (45401 ^ _780205) ^ [_1691924, _1691926, _1691928] : [-(c_List_Olistsp(_1691924, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1691924, tc_HOL_Obool)), _1691926), _1691928)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1691924), tc_HOL_Obool)), c_List_Olistsp(_1691924, _1691926)), c_List_Olistsp(_1691924, _1691928)))], (45403 ^ _780205) ^ [_1691984, _1691986, _1691988, _1691990] : [hBOOL(hAPP(c_List_Olistsp(_1691984, _1691986), _1691988)), hBOOL(hAPP(c_List_Olistsp(_1691984, _1691990), _1691988)), -(hBOOL(hAPP(c_List_Olistsp(_1691984, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1691984, tc_HOL_Obool)), _1691986), _1691990)), _1691988)))], (45413 ^ _780205) ^ [_1692194, _1692196, _1692198, _1692200] : [hBOOL(hAPP(c_List_Olistsp(_1692194, _1692196), hAPP(hAPP(c_List_Olist_OCons(_1692194), _1692198), _1692200))), 45416 ^ _780205 : [(45417 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1692196, _1692198)))], (45419 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1692194, _1692196), _1692200)))]]], (45421 ^ _780205) ^ [_1692337, _1692339, _1692341, _1692343] : [-(hBOOL(hAPP(c_List_Olistsp(_1692337, _1692339), hAPP(hAPP(c_List_Olist_OCons(_1692337), _1692341), _1692343)))), hBOOL(hAPP(_1692339, _1692341)), hBOOL(hAPP(c_List_Olistsp(_1692337, _1692339), _1692343))], (45431 ^ _780205) ^ [_1692537, _1692539, _1692541, _1692543] : [hBOOL(hAPP(c_List_Olistsp(_1692537, _1692539), hAPP(hAPP(c_List_Oappend(_1692537), _1692541), _1692543))), 45434 ^ _780205 : [(45435 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1692537, _1692539), _1692541)))], (45437 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1692537, _1692539), _1692543)))]]], (45439 ^ _780205) ^ [_1692686, _1692688, _1692690, _1692692] : [-(hBOOL(hAPP(c_List_Olistsp(_1692686, _1692688), hAPP(hAPP(c_List_Oappend(_1692686), _1692690), _1692692)))), hBOOL(hAPP(c_List_Olistsp(_1692686, _1692688), _1692690)), hBOOL(hAPP(c_List_Olistsp(_1692686, _1692688), _1692692))], (45449 ^ _780205) ^ [_1692871, _1692873, _1692875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1692871, tc_HOL_Obool)), _1692873), _1692875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1692871), tc_HOL_Obool)), c_List_Olistsp(_1692871, _1692873)), c_List_Olistsp(_1692871, _1692875))))], (45455 ^ _780205) ^ [_1693024, _1693026, _1693028] : [hBOOL(hAPP(c_List_Olistsp(_1693024, hAPP(hAPP(c_COMBC(_1693024, tc_fun(_1693024, tc_HOL_Obool), tc_HOL_Obool), c_member(_1693024)), _1693026)), _1693028)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1693024)), _1693028), c_List_Olists(_1693024, _1693026))))], (45461 ^ _780205) ^ [_1693163, _1693165, _1693167] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1693163)), _1693167), c_List_Olists(_1693163, _1693165))), -(hBOOL(hAPP(c_List_Olistsp(_1693163, hAPP(hAPP(c_COMBC(_1693163, tc_fun(_1693163, tc_HOL_Obool), tc_HOL_Obool), c_member(_1693163)), _1693165)), _1693167)))], (45467 ^ _780205) ^ [_1693308, _1693310, _1693312, _1693314, _1693316] : [-(c_Enum_Oproduct(_1693308, _1693310, hAPP(hAPP(c_List_Olist_OCons(_1693308), _1693312), _1693314), _1693316) = hAPP(hAPP(c_List_Oappend(tc_prod(_1693308, _1693310)), hAPP(hAPP(c_List_Omap(_1693310, tc_prod(_1693308, _1693310)), hAPP(c_Product__Type_OPair(_1693308, _1693310), _1693312)), _1693316)), c_Enum_Oproduct(_1693308, _1693310, _1693314, _1693316)))], (45469 ^ _780205) ^ [_1693410, _1693412, _1693414, _1693416, _1693418] : [c_List_Olist__all2(_1693410, _1693412, _1693414, _1693416, _1693418), 45472 ^ _780205 : [(45473 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693410)), _1693416) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693412)), _1693418))], (45475 ^ _780205) ^ [_1693576] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1693410, _1693412)), _1693576), hAPP(c_List_Oset(tc_prod(_1693410, _1693412)), hAPP(hAPP(c_List_Ozip(_1693410, _1693412), _1693416), _1693418)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1693410, _1693412, tc_HOL_Obool), _1693414), _1693576)))]]], (45481 ^ _780205) ^ [_1693735, _1693737, _1693739, _1693741, _1693743] : [-(c_List_Olist__all2(_1693735, _1693737, _1693739, _1693741, _1693743)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693735)), _1693741) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693737)), _1693743), 45487 ^ _780205 : [(45488 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1693735, _1693737)), 45486 ^ [_1693735, _1693737, _1693739, _1693741, _1693743]), hAPP(c_List_Oset(tc_prod(_1693735, _1693737)), hAPP(hAPP(c_List_Ozip(_1693735, _1693737), _1693741), _1693743)))))], (45490 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1693735, _1693737, tc_HOL_Obool), _1693739), 45486 ^ [_1693735, _1693737, _1693739, _1693741, _1693743]))]]], (45494 ^ _780205) ^ [_1694106, _1694108, _1694110, _1694112, _1694114, _1694116, _1694118] : [c_List_Olist__all2(_1694106, _1694108, _1694110, _1694112, hAPP(hAPP(c_List_Omap(_1694114, _1694108), _1694116), _1694118)), -(c_List_Olist__all2(_1694106, _1694114, hAPP(hAPP(c_COMBC(_1694106, tc_fun(_1694114, _1694108), tc_fun(_1694114, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1694108, tc_HOL_Obool), tc_fun(tc_fun(_1694114, _1694108), tc_fun(_1694114, tc_HOL_Obool)), _1694106), c_COMBB(_1694108, tc_HOL_Obool, _1694114)), _1694110)), _1694116), _1694112, _1694118))], (45500 ^ _780205) ^ [_1694303, _1694305, _1694307, _1694309, _1694311, _1694313, _1694315] : [c_List_Olist__all2(_1694303, _1694311, hAPP(hAPP(c_COMBC(_1694303, tc_fun(_1694311, _1694305), tc_fun(_1694311, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1694305, tc_HOL_Obool), tc_fun(tc_fun(_1694311, _1694305), tc_fun(_1694311, tc_HOL_Obool)), _1694303), c_COMBB(_1694305, tc_HOL_Obool, _1694311)), _1694307)), _1694313), _1694309, _1694315), -(c_List_Olist__all2(_1694303, _1694305, _1694307, _1694309, hAPP(hAPP(c_List_Omap(_1694311, _1694305), _1694313), _1694315)))], (45506 ^ _780205) ^ [_1694536, _1694538, _1694540, _1694542, _1694544, _1694546, _1694548] : [c_List_Olist__all2(_1694536, _1694538, _1694540, hAPP(hAPP(c_List_Omap(_1694542, _1694536), _1694544), _1694546), _1694548), -(c_List_Olist__all2(_1694542, _1694538, hAPP(hAPP(c_COMBB(_1694536, tc_fun(_1694538, tc_HOL_Obool), _1694542), _1694540), _1694544), _1694546, _1694548))], (45512 ^ _780205) ^ [_1694675, _1694677, _1694679, _1694681, _1694683, _1694685, _1694687] : [c_List_Olist__all2(_1694681, _1694677, hAPP(hAPP(c_COMBB(_1694675, tc_fun(_1694677, tc_HOL_Obool), _1694681), _1694679), _1694683), _1694685, _1694687), -(c_List_Olist__all2(_1694675, _1694677, _1694679, hAPP(hAPP(c_List_Omap(_1694681, _1694675), _1694683), _1694685), _1694687))], (45518 ^ _780205) ^ [_1694820, _1694822, _1694824, _1694826, _1694828, _1694830] : [c_List_Olist__all2(_1694820, _1694822, _1694824, _1694826, _1694828), -(c_List_Olist__all2(_1694820, _1694822, _1694824, hAPP(hAPP(c_List_Odrop(_1694820), _1694830), _1694826), hAPP(hAPP(c_List_Odrop(_1694822), _1694830), _1694828)))], (45524 ^ _780205) ^ [_1694949, _1694951, _1694953, _1694955, _1694957, _1694959, _1694961] : [c_List_Olist__all2(_1694949, _1694951, _1694953, _1694955, _1694957), c_List_Olist__all2(_1694949, _1694951, _1694953, _1694959, _1694961), -(c_List_Olist__all2(_1694949, _1694951, _1694953, hAPP(hAPP(c_List_Oappend(_1694949), _1694955), _1694959), hAPP(hAPP(c_List_Oappend(_1694951), _1694957), _1694961)))], (45534 ^ _780205) ^ [_1695148, _1695150, _1695152, _1695154, _1695156, _1695158, _1695160] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695148)), _1695150) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695152)), _1695154), 45537 ^ _780205 : [(45538 ^ _780205) ^ [] : [c_List_Olist__all2(_1695148, _1695152, _1695156, hAPP(hAPP(c_List_Oappend(_1695148), _1695150), _1695158), hAPP(hAPP(c_List_Oappend(_1695152), _1695154), _1695160)), 45541 ^ _780205 : [(45542 ^ _780205) ^ [] : [-(c_List_Olist__all2(_1695148, _1695152, _1695156, _1695150, _1695154))], (45544 ^ _780205) ^ [] : [-(c_List_Olist__all2(_1695148, _1695152, _1695156, _1695158, _1695160))]]], (45546 ^ _780205) ^ [] : [-(c_List_Olist__all2(_1695148, _1695152, _1695156, hAPP(hAPP(c_List_Oappend(_1695148), _1695150), _1695158), hAPP(hAPP(c_List_Oappend(_1695152), _1695154), _1695160))), c_List_Olist__all2(_1695148, _1695152, _1695156, _1695150, _1695154), c_List_Olist__all2(_1695148, _1695152, _1695156, _1695158, _1695160)]]], (45556 ^ _780205) ^ [_1695600, _1695602, _1695604, _1695606, _1695608, _1695610, _1695612] : [c_List_Olist__all2(_1695600, _1695602, _1695604, hAPP(hAPP(c_List_Olist_OCons(_1695600), _1695606), _1695608), hAPP(hAPP(c_List_Olist_OCons(_1695602), _1695610), _1695612)), 45559 ^ _780205 : [(45560 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1695604, _1695606), _1695610)))], (45562 ^ _780205) ^ [] : [-(c_List_Olist__all2(_1695600, _1695602, _1695604, _1695608, _1695612))]]], (45564 ^ _780205) ^ [_1695763, _1695765, _1695767, _1695769, _1695771, _1695773, _1695775] : [-(c_List_Olist__all2(_1695763, _1695765, _1695767, hAPP(hAPP(c_List_Olist_OCons(_1695763), _1695769), _1695771), hAPP(hAPP(c_List_Olist_OCons(_1695765), _1695773), _1695775))), hBOOL(hAPP(hAPP(_1695767, _1695769), _1695773)), c_List_Olist__all2(_1695763, _1695765, _1695767, _1695771, _1695775)], (45574 ^ _780205) ^ [_1695968, _1695970, _1695972, _1695974, _1695976, _1695978] : [c_List_Olist__all2(_1695968, _1695970, _1695972, _1695974, _1695976), -(c_List_Olist__all2(_1695968, _1695970, _1695972, hAPP(hAPP(c_List_Otake(_1695968), _1695978), _1695974), hAPP(hAPP(c_List_Otake(_1695970), _1695978), _1695976)))], (45580 ^ _780205) ^ [_1696115, _1696117, _1696119] : [_1696115 = _1696117, -(c_List_Olist__all2(_1696119, _1696119, c_fequal, _1696115, _1696117))], (45586 ^ _780205) ^ [_1696196, _1696198, _1696200] : [c_List_Olist__all2(_1696200, _1696200, c_fequal, _1696196, _1696198), -(_1696196 = _1696198)], (45592 ^ _780205) ^ [_1696283, _1696285, _1696287, _1696289, _1696291] : [c_List_Olist__all2(_1696283, _1696285, _1696287, _1696289, _1696291), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696283)), _1696289) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696285)), _1696291))], (45598 ^ _780205) ^ [_1696421, _1696423, _1696425, _1696427] : [c_List_Olist__all2(_1696421, _1696423, _1696425, c_List_Olist_ONil(_1696421), _1696427), -(_1696427 = c_List_Olist_ONil(_1696423))], (45604 ^ _780205) ^ [_1696512, _1696514, _1696516, _1696518] : [_1696518 = c_List_Olist_ONil(_1696514), -(c_List_Olist__all2(_1696512, _1696514, _1696516, c_List_Olist_ONil(_1696512), _1696518))], (45610 ^ _780205) ^ [_1696630, _1696632, _1696634, _1696636] : [c_List_Olist__all2(_1696630, _1696632, _1696634, _1696636, c_List_Olist_ONil(_1696632)), -(_1696636 = c_List_Olist_ONil(_1696630))], (45616 ^ _780205) ^ [_1696721, _1696723, _1696725, _1696727] : [_1696727 = c_List_Olist_ONil(_1696721), -(c_List_Olist__all2(_1696721, _1696723, _1696725, _1696727, c_List_Olist_ONil(_1696723)))], (45622 ^ _780205) ^ [_1696818, _1696820, _1696822] : [-(c_Enum_Oproduct(_1696818, _1696820, c_List_Olist_ONil(_1696818), _1696822) = c_List_Olist_ONil(tc_prod(_1696818, _1696820)))], (45624 ^ _780205) ^ [_1696881, _1696883, _1696885, _1696887, _1696889] : [c_List_Olist__all2(_1696881, _1696883, _1696885, _1696887, _1696889), 45627 ^ _780205 : [(45628 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696881)), _1696887) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696883)), _1696889))], (45630 ^ _780205) ^ [_1697044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697044), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696881)), _1696887))), -(hBOOL(hAPP(hAPP(_1696885, hAPP(hAPP(c_List_Onth(_1696881), _1696887), _1697044)), hAPP(hAPP(c_List_Onth(_1696883), _1696889), _1697044))))]]], (45636 ^ _780205) ^ [_1697197, _1697199, _1697201, _1697203, _1697205] : [-(c_List_Olist__all2(_1697197, _1697199, _1697201, _1697203, _1697205)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697197)), _1697203) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697199)), _1697205), 45642 ^ _780205 : [(45643 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45641 ^ [_1697197, _1697199, _1697201, _1697203, _1697205]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697197)), _1697203))))], (45645 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1697201, hAPP(hAPP(c_List_Onth(_1697197), _1697203), 45641 ^ [_1697197, _1697199, _1697201, _1697203, _1697205])), hAPP(hAPP(c_List_Onth(_1697199), _1697205), 45641 ^ [_1697197, _1697199, _1697201, _1697203, _1697205])))]]], (45649 ^ _780205) ^ [_1697557, _1697559, _1697561, _1697563, _1697565, _1697567] : [c_List_Olist__all2(_1697557, _1697559, _1697561, _1697563, _1697565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697567), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697557)), _1697563))), -(hBOOL(hAPP(hAPP(_1697561, hAPP(hAPP(c_List_Onth(_1697557), _1697563), _1697567)), hAPP(hAPP(c_List_Onth(_1697559), _1697565), _1697567))))], (45659 ^ _780205) ^ [_1697774, _1697776, _1697778, _1697780, _1697782, _1697784] : [c_List_Olist__all2(_1697774, _1697776, _1697778, _1697780, _1697782), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697784), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697776)), _1697782))), -(hBOOL(hAPP(hAPP(_1697778, hAPP(hAPP(c_List_Onth(_1697774), _1697780), _1697784)), hAPP(hAPP(c_List_Onth(_1697776), _1697782), _1697784))))], (45669 ^ _780205) ^ [_1697991, _1697993, _1697995, _1697997, _1697999, _1698001, _1698003, _1698005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697991), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697993)), _1697995))), c_List_Olist__all2(_1697993, _1697997, _1697999, _1697995, _1698001), hBOOL(hAPP(hAPP(_1697999, _1698003), _1698005)), -(c_List_Olist__all2(_1697993, _1697997, _1697999, hAPP(hAPP(c_List_Olist__update(_1697993, _1697995), _1697991), _1698003), hAPP(hAPP(c_List_Olist__update(_1697997, _1698001), _1697991), _1698005)))], (45683 ^ _780205) ^ [_1698290, _1698292, _1698294, _1698296, _1698298, _1698300, _1698302, _1698304] : [c_List_Olist__all2(_1698290, _1698292, _1698294, _1698296, _1698298), hBOOL(hAPP(hAPP(_1698294, _1698300), _1698302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1698304), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698292)), _1698298))), -(c_List_Olist__all2(_1698290, _1698292, _1698294, hAPP(hAPP(c_List_Olist__update(_1698290, _1698296), _1698304), _1698300), hAPP(hAPP(c_List_Olist__update(_1698292, _1698298), _1698304), _1698302)))], (45697 ^ _780205) ^ [_1698589, _1698591, _1698593, _1698595] : [hBOOL(hAPP(c_List_Odistinct(_1698589), _1698591)), hBOOL(hAPP(c_List_Odistinct(_1698593), _1698595)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1698589, _1698593)), c_Enum_Oproduct(_1698589, _1698593, _1698591, _1698595))))], (45707 ^ _780205) ^ [_1698766, _1698768, _1698770, _1698772] : [-(hAPP(c_List_Oset(tc_prod(_1698766, _1698768)), c_Enum_Oproduct(_1698766, _1698768, _1698770, _1698772)) = hAPP(hAPP(c_Product__Type_OSigma(_1698766, _1698768), hAPP(c_List_Oset(_1698766), _1698770)), hAPP(c_COMBK(tc_fun(_1698768, tc_HOL_Obool), _1698766), hAPP(c_List_Oset(_1698768), _1698772))))], (45709 ^ _780205) ^ [_1698836, _1698838] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1698836), tc_fun(_1698836, tc_HOL_Obool), c_List_Oset(_1698836)), hAPP(c_List_Oset(tc_List_Olist(_1698836)), c_Enum_Osublists(_1698836, _1698838))) = hAPP(c_Set_OPow(_1698836), hAPP(c_List_Oset(_1698836), _1698838)))], (45711 ^ _780205) ^ [_1698895, _1698897] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1698895))), c_Enum_Osublists(_1698895, _1698897)) = 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(_1698895)), _1698897)))], (45713 ^ _780205) ^ [_1698942] : [-(c_Enum_Osublists(_1698942, c_List_Olist_ONil(_1698942)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698942)), c_List_Olist_ONil(_1698942)), c_List_Olist_ONil(tc_List_Olist(_1698942))))], (45715 ^ _780205) ^ [_1698986, _1698988, _1698990] : [-(c_Enum_Osublists(_1698986, hAPP(hAPP(c_List_Olist_OCons(_1698986), _1698988), _1698990)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1698986)), tc_List_Olist(tc_List_Olist(_1698986))), c_Enum_Osublists(_1698986, _1698990)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1698986)), tc_List_Olist(tc_List_Olist(_1698986)), tc_List_Olist(tc_List_Olist(_1698986))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1698986)), tc_fun(tc_List_Olist(tc_List_Olist(_1698986)), tc_List_Olist(tc_List_Olist(_1698986))), tc_List_Olist(tc_List_Olist(_1698986))), c_List_Oappend(tc_List_Olist(_1698986))), hAPP(c_List_Omap(tc_List_Olist(_1698986), tc_List_Olist(_1698986)), hAPP(c_List_Olist_OCons(_1698986), _1698988)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1698986))))))], (45717 ^ _780205) ^ [_1699120, _1699122] : [hBOOL(hAPP(c_List_Odistinct(_1699120), _1699122)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1699120, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699120), tc_fun(_1699120, tc_HOL_Obool)), c_List_Oset(_1699120)), c_Enum_Osublists(_1699120, _1699122)))))], (45723 ^ _780205) ^ [_1699257, _1699259, _1699261] : [-(hAPP(c_List_Oset(tc_List_Olist(_1699257)), c_Enum_On__lists(_1699257, _1699259, _1699261)) = hAPP(c_Set_OCollect(tc_List_Olist(_1699257)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1699257), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1699257)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699257), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1699257)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1699257)))), _1699259))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699257), tc_fun(_1699257, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1699257, tc_HOL_Obool), tc_fun(tc_fun(_1699257, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1699257)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1699257, tc_HOL_Obool))), c_List_Oset(_1699257))), hAPP(c_List_Oset(_1699257), _1699261)))))], (45725 ^ _780205) ^ [_1699402, _1699404] : [-(c_Enum_Oenum__the(_1699402, _1699404) = c_HOL_OThe(_1699402, _1699404))], (45727 ^ _780205) ^ [_1699433, _1699435, _1699437] : [hBOOL(hAPP(c_List_Odistinct(_1699433), _1699435)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1699433)), c_Enum_On__lists(_1699433, _1699437, _1699435))))], (45733 ^ _780205) ^ [_1699549, _1699551] : [_1699549 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1699551, _1699549, c_List_Olist_ONil(_1699551)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699551)), c_List_Olist_ONil(_1699551)), c_List_Olist_ONil(tc_List_Olist(_1699551))))], (45739 ^ _780205) ^ [_1699664, _1699666] : [-(_1699664 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1699666, _1699664, c_List_Olist_ONil(_1699666)) = c_List_Olist_ONil(tc_List_Olist(_1699666)))], (45745 ^ _780205) ^ [_1699712, _1699714] : [-(c_Enum_On__lists(_1699712, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1699714) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699712)), c_List_Olist_ONil(_1699712)), c_List_Olist_ONil(tc_List_Olist(_1699712))))], (45747 ^ _780205) ^ [_1699757, _1699759, _1699761] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699757))), c_Enum_On__lists(_1699757, _1699759, _1699761)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699757)), _1699761)), _1699759))], (45749 ^ _780205) ^ [_1699810, _1699812, _1699814, _1699816] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699810)), _1699812), hAPP(c_List_Oset(tc_List_Olist(_1699810)), c_Enum_On__lists(_1699810, _1699814, _1699816)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699810)), _1699812) = _1699814)], (45755 ^ _780205) ^ [_1699945, _1699947, _1699949, _1699951, _1699953] : [45757 ^ _780205 : [(45758 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1699945, _1699947)), 45756 ^ [_1699945, _1699947, _1699949, _1699951, _1699953]), hAPP(c_List_Oset(tc_prod(_1699945, _1699947)), hAPP(hAPP(c_List_Ozip(_1699945, _1699947), _1699949), _1699951)))))], (45760 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1699945, _1699947, tc_HOL_Obool), _1699953), 45756 ^ [_1699945, _1699947, _1699949, _1699951, _1699953]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699945)), _1699949) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699947)), _1699951), -(c_List_Olist__all2(_1699945, _1699947, _1699953, _1699949, _1699951))], (45768 ^ _780205) ^ [_1700284, _1700286, _1700288, _1700290] : [45770 ^ _780205 : [(45771 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45769 ^ [_1700284, _1700286, _1700288, _1700290]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700284)), _1700286))))], (45773 ^ _780205) ^ [] : [hBOOL(hAPP(_1700288, hAPP(hAPP(c_List_Onth(_1700284), _1700286), 45769 ^ [_1700284, _1700286, _1700288, _1700290])))]], hBOOL(hAPP(hAPP(c_member(_1700284), _1700290), hAPP(c_List_Oset(_1700284), _1700286))), -(hBOOL(hAPP(_1700288, _1700290)))], (45781 ^ _780205) ^ [_1700580, _1700582, _1700584, _1700586, _1700588] : [c_Finite__Set_Ofun__left__comm(_1700580, _1700582, _1700584), -(hAPP(hAPP(c_Finite__Set_Ofold(_1700580, _1700582, _1700584), _1700586), hAPP(c_List_Oset(_1700580), _1700588)) = hAPP(c_List_Ofoldl(_1700582, _1700580, hAPP(c_COMBC(_1700580, _1700582, _1700582), _1700584), _1700586), c_List_Oremdups(_1700580, _1700588)))], (45787 ^ _780205) ^ [_1700731, _1700733, _1700735, _1700737, _1700739] : [c_Fun_Oinj__on(_1700731, _1700733, _1700735, hAPP(hAPP(c_Set_Oinsert(_1700731), _1700737), hAPP(c_List_Oset(_1700731), _1700739))), -(hAPP(hAPP(c_List_Omap(_1700731, _1700733), _1700735), hAPP(c_List_OremoveAll(_1700731, _1700737), _1700739)) = hAPP(c_List_OremoveAll(_1700733, hAPP(_1700735, _1700737)), hAPP(hAPP(c_List_Omap(_1700731, _1700733), _1700735), _1700739)))], (45793 ^ _780205) ^ [_1700910, _1700912] : [-(hBOOL(hAPP(c_List_Odistinct(_1700910), c_List_Oremdups(_1700910, _1700912))))], (45795 ^ _780205) ^ [_1700942, _1700944] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700942)), c_List_Oremdups(_1700942, _1700944))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700942)), _1700944))))], (45797 ^ _780205) ^ [_1700989, _1700991] : [hBOOL(hAPP(c_List_Odistinct(_1700989), _1700991)), -(c_List_Oremdups(_1700989, _1700991) = _1700991)], (45803 ^ _780205) ^ [_1701080, _1701082, _1701084] : [hBOOL(hAPP(c_List_Odistinct(_1701080), _1701082)), -(hBOOL(hAPP(c_List_Odistinct(_1701080), hAPP(c_List_OremoveAll(_1701080, _1701084), _1701082))))], (45809 ^ _780205) ^ [_1701202, _1701204] : [c_List_Oremdups(_1701202, _1701204) = _1701204, -(hBOOL(hAPP(c_List_Odistinct(_1701202), _1701204)))], (45815 ^ _780205) ^ [_1701289, _1701291] : [hBOOL(hAPP(c_List_Odistinct(_1701289), _1701291)), -(c_List_Oremdups(_1701289, _1701291) = _1701291)], (45821 ^ _780205) ^ [_1701382, _1701384] : [-(hAPP(c_List_Oset(_1701382), c_List_Oremdups(_1701382, _1701384)) = hAPP(c_List_Oset(_1701382), _1701384))], (45823 ^ _780205) ^ [_1701435, _1701437] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701435)), c_List_Oremdups(_1701435, _1701437)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701435)), _1701437), -(c_List_Oremdups(_1701435, _1701437) = _1701437)], (45829 ^ _780205) ^ [_1701548, _1701550] : [c_List_Oremdups(_1701548, _1701550) = _1701550, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701548)), c_List_Oremdups(_1701548, _1701550)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701548)), _1701550))], (45835 ^ _780205) ^ [_1701667, _1701669] : [-(c_List_Oremdups(_1701667, c_List_Oremdups(_1701667, _1701669)) = c_List_Oremdups(_1701667, _1701669))], (45837 ^ _780205) ^ [_1701716, _1701718] : [c_List_Oremdups(_1701716, _1701718) = c_List_Olist_ONil(_1701716), -(_1701718 = c_List_Olist_ONil(_1701716))], (45843 ^ _780205) ^ [_1701803, _1701805] : [_1701805 = c_List_Olist_ONil(_1701803), -(c_List_Oremdups(_1701803, _1701805) = c_List_Olist_ONil(_1701803))], (45849 ^ _780205) ^ [_1701896, _1701898] : [-(hAPP(c_List_OremoveAll(_1701896, _1701898), c_List_Olist_ONil(_1701896)) = c_List_Olist_ONil(_1701896))], (45851 ^ _780205) ^ [_1701946, _1701948] : [c_List_Olist_ONil(_1701946) = c_List_Oremdups(_1701946, _1701948), -(_1701948 = c_List_Olist_ONil(_1701946))], (45857 ^ _780205) ^ [_1702033, _1702035] : [_1702035 = c_List_Olist_ONil(_1702033), -(c_List_Olist_ONil(_1702033) = c_List_Oremdups(_1702033, _1702035))], (45863 ^ _780205) ^ [_1702126] : [-(c_List_Oremdups(_1702126, c_List_Olist_ONil(_1702126)) = c_List_Olist_ONil(_1702126))], (45865 ^ _780205) ^ [_1702171, _1702173, _1702175, _1702177] : [_1702171 = _1702173, -(hAPP(c_List_OremoveAll(_1702175, _1702171), hAPP(hAPP(c_List_Olist_OCons(_1702175), _1702173), _1702177)) = hAPP(c_List_OremoveAll(_1702175, _1702171), _1702177))], (45871 ^ _780205) ^ [_1702286, _1702288, _1702290, _1702292] : [-(_1702286 = _1702288), -(hAPP(c_List_OremoveAll(_1702290, _1702286), hAPP(hAPP(c_List_Olist_OCons(_1702290), _1702288), _1702292)) = hAPP(hAPP(c_List_Olist_OCons(_1702290), _1702288), hAPP(c_List_OremoveAll(_1702290, _1702286), _1702292)))], (45877 ^ _780205) ^ [_1702356, _1702358, _1702360, _1702362] : [-(hAPP(c_List_OremoveAll(_1702356, _1702358), hAPP(hAPP(c_List_Oappend(_1702356), _1702360), _1702362)) = hAPP(hAPP(c_List_Oappend(_1702356), hAPP(c_List_OremoveAll(_1702356, _1702358), _1702360)), hAPP(c_List_OremoveAll(_1702356, _1702358), _1702362)))], (45879 ^ _780205) ^ [_1702419, _1702421, _1702423, _1702425] : [-(c_List_Oremdups(_1702419, hAPP(hAPP(c_List_Omap(_1702421, _1702419), _1702423), c_List_Oremdups(_1702421, _1702425))) = c_List_Oremdups(_1702419, hAPP(hAPP(c_List_Omap(_1702421, _1702419), _1702423), _1702425)))], (45881 ^ _780205) ^ [_1702475, _1702477, _1702479] : [hBOOL(hAPP(c_List_Odistinct(_1702475), _1702477)), -(c_List_Oremove1(_1702475, _1702479, c_List_Oremdups(_1702475, _1702477)) = c_List_Oremdups(_1702475, c_List_Oremove1(_1702475, _1702479, _1702477)))], (45887 ^ _780205) ^ [_1702586, _1702588, _1702590] : [-(hBOOL(hAPP(hAPP(c_member(_1702586), _1702588), hAPP(c_List_Oset(_1702586), _1702590)))), -(hAPP(c_List_OremoveAll(_1702586, _1702588), _1702590) = _1702590)], (45893 ^ _780205) ^ [_1702642, _1702644, _1702646] : [hBOOL(hAPP(c_List_Odistinct(_1702642), _1702644)), -(c_List_Oremove1(_1702642, _1702646, _1702644) = hAPP(c_List_OremoveAll(_1702642, _1702646), _1702644))], (45899 ^ _780205) ^ [_1702761, _1702763, _1702765] : [hBOOL(hAPP(hAPP(c_member(_1702761), _1702763), hAPP(c_List_Oset(_1702761), _1702765))), -(c_List_Oremdups(_1702761, hAPP(hAPP(c_List_Olist_OCons(_1702761), _1702763), _1702765)) = c_List_Oremdups(_1702761, _1702765))], (45905 ^ _780205) ^ [_1702886, _1702888, _1702890] : [-(hBOOL(hAPP(hAPP(c_member(_1702886), _1702888), hAPP(c_List_Oset(_1702886), _1702890)))), -(c_List_Oremdups(_1702886, hAPP(hAPP(c_List_Olist_OCons(_1702886), _1702888), _1702890)) = hAPP(hAPP(c_List_Olist_OCons(_1702886), _1702888), c_List_Oremdups(_1702886, _1702890)))], (45911 ^ _780205) ^ [_1702960, _1702962] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702960)), c_List_Oremdups(_1702960, _1702962)) = hAPP(c_Finite__Set_Ocard(_1702960), hAPP(c_List_Oset(_1702960), _1702962)))], (45913 ^ _780205) ^ [_1703005, _1703007, _1703009, _1703011, _1703013] : [c_Fun_Oinj__on(_1703005, _1703007, _1703009, c_Orderings_Otop__class_Otop(tc_fun(_1703005, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1703005, _1703007), _1703009), hAPP(c_List_OremoveAll(_1703005, _1703011), _1703013)) = hAPP(c_List_OremoveAll(_1703007, hAPP(_1703009, _1703011)), hAPP(hAPP(c_List_Omap(_1703005, _1703007), _1703009), _1703013)))], (45919 ^ _780205) ^ [_1703168, _1703170, _1703172] : [-(hAPP(c_List_Oset(_1703168), hAPP(c_List_OremoveAll(_1703168, _1703170), _1703172)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1703168, tc_HOL_Obool)), hAPP(c_List_Oset(_1703168), _1703172)), hAPP(hAPP(c_Set_Oinsert(_1703168), _1703170), c_Orderings_Obot__class_Obot(tc_fun(_1703168, tc_HOL_Obool)))))], (45921 ^ _780205) ^ [_1703235, _1703237] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703235)), c_List_Oremdups(_1703235, c_List_Oconcat(_1703235, _1703237))) = hAPP(c_Finite__Set_Ocard(_1703235), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1703235), tc_fun(_1703235, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1703235)), _1703237)), c_List_Oset(_1703235))))], (45923 ^ _780205) ^ [_1703301, _1703303] : [class_Orderings_Olinorder(_1703301), -(c_List_Olinorder__class_Osorted__list__of__set(_1703301, hAPP(c_List_Oset(_1703301), _1703303)) = c_List_Olinorder__class_Osort__key(_1703301, _1703301, c_COMBI(_1703301), c_List_Oremdups(_1703301, _1703303)))], (45929 ^ _780205) ^ [_1703412, _1703414, _1703416] : [class_Orderings_Olinorder(_1703412), -(c_List_Olinorder__class_Osort__key(_1703414, _1703412, _1703416, c_List_Olist_ONil(_1703414)) = c_List_Olist_ONil(_1703414))], (45935 ^ _780205) ^ [_1703507, _1703509, _1703511] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1703507), tc_List_Olist(_1703507), c_List_Oappend(_1703507), _1703509), _1703511) = hAPP(hAPP(c_List_Oappend(_1703507), _1703509), c_List_Oconcat(_1703507, _1703511)))], (45937 ^ _780205) ^ [_1703559, _1703561] : [-(c_List_Oconcat(_1703559, _1703561) = hAPP(c_List_Ofoldl(tc_List_Olist(_1703559), tc_List_Olist(_1703559), c_List_Oappend(_1703559), c_List_Olist_ONil(_1703559)), _1703561))], (45939 ^ _780205) ^ [_1703603, _1703605, _1703607, _1703609] : [class_Orderings_Olinorder(_1703603), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703605)), c_List_Olinorder__class_Osort__key(_1703605, _1703603, _1703607, _1703609)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703605)), _1703609))], (45945 ^ _780205) ^ [_1703720, _1703722, _1703724, _1703726] : [class_Orderings_Olinorder(_1703720), -(hAPP(c_List_Oset(_1703722), c_List_Olinorder__class_Osort__key(_1703722, _1703720, _1703724, _1703726)) = hAPP(c_List_Oset(_1703722), _1703726))], (45951 ^ _780205) ^ [_1703829, _1703831, _1703833, _1703835] : [class_Orderings_Olinorder(_1703829), 45954 ^ _780205 : [(45955 ^ _780205) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1703831), c_List_Olinorder__class_Osort__key(_1703831, _1703829, _1703833, _1703835))), -(hBOOL(hAPP(c_List_Odistinct(_1703831), _1703835)))], (45961 ^ _780205) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1703831), _1703835)), -(hBOOL(hAPP(c_List_Odistinct(_1703831), c_List_Olinorder__class_Osort__key(_1703831, _1703829, _1703833, _1703835))))]]], (45967 ^ _780205) ^ [_1704085] : [-(c_List_Oconcat(_1704085, c_List_Olist_ONil(tc_List_Olist(_1704085))) = c_List_Olist_ONil(_1704085))], (45969 ^ _780205) ^ [_1704117, _1704119, _1704121] : [-(c_List_Oconcat(_1704117, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704117)), _1704119), _1704121)) = hAPP(hAPP(c_List_Oappend(_1704117), _1704119), c_List_Oconcat(_1704117, _1704121)))], (45981 ^ _780205) ^ [_1704389, _1704391] : [45983 ^ _780205 : [(45984 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704389)), 45982 ^ [_1704389, _1704391]), hAPP(c_List_Oset(tc_List_Olist(_1704389)), _1704391))))], (45986 ^ _780205) ^ [] : [45982 ^ [_1704389, _1704391] = c_List_Olist_ONil(_1704389)]], -(c_List_Oconcat(_1704389, _1704391) = c_List_Olist_ONil(_1704389))], (45971 ^ _780205) ^ [_1704183, _1704185] : [c_List_Oconcat(_1704183, _1704185) = c_List_Olist_ONil(_1704183), 45974 ^ _780205 : [(45975 ^ _780205) ^ [_1704274] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704183)), _1704274), hAPP(c_List_Oset(tc_List_Olist(_1704183)), _1704185))), -(_1704274 = c_List_Olist_ONil(_1704183))]]], (46000 ^ _780205) ^ [_1704801, _1704803] : [46002 ^ _780205 : [(46003 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704801)), 46001 ^ [_1704801, _1704803]), hAPP(c_List_Oset(tc_List_Olist(_1704801)), _1704803))))], (46005 ^ _780205) ^ [] : [46001 ^ [_1704801, _1704803] = c_List_Olist_ONil(_1704801)]], -(c_List_Olist_ONil(_1704801) = c_List_Oconcat(_1704801, _1704803))], (45990 ^ _780205) ^ [_1704595, _1704597] : [c_List_Olist_ONil(_1704595) = c_List_Oconcat(_1704595, _1704597), 45993 ^ _780205 : [(45994 ^ _780205) ^ [_1704686] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704595)), _1704686), hAPP(c_List_Oset(tc_List_Olist(_1704595)), _1704597))), -(_1704686 = c_List_Olist_ONil(_1704595))]]], (46009 ^ _780205) ^ [_1704992, _1704994, _1704996, _1704998] : [-(hAPP(hAPP(c_List_Omap(_1704992, _1704994), _1704996), c_List_Oconcat(_1704992, _1704998)) = c_List_Oconcat(_1704994, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704992), tc_List_Olist(_1704994)), hAPP(c_List_Omap(_1704992, _1704994), _1704996)), _1704998)))], (46011 ^ _780205) ^ [_1705055, _1705057] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705055)), c_List_Oconcat(_1705055, _1705057)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1705055), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1705055))), _1705057)))], (46013 ^ _780205) ^ [_1705108, _1705110] : [-(hAPP(c_List_Oset(_1705108), c_List_Oconcat(_1705108, _1705110)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1705108), tc_fun(_1705108, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1705108)), _1705110)), c_List_Oset(_1705108)))], (46015 ^ _780205) ^ [_1705164, _1705166, _1705168, _1705170, _1705172] : [class_Orderings_Olinorder(_1705164), -(c_List_Olinorder__class_Osort__key(_1705166, _1705164, _1705168, hAPP(hAPP(c_List_Olist_OCons(_1705166), _1705170), _1705172)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705166, _1705164, _1705168), _1705170), c_List_Olinorder__class_Osort__key(_1705166, _1705164, _1705168, _1705172)))], (46021 ^ _780205) ^ [_1705301, _1705303, _1705305] : [-(c_List_Oconcat(_1705301, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1705301)), _1705303), _1705305)) = hAPP(hAPP(c_List_Oappend(_1705301), c_List_Oconcat(_1705301, _1705303)), c_List_Oconcat(_1705301, _1705305)))], (46023 ^ _780205) ^ [_1705355, _1705357] : [class_Orderings_Olinorder(_1705355), -(c_List_Olinorder__class_Osort__key(_1705355, _1705355, c_COMBI(_1705355), _1705357) = hAPP(c_List_Ofoldl(tc_List_Olist(_1705355), _1705355, hAPP(c_COMBC(_1705355, tc_List_Olist(_1705355), tc_List_Olist(_1705355)), c_List_Olinorder__class_Oinsort__key(_1705355, _1705355, c_COMBI(_1705355))), c_List_Olist_ONil(_1705355)), _1705357))], (46029 ^ _780205) ^ [_1705502, _1705504, _1705506] : [46031 ^ _780205 : [(46032 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1705502), tc_List_Olist(_1705502))), 46030 ^ [_1705502, _1705504, _1705506]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1705502), tc_List_Olist(_1705502))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1705502), tc_List_Olist(_1705502)), _1705504), _1705506)))))], (46034 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1705502), tc_List_Olist(_1705502), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1705502), tc_fun(tc_List_Olist(_1705502), tc_Nat_Onat), tc_fun(tc_List_Olist(_1705502), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1705502), tc_Nat_Onat), tc_fun(tc_List_Olist(_1705502), tc_HOL_Obool)), tc_List_Olist(_1705502)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1705502))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1705502)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1705502))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1705502)))), 46030 ^ [_1705502, _1705504, _1705506]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705502))), _1705504) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705502))), _1705506), 46039 ^ _780205 : [(46040 ^ _780205) ^ [] : [c_List_Oconcat(_1705502, _1705504) = c_List_Oconcat(_1705502, _1705506), -(_1705504 = _1705506)], (46046 ^ _780205) ^ [] : [_1705504 = _1705506, -(c_List_Oconcat(_1705502, _1705504) = c_List_Oconcat(_1705502, _1705506))]]], (46052 ^ _780205) ^ [_1706229, _1706231, _1706233] : [c_List_Oconcat(_1706229, _1706231) = c_List_Oconcat(_1706229, _1706233), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1706229))), _1706231) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1706229))), _1706233), 46062 ^ _780205 : [(46063 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1706229), tc_List_Olist(_1706229))), 46061 ^ [_1706229, _1706231, _1706233]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1706229), tc_List_Olist(_1706229))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1706229), tc_List_Olist(_1706229)), _1706231), _1706233)))))], (46065 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1706229), tc_List_Olist(_1706229), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1706229), tc_fun(tc_List_Olist(_1706229), tc_Nat_Onat), tc_fun(tc_List_Olist(_1706229), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1706229), tc_Nat_Onat), tc_fun(tc_List_Olist(_1706229), tc_HOL_Obool)), tc_List_Olist(_1706229)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1706229))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1706229)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1706229))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1706229)))), 46061 ^ [_1706229, _1706231, _1706233]))]], -(_1706231 = _1706233)], (46069 ^ _780205) ^ [_1706870, _1706872, _1706874, _1706876] : [-(c_List_Oconcat(_1706870, hAPP(hAPP(c_List_Omap(_1706872, tc_List_Olist(_1706870)), hAPP(hAPP(c_COMBC(_1706872, tc_List_Olist(_1706870), tc_List_Olist(_1706870)), hAPP(hAPP(c_COMBB(_1706870, tc_fun(tc_List_Olist(_1706870), tc_List_Olist(_1706870)), _1706872), c_List_Olist_OCons(_1706870)), _1706874)), c_List_Olist_ONil(_1706870))), _1706876)) = hAPP(hAPP(c_List_Omap(_1706872, _1706870), _1706874), _1706876))], (46071 ^ _780205) ^ [_1706957, _1706959, _1706961] : [-(c_Enum_On__lists(_1706957, hAPP(c_Nat_OSuc, _1706959), _1706961) = c_List_Oconcat(tc_List_Olist(_1706957), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1706957), tc_List_Olist(tc_List_Olist(_1706957))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1706957), tc_List_Olist(_1706957), tc_List_Olist(tc_List_Olist(_1706957))), hAPP(hAPP(c_COMBB(tc_fun(_1706957, tc_List_Olist(_1706957)), tc_fun(tc_List_Olist(_1706957), tc_List_Olist(tc_List_Olist(_1706957))), tc_List_Olist(_1706957)), c_List_Omap(_1706957, tc_List_Olist(_1706957))), hAPP(c_COMBC(_1706957, tc_List_Olist(_1706957), tc_List_Olist(_1706957)), c_List_Olist_OCons(_1706957)))), _1706961)), c_Enum_On__lists(_1706957, _1706959, _1706961))))], (46073 ^ _780205) ^ [_1707077, _1707079, _1707081, _1707083] : [-(c_List_Otranspose(_1707077, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1707077)), hAPP(hAPP(c_List_Olist_OCons(_1707077), _1707079), _1707081)), _1707083)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1707077)), hAPP(hAPP(c_List_Olist_OCons(_1707077), _1707079), c_List_Oconcat(_1707077, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707077), tc_List_Olist(_1707077)), c_List_Olist_Olist__case(tc_List_Olist(_1707077), _1707077, c_List_Olist_ONil(_1707077), hAPP(hAPP(c_COMBB(tc_List_Olist(_1707077), tc_fun(tc_List_Olist(_1707077), tc_List_Olist(_1707077)), _1707077), c_COMBK(tc_List_Olist(_1707077), tc_List_Olist(_1707077))), hAPP(hAPP(c_COMBC(_1707077, tc_List_Olist(_1707077), tc_List_Olist(_1707077)), c_List_Olist_OCons(_1707077)), c_List_Olist_ONil(_1707077))))), _1707083)))), c_List_Otranspose(_1707077, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1707077)), _1707081), c_List_Oconcat(tc_List_Olist(_1707077), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707077), tc_List_Olist(tc_List_Olist(_1707077))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1707077)), _1707077, c_List_Olist_ONil(tc_List_Olist(_1707077)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1707077), tc_List_Olist(tc_List_Olist(_1707077))), _1707077), hAPP(hAPP(c_COMBC(tc_List_Olist(_1707077), tc_List_Olist(tc_List_Olist(_1707077)), tc_List_Olist(tc_List_Olist(_1707077))), c_List_Olist_OCons(tc_List_Olist(_1707077))), c_List_Olist_ONil(tc_List_Olist(_1707077)))))), _1707083))))))], (46075 ^ _780205) ^ [_1707303, _1707305] : [-(c_List_Oconcat(_1707303, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707303), tc_List_Olist(_1707303)), c_List_Olist_Olist__case(tc_List_Olist(_1707303), _1707303, c_List_Olist_ONil(_1707303), hAPP(hAPP(c_COMBB(tc_List_Olist(_1707303), tc_fun(tc_List_Olist(_1707303), tc_List_Olist(_1707303)), _1707303), c_COMBK(tc_List_Olist(_1707303), tc_List_Olist(_1707303))), hAPP(hAPP(c_COMBC(_1707303, tc_List_Olist(_1707303), tc_List_Olist(_1707303)), c_List_Olist_OCons(_1707303)), c_List_Olist_ONil(_1707303))))), _1707305)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707303), _1707303), c_List_Ohd(_1707303)), hAPP(c_List_Ofilter(tc_List_Olist(_1707303), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1707303)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1707303), tc_List_Olist(_1707303), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1707303)))), _1707305)))], (46077 ^ _780205) ^ [_1707446, _1707448, _1707450] : [-(hAPP(c_List_Ofilter(_1707446, _1707448), c_List_Oconcat(_1707446, _1707450)) = c_List_Oconcat(_1707446, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707446), tc_List_Olist(_1707446)), c_List_Ofilter(_1707446, _1707448)), _1707450)))], (46079 ^ _780205) ^ [_1707501, _1707503, _1707505, _1707507, _1707509] : [class_Orderings_Olinorder(_1707501), -(hAPP(c_List_Ofilter(_1707503, _1707505), c_List_Olinorder__class_Osort__key(_1707503, _1707501, _1707507, _1707509)) = c_List_Olinorder__class_Osort__key(_1707503, _1707501, _1707507, hAPP(c_List_Ofilter(_1707503, _1707505), _1707509)))], (46085 ^ _780205) ^ [_1707626, _1707628, _1707630] : [hBOOL(hAPP(c_List_Odistinct(_1707626), _1707628)), -(hBOOL(hAPP(c_List_Odistinct(_1707626), hAPP(c_List_Ofilter(_1707626, _1707630), _1707628))))], (46091 ^ _780205) ^ [_1707733, _1707735, _1707737] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1707733, tc_HOL_Obool)), hAPP(c_List_Oset(_1707733), hAPP(c_List_Ofilter(_1707733, _1707735), _1707737))), hAPP(c_List_Oset(_1707733), _1707737))))], (46103 ^ _780205) ^ [_1708004, _1708006, _1708008] : [46105 ^ _780205 : [(46106 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1708004), 46104 ^ [_1708004, _1708006, _1708008]), hAPP(c_List_Oset(_1708004), _1708008))))], (46108 ^ _780205) ^ [] : [hBOOL(hAPP(_1708006, 46104 ^ [_1708004, _1708006, _1708008]))]], -(hAPP(c_List_Ofilter(_1708004, _1708006), _1708008) = _1708008)], (46093 ^ _780205) ^ [_1707804, _1707806, _1707808] : [hAPP(c_List_Ofilter(_1707804, _1707806), _1707808) = _1707808, 46096 ^ _780205 : [(46097 ^ _780205) ^ [_1707895] : [hBOOL(hAPP(hAPP(c_member(_1707804), _1707895), hAPP(c_List_Oset(_1707804), _1707808))), -(hBOOL(hAPP(_1707806, _1707895)))]]], (46112 ^ _780205) ^ [_1708196, _1708198, _1708200] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708196)), hAPP(c_List_Ofilter(_1708196, _1708198), _1708200))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708196)), hAPP(c_List_Ofilter(_1708196, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1708196), c_fNot), _1708198)), _1708200))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708196)), _1708200))], (46114 ^ _780205) ^ [_1708272, _1708274, _1708276] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708272)), hAPP(c_List_Ofilter(_1708272, _1708274), _1708276))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708272)), _1708276))))], (46116 ^ _780205) ^ [_1708324, _1708326, _1708328, _1708330] : [-(hAPP(c_List_Ofilter(_1708324, _1708326), hAPP(c_List_Ofilter(_1708324, _1708328), _1708330)) = hAPP(c_List_Ofilter(_1708324, hAPP(hAPP(c_COMBS(_1708324, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1708324), c_fconj), _1708328)), _1708326)), _1708330))], (46118 ^ _780205) ^ [_1708391, _1708393, _1708395, _1708397] : [-(hAPP(c_List_Ofilter(_1708391, _1708393), c_List_Oremove1(_1708391, _1708395, _1708397)) = c_List_Oremove1(_1708391, _1708395, hAPP(c_List_Ofilter(_1708391, _1708393), _1708397)))], (46120 ^ _780205) ^ [_1708436, _1708438, _1708440, _1708442] : [-(hBOOL(hAPP(_1708436, _1708438))), -(c_List_Oremove1(_1708440, _1708438, hAPP(c_List_Ofilter(_1708440, _1708436), _1708442)) = hAPP(c_List_Ofilter(_1708440, _1708436), _1708442))], (46126 ^ _780205) ^ [_1708494, _1708496, _1708498, _1708500, _1708502, _1708504] : [class_Orderings_Olinorder(_1708494), -(hBOOL(hAPP(_1708496, _1708498))), -(hAPP(c_List_Ofilter(_1708500, _1708496), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1708500, _1708494, _1708502), _1708498), _1708504)) = hAPP(c_List_Ofilter(_1708500, _1708496), _1708504))], (46136 ^ _780205) ^ [_1708640, _1708642, _1708644] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1708640), tc_List_Olist(_1708640)), c_List_Opartition(_1708640, _1708642, _1708644)) = hAPP(c_List_Ofilter(_1708640, _1708642), _1708644))], (46138 ^ _780205) ^ [_1708687, _1708689, _1708691, _1708693, _1708695] : [-(hAPP(c_List_Ofilter(_1708687, _1708689), hAPP(hAPP(c_List_Omap(_1708691, _1708687), _1708693), _1708695)) = hAPP(hAPP(c_List_Omap(_1708691, _1708687), _1708693), hAPP(c_List_Ofilter(_1708691, hAPP(c_Fun_Ocomp(_1708687, tc_HOL_Obool, _1708691, _1708689), _1708693)), _1708695)))], (46140 ^ _780205) ^ [_1708756, _1708758] : [-(hAPP(c_List_Ofilter(_1708756, _1708758), c_List_Olist_ONil(_1708756)) = c_List_Olist_ONil(_1708756))], (46142 ^ _780205) ^ [_1708791] : [-(c_List_Otranspose(_1708791, c_List_Olist_ONil(tc_List_Olist(_1708791))) = c_List_Olist_ONil(tc_List_Olist(_1708791)))], (46144 ^ _780205) ^ [_1708840, _1708842, _1708844, _1708846] : [hBOOL(hAPP(_1708840, _1708842)), -(hAPP(c_List_Ofilter(_1708844, _1708840), hAPP(hAPP(c_List_Olist_OCons(_1708844), _1708842), _1708846)) = hAPP(hAPP(c_List_Olist_OCons(_1708844), _1708842), hAPP(c_List_Ofilter(_1708844, _1708840), _1708846)))], (46150 ^ _780205) ^ [_1708975, _1708977, _1708979, _1708981] : [-(hBOOL(hAPP(_1708975, _1708977))), -(hAPP(c_List_Ofilter(_1708979, _1708975), hAPP(hAPP(c_List_Olist_OCons(_1708979), _1708977), _1708981)) = hAPP(c_List_Ofilter(_1708979, _1708975), _1708981))], (46156 ^ _780205) ^ [_1709039, _1709041, _1709043, _1709045] : [-(hAPP(c_List_Ofilter(_1709039, _1709041), hAPP(hAPP(c_List_Oappend(_1709039), _1709043), _1709045)) = hAPP(hAPP(c_List_Oappend(_1709039), hAPP(c_List_Ofilter(_1709039, _1709041), _1709043)), hAPP(c_List_Ofilter(_1709039, _1709041), _1709045)))], (46168 ^ _780205) ^ [_1709325, _1709327, _1709329] : [46170 ^ _780205 : [(46171 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709325), 46169 ^ [_1709325, _1709327, _1709329]), hAPP(c_List_Oset(_1709325), _1709329))))], (46173 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1709327, 46169 ^ [_1709325, _1709327, _1709329])))]], -(hAPP(c_List_Ofilter(_1709325, _1709327), _1709329) = c_List_Olist_ONil(_1709325))], (46158 ^ _780205) ^ [_1709120, _1709122, _1709124] : [hAPP(c_List_Ofilter(_1709120, _1709122), _1709124) = c_List_Olist_ONil(_1709120), 46161 ^ _780205 : [(46162 ^ _780205) ^ [_1709217] : [hBOOL(hAPP(hAPP(c_member(_1709120), _1709217), hAPP(c_List_Oset(_1709120), _1709124))), hBOOL(hAPP(_1709122, _1709217))]]], (46177 ^ _780205) ^ [_1709442, _1709444] : [-(c_List_OremoveAll(_1709442, _1709444) = c_List_Ofilter(_1709442, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1709442), c_fNot), hAPP(c_fequal, _1709444))))], (46179 ^ _780205) ^ [_1709486, _1709488, _1709490] : [-(c_List_Oremdups(_1709486, hAPP(c_List_Ofilter(_1709486, _1709488), _1709490)) = hAPP(c_List_Ofilter(_1709486, _1709488), c_List_Oremdups(_1709486, _1709490)))], (46181 ^ _780205) ^ [_1709527, _1709529, _1709531, _1709533] : [-(hBOOL(hAPP(_1709527, _1709529))), -(hAPP(c_List_OremoveAll(_1709531, _1709529), hAPP(c_List_Ofilter(_1709531, _1709527), _1709533)) = hAPP(c_List_Ofilter(_1709531, _1709527), _1709533))], (46187 ^ _780205) ^ [_1709587, _1709589, _1709591] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1709587), tc_List_Olist(_1709587)), c_List_Opartition(_1709587, _1709589, _1709591)) = hAPP(c_List_Ofilter(_1709587, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1709587, c_fNot), _1709589)), _1709591))], (46189 ^ _780205) ^ [_1709642, _1709644] : [-(c_List_Otranspose(_1709642, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1709642)), c_List_Olist_ONil(_1709642)), _1709644)) = c_List_Otranspose(_1709642, _1709644))], (46191 ^ _780205) ^ [_1709685, _1709687, _1709689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709685), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1709687))), c_List_Otranspose(_1709687, _1709689)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1709687)), c_List_Otranspose(_1709687, _1709689)), _1709685) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1709687), _1709687), hAPP(hAPP(c_COMBC(tc_List_Olist(_1709687), tc_Nat_Onat, _1709687), c_List_Onth(_1709687)), _1709685)), hAPP(c_List_Ofilter(tc_List_Olist(_1709687), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1709687)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709685)), c_Nat_Osize__class_Osize(tc_List_Olist(_1709687)))), _1709689)))], (46197 ^ _780205) ^ [_1709928, _1709930, _1709932, _1709934] : [-(c_List_Otranspose(_1709928, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1709930), tc_List_Olist(_1709928)), hAPP(c_List_Omap(_1709930, _1709928), _1709932)), _1709934)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1709930), tc_List_Olist(_1709928)), hAPP(c_List_Omap(_1709930, _1709928), _1709932)), c_List_Otranspose(_1709930, _1709934)))], (46199 ^ _780205) ^ [_1710001, _1710003, _1710005] : [-(hAPP(c_List_Oset(_1710001), hAPP(c_List_Ofilter(_1710001, _1710003), _1710005)) = hAPP(c_Set_OCollect(_1710001), hAPP(hAPP(c_COMBS(_1710001, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1710001), c_fconj), hAPP(hAPP(c_COMBC(_1710001, tc_fun(_1710001, tc_HOL_Obool), tc_HOL_Obool), c_member(_1710001)), hAPP(c_List_Oset(_1710001), _1710005)))), _1710003)))], (46201 ^ _780205) ^ [_1710084, _1710086, _1710088, _1710090, _1710092] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710084)), hAPP(c_List_Ofilter(_1710084, _1710086), hAPP(hAPP(c_List_Omap(_1710088, _1710084), _1710090), _1710092))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710088)), hAPP(c_List_Ofilter(_1710088, hAPP(c_Fun_Ocomp(_1710084, tc_HOL_Obool, _1710088, _1710086), _1710090)), _1710092)))], (46203 ^ _780205) ^ [_1710158, _1710160, _1710162, _1710164] : [hBOOL(hAPP(hAPP(c_member(_1710158), _1710160), hAPP(c_List_Oset(_1710158), _1710162))), -(hBOOL(hAPP(_1710164, _1710160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710158)), hAPP(c_List_Ofilter(_1710158, _1710164), _1710162))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710158)), _1710162))))], (46213 ^ _780205) ^ [_1710332, _1710334, _1710336] : [-(c_List_Opartition(_1710332, _1710334, _1710336) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710332), tc_List_Olist(_1710332)), hAPP(c_List_Ofilter(_1710332, _1710334), _1710336)), hAPP(c_List_Ofilter(_1710332, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1710332, c_fNot), _1710334)), _1710336)))], (46215 ^ _780205) ^ [_1710396, _1710398, _1710400] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1710396, tc_HOL_Obool)), hAPP(c_List_Oset(_1710396), _1710398)), hAPP(hAPP(c_Set_Oinsert(_1710396), _1710400), c_Orderings_Obot__class_Obot(tc_fun(_1710396, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1710396), hAPP(c_List_Ofilter(_1710396, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1710396), c_fNot), hAPP(hAPP(c_COMBC(_1710396, _1710396, tc_HOL_Obool), c_fequal), _1710400))), _1710398)))], (46217 ^ _780205) ^ [_1710483, _1710485, _1710487] : [hBOOL(hAPP(c_List_Odistinct(_1710483), _1710485)), -(hAPP(c_List_Ofilter(_1710483, hAPP(hAPP(c_COMBC(_1710483, tc_fun(_1710483, tc_HOL_Obool), tc_HOL_Obool), c_member(_1710483)), hAPP(c_List_Oset(_1710483), c_List_Osublist(_1710483, _1710485, _1710487)))), _1710485) = c_List_Osublist(_1710483, _1710485, _1710487))], (46233 ^ _780205) ^ [_1710863, _1710865] : [46235 ^ _780205 : [(46236 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710863)), 46234 ^ [_1710863, _1710865]), hAPP(c_List_Oset(tc_List_Olist(_1710863)), _1710865))))], (46238 ^ _780205) ^ [] : [46234 ^ [_1710863, _1710865] = c_List_Olist_ONil(_1710863)]], -(c_List_Otranspose(_1710863, _1710865) = c_List_Olist_ONil(tc_List_Olist(_1710863)))], (46223 ^ _780205) ^ [_1710653, _1710655] : [c_List_Otranspose(_1710653, _1710655) = c_List_Olist_ONil(tc_List_Olist(_1710653)), 46226 ^ _780205 : [(46227 ^ _780205) ^ [_1710748] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1710653)), _1710748), hAPP(c_List_Oset(tc_List_Olist(_1710653)), _1710655))), -(_1710748 = c_List_Olist_ONil(_1710653))]]], (46242 ^ _780205) ^ [_1711058, _1711060, _1711062] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711058)), hAPP(c_List_Ofilter(_1711058, _1711060), _1711062)) = 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(_1711058)), _1711062)))), hAPP(hAPP(c_COMBB(_1711058, tc_HOL_Obool, tc_Nat_Onat), _1711060), hAPP(c_List_Onth(_1711058), _1711062))))))], (46244 ^ _780205) ^ [_1711138, _1711140] : [-(c_List_Oconcat(tc_List_Olist(_1711138), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1711138), tc_List_Olist(tc_List_Olist(_1711138))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1711138)), _1711138, c_List_Olist_ONil(tc_List_Olist(_1711138)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1711138), tc_List_Olist(tc_List_Olist(_1711138))), _1711138), hAPP(hAPP(c_COMBC(tc_List_Olist(_1711138), tc_List_Olist(tc_List_Olist(_1711138)), tc_List_Olist(tc_List_Olist(_1711138))), c_List_Olist_OCons(tc_List_Olist(_1711138))), c_List_Olist_ONil(tc_List_Olist(_1711138)))))), _1711140)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1711138), tc_List_Olist(_1711138)), c_List_Otl(_1711138)), hAPP(c_List_Ofilter(tc_List_Olist(_1711138), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1711138)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1711138), tc_List_Olist(_1711138), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1711138)))), _1711140)))], (46246 ^ _780205) ^ [_1711290, _1711292, _1711294, _1711296] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1711290)), c_List_Otranspose__rel(_1711290)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1711290)), hAPP(hAPP(c_List_Olist_OCons(_1711290), _1711292), _1711294)), _1711296))), -(c_List_Otranspose(_1711290, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1711290)), hAPP(hAPP(c_List_Olist_OCons(_1711290), _1711292), _1711294)), _1711296)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1711290)), hAPP(hAPP(c_List_Olist_OCons(_1711290), _1711292), c_List_Oconcat(_1711290, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1711290), tc_List_Olist(_1711290)), c_List_Olist_Olist__case(tc_List_Olist(_1711290), _1711290, c_List_Olist_ONil(_1711290), hAPP(hAPP(c_COMBB(tc_List_Olist(_1711290), tc_fun(tc_List_Olist(_1711290), tc_List_Olist(_1711290)), _1711290), c_COMBK(tc_List_Olist(_1711290), tc_List_Olist(_1711290))), hAPP(hAPP(c_COMBC(_1711290, tc_List_Olist(_1711290), tc_List_Olist(_1711290)), c_List_Olist_OCons(_1711290)), c_List_Olist_ONil(_1711290))))), _1711296)))), c_List_Otranspose(_1711290, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1711290)), _1711294), c_List_Oconcat(tc_List_Olist(_1711290), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1711290), tc_List_Olist(tc_List_Olist(_1711290))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1711290)), _1711290, c_List_Olist_ONil(tc_List_Olist(_1711290)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1711290), tc_List_Olist(tc_List_Olist(_1711290))), _1711290), hAPP(hAPP(c_COMBC(tc_List_Olist(_1711290), tc_List_Olist(tc_List_Olist(_1711290)), tc_List_Olist(tc_List_Olist(_1711290))), c_List_Olist_OCons(tc_List_Olist(_1711290))), c_List_Olist_ONil(tc_List_Olist(_1711290)))))), _1711296))))))], (46252 ^ _780205) ^ [_1711823, _1711825] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1711823)), c_List_Otranspose__rel(_1711823)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1711823)), c_List_Olist_ONil(_1711823)), _1711825))), -(c_List_Otranspose(_1711823, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1711823)), c_List_Olist_ONil(_1711823)), _1711825)) = c_List_Otranspose(_1711823, _1711825))], (46258 ^ _780205) ^ [_1711982, _1711984, _1711986, _1711988] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1711982, tc_Nat_Onat), _1711982), c_Product__Type_Ofst(_1711982, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1711982, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1711982, tc_Nat_Onat)), _1711984), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1711982, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1711982, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1711982, tc_Nat_Onat), _1711986), _1711988))) = hAPP(hAPP(c_List_Omap(tc_prod(_1711982, tc_Nat_Onat), _1711982), c_Product__Type_Ofst(_1711982, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1711982, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1711982, tc_Nat_Onat)), _1711984), c_Product__Type_Osnd(_1711982, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1711982, tc_Nat_Onat), _1711986), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1711988)))))], (46260 ^ _780205) ^ [_1712125, _1712127] : [-(c_Random_Oselect__weight(_1712125, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1712125), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1712125, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1712125, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1712125)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1712127)) = c_Random_Oselect__weight(_1712125, _1712127))], (46262 ^ _780205) ^ [_1712188, _1712190] : [-(c_Random_Opick(_1712188, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1712188), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1712188, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1712188, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1712188)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1712190)) = c_Random_Opick(_1712188, _1712190))], (46264 ^ _780205) ^ [_1712251] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1712251)), c_List_Otranspose__rel(_1712251)), c_List_Olist_ONil(tc_List_Olist(_1712251)))), -(c_List_Otranspose(_1712251, c_List_Olist_ONil(tc_List_Olist(_1712251))) = c_List_Olist_ONil(tc_List_Olist(_1712251)))], (46270 ^ _780205) ^ [_1712378, _1712380] : [-(c_List_Ofoldr(tc_List_Olist(_1712378), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1712378)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1712378))), c_List_Otranspose(_1712378, _1712380), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1712378))), hAPP(c_List_Ofilter(tc_List_Olist(_1712378), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1712378)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1712378), tc_List_Olist(_1712378), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1712378)))), _1712380)))], (46272 ^ _780205) ^ [_1712475, _1712477, _1712479, _1712481] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712475)), _1712477))), c_List_Ofoldr(tc_List_Olist(_1712479), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1712479)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1712479))), _1712481, 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(_1712475)), _1712477)), c_List_Ofoldr(tc_List_Olist(_1712479), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1712479)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1712479), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1712479)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1712479)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1712479), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1712479)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1712479), tc_List_Olist(_1712479), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1712479)))), _1712481), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (46274 ^ _780205) ^ [_1712644, _1712646, _1712648, _1712650] : [-(c_List_Ofoldr(_1712644, _1712646, _1712648, c_List_Olist_ONil(_1712644), _1712650) = _1712650)], (46276 ^ _780205) ^ [_1712681, _1712683, _1712685, _1712687, _1712689, _1712691] : [-(c_List_Ofoldr(_1712681, _1712683, _1712685, hAPP(hAPP(c_List_Olist_OCons(_1712681), _1712687), _1712689), _1712691) = hAPP(hAPP(_1712685, _1712687), c_List_Ofoldr(_1712681, _1712683, _1712685, _1712689, _1712691)))], (46278 ^ _780205) ^ [_1712740, _1712742, _1712744, _1712746, _1712748, _1712750] : [-(c_List_Ofoldr(_1712740, _1712742, _1712744, hAPP(hAPP(c_List_Oappend(_1712740), _1712746), _1712748), _1712750) = c_List_Ofoldr(_1712740, _1712742, _1712744, _1712746, c_List_Ofoldr(_1712740, _1712742, _1712744, _1712748, _1712750)))], (46280 ^ _780205) ^ [_1712799, _1712801, _1712803] : [class_Groups_Oab__semigroup__add(_1712799), -(c_List_Ofoldr(_1712799, _1712799, c_Groups_Oplus__class_Oplus(_1712799), _1712801, _1712803) = hAPP(c_List_Ofoldl(_1712799, _1712799, c_Groups_Oplus__class_Oplus(_1712799), _1712803), _1712801))], (46286 ^ _780205) ^ [_1712912, _1712914, _1712916, _1712918, _1712920, _1712922, _1712924] : [-(c_List_Ofoldr(_1712912, _1712914, _1712916, hAPP(hAPP(c_List_Omap(_1712918, _1712912), _1712920), _1712922), _1712924) = c_List_Ofoldr(_1712918, _1712914, hAPP(c_Fun_Ocomp(_1712912, tc_fun(_1712914, _1712914), _1712918, _1712916), _1712920), _1712922, _1712924))], (46288 ^ _780205) ^ [_1712979, _1712981] : [class_Groups_Omonoid__add(_1712979), -(hAPP(c_List_Ofoldl(_1712979, _1712979, c_Groups_Oplus__class_Oplus(_1712979), c_Groups_Ozero__class_Ozero(_1712979)), _1712981) = c_List_Ofoldr(_1712979, _1712979, c_Groups_Oplus__class_Oplus(_1712979), _1712981, c_Groups_Ozero__class_Ozero(_1712979)))], (46294 ^ _780205) ^ [_1713098, _1713100, _1713102] : [class_Groups_Omonoid__add(_1713098), -(hAPP(c_List_Ofoldl(_1713098, _1713098, c_Groups_Oplus__class_Oplus(_1713098), _1713100), _1713102) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1713098), _1713100), c_List_Ofoldr(_1713098, _1713098, c_Groups_Oplus__class_Oplus(_1713098), _1713102, c_Groups_Ozero__class_Ozero(_1713098))))], (46300 ^ _780205) ^ [_1713231, _1713233] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1713231))), c_List_Otranspose(_1713231, _1713233)) = c_List_Ofoldr(tc_List_Olist(_1713231), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1713231)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1713231))), _1713233, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46302 ^ _780205) ^ [_1713292, _1713294, _1713296] : [-(c_List_Osublist(_1713292, _1713294, _1713296) = hAPP(hAPP(c_List_Omap(tc_prod(_1713292, tc_Nat_Onat), _1713292), c_Product__Type_Ofst(_1713292, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1713292, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1713292, 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(_1713292, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1713292, tc_Nat_Onat))), _1713296)), hAPP(hAPP(c_List_Ozip(_1713292, tc_Nat_Onat), _1713294), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713292)), _1713294))))))], (46304 ^ _780205) ^ [_1713395, _1713397, _1713399, _1713401] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1713395, tc_Nat_Onat), _1713395), c_Product__Type_Ofst(_1713395, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1713395, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1713395, 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(_1713395, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1713395, tc_Nat_Onat))), _1713397)), hAPP(hAPP(c_List_Ozip(_1713395, tc_Nat_Onat), _1713399), c_List_Oupt(_1713401, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713401), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713395)), _1713399)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1713395, tc_Nat_Onat), _1713395), c_Product__Type_Ofst(_1713395, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1713395, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1713395, 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(_1713395, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1713395, 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(_1713395, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1713395, tc_Nat_Onat))), _1713401))), _1713397)), hAPP(hAPP(c_List_Ozip(_1713395, tc_Nat_Onat), _1713399), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713395)), _1713399))))))], (46306 ^ _780205) ^ [_1713600, _1713602] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1713600), _1713602) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1713600, _1713602)))], (46308 ^ _780205) ^ [_1713637, _1713639] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1713637, _1713639)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1713637), _1713639))], (46310 ^ _780205) ^ [_1713683, _1713685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713683), _1713685)), -(c_List_Oupt(_1713683, hAPP(c_Nat_OSuc, _1713685)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1713683, _1713685)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1713685), c_List_Olist_ONil(tc_Nat_Onat))))], (46316 ^ _780205) ^ [_1713806, _1713808] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713806), _1713808))), -(c_List_Oupt(_1713806, hAPP(c_Nat_OSuc, _1713808)) = c_List_Olist_ONil(tc_Nat_Onat))], (46322 ^ _780205) ^ [_1713855, _1713857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713855), _1713857)), -(c_List_Oupt(_1713855, hAPP(c_Nat_OSuc, _1713857)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1713855, _1713857)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1713857), c_List_Olist_ONil(tc_Nat_Onat))))], (46328 ^ _780205) ^ [_1713984, _1713986, _1713988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713984), _1713986)), -(c_List_Oupt(_1713984, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713986), _1713988)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1713984, _1713986)), c_List_Oupt(_1713986, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713986), _1713988))))], (46334 ^ _780205) ^ [_1714136, _1714138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714136), _1714138)), -(c_List_Oupt(_1714136, _1714138) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1714136), c_List_Oupt(hAPP(c_Nat_OSuc, _1714136), _1714138)))], (46340 ^ _780205) ^ [_1714247, _1714249] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714247), _1714249))), -(c_List_Oupt(_1714247, _1714249) = c_List_Olist_ONil(tc_Nat_Onat))], (46346 ^ _780205) ^ [_1714293, _1714295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714293), _1714295)), -(c_List_Oupt(_1714293, _1714295) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1714293), c_List_Oupt(hAPP(c_Nat_OSuc, _1714293), _1714295)))], (46352 ^ _780205) ^ [_1714410, _1714412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1714410), _1714412)), -(c_List_Oupt(_1714412, _1714410) = c_List_Olist_ONil(tc_Nat_Onat))], (46368 ^ _780205) ^ [_1714620, _1714622] : [46369 ^ _780205 : [(46370 ^ _780205) ^ [] : [_1714622 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46372 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1714622), _1714620))]], -(c_List_Oupt(_1714620, _1714622) = c_List_Olist_ONil(tc_Nat_Onat))], (46358 ^ _780205) ^ [_1714518, _1714520] : [c_List_Oupt(_1714518, _1714520) = c_List_Olist_ONil(tc_Nat_Onat), -(_1714520 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1714520), _1714518)))], (46376 ^ _780205) ^ [_1714753] : [-(c_List_Oupt(_1714753, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (46378 ^ _780205) ^ [_1714779, _1714781, _1714783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1714779), _1714781)), _1714783)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1714781), c_List_Oupt(_1714779, _1714783)) = c_List_Oupt(_1714779, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1714779), _1714781)))], (46384 ^ _780205) ^ [_1714916, _1714918] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1714916), _1714918)) = c_List_Oupt(_1714916, _1714918))], (46386 ^ _780205) ^ [_1714953, _1714955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714953), _1714955)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1714953, _1714955)) = _1714953)], (46392 ^ _780205) ^ [_1715052, _1715054, _1715056] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1715052), c_List_Oupt(_1715054, _1715056)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1715054), _1715052), _1715056))], (46394 ^ _780205) ^ [_1715097, _1715099] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1715097, _1715099))))], (46396 ^ _780205) ^ [_1715127, _1715129] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1715127, _1715129)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1715129), _1715127))], (46398 ^ _780205) ^ [_1715173, _1715175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715173)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715175))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715173), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715175)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715173)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715173)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715175))))], (46404 ^ _780205) ^ [_1715326, _1715328] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715326)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715328)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715326), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1715328)) = c_List_Olist_ONil(tc_Nat_Onat))], (46410 ^ _780205) ^ [_1715405, _1715407, _1715409, _1715411] : [c_List_Oupt(_1715405, _1715407) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1715409), _1715411), 46413 ^ _780205 : [(46414 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715405), _1715407)))], (46416 ^ _780205) ^ [] : [-(_1715405 = _1715409)], (46418 ^ _780205) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1715405), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1715407) = _1715411)]]], (46420 ^ _780205) ^ [_1715578, _1715580, _1715582, _1715584] : [-(c_List_Oupt(_1715578, _1715580) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1715582), _1715584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715578), _1715580)), _1715578 = _1715582, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1715578), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1715580) = _1715584], (46434 ^ _780205) ^ [_1715819, _1715821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715819), _1715821)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1715819, _1715821)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1715821), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (46440 ^ _780205) ^ [_1715930, _1715932] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1715930, _1715932)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1715930), hAPP(c_Nat_OSuc, _1715932)))], (46442 ^ _780205) ^ [_1715970, _1715972] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1715970, _1715972) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1715970, hAPP(c_Nat_OSuc, _1715972))))], (46444 ^ _780205) ^ [_1716008] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1716008) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1716008)))], (46446 ^ _780205) ^ [_1716040, _1716042, _1716044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1716040), _1716042)), _1716044)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1716040, _1716044)), _1716042) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1716040), _1716042))], (46452 ^ _780205) ^ [_1716171, _1716173] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1716171, _1716173) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1716171), hAPP(c_Nat_OSuc, _1716173))))], (46454 ^ _780205) ^ [_1716212, _1716214] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1716212, _1716214) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1716212), _1716214)))], (46456 ^ _780205) ^ [_1716250] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1716250) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1716250))))], (46458 ^ _780205) ^ [_1716285, _1716287] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1716285), hAPP(c_List_Onth(_1716285), _1716287)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716285)), _1716287))) = _1716287)], (46460 ^ _780205) ^ [_1716334, _1716336, _1716338, _1716340] : [class_Groups_Ocomm__monoid__add(_1716334), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1716334), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1716334), _1716336), c_List_Oupt(_1716338, _1716340))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1716334), _1716336), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1716338, _1716340))))], (46466 ^ _780205) ^ [_1716477, _1716479, _1716481, _1716483] : [class_Groups_Ocomm__monoid__add(_1716477), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1716477), _1716479), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1716481, _1716483))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1716477), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1716477), _1716479), c_List_Oupt(_1716481, _1716483))))], (46472 ^ _780205) ^ [_1716620, _1716622, _1716624, _1716626, _1716628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1716620), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1716622), _1716624))), -(hAPP(hAPP(c_List_Onth(_1716626), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1716626), _1716628), c_List_Oupt(_1716624, _1716622))), _1716620) = hAPP(_1716628, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1716624), _1716620)))], (46478 ^ _780205) ^ [_1716783, _1716785, _1716787] : [46479 ^ _780205 : [(46480 ^ _780205) ^ [] : [-(_1716783 = c_List_Olist_ONil(tc_List_Olist(_1716785)))], (46482 ^ _780205) ^ [] : [_1716787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 46486 ^ _780205 : [(46487 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46485 ^ [_1716783, _1716785, _1716787]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1716785))), _1716783))))], (46489 ^ _780205) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716785)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1716785)), _1716783), 46485 ^ [_1716783, _1716785, _1716787])) = _1716787]], -(c_List_Otranspose(_1716785, _1716783) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1716785)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1716785)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1716785), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1716785)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1716785)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1716785), hAPP(hAPP(c_COMBB(tc_List_Olist(_1716785), tc_fun(tc_Nat_Onat, _1716785), tc_Nat_Onat), c_List_Onth(_1716785)), hAPP(c_List_Onth(tc_List_Olist(_1716785)), _1716783))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1716785))), _1716783)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1716787)))], (46493 ^ _780205) ^ [_1717293, _1717295, _1717297, _1717299, _1717301] : [class_Orderings_Olinorder(_1717293), hBOOL(hAPP(hAPP(c_member(_1717295), _1717297), hAPP(c_List_Oset(_1717295), _1717299))), c_List_Olinorder__class_Osorted(_1717293, hAPP(hAPP(c_List_Omap(_1717295, _1717293), _1717301), _1717299)), hAPP(c_List_Ohd(_1717295), hAPP(c_List_Ofilter(_1717295, hAPP(hAPP(c_COMBB(_1717293, tc_HOL_Obool, _1717295), hAPP(c_fequal, hAPP(_1717301, _1717297))), _1717301)), _1717299)) = _1717297, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1717295, _1717293, _1717301), _1717297), c_List_Oremove1(_1717295, _1717297, _1717299)) = _1717299)], (46511 ^ _780205) ^ [_1717672] : [class_Orderings_Olinorder(_1717672), -(c_List_Olinorder__class_Osorted(_1717672, c_List_Olist_ONil(_1717672)))], (46517 ^ _780205) ^ [_1717749, _1717751] : [class_Orderings_Olinorder(_1717749), -(c_List_Olinorder__class_Osorted(_1717749, hAPP(hAPP(c_List_Olist_OCons(_1717749), _1717751), c_List_Olist_ONil(_1717749))))], (46523 ^ _780205) ^ [_1717844, _1717846] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1717844, _1717846)))], (46525 ^ _780205) ^ [_1717872, _1717874] : [class_Orderings_Olinorder(_1717872), -(c_List_Olinorder__class_Osorted(_1717872, c_List_Olinorder__class_Osort__key(_1717872, _1717872, c_COMBI(_1717872), _1717874)))], (46531 ^ _780205) ^ [_1717961, _1717963, _1717965] : [class_Orderings_Olinorder(_1717961), c_List_Olinorder__class_Osorted(_1717961, _1717963), -(c_List_Olinorder__class_Osorted(_1717961, c_List_Olinorder__class_Oinsort__insert__key(_1717961, _1717961, c_COMBI(_1717961), _1717965, _1717963)))], (46541 ^ _780205) ^ [_1718108, _1718110, _1718112] : [class_Orderings_Olinorder(_1718108), c_List_Olinorder__class_Osorted(_1718108, _1718110), -(c_List_Olinorder__class_Osorted(_1718108, hAPP(hAPP(c_List_Odrop(_1718108), _1718112), _1718110)))], (46551 ^ _780205) ^ [_1718255, _1718257] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1718255, _1718257)))], (46553 ^ _780205) ^ [_1718283, _1718285, _1718287] : [class_Orderings_Olinorder(_1718283), c_List_Olinorder__class_Osorted(_1718283, _1718285), -(c_List_Olinorder__class_Osorted(_1718283, hAPP(hAPP(c_List_Otake(_1718283), _1718287), _1718285)))], (46563 ^ _780205) ^ [_1718430, _1718432, _1718434] : [class_Orderings_Olinorder(_1718430), c_List_Olinorder__class_Osorted(_1718430, _1718432), -(c_List_Olinorder__class_Osorted(_1718430, c_List_Oremove1(_1718430, _1718434, _1718432)))], (46573 ^ _780205) ^ [_1718569, _1718571] : [class_Orderings_Olinorder(_1718569), c_List_Olinorder__class_Osorted(_1718569, _1718571), -(c_List_Olinorder__class_Osorted(_1718569, hAPP(c_List_Otl(_1718569), _1718571)))], (46583 ^ _780205) ^ [_1718706, _1718708, _1718710] : [class_Orderings_Olinorder(_1718706), 46586 ^ _780205 : [(46587 ^ _780205) ^ [] : [c_List_Olinorder__class_Osorted(_1718706, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1718706, _1718706, c_COMBI(_1718706)), _1718708), _1718710)), -(c_List_Olinorder__class_Osorted(_1718706, _1718710))], (46593 ^ _780205) ^ [] : [c_List_Olinorder__class_Osorted(_1718706, _1718710), -(c_List_Olinorder__class_Osorted(_1718706, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1718706, _1718706, c_COMBI(_1718706)), _1718708), _1718710)))]]], (46599 ^ _780205) ^ [_1718953, _1718955] : [class_Orderings_Olinorder(_1718953), -(_1718955 = c_List_Olist_ONil(_1718953)), c_List_Olinorder__class_Osorted(_1718953, _1718955), -(c_List_Olinorder__class_Osorted(_1718953, c_List_Obutlast(_1718953, _1718955)))], (46613 ^ _780205) ^ [_1719145] : [class_Orderings_Olinorder(_1719145), -(c_List_Olinorder__class_Osorted(_1719145, c_List_Olist_ONil(_1719145)))], (46619 ^ _780205) ^ [_1719222, _1719224, _1719226, _1719228] : [class_Orderings_Olinorder(_1719222), 46622 ^ _780205 : [(46623 ^ _780205) ^ [] : [c_List_Olinorder__class_Osorted(_1719222, hAPP(hAPP(c_List_Olist_OCons(_1719222), _1719224), hAPP(hAPP(c_List_Olist_OCons(_1719222), _1719226), _1719228))), 46626 ^ _780205 : [(46627 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719222), _1719224), _1719226)))], (46629 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1719222, hAPP(hAPP(c_List_Olist_OCons(_1719222), _1719226), _1719228)))]]], (46631 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1719222, hAPP(hAPP(c_List_Olist_OCons(_1719222), _1719224), hAPP(hAPP(c_List_Olist_OCons(_1719222), _1719226), _1719228)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719222), _1719224), _1719226)), c_List_Olinorder__class_Osorted(_1719222, hAPP(hAPP(c_List_Olist_OCons(_1719222), _1719226), _1719228))]]], (46641 ^ _780205) ^ [_1719608, _1719610, _1719612, _1719614] : [class_Orderings_Olinorder(_1719608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719608), _1719610), _1719612)), c_List_Olinorder__class_Osorted(_1719608, hAPP(hAPP(c_List_Olist_OCons(_1719608), _1719612), _1719614)), -(c_List_Olinorder__class_Osorted(_1719608, hAPP(hAPP(c_List_Olist_OCons(_1719608), _1719610), hAPP(hAPP(c_List_Olist_OCons(_1719608), _1719612), _1719614))))], (46655 ^ _780205) ^ [_1719861, _1719863] : [class_Orderings_Olinorder(_1719861), c_List_Olinorder__class_Osorted(_1719861, _1719863), -(c_List_Olinorder__class_Osorted(_1719861, c_List_Oremdups(_1719861, _1719863)))], (46665 ^ _780205) ^ [_1719994, _1719996, _1719998] : [class_Orderings_Olinorder(_1719994), c_List_Olinorder__class_Osorted(_1719994, _1719996), hBOOL(hAPP(c_List_Odistinct(_1719994), _1719996)), c_List_Olinorder__class_Osorted(_1719994, _1719998), hBOOL(hAPP(c_List_Odistinct(_1719994), _1719998)), hAPP(c_List_Oset(_1719994), _1719996) = hAPP(c_List_Oset(_1719994), _1719998), -(_1719996 = _1719998)], (46691 ^ _780205) ^ [_1720377, _1720379, _1720381, _1720383] : [class_Orderings_Olinorder(_1720377), -(c_List_Olinorder__class_Osorted(_1720377, hAPP(hAPP(c_List_Omap(_1720379, _1720377), _1720381), c_List_Olinorder__class_Osort__key(_1720379, _1720377, _1720381, _1720383))))], (46697 ^ _780205) ^ [_1720484, _1720486, _1720488, _1720490, _1720492] : [class_Orderings_Olinorder(_1720484), c_List_Olinorder__class_Osorted(_1720484, hAPP(hAPP(c_List_Omap(_1720486, _1720484), _1720488), _1720490)), -(c_List_Olinorder__class_Osorted(_1720484, hAPP(hAPP(c_List_Omap(_1720486, _1720484), _1720488), c_List_Olinorder__class_Oinsort__insert__key(_1720486, _1720484, _1720488, _1720492, _1720490))))], (46707 ^ _780205) ^ [_1720671, _1720673, _1720675, _1720677, _1720679] : [class_Orderings_Olinorder(_1720671), c_List_Olinorder__class_Osorted(_1720671, hAPP(hAPP(c_List_Omap(_1720673, _1720671), _1720675), _1720677)), -(c_List_Olinorder__class_Osorted(_1720671, hAPP(hAPP(c_List_Omap(_1720673, _1720671), _1720675), c_List_Oremove1(_1720673, _1720679, _1720677))))], (46717 ^ _780205) ^ [_1720854, _1720856, _1720858, _1720860, _1720862] : [class_Orderings_Olinorder(_1720854), 46720 ^ _780205 : [(46721 ^ _780205) ^ [] : [c_List_Olinorder__class_Osorted(_1720854, hAPP(hAPP(c_List_Omap(_1720856, _1720854), _1720858), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720856, _1720854, _1720858), _1720860), _1720862))), -(c_List_Olinorder__class_Osorted(_1720854, hAPP(hAPP(c_List_Omap(_1720856, _1720854), _1720858), _1720862)))], (46727 ^ _780205) ^ [] : [c_List_Olinorder__class_Osorted(_1720854, hAPP(hAPP(c_List_Omap(_1720856, _1720854), _1720858), _1720862)), -(c_List_Olinorder__class_Osorted(_1720854, hAPP(hAPP(c_List_Omap(_1720856, _1720854), _1720858), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720856, _1720854, _1720858), _1720860), _1720862))))]]], (46733 ^ _780205) ^ [_1721161, _1721163, _1721165, _1721167, _1721169] : [class_Orderings_Olinorder(_1721161), -(c_List_Olinorder__class_Osorted(_1721161, hAPP(hAPP(c_List_Omap(_1721163, _1721161), _1721165), hAPP(c_List_Ofilter(_1721163, hAPP(hAPP(c_COMBC(_1721163, _1721161, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1721161, tc_fun(_1721161, tc_HOL_Obool), _1721163), c_fequal), _1721165)), hAPP(_1721167, _1721169))), _1721169))))], (46739 ^ _780205) ^ [_1721324, _1721326, _1721328, _1721330, _1721332] : [class_Orderings_Olinorder(_1721324), c_List_Olinorder__class_Osorted(_1721324, hAPP(hAPP(c_List_Omap(_1721326, _1721324), _1721328), _1721330)), -(c_List_Olinorder__class_Osorted(_1721324, hAPP(hAPP(c_List_Omap(_1721326, _1721324), _1721328), hAPP(c_List_Ofilter(_1721326, _1721332), _1721330))))], (46749 ^ _780205) ^ [_1721511, _1721513, _1721515] : [class_Orderings_Olinorder(_1721511), -(c_List_Olinorder__class_Osorted(_1721511, hAPP(c_List_Ofilter(_1721511, hAPP(hAPP(c_COMBC(_1721511, _1721511, tc_HOL_Obool), c_fequal), hAPP(_1721513, _1721515))), _1721515)))], (46755 ^ _780205) ^ [_1721626, _1721628, _1721630] : [class_Orderings_Olinorder(_1721626), 46758 ^ _780205 : [(46759 ^ _780205) ^ [] : [c_List_Olinorder__class_Osorted(_1721626, hAPP(hAPP(c_List_Olist_OCons(_1721626), _1721628), _1721630)), 46762 ^ _780205 : [(46763 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1721626, _1721630))], (46765 ^ _780205) ^ [_1721812] : [hBOOL(hAPP(hAPP(c_member(_1721626), _1721812), hAPP(c_List_Oset(_1721626), _1721630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1721626), _1721628), _1721812)))]]], (46771 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1721626, hAPP(hAPP(c_List_Olist_OCons(_1721626), _1721628), _1721630))), c_List_Olinorder__class_Osorted(_1721626, _1721630), 46777 ^ _780205 : [(46778 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1721626), 46776 ^ [_1721626, _1721628, _1721630]), hAPP(c_List_Oset(_1721626), _1721630))))], (46780 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1721626), _1721628), 46776 ^ [_1721626, _1721628, _1721630]))]]]]], (46784 ^ _780205) ^ [_1722151, _1722153, _1722155] : [class_Orderings_Olinorder(_1722151), 46787 ^ _780205 : [(46788 ^ _780205) ^ [] : [c_List_Olinorder__class_Osorted(_1722151, hAPP(hAPP(c_List_Oappend(_1722151), _1722153), _1722155)), 46791 ^ _780205 : [(46792 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1722151, _1722153))], (46794 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1722151, _1722155))], (46796 ^ _780205) ^ [_1722387] : [hBOOL(hAPP(hAPP(c_member(_1722151), _1722387), hAPP(c_List_Oset(_1722151), _1722153))), 46799 ^ _780205 : [(46800 ^ _780205) ^ [_1722497] : [hBOOL(hAPP(hAPP(c_member(_1722151), _1722497), hAPP(c_List_Oset(_1722151), _1722155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1722151), _1722387), _1722497)))]]]]], (46806 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1722151, hAPP(hAPP(c_List_Oappend(_1722151), _1722153), _1722155))), c_List_Olinorder__class_Osorted(_1722151, _1722153), c_List_Olinorder__class_Osorted(_1722151, _1722155), 46816 ^ _780205 : [(46817 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1722151), 46815 ^ [_1722151, _1722153, _1722155]), hAPP(c_List_Oset(_1722151), _1722153))))], (46820 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1722151), 46818 ^ [_1722151, _1722153, _1722155]), hAPP(c_List_Oset(_1722151), _1722155))))], (46822 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1722151), 46815 ^ [_1722151, _1722153, _1722155]), 46818 ^ [_1722151, _1722153, _1722155]))]]]]], (46826 ^ _780205) ^ [_1722999, _1723001, _1723003, _1723005, _1723007, _1723009] : [class_Orderings_Olinorder(_1722999), c_List_Olinorder__class_Osorted(_1722999, hAPP(hAPP(c_List_Omap(_1723001, _1722999), _1723003), _1723005)), hBOOL(hAPP(_1723007, _1723009)), -(hAPP(c_List_Ofilter(_1723001, _1723007), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1723001, _1722999, _1723003), _1723009), _1723005)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1723001, _1722999, _1723003), _1723009), hAPP(c_List_Ofilter(_1723001, _1723007), _1723005)))], (46840 ^ _780205) ^ [_1723288, _1723290, _1723292] : [class_Orderings_Olinorder(_1723288), 46843 ^ _780205 : [(46844 ^ _780205) ^ [] : [c_List_Olinorder__class_Osorted(_1723288, hAPP(hAPP(c_List_Olist_OCons(_1723288), _1723290), _1723292)), 46847 ^ _780205 : [(46854 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1723288, _1723292))], (46848 ^ _780205) ^ [_1723456] : [hBOOL(hAPP(hAPP(c_member(_1723288), _1723456), hAPP(c_List_Oset(_1723288), _1723292))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723288), _1723290), _1723456)))]]], (46856 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1723288, hAPP(hAPP(c_List_Olist_OCons(_1723288), _1723290), _1723292))), 46860 ^ _780205 : [(46861 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1723288), 46859 ^ [_1723288, _1723290, _1723292]), hAPP(c_List_Oset(_1723288), _1723292))))], (46863 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723288), _1723290), 46859 ^ [_1723288, _1723290, _1723292]))]], c_List_Olinorder__class_Osorted(_1723288, _1723292)]]], (46869 ^ _780205) ^ [_1723814, _1723816] : [class_Orderings_Olinorder(_1723814), hBOOL(hAPP(c_Finite__Set_Ofinite(_1723814), _1723816)), 46876 ^ _780205 : [(46877 ^ _780205) ^ [] : [-(hAPP(c_List_Oset(_1723814), c_List_Olinorder__class_Osorted__list__of__set(_1723814, _1723816)) = _1723816)], (46879 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1723814, c_List_Olinorder__class_Osorted__list__of__set(_1723814, _1723816)))], (46881 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1723814), c_List_Olinorder__class_Osorted__list__of__set(_1723814, _1723816))))]]], (46883 ^ _780205) ^ [_1724035, _1724037, _1724039] : [class_Orderings_Olinorder(_1724035), hBOOL(hAPP(hAPP(c_member(_1724035), _1724037), hAPP(c_List_Oset(_1724035), _1724039))), c_List_Olinorder__class_Osorted(_1724035, _1724039), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1724035, _1724035, c_COMBI(_1724035)), _1724037), c_List_Oremove1(_1724035, _1724037, _1724039)) = _1724039)], (46897 ^ _780205) ^ [_1724276, _1724278, _1724280, _1724282] : [class_Orderings_Olinorder(_1724276), c_List_Olinorder__class_Osorted(_1724276, _1724278), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724280), _1724282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724282), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724276)), _1724278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1724276), hAPP(hAPP(c_List_Onth(_1724276), _1724278), _1724280)), hAPP(hAPP(c_List_Onth(_1724276), _1724278), _1724282))))], (46915 ^ _780205) ^ [_1724603, _1724605] : [class_Orderings_Olinorder(_1724603), 46918 ^ _780205 : [(46933 ^ _780205) ^ [] : [46935 ^ _780205 : [(46936 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46934 ^ [_1724603, _1724605]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724603)), _1724605))))], (46939 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46937 ^ [_1724603, _1724605]), 46934 ^ [_1724603, _1724605])))], (46941 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1724603), hAPP(hAPP(c_List_Onth(_1724603), _1724605), 46937 ^ [_1724603, _1724605])), hAPP(hAPP(c_List_Onth(_1724603), _1724605), 46934 ^ [_1724603, _1724605])))]], -(c_List_Olinorder__class_Osorted(_1724603, _1724605))], (46919 ^ _780205) ^ [] : [c_List_Olinorder__class_Osorted(_1724603, _1724605), 46922 ^ _780205 : [(46923 ^ _780205) ^ [_1724774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724774), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724603)), _1724605))), 46926 ^ _780205 : [(46927 ^ _780205) ^ [_1724891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724891), _1724774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1724603), hAPP(hAPP(c_List_Onth(_1724603), _1724605), _1724891)), hAPP(hAPP(c_List_Onth(_1724603), _1724605), _1724774))))]]]]]]], (46945 ^ _780205) ^ [_1725327, _1725329, _1725331, _1725333, _1725335] : [class_Orderings_Olinorder(_1725327), c_Fun_Oinj__on(_1725329, _1725327, _1725331, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1725329, tc_HOL_Obool)), hAPP(c_List_Oset(_1725329), _1725333)), hAPP(c_List_Oset(_1725329), _1725335))), c_List_Olinorder__class_Osorted(_1725327, hAPP(hAPP(c_List_Omap(_1725329, _1725327), _1725331), _1725333)), hBOOL(hAPP(c_List_Odistinct(_1725327), hAPP(hAPP(c_List_Omap(_1725329, _1725327), _1725331), _1725333))), c_List_Olinorder__class_Osorted(_1725327, hAPP(hAPP(c_List_Omap(_1725329, _1725327), _1725331), _1725335)), hBOOL(hAPP(c_List_Odistinct(_1725327), hAPP(hAPP(c_List_Omap(_1725329, _1725327), _1725331), _1725335))), hAPP(c_List_Oset(_1725329), _1725333) = hAPP(c_List_Oset(_1725329), _1725335), -(_1725333 = _1725335)], (46975 ^ _780205) ^ [_1725910, _1725912, _1725914] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1725910), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1725910))), _1725912))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725914), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1725910))), _1725912))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1725910), _1725910), hAPP(hAPP(c_COMBC(tc_List_Olist(_1725910), tc_Nat_Onat, _1725910), c_List_Onth(_1725910)), _1725914)), hAPP(c_List_Ofilter(tc_List_Olist(_1725910), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1725910)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725914)), c_Nat_Osize__class_Osize(tc_List_Olist(_1725910)))), c_List_Otranspose(_1725910, _1725912))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1725910)), _1725912), _1725914))], (46985 ^ _780205) ^ [_1726237, _1726239, _1726241, _1726243] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1726237), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1726237))), _1726239))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726241), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1726237))), c_List_Otranspose(_1726237, _1726239)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726243), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1726237))), hAPP(c_List_Ofilter(tc_List_Olist(_1726237), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1726237)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726241)), c_Nat_Osize__class_Osize(tc_List_Olist(_1726237)))), _1726239)))), -(hAPP(hAPP(c_List_Onth(_1726237), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1726237)), c_List_Otranspose(_1726237, _1726239)), _1726241)), _1726243) = hAPP(hAPP(c_List_Onth(_1726237), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1726237)), _1726239), _1726243)), _1726241))], (46999 ^ _780205) ^ [_1726660, _1726662] : [-(c_Fun_Oinj__on(tc_List_Olist(_1726660), tc_List_Olist(_1726660), c_List_Orev(_1726660), _1726662))], (47001 ^ _780205) ^ [_1726708, _1726710] : [hBOOL(hAPP(c_List_Odistinct(_1726708), hAPP(c_List_Orev(_1726708), _1726710))), -(hBOOL(hAPP(c_List_Odistinct(_1726708), _1726710)))], (47007 ^ _780205) ^ [_1726807, _1726809] : [hBOOL(hAPP(c_List_Odistinct(_1726807), _1726809)), -(hBOOL(hAPP(c_List_Odistinct(_1726807), hAPP(c_List_Orev(_1726807), _1726809))))], (47013 ^ _780205) ^ [_1726927, _1726929] : [hAPP(c_List_Orev(_1726927), _1726929) = c_List_Olist_ONil(_1726927), -(_1726929 = c_List_Olist_ONil(_1726927))], (47019 ^ _780205) ^ [_1727018, _1727020] : [_1727020 = c_List_Olist_ONil(_1727018), -(hAPP(c_List_Orev(_1727018), _1727020) = c_List_Olist_ONil(_1727018))], (47025 ^ _780205) ^ [_1727130, _1727132] : [c_List_Olist_ONil(_1727130) = hAPP(c_List_Orev(_1727130), _1727132), -(_1727132 = c_List_Olist_ONil(_1727130))], (47031 ^ _780205) ^ [_1727221, _1727223] : [_1727223 = c_List_Olist_ONil(_1727221), -(c_List_Olist_ONil(_1727221) = hAPP(c_List_Orev(_1727221), _1727223))], (47037 ^ _780205) ^ [_1727318] : [-(hAPP(c_List_Orev(_1727318), c_List_Olist_ONil(_1727318)) = c_List_Olist_ONil(_1727318))], (47039 ^ _780205) ^ [_1727368, _1727370, _1727372] : [hAPP(hAPP(c_List_Olist_OCons(_1727368), _1727370), c_List_Olist_ONil(_1727368)) = hAPP(c_List_Orev(_1727368), _1727372), -(_1727372 = hAPP(hAPP(c_List_Olist_OCons(_1727368), _1727370), c_List_Olist_ONil(_1727368)))], (47045 ^ _780205) ^ [_1727493, _1727495, _1727497] : [_1727497 = hAPP(hAPP(c_List_Olist_OCons(_1727493), _1727495), c_List_Olist_ONil(_1727493)), -(hAPP(hAPP(c_List_Olist_OCons(_1727493), _1727495), c_List_Olist_ONil(_1727493)) = hAPP(c_List_Orev(_1727493), _1727497))], (47051 ^ _780205) ^ [_1727642, _1727644, _1727646] : [hAPP(c_List_Orev(_1727642), _1727644) = hAPP(hAPP(c_List_Olist_OCons(_1727642), _1727646), c_List_Olist_ONil(_1727642)), -(_1727644 = hAPP(hAPP(c_List_Olist_OCons(_1727642), _1727646), c_List_Olist_ONil(_1727642)))], (47057 ^ _780205) ^ [_1727767, _1727769, _1727771] : [_1727769 = hAPP(hAPP(c_List_Olist_OCons(_1727767), _1727771), c_List_Olist_ONil(_1727767)), -(hAPP(c_List_Orev(_1727767), _1727769) = hAPP(hAPP(c_List_Olist_OCons(_1727767), _1727771), c_List_Olist_ONil(_1727767)))], (47063 ^ _780205) ^ [_1727898, _1727900, _1727902] : [-(hAPP(c_List_Orev(_1727898), hAPP(hAPP(c_List_Oappend(_1727898), _1727900), _1727902)) = hAPP(hAPP(c_List_Oappend(_1727898), hAPP(c_List_Orev(_1727898), _1727902)), hAPP(c_List_Orev(_1727898), _1727900)))], (47065 ^ _780205) ^ [_1727956, _1727958] : [-(hAPP(c_List_Orev(_1727956), c_List_Oconcat(_1727956, _1727958)) = c_List_Oconcat(_1727956, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1727956), tc_List_Olist(_1727956)), c_List_Orev(_1727956)), hAPP(c_List_Orev(tc_List_Olist(_1727956)), _1727958))))], (47067 ^ _780205) ^ [_1728014, _1728016, _1728018, _1728020] : [-(hAPP(c_List_Orev(_1728014), hAPP(hAPP(c_List_Omap(_1728016, _1728014), _1728018), _1728020)) = hAPP(hAPP(c_List_Omap(_1728016, _1728014), _1728018), hAPP(c_List_Orev(_1728016), _1728020)))], (47069 ^ _780205) ^ [_1728071, _1728073, _1728075] : [-(hAPP(c_List_Orev(_1728071), hAPP(c_List_Ofilter(_1728071, _1728073), _1728075)) = hAPP(c_List_Ofilter(_1728071, _1728073), hAPP(c_List_Orev(_1728071), _1728075)))], (47071 ^ _780205) ^ [_1728120, _1728122, _1728124, _1728126] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728120)), _1728122) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728124)), _1728126), -(hAPP(hAPP(c_List_Ozip(_1728120, _1728124), hAPP(c_List_Orev(_1728120), _1728122)), hAPP(c_List_Orev(_1728124), _1728126)) = hAPP(c_List_Orev(tc_prod(_1728120, _1728124)), hAPP(hAPP(c_List_Ozip(_1728120, _1728124), _1728122), _1728126)))], (47077 ^ _780205) ^ [_1728301, _1728303] : [-(hAPP(c_List_Oset(_1728301), hAPP(c_List_Orev(_1728301), _1728303)) = hAPP(c_List_Oset(_1728301), _1728303))], (47079 ^ _780205) ^ [_1728365, _1728367, _1728369, _1728371, _1728373] : [c_List_Olist__all2(_1728365, _1728367, _1728369, hAPP(c_List_Orev(_1728365), _1728371), hAPP(c_List_Orev(_1728367), _1728373)), -(c_List_Olist__all2(_1728365, _1728367, _1728369, _1728371, _1728373))], (47085 ^ _780205) ^ [_1728476, _1728478, _1728480, _1728482, _1728484] : [c_List_Olist__all2(_1728476, _1728478, _1728480, _1728482, _1728484), -(c_List_Olist__all2(_1728476, _1728478, _1728480, hAPP(c_List_Orev(_1728476), _1728482), hAPP(c_List_Orev(_1728478), _1728484)))], (47091 ^ _780205) ^ [_1728617, _1728619, _1728621, _1728623, _1728625] : [c_List_Olist__all2(_1728617, _1728619, _1728621, hAPP(c_List_Orev(_1728617), _1728623), _1728625), -(c_List_Olist__all2(_1728617, _1728619, _1728621, _1728623, hAPP(c_List_Orev(_1728619), _1728625)))], (47097 ^ _780205) ^ [_1728728, _1728730, _1728732, _1728734, _1728736] : [c_List_Olist__all2(_1728728, _1728730, _1728732, _1728734, hAPP(c_List_Orev(_1728730), _1728736)), -(c_List_Olist__all2(_1728728, _1728730, _1728732, hAPP(c_List_Orev(_1728728), _1728734), _1728736))], (47103 ^ _780205) ^ [_1728845, _1728847] : [-(hAPP(c_List_Orev(_1728845), hAPP(c_List_Orev(_1728845), _1728847)) = _1728847)], (47105 ^ _780205) ^ [_1728898, _1728900, _1728902] : [hAPP(c_List_Orev(_1728898), _1728900) = _1728902, -(_1728900 = hAPP(c_List_Orev(_1728898), _1728902))], (47111 ^ _780205) ^ [_1728993, _1728995, _1728997] : [_1728995 = hAPP(c_List_Orev(_1728993), _1728997), -(hAPP(c_List_Orev(_1728993), _1728995) = _1728997)], (47117 ^ _780205) ^ [_1729112, _1729114, _1729116] : [hAPP(c_List_Orev(_1729112), _1729114) = hAPP(c_List_Orev(_1729112), _1729116), -(_1729114 = _1729116)], (47123 ^ _780205) ^ [_1729207, _1729209, _1729211] : [_1729209 = _1729211, -(hAPP(c_List_Orev(_1729207), _1729209) = hAPP(c_List_Orev(_1729207), _1729211))], (47129 ^ _780205) ^ [_1729308, _1729310] : [class_Groups_Ocomm__monoid__add(_1729308), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1729308), hAPP(c_List_Orev(_1729308), _1729310)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1729308), _1729310))], (47135 ^ _780205) ^ [_1729413, _1729415] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729413)), hAPP(c_List_Orev(_1729413), _1729415)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729413)), _1729415))], (47137 ^ _780205) ^ [_1729457, _1729459, _1729461, _1729463, _1729465] : [-(hAPP(c_List_Ofoldl(_1729457, _1729459, _1729461, _1729463), _1729465) = c_List_Ofoldr(_1729459, _1729457, hAPP(c_COMBC(_1729457, _1729459, _1729457), _1729461), hAPP(c_List_Orev(_1729459), _1729465), _1729463))], (47139 ^ _780205) ^ [_1729514, _1729516, _1729518, _1729520, _1729522] : [-(c_List_Ofoldr(_1729514, _1729516, _1729518, _1729520, _1729522) = hAPP(c_List_Ofoldl(_1729516, _1729514, hAPP(c_COMBC(_1729514, _1729516, _1729516), _1729518), _1729522), hAPP(c_List_Orev(_1729514), _1729520)))], (47141 ^ _780205) ^ [_1729592, _1729594, _1729596, _1729598] : [hAPP(c_List_Orev(_1729592), _1729594) = hAPP(hAPP(c_List_Olist_OCons(_1729592), _1729596), _1729598), -(_1729594 = hAPP(hAPP(c_List_Oappend(_1729592), hAPP(c_List_Orev(_1729592), _1729598)), hAPP(hAPP(c_List_Olist_OCons(_1729592), _1729596), c_List_Olist_ONil(_1729592))))], (47147 ^ _780205) ^ [_1729741, _1729743, _1729745, _1729747] : [_1729743 = hAPP(hAPP(c_List_Oappend(_1729741), hAPP(c_List_Orev(_1729741), _1729747)), hAPP(hAPP(c_List_Olist_OCons(_1729741), _1729745), c_List_Olist_ONil(_1729741))), -(hAPP(c_List_Orev(_1729741), _1729743) = hAPP(hAPP(c_List_Olist_OCons(_1729741), _1729745), _1729747))], (47153 ^ _780205) ^ [_1729896, _1729898, _1729900] : [-(hAPP(c_List_Orev(_1729896), hAPP(hAPP(c_List_Olist_OCons(_1729896), _1729898), _1729900)) = hAPP(hAPP(c_List_Oappend(_1729896), hAPP(c_List_Orev(_1729896), _1729900)), hAPP(hAPP(c_List_Olist_OCons(_1729896), _1729898), c_List_Olist_ONil(_1729896))))], (47155 ^ _780205) ^ [_1729955, _1729957] : [-(_1729955 = c_List_Olist_ONil(_1729957)), -(hAPP(c_List_Ohd(_1729957), hAPP(c_List_Orev(_1729957), _1729955)) = c_List_Olast(_1729957, _1729955))], (47161 ^ _780205) ^ [_1730002, _1730004] : [-(_1730002 = c_List_Olist_ONil(_1730004)), -(c_List_Olast(_1730004, hAPP(c_List_Orev(_1730004), _1730002)) = hAPP(c_List_Ohd(_1730004), _1730002))], (47167 ^ _780205) ^ [_1730053, _1730055] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1730053), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1730053))), c_List_Otranspose(_1730053, _1730055)))))], (47169 ^ _780205) ^ [_1730099, _1730101] : [-(hAPP(c_List_Orev(_1730099), _1730101) = hAPP(c_List_Ofoldl(tc_List_Olist(_1730099), _1730099, hAPP(c_COMBC(_1730099, tc_List_Olist(_1730099), tc_List_Olist(_1730099)), c_List_Olist_OCons(_1730099)), c_List_Olist_ONil(_1730099)), _1730101))], (47171 ^ _780205) ^ [_1730154, _1730156, _1730158] : [-(hAPP(c_List_Orev(_1730154), hAPP(hAPP(c_List_Odrop(_1730154), _1730156), _1730158)) = hAPP(hAPP(c_List_Otake(_1730154), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730154)), _1730158)), _1730156)), hAPP(c_List_Orev(_1730154), _1730158)))], (47173 ^ _780205) ^ [_1730220, _1730222, _1730224] : [-(hAPP(c_List_Orev(_1730220), hAPP(hAPP(c_List_Otake(_1730220), _1730222), _1730224)) = hAPP(hAPP(c_List_Odrop(_1730220), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730220)), _1730224)), _1730222)), hAPP(c_List_Orev(_1730220), _1730224)))], (47175 ^ _780205) ^ [_1730286, _1730288, _1730290] : [-(hAPP(c_List_Orotate(_1730286, _1730288), hAPP(c_List_Orev(_1730286), _1730290)) = hAPP(c_List_Orev(_1730286), hAPP(c_List_Orotate(_1730286, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730286)), _1730290)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1730288, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730286)), _1730290)))), _1730290)))], (47177 ^ _780205) ^ [_1730359, _1730361, _1730363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730359), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730361)), _1730363))), -(hAPP(hAPP(c_List_Onth(_1730361), hAPP(c_List_Orev(_1730361), _1730363)), _1730359) = hAPP(hAPP(c_List_Onth(_1730361), _1730363), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730361)), _1730363)), hAPP(c_Nat_OSuc, _1730359))))], (47183 ^ _780205) ^ [_1730536, _1730538, _1730540, _1730542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730536), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730538)), _1730540))), -(hAPP(c_List_Orev(_1730538), hAPP(hAPP(c_List_Olist__update(_1730538, _1730540), _1730536), _1730542)) = hAPP(hAPP(c_List_Olist__update(_1730538, hAPP(c_List_Orev(_1730538), _1730540)), 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(_1730538)), _1730540)), _1730536)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1730542))], (47189 ^ _780205) ^ [_1730735, _1730737, _1730739, _1730741] : [class_Orderings_Olinorder(_1730735), c_List_Olinorder__class_Osorted(_1730735, hAPP(c_List_Orev(_1730735), _1730737)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1730739), _1730741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730741), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730735)), _1730737))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1730735), hAPP(hAPP(c_List_Onth(_1730735), _1730737), _1730741)), hAPP(hAPP(c_List_Onth(_1730735), _1730737), _1730739))))], (47207 ^ _780205) ^ [_1731072, _1731074, _1731076] : [class_Orderings_Olinorder(_1731072), c_List_Olinorder__class_Osorted(_1731072, hAPP(c_List_Orev(_1731072), _1731074)), 47214 ^ _780205 : [(47215 ^ _780205) ^ [] : [_1731074 = c_List_Olist_ONil(_1731072), -(c_List_Ofoldr(_1731072, _1731072, c_Orderings_Oord__class_Omax(_1731072), _1731074, _1731076) = _1731076)], (47221 ^ _780205) ^ [] : [-(_1731074 = c_List_Olist_ONil(_1731072)), -(c_List_Ofoldr(_1731072, _1731072, c_Orderings_Oord__class_Omax(_1731072), _1731074, _1731076) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1731072), hAPP(hAPP(c_List_Onth(_1731072), _1731074), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1731076))]]], (47227 ^ _780205) ^ [_1731386, _1731388] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731386), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1731386))), _1731388))), 47230 ^ _780205 : [(47231 ^ _780205) ^ [] : [_1731388 = c_List_Olist_ONil(tc_List_Olist(_1731386)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731386))), c_List_Otranspose(_1731386, _1731388)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47237 ^ _780205) ^ [] : [-(_1731388 = c_List_Olist_ONil(tc_List_Olist(_1731386))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731386))), c_List_Otranspose(_1731386, _1731388)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731386)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1731386)), _1731388), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (47243 ^ _780205) ^ [_1731696, _1731698, _1731700] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731696), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1731696))), _1731698))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731700), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731696))), _1731698))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731696))), hAPP(c_List_Ofilter(tc_List_Olist(_1731696), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1731696)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731700)), c_Nat_Osize__class_Osize(tc_List_Olist(_1731696)))), c_List_Otranspose(_1731696, _1731698))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731696)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1731696)), _1731698), _1731700)))], (47253 ^ _780205) ^ [_1732005, _1732007] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732005), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1732005))), _1732007))), -(c_List_Otranspose(_1732005, c_List_Otranspose(_1732005, _1732007)) = c_List_OtakeWhile(tc_List_Olist(_1732005), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1732005)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1732005), tc_List_Olist(_1732005), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1732005))), _1732007))], (47259 ^ _780205) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (47261 ^ _780205) ^ [_1732216, _1732218, _1732220] : [class_Orderings_Olinorder(_1732216), c_List_Olinorder__class_Osorted(_1732216, _1732218), -(c_List_Olinorder__class_Osorted(_1732216, c_List_OtakeWhile(_1732216, _1732220, _1732218)))], (47271 ^ _780205) ^ [_1732355, _1732357, _1732359] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732355)), c_List_OtakeWhile(_1732355, _1732357, _1732359))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732355)), _1732359))))], (47283 ^ _780205) ^ [_1732619, _1732621, _1732623] : [47285 ^ _780205 : [(47286 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1732619), 47284 ^ [_1732619, _1732621, _1732623]), hAPP(c_List_Oset(_1732619), _1732623))))], (47288 ^ _780205) ^ [] : [hBOOL(hAPP(_1732621, 47284 ^ [_1732619, _1732621, _1732623]))]], -(c_List_OtakeWhile(_1732619, _1732621, _1732623) = _1732623)], (47273 ^ _780205) ^ [_1732423, _1732425, _1732427] : [c_List_OtakeWhile(_1732423, _1732425, _1732427) = _1732427, 47276 ^ _780205 : [(47277 ^ _780205) ^ [_1732510] : [hBOOL(hAPP(hAPP(c_member(_1732423), _1732510), hAPP(c_List_Oset(_1732423), _1732427))), -(hBOOL(hAPP(_1732425, _1732510)))]]], (47292 ^ _780205) ^ [_1732807, _1732809, _1732811, _1732813] : [hBOOL(hAPP(hAPP(c_member(_1732807), _1732809), hAPP(c_List_Oset(_1732807), c_List_OtakeWhile(_1732807, _1732811, _1732813)))), 47295 ^ _780205 : [(47296 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1732807), _1732809), hAPP(c_List_Oset(_1732807), _1732813))))], (47298 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1732811, _1732809)))]]], (47300 ^ _780205) ^ [_1732974, _1732976, _1732978, _1732980, _1732982] : [-(hAPP(hAPP(c_List_Ozip(_1732974, _1732976), _1732978), c_List_OtakeWhile(_1732976, _1732980, _1732982)) = c_List_OtakeWhile(tc_prod(_1732974, _1732976), hAPP(c_Fun_Ocomp(_1732976, tc_HOL_Obool, tc_prod(_1732974, _1732976), _1732980), c_Product__Type_Osnd(_1732974, _1732976)), hAPP(hAPP(c_List_Ozip(_1732974, _1732976), _1732978), _1732982)))], (47302 ^ _780205) ^ [_1733048, _1733050, _1733052, _1733054, _1733056] : [-(hAPP(hAPP(c_List_Ozip(_1733048, _1733050), c_List_OtakeWhile(_1733048, _1733052, _1733054)), _1733056) = c_List_OtakeWhile(tc_prod(_1733048, _1733050), hAPP(c_Fun_Ocomp(_1733048, tc_HOL_Obool, tc_prod(_1733048, _1733050), _1733052), c_Product__Type_Ofst(_1733048, _1733050)), hAPP(hAPP(c_List_Ozip(_1733048, _1733050), _1733054), _1733056)))], (47304 ^ _780205) ^ [_1733122, _1733124, _1733126, _1733128, _1733130] : [-(c_List_OtakeWhile(_1733122, _1733124, hAPP(hAPP(c_List_Omap(_1733126, _1733122), _1733128), _1733130)) = hAPP(hAPP(c_List_Omap(_1733126, _1733122), _1733128), c_List_OtakeWhile(_1733126, hAPP(c_Fun_Ocomp(_1733122, tc_HOL_Obool, _1733126, _1733124), _1733128), _1733130)))], (47306 ^ _780205) ^ [_1733183, _1733185, _1733187, _1733189, _1733191] : [-(hBOOL(hAPP(_1733183, _1733185))), -(c_List_OtakeWhile(_1733187, _1733183, hAPP(hAPP(c_List_Oappend(_1733187), _1733189), hAPP(hAPP(c_List_Olist_OCons(_1733187), _1733185), _1733191))) = c_List_OtakeWhile(_1733187, _1733183, _1733189))], (47312 ^ _780205) ^ [_1733266, _1733268, _1733270, _1733272] : [hBOOL(hAPP(_1733266, _1733268)), -(c_List_OtakeWhile(_1733270, _1733266, hAPP(hAPP(c_List_Olist_OCons(_1733270), _1733268), _1733272)) = hAPP(hAPP(c_List_Olist_OCons(_1733270), _1733268), c_List_OtakeWhile(_1733270, _1733266, _1733272)))], (47318 ^ _780205) ^ [_1733393, _1733395, _1733397, _1733399] : [-(hBOOL(hAPP(_1733393, _1733395))), -(c_List_OtakeWhile(_1733397, _1733393, hAPP(hAPP(c_List_Olist_OCons(_1733397), _1733395), _1733399)) = c_List_Olist_ONil(_1733397))], (47324 ^ _780205) ^ [_1733451, _1733453] : [-(c_List_OtakeWhile(_1733451, _1733453, c_List_Olist_ONil(_1733451)) = c_List_Olist_ONil(_1733451))], (47326 ^ _780205) ^ [_1733484, _1733486, _1733488] : [-(c_List_OtakeWhile(_1733484, _1733486, _1733488) = hAPP(hAPP(c_List_Otake(_1733484), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733484)), c_List_OtakeWhile(_1733484, _1733486, _1733488))), _1733488))], (47328 ^ _780205) ^ [_1733534, _1733536, _1733538] : [hBOOL(hAPP(c_List_Odistinct(_1733534), _1733536)), -(hBOOL(hAPP(c_List_Odistinct(_1733534), c_List_OtakeWhile(_1733534, _1733538, _1733536))))], (47334 ^ _780205) ^ [_1733637] : [-(c_List_Oreturn__list(_1733637) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1733637))], (47336 ^ _780205) ^ [_1733665, _1733667, _1733669, _1733671, _1733673] : [hBOOL(hAPP(hAPP(c_member(_1733665), _1733667), hAPP(c_List_Oset(_1733665), _1733669))), -(hBOOL(hAPP(_1733671, _1733667))), -(c_List_OtakeWhile(_1733665, _1733671, hAPP(hAPP(c_List_Oappend(_1733665), _1733669), _1733673)) = c_List_OtakeWhile(_1733665, _1733671, _1733669))], (47346 ^ _780205) ^ [_1733823, _1733825, _1733827, _1733829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1733823), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733825)), c_List_OtakeWhile(_1733825, _1733827, _1733829)))), -(hAPP(hAPP(c_List_Onth(_1733825), c_List_OtakeWhile(_1733825, _1733827, _1733829)), _1733823) = hAPP(hAPP(c_List_Onth(_1733825), _1733829), _1733823))], (47352 ^ _780205) ^ [_1733976, _1733978, _1733980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733976)), c_List_OtakeWhile(_1733976, _1733978, _1733980))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733976)), _1733980))), hBOOL(hAPP(_1733978, hAPP(hAPP(c_List_Onth(_1733976), _1733980), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733976)), c_List_OtakeWhile(_1733976, _1733978, _1733980)))))], (47358 ^ _780205) ^ [_1734143, _1734145] : [-(_1734143 = c_List_Olist_ONil(_1734145)), hBOOL(hAPP(c_List_Odistinct(_1734145), _1734143)), -(c_List_OtakeWhile(_1734145, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1734145), c_fNot), hAPP(hAPP(c_COMBC(_1734145, _1734145, tc_HOL_Obool), c_fequal), c_List_Olast(_1734145, _1734143))), _1734143) = c_List_Obutlast(_1734145, _1734143))], (47368 ^ _780205) ^ [_1734340, _1734342, _1734344, _1734346, _1734348] : [class_Orderings_Olinorder(_1734340), c_List_Olinorder__class_Osorted(_1734340, hAPP(c_List_Orev(_1734340), hAPP(hAPP(c_List_Omap(_1734342, _1734340), _1734344), _1734346))), -(hAPP(c_List_Ofilter(_1734342, hAPP(hAPP(c_COMBB(_1734340, tc_HOL_Obool, _1734342), hAPP(c_Orderings_Oord__class_Oless(_1734340), _1734348)), _1734344)), _1734346) = c_List_OtakeWhile(_1734342, hAPP(hAPP(c_COMBB(_1734340, tc_HOL_Obool, _1734342), hAPP(c_Orderings_Oord__class_Oless(_1734340), _1734348)), _1734344), _1734346))], (47378 ^ _780205) ^ [_1734587] : [c_List_Onat__list(_1734587), -(c_List_Oembed__list(c_List_Oreturn__list(_1734587)) = _1734587)], (47384 ^ _780205) ^ [_1734668, _1734670] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1734668), _1734670) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1734668)), c_List_Oembed__list(_1734670))))], (47386 ^ _780205) ^ [_1734711] : [-(c_List_Oembed__list(_1734711) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1734711))], (47388 ^ _780205) ^ [_1734739, _1734741, _1734743] : [hBOOL(hAPP(c_List_Odistinct(_1734739), _1734741)), hBOOL(hAPP(hAPP(c_member(_1734739), _1734743), hAPP(c_List_Oset(_1734739), _1734741))), -(c_List_OtakeWhile(_1734739, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1734739), c_fNot), hAPP(hAPP(c_COMBC(_1734739, _1734739, tc_HOL_Obool), c_fequal), _1734743)), hAPP(c_List_Orev(_1734739), _1734741)) = hAPP(c_List_Orev(_1734739), hAPP(c_List_Otl(_1734739), c_List_OdropWhile(_1734739, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1734739), c_fNot), hAPP(hAPP(c_COMBC(_1734739, _1734739, tc_HOL_Obool), c_fequal), _1734743)), _1734741))))], (47398 ^ _780205) ^ [_1735030, _1735032, _1735034] : [hBOOL(hAPP(c_List_Odistinct(_1735030), _1735032)), hBOOL(hAPP(hAPP(c_member(_1735030), _1735034), hAPP(c_List_Oset(_1735030), _1735032))), -(c_List_OdropWhile(_1735030, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1735030), c_fNot), hAPP(hAPP(c_COMBC(_1735030, _1735030, tc_HOL_Obool), c_fequal), _1735034)), hAPP(c_List_Orev(_1735030), _1735032)) = hAPP(hAPP(c_List_Olist_OCons(_1735030), _1735034), hAPP(c_List_Orev(_1735030), c_List_OtakeWhile(_1735030, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1735030), c_fNot), hAPP(hAPP(c_COMBC(_1735030, _1735030, tc_HOL_Obool), c_fequal), _1735034)), _1735032))))], (47408 ^ _780205) ^ [_1735327, _1735329, _1735331] : [-(hAPP(hAPP(c_List_Oappend(_1735327), c_List_OtakeWhile(_1735327, _1735329, _1735331)), c_List_OdropWhile(_1735327, _1735329, _1735331)) = _1735331)], (47410 ^ _780205) ^ [_1735370, _1735372, _1735374] : [class_Orderings_Olinorder(_1735370), c_List_Olinorder__class_Osorted(_1735370, _1735372), -(c_List_Olinorder__class_Osorted(_1735370, c_List_OdropWhile(_1735370, _1735374, _1735372)))], (47420 ^ _780205) ^ [_1735509, _1735511, _1735513] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735509)), c_List_OdropWhile(_1735509, _1735511, _1735513))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735509)), _1735513))))], (47432 ^ _780205) ^ [_1735777, _1735779, _1735781] : [47434 ^ _780205 : [(47435 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735777), 47433 ^ [_1735777, _1735779, _1735781]), hAPP(c_List_Oset(_1735777), _1735781))))], (47437 ^ _780205) ^ [] : [hBOOL(hAPP(_1735779, 47433 ^ [_1735777, _1735779, _1735781]))]], -(c_List_OdropWhile(_1735777, _1735779, _1735781) = c_List_Olist_ONil(_1735777))], (47422 ^ _780205) ^ [_1735577, _1735579, _1735581] : [c_List_OdropWhile(_1735577, _1735579, _1735581) = c_List_Olist_ONil(_1735577), 47425 ^ _780205 : [(47426 ^ _780205) ^ [_1735668] : [hBOOL(hAPP(hAPP(c_member(_1735577), _1735668), hAPP(c_List_Oset(_1735577), _1735581))), -(hBOOL(hAPP(_1735579, _1735668)))]]], (47441 ^ _780205) ^ [_1735984, _1735986, _1735988, _1735990] : [hBOOL(hAPP(_1735984, _1735986)), -(c_List_OdropWhile(_1735988, _1735984, hAPP(hAPP(c_List_Olist_OCons(_1735988), _1735986), _1735990)) = c_List_OdropWhile(_1735988, _1735984, _1735990))], (47447 ^ _780205) ^ [_1736095, _1736097, _1736099, _1736101] : [-(hBOOL(hAPP(_1736095, _1736097))), -(c_List_OdropWhile(_1736099, _1736095, hAPP(hAPP(c_List_Olist_OCons(_1736099), _1736097), _1736101)) = hAPP(hAPP(c_List_Olist_OCons(_1736099), _1736097), _1736101))], (47453 ^ _780205) ^ [_1736159, _1736161] : [-(c_List_OdropWhile(_1736159, _1736161, c_List_Olist_ONil(_1736159)) = c_List_Olist_ONil(_1736159))], (47455 ^ _780205) ^ [_1736192, _1736194, _1736196] : [hBOOL(hAPP(c_List_Odistinct(_1736192), _1736194)), -(hBOOL(hAPP(c_List_Odistinct(_1736192), c_List_OdropWhile(_1736192, _1736196, _1736194))))], (47461 ^ _780205) ^ [_1736294, _1736296, _1736298] : [-(c_List_OdropWhile(_1736294, _1736296, _1736298) = c_List_Olist_ONil(_1736294)), hBOOL(hAPP(_1736296, hAPP(c_List_Ohd(_1736294), c_List_OdropWhile(_1736294, _1736296, _1736298))))], (47467 ^ _780205) ^ [_1736400, _1736402, _1736404, _1736406, _1736408] : [-(c_List_OdropWhile(_1736400, _1736402, hAPP(hAPP(c_List_Omap(_1736404, _1736400), _1736406), _1736408)) = hAPP(hAPP(c_List_Omap(_1736404, _1736400), _1736406), c_List_OdropWhile(_1736404, hAPP(c_Fun_Ocomp(_1736400, tc_HOL_Obool, _1736404, _1736402), _1736406), _1736408)))], (47469 ^ _780205) ^ [_1736465, _1736467, _1736469, _1736471, _1736473] : [hBOOL(hAPP(hAPP(c_member(_1736465), _1736467), hAPP(c_List_Oset(_1736465), _1736469))), -(hBOOL(hAPP(_1736471, _1736467))), -(c_List_OdropWhile(_1736465, _1736471, hAPP(hAPP(c_List_Oappend(_1736465), _1736469), _1736473)) = hAPP(hAPP(c_List_Oappend(_1736465), c_List_OdropWhile(_1736465, _1736471, _1736469)), _1736473))], (47479 ^ _780205) ^ [_1736663, _1736665, _1736667, _1736669, _1736671] : [c_List_OdropWhile(_1736663, _1736665, _1736667) = hAPP(hAPP(c_List_Olist_OCons(_1736663), _1736669), _1736671), 47482 ^ _780205 : [(47483 ^ _780205) ^ [] : [-(_1736667 = hAPP(hAPP(c_List_Oappend(_1736663), c_List_OtakeWhile(_1736663, _1736665, _1736667)), hAPP(hAPP(c_List_Olist_OCons(_1736663), _1736669), _1736671)))], (47485 ^ _780205) ^ [] : [hBOOL(hAPP(_1736665, _1736669))]]], (47487 ^ _780205) ^ [_1736844, _1736846, _1736848, _1736850, _1736852] : [-(c_List_OdropWhile(_1736844, _1736846, _1736848) = hAPP(hAPP(c_List_Olist_OCons(_1736844), _1736850), _1736852)), _1736848 = hAPP(hAPP(c_List_Oappend(_1736844), c_List_OtakeWhile(_1736844, _1736846, _1736848)), hAPP(hAPP(c_List_Olist_OCons(_1736844), _1736850), _1736852)), -(hBOOL(hAPP(_1736846, _1736850)))], (47497 ^ _780205) ^ [_1737058, _1737060, _1737062] : [-(c_List_OdropWhile(_1737058, _1737060, _1737062) = hAPP(hAPP(c_List_Odrop(_1737058), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737058)), c_List_OtakeWhile(_1737058, _1737060, _1737062))), _1737062))], (47499 ^ _780205) ^ [_1737108, _1737110, _1737112, _1737114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737108), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737110)), c_List_OdropWhile(_1737110, _1737112, _1737114)))), -(hAPP(hAPP(c_List_Onth(_1737110), c_List_OdropWhile(_1737110, _1737112, _1737114)), _1737108) = hAPP(hAPP(c_List_Onth(_1737110), _1737114), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737108), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737110)), c_List_OtakeWhile(_1737110, _1737112, _1737114)))))], (47505 ^ _780205) ^ [_1737295, _1737297, _1737299, _1737301, _1737303] : [class_Groups_Omonoid__add(_1737295), 47511 ^ _780205 : [(47512 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737297), 47510 ^ [_1737295, _1737297, _1737299, _1737301, _1737303]), hAPP(c_List_Oset(_1737297), _1737299))))], (47514 ^ _780205) ^ [] : [hBOOL(hAPP(_1737301, 47510 ^ [_1737295, _1737297, _1737299, _1737301, _1737303]))], (47516 ^ _780205) ^ [] : [hAPP(_1737303, 47510 ^ [_1737295, _1737297, _1737299, _1737301, _1737303]) = c_Groups_Ozero__class_Ozero(_1737295)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1737295), hAPP(hAPP(c_List_Omap(_1737297, _1737295), _1737303), hAPP(c_List_Ofilter(_1737297, _1737301), _1737299))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1737295), hAPP(hAPP(c_List_Omap(_1737297, _1737295), _1737303), _1737299)))], (47520 ^ _780205) ^ [_1737686, _1737688] : [class_Orderings_Olinorder(_1737686), 47527 ^ _780205 : [(47528 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47525 ^ [_1737686, _1737688]), 47526 ^ [_1737686, _1737688])))], (47530 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47526 ^ [_1737686, _1737688]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737686)), _1737688))))], (47532 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1737686), hAPP(hAPP(c_List_Onth(_1737686), _1737688), 47525 ^ [_1737686, _1737688])), hAPP(hAPP(c_List_Onth(_1737686), _1737688), 47526 ^ [_1737686, _1737688])))]], -(c_List_Olinorder__class_Osorted(_1737686, _1737688))], (47536 ^ _780205) ^ [_1738057, _1738059, _1738061] : [47538 ^ _780205 : [(47539 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738057), 47537 ^ [_1738057, _1738059, _1738061]), hAPP(c_List_Oset(_1738057), c_List_OdropWhile(_1738057, _1738059, _1738061)))))], (47541 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1738059, 47537 ^ [_1738057, _1738059, _1738061])))]], -(c_List_OtakeWhile(_1738057, _1738059, _1738061) = hAPP(c_List_Ofilter(_1738057, _1738059), _1738061))], (47545 ^ _780205) ^ [_1738178, _1738180, _1738182, _1738184] : [47547 ^ _780205 : [(47548 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47546 ^ [_1738178, _1738180, _1738182, _1738184]), _1738178)))], (47550 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47546 ^ [_1738178, _1738180, _1738182, _1738184]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738180)), _1738182))))], (47552 ^ _780205) ^ [] : [hBOOL(hAPP(_1738184, hAPP(hAPP(c_List_Onth(_1738180), _1738182), 47546 ^ [_1738178, _1738180, _1738182, _1738184])))]], 47555 ^ _780205 : [(47556 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738178), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738180)), _1738182))))], (47558 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1738184, hAPP(hAPP(c_List_Onth(_1738180), _1738182), _1738178))))]], -(c_List_OtakeWhile(_1738180, _1738184, _1738182) = hAPP(hAPP(c_List_Otake(_1738180), _1738178), _1738182))], (47562 ^ _780205) ^ [_1738582, _1738584, _1738586, _1738588] : [47564 ^ _780205 : [(47565 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47563 ^ [_1738582, _1738584, _1738586, _1738588]), _1738582)))], (47567 ^ _780205) ^ [] : [hBOOL(hAPP(_1738584, hAPP(hAPP(c_List_Onth(_1738586), _1738588), 47563 ^ [_1738582, _1738584, _1738586, _1738588])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1738582), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738586)), _1738588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1738582), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738586)), c_List_OtakeWhile(_1738586, _1738584, _1738588)))))], (47575 ^ _780205) ^ [_1738890, _1738892] : [class_Orderings_Olinorder(_1738890), 47578 ^ _780205 : [(47579 ^ _780205) ^ [] : [c_List_Olinorder__class_Osorted(_1738890, _1738892), -(_1738892 = c_List_Olist_ONil(_1738890)), 47588 ^ _780205 : [(47589 ^ _780205) ^ [] : [-(_1738892 = hAPP(hAPP(c_List_Olist_OCons(_1738890), 47587 ^ [_1738890, _1738892]), 47586 ^ [_1738890, _1738892]))], (47597 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1738890, 47586 ^ [_1738890, _1738892]))], (47591 ^ _780205) ^ [_1739224] : [hBOOL(hAPP(hAPP(c_member(_1738890), _1739224), hAPP(c_List_Oset(_1738890), 47586 ^ [_1738890, _1738892]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1738890), 47587 ^ [_1738890, _1738892]), _1739224)))]]], (47599 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1738890, _1738892)), 47600 ^ _780205 : [(47601 ^ _780205) ^ [] : [_1738892 = c_List_Olist_ONil(_1738890)], (47603 ^ _780205) ^ [_1739450, _1739452] : [_1738892 = hAPP(hAPP(c_List_Olist_OCons(_1738890), _1739450), _1739452), 47609 ^ _780205 : [(47610 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738890), 47608 ^ [_1738890, _1738892, _1739450, _1739452]), hAPP(c_List_Oset(_1738890), _1739452))))], (47612 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1738890), _1739450), 47608 ^ [_1738890, _1738892, _1739450, _1739452]))]], c_List_Olinorder__class_Osorted(_1738890, _1739452)]]]]], (47618 ^ _780205) ^ [_1739771, _1739773, _1739775] : [hBOOL(hAPP(hAPP(c_member(_1739771), _1739773), hAPP(c_List_Oset(_1739771), _1739775))), -(c_List_Oinsert(_1739771, _1739773, _1739775) = _1739775)], (47624 ^ _780205) ^ [_1739876, _1739878, _1739880] : [-(hBOOL(hAPP(hAPP(c_member(_1739876), _1739878), hAPP(c_List_Oset(_1739876), _1739880)))), -(c_List_Oinsert(_1739876, _1739878, _1739880) = hAPP(hAPP(c_List_Olist_OCons(_1739876), _1739878), _1739880))], (47630 ^ _780205) ^ [_1739936, _1739938, _1739940] : [-(hBOOL(hAPP(hAPP(c_member(_1739936), _1739938), hAPP(c_List_Oset(_1739936), _1739940)))), -(c_List_Oinsert(_1739936, _1739938, _1739940) = hAPP(hAPP(c_List_Olist_OCons(_1739936), _1739938), _1739940))], (47636 ^ _780205) ^ [_1739998, _1740000, _1740002] : [-(c_List_Oinsert(_1739998, _1740000, c_List_Oremdups(_1739998, _1740002)) = c_List_Oremdups(_1739998, c_List_Oinsert(_1739998, _1740000, _1740002)))], (47638 ^ _780205) ^ [_1740039, _1740041, _1740043] : [hBOOL(hAPP(c_List_Odistinct(_1740039), _1740041)), -(hBOOL(hAPP(c_List_Odistinct(_1740039), c_List_Oinsert(_1740039, _1740043, _1740041))))], (47644 ^ _780205) ^ [_1740142, _1740144, _1740146] : [hBOOL(hAPP(hAPP(c_member(_1740142), _1740144), hAPP(c_List_Oset(_1740142), _1740146))), -(c_List_Oinsert(_1740142, _1740144, _1740146) = _1740146)], (47650 ^ _780205) ^ [_1740253, _1740255, _1740257] : [-(hAPP(c_List_Oset(_1740253), c_List_Oinsert(_1740253, _1740255, _1740257)) = hAPP(hAPP(c_Set_Oinsert(_1740253), _1740255), hAPP(c_List_Oset(_1740253), _1740257)))], (47652 ^ _780205) ^ [_1740302, _1740304] : [-(c_List_Oinsert(_1740302, _1740304, c_List_Olist_ONil(_1740302)) = hAPP(hAPP(c_List_Olist_OCons(_1740302), _1740304), c_List_Olist_ONil(_1740302)))], (47654 ^ _780205) ^ [_1740343, _1740345, _1740347, _1740349] : [-(c_List_Omaps(_1740343, _1740345, _1740347, _1740349) = c_List_Oconcat(_1740345, hAPP(hAPP(c_List_Omap(_1740343, tc_List_Olist(_1740345)), _1740347), _1740349)))], (47656 ^ _780205) ^ [_1740391, _1740393, _1740395, _1740397] : [-(c_List_Oconcat(_1740391, hAPP(hAPP(c_List_Omap(_1740393, tc_List_Olist(_1740391)), _1740395), _1740397)) = c_List_Omaps(_1740393, _1740391, _1740395, _1740397))], (47658 ^ _780205) ^ [_1740439, _1740441, _1740443] : [-(c_List_Omaps(_1740439, _1740441, _1740443, c_List_Olist_ONil(_1740439)) = c_List_Olist_ONil(_1740441))], (47660 ^ _780205) ^ [_1740475, _1740477, _1740479, _1740481, _1740483] : [-(c_List_Omaps(_1740475, _1740477, _1740479, hAPP(hAPP(c_List_Olist_OCons(_1740475), _1740481), _1740483)) = hAPP(hAPP(c_List_Oappend(_1740477), hAPP(_1740479, _1740481)), c_List_Omaps(_1740475, _1740477, _1740479, _1740483)))], (47662 ^ _780205) ^ [_1740535, _1740537] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1740535)), _1740537)), 47668 ^ _780205 : [(47669 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1740535)), 47667 ^ [_1740535, _1740537]), hAPP(c_List_Oset(tc_List_Olist(_1740535)), _1740537))))], (47671 ^ _780205) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1740535), 47667 ^ [_1740535, _1740537]))]], 47675 ^ _780205 : [(47676 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1740535)), 47674 ^ [_1740535, _1740537]), hAPP(c_List_Oset(tc_List_Olist(_1740535)), _1740537))))], (47679 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1740535)), 47677 ^ [_1740535, _1740537]), hAPP(c_List_Oset(tc_List_Olist(_1740535)), _1740537))))], (47681 ^ _780205) ^ [] : [47674 ^ [_1740535, _1740537] = 47677 ^ [_1740535, _1740537]], (47683 ^ _780205) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1740535, tc_HOL_Obool)), hAPP(c_List_Oset(_1740535), 47674 ^ [_1740535, _1740537])), hAPP(c_List_Oset(_1740535), 47677 ^ [_1740535, _1740537])) = c_Orderings_Obot__class_Obot(tc_fun(_1740535, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1740535), c_List_Oconcat(_1740535, _1740537))))], (47687 ^ _780205) ^ [_1741252, _1741254, _1741256, _1741258, _1741260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1741252, _1741254)), hAPP(_1741252, _1741256))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1741258, _1741258)), hAPP(hAPP(c_Product__Type_OPair(_1741258, _1741258), _1741254), _1741256)), c_List_Omeasures(_1741258, _1741260))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1741258, _1741258)), hAPP(hAPP(c_Product__Type_OPair(_1741258, _1741258), _1741254), _1741256)), c_List_Omeasures(_1741258, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1741258, tc_Nat_Onat)), _1741252), _1741260)))))], (47697 ^ _780205) ^ [_1741525, _1741527] : [-(c_Wellfounded_Owf(_1741525, c_List_Omeasures(_1741525, _1741527)))], (47699 ^ _780205) ^ [_1741568, _1741570, _1741572] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1741568, _1741568)), hAPP(hAPP(c_Product__Type_OPair(_1741568, _1741568), _1741570), _1741572)), c_List_Omeasures(_1741568, c_List_Olist_ONil(tc_fun(_1741568, tc_Nat_Onat)))))], (47701 ^ _780205) ^ [_1741622, _1741624] : [-(c_List_Omeasures(_1741622, _1741624) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1741622), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1741622, tc_List_Olist(tc_fun(_1741622, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1741622, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1741622, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1741622), c_List_Omap(tc_fun(_1741622, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1741622, tc_Nat_Onat), _1741622, tc_Nat_Onat), c_COMBI(tc_fun(_1741622, tc_Nat_Onat))))), _1741624)))], (47703 ^ _780205) ^ [_1741719, _1741721, _1741723, _1741725, _1741727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1741719, _1741721)), hAPP(_1741719, _1741723))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1741725, _1741725)), hAPP(hAPP(c_Product__Type_OPair(_1741725, _1741725), _1741721), _1741723)), c_List_Omeasures(_1741725, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1741725, tc_Nat_Onat)), _1741719), _1741727)))))], (47709 ^ _780205) ^ [_1741914, _1741916, _1741918, _1741920, _1741922] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1741914, _1741914)), hAPP(hAPP(c_Product__Type_OPair(_1741914, _1741914), _1741916), _1741918)), c_List_Omeasures(_1741914, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1741914, tc_Nat_Onat)), _1741920), _1741922)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1741920, _1741916)), hAPP(_1741920, _1741918)))), 47716 ^ _780205 : [(47717 ^ _780205) ^ [] : [-(hAPP(_1741920, _1741916) = hAPP(_1741920, _1741918))], (47719 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1741914, _1741914)), hAPP(hAPP(c_Product__Type_OPair(_1741914, _1741914), _1741916), _1741918)), c_List_Omeasures(_1741914, _1741922))))]]], (47721 ^ _780205) ^ [_1742193, _1742195, _1742197, _1742199, _1742201] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1742193, _1742193)), hAPP(hAPP(c_Product__Type_OPair(_1742193, _1742193), _1742195), _1742197)), c_List_Omeasures(_1742193, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1742193, tc_Nat_Onat)), _1742199), _1742201))))), 47722 ^ _780205 : [(47723 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1742199, _1742195)), hAPP(_1742199, _1742197)))], (47725 ^ _780205) ^ [] : [hAPP(_1742199, _1742195) = hAPP(_1742199, _1742197), hBOOL(hAPP(hAPP(c_member(tc_prod(_1742193, _1742193)), hAPP(hAPP(c_Product__Type_OPair(_1742193, _1742193), _1742195), _1742197)), c_List_Omeasures(_1742193, _1742201)))]]], (47733 ^ _780205) ^ [_1742516, _1742518, _1742520, _1742522, _1742524, _1742526, _1742528, _1742530] : [47735 ^ _780205 : [(47736 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742516), 47734 ^ [_1742516, _1742518, _1742520, _1742522, _1742524, _1742526, _1742528, _1742530]), hAPP(c_List_Oset(_1742516), _1742518))))], (47738 ^ _780205) ^ [] : [hAPP(c_Fun_Ocomp(_1742520, _1742520, _1742522, hAPP(_1742524, 47734 ^ [_1742516, _1742518, _1742520, _1742522, _1742524, _1742526, _1742528, _1742530])), _1742526) = hAPP(c_Fun_Ocomp(_1742522, _1742520, _1742522, _1742526), hAPP(_1742528, 47734 ^ [_1742516, _1742518, _1742520, _1742522, _1742524, _1742526, _1742528, _1742530]))]], -(hAPP(c_List_Ofoldl(_1742520, _1742516, hAPP(c_COMBC(_1742516, _1742520, _1742520), _1742524), hAPP(_1742526, _1742530)), _1742518) = hAPP(_1742526, hAPP(c_List_Ofoldl(_1742522, _1742516, hAPP(c_COMBC(_1742516, _1742522, _1742522), _1742528), _1742530), _1742518)))], (47742 ^ _780205) ^ [_1742885, _1742887, _1742889, _1742891] : [class_Orderings_Oorder(_1742885), class_Enum_Oenum(_1742887), 47749 ^ _780205 : [(47750 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1742887, _1742885)), _1742889), _1742891)), 47753 ^ _780205 : [(47754 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1742887, _1742885)), _1742889), _1742891)))], (47756 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1742887), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1742887), c_fNot), hAPP(hAPP(c_COMBS(_1742887, _1742885, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1742885, tc_fun(_1742885, tc_HOL_Obool), _1742887), c_fequal), _1742889)), _1742891)))))]]], (47758 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1742887, _1742885)), _1742889), _1742891))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1742887, _1742885)), _1742889), _1742891)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1742887), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1742887), c_fNot), hAPP(hAPP(c_COMBS(_1742887, _1742885, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1742885, tc_fun(_1742885, tc_HOL_Obool), _1742887), c_fequal), _1742889)), _1742891))))]]], (47768 ^ _780205) ^ [_1743405, _1743407, _1743409] : [class_Enum_Oenum(_1743405), class_Enum_Oenum(_1743407), 47775 ^ _780205 : [(47776 ^ _780205) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1743407, _1743405)), _1743409)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1743407), hAPP(hAPP(c_COMBB(tc_fun(_1743405, tc_HOL_Obool), tc_HOL_Obool, _1743407), c_Enum_Oenum__class_Oenum__ex(_1743405)), hAPP(hAPP(c_COMBB(tc_fun(_1743405, tc_prod(_1743407, _1743405)), tc_fun(_1743405, tc_HOL_Obool), _1743407), hAPP(c_COMBB(tc_prod(_1743407, _1743405), tc_HOL_Obool, _1743405), _1743409)), c_Product__Type_OPair(_1743407, _1743405))))))], (47782 ^ _780205) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1743407), hAPP(hAPP(c_COMBB(tc_fun(_1743405, tc_HOL_Obool), tc_HOL_Obool, _1743407), c_Enum_Oenum__class_Oenum__ex(_1743405)), hAPP(hAPP(c_COMBB(tc_fun(_1743405, tc_prod(_1743407, _1743405)), tc_fun(_1743405, tc_HOL_Obool), _1743407), hAPP(c_COMBB(tc_prod(_1743407, _1743405), tc_HOL_Obool, _1743405), _1743409)), c_Product__Type_OPair(_1743407, _1743405))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1743407, _1743405)), _1743409)))]]], (47788 ^ _780205) ^ [_1743844, _1743846] : [class_Enum_Oenum(_1743844), 47791 ^ _780205 : [(47792 ^ _780205) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1743844), _1743846)), -(hBOOL(hAPP(_1743846, 47795 ^ [_1743844, _1743846])))], (47799 ^ _780205) ^ [] : [47800 ^ _780205 : [(47801 ^ _780205) ^ [_1744024] : [hBOOL(hAPP(_1743846, _1744024))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1743844), _1743846)))]]], (47805 ^ _780205) ^ [_1744087, _1744089] : [class_Enum_Oenum(_1744087), 47808 ^ _780205 : [(47809 ^ _780205) ^ [] : [47810 ^ _780205 : [(47811 ^ _780205) ^ [_1744189] : [hBOOL(hAPP(_1744089, _1744189))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1744087), _1744089)))], (47815 ^ _780205) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1744087), _1744089)), -(hBOOL(hAPP(_1744089, 47818 ^ [_1744087, _1744089])))]]], (47822 ^ _780205) ^ [_1744330, _1744332, _1744334, _1744336, _1744338] : [47823 ^ _780205 : [(47824 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744330)), hAPP(hAPP(c_List_Otake(_1744330), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744330)), _1744332)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744334)), _1744336))), _1744332)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744334)), hAPP(hAPP(c_List_Otake(_1744334), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744330)), _1744332)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744334)), _1744336))), _1744336)))], (47826 ^ _780205) ^ [] : [hBOOL(hAPP(_1744338, hAPP(hAPP(c_List_Ozip(_1744330, _1744334), hAPP(hAPP(c_List_Otake(_1744330), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744330)), _1744332)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744334)), _1744336))), _1744332)), hAPP(hAPP(c_List_Otake(_1744334), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744330)), _1744332)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744334)), _1744336))), _1744336))))]], -(hBOOL(hAPP(_1744338, hAPP(hAPP(c_List_Ozip(_1744330, _1744334), _1744332), _1744336))))], (47830 ^ _780205) ^ [_1744742, _1744744, _1744746, _1744748] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1744742, _1744744, _1744746, _1744748) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1744742, _1744744), _1744746), _1744748)))], (47832 ^ _780205) ^ [_1744787, _1744789, _1744791, _1744793] : [47834 ^ _780205 : [(47835 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744787), 47833 ^ [_1744787, _1744789, _1744791, _1744793]), hAPP(c_List_Oset(_1744787), _1744789))))], (47837 ^ _780205) ^ [] : [hBOOL(hAPP(_1744791, 47833 ^ [_1744787, _1744789, _1744791, _1744793]))]], -(c_List_OdropWhile(_1744787, _1744791, hAPP(hAPP(c_List_Oappend(_1744787), _1744789), _1744793)) = c_List_OdropWhile(_1744787, _1744791, _1744793))], (47841 ^ _780205) ^ [_1745005, _1745007, _1745009, _1745011, _1745013] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745005)), _1745007) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745009)), _1745011), 47847 ^ _780205 : [(47848 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47846 ^ [_1745005, _1745007, _1745009, _1745011, _1745013]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745005)), _1745007))))], (47850 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1745013, hAPP(hAPP(c_List_Onth(_1745005), _1745007), 47846 ^ [_1745005, _1745007, _1745009, _1745011, _1745013])), hAPP(hAPP(c_List_Onth(_1745009), _1745011), 47846 ^ [_1745005, _1745007, _1745009, _1745011, _1745013])))]], -(c_List_Olist__all2(_1745005, _1745009, _1745013, _1745007, _1745011))], (47854 ^ _780205) ^ [_1745363, _1745365] : [class_Orderings_Olinorder(_1745363), hBOOL(hAPP(c_Finite__Set_Ofinite(_1745363), _1745365)), 47862 ^ _780205 : [(47863 ^ _780205) ^ [] : [-(hAPP(c_List_Oset(_1745363), 47861 ^ [_1745363, _1745365]) = _1745365)], (47865 ^ _780205) ^ [] : [-(c_List_Olinorder__class_Osorted(_1745363, 47861 ^ [_1745363, _1745365]))], (47867 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1745363), 47861 ^ [_1745363, _1745365])))], (47869 ^ _780205) ^ [_1745689] : [-(_1745689 = 47861 ^ [_1745363, _1745365]), hAPP(c_List_Oset(_1745363), _1745689) = _1745365, c_List_Olinorder__class_Osorted(_1745363, _1745689), hBOOL(hAPP(c_List_Odistinct(_1745363), _1745689))]]], (47883 ^ _780205) ^ [_1745920, _1745922, _1745924, _1745926] : [47885 ^ _780205 : [(47886 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745920), 47884 ^ [_1745920, _1745922, _1745924, _1745926]), hAPP(c_List_Oset(_1745920), _1745922))))], (47888 ^ _780205) ^ [] : [hBOOL(hAPP(_1745924, 47884 ^ [_1745920, _1745922, _1745924, _1745926]))]], -(c_List_OtakeWhile(_1745920, _1745924, hAPP(hAPP(c_List_Oappend(_1745920), _1745922), _1745926)) = hAPP(hAPP(c_List_Oappend(_1745920), _1745922), c_List_OtakeWhile(_1745920, _1745924, _1745926)))], (47892 ^ _780205) ^ [_1746154, _1746156, _1746158, _1746160, _1746162] : [class_Orderings_Olinorder(_1746154), 47898 ^ _780205 : [(47899 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1746156), 47897 ^ [_1746154, _1746156, _1746158, _1746160, _1746162]), hAPP(c_List_Oset(_1746156), _1746158))))], (47901 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746154), hAPP(_1746160, _1746162)), hAPP(_1746160, 47897 ^ [_1746154, _1746156, _1746158, _1746160, _1746162])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1746156, _1746154, _1746160), _1746162), _1746158) = hAPP(hAPP(c_List_Olist_OCons(_1746156), _1746162), _1746158))], (47905 ^ _780205) ^ [_1746497, _1746499, _1746501, _1746503, _1746505] : [hAPP(hAPP(c_List_Olist_OCons(_1746497), _1746499), _1746501) = hAPP(c_List_Ofilter(_1746497, _1746503), _1746505), 47910 ^ _780205 : [(47911 ^ _780205) ^ [] : [-(_1746505 = hAPP(hAPP(c_List_Oappend(_1746497), 47908 ^ [_1746497, _1746499, _1746501, _1746503, _1746505]), hAPP(hAPP(c_List_Olist_OCons(_1746497), _1746499), 47909 ^ [_1746497, _1746499, _1746501, _1746503, _1746505])))], (47919 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1746503, _1746499)))], (47921 ^ _780205) ^ [] : [-(_1746501 = hAPP(c_List_Ofilter(_1746497, _1746503), 47909 ^ [_1746497, _1746499, _1746501, _1746503, _1746505]))], (47913 ^ _780205) ^ [_1746811] : [hBOOL(hAPP(hAPP(c_member(_1746497), _1746811), hAPP(c_List_Oset(_1746497), 47908 ^ [_1746497, _1746499, _1746501, _1746503, _1746505]))), hBOOL(hAPP(_1746503, _1746811))]]], (47923 ^ _780205) ^ [_1747015, _1747017, _1747019, _1747021, _1747023] : [-(hAPP(hAPP(c_List_Olist_OCons(_1747015), _1747017), _1747019) = hAPP(c_List_Ofilter(_1747015, _1747021), _1747023)), 47924 ^ _780205 : [(47925 ^ _780205) ^ [_1747143, _1747145] : [_1747023 = hAPP(hAPP(c_List_Oappend(_1747015), _1747145), hAPP(hAPP(c_List_Olist_OCons(_1747015), _1747017), _1747143)), 47931 ^ _780205 : [(47932 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747015), 47930 ^ [_1747015, _1747017, _1747019, _1747021, _1747023, _1747143, _1747145]), hAPP(c_List_Oset(_1747015), _1747145))))], (47934 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1747021, 47930 ^ [_1747015, _1747017, _1747019, _1747021, _1747023, _1747143, _1747145])))]], hBOOL(hAPP(_1747021, _1747017)), _1747019 = hAPP(c_List_Ofilter(_1747015, _1747021), _1747143)]]], (47944 ^ _780205) ^ [_1747565, _1747567, _1747569, _1747571, _1747573] : [hAPP(c_List_Ofilter(_1747565, _1747567), _1747569) = hAPP(hAPP(c_List_Olist_OCons(_1747565), _1747571), _1747573), 47949 ^ _780205 : [(47950 ^ _780205) ^ [] : [-(_1747569 = hAPP(hAPP(c_List_Oappend(_1747565), 47947 ^ [_1747565, _1747567, _1747569, _1747571, _1747573]), hAPP(hAPP(c_List_Olist_OCons(_1747565), _1747571), 47948 ^ [_1747565, _1747567, _1747569, _1747571, _1747573])))], (47958 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1747567, _1747571)))], (47960 ^ _780205) ^ [] : [-(_1747573 = hAPP(c_List_Ofilter(_1747565, _1747567), 47948 ^ [_1747565, _1747567, _1747569, _1747571, _1747573]))], (47952 ^ _780205) ^ [_1747879] : [hBOOL(hAPP(hAPP(c_member(_1747565), _1747879), hAPP(c_List_Oset(_1747565), 47947 ^ [_1747565, _1747567, _1747569, _1747571, _1747573]))), hBOOL(hAPP(_1747567, _1747879))]]], (47962 ^ _780205) ^ [_1748083, _1748085, _1748087, _1748089, _1748091] : [-(hAPP(c_List_Ofilter(_1748083, _1748085), _1748087) = hAPP(hAPP(c_List_Olist_OCons(_1748083), _1748089), _1748091)), 47963 ^ _780205 : [(47964 ^ _780205) ^ [_1748211, _1748213] : [_1748087 = hAPP(hAPP(c_List_Oappend(_1748083), _1748213), hAPP(hAPP(c_List_Olist_OCons(_1748083), _1748089), _1748211)), 47970 ^ _780205 : [(47971 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748083), 47969 ^ [_1748083, _1748085, _1748087, _1748089, _1748091, _1748211, _1748213]), hAPP(c_List_Oset(_1748083), _1748213))))], (47973 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1748085, 47969 ^ [_1748083, _1748085, _1748087, _1748089, _1748091, _1748211, _1748213])))]], hBOOL(hAPP(_1748085, _1748089)), _1748091 = hAPP(c_List_Ofilter(_1748083, _1748085), _1748211)]]], (47983 ^ _780205) ^ [_1748609, _1748611, _1748613, _1748615] : [class_Orderings_Oorder(_1748609), class_Enum_Oenum(_1748611), 47990 ^ _780205 : [(47991 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1748611, _1748609)), _1748613), _1748615)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1748611), hAPP(hAPP(c_COMBS(_1748611, _1748609, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1748609, tc_fun(_1748609, tc_HOL_Obool), _1748611), c_Orderings_Oord__class_Oless__eq(_1748609)), _1748613)), _1748615))))], (47997 ^ _780205) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1748611), hAPP(hAPP(c_COMBS(_1748611, _1748609, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1748609, tc_fun(_1748609, tc_HOL_Obool), _1748611), c_Orderings_Oord__class_Oless__eq(_1748609)), _1748613)), _1748615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1748611, _1748609)), _1748613), _1748615)))]]], (48003 ^ _780205) ^ [_1748999, _1749001] : [class_Enum_Oenum(_1748999), 48006 ^ _780205 : [(48007 ^ _780205) ^ [] : [hBOOL(hAPP(_1749001, 48008 ^ [_1748999, _1749001])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1748999), _1749001)))], (48014 ^ _780205) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1748999), _1749001)), 48017 ^ _780205 : [(48018 ^ _780205) ^ [_1749217] : [-(hBOOL(hAPP(_1749001, _1749217)))]]]]], (48020 ^ _780205) ^ [_1749252, _1749254] : [class_Enum_Oenum(_1749252), 48023 ^ _780205 : [(48024 ^ _780205) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1749252), _1749254)), 48027 ^ _780205 : [(48028 ^ _780205) ^ [_1749378] : [-(hBOOL(hAPP(_1749254, _1749378)))]]], (48030 ^ _780205) ^ [] : [hBOOL(hAPP(_1749254, 48031 ^ [_1749252, _1749254])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1749252), _1749254)))]]], (48037 ^ _780205) ^ [_1749505, _1749507, _1749509] : [class_Enum_Oenum(_1749505), class_Enum_Oenum(_1749507), 48044 ^ _780205 : [(48045 ^ _780205) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1749507, _1749505)), _1749509)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1749507), hAPP(hAPP(c_COMBB(tc_fun(_1749505, tc_HOL_Obool), tc_HOL_Obool, _1749507), c_Enum_Oenum__class_Oenum__all(_1749505)), hAPP(hAPP(c_COMBB(tc_fun(_1749505, tc_prod(_1749507, _1749505)), tc_fun(_1749505, tc_HOL_Obool), _1749507), hAPP(c_COMBB(tc_prod(_1749507, _1749505), tc_HOL_Obool, _1749505), _1749509)), c_Product__Type_OPair(_1749507, _1749505))))))], (48051 ^ _780205) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1749507), hAPP(hAPP(c_COMBB(tc_fun(_1749505, tc_HOL_Obool), tc_HOL_Obool, _1749507), c_Enum_Oenum__class_Oenum__all(_1749505)), hAPP(hAPP(c_COMBB(tc_fun(_1749505, tc_prod(_1749507, _1749505)), tc_fun(_1749505, tc_HOL_Obool), _1749507), hAPP(c_COMBB(tc_prod(_1749507, _1749505), tc_HOL_Obool, _1749505), _1749509)), c_Product__Type_OPair(_1749507, _1749505))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1749507, _1749505)), _1749509)))]]], (48057 ^ _780205) ^ [_1749944, _1749946, _1749948, _1749950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749944), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749946)), _1749948))), 48063 ^ _780205 : [(48064 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1749946), 48062 ^ [_1749944, _1749946, _1749948, _1749950]), hAPP(c_List_Oset(_1749946), _1749948))))], (48066 ^ _780205) ^ [] : [hBOOL(hAPP(_1749950, 48062 ^ [_1749944, _1749946, _1749948, _1749950]))]], -(hBOOL(hAPP(_1749950, hAPP(hAPP(c_List_Onth(_1749946), _1749948), _1749944))))], (48070 ^ _780205) ^ [_1750230, _1750232, _1750234] : [class_Orderings_Olinorder(_1750230), 48076 ^ _780205 : [(48077 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750230), 48075 ^ [_1750230, _1750232, _1750234]), hAPP(c_List_Oset(_1750230), _1750232))))], (48079 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1750230), _1750234), 48075 ^ [_1750230, _1750232, _1750234]))]], c_List_Olinorder__class_Osorted(_1750230, _1750232), -(c_List_Olinorder__class_Osorted(_1750230, hAPP(hAPP(c_List_Olist_OCons(_1750230), _1750234), _1750232)))], (48087 ^ _780205) ^ [_1750564, _1750566, _1750568] : [c_List_Olist__ex(_1750564, _1750566, _1750568), 48091 ^ _780205 : [(48092 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48090 ^ [_1750564, _1750566, _1750568]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750564)), _1750568))))], (48094 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1750566, hAPP(hAPP(c_List_Onth(_1750564), _1750568), 48090 ^ [_1750564, _1750566, _1750568]))))]]], (48096 ^ _780205) ^ [_1750734, _1750736, _1750738] : [-(c_List_Olist__ex(_1750734, _1750736, _1750738)), 48097 ^ _780205 : [(48098 ^ _780205) ^ [_1750799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750799), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750734)), _1750738))), hBOOL(hAPP(_1750736, hAPP(hAPP(c_List_Onth(_1750734), _1750738), _1750799)))]]], (48106 ^ _780205) ^ [_1750972, _1750974, _1750976] : [hBOOL(hAPP(hAPP(c_member(_1750972), _1750974), hAPP(c_List_Oset(_1750972), _1750976))), -(_1750976 = hAPP(hAPP(c_List_Oappend(_1750972), 48109 ^ [_1750972, _1750974, _1750976]), hAPP(hAPP(c_List_Olist_OCons(_1750972), _1750974), 48110 ^ [_1750972, _1750974, _1750976])))], (48114 ^ _780205) ^ [_1751131, _1751133, _1751135] : [48115 ^ _780205 : [(48116 ^ _780205) ^ [_1751208, _1751210] : [_1751135 = hAPP(hAPP(c_List_Oappend(_1751131), _1751210), hAPP(hAPP(c_List_Olist_OCons(_1751131), _1751133), _1751208))]], -(hBOOL(hAPP(hAPP(c_member(_1751131), _1751133), hAPP(c_List_Oset(_1751131), _1751135))))], (48120 ^ _780205) ^ [_1751303, _1751305] : [c_List_Olist__ex(_1751303, _1751305, c_List_Olist_ONil(_1751303))], (48132 ^ _780205) ^ [_1751464, _1751466, _1751468, _1751470] : [48133 ^ _780205 : [(48134 ^ _780205) ^ [] : [c_List_Olist__ex(_1751464, _1751466, _1751468)], (48136 ^ _780205) ^ [] : [c_List_Olist__ex(_1751464, _1751466, _1751470)]], -(c_List_Olist__ex(_1751464, _1751466, hAPP(hAPP(c_List_Oappend(_1751464), _1751468), _1751470)))], (48122 ^ _780205) ^ [_1751352, _1751354, _1751356, _1751358] : [c_List_Olist__ex(_1751352, _1751354, hAPP(hAPP(c_List_Oappend(_1751352), _1751356), _1751358)), -(c_List_Olist__ex(_1751352, _1751354, _1751356)), -(c_List_Olist__ex(_1751352, _1751354, _1751358))], (48140 ^ _780205) ^ [_1751625, _1751627, _1751629] : [c_List_Olist__ex(_1751625, _1751627, _1751629), 48144 ^ _780205 : [(48145 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751625), 48143 ^ [_1751625, _1751627, _1751629]), hAPP(c_List_Oset(_1751625), _1751629))))], (48147 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1751627, 48143 ^ [_1751625, _1751627, _1751629])))]]], (48149 ^ _780205) ^ [_1751779, _1751781, _1751783] : [-(c_List_Olist__ex(_1751779, _1751781, _1751783)), 48150 ^ _780205 : [(48151 ^ _780205) ^ [_1751836] : [hBOOL(hAPP(hAPP(c_member(_1751779), _1751836), hAPP(c_List_Oset(_1751779), _1751783))), hBOOL(hAPP(_1751781, _1751836))]]], (48159 ^ _780205) ^ [_1751993, _1751995, _1751997] : [c_List_Olist__ex(_1751993, _1751995, hAPP(c_List_Orev(_1751993), _1751997)), -(c_List_Olist__ex(_1751993, _1751995, _1751997))], (48165 ^ _780205) ^ [_1752082, _1752084, _1752086] : [c_List_Olist__ex(_1752082, _1752084, _1752086), -(c_List_Olist__ex(_1752082, _1752084, hAPP(c_List_Orev(_1752082), _1752086)))], (48181 ^ _780205) ^ [_1752312, _1752314, _1752316, _1752318] : [48182 ^ _780205 : [(48183 ^ _780205) ^ [] : [hBOOL(hAPP(_1752314, _1752316))], (48185 ^ _780205) ^ [] : [c_List_Olist__ex(_1752312, _1752314, _1752318)]], -(c_List_Olist__ex(_1752312, _1752314, hAPP(hAPP(c_List_Olist_OCons(_1752312), _1752316), _1752318)))], (48171 ^ _780205) ^ [_1752198, _1752200, _1752202, _1752204] : [c_List_Olist__ex(_1752198, _1752200, hAPP(hAPP(c_List_Olist_OCons(_1752198), _1752202), _1752204)), -(hBOOL(hAPP(_1752200, _1752202))), -(c_List_Olist__ex(_1752198, _1752200, _1752204))], (48189 ^ _780205) ^ [_1752475, _1752477, _1752479] : [hBOOL(hAPP(hAPP(c_member(_1752475), _1752477), hAPP(c_List_Oset(_1752475), _1752479))), 48194 ^ _780205 : [(48195 ^ _780205) ^ [] : [-(_1752479 = hAPP(hAPP(c_List_Oappend(_1752475), 48192 ^ [_1752475, _1752477, _1752479]), hAPP(hAPP(c_List_Olist_OCons(_1752475), _1752477), 48193 ^ [_1752475, _1752477, _1752479])))], (48197 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1752475), _1752477), hAPP(c_List_Oset(_1752475), 48192 ^ [_1752475, _1752477, _1752479])))]]], (48199 ^ _780205) ^ [_1752730, _1752732, _1752734] : [-(hBOOL(hAPP(hAPP(c_member(_1752730), _1752732), hAPP(c_List_Oset(_1752730), _1752734)))), 48200 ^ _780205 : [(48201 ^ _780205) ^ [_1752819] : [48202 ^ _780205 : [(48203 ^ _780205) ^ [_1752892] : [_1752734 = hAPP(hAPP(c_List_Oappend(_1752730), _1752819), hAPP(hAPP(c_List_Olist_OCons(_1752730), _1752732), _1752892))]], -(hBOOL(hAPP(hAPP(c_member(_1752730), _1752732), hAPP(c_List_Oset(_1752730), _1752819))))]]], (48209 ^ _780205) ^ [_1753031, _1753033, _1753035] : [hBOOL(hAPP(hAPP(c_member(_1753031), _1753033), hAPP(c_List_Oset(_1753031), _1753035))), 48214 ^ _780205 : [(48215 ^ _780205) ^ [] : [-(_1753035 = hAPP(hAPP(c_List_Oappend(_1753031), 48212 ^ [_1753031, _1753033, _1753035]), hAPP(hAPP(c_List_Olist_OCons(_1753031), _1753033), 48213 ^ [_1753031, _1753033, _1753035])))], (48217 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1753031), _1753033), hAPP(c_List_Oset(_1753031), 48213 ^ [_1753031, _1753033, _1753035])))]]], (48219 ^ _780205) ^ [_1753286, _1753288, _1753290] : [-(hBOOL(hAPP(hAPP(c_member(_1753286), _1753288), hAPP(c_List_Oset(_1753286), _1753290)))), 48220 ^ _780205 : [(48221 ^ _780205) ^ [_1753375, _1753377] : [_1753290 = hAPP(hAPP(c_List_Oappend(_1753286), _1753377), hAPP(hAPP(c_List_Olist_OCons(_1753286), _1753288), _1753375)), -(hBOOL(hAPP(hAPP(c_member(_1753286), _1753288), hAPP(c_List_Oset(_1753286), _1753375))))]]], (48239 ^ _780205) ^ [_1753790, _1753792, _1753794] : [48241 ^ _780205 : [(48242 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48240 ^ [_1753790, _1753792, _1753794]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753790)), _1753794))))], (48244 ^ _780205) ^ [] : [hBOOL(hAPP(_1753792, hAPP(hAPP(c_List_Onth(_1753790), _1753794), 48240 ^ [_1753790, _1753792, _1753794])))]], -(c_List_Olist__all(_1753790, _1753792, _1753794))], (48229 ^ _780205) ^ [_1753576, _1753578, _1753580] : [c_List_Olist__all(_1753576, _1753578, _1753580), 48232 ^ _780205 : [(48233 ^ _780205) ^ [_1753665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1753665), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753576)), _1753580))), -(hBOOL(hAPP(_1753578, hAPP(hAPP(c_List_Onth(_1753576), _1753580), _1753665))))]]], (48248 ^ _780205) ^ [] : [-(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))))], (48250 ^ _780205) ^ [_1754016, _1754018] : [-(c_List_Olist__all(_1754016, _1754018, c_List_Olist_ONil(_1754016)))], (48252 ^ _780205) ^ [_1754065, _1754067, _1754069, _1754071] : [c_List_Olist__all(_1754065, _1754067, hAPP(hAPP(c_List_Oappend(_1754065), _1754069), _1754071)), 48255 ^ _780205 : [(48256 ^ _780205) ^ [] : [-(c_List_Olist__all(_1754065, _1754067, _1754069))], (48258 ^ _780205) ^ [] : [-(c_List_Olist__all(_1754065, _1754067, _1754071))]]], (48260 ^ _780205) ^ [_1754190, _1754192, _1754194, _1754196] : [-(c_List_Olist__all(_1754190, _1754192, hAPP(hAPP(c_List_Oappend(_1754190), _1754194), _1754196))), c_List_Olist__all(_1754190, _1754192, _1754194), c_List_Olist__all(_1754190, _1754192, _1754196)], (48270 ^ _780205) ^ [_1754351] : [class_Nat_Osize(_1754351), -(c_FunDef_Ois__measure(_1754351, c_Nat_Osize__class_Osize(_1754351)))], (48276 ^ _780205) ^ [_1754428, _1754430] : [-(c_FunDef_Ois__measure(_1754428, _1754430))], (48278 ^ _780205) ^ [_1754453, _1754455] : [-(c_FunDef_Ois__measure(_1754453, _1754455))], (48280 ^ _780205) ^ [_1754478, _1754480] : [-(c_FunDef_Ois__measure(_1754478, _1754480))], (48292 ^ _780205) ^ [_1754711, _1754713, _1754715] : [48294 ^ _780205 : [(48295 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754711), 48293 ^ [_1754711, _1754713, _1754715]), hAPP(c_List_Oset(_1754711), _1754715))))], (48297 ^ _780205) ^ [] : [hBOOL(hAPP(_1754713, 48293 ^ [_1754711, _1754713, _1754715]))]], -(c_List_Olist__all(_1754711, _1754713, _1754715))], (48282 ^ _780205) ^ [_1754521, _1754523, _1754525] : [c_List_Olist__all(_1754521, _1754523, _1754525), 48285 ^ _780205 : [(48286 ^ _780205) ^ [_1754602] : [hBOOL(hAPP(hAPP(c_member(_1754521), _1754602), hAPP(c_List_Oset(_1754521), _1754525))), -(hBOOL(hAPP(_1754523, _1754602)))]]], (48301 ^ _780205) ^ [_1754893, _1754895, _1754897] : [c_FunDef_Ois__measure(_1754893, _1754895), -(c_FunDef_Ois__measure(tc_prod(_1754893, _1754897), hAPP(hAPP(c_COMBB(_1754893, tc_Nat_Onat, tc_prod(_1754893, _1754897)), _1754895), c_Product__Type_Ofst(_1754893, _1754897))))], (48307 ^ _780205) ^ [_1755010, _1755012, _1755014] : [c_FunDef_Ois__measure(_1755010, _1755012), -(c_FunDef_Ois__measure(tc_prod(_1755014, _1755010), hAPP(hAPP(c_COMBB(_1755010, tc_Nat_Onat, tc_prod(_1755014, _1755010)), _1755012), c_Product__Type_Osnd(_1755014, _1755010))))], (48313 ^ _780205) ^ [_1755145, _1755147, _1755149] : [c_List_Olist__all(_1755145, _1755147, hAPP(c_List_Orev(_1755145), _1755149)), -(c_List_Olist__all(_1755145, _1755147, _1755149))], (48319 ^ _780205) ^ [_1755234, _1755236, _1755238] : [c_List_Olist__all(_1755234, _1755236, _1755238), -(c_List_Olist__all(_1755234, _1755236, hAPP(c_List_Orev(_1755234), _1755238)))], (48325 ^ _780205) ^ [_1755350, _1755352, _1755354, _1755356] : [c_List_Olist__all(_1755350, _1755352, hAPP(hAPP(c_List_Olist_OCons(_1755350), _1755354), _1755356)), 48328 ^ _780205 : [(48329 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1755352, _1755354)))], (48331 ^ _780205) ^ [] : [-(c_List_Olist__all(_1755350, _1755352, _1755356))]]], (48333 ^ _780205) ^ [_1755477, _1755479, _1755481, _1755483] : [-(c_List_Olist__all(_1755477, _1755479, hAPP(hAPP(c_List_Olist_OCons(_1755477), _1755481), _1755483))), hBOOL(hAPP(_1755479, _1755481)), c_List_Olist__all(_1755477, _1755479, _1755483)], (48343 ^ _780205) ^ [_1755658, _1755660, _1755662] : [48345 ^ _780205 : [(48346 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1755658), 48344 ^ [_1755658, _1755660, _1755662]), hAPP(c_List_Oset(_1755658), _1755660))))], (48348 ^ _780205) ^ [] : [hBOOL(hAPP(_1755662, 48344 ^ [_1755658, _1755660, _1755662]))]], -(c_List_Olist__all(_1755658, _1755662, _1755660))], (48352 ^ _780205) ^ [_1755834, _1755836, _1755838] : [c_List_Olist__all(_1755834, _1755838, _1755836), 48355 ^ _780205 : [(48356 ^ _780205) ^ [_1755915] : [hBOOL(hAPP(hAPP(c_member(_1755834), _1755915), hAPP(c_List_Oset(_1755834), _1755836))), -(hBOOL(hAPP(_1755838, _1755915)))]]], (48372 ^ _780205) ^ [_1756238, _1756240, _1756242] : [48374 ^ _780205 : [(48375 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756238), 48373 ^ [_1756238, _1756240, _1756242]), hAPP(c_List_Oset(_1756238), _1756242))))], (48377 ^ _780205) ^ [] : [hBOOL(hAPP(_1756240, 48373 ^ [_1756238, _1756240, _1756242]))]], -(c_List_Olist__all(_1756238, _1756240, _1756242))], (48362 ^ _780205) ^ [_1756048, _1756050, _1756052] : [c_List_Olist__all(_1756048, _1756050, _1756052), 48365 ^ _780205 : [(48366 ^ _780205) ^ [_1756129] : [hBOOL(hAPP(hAPP(c_member(_1756048), _1756129), hAPP(c_List_Oset(_1756048), _1756052))), -(hBOOL(hAPP(_1756050, _1756129)))]]], (48397 ^ _780205) ^ [_1756717, _1756719, _1756721, _1756723] : [-(c_List_Olist__ex1(_1756717, _1756719, hAPP(hAPP(c_List_Olist_OCons(_1756717), _1756721), _1756723))), 48400 ^ _780205 : [(48401 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1756719, _1756721)))], (48403 ^ _780205) ^ [] : [c_List_Olist__all(_1756717, hAPP(hAPP(c_COMBS(_1756717, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1756717), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756717), c_fNot), _1756719))), hAPP(c_fequal, _1756721)), _1756723)]], 48404 ^ _780205 : [(48405 ^ _780205) ^ [] : [hBOOL(hAPP(_1756719, _1756721))], (48407 ^ _780205) ^ [] : [c_List_Olist__ex1(_1756717, _1756719, _1756723)]]], (48381 ^ _780205) ^ [_1756441, _1756443, _1756445, _1756447] : [c_List_Olist__ex1(_1756441, _1756443, hAPP(hAPP(c_List_Olist_OCons(_1756441), _1756445), _1756447)), 48384 ^ _780205 : [(48385 ^ _780205) ^ [] : [hBOOL(hAPP(_1756443, _1756445)), -(c_List_Olist__all(_1756441, hAPP(hAPP(c_COMBS(_1756441, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1756441), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756441), c_fNot), _1756443))), hAPP(c_fequal, _1756445)), _1756447))], (48391 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1756443, _1756445))), -(c_List_Olist__ex1(_1756441, _1756443, _1756447))]]], (48411 ^ _780205) ^ [] : [-(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)))], (48413 ^ _780205) ^ [_1757055, _1757057] : [c_List_Olist__ex1(_1757055, _1757057, c_List_Olist_ONil(_1757055))], (48415 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48417 ^ _780205) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48419 ^ _780205) ^ [_1757137, _1757139, _1757141] : [c_List_Olist__ex1(_1757137, _1757139, _1757141), 48423 ^ _780205 : [(48424 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757137), 48422 ^ [_1757137, _1757139, _1757141]), hAPP(c_List_Oset(_1757137), _1757141))))], (48426 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1757139, 48422 ^ [_1757137, _1757139, _1757141])))], (48428 ^ _780205) ^ [_1757383] : [-(_1757383 = 48422 ^ [_1757137, _1757139, _1757141]), hBOOL(hAPP(hAPP(c_member(_1757137), _1757383), hAPP(c_List_Oset(_1757137), _1757141))), hBOOL(hAPP(_1757139, _1757383))]]], (48438 ^ _780205) ^ [_1757570, _1757572, _1757574] : [-(c_List_Olist__ex1(_1757570, _1757572, _1757574)), 48439 ^ _780205 : [(48440 ^ _780205) ^ [_1757664] : [hBOOL(hAPP(hAPP(c_member(_1757570), _1757664), hAPP(c_List_Oset(_1757570), _1757574))), hBOOL(hAPP(_1757572, _1757664)), 48448 ^ _780205 : [(48449 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757570), 48447 ^ [_1757570, _1757572, _1757574, _1757664]), hAPP(c_List_Oset(_1757570), _1757574))))], (48451 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1757572, 48447 ^ [_1757570, _1757572, _1757574, _1757664])))], (48453 ^ _780205) ^ [] : [48447 ^ [_1757570, _1757572, _1757574, _1757664] = _1757664]]]]], (48457 ^ _780205) ^ [_1758017, _1758019, _1758021, _1758023, _1758025] : [_1758017 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1758019, _1758021, _1758023, _1758025), _1758017) = c_Lazy__Sequence_Ohit__bound(_1758021))], (48463 ^ _780205) ^ [_1758114, _1758116, _1758118, _1758120, _1758122] : [-(_1758114 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1758116, _1758118, _1758120, _1758122), _1758114) = c_Lazy__Sequence_Ohb__bind(_1758116, _1758118, hAPP(_1758120, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1758114), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1758116, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1758118))), _1758122), _1758114)))], (48469 ^ _780205) ^ [_1758212, _1758214, _1758216, _1758218, _1758220] : [_1758212 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1758214, _1758216, _1758218, _1758220), _1758212) = c_Lazy__Sequence_Oempty(_1758216))], (48475 ^ _780205) ^ [_1758309, _1758311, _1758313, _1758315, _1758317] : [-(_1758309 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1758311, _1758313, _1758315, _1758317), _1758309) = hAPP(c_Lazy__Sequence_Obind(_1758311, _1758313, hAPP(_1758315, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1758309), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1758311, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1758313)), _1758317), _1758309)))], (48481 ^ _780205) ^ [_1758389, _1758391, _1758393, _1758395, _1758397, _1758399, _1758401] : [-(c_New__Random__Sequence_Opos__decr__bind(_1758389, _1758391, _1758393, _1758395, _1758397, _1758399, _1758401) = c_New__DSequence_Opos__decr__bind(_1758389, _1758391, hAPP(hAPP(hAPP(_1758393, _1758397), _1758399), _1758401), hAPP(hAPP(c_COMBC(_1758389, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1758391))), hAPP(hAPP(c_COMBC(_1758389, 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(_1758391)))), hAPP(hAPP(c_COMBC(_1758389, 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(_1758391))))), _1758395), _1758397)), _1758399)), _1758401)))], (48483 ^ _780205) ^ [_1758500, _1758502, _1758504, _1758506, _1758508, _1758510, _1758512] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1758500, _1758502, _1758504, _1758506, _1758508, _1758510, _1758512) = c_New__DSequence_Oneg__decr__bind(_1758500, _1758502, hAPP(hAPP(hAPP(_1758504, _1758508), _1758510), _1758512), hAPP(hAPP(c_COMBC(_1758500, 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(_1758502)))), hAPP(hAPP(c_COMBC(_1758500, 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(_1758502))))), hAPP(hAPP(c_COMBC(_1758500, 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(_1758502)))))), _1758506), _1758508)), _1758510)), _1758512)))], (48485 ^ _780205) ^ [_1758617, _1758619, _1758621, _1758623, _1758625] : [-(hAPP(c_New__DSequence_Oneg__bind(_1758617, _1758619, _1758621, _1758623), _1758625) = c_Lazy__Sequence_Ohb__bind(_1758617, _1758619, hAPP(_1758621, _1758625), hAPP(hAPP(c_COMBC(_1758617, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1758619))), _1758623), _1758625)))], (48487 ^ _780205) ^ [_1758678, _1758680] : [-(hAPP(c_New__DSequence_Opos__empty(_1758678), _1758680) = c_Lazy__Sequence_Oempty(_1758678))], (48489 ^ _780205) ^ [_1758710, _1758712, _1758714, _1758716] : [-(c_New__Random__Sequence_Opos__empty(_1758710, _1758712, _1758714, _1758716) = c_New__DSequence_Opos__empty(_1758710))], (48491 ^ _780205) ^ [_1758746, _1758748, _1758750, _1758752, _1758754, _1758756, _1758758] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1758746, _1758748, _1758750, _1758752), _1758754), _1758756), _1758758) = c_New__DSequence_Oneg__bind(_1758746, _1758748, hAPP(hAPP(hAPP(_1758750, _1758754), _1758756), _1758758), hAPP(hAPP(c_COMBC(_1758746, 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(_1758748)))), hAPP(hAPP(c_COMBC(_1758746, 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(_1758748))))), hAPP(hAPP(c_COMBC(_1758746, 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(_1758748)))))), _1758752), _1758754)), _1758756)), _1758758)))], (48493 ^ _780205) ^ [_1758869, _1758871, _1758873, _1758875, _1758877] : [-(hAPP(c_New__DSequence_Opos__bind(_1758869, _1758871, _1758873, _1758875), _1758877) = hAPP(c_Lazy__Sequence_Obind(_1758869, _1758871, hAPP(_1758873, _1758877)), hAPP(hAPP(c_COMBC(_1758869, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1758871)), _1758875), _1758877)))], (48495 ^ _780205) ^ [_1758930, _1758932, _1758934, _1758936] : [-(c_New__Random__Sequence_Oneg__map(_1758930, _1758932, _1758934, _1758936) = c_New__Random__Sequence_Oneg__bind(_1758930, _1758932, _1758936, hAPP(c_Fun_Ocomp(_1758932, 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(_1758932)))))), _1758930, c_New__Random__Sequence_Oneg__single(_1758932)), _1758934)))], (48497 ^ _780205) ^ [_1758995, _1758997, _1758999, _1759001, _1759003] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1758995), _1758997), _1758999), _1759001), _1759003) = c_New__DSequence_Oneg__single(_1758995, _1758997))], (48499 ^ _780205) ^ [_1759043, _1759045, _1759047, _1759049, _1759051, _1759053, _1759055] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1759043, _1759045, _1759047, _1759049), _1759051), _1759053), _1759055) = c_New__DSequence_Opos__bind(_1759043, _1759045, hAPP(hAPP(hAPP(_1759047, _1759051), _1759053), _1759055), hAPP(hAPP(c_COMBC(_1759043, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1759045))), hAPP(hAPP(c_COMBC(_1759043, 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(_1759045)))), hAPP(hAPP(c_COMBC(_1759043, 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(_1759045))))), _1759049), _1759051)), _1759053)), _1759055)))], (48501 ^ _780205) ^ [_1759160, _1759162, _1759164] : [-(hAPP(c_New__DSequence_Oneg__single(_1759160, _1759162), _1759164) = c_Lazy__Sequence_Ohb__single(_1759160, _1759162))], (48503 ^ _780205) ^ [_1759196, _1759198, _1759200, _1759202] : [-(c_New__Random__Sequence_Opos__map(_1759196, _1759198, _1759200, _1759202) = c_New__Random__Sequence_Opos__bind(_1759196, _1759198, _1759202, hAPP(c_Fun_Ocomp(_1759198, 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(_1759198))))), _1759196, c_New__Random__Sequence_Opos__single(_1759198)), _1759200)))], (48505 ^ _780205) ^ [_1759259, _1759261, _1759263, _1759265, _1759267] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1759259), _1759261), _1759263), _1759265), _1759267) = c_New__DSequence_Opos__single(_1759259, _1759261))], (48507 ^ _780205) ^ [_1759307, _1759309, _1759311] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759307)), c_List_Osplice(_1759307, _1759309, _1759311)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759307)), _1759309)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759307)), _1759311)))], (48509 ^ _780205) ^ [_1759365, _1759367, _1759369, _1759371, _1759373] : [-(c_List_Osplice(_1759365, hAPP(hAPP(c_List_Olist_OCons(_1759365), _1759367), _1759369), hAPP(hAPP(c_List_Olist_OCons(_1759365), _1759371), _1759373)) = hAPP(hAPP(c_List_Olist_OCons(_1759365), _1759367), hAPP(hAPP(c_List_Olist_OCons(_1759365), _1759371), c_List_Osplice(_1759365, _1759369, _1759373))))], (48511 ^ _780205) ^ [_1759436, _1759438] : [-(c_List_Osplice(_1759436, c_List_Olist_ONil(_1759436), _1759438) = _1759438)], (48513 ^ _780205) ^ [_1759467, _1759469] : [-(c_List_Osplice(_1759467, _1759469, c_List_Olist_ONil(_1759467)) = _1759469)], (48515 ^ _780205) ^ [_1759498, _1759500, _1759502] : [-(c_List_Osplice(_1759498, hAPP(hAPP(c_List_Olist_OCons(_1759498), _1759500), _1759502), c_List_Olist_ONil(_1759498)) = hAPP(hAPP(c_List_Olist_OCons(_1759498), _1759500), _1759502))], (48517 ^ _780205) ^ [_1759547, _1759549, _1759551] : [-(hAPP(c_New__DSequence_Opos__single(_1759547, _1759549), _1759551) = hAPP(c_Lazy__Sequence_Osingle(_1759547), _1759549))], (48519 ^ _780205) ^ [_1759600, _1759602] : [c_Wellfounded_Oacyclic(_1759600, hAPP(c_Set_OCollect(tc_prod(_1759600, _1759600)), hAPP(c_Product__Type_Oprod_Oprod__case(_1759600, _1759600, tc_HOL_Obool), c_Predicate_Oconversep(_1759600, _1759600, _1759602)))), -(c_Wellfounded_Oacyclic(_1759600, hAPP(c_Set_OCollect(tc_prod(_1759600, _1759600)), hAPP(c_Product__Type_Oprod_Oprod__case(_1759600, _1759600, tc_HOL_Obool), _1759602))))], (48525 ^ _780205) ^ [_1759741, _1759743] : [c_Wellfounded_Oacyclic(_1759741, hAPP(c_Set_OCollect(tc_prod(_1759741, _1759741)), hAPP(c_Product__Type_Oprod_Oprod__case(_1759741, _1759741, tc_HOL_Obool), _1759743))), -(c_Wellfounded_Oacyclic(_1759741, hAPP(c_Set_OCollect(tc_prod(_1759741, _1759741)), hAPP(c_Product__Type_Oprod_Oprod__case(_1759741, _1759741, tc_HOL_Obool), c_Predicate_Oconversep(_1759741, _1759741, _1759743)))))], (48531 ^ _780205) ^ [_1759888, _1759890, _1759892, _1759894] : [-(c_Predicate_Oconversep(_1759888, _1759890, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1759888, tc_fun(_1759890, tc_HOL_Obool))), _1759892), _1759894)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1759890, tc_fun(_1759888, tc_HOL_Obool))), c_Predicate_Oconversep(_1759888, _1759890, _1759892)), c_Predicate_Oconversep(_1759888, _1759890, _1759894)))], (48533 ^ _780205) ^ [_1759957, _1759959, _1759961, _1759963] : [-(c_Predicate_Oconversep(_1759957, _1759959, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1759957, tc_fun(_1759959, tc_HOL_Obool))), _1759961), _1759963)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1759959, tc_fun(_1759957, tc_HOL_Obool))), c_Predicate_Oconversep(_1759957, _1759959, _1759961)), c_Predicate_Oconversep(_1759957, _1759959, _1759963)))], (48535 ^ _780205) ^ [_1760026, _1760028, _1760030, _1760032, _1760034] : [-(c_Predicate_Oconversep(_1760026, _1760028, c_Predicate_Opred__comp(_1760026, _1760030, _1760028, _1760032, _1760034)) = c_Predicate_Opred__comp(_1760028, _1760030, _1760026, c_Predicate_Oconversep(_1760030, _1760028, _1760034), c_Predicate_Oconversep(_1760026, _1760030, _1760032)))], (48537 ^ _780205) ^ [_1760099, _1760101, _1760103] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1760099, _1760099, hAPP(hAPP(c_COMBB(tc_fun(_1760099, tc_HOL_Obool), tc_fun(_1760099, tc_HOL_Obool), _1760099), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1760099), c_fNot)), c_fequal)), _1760101), _1760103)), _1760101 = _1760103], (48543 ^ _780205) ^ [_1760237, _1760239, _1760241] : [-(_1760239 = _1760241), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1760237, _1760237, hAPP(hAPP(c_COMBB(tc_fun(_1760237, tc_HOL_Obool), tc_fun(_1760237, tc_HOL_Obool), _1760237), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1760237), c_fNot)), c_fequal)), _1760239), _1760241)))], (48549 ^ _780205) ^ [_1760309, _1760311, _1760313, _1760315, _1760317] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1760309, _1760311, _1760313), _1760315), _1760317)), -(hBOOL(hAPP(hAPP(_1760313, _1760317), _1760315)))], (48555 ^ _780205) ^ [_1760420, _1760422, _1760424, _1760426, _1760428] : [hBOOL(hAPP(hAPP(_1760420, _1760422), _1760424)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1760426, _1760428, _1760420), _1760424), _1760422)))], (48561 ^ _780205) ^ [_1760555, _1760557, _1760559, _1760561, _1760563] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1760555, _1760557, _1760559), _1760561), _1760563)), -(hBOOL(hAPP(hAPP(_1760559, _1760563), _1760561)))], (48567 ^ _780205) ^ [_1760662, _1760664, _1760666, _1760668, _1760670] : [hBOOL(hAPP(hAPP(_1760666, _1760670), _1760668)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1760662, _1760664, _1760666), _1760668), _1760670)))], (48573 ^ _780205) ^ [_1760799, _1760801, _1760803, _1760805, _1760807] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1760799, _1760801, _1760803), _1760805), _1760807)), -(hBOOL(hAPP(hAPP(_1760803, _1760807), _1760805)))], (48579 ^ _780205) ^ [_1760906, _1760908, _1760910, _1760912, _1760914] : [hBOOL(hAPP(hAPP(_1760910, _1760914), _1760912)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1760906, _1760908, _1760910), _1760912), _1760914)))], (48585 ^ _780205) ^ [_1761019, _1761021, _1761023] : [-(c_Predicate_Oconversep(_1761019, _1761021, c_Predicate_Oconversep(_1761021, _1761019, _1761023)) = _1761023)], (48587 ^ _780205) ^ [_1761054] : [-(c_Predicate_Oconversep(_1761054, _1761054, c_fequal) = c_fequal)], (48589 ^ _780205) ^ [_1761105, _1761107, _1761109, _1761111, _1761113] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1761105, _1761107, hAPP(hAPP(c_COMBC(_1761105, tc_fun(tc_prod(_1761105, _1761107), tc_HOL_Obool), tc_fun(_1761107, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1761107, tc_fun(tc_fun(tc_prod(_1761105, _1761107), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1761105, _1761107), tc_HOL_Obool), tc_fun(_1761107, tc_HOL_Obool)), _1761105), c_COMBC(_1761107, tc_fun(tc_prod(_1761105, _1761107), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1761107, tc_prod(_1761105, _1761107)), tc_fun(_1761107, tc_fun(tc_fun(tc_prod(_1761105, _1761107), tc_HOL_Obool), tc_HOL_Obool)), _1761105), hAPP(c_COMBB(tc_prod(_1761105, _1761107), tc_fun(tc_fun(tc_prod(_1761105, _1761107), tc_HOL_Obool), tc_HOL_Obool), _1761107), c_member(tc_prod(_1761105, _1761107)))), c_Product__Type_OPair(_1761105, _1761107)))), _1761109)), _1761111), _1761113)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1761107, _1761105)), hAPP(hAPP(c_Product__Type_OPair(_1761107, _1761105), _1761111), _1761113)), hAPP(c_Relation_Oconverse(_1761105, _1761107), _1761109))))], (48595 ^ _780205) ^ [_1761488, _1761490, _1761492, _1761494, _1761496] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1761490, _1761488)), hAPP(hAPP(c_Product__Type_OPair(_1761490, _1761488), _1761494), _1761496)), hAPP(c_Relation_Oconverse(_1761488, _1761490), _1761492))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1761488, _1761490, hAPP(hAPP(c_COMBC(_1761488, tc_fun(tc_prod(_1761488, _1761490), tc_HOL_Obool), tc_fun(_1761490, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1761490, tc_fun(tc_fun(tc_prod(_1761488, _1761490), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1761488, _1761490), tc_HOL_Obool), tc_fun(_1761490, tc_HOL_Obool)), _1761488), c_COMBC(_1761490, tc_fun(tc_prod(_1761488, _1761490), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1761490, tc_prod(_1761488, _1761490)), tc_fun(_1761490, tc_fun(tc_fun(tc_prod(_1761488, _1761490), tc_HOL_Obool), tc_HOL_Obool)), _1761488), hAPP(c_COMBB(tc_prod(_1761488, _1761490), tc_fun(tc_fun(tc_prod(_1761488, _1761490), tc_HOL_Obool), tc_HOL_Obool), _1761490), c_member(tc_prod(_1761488, _1761490)))), c_Product__Type_OPair(_1761488, _1761490)))), _1761492)), _1761494), _1761496)))], (48601 ^ _780205) ^ [_1761877, _1761879, _1761881, _1761883] : [-(c_Lazy__Sequence_Oproduct(_1761877, _1761879, _1761881, _1761883) = hAPP(c_Lazy__Sequence_Obind(_1761877, tc_prod(_1761877, _1761879), _1761881), hAPP(hAPP(c_COMBB(tc_fun(_1761879, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1761877, _1761879))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1761877, _1761879)), _1761877), c_Lazy__Sequence_Obind(_1761879, tc_prod(_1761877, _1761879), _1761883)), hAPP(hAPP(c_COMBB(tc_fun(_1761879, tc_prod(_1761877, _1761879)), tc_fun(_1761879, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1761877, _1761879))), _1761877), hAPP(c_COMBB(tc_prod(_1761877, _1761879), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1761877, _1761879)), _1761879), c_Lazy__Sequence_Osingle(tc_prod(_1761877, _1761879)))), c_Product__Type_OPair(_1761877, _1761879)))))], (48603 ^ _780205) ^ [_1761994, _1761996, _1761998] : [-(_1761994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1761996), c_List_Oreplicate(_1761996, _1761994, _1761998)) = c_List_Oreplicate(_1761996, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1761994), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1761998))], (48609 ^ _780205) ^ [_1762051, _1762053, _1762055] : [-(c_List_Oreplicate(_1762051, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762051)), hAPP(c_List_Ofilter(_1762051, hAPP(c_fequal, _1762053)), _1762055)), _1762053) = hAPP(c_List_Ofilter(_1762051, hAPP(c_fequal, _1762053)), _1762055))], (48611 ^ _780205) ^ [_1762107, _1762109, _1762111] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762107)), c_List_Oreplicate(_1762107, _1762109, _1762111)) = _1762109)], (48613 ^ _780205) ^ [_1762145, _1762147, _1762149, _1762151] : [-(hAPP(hAPP(c_List_Omap(_1762145, _1762147), hAPP(c_COMBK(_1762147, _1762145), _1762149)), _1762151) = c_List_Oreplicate(_1762147, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762145)), _1762151), _1762149))], (48615 ^ _780205) ^ [_1762200, _1762202, _1762204, _1762206] : [-(hAPP(hAPP(c_List_Oappend(_1762200), c_List_Oreplicate(_1762200, _1762202, _1762204)), hAPP(hAPP(c_List_Olist_OCons(_1762200), _1762204), _1762206)) = hAPP(hAPP(c_List_Olist_OCons(_1762200), _1762204), hAPP(hAPP(c_List_Oappend(_1762200), c_List_Oreplicate(_1762200, _1762202, _1762204)), _1762206)))], (48617 ^ _780205) ^ [_1762269, _1762271, _1762273] : [-(c_List_Oreplicate(_1762269, hAPP(c_Nat_OSuc, _1762271), _1762273) = hAPP(hAPP(c_List_Olist_OCons(_1762269), _1762273), c_List_Oreplicate(_1762269, _1762271, _1762273)))], (48619 ^ _780205) ^ [_1762315, _1762317, _1762319] : [-(hAPP(c_List_Orev(_1762315), c_List_Oreplicate(_1762315, _1762317, _1762319)) = c_List_Oreplicate(_1762315, _1762317, _1762319))], (48621 ^ _780205) ^ [_1762355, _1762357, _1762359, _1762361] : [-(hAPP(hAPP(c_List_Otake(_1762355), _1762357), c_List_Oreplicate(_1762355, _1762359, _1762361)) = c_List_Oreplicate(_1762355, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1762357), _1762359), _1762361))], (48623 ^ _780205) ^ [_1762406, _1762408, _1762410, _1762412] : [-(hAPP(hAPP(c_List_Odrop(_1762406), _1762408), c_List_Oreplicate(_1762406, _1762410, _1762412)) = c_List_Oreplicate(_1762406, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1762410), _1762408), _1762412))], (48625 ^ _780205) ^ [_1762453, _1762455, _1762457] : [-(_1762453 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1762455), c_List_Oreplicate(_1762455, _1762453, _1762457)) = _1762457)], (48631 ^ _780205) ^ [_1762496, _1762498, _1762500] : [-(_1762496 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1762498, c_List_Oreplicate(_1762498, _1762496, _1762500)) = _1762500)], (48637 ^ _780205) ^ [_1762541, _1762543, _1762545, _1762547, _1762549, _1762551] : [-(hAPP(hAPP(c_List_Ozip(_1762541, _1762543), c_List_Oreplicate(_1762541, _1762545, _1762547)), c_List_Oreplicate(_1762543, _1762549, _1762551)) = c_List_Oreplicate(tc_prod(_1762541, _1762543), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1762545), _1762549), hAPP(hAPP(c_Product__Type_OPair(_1762541, _1762543), _1762547), _1762551)))], (48639 ^ _780205) ^ [_1762634, _1762636, _1762638, _1762640] : [48646 ^ _780205 : [(48647 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1762640, _1762638)))], (48649 ^ _780205) ^ [] : [_1762636 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48640 ^ _780205 : [(48641 ^ _780205) ^ [_1762706] : [hBOOL(hAPP(hAPP(c_member(_1762634), _1762706), hAPP(c_List_Oset(_1762634), c_List_Oreplicate(_1762634, _1762636, _1762638)))), hBOOL(hAPP(_1762640, _1762706))]]], (48651 ^ _780205) ^ [_1762876, _1762878, _1762880, _1762882] : [48659 ^ _780205 : [(48660 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1762876), 48658 ^ [_1762876, _1762878, _1762880, _1762882]), hAPP(c_List_Oset(_1762876), c_List_Oreplicate(_1762876, _1762878, _1762880)))))], (48662 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1762882, 48658 ^ [_1762876, _1762878, _1762880, _1762882])))]], hBOOL(hAPP(_1762882, _1762880)), -(_1762878 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48664 ^ _780205) ^ [_1763132, _1763134, _1763136, _1763138] : [48666 ^ _780205 : [(48667 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763132), 48665 ^ [_1763132, _1763134, _1763136, _1763138]), hAPP(c_List_Oset(_1763132), c_List_Oreplicate(_1763132, _1763134, _1763136)))))], (48669 ^ _780205) ^ [] : [hBOOL(hAPP(_1763138, 48665 ^ [_1763132, _1763134, _1763136, _1763138]))]], -(hBOOL(hAPP(_1763138, _1763136))), -(_1763134 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48677 ^ _780205) ^ [_1763339, _1763341, _1763343, _1763345] : [48678 ^ _780205 : [(48679 ^ _780205) ^ [] : [hBOOL(hAPP(_1763345, _1763343))], (48681 ^ _780205) ^ [] : [_1763341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48682 ^ _780205 : [(48683 ^ _780205) ^ [_1763464] : [hBOOL(hAPP(hAPP(c_member(_1763339), _1763464), hAPP(c_List_Oset(_1763339), c_List_Oreplicate(_1763339, _1763341, _1763343)))), -(hBOOL(hAPP(_1763345, _1763464)))]]], (48689 ^ _780205) ^ [_1763615, _1763617, _1763619, _1763621, _1763623] : [c_List_Oreplicate(_1763615, _1763617, _1763619) = c_List_Oreplicate(_1763615, _1763621, _1763623), 48692 ^ _780205 : [(48693 ^ _780205) ^ [] : [-(_1763617 = _1763621)], (48695 ^ _780205) ^ [] : [-(_1763617 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1763619 = _1763623)]]], (48701 ^ _780205) ^ [_1763751, _1763753, _1763755, _1763757, _1763759] : [-(c_List_Oreplicate(_1763751, _1763753, _1763755) = c_List_Oreplicate(_1763751, _1763757, _1763759)), _1763753 = _1763757, 48706 ^ _780205 : [(48707 ^ _780205) ^ [] : [_1763753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48709 ^ _780205) ^ [] : [_1763755 = _1763759]]], (48713 ^ _780205) ^ [_1763950, _1763952, _1763954, _1763956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763950), _1763952)), -(hAPP(hAPP(c_List_Onth(_1763954), c_List_Oreplicate(_1763954, _1763952, _1763956)), _1763950) = _1763956)], (48719 ^ _780205) ^ [_1764065, _1764067, _1764069, _1764071] : [-(c_List_Oreplicate(_1764065, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1764067), _1764069), _1764071) = hAPP(hAPP(c_List_Oappend(_1764065), c_List_Oreplicate(_1764065, _1764067, _1764071)), c_List_Oreplicate(_1764065, _1764069, _1764071)))], (48721 ^ _780205) ^ [_1764120, _1764122, _1764124, _1764126] : [-(hAPP(hAPP(c_List_Oappend(_1764120), c_List_Oreplicate(_1764120, _1764122, _1764124)), c_List_Oreplicate(_1764120, _1764126, _1764124)) = hAPP(hAPP(c_List_Oappend(_1764120), c_List_Oreplicate(_1764120, _1764126, _1764124)), c_List_Oreplicate(_1764120, _1764122, _1764124)))], (48723 ^ _780205) ^ [_1764196, _1764198, _1764200, _1764202] : [hBOOL(hAPP(_1764196, _1764198)), -(hAPP(c_List_Ofilter(_1764200, _1764196), c_List_Oreplicate(_1764200, _1764202, _1764198)) = c_List_Oreplicate(_1764200, _1764202, _1764198))], (48729 ^ _780205) ^ [_1764303, _1764305, _1764307, _1764309] : [-(hBOOL(hAPP(_1764303, _1764305))), -(hAPP(c_List_Ofilter(_1764307, _1764303), c_List_Oreplicate(_1764307, _1764309, _1764305)) = c_List_Olist_ONil(_1764307))], (48735 ^ _780205) ^ [_1764359, _1764361] : [-(c_List_Oconcat(_1764359, c_List_Oreplicate(tc_List_Olist(_1764359), _1764361, c_List_Olist_ONil(_1764359))) = c_List_Olist_ONil(_1764359))], (48737 ^ _780205) ^ [_1764397, _1764399] : [-(c_List_Oreplicate(_1764397, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1764399) = c_List_Olist_ONil(_1764397))], (48739 ^ _780205) ^ [_1764446, _1764448, _1764450] : [c_List_Olist_ONil(_1764446) = c_List_Oreplicate(_1764446, _1764448, _1764450), -(_1764448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48745 ^ _780205) ^ [_1764533, _1764535, _1764537] : [_1764535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1764533) = c_List_Oreplicate(_1764533, _1764535, _1764537))], (48751 ^ _780205) ^ [_1764644, _1764646, _1764648] : [c_List_Oreplicate(_1764644, _1764646, _1764648) = c_List_Olist_ONil(_1764644), -(_1764646 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48757 ^ _780205) ^ [_1764731, _1764733, _1764735] : [_1764733 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1764731, _1764733, _1764735) = c_List_Olist_ONil(_1764731))], (48763 ^ _780205) ^ [_1764824, _1764826, _1764828, _1764830, _1764832] : [-(hAPP(hAPP(c_List_Omap(_1764824, _1764826), _1764828), c_List_Oreplicate(_1764824, _1764830, _1764832)) = c_List_Oreplicate(_1764826, _1764830, hAPP(_1764828, _1764832)))], (48765 ^ _780205) ^ [_1764896, _1764898, _1764900, _1764902] : [hBOOL(hAPP(hAPP(c_member(_1764896), _1764898), hAPP(c_List_Oset(_1764896), c_List_Oreplicate(_1764896, _1764900, _1764902)))), 48768 ^ _780205 : [(48769 ^ _780205) ^ [] : [-(_1764898 = _1764902)], (48771 ^ _780205) ^ [] : [_1764900 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (48773 ^ _780205) ^ [_1765039, _1765041, _1765043, _1765045] : [-(hBOOL(hAPP(hAPP(c_member(_1765039), _1765041), hAPP(c_List_Oset(_1765039), c_List_Oreplicate(_1765039, _1765043, _1765045))))), _1765041 = _1765045, -(_1765043 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48783 ^ _780205) ^ [_1765213, _1765215, _1765217] : [-(hAPP(hAPP(c_List_Oappend(_1765213), c_List_Oreplicate(_1765213, _1765215, _1765217)), hAPP(hAPP(c_List_Olist_OCons(_1765213), _1765217), c_List_Olist_ONil(_1765213))) = hAPP(hAPP(c_List_Olist_OCons(_1765213), _1765217), c_List_Oreplicate(_1765213, _1765215, _1765217)))], (48785 ^ _780205) ^ [_1765274, _1765276, _1765278] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1765274), hAPP(c_COMBK(_1765274, tc_Nat_Onat), _1765276)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1765278)) = c_List_Oreplicate(_1765274, _1765278, _1765276))], (48787 ^ _780205) ^ [_1765319, _1765321, _1765323] : [-(_1765319 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1765321), c_List_Oreplicate(_1765321, _1765319, _1765323)) = hAPP(hAPP(c_Set_Oinsert(_1765321), _1765323), c_Orderings_Obot__class_Obot(tc_fun(_1765321, tc_HOL_Obool))))], (48793 ^ _780205) ^ [_1765391, _1765393, _1765395] : [_1765391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1765393), c_List_Oreplicate(_1765393, _1765391, _1765395)) = c_Orderings_Obot__class_Obot(tc_fun(_1765393, tc_HOL_Obool)))], (48799 ^ _780205) ^ [_1765492, _1765494, _1765496] : [-(_1765492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1765494), c_List_Oreplicate(_1765494, _1765492, _1765496)) = hAPP(hAPP(c_Set_Oinsert(_1765494), _1765496), c_Orderings_Obot__class_Obot(tc_fun(_1765494, tc_HOL_Obool))))], (48805 ^ _780205) ^ [_1765554, _1765556, _1765558] : [-(hAPP(c_List_Oset(_1765554), c_List_Oreplicate(_1765554, hAPP(c_Nat_OSuc, _1765556), _1765558)) = hAPP(hAPP(c_Set_Oinsert(_1765554), _1765558), c_Orderings_Obot__class_Obot(tc_fun(_1765554, tc_HOL_Obool))))], (48807 ^ _780205) ^ [_1765606, _1765608] : [class_Lazy__Sequence_Osmall__lazy(_1765606), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1765606), _1765608) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1765606), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1765606)), c_List_Olist_ONil(_1765606)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1765606))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1765608)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1765606, tc_List_Olist(_1765606)), tc_List_Olist(_1765606), c_Lazy__Sequence_Oproduct(_1765606, tc_List_Olist(_1765606), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1765606, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1765608), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1765606), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1765608), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1765606, tc_List_Olist(_1765606), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1765606))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1765606), tc_List_Olist(_1765606)), tc_fun(tc_List_Olist(_1765606), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1765606))), _1765606), hAPP(c_COMBB(tc_List_Olist(_1765606), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1765606)), tc_List_Olist(_1765606)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1765606)))), c_List_Olist_OCons(_1765606))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1765606)))))], (48813 ^ _780205) ^ [_1765967, _1765969] : [-(c_Predicate_Opred__comp(_1765967, _1765967, _1765967, c_fequal, c_Predicate_Opred__comp(_1765967, _1765967, _1765967, _1765969, c_fequal)) = _1765969)], (48815 ^ _780205) ^ [_1766004, _1766006, _1766008] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1766004, _1766006), _1766008) = c_Lazy__Sequence_Oproduct(_1766004, _1766006, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1766004, _1766008), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1766006, _1766008))), class_Lazy__Sequence_Osmall__lazy(_1766004), class_Lazy__Sequence_Osmall__lazy(_1766006)], (48825 ^ _780205) ^ [_1766167, _1766169, _1766171, _1766173] : [-(hAPP(c_New__DSequence_Opos__union(_1766167, _1766169, _1766171), _1766173) = c_Lazy__Sequence_Oappend(_1766167, hAPP(_1766169, _1766173), hAPP(_1766171, _1766173)))], (48827 ^ _780205) ^ [_1766213, _1766215, _1766217] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1766213)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1766213, _1766215, _1766217)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1766213)), _1766217)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48829 ^ _780205) ^ [_1766264, _1766266, _1766268, _1766270] : [-(c_Lazy__Sequence_Oappend(_1766264, c_Lazy__Sequence_Olazy__sequence_OInsert(_1766264, _1766266, _1766268), _1766270) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1766264, _1766266, c_Lazy__Sequence_Oappend(_1766264, _1766268, _1766270)))], (48831 ^ _780205) ^ [_1766333, _1766335, _1766337, _1766339, _1766341] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1766333, _1766335, _1766337) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1766333, _1766339, _1766341), 48834 ^ _780205 : [(48835 ^ _780205) ^ [] : [-(_1766335 = _1766339)], (48837 ^ _780205) ^ [] : [-(_1766337 = _1766341)]]], (48839 ^ _780205) ^ [_1766454, _1766456, _1766458, _1766460, _1766462] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1766454, _1766456, _1766458) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1766454, _1766460, _1766462)), _1766456 = _1766460, _1766458 = _1766462], (48849 ^ _780205) ^ [_1766613, _1766615, _1766617, _1766619, _1766621, _1766623] : [-(c_New__Random__Sequence_Opos__union(_1766613, _1766615, _1766617, _1766619, _1766621, _1766623) = c_New__DSequence_Opos__union(_1766613, hAPP(hAPP(hAPP(_1766615, _1766619), _1766621), _1766623), hAPP(hAPP(hAPP(_1766617, _1766619), _1766621), _1766623)))], (48851 ^ _780205) ^ [_1766675, _1766677, _1766679, _1766681] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1766675, _1766677), c_Lazy__Sequence_Olazy__sequence_OInsert(_1766675, _1766679, _1766681)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1766677, _1766679)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1766675, _1766677), _1766681))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48853 ^ _780205) ^ [_1766744, _1766746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1766744), _1766746)), -(c_Lazy__Sequence_Osmall__lazy_H(_1766744, _1766746) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (48859 ^ _780205) ^ [_1766831, _1766833] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1766831), _1766833))), -(c_Lazy__Sequence_Osmall__lazy_H(_1766831, _1766833) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1766833), c_Lazy__Sequence_Osmall__lazy_H(_1766831, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1766833), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48865 ^ _780205) ^ [_1766893, _1766895] : [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), _1766893), _1766895))), 48868 ^ _780205 : [(48869 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1766893), _1766895)), -(c_Lazy__Sequence_Osmall__lazy_H(_1766893, _1766895) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (48875 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1766893), _1766895))), -(c_Lazy__Sequence_Osmall__lazy_H(_1766893, _1766895) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1766895), c_Lazy__Sequence_Osmall__lazy_H(_1766893, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1766895), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (48881 ^ _780205) ^ [_1767149] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1767149) = c_Lazy__Sequence_Osmall__lazy_H(_1767149, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1767149)))], (48883 ^ _780205) ^ [_1767181, _1767183, _1767185] : [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), _1767181), _1767183))), -(hBOOL(hAPP(hAPP(_1767185, _1767181), _1767183))), 48890 ^ _780205 : [(48891 ^ _780205) ^ [] : [-(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), 48888 ^ [_1767181, _1767183, _1767185]), 48889 ^ [_1767181, _1767183, _1767185]))))], (48899 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1767185, 48888 ^ [_1767181, _1767183, _1767185]), 48889 ^ [_1767181, _1767183, _1767185]))], (48893 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48888 ^ [_1767181, _1767183, _1767185]), 48889 ^ [_1767181, _1767183, _1767185]))), -(hBOOL(hAPP(hAPP(_1767185, 48888 ^ [_1767181, _1767183, _1767185]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48889 ^ [_1767181, _1767183, _1767185]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (48903 ^ _780205) ^ [_1767633, _1767635] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1767633)), _1767635) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1767633, tc_Lazy__Sequence_Olazy__sequence(_1767633)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1767633, tc_Lazy__Sequence_Olazy__sequence(_1767633), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1767633), tc_Nat_Onat), _1767633), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1767633), 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(_1767633)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1767633)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1767633), _1767635)))], (48905 ^ _780205) ^ [_1767729, _1767731, _1767733] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1767729, _1767731), _1767733) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1767729, tc_Lazy__Sequence_Olazy__sequence(_1767729)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1767729, tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1767729, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_Nat_Onat)), _1767729), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1767729), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1767729)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1767729, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1767729), tc_Nat_Onat)), _1767729), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1767729))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1767729), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1767731))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1767729, _1767731))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1767729), _1767733)))], (48907 ^ _780205) ^ [_1767922, _1767924, _1767926, _1767928, _1767930] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1767922, _1767924, _1767926, _1767928, _1767930) = c_Option_Ooption_Ooption__case(_1767922, tc_prod(_1767924, tc_Lazy__Sequence_Olazy__sequence(_1767924)), _1767926, hAPP(c_Product__Type_Oprod_Oprod__case(_1767924, tc_Lazy__Sequence_Olazy__sequence(_1767924), _1767922), _1767928), hAPP(c_Lazy__Sequence_Oyield(_1767924), _1767930)))], (48909 ^ _780205) ^ [_1767984] : [-(c_Lazy__Sequence_Oyieldn(_1767984) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1767984), _1767984, c_Lazy__Sequence_Oyield(_1767984)))], (48911 ^ _780205) ^ [_1768017, _1768019, _1768021, _1768023, _1768025, _1768027] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1768017, _1768019, _1768021, _1768023, c_Lazy__Sequence_Olazy__sequence_OInsert(_1768019, _1768025, _1768027)) = hAPP(hAPP(_1768023, _1768025), _1768027))], (48913 ^ _780205) ^ [_1768066, _1768068, _1768070, _1768072, _1768074] : [48915 ^ _780205 : [(48916 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1768066), 48914 ^ [_1768066, _1768068, _1768070, _1768072, _1768074]), _1768068)))], (48918 ^ _780205) ^ [] : [c_Relation_Orefl__on(_1768070, hAPP(_1768072, 48914 ^ [_1768066, _1768068, _1768070, _1768072, _1768074]), hAPP(_1768074, 48914 ^ [_1768066, _1768068, _1768070, _1768072, _1768074]))]], -(c_Relation_Orefl__on(_1768070, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1768066, tc_fun(_1768070, tc_HOL_Obool)), _1768068), _1768072), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1768066, tc_fun(tc_prod(_1768070, _1768070), tc_HOL_Obool)), _1768068), _1768074)))], (48922 ^ _780205) ^ [_1768352, _1768354, _1768356] : [hBOOL(hAPP(hAPP(c_List_Omember(_1768352), _1768354), _1768356)), -(hBOOL(hAPP(hAPP(c_member(_1768352), _1768356), hAPP(c_List_Oset(_1768352), _1768354))))], (48928 ^ _780205) ^ [_1768465, _1768467, _1768469] : [hBOOL(hAPP(hAPP(c_member(_1768465), _1768469), hAPP(c_List_Oset(_1768465), _1768467))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1768465), _1768467), _1768469)))], (48934 ^ _780205) ^ [_1768596, _1768598] : [hBOOL(hAPP(hAPP(c_List_Omember(_1768596), c_List_Olist_ONil(_1768596)), _1768598))], (48936 ^ _780205) ^ [_1768630] : [-(c_List_Omember(_1768630) = c_List_Oset(_1768630))], (48948 ^ _780205) ^ [_1768812, _1768814, _1768816, _1768818] : [48949 ^ _780205 : [(48950 ^ _780205) ^ [] : [_1768814 = _1768818], (48952 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1768812), _1768816), _1768818))]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1768812), hAPP(hAPP(c_List_Olist_OCons(_1768812), _1768814), _1768816)), _1768818)))], (48938 ^ _780205) ^ [_1768678, _1768680, _1768682, _1768684] : [hBOOL(hAPP(hAPP(c_List_Omember(_1768678), hAPP(hAPP(c_List_Olist_OCons(_1768678), _1768680), _1768682)), _1768684)), -(_1768680 = _1768684), -(hBOOL(hAPP(hAPP(c_List_Omember(_1768678), _1768682), _1768684)))], (48956 ^ _780205) ^ [_1768995, _1768997, _1768999] : [hBOOL(hAPP(hAPP(c_member(_1768995), _1768997), hAPP(c_List_Oset(_1768995), _1768999))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1768995), _1768999), _1768997)))], (48962 ^ _780205) ^ [_1769108, _1769110, _1769112] : [hBOOL(hAPP(hAPP(c_List_Omember(_1769108), _1769112), _1769110)), -(hBOOL(hAPP(hAPP(c_member(_1769108), _1769110), hAPP(c_List_Oset(_1769108), _1769112))))], (48968 ^ _780205) ^ [_1769245, _1769247, _1769249] : [c_List_Olist__ex1(_1769245, _1769247, _1769249), 48972 ^ _780205 : [(48973 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769245), 48971 ^ [_1769245, _1769247, _1769249]), hAPP(c_List_Oset(_1769245), _1769249))))], (48975 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1769247, 48971 ^ [_1769245, _1769247, _1769249])))], (48977 ^ _780205) ^ [_1769491] : [-(_1769491 = 48971 ^ [_1769245, _1769247, _1769249]), hBOOL(hAPP(hAPP(c_member(_1769245), _1769491), hAPP(c_List_Oset(_1769245), _1769249))), hBOOL(hAPP(_1769247, _1769491))]]], (48987 ^ _780205) ^ [_1769678, _1769680, _1769682] : [-(c_List_Olist__ex1(_1769678, _1769680, _1769682)), 48988 ^ _780205 : [(48989 ^ _780205) ^ [_1769772] : [hBOOL(hAPP(hAPP(c_member(_1769678), _1769772), hAPP(c_List_Oset(_1769678), _1769682))), hBOOL(hAPP(_1769680, _1769772)), 48997 ^ _780205 : [(48998 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769678), 48996 ^ [_1769678, _1769680, _1769682, _1769772]), hAPP(c_List_Oset(_1769678), _1769682))))], (49000 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1769680, 48996 ^ [_1769678, _1769680, _1769682, _1769772])))], (49002 ^ _780205) ^ [] : [48996 ^ [_1769678, _1769680, _1769682, _1769772] = _1769772]]]]], (49006 ^ _780205) ^ [_1770107, _1770109, _1770111, _1770113] : [class_Groups_Ocomm__monoid__add(_1770107), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1770109, tc_HOL_Obool)), _1770111)), 49016 ^ _780205 : [(49017 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1770109, tc_HOL_Obool)), 49015 ^ [_1770107, _1770109, _1770111, _1770113]), _1770111)))], (49019 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1770109), 49015 ^ [_1770107, _1770109, _1770111, _1770113]))]], 49023 ^ _780205 : [(49024 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1770109, tc_HOL_Obool)), 49022 ^ [_1770107, _1770109, _1770111, _1770113]), _1770111)))], (49027 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1770109, tc_HOL_Obool)), 49025 ^ [_1770107, _1770109, _1770111, _1770113]), _1770111)))], (49029 ^ _780205) ^ [] : [49022 ^ [_1770107, _1770109, _1770111, _1770113] = 49025 ^ [_1770107, _1770109, _1770111, _1770113]], (49032 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770109), 49030 ^ [_1770107, _1770109, _1770111, _1770113]), 49022 ^ [_1770107, _1770109, _1770111, _1770113])))], (49034 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770109), 49030 ^ [_1770107, _1770109, _1770111, _1770113]), 49025 ^ [_1770107, _1770109, _1770111, _1770113])))], (49036 ^ _780205) ^ [] : [hAPP(_1770113, 49030 ^ [_1770107, _1770109, _1770111, _1770113]) = c_Groups_Ozero__class_Ozero(_1770107)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1770109, _1770107), _1770113), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1770109, tc_HOL_Obool), _1770111)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1770109, tc_HOL_Obool), _1770107), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1770109, _1770107), _1770113)), _1770111))], (49040 ^ _780205) ^ [_1771116, _1771118, _1771120] : [-(c_FunDef_OTHE__default(_1771118, _1771120, _1771116) = c_HOL_OThe(_1771118, _1771116)), 49041 ^ _780205 : [(49042 ^ _780205) ^ [_1771180] : [hBOOL(hAPP(_1771116, _1771180)), 49046 ^ _780205 : [(49047 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1771116, 49045 ^ [_1771116, _1771118, _1771120, _1771180])))], (49049 ^ _780205) ^ [] : [49045 ^ [_1771116, _1771118, _1771120, _1771180] = _1771180]]]]], (49053 ^ _780205) ^ [_1771374, _1771376, _1771378] : [-(c_FunDef_OTHE__default(_1771376, _1771378, _1771374) = _1771378), 49055 ^ _780205 : [(49056 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1771374, 49054 ^ [_1771374, _1771376, _1771378])))], (49058 ^ _780205) ^ [_1771496] : [hBOOL(hAPP(_1771374, _1771496)), -(_1771496 = 49054 ^ [_1771374, _1771376, _1771378])]]], (49066 ^ _780205) ^ [_1771635, _1771637, _1771639, _1771641, _1771643, _1771645, _1771647] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1771635, tc_fun(_1771637, tc_fun(_1771639, tc_HOL_Obool))), _1771641), _1771643), _1771645), _1771647)), 49070 ^ _780205 : [(49071 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771635), 49069 ^ [_1771635, _1771637, _1771639, _1771641, _1771643, _1771645, _1771647]), _1771641)))], (49073 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1771643, 49069 ^ [_1771635, _1771637, _1771639, _1771641, _1771643, _1771645, _1771647]), _1771645), _1771647)))]]], (49075 ^ _780205) ^ [_1771861, _1771863, _1771865, _1771867, _1771869, _1771871, _1771873] : [49077 ^ _780205 : [(49078 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771861), 49076 ^ [_1771861, _1771863, _1771865, _1771867, _1771869, _1771871, _1771873]), _1771863)))], (49080 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1771865, 49076 ^ [_1771861, _1771863, _1771865, _1771867, _1771869, _1771871, _1771873]), _1771867), _1771869))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1771861, tc_fun(_1771871, tc_fun(_1771873, tc_HOL_Obool))), _1771863), _1771865), _1771867), _1771869)))], (49084 ^ _780205) ^ [_1772119, _1772121] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1772119)), _1772121)), 49088 ^ _780205 : [(49089 ^ _780205) ^ [_1772220] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1772119)), _1772220), _1772121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772119)), _1772220)), 49087 ^ [_1772119, _1772121])))]]], (49095 ^ _780205) ^ [_1772359] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1772359)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1772359)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49097 ^ _780205) ^ [_1772391, _1772393] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1772391, _1772393), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1772391)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49099 ^ _780205) ^ [_1772424, _1772426] : [-(c_Lazy__Sequence_Oappend(_1772424, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1772424), _1772426) = _1772426)], (49101 ^ _780205) ^ [_1772470, _1772472, _1772474] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1772470) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1772470, _1772472, _1772474)], (49103 ^ _780205) ^ [_1772518, _1772520, _1772522] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1772518, _1772520, _1772522) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1772518)], (49105 ^ _780205) ^ [_1772551, _1772553, _1772555, _1772557] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1772551, _1772553, _1772555, _1772557, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1772553)) = _1772555)], (49107 ^ _780205) ^ [_1772606, _1772608, _1772610] : [c_List_Olist__all(tc_Int_Oint, _1772606, c_List_Oupto(_1772608, _1772610)), -(c_List_Oall__interval__int(_1772606, _1772608, _1772610))], (49113 ^ _780205) ^ [_1772691, _1772693, _1772695] : [c_List_Oall__interval__int(_1772691, _1772693, _1772695), -(c_List_Olist__all(tc_Int_Oint, _1772691, c_List_Oupto(_1772693, _1772695)))], (49119 ^ _780205) ^ [_1772800, _1772802, _1772804] : [c_List_Olist__ex(tc_Int_Oint, _1772800, c_List_Oupto(_1772802, _1772804)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1772800), _1772802, _1772804)], (49125 ^ _780205) ^ [_1772890, _1772892, _1772894] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1772890), _1772892, _1772894)), -(c_List_Olist__ex(tc_Int_Oint, _1772890, c_List_Oupto(_1772892, _1772894)))], (49141 ^ _780205) ^ [_1773137, _1773139, _1773141] : [49143 ^ _780205 : [(49144 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 49142 ^ [_1773137, _1773139, _1773141]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1773139, _1773141))))], (49146 ^ _780205) ^ [] : [hBOOL(hAPP(_1773137, 49142 ^ [_1773137, _1773139, _1773141]))]], -(c_List_Oall__interval__int(_1773137, _1773139, _1773141))], (49131 ^ _780205) ^ [_1772956, _1772958, _1772960] : [c_List_Oall__interval__int(_1772956, _1772958, _1772960), 49134 ^ _780205 : [(49135 ^ _780205) ^ [_1773034] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1773034), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1772958, _1772960))), -(hBOOL(hAPP(_1772956, _1773034)))]]], (49150 ^ _780205) ^ [_1773313, _1773315, _1773317, _1773319] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1773313, _1773315, _1773317, c_Code__Numeral_OSuc__code__numeral(_1773319)) = hAPP(hAPP(_1773317, _1773319), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1773313, _1773315, _1773317, _1773319)))], (49152 ^ _780205) ^ [_1773375, _1773377, _1773379, _1773381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1773375), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1773377, _1773379, _1773375, _1773381) = 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(_1773377)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1773377)))], (49158 ^ _780205) ^ [_1773506, _1773508, _1773510, _1773512] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1773506), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1773508, _1773510, _1773506, _1773512) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1773508, 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(_1773508)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1773510, _1773512)), 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(_1773508)))), 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(_1773508)))), 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(_1773508)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1773508, 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(_1773508)))), 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(_1773508)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1773508, _1773510, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1773506), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1773512))), 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(_1773508)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1773508))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1773508)))), 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(_1773508)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1773508, 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(_1773508)))), 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(_1773508)))), 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(_1773508))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1773508)))), 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(_1773508)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1773508)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1773508))))), tc_prod(_1773508, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1773508)), hAPP(hAPP(c_COMBB(_1773508, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1773508)))), tc_prod(_1773508, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1773508)), c_Product__Type_Ofst(_1773508, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (49164 ^ _780205) ^ [_1773885, _1773887, _1773889] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1773885, _1773887, _1773889, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1773887)], (49166 ^ _780205) ^ [_1773917, _1773919, _1773921] : [-(c_Random__Sequence_Oempty(_1773917, _1773919, _1773921) = 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(_1773917)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1773917)))], (49168 ^ _780205) ^ [_1773966, _1773968, _1773970, _1773972] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1773966), _1773968), _1773970), _1773972) = 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(_1773966)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1773966), _1773968)))], (49170 ^ _780205) ^ [_1774027, _1774029, _1774031, _1774033] : [-(c_Random__Sequence_Omap(_1774027, _1774029, _1774031, _1774033) = c_Random__Sequence_Obind(_1774027, _1774029, _1774033, hAPP(c_Fun_Ocomp(_1774029, 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(_1774029)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1774027, c_Random__Sequence_Osingle(_1774029)), _1774031)))], (49172 ^ _780205) ^ [_1774098, _1774100, _1774102, _1774104, _1774106, _1774108, _1774110] : [hBOOL(hAPP(hAPP(_1774098, hAPP(c_Product__Type_Osnd(_1774100, _1774102), _1774104)), hAPP(c_Product__Type_Ofst(_1774100, _1774102), _1774104))), 49179 ^ _780205 : [(49180 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1774098, 49178 ^ [_1774098, _1774100, _1774102, _1774104, _1774106, _1774108, _1774110]), 49177 ^ [_1774098, _1774100, _1774102, _1774104, _1774106, _1774108, _1774110])))], (49182 ^ _780205) ^ [] : [hBOOL(hAPP(_1774106, hAPP(hAPP(_1774108, 49177 ^ [_1774098, _1774100, _1774102, _1774104, _1774106, _1774108, _1774110]), 49178 ^ [_1774098, _1774100, _1774102, _1774104, _1774106, _1774108, _1774110])))]], -(hBOOL(hAPP(_1774106, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1774100, _1774102, _1774110), _1774108), _1774104))))], (49186 ^ _780205) ^ [_1774495, _1774497, _1774499, _1774501] : [-(hAPP(c_Relation_OImage(_1774495, _1774497, hAPP(c_Set_OCollect(tc_prod(_1774495, _1774497)), hAPP(c_Product__Type_Oprod_Oprod__case(_1774495, _1774497, tc_HOL_Obool), _1774499))), _1774501) = hAPP(c_Set_OCollect(_1774497), hAPP(hAPP(c_COMBB(tc_fun(_1774495, tc_HOL_Obool), tc_HOL_Obool, _1774497), c_HOL_OEx(_1774495)), hAPP(hAPP(c_COMBB(tc_fun(_1774495, tc_HOL_Obool), tc_fun(_1774495, tc_HOL_Obool), _1774497), hAPP(c_COMBS(_1774495, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1774495), c_fconj), hAPP(hAPP(c_COMBC(_1774495, tc_fun(_1774495, tc_HOL_Obool), tc_HOL_Obool), c_member(_1774495)), _1774501)))), hAPP(c_COMBC(_1774495, _1774497, tc_HOL_Obool), _1774499)))))], (49188 ^ _780205) ^ [_1774621, _1774623, _1774625, _1774627, _1774629] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1774621), tc_List_Olist(_1774621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1774621), tc_List_Olist(_1774621)), _1774623), _1774625)), c_List_Olexord(_1774621, _1774627))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1774621), tc_List_Olist(_1774621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1774621), tc_List_Olist(_1774621)), _1774625), _1774629)), c_List_Olexord(_1774621, _1774627))), c_Relation_Otrans(_1774621, _1774627), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1774621), tc_List_Olist(_1774621))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1774621), tc_List_Olist(_1774621)), _1774623), _1774629)), c_List_Olexord(_1774621, _1774627))))], (49202 ^ _780205) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (49204 ^ _780205) ^ [_1775018, _1775020, _1775022, _1775024] : [c_Relation_Otrans(_1775018, _1775020), c_Relation_Otrans(_1775022, _1775024), -(c_Relation_Otrans(tc_prod(_1775018, _1775022), c_Wellfounded_Olex__prod(_1775018, _1775022, _1775020, _1775024)))], (49214 ^ _780205) ^ [_1775171, _1775173, _1775175, _1775177, _1775179] : [c_Relation_Otrans(_1775171, _1775173), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775171, _1775171)), hAPP(hAPP(c_Product__Type_OPair(_1775171, _1775171), _1775175), _1775177)), _1775173)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775171, _1775171)), hAPP(hAPP(c_Product__Type_OPair(_1775171, _1775171), _1775177), _1775179)), _1775173)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775171, _1775171)), hAPP(hAPP(c_Product__Type_OPair(_1775171, _1775171), _1775175), _1775179)), _1775173)))], (49242 ^ _780205) ^ [_1775941, _1775943] : [49245 ^ _780205 : [(49246 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775941, _1775941)), hAPP(hAPP(c_Product__Type_OPair(_1775941, _1775941), 49243 ^ [_1775941, _1775943]), 49244 ^ [_1775941, _1775943])), _1775943)))], (49249 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775941, _1775941)), hAPP(hAPP(c_Product__Type_OPair(_1775941, _1775941), 49244 ^ [_1775941, _1775943]), 49247 ^ [_1775941, _1775943])), _1775943)))], (49251 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775941, _1775941)), hAPP(hAPP(c_Product__Type_OPair(_1775941, _1775941), 49243 ^ [_1775941, _1775943]), 49247 ^ [_1775941, _1775943])), _1775943))]], -(c_Relation_Otrans(_1775941, _1775943))], (49228 ^ _780205) ^ [_1775499, _1775501] : [c_Relation_Otrans(_1775499, _1775501), 49231 ^ _780205 : [(49232 ^ _780205) ^ [_1775635, _1775637] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775499, _1775499)), hAPP(hAPP(c_Product__Type_OPair(_1775499, _1775499), _1775637), _1775635)), _1775501)), 49235 ^ _780205 : [(49236 ^ _780205) ^ [_1775778] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775499, _1775499)), hAPP(hAPP(c_Product__Type_OPair(_1775499, _1775499), _1775635), _1775778)), _1775501)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775499, _1775499)), hAPP(hAPP(c_Product__Type_OPair(_1775499, _1775499), _1775637), _1775778)), _1775501)))]]]]], (49255 ^ _780205) ^ [_1776361, _1776363] : [-(c_Relation_Otrans(_1776361, c_Transitive__Closure_Ortrancl(_1776361, _1776363)))], (49257 ^ _780205) ^ [_1776389] : [-(c_Relation_Otrans(tc_fun(_1776389, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1776389)))], (49259 ^ _780205) ^ [_1776417, _1776419] : [-(c_Relation_Otrans(_1776417, c_Relation_OId__on(_1776417, _1776419)))], (49261 ^ _780205) ^ [_1776445, _1776447] : [c_Relation_Otrans(_1776445, _1776447), -(c_Transitive__Closure_Otrancl(_1776445, _1776447) = _1776447)], (49267 ^ _780205) ^ [_1776528, _1776530] : [-(c_Relation_Otrans(_1776528, c_Transitive__Closure_Otrancl(_1776528, _1776530)))], (49269 ^ _780205) ^ [_1776556] : [-(c_Relation_Otrans(_1776556, c_Relation_OId(_1776556)))], (49271 ^ _780205) ^ [_1776581, _1776583] : [c_Relation_Otrans(_1776581, _1776583), -(c_Relation_Otrans(tc_List_Olist(_1776581), c_List_Olexord(_1776581, _1776583)))], (49277 ^ _780205) ^ [_1776683, _1776685] : [c_Relation_Otrans(_1776683, hAPP(c_Relation_Oconverse(_1776683, _1776683), _1776685)), -(c_Relation_Otrans(_1776683, _1776685))], (49283 ^ _780205) ^ [_1776768, _1776770] : [c_Relation_Otrans(_1776768, _1776770), -(c_Relation_Otrans(_1776768, hAPP(c_Relation_Oconverse(_1776768, _1776768), _1776770)))], (49289 ^ _780205) ^ [_1776859, _1776861, _1776863] : [hBOOL(hAPP(hAPP(c_member(_1776861), _1776859), c_Orderings_Obot__class_Obot(tc_fun(_1776861, tc_HOL_Obool)))), hBOOL(hAPP(_1776863, _1776859))], (49295 ^ _780205) ^ [_1776965, _1776967] : [c_Relation_Otrans(_1776965, _1776967), -(c_Relation_Otrans(tc_List_Olist(_1776965), c_List_Olistrel(_1776965, _1776967)))], (49301 ^ _780205) ^ [_1777052, _1777054, _1777056, _1777058] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1777052), _1777054)), 49304 ^ _780205 : [(49315 ^ _780205) ^ [] : [49317 ^ _780205 : [(49318 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777052), 49316 ^ [_1777052, _1777054, _1777056, _1777058]), _1777054)))], (49320 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1777056), hAPP(c_Set_OCollect(_1777056), hAPP(hAPP(c_COMBC(_1777056, _1777052, tc_HOL_Obool), _1777058), 49316 ^ [_1777052, _1777054, _1777056, _1777058]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1777056), hAPP(c_Set_OCollect(_1777056), hAPP(hAPP(c_COMBB(tc_fun(_1777052, tc_HOL_Obool), tc_HOL_Obool, _1777056), c_HOL_OEx(_1777052)), hAPP(hAPP(c_COMBB(tc_fun(_1777052, tc_HOL_Obool), tc_fun(_1777052, tc_HOL_Obool), _1777056), hAPP(c_COMBS(_1777052, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1777052), c_fconj), hAPP(hAPP(c_COMBC(_1777052, tc_fun(_1777052, tc_HOL_Obool), tc_HOL_Obool), c_member(_1777052)), _1777054)))), _1777058))))))], (49305 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1777056), hAPP(c_Set_OCollect(_1777056), hAPP(hAPP(c_COMBB(tc_fun(_1777052, tc_HOL_Obool), tc_HOL_Obool, _1777056), c_HOL_OEx(_1777052)), hAPP(hAPP(c_COMBB(tc_fun(_1777052, tc_HOL_Obool), tc_fun(_1777052, tc_HOL_Obool), _1777056), hAPP(c_COMBS(_1777052, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1777052), c_fconj), hAPP(hAPP(c_COMBC(_1777052, tc_fun(_1777052, tc_HOL_Obool), tc_HOL_Obool), c_member(_1777052)), _1777054)))), _1777058))))), 49308 ^ _780205 : [(49309 ^ _780205) ^ [_1777360] : [hBOOL(hAPP(hAPP(c_member(_1777052), _1777360), _1777054)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1777056), hAPP(c_Set_OCollect(_1777056), hAPP(hAPP(c_COMBC(_1777056, _1777052, tc_HOL_Obool), _1777058), _1777360)))))]]]]], (49335 ^ _780205) ^ [_1777971, _1777973] : [49336 ^ _780205 : [(49337 ^ _780205) ^ [_1778037] : [hBOOL(hAPP(_1777973, _1778037))]], 49339 ^ _780205 : [(49340 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777971), 49338 ^ [_1777971, _1777973]), c_Orderings_Otop__class_Otop(tc_fun(_1777971, tc_HOL_Obool)))))], (49342 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1777973, 49338 ^ [_1777971, _1777973])))]]], (49324 ^ _780205) ^ [_1777771, _1777773] : [-(hBOOL(hAPP(_1777773, 49331 ^ [_1777771, _1777773]))), 49325 ^ _780205 : [(49326 ^ _780205) ^ [_1777832] : [hBOOL(hAPP(hAPP(c_member(_1777771), _1777832), c_Orderings_Otop__class_Otop(tc_fun(_1777771, tc_HOL_Obool)))), hBOOL(hAPP(_1777773, _1777832))]]], (49344 ^ _780205) ^ [_1778140, _1778142, _1778144] : [c_Relation_Otrans(_1778140, _1778142), c_Relation_Otrans(_1778140, _1778144), -(c_Relation_Otrans(_1778140, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1778140, _1778140), tc_HOL_Obool)), _1778142), _1778144)))], (49354 ^ _780205) ^ [_1778301] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1778301, tc_HOL_Obool) = c_Set_OBex(_1778301))], (49356 ^ _780205) ^ [_1778329, _1778331] : [c_Relation_Otrans(_1778329, _1778331), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778329, _1778329), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1778329, _1778329, _1778329), _1778331), _1778331)), _1778331)))], (49362 ^ _780205) ^ [_1778452, _1778454] : [c_Relation_Otrans(_1778452, _1778454), -(c_Relation_Otrans(_1778452, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1778452, _1778452), tc_HOL_Obool)), _1778454), c_Relation_OId(_1778452))))], (49368 ^ _780205) ^ [_1778561, _1778563, _1778565, _1778567] : [c_Relation_Otrans(_1778561, _1778563), -(c_Relation_Otrans(_1778565, hAPP(hAPP(c_Relation_Oinv__image(_1778561, _1778565), _1778563), _1778567)))], (49374 ^ _780205) ^ [_1778660, _1778662] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1778660, tc_HOL_Obool), _1778662) = hAPP(c_Set_OCollect(_1778660), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778660, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1778660), c_HOL_OEx(tc_fun(_1778660, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778660, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1778660, tc_HOL_Obool), tc_HOL_Obool), _1778660), hAPP(c_COMBS(tc_fun(_1778660, 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(_1778660, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1778660, tc_HOL_Obool), tc_fun(tc_fun(_1778660, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1778660, tc_HOL_Obool))), _1778662)))), c_member(_1778660)))))], (49376 ^ _780205) ^ [_1778806, _1778808, _1778810] : [c_List_Olist__ex(_1778806, _1778808, _1778810), 49380 ^ _780205 : [(49381 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1778806), 49379 ^ [_1778806, _1778808, _1778810]), hAPP(c_List_Oset(_1778806), _1778810))))], (49383 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1778808, 49379 ^ [_1778806, _1778808, _1778810])))]]], (49385 ^ _780205) ^ [_1778960, _1778962, _1778964] : [-(c_List_Olist__ex(_1778960, _1778962, _1778964)), 49386 ^ _780205 : [(49387 ^ _780205) ^ [_1779017] : [hBOOL(hAPP(hAPP(c_member(_1778960), _1779017), hAPP(c_List_Oset(_1778960), _1778964))), hBOOL(hAPP(_1778962, _1779017))]]], (49405 ^ _780205) ^ [_1779364, _1779366, _1779368] : [c_List_Olist__ex(_1779364, _1779368, _1779366), 49409 ^ _780205 : [(49410 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779364), 49408 ^ [_1779364, _1779366, _1779368]), hAPP(c_List_Oset(_1779364), _1779366))))], (49412 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1779368, 49408 ^ [_1779364, _1779366, _1779368])))]]], (49395 ^ _780205) ^ [_1779174, _1779176, _1779178] : [-(c_List_Olist__ex(_1779174, _1779178, _1779176)), 49396 ^ _780205 : [(49397 ^ _780205) ^ [_1779231] : [hBOOL(hAPP(hAPP(c_member(_1779174), _1779231), hAPP(c_List_Oset(_1779174), _1779176))), hBOOL(hAPP(_1779178, _1779231))]]], (49414 ^ _780205) ^ [_1779524, _1779526, _1779528, _1779530] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1779524, tc_fun(_1779526, tc_HOL_Obool)), _1779528), _1779530) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1779526, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1779526, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1779524, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1779526, tc_HOL_Obool)), c_HOL_OEx(_1779524)), hAPP(hAPP(c_COMBB(tc_fun(_1779524, tc_HOL_Obool), tc_fun(_1779524, tc_HOL_Obool), tc_fun(_1779526, tc_HOL_Obool)), hAPP(c_COMBS(_1779524, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1779524), c_fconj), hAPP(hAPP(c_COMBC(_1779524, tc_fun(_1779524, tc_HOL_Obool), tc_HOL_Obool), c_member(_1779524)), _1779528)))), hAPP(hAPP(c_COMBC(tc_fun(_1779526, tc_HOL_Obool), tc_fun(_1779524, tc_fun(_1779526, tc_HOL_Obool)), tc_fun(_1779524, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779526, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1779524, tc_fun(_1779526, tc_HOL_Obool)), tc_fun(_1779524, tc_HOL_Obool)), tc_fun(_1779526, tc_HOL_Obool)), c_COMBB(tc_fun(_1779526, tc_HOL_Obool), tc_HOL_Obool, _1779524)), c_fequal)), _1779530))))))], (49416 ^ _780205) ^ [_1779708, _1779710, _1779712, _1779714] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1779708, tc_fun(_1779710, tc_HOL_Obool)), _1779712), _1779714) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1779710, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1779710, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1779708, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1779710, tc_HOL_Obool)), c_HOL_OEx(_1779708)), hAPP(hAPP(c_COMBB(tc_fun(_1779708, tc_HOL_Obool), tc_fun(_1779708, tc_HOL_Obool), tc_fun(_1779710, tc_HOL_Obool)), hAPP(c_COMBS(_1779708, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1779708), c_fconj), hAPP(hAPP(c_COMBC(_1779708, tc_fun(_1779708, tc_HOL_Obool), tc_HOL_Obool), c_member(_1779708)), _1779712)))), hAPP(hAPP(c_COMBC(tc_fun(_1779710, tc_HOL_Obool), tc_fun(_1779708, tc_fun(_1779710, tc_HOL_Obool)), tc_fun(_1779708, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779710, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1779708, tc_fun(_1779710, tc_HOL_Obool)), tc_fun(_1779708, tc_HOL_Obool)), tc_fun(_1779710, tc_HOL_Obool)), c_COMBB(tc_fun(_1779710, tc_HOL_Obool), tc_HOL_Obool, _1779708)), c_fequal)), _1779714))))))], (49418 ^ _780205) ^ [_1779892, _1779894, _1779896, _1779898] : [class_Complete__Lattice_Ocomplete__lattice(_1779892), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1779894, _1779892), _1779896), _1779898) = c_Complete__Lattice_OSup__class_OSup(_1779892, hAPP(c_Set_OCollect(_1779892), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779894, _1779892), tc_HOL_Obool), tc_HOL_Obool, _1779892), c_HOL_OEx(tc_fun(_1779894, _1779892))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779894, _1779892), tc_HOL_Obool), tc_fun(tc_fun(_1779894, _1779892), tc_HOL_Obool), _1779892), hAPP(c_COMBS(tc_fun(_1779894, _1779892), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1779894, _1779892)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1779894, _1779892), tc_fun(tc_fun(_1779894, _1779892), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1779894, _1779892))), _1779896)))), hAPP(hAPP(c_COMBC(_1779892, tc_fun(tc_fun(_1779894, _1779892), _1779892), tc_fun(tc_fun(_1779894, _1779892), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1779892, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1779894, _1779892), _1779892), tc_fun(tc_fun(_1779894, _1779892), tc_HOL_Obool)), _1779892), c_COMBB(_1779892, tc_HOL_Obool, tc_fun(_1779894, _1779892))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1779894, _1779892), _1779894, _1779892), c_COMBI(tc_fun(_1779894, _1779892))), _1779898)))))))], (49424 ^ _780205) ^ [_1780335, _1780337, _1780339, _1780341] : [class_Complete__Lattice_Ocomplete__lattice(_1780335), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1780337, _1780335), _1780339), _1780341) = c_Complete__Lattice_OSup__class_OSup(_1780335, hAPP(c_Set_OCollect(_1780335), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1780337, _1780335), tc_HOL_Obool), tc_HOL_Obool, _1780335), c_HOL_OEx(tc_fun(_1780337, _1780335))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1780337, _1780335), tc_HOL_Obool), tc_fun(tc_fun(_1780337, _1780335), tc_HOL_Obool), _1780335), hAPP(c_COMBS(tc_fun(_1780337, _1780335), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1780337, _1780335)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1780337, _1780335), tc_fun(tc_fun(_1780337, _1780335), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1780337, _1780335))), _1780339)))), hAPP(hAPP(c_COMBC(_1780335, tc_fun(tc_fun(_1780337, _1780335), _1780335), tc_fun(tc_fun(_1780337, _1780335), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1780335, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1780337, _1780335), _1780335), tc_fun(tc_fun(_1780337, _1780335), tc_HOL_Obool)), _1780335), c_COMBB(_1780335, tc_HOL_Obool, tc_fun(_1780337, _1780335))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1780337, _1780335), _1780337, _1780335), c_COMBI(tc_fun(_1780337, _1780335))), _1780341)))))))], (49430 ^ _780205) ^ [_1780778, _1780780, _1780782, _1780784] : [class_Complete__Lattice_Ocomplete__lattice(_1780778), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1780780, _1780778), _1780782), _1780784) = c_Complete__Lattice_OInf__class_OInf(_1780778, hAPP(c_Set_OCollect(_1780778), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1780780, _1780778), tc_HOL_Obool), tc_HOL_Obool, _1780778), c_HOL_OEx(tc_fun(_1780780, _1780778))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1780780, _1780778), tc_HOL_Obool), tc_fun(tc_fun(_1780780, _1780778), tc_HOL_Obool), _1780778), hAPP(c_COMBS(tc_fun(_1780780, _1780778), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1780780, _1780778)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1780780, _1780778), tc_fun(tc_fun(_1780780, _1780778), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1780780, _1780778))), _1780782)))), hAPP(hAPP(c_COMBC(_1780778, tc_fun(tc_fun(_1780780, _1780778), _1780778), tc_fun(tc_fun(_1780780, _1780778), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1780778, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1780780, _1780778), _1780778), tc_fun(tc_fun(_1780780, _1780778), tc_HOL_Obool)), _1780778), c_COMBB(_1780778, tc_HOL_Obool, tc_fun(_1780780, _1780778))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1780780, _1780778), _1780780, _1780778), c_COMBI(tc_fun(_1780780, _1780778))), _1780784)))))))], (49436 ^ _780205) ^ [_1781221, _1781223, _1781225, _1781227] : [class_Complete__Lattice_Ocomplete__lattice(_1781221), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1781223, _1781221), _1781225), _1781227) = c_Complete__Lattice_OInf__class_OInf(_1781221, hAPP(c_Set_OCollect(_1781221), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1781223, _1781221), tc_HOL_Obool), tc_HOL_Obool, _1781221), c_HOL_OEx(tc_fun(_1781223, _1781221))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1781223, _1781221), tc_HOL_Obool), tc_fun(tc_fun(_1781223, _1781221), tc_HOL_Obool), _1781221), hAPP(c_COMBS(tc_fun(_1781223, _1781221), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1781223, _1781221)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1781223, _1781221), tc_fun(tc_fun(_1781223, _1781221), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1781223, _1781221))), _1781225)))), hAPP(hAPP(c_COMBC(_1781221, tc_fun(tc_fun(_1781223, _1781221), _1781221), tc_fun(tc_fun(_1781223, _1781221), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1781221, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1781223, _1781221), _1781221), tc_fun(tc_fun(_1781223, _1781221), tc_HOL_Obool)), _1781221), c_COMBB(_1781221, tc_HOL_Obool, tc_fun(_1781223, _1781221))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1781223, _1781221), _1781223, _1781221), c_COMBI(tc_fun(_1781223, _1781221))), _1781227)))))))], (49442 ^ _780205) ^ [_1781664, _1781666, _1781668, _1781670] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1781664), _1781666)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1781664), _1781668)), -(_1781668 = c_Orderings_Obot__class_Obot(tc_fun(_1781664, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1781664, _1781670, _1781666, _1781668)), 49456 ^ _780205 : [(49457 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781664), 49455 ^ [_1781664, _1781666, _1781668, _1781670]), _1781666)))], (49459 ^ _780205) ^ [_1782009] : [hBOOL(hAPP(hAPP(c_member(_1781664), _1782009), _1781668)), hBOOL(hAPP(hAPP(_1781670, 49455 ^ [_1781664, _1781666, _1781668, _1781670]), _1782009))]]], (49467 ^ _780205) ^ [_1782190, _1782192] : [c_Predicate_Otransp(_1782190, _1782192), -(c_Relation_Otrans(_1782190, hAPP(c_Set_OCollect(tc_prod(_1782190, _1782190)), hAPP(c_Product__Type_Oprod_Oprod__case(_1782190, _1782190, tc_HOL_Obool), _1782192))))], (49473 ^ _780205) ^ [_1782293, _1782295] : [c_Relation_Otrans(_1782293, hAPP(c_Set_OCollect(tc_prod(_1782293, _1782293)), hAPP(c_Product__Type_Oprod_Oprod__case(_1782293, _1782293, tc_HOL_Obool), _1782295))), -(c_Predicate_Otransp(_1782293, _1782295))], (49479 ^ _780205) ^ [_1782402, _1782404, _1782406, _1782408, _1782410] : [c_Predicate_Otransp(_1782402, _1782404), hBOOL(hAPP(hAPP(_1782404, _1782406), _1782408)), hBOOL(hAPP(hAPP(_1782404, _1782408), _1782410)), -(hBOOL(hAPP(hAPP(_1782404, _1782406), _1782410)))], (49493 ^ _780205) ^ [_1782631, _1782633] : [c_Equiv__Relations_Oequivp(_1782631, _1782633), 49496 ^ _780205 : [(49497 ^ _780205) ^ [] : [-(c_Predicate_Oreflp(_1782631, _1782633))], (49499 ^ _780205) ^ [] : [-(c_Predicate_Osymp(_1782631, _1782633))], (49501 ^ _780205) ^ [] : [-(c_Predicate_Otransp(_1782631, _1782633))]]], (49503 ^ _780205) ^ [_1782762, _1782764] : [c_Predicate_Oreflp(_1782762, _1782764), c_Predicate_Osymp(_1782762, _1782764), c_Predicate_Otransp(_1782762, _1782764), -(c_Equiv__Relations_Oequivp(_1782762, _1782764))], (49517 ^ _780205) ^ [_1782943, _1782945, _1782947, _1782949] : [c_Predicate_Osymp(_1782943, _1782945), hBOOL(hAPP(hAPP(_1782945, _1782947), _1782949)), -(hBOOL(hAPP(hAPP(_1782945, _1782949), _1782947)))], (49527 ^ _780205) ^ [_1783115, _1783117] : [c_Equiv__Relations_Oequivp(_1783115, _1783117), 49530 ^ _780205 : [(49531 ^ _780205) ^ [] : [-(c_Predicate_Oreflp(_1783115, _1783117))], (49533 ^ _780205) ^ [] : [-(c_Predicate_Osymp(_1783115, _1783117))], (49535 ^ _780205) ^ [] : [-(c_Predicate_Otransp(_1783115, _1783117))]]], (49537 ^ _780205) ^ [_1783238, _1783240] : [-(c_Equiv__Relations_Oequivp(_1783238, _1783240)), c_Predicate_Oreflp(_1783238, _1783240), c_Predicate_Osymp(_1783238, _1783240), c_Predicate_Otransp(_1783238, _1783240)], (49551 ^ _780205) ^ [_1783442, _1783444, _1783446, _1783448] : [c_Wellfounded_Omax__extp(_1783442, _1783444, _1783446, _1783448), 49554 ^ _780205 : [(49555 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1783442), _1783446)))], (49557 ^ _780205) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1783442), _1783448)))], (49559 ^ _780205) ^ [] : [_1783448 = c_Orderings_Obot__class_Obot(tc_fun(_1783442, tc_HOL_Obool))], (49561 ^ _780205) ^ [_1783658] : [hBOOL(hAPP(hAPP(c_member(_1783442), _1783658), _1783446)), 49565 ^ _780205 : [(49566 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1783442), 49564 ^ [_1783442, _1783444, _1783446, _1783448, _1783658]), _1783448)))], (49568 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1783444, _1783658), 49564 ^ [_1783442, _1783444, _1783446, _1783448, _1783658])))]]]]], (49570 ^ _780205) ^ [_1783842, _1783844, _1783846, _1783848] : [-(c_Wellfounded_Omax__extp(_1783842, _1783844, _1783846, _1783848)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1783842), _1783846)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1783842), _1783848)), -(_1783848 = c_Orderings_Obot__class_Obot(tc_fun(_1783842, tc_HOL_Obool))), 49584 ^ _780205 : [(49585 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1783842), 49583 ^ [_1783842, _1783844, _1783846, _1783848]), _1783846)))], (49587 ^ _780205) ^ [_1784187] : [hBOOL(hAPP(hAPP(c_member(_1783842), _1784187), _1783848)), hBOOL(hAPP(hAPP(_1783844, 49583 ^ [_1783842, _1783844, _1783846, _1783848]), _1784187))]]], (49595 ^ _780205) ^ [_1784355, _1784357] : [c_Relation_Otrans(_1784355, _1784357), c_Relation_Oantisym(_1784355, _1784357), -(c_Relation_Otrans(_1784355, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1784355, _1784355), tc_HOL_Obool)), _1784357), c_Relation_OId(_1784355))))], (49605 ^ _780205) ^ [_1784516, _1784518] : [-(c_Relation_Oantisym(_1784516, c_Relation_OId__on(_1784516, _1784518)))], (49607 ^ _780205) ^ [_1784544] : [-(c_Relation_Oantisym(_1784544, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1784544, _1784544), tc_HOL_Obool))))], (49609 ^ _780205) ^ [_1784590, _1784592] : [c_Relation_Oantisym(_1784590, hAPP(c_Relation_Oconverse(_1784590, _1784590), _1784592)), -(c_Relation_Oantisym(_1784590, _1784592))], (49615 ^ _780205) ^ [_1784675, _1784677] : [c_Relation_Oantisym(_1784675, _1784677), -(c_Relation_Oantisym(_1784675, hAPP(c_Relation_Oconverse(_1784675, _1784675), _1784677)))], (49621 ^ _780205) ^ [_1784766] : [-(c_Relation_Oantisym(_1784766, c_Relation_OId(_1784766)))], (49623 ^ _780205) ^ [_1784791, _1784793, _1784795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1784791, _1784791), tc_HOL_Obool)), _1784793), _1784795)), c_Relation_Oantisym(_1784791, _1784795), -(c_Relation_Oantisym(_1784791, _1784793))], (49633 ^ _780205) ^ [_1784950, _1784952, _1784954, _1784956] : [c_Relation_Oantisym(_1784950, _1784952), hBOOL(hAPP(hAPP(c_member(tc_prod(_1784950, _1784950)), hAPP(hAPP(c_Product__Type_OPair(_1784950, _1784950), _1784954), _1784956)), _1784952)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1784950, _1784950)), hAPP(hAPP(c_Product__Type_OPair(_1784950, _1784950), _1784956), _1784954)), _1784952)), -(_1784954 = _1784956)], (49661 ^ _780205) ^ [_1785559, _1785561] : [49664 ^ _780205 : [(49665 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785559, _1785559)), hAPP(hAPP(c_Product__Type_OPair(_1785559, _1785559), 49662 ^ [_1785559, _1785561]), 49663 ^ [_1785559, _1785561])), _1785561)))], (49667 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785559, _1785559)), hAPP(hAPP(c_Product__Type_OPair(_1785559, _1785559), 49663 ^ [_1785559, _1785561]), 49662 ^ [_1785559, _1785561])), _1785561)))], (49669 ^ _780205) ^ [] : [49662 ^ [_1785559, _1785561] = 49663 ^ [_1785559, _1785561]]], -(c_Relation_Oantisym(_1785559, _1785561))], (49647 ^ _780205) ^ [_1785234, _1785236] : [c_Relation_Oantisym(_1785234, _1785236), 49650 ^ _780205 : [(49651 ^ _780205) ^ [_1785346, _1785348] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785234, _1785234)), hAPP(hAPP(c_Product__Type_OPair(_1785234, _1785234), _1785348), _1785346)), _1785236)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1785234, _1785234)), hAPP(hAPP(c_Product__Type_OPair(_1785234, _1785234), _1785346), _1785348)), _1785236)), -(_1785348 = _1785346)]]], (49673 ^ _780205) ^ [_1785895, _1785897] : [c_Relation_Oantisym(_1785895, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1785895, _1785895), tc_HOL_Obool)), _1785897), c_Relation_OId(_1785895))), -(c_Relation_Oantisym(_1785895, _1785897))], (49679 ^ _780205) ^ [_1786000, _1786002] : [c_Relation_Oantisym(_1786000, _1786002), -(c_Relation_Oantisym(_1786000, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1786000, _1786000), tc_HOL_Obool)), _1786002), c_Relation_OId(_1786000))))], (49685 ^ _780205) ^ [_1786111, _1786113] : [c_Wellfounded_Oacyclic(_1786111, _1786113), -(c_Relation_Oantisym(_1786111, c_Transitive__Closure_Ortrancl(_1786111, _1786113)))], (49691 ^ _780205) ^ [_1786194, _1786196, _1786198, _1786200, _1786202, _1786204] : [-(c_Partial__Function_Ofun__lub(_1786194, _1786196, _1786198, _1786200, _1786202, _1786204) = hAPP(_1786200, hAPP(c_Set_OCollect(_1786194), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1786198, _1786194), tc_HOL_Obool), tc_HOL_Obool, _1786194), c_HOL_OEx(tc_fun(_1786198, _1786194))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1786198, _1786194), tc_HOL_Obool), tc_fun(tc_fun(_1786198, _1786194), tc_HOL_Obool), _1786194), hAPP(c_COMBS(tc_fun(_1786198, _1786194), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1786198, _1786194)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1786198, _1786194), tc_fun(tc_fun(_1786198, _1786194), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1786198, _1786194))), _1786202)))), hAPP(hAPP(c_COMBC(_1786194, tc_fun(tc_fun(_1786198, _1786194), _1786194), tc_fun(tc_fun(_1786198, _1786194), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1786194, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1786198, _1786194), _1786194), tc_fun(tc_fun(_1786198, _1786194), tc_HOL_Obool)), _1786194), c_COMBB(_1786194, tc_HOL_Obool, tc_fun(_1786198, _1786194))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1786198, _1786194), _1786198, _1786194), c_COMBI(tc_fun(_1786198, _1786194))), _1786204)))))))], (49693 ^ _780205) ^ [_1786407, _1786409] : [c_Relation_Osym(_1786407, _1786409), c_Relation_Otrans(_1786407, _1786409), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1786407, _1786407), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1786407, _1786407, _1786407), hAPP(c_Relation_Oconverse(_1786407, _1786407), _1786409)), _1786409)), _1786409)))], (49703 ^ _780205) ^ [_1786594, _1786596, _1786598, _1786600] : [c_Relation_Osym(_1786594, _1786596), hBOOL(hAPP(hAPP(c_member(tc_prod(_1786594, _1786594)), hAPP(hAPP(c_Product__Type_OPair(_1786594, _1786594), _1786598), _1786600)), _1786596)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786594, _1786594)), hAPP(hAPP(c_Product__Type_OPair(_1786594, _1786594), _1786600), _1786598)), _1786596)))], (49723 ^ _780205) ^ [_1787085, _1787087] : [49726 ^ _780205 : [(49727 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1787085, _1787085)), hAPP(hAPP(c_Product__Type_OPair(_1787085, _1787085), 49724 ^ [_1787085, _1787087]), 49725 ^ [_1787085, _1787087])), _1787087)))], (49729 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1787085, _1787085)), hAPP(hAPP(c_Product__Type_OPair(_1787085, _1787085), 49725 ^ [_1787085, _1787087]), 49724 ^ [_1787085, _1787087])), _1787087))]], -(c_Relation_Osym(_1787085, _1787087))], (49713 ^ _780205) ^ [_1786822, _1786824] : [c_Relation_Osym(_1786822, _1786824), 49716 ^ _780205 : [(49717 ^ _780205) ^ [_1786928, _1786930] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1786822, _1786822)), hAPP(hAPP(c_Product__Type_OPair(_1786822, _1786822), _1786930), _1786928)), _1786824)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786822, _1786822)), hAPP(hAPP(c_Product__Type_OPair(_1786822, _1786822), _1786928), _1786930)), _1786824)))]]], (49733 ^ _780205) ^ [_1787350, _1787352] : [c_Relation_Osym(_1787350, _1787352), -(c_Relation_Osym(_1787350, c_Transitive__Closure_Ortrancl(_1787350, _1787352)))], (49739 ^ _780205) ^ [_1787433, _1787435] : [-(c_Relation_Osym(_1787433, c_Relation_OId__on(_1787433, _1787435)))], (49741 ^ _780205) ^ [_1787461, _1787463] : [c_Relation_Osym(_1787461, _1787463), -(c_Relation_Osym(_1787461, c_Transitive__Closure_Otrancl(_1787461, _1787463)))], (49747 ^ _780205) ^ [_1787544, _1787546, _1787548] : [c_Relation_Osym(_1787544, _1787546), c_Relation_Osym(_1787544, _1787548), -(c_Relation_Osym(_1787544, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1787544, _1787544), tc_HOL_Obool)), _1787546), _1787548)))], (49757 ^ _780205) ^ [_1787705] : [-(c_Relation_Osym(_1787705, c_Relation_OId(_1787705)))], (49759 ^ _780205) ^ [_1787745, _1787747] : [c_Relation_Osym(_1787745, _1787747), -(hAPP(c_Relation_Oconverse(_1787745, _1787745), _1787747) = _1787747)], (49765 ^ _780205) ^ [_1787830, _1787832] : [hAPP(c_Relation_Oconverse(_1787830, _1787830), _1787832) = _1787832, -(c_Relation_Osym(_1787830, _1787832))], (49771 ^ _780205) ^ [_1787936, _1787938] : [c_Relation_Osym(_1787936, hAPP(c_Relation_Oconverse(_1787936, _1787936), _1787938)), -(c_Relation_Osym(_1787936, _1787938))], (49777 ^ _780205) ^ [_1788021, _1788023] : [c_Relation_Osym(_1788021, _1788023), -(c_Relation_Osym(_1788021, hAPP(c_Relation_Oconverse(_1788021, _1788021), _1788023)))], (49783 ^ _780205) ^ [_1788112, _1788114] : [c_Relation_Osym(_1788112, _1788114), -(c_Relation_Osym(tc_List_Olist(_1788112), c_List_Olistrel(_1788112, _1788114)))], (49789 ^ _780205) ^ [_1788199, _1788201, _1788203] : [c_Relation_Osym(_1788199, _1788201), c_Relation_Osym(_1788199, _1788203), -(c_Relation_Osym(_1788199, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1788199, _1788199), tc_HOL_Obool)), _1788201), _1788203)))], (49799 ^ _780205) ^ [_1788360, _1788362] : [-(c_Relation_Osym(_1788360, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1788360, _1788360), tc_HOL_Obool)), _1788362), hAPP(c_Relation_Oconverse(_1788360, _1788360), _1788362))))], (49801 ^ _780205) ^ [_1788405, _1788407, _1788409, _1788411] : [c_Relation_Osym(_1788405, _1788407), -(c_Relation_Osym(_1788409, hAPP(hAPP(c_Relation_Oinv__image(_1788405, _1788409), _1788407), _1788411)))], (49807 ^ _780205) ^ [_1788504, _1788506] : [-(c_Relation_Osym(_1788504, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1788504, _1788504), tc_HOL_Obool)), _1788506), hAPP(c_Relation_Oconverse(_1788504, _1788504), _1788506))))], (49809 ^ _780205) ^ [_1788567, _1788569, _1788571] : [c_Equiv__Relations_Oequiv(_1788567, _1788569, _1788571), 49812 ^ _780205 : [(49813 ^ _780205) ^ [] : [-(c_Relation_Orefl__on(_1788567, _1788569, _1788571))], (49815 ^ _780205) ^ [] : [-(c_Relation_Osym(_1788567, _1788571))], (49817 ^ _780205) ^ [] : [-(c_Relation_Otrans(_1788567, _1788571))]]], (49819 ^ _780205) ^ [_1788696, _1788698, _1788700] : [-(c_Equiv__Relations_Oequiv(_1788696, _1788698, _1788700)), c_Relation_Orefl__on(_1788696, _1788698, _1788700), c_Relation_Osym(_1788696, _1788700), c_Relation_Otrans(_1788696, _1788700)], (49833 ^ _780205) ^ [_1788889, _1788891, _1788893] : [c_Relation_Orefl__on(_1788889, _1788891, _1788893), c_Relation_Osym(_1788889, _1788893), c_Relation_Otrans(_1788889, _1788893), -(c_Equiv__Relations_Oequiv(_1788889, _1788891, _1788893))], (49847 ^ _780205) ^ [_1789080, _1789082, _1789084] : [c_Equiv__Relations_Oequiv(_1789080, _1789082, _1789084), 49850 ^ _780205 : [(49851 ^ _780205) ^ [] : [-(c_Relation_Orefl__on(_1789080, _1789082, _1789084))], (49853 ^ _780205) ^ [] : [-(c_Relation_Osym(_1789080, _1789084))], (49855 ^ _780205) ^ [] : [-(c_Relation_Otrans(_1789080, _1789084))]]], (49857 ^ _780205) ^ [_1789232, _1789234] : [c_Predicate_Osymp(_1789232, _1789234), -(c_Relation_Osym(_1789232, hAPP(c_Set_OCollect(tc_prod(_1789232, _1789232)), hAPP(c_Product__Type_Oprod_Oprod__case(_1789232, _1789232, tc_HOL_Obool), _1789234))))], (49863 ^ _780205) ^ [_1789335, _1789337] : [c_Relation_Osym(_1789335, hAPP(c_Set_OCollect(tc_prod(_1789335, _1789335)), hAPP(c_Product__Type_Oprod_Oprod__case(_1789335, _1789335, tc_HOL_Obool), _1789337))), -(c_Predicate_Osymp(_1789335, _1789337))], (49869 ^ _780205) ^ [_1789444, _1789446] : [49870 ^ _780205 : [(49871 ^ _780205) ^ [_1789500] : [hBOOL(hAPP(hAPP(_1789444, _1789500), _1789500))]], c_Predicate_Osymp(_1789446, _1789444), c_Predicate_Otransp(_1789446, _1789444), -(c_Equiv__Relations_Opart__equivp(_1789446, _1789444))], (49883 ^ _780205) ^ [_1789663, _1789665] : [c_Equiv__Relations_Opart__equivp(_1789663, _1789665), 49887 ^ _780205 : [(49888 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1789665, 49886 ^ [_1789663, _1789665]), 49886 ^ [_1789663, _1789665])))], (49890 ^ _780205) ^ [] : [-(c_Predicate_Osymp(_1789663, _1789665))], (49892 ^ _780205) ^ [] : [-(c_Predicate_Otransp(_1789663, _1789665))]]], (49894 ^ _780205) ^ [_1789815, _1789817] : [-(c_Equiv__Relations_Opart__equivp(_1789815, _1789817)), 49897 ^ _780205 : [(49898 ^ _780205) ^ [_1789892] : [hBOOL(hAPP(hAPP(_1789817, _1789892), _1789892))]], c_Predicate_Osymp(_1789815, _1789817), c_Predicate_Otransp(_1789815, _1789817)], (49908 ^ _780205) ^ [_1790021, _1790023, _1790025, _1790027, _1790029] : [c_Equiv__Relations_Opart__equivp(_1790021, _1790023), hBOOL(hAPP(hAPP(_1790023, _1790025), _1790027)), hBOOL(hAPP(hAPP(_1790023, _1790027), _1790029)), -(hBOOL(hAPP(hAPP(_1790023, _1790025), _1790029)))], (49922 ^ _780205) ^ [_1790250, _1790252, _1790254, _1790256] : [c_Equiv__Relations_Opart__equivp(_1790250, _1790252), hBOOL(hAPP(hAPP(_1790252, _1790254), _1790256)), -(hBOOL(hAPP(hAPP(_1790252, _1790256), _1790254)))], (49963 ^ _780205) ^ [_1791003, _1791005] : [-(c_Equiv__Relations_Opart__equivp(_1791003, _1791005)), 49966 ^ _780205 : [(49967 ^ _780205) ^ [_1791123] : [hBOOL(hAPP(hAPP(_1791005, _1791123), _1791123))]], 49984 ^ _780205 : [(49985 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1791005, 49968 ^ [_1791003, _1791005]), 49968 ^ [_1791003, _1791005])))], (49987 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1791005, 49969 ^ [_1791003, _1791005]), 49969 ^ [_1791003, _1791005])))], (49989 ^ _780205) ^ [] : [-(hAPP(_1791005, 49968 ^ [_1791003, _1791005]) = hAPP(_1791005, 49969 ^ [_1791003, _1791005]))], (49991 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1791005, 49968 ^ [_1791003, _1791005]), 49969 ^ [_1791003, _1791005]))]], 49972 ^ _780205 : [(49973 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1791005, 49968 ^ [_1791003, _1791005]), 49969 ^ [_1791003, _1791005])))], (49975 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1791005, 49968 ^ [_1791003, _1791005]), 49968 ^ [_1791003, _1791005])), hBOOL(hAPP(hAPP(_1791005, 49969 ^ [_1791003, _1791005]), 49969 ^ [_1791003, _1791005])), hAPP(_1791005, 49968 ^ [_1791003, _1791005]) = hAPP(_1791005, 49969 ^ [_1791003, _1791005])]]], (49932 ^ _780205) ^ [_1790422, _1790424] : [c_Equiv__Relations_Opart__equivp(_1790422, _1790424), 49936 ^ _780205 : [(49937 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1790424, 49935 ^ [_1790422, _1790424]), 49935 ^ [_1790422, _1790424])))], (49939 ^ _780205) ^ [_1790595, _1790597] : [hBOOL(hAPP(hAPP(_1790424, _1790597), _1790595)), 49942 ^ _780205 : [(49943 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1790424, _1790597), _1790597)))], (49945 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1790424, _1790595), _1790595)))], (49947 ^ _780205) ^ [] : [-(hAPP(_1790424, _1790597) = hAPP(_1790424, _1790595))]]], (49949 ^ _780205) ^ [_1790764, _1790766] : [-(hBOOL(hAPP(hAPP(_1790424, _1790766), _1790764))), hBOOL(hAPP(hAPP(_1790424, _1790766), _1790766)), hBOOL(hAPP(hAPP(_1790424, _1790764), _1790764)), hAPP(_1790424, _1790766) = hAPP(_1790424, _1790764)]]], (49995 ^ _780205) ^ [_1791671, _1791673] : [c_Equiv__Relations_Oequivp(_1791671, _1791673), -(c_Equiv__Relations_Opart__equivp(_1791671, _1791673))], (50001 ^ _780205) ^ [_1791748, _1791750] : [c_Equiv__Relations_Opart__equivp(_1791748, _1791750), 50005 ^ _780205 : [(50006 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1791750, 50004 ^ [_1791748, _1791750]), 50004 ^ [_1791748, _1791750])))], (50008 ^ _780205) ^ [] : [-(c_Predicate_Osymp(_1791748, _1791750))], (50010 ^ _780205) ^ [] : [-(c_Predicate_Otransp(_1791748, _1791750))]]], (50012 ^ _780205) ^ [_1791908, _1791910] : [c_Equiv__Relations_Opart__equivp(_1791908, _1791910), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1791908, tc_HOL_Obool)), 50015 ^ [_1791908, _1791910]), hAPP(hAPP(c_COMBB(tc_fun(_1791908, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1791908, tc_HOL_Obool)), c_HOL_OEx(_1791908)), hAPP(hAPP(c_COMBB(tc_fun(_1791908, tc_HOL_Obool), tc_fun(_1791908, tc_HOL_Obool), tc_fun(_1791908, tc_HOL_Obool)), hAPP(c_COMBS(_1791908, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1791908), c_fconj), hAPP(hAPP(c_COMBS(_1791908, _1791908, tc_HOL_Obool), _1791910), c_COMBI(_1791908))))), hAPP(hAPP(c_COMBC(tc_fun(_1791908, tc_HOL_Obool), tc_fun(_1791908, tc_fun(_1791908, tc_HOL_Obool)), tc_fun(_1791908, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1791908, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1791908, tc_fun(_1791908, tc_HOL_Obool)), tc_fun(_1791908, tc_HOL_Obool)), tc_fun(_1791908, tc_HOL_Obool)), c_COMBB(tc_fun(_1791908, tc_HOL_Obool), tc_HOL_Obool, _1791908)), c_fequal)), _1791910))))))], (50019 ^ _780205) ^ [_1792269, _1792271, _1792273] : [c_Fun_Oinj__on(_1792269, _1792271, _1792273, c_Orderings_Otop__class_Otop(tc_fun(_1792269, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1792271, _1792269, _1792269, c_Hilbert__Choice_Oinv__into(_1792269, _1792271, c_Orderings_Otop__class_Otop(tc_fun(_1792269, tc_HOL_Obool)), _1792273)), _1792273) = c_Fun_Oid(_1792269))], (50025 ^ _780205) ^ [_1792420, _1792422, _1792424] : [c_Fun_Oinj__on(_1792420, _1792422, _1792424, c_Orderings_Otop__class_Otop(tc_fun(_1792420, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1792422, _1792420, _1792420, c_Hilbert__Choice_Oinv__into(_1792420, _1792422, c_Orderings_Otop__class_Otop(tc_fun(_1792420, tc_HOL_Obool)), _1792424)), _1792424) = c_Fun_Oid(_1792420))], (50031 ^ _780205) ^ [_1792549, _1792551, _1792553] : [hAPP(c_Fun_Ocomp(_1792551, _1792549, _1792549, c_Hilbert__Choice_Oinv__into(_1792549, _1792551, c_Orderings_Otop__class_Otop(tc_fun(_1792549, tc_HOL_Obool)), _1792553)), _1792553) = c_Fun_Oid(_1792549), -(c_Fun_Oinj__on(_1792549, _1792551, _1792553, c_Orderings_Otop__class_Otop(tc_fun(_1792549, tc_HOL_Obool))))], (50037 ^ _780205) ^ [_1792684] : [-(c_Hilbert__Choice_Oinv__into(_1792684, _1792684, c_Orderings_Otop__class_Otop(tc_fun(_1792684, tc_HOL_Obool)), c_Fun_Oid(_1792684)) = c_Fun_Oid(_1792684))], (50039 ^ _780205) ^ [_1792721, _1792723, _1792725, _1792727] : [c_Fun_Oinj__on(_1792721, _1792723, _1792725, c_Orderings_Otop__class_Otop(tc_fun(_1792721, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1792721, _1792723, c_Orderings_Otop__class_Otop(tc_fun(_1792721, tc_HOL_Obool)), _1792725), hAPP(_1792725, _1792727)) = _1792727)], (50045 ^ _780205) ^ [_1792848, _1792850, _1792852, _1792854, _1792856] : [c_Fun_Oinj__on(_1792848, _1792850, _1792852, c_Orderings_Otop__class_Otop(tc_fun(_1792848, tc_HOL_Obool))), hAPP(_1792852, _1792854) = _1792856, -(hAPP(c_Hilbert__Choice_Oinv__into(_1792848, _1792850, c_Orderings_Otop__class_Otop(tc_fun(_1792848, tc_HOL_Obool)), _1792852), _1792856) = _1792854)], (50055 ^ _780205) ^ [_1793035, _1793037, _1793039, _1793041, _1793043, _1793045] : [c_Fun_Oinj__on(_1793035, _1793037, _1793039, _1793041), hBOOL(hAPP(hAPP(c_member(_1793035), _1793043), _1793041)), hAPP(_1793039, _1793043) = _1793045, -(hAPP(c_Hilbert__Choice_Oinv__into(_1793035, _1793037, _1793041, _1793039), _1793045) = _1793043)], (50069 ^ _780205) ^ [_1793280, _1793282, _1793284, _1793286, _1793288] : [c_Fun_Oinj__on(_1793280, _1793282, _1793284, _1793286), hBOOL(hAPP(hAPP(c_member(_1793280), _1793288), _1793286)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1793280, _1793282, _1793286, _1793284), hAPP(_1793284, _1793288)) = _1793288)], (50079 ^ _780205) ^ [_1793461, _1793463, _1793465, _1793467, _1793469, _1793471] : [hAPP(c_Hilbert__Choice_Oinv__into(_1793461, _1793463, _1793465, _1793467), _1793469) = hAPP(c_Hilbert__Choice_Oinv__into(_1793461, _1793463, _1793465, _1793467), _1793471), hBOOL(hAPP(hAPP(c_member(_1793463), _1793469), hAPP(c_Set_Oimage(_1793461, _1793463, _1793467), _1793465))), hBOOL(hAPP(hAPP(c_member(_1793463), _1793471), hAPP(c_Set_Oimage(_1793461, _1793463, _1793467), _1793465))), -(_1793469 = _1793471)], (50093 ^ _780205) ^ [_1793754, _1793756, _1793758, _1793760, _1793762] : [hBOOL(hAPP(hAPP(c_member(_1793754), _1793756), hAPP(c_Set_Oimage(_1793758, _1793754, _1793760), _1793762))), -(hBOOL(hAPP(hAPP(c_member(_1793758), hAPP(c_Hilbert__Choice_Oinv__into(_1793758, _1793754, _1793762, _1793760), _1793756)), _1793762)))], (50099 ^ _780205) ^ [_1793895, _1793897, _1793899, _1793901, _1793903] : [hBOOL(hAPP(hAPP(c_member(_1793895), _1793897), hAPP(c_Set_Oimage(_1793899, _1793895, _1793901), _1793903))), -(hAPP(_1793901, hAPP(c_Hilbert__Choice_Oinv__into(_1793899, _1793895, _1793903, _1793901), _1793897)) = _1793897)], (50105 ^ _780205) ^ [_1794046, _1794048, _1794050] : [hAPP(c_Set_Oimage(_1794046, _1794048, _1794050), c_Orderings_Otop__class_Otop(tc_fun(_1794046, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1794048, tc_HOL_Obool)), 50108 ^ _780205 : [(50109 ^ _780205) ^ [_1794157] : [-(hAPP(_1794050, hAPP(c_Hilbert__Choice_Oinv__into(_1794046, _1794048, c_Orderings_Otop__class_Otop(tc_fun(_1794046, tc_HOL_Obool)), _1794050), _1794157)) = _1794157)]]], (50111 ^ _780205) ^ [_1794196, _1794198, _1794200] : [hAPP(_1794200, hAPP(c_Hilbert__Choice_Oinv__into(_1794196, _1794198, c_Orderings_Otop__class_Otop(tc_fun(_1794196, tc_HOL_Obool)), _1794200), 50112 ^ [_1794196, _1794198, _1794200])) = 50112 ^ [_1794196, _1794198, _1794200], -(hAPP(c_Set_Oimage(_1794196, _1794198, _1794200), c_Orderings_Otop__class_Otop(tc_fun(_1794196, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1794198, tc_HOL_Obool)))], (50118 ^ _780205) ^ [_1794396, _1794398, _1794400, _1794402] : [hAPP(c_Set_Oimage(_1794396, _1794398, _1794400), c_Orderings_Otop__class_Otop(tc_fun(_1794396, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1794398, tc_HOL_Obool)), -(hAPP(_1794400, hAPP(c_Hilbert__Choice_Oinv__into(_1794396, _1794398, c_Orderings_Otop__class_Otop(tc_fun(_1794396, tc_HOL_Obool)), _1794400), _1794402)) = _1794402)], (50124 ^ _780205) ^ [_1794543, _1794545, _1794547, _1794549] : [hAPP(c_Set_Oimage(_1794543, _1794545, _1794547), c_Orderings_Otop__class_Otop(tc_fun(_1794543, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1794545, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1794543, _1794545, _1794547), hAPP(c_Set_Oimage(_1794545, _1794543, c_Hilbert__Choice_Oinv__into(_1794543, _1794545, c_Orderings_Otop__class_Otop(tc_fun(_1794543, tc_HOL_Obool)), _1794547)), _1794549)) = _1794549)], (50130 ^ _780205) ^ [_1794706, _1794708, _1794710, _1794712, _1794714, _1794716] : [hAPP(c_Set_Oimage(_1794706, _1794708, _1794710), _1794712) = _1794714, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794708, tc_HOL_Obool)), _1794716), _1794714)), -(hAPP(c_Set_Oimage(_1794706, _1794708, _1794710), hAPP(c_Set_Oimage(_1794708, _1794706, c_Hilbert__Choice_Oinv__into(_1794706, _1794708, _1794712, _1794710)), _1794716)) = _1794716)], (50140 ^ _780205) ^ [_1794923, _1794925, _1794927, _1794929, _1794931] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1794923, _1794925, _1794927, _1794929), _1794931) = c_Hilbert__Choice_OEps(_1794923, hAPP(hAPP(c_COMBS(_1794923, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1794923), c_fconj), hAPP(hAPP(c_COMBC(_1794923, tc_fun(_1794923, tc_HOL_Obool), tc_HOL_Obool), c_member(_1794923)), _1794927))), hAPP(hAPP(c_COMBC(_1794923, _1794925, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1794925, tc_fun(_1794925, tc_HOL_Obool), _1794923), c_fequal), _1794929)), _1794931))))], (50142 ^ _780205) ^ [_1795023, _1795025, _1795027, _1795029] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1795023, _1795025, c_Orderings_Otop__class_Otop(tc_fun(_1795023, tc_HOL_Obool)), _1795027), _1795029) = c_Hilbert__Choice_OEps(_1795023, hAPP(hAPP(c_COMBC(_1795023, _1795025, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1795025, tc_fun(_1795025, tc_HOL_Obool), _1795023), c_fequal), _1795027)), _1795029)))], (50144 ^ _780205) ^ [_1795091, _1795093, _1795095, _1795097, _1795099] : [c_Fun_Oinj__on(_1795091, _1795093, _1795095, c_Orderings_Otop__class_Otop(tc_fun(_1795091, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1795093, _1795097, _1795091, hAPP(c_Fun_Ocomp(_1795091, _1795097, _1795093, _1795099), c_Hilbert__Choice_Oinv__into(_1795091, _1795093, c_Orderings_Otop__class_Otop(tc_fun(_1795091, tc_HOL_Obool)), _1795095))), _1795095) = _1795099)], (50150 ^ _780205) ^ [_1795240, _1795242, _1795244] : [hAPP(c_Set_Oimage(_1795240, _1795242, _1795244), c_Orderings_Otop__class_Otop(tc_fun(_1795240, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1795242, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1795242, _1795240, c_Hilbert__Choice_Oinv__into(_1795240, _1795242, c_Orderings_Otop__class_Otop(tc_fun(_1795240, tc_HOL_Obool)), _1795244), c_Orderings_Otop__class_Otop(tc_fun(_1795242, tc_HOL_Obool))))], (50156 ^ _780205) ^ [_1795387, _1795389, _1795391, _1795393] : [c_Fun_Oinj__on(_1795387, _1795389, _1795391, c_Orderings_Otop__class_Otop(tc_fun(_1795387, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1795389, _1795387, c_Hilbert__Choice_Oinv__into(_1795387, _1795389, c_Orderings_Otop__class_Otop(tc_fun(_1795387, tc_HOL_Obool)), _1795391)), hAPP(c_Set_Oimage(_1795387, _1795389, _1795391), _1795393)) = _1795393)], (50162 ^ _780205) ^ [_1795530, _1795532, _1795534, _1795536] : [c_Fun_Oinj__on(_1795530, _1795532, _1795534, c_Orderings_Otop__class_Otop(tc_fun(_1795530, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1795532, _1795530, c_Hilbert__Choice_Oinv__into(_1795530, _1795532, c_Orderings_Otop__class_Otop(tc_fun(_1795530, tc_HOL_Obool)), _1795534)), hAPP(c_Set_Oimage(_1795530, _1795532, _1795534), _1795536)) = _1795536)], (50168 ^ _780205) ^ [_1795673, _1795675, _1795677] : [c_Fun_Oinj__on(_1795673, _1795675, _1795677, c_Orderings_Otop__class_Otop(tc_fun(_1795673, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1795675, _1795673, c_Hilbert__Choice_Oinv__into(_1795673, _1795675, c_Orderings_Otop__class_Otop(tc_fun(_1795673, tc_HOL_Obool)), _1795677)), c_Orderings_Otop__class_Otop(tc_fun(_1795675, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1795673, tc_HOL_Obool)))], (50174 ^ _780205) ^ [_1795820, _1795822, _1795824, _1795826, _1795828] : [c_Fun_Oinj__on(_1795820, _1795822, _1795824, _1795826), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1795820, tc_HOL_Obool)), _1795828), _1795826)), -(hAPP(c_Set_Oimage(_1795822, _1795820, c_Hilbert__Choice_Oinv__into(_1795820, _1795822, _1795826, _1795824)), hAPP(c_Set_Oimage(_1795820, _1795822, _1795824), _1795828)) = _1795828)], (50184 ^ _780205) ^ [_1796023, _1796025, _1796027, _1796029, _1796031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1796023, tc_HOL_Obool)), _1796025), hAPP(c_Set_Oimage(_1796027, _1796023, _1796029), _1796031))), -(c_Fun_Oinj__on(_1796023, _1796027, c_Hilbert__Choice_Oinv__into(_1796027, _1796023, _1796031, _1796029), _1796025))], (50190 ^ _780205) ^ [_1796154, _1796156, _1796158, _1796160, _1796162, _1796164, _1796166] : [c_Fun_Oinj__on(_1796154, _1796156, _1796158, hAPP(c_Set_Oimage(_1796160, _1796154, _1796162), _1796164)), c_Fun_Oinj__on(_1796160, _1796154, _1796162, _1796164), hBOOL(hAPP(hAPP(c_member(_1796156), _1796166), hAPP(c_Set_Oimage(_1796154, _1796156, _1796158), hAPP(c_Set_Oimage(_1796160, _1796154, _1796162), _1796164)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1796160, _1796156, _1796164, hAPP(c_Fun_Ocomp(_1796154, _1796156, _1796160, _1796158), _1796162)), _1796166) = hAPP(hAPP(c_Fun_Ocomp(_1796154, _1796160, _1796156, c_Hilbert__Choice_Oinv__into(_1796160, _1796154, _1796164, _1796162)), c_Hilbert__Choice_Oinv__into(_1796154, _1796156, hAPP(c_Set_Oimage(_1796160, _1796154, _1796162), _1796164), _1796158)), _1796166))], (50204 ^ _780205) ^ [_1796535, _1796537, _1796539] : [hAPP(c_Set_Oimage(_1796535, _1796537, _1796539), c_Orderings_Otop__class_Otop(tc_fun(_1796535, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1796537, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1796535, _1796537, _1796537, _1796539), c_Hilbert__Choice_Oinv__into(_1796535, _1796537, c_Orderings_Otop__class_Otop(tc_fun(_1796535, tc_HOL_Obool)), _1796539)) = c_Fun_Oid(_1796537))], (50210 ^ _780205) ^ [_1796684, _1796686, _1796688] : [hAPP(c_Fun_Ocomp(_1796684, _1796686, _1796686, _1796688), c_Hilbert__Choice_Oinv__into(_1796684, _1796686, c_Orderings_Otop__class_Otop(tc_fun(_1796684, tc_HOL_Obool)), _1796688)) = c_Fun_Oid(_1796686), -(hAPP(c_Set_Oimage(_1796684, _1796686, _1796688), c_Orderings_Otop__class_Otop(tc_fun(_1796684, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1796686, tc_HOL_Obool)))], (50216 ^ _780205) ^ [_1796839, _1796841, _1796843, _1796845, _1796847] : [c_Fun_Oinj__on(_1796839, _1796841, _1796843, c_Orderings_Otop__class_Otop(tc_fun(_1796839, tc_HOL_Obool))), 50222 ^ _780205 : [(50223 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796841), 50221 ^ [_1796839, _1796841, _1796843, _1796845, _1796847]), hAPP(c_Set_Oimage(_1796839, _1796841, _1796843), c_Orderings_Otop__class_Otop(tc_fun(_1796839, tc_HOL_Obool))))))], (50225 ^ _780205) ^ [] : [hBOOL(hAPP(_1796845, hAPP(c_Hilbert__Choice_Oinv__into(_1796839, _1796841, c_Orderings_Otop__class_Otop(tc_fun(_1796839, tc_HOL_Obool)), _1796843), 50221 ^ [_1796839, _1796841, _1796843, _1796845, _1796847])))]], -(hBOOL(hAPP(_1796845, _1796847)))], (50229 ^ _780205) ^ [_1797165, _1797167, _1797169, _1797171, _1797173, _1797175] : [class_Groups_Ocomm__monoid__mult(_1797165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1797167), _1797169)), 50239 ^ _780205 : [(50240 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797167), 50238 ^ [_1797165, _1797167, _1797169, _1797171, _1797173, _1797175]), _1797169)))], (50242 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1797171), hAPP(_1797173, 50238 ^ [_1797165, _1797167, _1797169, _1797171, _1797173, _1797175])))]], 50246 ^ _780205 : [(50247 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797167), 50245 ^ [_1797165, _1797167, _1797169, _1797171, _1797173, _1797175]), _1797169)))], (50250 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797167), 50248 ^ [_1797165, _1797167, _1797169, _1797171, _1797173, _1797175]), _1797169)))], (50252 ^ _780205) ^ [] : [50245 ^ [_1797165, _1797167, _1797169, _1797171, _1797173, _1797175] = 50248 ^ [_1797165, _1797167, _1797169, _1797171, _1797173, _1797175]], (50254 ^ _780205) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1797171, tc_HOL_Obool)), hAPP(_1797173, 50245 ^ [_1797165, _1797167, _1797169, _1797171, _1797173, _1797175])), hAPP(_1797173, 50248 ^ [_1797165, _1797167, _1797169, _1797171, _1797173, _1797175])) = c_Orderings_Obot__class_Obot(tc_fun(_1797171, tc_HOL_Obool))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1797165, _1797171, c_Groups_Otimes__class_Otimes(_1797165)), _1797175), c_Groups_Oone__class_Oone(_1797165)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1797167, tc_fun(_1797171, tc_HOL_Obool)), _1797169), _1797173)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1797165, _1797167, c_Groups_Otimes__class_Otimes(_1797165)), hAPP(hAPP(c_COMBB(tc_fun(_1797171, tc_HOL_Obool), _1797165, _1797167), hAPP(hAPP(c_Finite__Set_Ofold__image(_1797165, _1797171, c_Groups_Otimes__class_Otimes(_1797165)), _1797175), c_Groups_Oone__class_Oone(_1797165))), _1797173)), c_Groups_Oone__class_Oone(_1797165)), _1797169))], (50258 ^ _780205) ^ [_1798125, _1798127] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1798125), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1798127, hAPP(c_Code__Numeral_Onat__of, 50263 ^ [_1798125, _1798127]))), -(hBOOL(hAPP(_1798127, _1798125)))], (50269 ^ _780205) ^ [_1798307] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1798307), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1798307 = hAPP(c_Code__Numeral_Onat__of, 50272 ^ [_1798307]))], (50276 ^ _780205) ^ [_1798412, _1798414] : [50278 ^ _780205 : [(50279 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50277 ^ [_1798412, _1798414]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (50281 ^ _780205) ^ [] : [hBOOL(hAPP(_1798412, hAPP(c_Code__Numeral_Oof__nat, 50277 ^ [_1798412, _1798414])))]], -(hBOOL(hAPP(_1798412, _1798414)))], (50286 ^ _780205) ^ [_1798579] : [-(_1798579 = hAPP(c_Code__Numeral_Oof__nat, 50284 ^ [_1798579]))], (50288 ^ _780205) ^ [_1798607] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50284 ^ [_1798607]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (50290 ^ _780205) ^ [_1798642, _1798644, _1798646, _1798648] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1798642, _1798644, _1798646, _1798648, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1798644)) = _1798646)], (50292 ^ _780205) ^ [_1798688, _1798690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1798688), _1798690)), -(c_Quickcheck_Obeyond(_1798688, _1798690) = _1798690)], (50298 ^ _780205) ^ [_1798775, _1798777] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1798775), _1798777))), -(c_Quickcheck_Obeyond(_1798775, _1798777) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (50304 ^ _780205) ^ [_1798821] : [-(c_Quickcheck_Obeyond(_1798821, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (50306 ^ _780205) ^ [_1798847, _1798849, _1798851, _1798853, _1798855, _1798857] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1798847, _1798849, _1798851, _1798853, c_Lazy__Sequence_Olazy__sequence_OInsert(_1798849, _1798855, _1798857)) = hAPP(hAPP(hAPP(_1798853, _1798855), _1798857), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1798847, _1798849, _1798851, _1798853, _1798857)))], (50308 ^ _780205) ^ [_1798905, _1798907, _1798909, _1798911] : [c_Fun_Obij__betw(_1798905, _1798907, _1798909, c_Orderings_Otop__class_Otop(tc_fun(_1798905, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1798907, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1798905, _1798907, _1798909), hAPP(c_Set_OCollect(_1798905), _1798911)) = hAPP(c_Set_OCollect(_1798907), hAPP(hAPP(c_COMBB(_1798905, tc_HOL_Obool, _1798907), _1798911), c_Hilbert__Choice_Oinv__into(_1798905, _1798907, c_Orderings_Otop__class_Otop(tc_fun(_1798905, tc_HOL_Obool)), _1798909))))], (50314 ^ _780205) ^ [_1799086, _1799088, _1799090, _1799092, _1799094, _1799096] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1799086, _1799088, _1799090, _1799092), _1799094), _1799096) = hAPP(_1799092, hAPP(hAPP(c_Product__Type_OPair(_1799086, _1799088), _1799094), _1799096)))], (50316 ^ _780205) ^ [_1799142, _1799144, _1799146, _1799148, _1799150] : [hBOOL(hAPP(_1799142, hAPP(hAPP(c_Product__Type_OPair(_1799144, _1799146), _1799148), _1799150))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1799144, _1799146, tc_HOL_Obool, _1799142), _1799148), _1799150)))], (50322 ^ _780205) ^ [_1799267, _1799269] : [-(c_Fun_Obij__betw(_1799267, _1799267, c_Fun_Oid(_1799267), _1799269, _1799269))], (50324 ^ _780205) ^ [_1799297, _1799299, _1799301, _1799303, _1799305] : [c_Fun_Obij__betw(_1799297, _1799299, _1799301, _1799303, _1799305), -(c_Fun_Obij__betw(_1799299, _1799297, c_Hilbert__Choice_Oinv__into(_1799297, _1799299, _1799303, _1799301), _1799305, _1799303))], (50330 ^ _780205) ^ [_1799402, _1799404, _1799406, _1799408, _1799410, _1799412] : [c_Fun_Obij__betw(_1799402, _1799404, _1799406, _1799408, _1799410), hBOOL(hAPP(hAPP(c_member(_1799402), _1799412), _1799408)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1799404, _1799402, _1799410, c_Hilbert__Choice_Oinv__into(_1799402, _1799404, _1799408, _1799406)), _1799412) = hAPP(_1799406, _1799412))], (50340 ^ _780205) ^ [_1799599, _1799601, _1799603] : [c_Fun_Obij__betw(_1799599, _1799601, _1799603, c_Orderings_Otop__class_Otop(tc_fun(_1799599, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799601, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1799601, _1799599, c_Orderings_Otop__class_Otop(tc_fun(_1799601, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1799599, _1799601, c_Orderings_Otop__class_Otop(tc_fun(_1799599, tc_HOL_Obool)), _1799603)) = _1799603)], (50346 ^ _780205) ^ [_1799744, _1799746, _1799748] : [c_Fun_Obij__betw(_1799744, _1799746, _1799748, c_Orderings_Otop__class_Otop(tc_fun(_1799744, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799746, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1799746, _1799744, c_Hilbert__Choice_Oinv__into(_1799744, _1799746, c_Orderings_Otop__class_Otop(tc_fun(_1799744, tc_HOL_Obool)), _1799748), c_Orderings_Otop__class_Otop(tc_fun(_1799746, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799744, tc_HOL_Obool))))], (50352 ^ _780205) ^ [_1799895, _1799897, _1799899, _1799901, _1799903] : [c_Fun_Obij__betw(_1799895, _1799897, _1799899, c_Orderings_Otop__class_Otop(tc_fun(_1799895, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799897, tc_HOL_Obool))), c_Fun_Obij__betw(_1799901, _1799895, _1799903, c_Orderings_Otop__class_Otop(tc_fun(_1799901, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799895, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1799901, _1799897, c_Orderings_Otop__class_Otop(tc_fun(_1799901, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1799895, _1799897, _1799901, _1799899), _1799903)) = hAPP(c_Fun_Ocomp(_1799895, _1799901, _1799897, c_Hilbert__Choice_Oinv__into(_1799901, _1799895, c_Orderings_Otop__class_Otop(tc_fun(_1799901, tc_HOL_Obool)), _1799903)), c_Hilbert__Choice_Oinv__into(_1799895, _1799897, c_Orderings_Otop__class_Otop(tc_fun(_1799895, tc_HOL_Obool)), _1799899)))], (50362 ^ _780205) ^ [_1800180, _1800182, _1800184, _1800186, _1800188, _1800190] : [c_Fun_Obij__betw(_1800180, _1800182, _1800184, c_Orderings_Otop__class_Otop(tc_fun(_1800180, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800182, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1800180, _1800182, _1800184), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1800186, tc_fun(_1800180, tc_HOL_Obool)), _1800188), _1800190)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1800186, tc_fun(_1800182, tc_HOL_Obool)), _1800188), hAPP(hAPP(c_COMBB(tc_fun(_1800180, tc_HOL_Obool), tc_fun(_1800182, tc_HOL_Obool), _1800186), c_Set_Oimage(_1800180, _1800182, _1800184)), _1800190)))], (50368 ^ _780205) ^ [_1800393, _1800395, _1800397, _1800399, _1800401, _1800403, _1800405, _1800407] : [c_Fun_Obij__betw(_1800393, _1800395, _1800397, _1800399, _1800401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800393, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1800403, _1800393, _1800405), _1800407)), _1800399)), 50375 ^ _780205 : [(50376 ^ _780205) ^ [] : [c_Fun_Obij__betw(_1800403, _1800393, _1800405, _1800407, _1800399), -(c_Fun_Obij__betw(_1800403, _1800395, hAPP(c_Fun_Ocomp(_1800393, _1800395, _1800403, _1800397), _1800405), _1800407, _1800401))], (50382 ^ _780205) ^ [] : [c_Fun_Obij__betw(_1800403, _1800395, hAPP(c_Fun_Ocomp(_1800393, _1800395, _1800403, _1800397), _1800405), _1800407, _1800401), -(c_Fun_Obij__betw(_1800403, _1800393, _1800405, _1800407, _1800399))]]], (50388 ^ _780205) ^ [_1800782, _1800784, _1800786, _1800788, _1800790, _1800792, _1800794, _1800796] : [c_Fun_Obij__betw(_1800782, _1800784, _1800786, _1800788, _1800790), c_Fun_Obij__betw(_1800784, _1800792, _1800794, _1800790, _1800796), -(c_Fun_Obij__betw(_1800782, _1800792, hAPP(c_Fun_Ocomp(_1800784, _1800792, _1800782, _1800794), _1800786), _1800788, _1800796))], (50398 ^ _780205) ^ [_1800969, _1800971, _1800973, _1800975, _1800977, _1800979, _1800981, _1800983] : [c_Fun_Obij__betw(_1800969, _1800971, _1800973, _1800975, _1800977), 50401 ^ _780205 : [(50402 ^ _780205) ^ [] : [c_Fun_Obij__betw(_1800971, _1800979, _1800981, _1800977, _1800983), -(c_Fun_Obij__betw(_1800969, _1800979, hAPP(c_Fun_Ocomp(_1800971, _1800979, _1800969, _1800981), _1800973), _1800975, _1800983))], (50408 ^ _780205) ^ [] : [c_Fun_Obij__betw(_1800969, _1800979, hAPP(c_Fun_Ocomp(_1800971, _1800979, _1800969, _1800981), _1800973), _1800975, _1800983), -(c_Fun_Obij__betw(_1800971, _1800979, _1800981, _1800977, _1800983))]]], (50414 ^ _780205) ^ [_1801260, _1801262, _1801264, _1801266, _1801268] : [c_Fun_Obij__betw(_1801260, _1801262, _1801264, c_Orderings_Otop__class_Otop(tc_fun(_1801260, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1801262, tc_HOL_Obool))), c_Fun_Obij__betw(_1801262, _1801266, _1801268, c_Orderings_Otop__class_Otop(tc_fun(_1801262, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1801266, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1801260, _1801266, hAPP(c_Fun_Ocomp(_1801262, _1801266, _1801260, _1801268), _1801264), c_Orderings_Otop__class_Otop(tc_fun(_1801260, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1801266, tc_HOL_Obool))))], (50424 ^ _780205) ^ [_1801495, _1801497, _1801499, _1801501, _1801503] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1801495, _1801497, tc_HOL_Obool, _1801499), _1801501), _1801503)), -(hBOOL(hAPP(_1801499, hAPP(hAPP(c_Product__Type_OPair(_1801495, _1801497), _1801501), _1801503))))], (50430 ^ _780205) ^ [_1801620, _1801622, _1801624, _1801626, _1801628] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1801620, _1801622, tc_HOL_Obool, _1801624), _1801626), _1801628)), -(hBOOL(hAPP(_1801624, hAPP(hAPP(c_Product__Type_OPair(_1801620, _1801622), _1801626), _1801628))))], (50436 ^ _780205) ^ [_1801745, _1801747, _1801749, _1801751, _1801753, _1801755] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1801745, _1801747, _1801749, _1801751), _1801753), _1801755) = hAPP(_1801751, hAPP(hAPP(c_Product__Type_OPair(_1801745, _1801747), _1801753), _1801755)))], (50438 ^ _780205) ^ [_1801801, _1801803, _1801805, _1801807] : [c_Fun_Obij__betw(_1801801, _1801803, _1801805, c_Orderings_Otop__class_Otop(tc_fun(_1801801, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1801803, tc_HOL_Obool))), 50441 ^ _780205 : [(50442 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1801801), hAPP(c_Set_Ovimage(_1801801, _1801803, _1801805), _1801807))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1801803), _1801807)))], (50448 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1801803), _1801807)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1801801), hAPP(c_Set_Ovimage(_1801801, _1801803, _1801805), _1801807))))]]], (50454 ^ _780205) ^ [_1802091, _1802093, _1802095, _1802097] : [c_Fun_Obij__betw(_1802091, _1802093, _1802095, c_Orderings_Otop__class_Otop(tc_fun(_1802091, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1802093, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1802091, _1802093, _1802095), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1802091, tc_HOL_Obool)), _1802097)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1802093, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1802091, _1802093, _1802095), _1802097)))], (50460 ^ _780205) ^ [_1802276, _1802278, _1802280] : [c_Fun_Obij__betw(_1802276, _1802278, _1802280, c_Orderings_Otop__class_Otop(tc_fun(_1802276, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1802278, tc_HOL_Obool))), 50463 ^ _780205 : [(50464 ^ _780205) ^ [] : [-(c_Fun_Oinj__on(_1802276, _1802278, _1802280, c_Orderings_Otop__class_Otop(tc_fun(_1802276, tc_HOL_Obool))))], (50466 ^ _780205) ^ [] : [-(hAPP(c_Set_Oimage(_1802276, _1802278, _1802280), c_Orderings_Otop__class_Otop(tc_fun(_1802276, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1802278, tc_HOL_Obool)))]]], (50468 ^ _780205) ^ [_1802451, _1802453, _1802455] : [-(c_Fun_Obij__betw(_1802451, _1802453, _1802455, c_Orderings_Otop__class_Otop(tc_fun(_1802451, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1802453, tc_HOL_Obool)))), c_Fun_Oinj__on(_1802451, _1802453, _1802455, c_Orderings_Otop__class_Otop(tc_fun(_1802451, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1802451, _1802453, _1802455), c_Orderings_Otop__class_Otop(tc_fun(_1802451, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1802453, tc_HOL_Obool))], (50478 ^ _780205) ^ [_1802660, _1802662, _1802664] : [c_Fun_Oinj__on(_1802660, _1802662, _1802664, c_Orderings_Otop__class_Otop(tc_fun(_1802660, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1802660, _1802662, _1802664), c_Orderings_Otop__class_Otop(tc_fun(_1802660, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1802662, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1802660, _1802662, _1802664, c_Orderings_Otop__class_Otop(tc_fun(_1802660, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1802662, tc_HOL_Obool))))], (50488 ^ _780205) ^ [_1802867, _1802869, _1802871, _1802873, _1802875, _1802877, _1802879] : [c_Fun_Obij__betw(_1802867, _1802869, _1802871, _1802873, _1802875), c_Fun_Obij__betw(_1802867, _1802869, _1802871, _1802877, _1802879), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1802869, tc_HOL_Obool)), _1802875), _1802879) = c_Orderings_Obot__class_Obot(tc_fun(_1802869, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1802867, _1802869, _1802871, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1802867, tc_HOL_Obool)), _1802873), _1802877), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1802869, tc_HOL_Obool)), _1802875), _1802879)))], (50502 ^ _780205) ^ [_1803172, _1803174, _1803176, _1803178, _1803180, _1803182, _1803184] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803172, tc_HOL_Obool)), _1803174), _1803176) = c_Orderings_Obot__class_Obot(tc_fun(_1803172, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803178, tc_HOL_Obool)), _1803180), _1803182) = c_Orderings_Obot__class_Obot(tc_fun(_1803178, tc_HOL_Obool)), c_Fun_Obij__betw(_1803172, _1803178, _1803184, _1803174, _1803180), c_Fun_Obij__betw(_1803172, _1803178, _1803184, _1803176, _1803182), -(c_Fun_Obij__betw(_1803172, _1803178, _1803184, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1803172, tc_HOL_Obool)), _1803174), _1803176), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1803178, tc_HOL_Obool)), _1803180), _1803182)))], (50520 ^ _780205) ^ [_1803571, _1803573, _1803575, _1803577, _1803579, _1803581, _1803583] : [c_Fun_Obij__betw(_1803571, _1803573, _1803575, _1803577, _1803579), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803571, tc_HOL_Obool)), _1803581), _1803577)), hAPP(c_Set_Oimage(_1803571, _1803573, _1803575), _1803581) = _1803583, -(c_Fun_Obij__betw(_1803571, _1803573, _1803575, _1803581, _1803583))], (50534 ^ _780205) ^ [_1803828, _1803830, _1803832] : [c_Fun_Obij__betw(_1803828, _1803830, _1803832, c_Orderings_Otop__class_Otop(tc_fun(_1803828, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1803830, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1803828, _1803830, _1803832), c_Orderings_Otop__class_Otop(tc_fun(_1803828, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1803830, tc_HOL_Obool)))], (50540 ^ _780205) ^ [_1803967, _1803969, _1803971, _1803973] : [c_Fun_Obij__betw(_1803967, _1803969, _1803971, _1803973, c_Orderings_Otop__class_Otop(tc_fun(_1803969, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1803967, _1803969, _1803971), c_Orderings_Otop__class_Otop(tc_fun(_1803967, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1803969, tc_HOL_Obool)))], (50546 ^ _780205) ^ [_1804122, _1804124, _1804126, _1804128, _1804130] : [c_Fun_Obij__betw(_1804122, _1804124, _1804126, _1804128, _1804130), 50549 ^ _780205 : [(50550 ^ _780205) ^ [] : [-(c_Fun_Oinj__on(_1804122, _1804124, _1804126, _1804128))], (50552 ^ _780205) ^ [] : [-(hAPP(c_Set_Oimage(_1804122, _1804124, _1804126), _1804128) = _1804130)]]], (50554 ^ _780205) ^ [_1804251, _1804253, _1804255, _1804257, _1804259] : [-(c_Fun_Obij__betw(_1804251, _1804253, _1804255, _1804257, _1804259)), c_Fun_Oinj__on(_1804251, _1804253, _1804255, _1804257), hAPP(c_Set_Oimage(_1804251, _1804253, _1804255), _1804257) = _1804259], (50564 ^ _780205) ^ [_1804418, _1804420, _1804422, _1804424] : [c_Fun_Oinj__on(_1804418, _1804420, _1804422, _1804424), -(c_Fun_Obij__betw(_1804418, _1804420, _1804422, _1804424, hAPP(c_Set_Oimage(_1804418, _1804420, _1804422), _1804424)))], (50570 ^ _780205) ^ [_1804523, _1804525, _1804527, _1804529, _1804531] : [c_Fun_Obij__betw(_1804523, _1804525, _1804527, _1804529, _1804531), -(c_Fun_Oinj__on(_1804523, _1804525, _1804527, _1804529))], (50576 ^ _780205) ^ [_1804616, _1804618, _1804620] : [c_Fun_Obij__betw(_1804616, _1804618, _1804620, c_Orderings_Otop__class_Otop(tc_fun(_1804616, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804618, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1804616, _1804618, _1804620, c_Orderings_Otop__class_Otop(tc_fun(_1804616, tc_HOL_Obool))))], (50582 ^ _780205) ^ [_1804735, _1804737, _1804739, _1804741, _1804743] : [c_Fun_Obij__betw(_1804735, _1804737, _1804739, _1804741, _1804743), -(c_Fun_Obij__betw(_1804737, _1804735, c_Fun_Othe__inv__into(_1804735, _1804737, _1804741, _1804739), _1804743, _1804741))], (50588 ^ _780205) ^ [_1804840, _1804842, _1804844, _1804846, _1804848] : [c_Fun_Obij__betw(_1804840, _1804842, _1804844, _1804846, _1804848), -(hAPP(c_Finite__Set_Ocard(_1804840), _1804846) = hAPP(c_Finite__Set_Ocard(_1804842), _1804848))], (50594 ^ _780205) ^ [_1804949, _1804951, _1804953, _1804955] : [c_Fun_Obij__betw(_1804949, _1804951, _1804953, _1804955, c_Orderings_Obot__class_Obot(tc_fun(_1804951, tc_HOL_Obool))), -(_1804955 = c_Orderings_Obot__class_Obot(tc_fun(_1804949, tc_HOL_Obool)))], (50600 ^ _780205) ^ [_1805056, _1805058, _1805060, _1805062] : [c_Fun_Obij__betw(_1805056, _1805058, _1805060, c_Orderings_Obot__class_Obot(tc_fun(_1805056, tc_HOL_Obool)), _1805062), -(_1805062 = c_Orderings_Obot__class_Obot(tc_fun(_1805058, tc_HOL_Obool)))], (50606 ^ _780205) ^ [_1805163, _1805165, _1805167, _1805169, _1805171] : [c_Fun_Obij__betw(_1805163, _1805165, _1805167, _1805169, _1805171), 50609 ^ _780205 : [(50610 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805163), _1805169)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1805165), _1805171)))], (50616 ^ _780205) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805165), _1805171)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1805163), _1805169)))]]], (50622 ^ _780205) ^ [_1805418, _1805420, _1805422, _1805424] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805418), _1805420)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1805422), _1805424)), 50629 ^ _780205 : [(50630 ^ _780205) ^ [] : [50631 ^ _780205 : [(50632 ^ _780205) ^ [_1805607] : [c_Fun_Obij__betw(_1805418, _1805422, _1805607, _1805420, _1805424)]], -(hAPP(c_Finite__Set_Ocard(_1805418), _1805420) = hAPP(c_Finite__Set_Ocard(_1805422), _1805424))], (50636 ^ _780205) ^ [] : [hAPP(c_Finite__Set_Ocard(_1805418), _1805420) = hAPP(c_Finite__Set_Ocard(_1805422), _1805424), -(c_Fun_Obij__betw(_1805418, _1805422, 50639 ^ [_1805418, _1805420, _1805422, _1805424], _1805420, _1805424))]]], (50643 ^ _780205) ^ [_1805790, _1805792, _1805794] : [c_Fun_Obij__betw(_1805790, _1805790, c_Fun_Oid(_1805790), _1805792, _1805794), -(_1805792 = _1805794)], (50649 ^ _780205) ^ [_1805875, _1805877, _1805879] : [_1805877 = _1805879, -(c_Fun_Obij__betw(_1805875, _1805875, c_Fun_Oid(_1805875), _1805877, _1805879))], (50655 ^ _780205) ^ [_1805966] : [-(c_Fun_Obij__betw(_1805966, _1805966, c_Fun_Oid(_1805966), c_Orderings_Otop__class_Otop(tc_fun(_1805966, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1805966, tc_HOL_Obool))))], (50657 ^ _780205) ^ [_1806004, _1806006, _1806008, _1806010] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1806004, _1806006, _1806008), c_Product__Type_Ocurry(_1806004, _1806006, _1806008, _1806010)) = _1806010)], (50659 ^ _780205) ^ [_1806045, _1806047, _1806049, _1806051] : [-(c_Product__Type_Ocurry(_1806045, _1806047, _1806049, hAPP(c_Product__Type_Oprod_Oprod__case(_1806045, _1806047, _1806049), _1806051)) = _1806051)], (50661 ^ _780205) ^ [_1806086, _1806088, _1806090, _1806092, _1806094] : [c_Fun_Obij__betw(_1806086, _1806088, _1806090, c_Orderings_Otop__class_Otop(tc_fun(_1806086, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1806088, tc_HOL_Obool))), 50664 ^ _780205 : [(50665 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1806086, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1806086, _1806088, _1806090), _1806092)), _1806094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1806088, tc_HOL_Obool)), _1806092), hAPP(c_Set_Oimage(_1806086, _1806088, _1806090), _1806094))))], (50671 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1806088, tc_HOL_Obool)), _1806092), hAPP(c_Set_Oimage(_1806086, _1806088, _1806090), _1806094))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1806086, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1806086, _1806088, _1806090), _1806092)), _1806094)))]]], (50677 ^ _780205) ^ [_1806439, _1806441, _1806443, _1806445] : [c_Fun_Obij__betw(_1806439, _1806441, _1806443, c_Orderings_Otop__class_Otop(tc_fun(_1806439, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1806441, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1806439, _1806441, _1806443), _1806445) = hAPP(c_Set_Oimage(_1806441, _1806439, c_Hilbert__Choice_Oinv__into(_1806439, _1806441, c_Orderings_Otop__class_Otop(tc_fun(_1806439, tc_HOL_Obool)), _1806443)), _1806445))], (50683 ^ _780205) ^ [_1806594, _1806596] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1806594), _1806596)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1806594, 50686 ^ [_1806594, _1806596], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1806594), _1806596)), _1806596))], (50690 ^ _780205) ^ [_1806715, _1806717, _1806719, _1806721, _1806723, _1806725] : [c_Fun_Oinj__on(_1806715, _1806717, _1806719, _1806721), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1806717, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1806715, _1806717, _1806719), _1806721)), _1806723)), c_Fun_Oinj__on(_1806717, _1806715, _1806725, _1806723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1806715, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1806717, _1806715, _1806725), _1806723)), _1806721)), -(c_Fun_Obij__betw(_1806715, _1806717, 50705 ^ [_1806715, _1806717, _1806719, _1806721, _1806723, _1806725], _1806721, _1806723))], (50709 ^ _780205) ^ [_1807082, _1807084] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1807082), _1807084)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1807082, 50712 ^ [_1807082, _1807084], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1807082), _1807084)), _1807084))], (50716 ^ _780205) ^ [_1807201, _1807203] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1807201), _1807203)), -(c_Fun_Obij__betw(_1807201, tc_Nat_Onat, 50719 ^ [_1807201, _1807203], _1807203, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1807201), _1807203))))], (50723 ^ _780205) ^ [_1807320, _1807322, _1807324, _1807326, _1807328] : [50725 ^ _780205 : [(50726 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1807320), 50724 ^ [_1807320, _1807322, _1807324, _1807326, _1807328]), _1807322)))], (50728 ^ _780205) ^ [] : [c_Relation_Orefl__on(_1807324, hAPP(_1807326, 50724 ^ [_1807320, _1807322, _1807324, _1807326, _1807328]), hAPP(_1807328, 50724 ^ [_1807320, _1807322, _1807324, _1807326, _1807328]))]], -(c_Relation_Orefl__on(_1807324, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1807320, tc_fun(_1807324, tc_HOL_Obool)), _1807322), _1807326), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1807320, tc_fun(tc_prod(_1807324, _1807324), tc_HOL_Obool)), _1807322), _1807328)))], (50732 ^ _780205) ^ [_1807588, _1807590, _1807592] : [c_Equiv__Relations_Oequivp(_1807588, _1807590), 50735 ^ _780205 : [(50747 ^ _780205) ^ [] : [50748 ^ _780205 : [(50749 ^ _780205) ^ [_1807877] : [hBOOL(hAPP(_1807592, _1807877))]], 50751 ^ _780205 : [(50752 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1807588), 50750 ^ [_1807588, _1807590, _1807592]), c_Quotient_ORespects(_1807588, _1807590))))], (50754 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1807592, 50750 ^ [_1807588, _1807590, _1807592])))]]], (50736 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1807592, 50743 ^ [_1807588, _1807590, _1807592]))), 50737 ^ _780205 : [(50738 ^ _780205) ^ [_1807710] : [hBOOL(hAPP(hAPP(c_member(_1807588), _1807710), c_Quotient_ORespects(_1807588, _1807590))), hBOOL(hAPP(_1807592, _1807710))]]]]], (50756 ^ _780205) ^ [_1808004, _1808006, _1808008] : [hBOOL(hAPP(hAPP(c_member(_1808004), _1808006), c_Quotient_ORespects(_1808004, _1808008))), -(hBOOL(hAPP(hAPP(_1808008, _1808006), _1808006)))], (50762 ^ _780205) ^ [_1808109, _1808111, _1808113] : [hBOOL(hAPP(hAPP(_1808113, _1808111), _1808111)), -(hBOOL(hAPP(hAPP(c_member(_1808109), _1808111), c_Quotient_ORespects(_1808109, _1808113))))], (50768 ^ _780205) ^ [_1808238, _1808240, _1808242] : [hBOOL(hAPP(c_Quotient_ORespects(_1808238, _1808240), _1808242)), -(hBOOL(hAPP(hAPP(_1808240, _1808242), _1808242)))], (50774 ^ _780205) ^ [_1808333, _1808335, _1808337] : [hBOOL(hAPP(hAPP(_1808335, _1808337), _1808337)), -(hBOOL(hAPP(c_Quotient_ORespects(_1808333, _1808335), _1808337)))], (50780 ^ _780205) ^ [_1808434, _1808436, _1808438, _1808440] : [c_Equiv__Relations_Oequivp(_1808434, _1808436), 50786 ^ _780205 : [(50787 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1808438, 50785 ^ [_1808434, _1808436, _1808438, _1808440])))], (50789 ^ _780205) ^ [] : [hBOOL(hAPP(_1808440, 50785 ^ [_1808434, _1808436, _1808438, _1808440]))]], 50792 ^ _780205 : [(50793 ^ _780205) ^ [_1808693] : [hBOOL(hAPP(_1808438, _1808693))]], 50795 ^ _780205 : [(50796 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808434), 50794 ^ [_1808434, _1808436, _1808438, _1808440]), c_Quotient_ORespects(_1808434, _1808436))))], (50798 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1808440, 50794 ^ [_1808434, _1808436, _1808438, _1808440])))]]], (50800 ^ _780205) ^ [_1808806, _1808808, _1808810, _1808812] : [c_Equiv__Relations_Oequivp(_1808806, _1808808), -(c_Quotient_OBabs(_1808806, _1808810, c_Quotient_ORespects(_1808806, _1808808), _1808812) = _1808812)], (50806 ^ _780205) ^ [_1808903, _1808905, _1808907, _1808909, _1808911] : [hBOOL(hAPP(hAPP(c_member(_1808903), _1808905), _1808907)), -(hAPP(c_Quotient_OBabs(_1808903, _1808909, _1808907, _1808911), _1808905) = hAPP(_1808911, _1808905))], (50812 ^ _780205) ^ [_1809022, _1809024, _1809026] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1809022, _1809022)), hAPP(hAPP(c_Product__Type_OPair(_1809022, _1809022), hAPP(_1809024, hAPP(c_Nat_OSuc, 50813 ^ [_1809022, _1809024, _1809026]))), hAPP(_1809024, 50813 ^ [_1809022, _1809024, _1809026]))), c_Transitive__Closure_Ortrancl(_1809022, _1809026))), c_Wellfounded_Owf(_1809022, c_Transitive__Closure_Otrancl(_1809022, _1809026)), 50821 ^ _780205 : [(50822 ^ _780205) ^ [_1809288] : [-(hAPP(_1809024, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50820 ^ [_1809022, _1809024, _1809026]), _1809288)) = hAPP(_1809024, 50820 ^ [_1809022, _1809024, _1809026]))]]], (50824 ^ _780205) ^ [_1809347, _1809349, _1809351, _1809353, _1809355, _1809357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809347, tc_HOL_Obool)), _1809349), _1809351)), 50830 ^ _780205 : [(50831 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1809347), 50829 ^ [_1809347, _1809349, _1809351, _1809353, _1809355, _1809357]), _1809351)))], (50833 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809353, tc_HOL_Obool)), hAPP(_1809355, 50829 ^ [_1809347, _1809349, _1809351, _1809353, _1809355, _1809357])), hAPP(_1809357, 50829 ^ [_1809347, _1809349, _1809351, _1809353, _1809355, _1809357])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809353, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1809347, tc_fun(_1809353, tc_HOL_Obool)), _1809351), _1809355)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1809347, tc_fun(_1809353, tc_HOL_Obool)), _1809351), _1809357))))], (50837 ^ _780205) ^ [_1809744, _1809746, _1809748, _1809750, _1809752] : [50839 ^ _780205 : [(50840 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1809744), 50838 ^ [_1809744, _1809746, _1809748, _1809750, _1809752]), _1809746)))], (50842 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809748, tc_HOL_Obool)), _1809750), hAPP(_1809752, 50838 ^ [_1809744, _1809746, _1809748, _1809750, _1809752])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809748, tc_HOL_Obool)), _1809750), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1809744, tc_fun(_1809748, tc_HOL_Obool)), _1809746), _1809752))))], (50846 ^ _780205) ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1810005, _1810007), tc_prod(_1810005, _1810007))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1810005, _1810007), tc_prod(_1810005, _1810007)), hAPP(hAPP(c_Product__Type_OPair(_1810005, _1810007), _1810009), _1810011)), hAPP(hAPP(c_Product__Type_OPair(_1810005, _1810007), _1810013), _1810015))), c_Transitive__Closure_Ortrancl(tc_prod(_1810005, _1810007), _1810017))), hBOOL(hAPP(hAPP(_1810019, _1810009), _1810011)), 50857 ^ _780205 : [(50858 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1810005, _1810007), tc_prod(_1810005, _1810007))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1810005, _1810007), tc_prod(_1810005, _1810007)), hAPP(hAPP(c_Product__Type_OPair(_1810005, _1810007), _1810009), _1810011)), hAPP(hAPP(c_Product__Type_OPair(_1810005, _1810007), 50855 ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019]), 50856 ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019]))), c_Transitive__Closure_Ortrancl(tc_prod(_1810005, _1810007), _1810017))))], (50862 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1810005, _1810007), tc_prod(_1810005, _1810007))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1810005, _1810007), tc_prod(_1810005, _1810007)), hAPP(hAPP(c_Product__Type_OPair(_1810005, _1810007), 50855 ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019]), 50856 ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019])), hAPP(hAPP(c_Product__Type_OPair(_1810005, _1810007), 50859 ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019]), 50860 ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019]))), _1810017)))], (50864 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1810019, 50855 ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019]), 50856 ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019])))], (50866 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1810019, 50859 ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019]), 50860 ^ [_1810005, _1810007, _1810009, _1810011, _1810013, _1810015, _1810017, _1810019]))]], -(hBOOL(hAPP(hAPP(_1810019, _1810013), _1810015)))], (50870 ^ _780205) ^ [_1811135, _1811137, _1811139, _1811141, _1811143, _1811145, _1811147] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1811135, _1811137), tc_prod(_1811135, _1811137))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1811135, _1811137), tc_prod(_1811135, _1811137)), hAPP(hAPP(c_Product__Type_OPair(_1811135, _1811137), _1811139), _1811141)), hAPP(hAPP(c_Product__Type_OPair(_1811135, _1811137), _1811143), _1811145))), c_Transitive__Closure_Ortrancl(tc_prod(_1811135, _1811137), _1811147))), -(hAPP(hAPP(c_Product__Type_OPair(_1811135, _1811137), _1811139), _1811141) = hAPP(hAPP(c_Product__Type_OPair(_1811135, _1811137), _1811143), _1811145)), 50879 ^ _780205 : [(50880 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1811135, _1811137), tc_prod(_1811135, _1811137))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1811135, _1811137), tc_prod(_1811135, _1811137)), hAPP(hAPP(c_Product__Type_OPair(_1811135, _1811137), _1811139), _1811141)), hAPP(hAPP(c_Product__Type_OPair(_1811135, _1811137), 50877 ^ [_1811135, _1811137, _1811139, _1811141, _1811143, _1811145, _1811147]), 50878 ^ [_1811135, _1811137, _1811139, _1811141, _1811143, _1811145, _1811147]))), _1811147)))], (50882 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1811135, _1811137), tc_prod(_1811135, _1811137))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1811135, _1811137), tc_prod(_1811135, _1811137)), hAPP(hAPP(c_Product__Type_OPair(_1811135, _1811137), 50877 ^ [_1811135, _1811137, _1811139, _1811141, _1811143, _1811145, _1811147]), 50878 ^ [_1811135, _1811137, _1811139, _1811141, _1811143, _1811145, _1811147])), hAPP(hAPP(c_Product__Type_OPair(_1811135, _1811137), _1811143), _1811145))), c_Transitive__Closure_Ortrancl(tc_prod(_1811135, _1811137), _1811147))))]]], (50884 ^ _780205) ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1811716, _1811718), tc_prod(_1811716, _1811718))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1811716, _1811718), tc_prod(_1811716, _1811718)), hAPP(hAPP(c_Product__Type_OPair(_1811716, _1811718), _1811720), _1811722)), hAPP(hAPP(c_Product__Type_OPair(_1811716, _1811718), _1811724), _1811726))), c_Transitive__Closure_Ortrancl(tc_prod(_1811716, _1811718), _1811728))), hBOOL(hAPP(hAPP(_1811730, _1811724), _1811726)), 50897 ^ _780205 : [(50898 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1811716, _1811718), tc_prod(_1811716, _1811718))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1811716, _1811718), tc_prod(_1811716, _1811718)), hAPP(hAPP(c_Product__Type_OPair(_1811716, _1811718), 50893 ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730]), 50894 ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730])), hAPP(hAPP(c_Product__Type_OPair(_1811716, _1811718), 50895 ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730]), 50896 ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730]))), _1811728)))], (50900 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1811716, _1811718), tc_prod(_1811716, _1811718))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1811716, _1811718), tc_prod(_1811716, _1811718)), hAPP(hAPP(c_Product__Type_OPair(_1811716, _1811718), 50895 ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730]), 50896 ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730])), hAPP(hAPP(c_Product__Type_OPair(_1811716, _1811718), _1811724), _1811726))), c_Transitive__Closure_Ortrancl(tc_prod(_1811716, _1811718), _1811728))))], (50902 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(_1811730, 50895 ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730]), 50896 ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730])))], (50904 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(_1811730, 50893 ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730]), 50894 ^ [_1811716, _1811718, _1811720, _1811722, _1811724, _1811726, _1811728, _1811730]))]], -(hBOOL(hAPP(hAPP(_1811730, _1811720), _1811722)))], (50908 ^ _780205) ^ [_1812776, _1812778, _1812780, _1812782, _1812784, _1812786] : [50911 ^ _780205 : [(50912 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1812776, _1812776)), hAPP(hAPP(c_Product__Type_OPair(_1812776, _1812776), 50909 ^ [_1812776, _1812778, _1812780, _1812782, _1812784, _1812786]), 50910 ^ [_1812776, _1812778, _1812780, _1812782, _1812784, _1812786])), _1812778)))], (50916 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1812780, _1812780)), hAPP(hAPP(c_Product__Type_OPair(_1812780, _1812780), 50913 ^ [_1812776, _1812778, _1812780, _1812782, _1812784, _1812786]), 50914 ^ [_1812776, _1812778, _1812780, _1812782, _1812784, _1812786])), _1812782)))], (50918 ^ _780205) ^ [] : [hAPP(hAPP(_1812784, 50909 ^ [_1812776, _1812778, _1812780, _1812782, _1812784, _1812786]), 50913 ^ [_1812776, _1812778, _1812780, _1812782, _1812784, _1812786]) = hAPP(hAPP(_1812784, 50910 ^ [_1812776, _1812778, _1812780, _1812782, _1812784, _1812786]), 50914 ^ [_1812776, _1812778, _1812780, _1812782, _1812784, _1812786])]], -(c_Equiv__Relations_Ocongruent2(_1812776, _1812780, _1812786, _1812778, _1812782, _1812784))], (50922 ^ _780205) ^ [_1813340, _1813342, _1813344, _1813346] : [50925 ^ _780205 : [(50926 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1813340, _1813340)), hAPP(hAPP(c_Product__Type_OPair(_1813340, _1813340), 50923 ^ [_1813340, _1813342, _1813344, _1813346]), 50924 ^ [_1813340, _1813342, _1813344, _1813346])), _1813342)))], (50928 ^ _780205) ^ [] : [hAPP(_1813344, 50923 ^ [_1813340, _1813342, _1813344, _1813346]) = hAPP(_1813344, 50924 ^ [_1813340, _1813342, _1813344, _1813346])]], -(c_Equiv__Relations_Ocongruent(_1813340, _1813346, _1813342, _1813344))], (50932 ^ _780205) ^ [_1813598, _1813600, _1813602] : [-(c_Lazy__Sequence_Oflat(_1813598, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1813598), _1813600, _1813602)) = c_Lazy__Sequence_Oappend(_1813598, _1813600, c_Lazy__Sequence_Oflat(_1813598, _1813602)))], (50944 ^ _780205) ^ [_1813846, _1813848, _1813850] : [50946 ^ _780205 : [(50947 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50945 ^ [_1813846, _1813848, _1813850]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1813848), _1813850))))], (50949 ^ _780205) ^ [] : [hBOOL(hAPP(_1813846, 50945 ^ [_1813846, _1813848, _1813850]))]], -(c_List_Oall__interval__nat(_1813846, _1813848, _1813850))], (50934 ^ _780205) ^ [_1813659, _1813661, _1813663] : [c_List_Oall__interval__nat(_1813659, _1813661, _1813663), 50937 ^ _780205 : [(50938 ^ _780205) ^ [_1813739] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1813739), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1813661), _1813663))), -(hBOOL(hAPP(_1813659, _1813739)))]]], (50953 ^ _780205) ^ [_1814026] : [-(c_Lazy__Sequence_Oflat(_1814026, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1814026))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1814026))], (50955 ^ _780205) ^ [_1814076, _1814078, _1814080] : [c_List_Olist__all(tc_Nat_Onat, _1814076, c_List_Oupt(_1814078, _1814080)), -(c_List_Oall__interval__nat(_1814076, _1814078, _1814080))], (50961 ^ _780205) ^ [_1814161, _1814163, _1814165] : [c_List_Oall__interval__nat(_1814161, _1814163, _1814165), -(c_List_Olist__all(tc_Nat_Onat, _1814161, c_List_Oupt(_1814163, _1814165)))], (50967 ^ _780205) ^ [_1814270, _1814272, _1814274] : [c_List_Olist__ex(tc_Nat_Onat, _1814270, c_List_Oupt(_1814272, _1814274)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1814270), _1814272, _1814274)], (50973 ^ _780205) ^ [_1814360, _1814362, _1814364] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1814360), _1814362, _1814364)), -(c_List_Olist__ex(tc_Nat_Onat, _1814360, c_List_Oupt(_1814362, _1814364)))], (50979 ^ _780205) ^ [_1814408, _1814410, _1814412, _1814414] : [-(hAPP(c_Lazy__Sequence_Obind(_1814408, _1814410, _1814412), _1814414) = c_Lazy__Sequence_Oflat(_1814410, c_Lazy__Sequence_Omap(_1814408, tc_Lazy__Sequence_Olazy__sequence(_1814410), _1814414, _1814412)))], (50981 ^ _780205) ^ [_1814454, _1814456, _1814458, _1814460, _1814462, _1814464, _1814466, _1814468] : [c_Finite__Set_Ofolding__image(_1814454, _1814456, _1814458, _1814460, _1814462), hBOOL(hAPP(c_Finite__Set_Ofinite(_1814456), _1814464)), 50991 ^ _780205 : [(50992 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1814456), 50990 ^ [_1814454, _1814456, _1814458, _1814460, _1814462, _1814464, _1814466, _1814468]), _1814464)))], (50994 ^ _780205) ^ [] : [hAPP(_1814466, 50990 ^ [_1814454, _1814456, _1814458, _1814460, _1814462, _1814464, _1814466, _1814468]) = hAPP(_1814468, 50990 ^ [_1814454, _1814456, _1814458, _1814460, _1814462, _1814464, _1814466, _1814468])]], -(hAPP(hAPP(_1814462, _1814466), _1814464) = hAPP(hAPP(_1814462, _1814468), _1814464))], (50998 ^ _780205) ^ [_1814859, _1814861, _1814863, _1814865, _1814867] : [-(c_Lazy__Sequence_Omap(_1814859, _1814861, _1814863, c_Lazy__Sequence_Olazy__sequence_OInsert(_1814859, _1814865, _1814867)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1814861, hAPP(_1814863, _1814865), c_Lazy__Sequence_Omap(_1814859, _1814861, _1814863, _1814867)))], (51000 ^ _780205) ^ [_1814911, _1814913, _1814915] : [-(c_Lazy__Sequence_Omap(_1814911, _1814913, _1814915, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1814911)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1814913))], (51002 ^ _780205) ^ [_1814947, _1814949, _1814951, _1814953, _1814955] : [-(c_New__DSequence_Opos__map(_1814947, _1814949, _1814951, _1814953, _1814955) = c_Lazy__Sequence_Omap(_1814947, _1814949, _1814951, hAPP(_1814953, _1814955)))], (51004 ^ _780205) ^ [_1814992, _1814994, _1814996] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1814992), _1814994)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1814992), _1814996))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1814992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1814994), _1814996)))], (51014 ^ _780205) ^ [_1815173] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815173), _1815173)))], (51016 ^ _780205) ^ [_1815201, _1815203] : [class_Rings_Ocomm__semiring__1(_1815201), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815201), _1815203), c_Groups_Ozero__class_Ozero(_1815201))))], (51022 ^ _780205) ^ [_1815294] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1815294)))], (51024 ^ _780205) ^ [_1815319, _1815321, _1815323] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1815319), _1815321)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1815319), _1815323))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1815319)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815321), _1815323)))], (51034 ^ _780205) ^ [_1815500, _1815502, _1815504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1815500)), 51037 ^ _780205 : [(51038 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1815500), _1815502)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1815500), _1815504))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815502), _1815504)))], (51044 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815502), _1815504)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1815500), _1815502)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1815500), _1815504))))]]], (51050 ^ _780205) ^ [_1815783, _1815785, _1815787, _1815789, _1815791] : [class_Groups_Ocomm__monoid__mult(_1815783), class_Rings_Odvd(_1815783), hBOOL(hAPP(c_Finite__Set_Ofinite(_1815785), _1815787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1815785, tc_HOL_Obool)), _1815789), _1815787)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815783), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1815785, _1815783), _1815791), _1815789)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1815785, _1815783), _1815791), _1815787))))], (51068 ^ _780205) ^ [_1816116, _1816118, _1816120, _1816122] : [class_Rings_Ocomm__ring(_1816116), class_Rings_Odvd(_1816116), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816116), _1816118), _1816120)), 51079 ^ _780205 : [(51080 ^ _780205) ^ [_1816369, _1816371] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816116), _1816118), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1816116), _1816371), _1816122))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816116), _1816118), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1816116), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1816116), _1816371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1816116), _1816369), _1816120))), _1816122))))], (51086 ^ _780205) ^ [_1816542, _1816544] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816116), _1816118), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1816116), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1816116), _1816544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1816116), _1816542), _1816120))), _1816122))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816116), _1816118), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1816116), _1816544), _1816122))))]]], (51092 ^ _780205) ^ [_1816729, _1816731, _1816733, _1816735] : [class_Rings_Ocomm__ring(_1816729), class_Rings_Odvd(_1816729), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816729), _1816731), _1816733)), 51103 ^ _780205 : [(51104 ^ _780205) ^ [_1816982, _1816984] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816729), _1816731), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1816729), _1816984), _1816735))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816729), _1816731), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1816729), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1816729), _1816984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1816729), _1816982), _1816733))), _1816735))))], (51110 ^ _780205) ^ [_1817155, _1817157] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816729), _1816731), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1816729), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1816729), _1817157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1816729), _1817155), _1816733))), _1816735))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816729), _1816731), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1816729), _1817157), _1816735))))]]], (51116 ^ _780205) ^ [_1817342, _1817344, _1817346, _1817348, _1817350] : [class_Divides_Osemiring__div(_1817342), -(_1817344 = c_Groups_Ozero__class_Ozero(_1817342)), -(_1817346 = c_Groups_Ozero__class_Ozero(_1817342)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817342), _1817344), _1817348)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817342), _1817346), _1817350)), 51135 ^ _780205 : [(51136 ^ _780205) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817342), _1817348), _1817344) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817342), _1817350), _1817346), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817342), _1817348), _1817346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817342), _1817344), _1817350))], (51142 ^ _780205) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817342), _1817348), _1817346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817342), _1817344), _1817350), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817342), _1817348), _1817344) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817342), _1817350), _1817346))]]], (51148 ^ _780205) ^ [_1817935, _1817937, _1817939, _1817941] : [class_Divides_Osemiring__div(_1817935), -(_1817937 = c_Groups_Ozero__class_Ozero(_1817935)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817935), _1817937), _1817939)), 51159 ^ _780205 : [(51160 ^ _780205) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817935), _1817939), _1817937) = _1817941, -(_1817939 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817935), _1817941), _1817937))], (51166 ^ _780205) ^ [] : [_1817939 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817935), _1817941), _1817937), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817935), _1817939), _1817937) = _1817941)]]], (51172 ^ _780205) ^ [_1818333, _1818335, _1818337] : [class_Rings_Odvd(_1818333), class_Rings_Osemiring__0(_1818333), 51179 ^ _780205 : [(51180 ^ _780205) ^ [] : [51181 ^ _780205 : [(51182 ^ _780205) ^ [_1818525] : [hBOOL(hAPP(_1818335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1818333), _1818337), _1818525)))]], 51184 ^ _780205 : [(51185 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818333), _1818337), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1818333), 51183 ^ [_1818333, _1818335, _1818337]), c_Groups_Ozero__class_Ozero(_1818333)))))], (51187 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1818335, 51183 ^ [_1818333, _1818335, _1818337])))]]], (51189 ^ _780205) ^ [] : [-(hBOOL(hAPP(_1818335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1818333), _1818337), 51196 ^ [_1818333, _1818335, _1818337])))), 51190 ^ _780205 : [(51191 ^ _780205) ^ [_1818662] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818333), _1818337), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1818333), _1818662), c_Groups_Ozero__class_Ozero(_1818333)))), hBOOL(hAPP(_1818335, _1818662))]]]]], (51200 ^ _780205) ^ [_1818835, _1818837, _1818839] : [class_Divides_Osemiring__div(_1818835), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818835), _1818837), _1818839)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1818835), _1818837), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1818835), _1818839), _1818837)) = _1818839)], (51210 ^ _780205) ^ [_1819012, _1819014, _1819016, _1819018] : [class_Divides_Osemiring__div(_1819012), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819012), _1819014), _1819016)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819012), _1819018), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819012), _1819016), _1819014)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819012), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819012), _1819018), _1819016)), _1819014))], (51220 ^ _780205) ^ [_1819225, _1819227, _1819229] : [class_Divides_Osemiring__div(_1819225), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819225), _1819227), _1819229)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819225), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819225), _1819229), _1819227)), _1819227) = _1819229)], (51230 ^ _780205) ^ [_1819402, _1819404, _1819406, _1819408] : [class_Divides_Osemiring__div(_1819402), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819402), _1819404), _1819406)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819402), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819402), _1819406), _1819404)), _1819408) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819402), _1819406), _1819408)), _1819404))], (51240 ^ _780205) ^ [_1819615, _1819617, _1819619, _1819621, _1819623] : [class_Divides_Osemiring__div(_1819615), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819615), _1819617), _1819619)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819615), _1819621), _1819623)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819615), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819615), _1819619), _1819617)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819615), _1819623), _1819621)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819615), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819615), _1819619), _1819623)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819615), _1819617), _1819621)))], (51254 ^ _780205) ^ [_1819936, _1819938, _1819940, _1819942] : [class_Rings_Oidom(_1819936), 51257 ^ _780205 : [(51268 ^ _780205) ^ [] : [51269 ^ _780205 : [(51270 ^ _780205) ^ [] : [_1819938 = c_Groups_Ozero__class_Ozero(_1819936)], (51272 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819936), _1819940), _1819942))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819936), _1819938), _1819940)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819936), _1819938), _1819942))))], (51258 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819936), _1819938), _1819940)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819936), _1819938), _1819942))), -(_1819938 = c_Groups_Ozero__class_Ozero(_1819936)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819936), _1819940), _1819942)))]]], (51276 ^ _780205) ^ [_1820294, _1820296, _1820298, _1820300] : [class_Rings_Oidom(_1820294), 51279 ^ _780205 : [(51290 ^ _780205) ^ [] : [51291 ^ _780205 : [(51292 ^ _780205) ^ [] : [_1820298 = c_Groups_Ozero__class_Ozero(_1820294)], (51294 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820294), _1820296), _1820300))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1820294), _1820296), _1820298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1820294), _1820300), _1820298))))], (51280 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1820294), _1820296), _1820298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1820294), _1820300), _1820298))), -(_1820298 = c_Groups_Ozero__class_Ozero(_1820294)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820294), _1820296), _1820300)))]]], (51298 ^ _780205) ^ [_1820652, _1820654, _1820656] : [class_Rings_Ocomm__semiring__1(_1820652), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820652), _1820654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1820652), _1820654), _1820656))))], (51304 ^ _780205) ^ [_1820759, _1820761, _1820763] : [class_Rings_Ocomm__semiring__1(_1820759), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820759), _1820761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1820759), _1820763), _1820761))))], (51310 ^ _780205) ^ [_1820866, _1820868, _1820870, _1820872] : [class_Rings_Ocomm__semiring__1(_1820866), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820866), _1820868), _1820870)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820866), _1820868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1820866), _1820870), _1820872))))], (51320 ^ _780205) ^ [_1821045, _1821047, _1821049, _1821051] : [class_Rings_Ocomm__semiring__1(_1821045), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821045), _1821047), _1821049)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821045), _1821047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1821045), _1821051), _1821049))))], (51330 ^ _780205) ^ [_1821224, _1821226, _1821228, _1821230, _1821232] : [class_Rings_Ocomm__semiring__1(_1821224), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821224), _1821226), _1821228)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821224), _1821230), _1821232)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1821224), _1821226), _1821230)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1821224), _1821228), _1821232))))], (51344 ^ _780205) ^ [_1821495, _1821497, _1821499, _1821501] : [class_Rings_Odvd(_1821495), _1821497 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1821495), _1821499), _1821501), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821495), _1821499), _1821497)))], (51354 ^ _780205) ^ [_1821660, _1821662, _1821664, _1821666] : [class_Rings_Ocomm__semiring__1(_1821660), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1821660), _1821662), _1821664)), _1821666)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821660), _1821662), _1821666)))], (51364 ^ _780205) ^ [_1821839, _1821841, _1821843, _1821845] : [class_Rings_Ocomm__semiring__1(_1821839), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1821839), _1821841), _1821843)), _1821845)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821839), _1821843), _1821845)))], (51384 ^ _780205) ^ [_1822168, _1822170, _1822172] : [51385 ^ _780205 : [(51386 ^ _780205) ^ [] : [_1822168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51388 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822170), _1822172))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1822168), _1822170)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1822168), _1822172))))], (51374 ^ _780205) ^ [_1822036, _1822038, _1822040] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1822036), _1822038)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1822036), _1822040))), -(_1822036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822038), _1822040)))], (51392 ^ _780205) ^ [_1822331, _1822333, _1822335, _1822337, _1822339] : [class_Rings_Ocomm__semiring__1(_1822331), hBOOL(hAPP(c_Finite__Set_Ofinite(_1822333), _1822335)), hBOOL(hAPP(hAPP(c_member(_1822333), _1822337), _1822335)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822331), hAPP(_1822339, _1822337)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1822333, _1822331), _1822339), _1822335))))], (51406 ^ _780205) ^ [_1822606, _1822608, _1822610] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822606, _1822608) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1822610), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 51409 ^ _780205 : [(51410 ^ _780205) ^ [] : [-(_1822606 = _1822608)], (51412 ^ _780205) ^ [] : [-(_1822608 = _1822610)]]], (51414 ^ _780205) ^ [_1822729, _1822731, _1822733] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822729, _1822731) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1822733), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1822729 = _1822731, _1822731 = _1822733], (51424 ^ _780205) ^ [_1822886] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822886, _1822886) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1822886), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51426 ^ _780205) ^ [_1822920, _1822922] : [_1822920 = _1822922, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822920, _1822922) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1822920), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51432 ^ _780205) ^ [_1823034, _1823036] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823034, _1823036), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823034), _1823036))], (51438 ^ _780205) ^ [_1823126, _1823128] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823126), _1823128))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823126, _1823128))], (51444 ^ _780205) ^ [_1823189, _1823191] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823189, _1823191) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823189), _1823191))], (51450 ^ _780205) ^ [_1823281, _1823283] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823281), _1823283))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823281, _1823283) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51456 ^ _780205) ^ [_1823329, _1823331] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823331, _1823329) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823329), _1823331)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823331), _1823329)))], (51466 ^ _780205) ^ [_1823491, _1823493] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823491), _1823493)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1823493, _1823491) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51472 ^ _780205) ^ [_1823590, _1823592] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823590), _1823592)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1823592, _1823590) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51478 ^ _780205) ^ [_1823689, _1823691] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823689), _1823691)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1823691, _1823689) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51494 ^ _780205) ^ [_1823962, _1823964] : [51495 ^ _780205 : [(51496 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823962), _1823964)))], (51498 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823964), _1823962))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1823962, _1823964) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51484 ^ _780205) ^ [_1823801, _1823803] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1823801, _1823803) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823801), _1823803)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823803), _1823801)))], (51512 ^ _780205) ^ [_1824286, _1824288] : [51513 ^ _780205 : [(51514 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824286), _1824288)))], (51516 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824288), _1824286))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1824286, _1824288) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51502 ^ _780205) ^ [_1824125, _1824127] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1824125, _1824127) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824125), _1824127)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824127), _1824125)))], (51530 ^ _780205) ^ [_1824610, _1824612] : [51531 ^ _780205 : [(51532 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824610), _1824612)))], (51534 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824612), _1824610))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1824610, _1824612))], (51520 ^ _780205) ^ [_1824449, _1824451] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1824449, _1824451), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824449), _1824451)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824451), _1824449)))], (51548 ^ _780205) ^ [_1824934, _1824936] : [51549 ^ _780205 : [(51550 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824934), _1824936)))], (51552 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824936), _1824934))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1824934, _1824936))], (51538 ^ _780205) ^ [_1824773, _1824775] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1824773, _1824775), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824773), _1824775)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824775), _1824773)))], (51556 ^ _780205) ^ [_1825082, _1825084, _1825086] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825082), _1825084)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825082), _1825086)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825082), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1825084), _1825086))))], (51566 ^ _780205) ^ [_1825257, _1825259, _1825261, _1825263] : [class_Rings_Ocomm__ring__1(_1825257), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825257), _1825259), _1825261)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825257), _1825259), _1825263)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825257), _1825259), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1825257), _1825261), _1825263))))], (51580 ^ _780205) ^ [_1825506, _1825508, _1825510] : [class_Rings_Ocomm__ring__1(_1825506), 51583 ^ _780205 : [(51584 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825506), _1825508), hAPP(c_Groups_Ouminus__class_Ouminus(_1825506), _1825510))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825506), _1825508), _1825510)))], (51590 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825506), _1825508), _1825510)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825506), _1825508), hAPP(c_Groups_Ouminus__class_Ouminus(_1825506), _1825510))))]]], (51596 ^ _780205) ^ [_1825774, _1825776, _1825778] : [class_Rings_Ocomm__ring__1(_1825774), 51599 ^ _780205 : [(51600 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825774), hAPP(c_Groups_Ouminus__class_Ouminus(_1825774), _1825776)), _1825778)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825774), _1825776), _1825778)))], (51606 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825774), _1825776), _1825778)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825774), hAPP(c_Groups_Ouminus__class_Ouminus(_1825774), _1825776)), _1825778)))]]], (51612 ^ _780205) ^ [_1826042, _1826044, _1826046] : [class_Divides_Oring__div(_1826042), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826042), _1826044), _1826046)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826042), hAPP(c_Groups_Ouminus__class_Ouminus(_1826042), _1826046)), _1826044) = hAPP(c_Groups_Ouminus__class_Ouminus(_1826042), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826042), _1826046), _1826044)))], (51622 ^ _780205) ^ [_1826239, _1826241, _1826243] : [class_Divides_Oring__div(_1826239), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826239), _1826241), _1826243)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826239), _1826243), hAPP(c_Groups_Ouminus__class_Ouminus(_1826239), _1826241)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1826239), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826239), _1826243), _1826241)))], (51632 ^ _780205) ^ [_1826436, _1826438, _1826440] : [class_Divides_Osemiring__div(_1826436), 51635 ^ _780205 : [(51636 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826436), _1826438), _1826440)), -(c_Divides_Odiv__class_Omod(_1826436, _1826440, _1826438) = c_Groups_Ozero__class_Ozero(_1826436))], (51642 ^ _780205) ^ [] : [c_Divides_Odiv__class_Omod(_1826436, _1826440, _1826438) = c_Groups_Ozero__class_Ozero(_1826436), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826436), _1826438), _1826440)))]]], (51648 ^ _780205) ^ [_1826686, _1826688, _1826690] : [class_Divides_Osemiring__div(_1826686), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826686), _1826688), _1826690)), -(c_Divides_Odiv__class_Omod(_1826686, _1826690, _1826688) = c_Groups_Ozero__class_Ozero(_1826686))], (51658 ^ _780205) ^ [_1826864, _1826866, _1826868, _1826870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826864, _1826866)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826868, _1826870))), 51661 ^ _780205 : [(51680 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826868), _1826870)))], (51662 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826864), _1826866)), 51665 ^ _780205 : [(51666 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826868), _1826864)))], (51668 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826866), _1826870)))], (51670 ^ _780205) ^ [] : [51671 ^ _780205 : [(51672 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826868), _1826864)))], (51674 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826864), _1826868))]], 51675 ^ _780205 : [(51676 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826866), _1826870)))], (51678 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826870), _1826866))]]]]]]], (51682 ^ _780205) ^ [_1827326, _1827328, _1827330, _1827332] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827326, _1827328)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827330, _1827332)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827330), _1827332)), 51685 ^ _780205 : [(51686 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827326), _1827328)))], (51688 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827330), _1827326)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827328), _1827332)), 51695 ^ _780205 : [(51696 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827330), _1827326)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827326), _1827330)))], (51702 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827328), _1827332)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827332), _1827328)))]]]]], (51712 ^ _780205) ^ [_1827869, _1827871, _1827873] : [class_Rings_Olinordered__idom(_1827869), 51715 ^ _780205 : [(51716 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827869), _1827871), hAPP(c_Groups_Oabs__class_Oabs(_1827869), _1827873))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827869), _1827871), _1827873)))], (51722 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827869), _1827871), _1827873)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827869), _1827871), hAPP(c_Groups_Oabs__class_Oabs(_1827869), _1827873))))]]], (51728 ^ _780205) ^ [_1828137, _1828139, _1828141] : [class_Rings_Olinordered__idom(_1828137), 51731 ^ _780205 : [(51732 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828137), hAPP(c_Groups_Oabs__class_Oabs(_1828137), _1828139)), _1828141)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828137), _1828139), _1828141)))], (51738 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828137), _1828139), _1828141)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828137), hAPP(c_Groups_Oabs__class_Oabs(_1828137), _1828139)), _1828141)))]]], (51744 ^ _780205) ^ [_1828405, _1828407, _1828409] : [class_Rings_Olinordered__idom(_1828405), hAPP(c_Groups_Oabs__class_Oabs(_1828405), _1828407) = hAPP(c_Groups_Oabs__class_Oabs(_1828405), _1828409), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828405), _1828407), _1828409)))], (51754 ^ _780205) ^ [_1828570, _1828572, _1828574, _1828576] : [class_Rings_Ocomm__semiring__1(_1828570), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828570), _1828572), _1828574)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828570), _1828574), _1828576)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828570), _1828572), _1828576)))], (51768 ^ _780205) ^ [_1828803, _1828805] : [class_Rings_Ocomm__semiring__1(_1828803), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828803), _1828805), _1828805)))], (51774 ^ _780205) ^ [_1828892, _1828894] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828892), _1828894)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828894), _1828892))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828894), _1828892)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1828892), _1828894)))], (51788 ^ _780205) ^ [_1829122, _1829124, _1829126] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829122), _1829124)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829124), _1829122))), 51803 ^ _780205 : [(51804 ^ _780205) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829122), _1829126)))], (51806 ^ _780205) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829126), _1829122))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829124), _1829126)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829126), _1829124)))], (51808 ^ _780205) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (51810 ^ _780205) ^ [_1829483, _1829485] : [class_Lattices_Obounded__lattice(_1829483), -(class_Lattices_Obounded__lattice(tc_fun(_1829485, _1829483)))], (51816 ^ _780205) ^ [_1829562, _1829564] : [class_Complete__Lattice_Ocomplete__lattice(_1829562), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1829564, _1829562)))], (51822 ^ _780205) ^ [_1829641, _1829643] : [class_Lattices_Obounded__lattice(_1829641), -(class_Lattices_Obounded__lattice__top(tc_fun(_1829643, _1829641)))], (51828 ^ _780205) ^ [_1829720, _1829722] : [class_Lattices_Obounded__lattice(_1829720), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1829722, _1829720)))], (51834 ^ _780205) ^ [_1829799, _1829801] : [class_Lattices_Olattice(_1829799), -(class_Lattices_Osemilattice__sup(tc_fun(_1829801, _1829799)))], (51840 ^ _780205) ^ [_1829878, _1829880] : [class_Lattices_Olattice(_1829878), -(class_Lattices_Osemilattice__inf(tc_fun(_1829880, _1829878)))], (51846 ^ _780205) ^ [_1829957, _1829959] : [class_Lattices_Odistrib__lattice(_1829957), -(class_Lattices_Odistrib__lattice(tc_fun(_1829959, _1829957)))], (51852 ^ _780205) ^ [_1830036, _1830038] : [class_Lattices_Oboolean__algebra(_1830036), -(class_Lattices_Oboolean__algebra(tc_fun(_1830038, _1830036)))], (51858 ^ _780205) ^ [_1830115, _1830117] : [class_Orderings_Opreorder(_1830115), -(class_Orderings_Opreorder(tc_fun(_1830117, _1830115)))], (51864 ^ _780205) ^ [_1830194, _1830196] : [-(class_Finite__Set_Ofinite(tc_fun(_1830194, _1830196))), class_Finite__Set_Ofinite(_1830194), class_Finite__Set_Ofinite(_1830196)], (51874 ^ _780205) ^ [_1830323, _1830325] : [class_Lattices_Olattice(_1830323), -(class_Lattices_Olattice(tc_fun(_1830325, _1830323)))], (51880 ^ _780205) ^ [_1830402, _1830404] : [class_Orderings_Oorder(_1830402), -(class_Orderings_Oorder(tc_fun(_1830404, _1830402)))], (51886 ^ _780205) ^ [_1830481, _1830483] : [class_Orderings_Otop(_1830481), -(class_Orderings_Otop(tc_fun(_1830483, _1830481)))], (51892 ^ _780205) ^ [_1830560, _1830562] : [class_Orderings_Oord(_1830560), -(class_Orderings_Oord(tc_fun(_1830562, _1830560)))], (51898 ^ _780205) ^ [_1830639, _1830641] : [class_Orderings_Obot(_1830639), -(class_Orderings_Obot(tc_fun(_1830641, _1830639)))], (51904 ^ _780205) ^ [_1830718, _1830720] : [class_Groups_Ouminus(_1830718), -(class_Groups_Ouminus(tc_fun(_1830720, _1830718)))], (51910 ^ _780205) ^ [_1830797, _1830799] : [class_Groups_Ominus(_1830797), -(class_Groups_Ominus(tc_fun(_1830799, _1830797)))], (51916 ^ _780205) ^ [_1830876, _1830878] : [-(class_Enum_Oenum(tc_fun(_1830876, _1830878))), class_Enum_Oenum(_1830876), class_Enum_Oenum(_1830878)], (51926 ^ _780205) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (51928 ^ _780205) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (51930 ^ _780205) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (51932 ^ _780205) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (51934 ^ _780205) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (51936 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (51938 ^ _780205) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (51940 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (51942 ^ _780205) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (51944 ^ _780205) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (51946 ^ _780205) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (51948 ^ _780205) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (51950 ^ _780205) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (51952 ^ _780205) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (51954 ^ _780205) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (51956 ^ _780205) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (51958 ^ _780205) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (51960 ^ _780205) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (51962 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (51964 ^ _780205) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (51966 ^ _780205) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (51968 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (51970 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (51972 ^ _780205) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (51974 ^ _780205) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (51976 ^ _780205) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (51978 ^ _780205) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (51980 ^ _780205) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (51982 ^ _780205) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (51984 ^ _780205) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (51986 ^ _780205) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (51988 ^ _780205) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (51990 ^ _780205) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (51992 ^ _780205) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (51994 ^ _780205) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (51996 ^ _780205) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (51998 ^ _780205) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (52000 ^ _780205) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (52002 ^ _780205) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (52004 ^ _780205) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (52006 ^ _780205) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (52008 ^ _780205) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (52010 ^ _780205) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (52012 ^ _780205) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (52014 ^ _780205) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (52016 ^ _780205) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (52018 ^ _780205) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (52020 ^ _780205) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (52022 ^ _780205) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (52024 ^ _780205) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (52026 ^ _780205) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (52028 ^ _780205) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (52030 ^ _780205) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (52032 ^ _780205) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (52034 ^ _780205) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (52036 ^ _780205) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (52038 ^ _780205) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (52040 ^ _780205) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (52042 ^ _780205) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (52044 ^ _780205) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (52046 ^ _780205) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (52048 ^ _780205) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (52050 ^ _780205) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (52052 ^ _780205) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (52054 ^ _780205) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (52056 ^ _780205) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (52058 ^ _780205) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (52060 ^ _780205) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (52062 ^ _780205) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (52064 ^ _780205) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (52066 ^ _780205) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (52068 ^ _780205) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (52070 ^ _780205) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (52072 ^ _780205) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (52074 ^ _780205) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (52076 ^ _780205) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (52078 ^ _780205) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (52080 ^ _780205) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (52082 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (52084 ^ _780205) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (52086 ^ _780205) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (52088 ^ _780205) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (52090 ^ _780205) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (52092 ^ _780205) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (52094 ^ _780205) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (52096 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (52098 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (52100 ^ _780205) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (52102 ^ _780205) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (52104 ^ _780205) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (52106 ^ _780205) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (52108 ^ _780205) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (52110 ^ _780205) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (52112 ^ _780205) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (52114 ^ _780205) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (52116 ^ _780205) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (52118 ^ _780205) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (52120 ^ _780205) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (52122 ^ _780205) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (52124 ^ _780205) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (52126 ^ _780205) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (52128 ^ _780205) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (52130 ^ _780205) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (52132 ^ _780205) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (52134 ^ _780205) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (52136 ^ _780205) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (52138 ^ _780205) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (52140 ^ _780205) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (52142 ^ _780205) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (52144 ^ _780205) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (52146 ^ _780205) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (52148 ^ _780205) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (52150 ^ _780205) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (52152 ^ _780205) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (52154 ^ _780205) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (52156 ^ _780205) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (52158 ^ _780205) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (52160 ^ _780205) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (52162 ^ _780205) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (52164 ^ _780205) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (52166 ^ _780205) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (52168 ^ _780205) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (52170 ^ _780205) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (52172 ^ _780205) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (52174 ^ _780205) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (52176 ^ _780205) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (52178 ^ _780205) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (52180 ^ _780205) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (52182 ^ _780205) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (52184 ^ _780205) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (52186 ^ _780205) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (52188 ^ _780205) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (52190 ^ _780205) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (52192 ^ _780205) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (52194 ^ _780205) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (52196 ^ _780205) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (52198 ^ _780205) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (52200 ^ _780205) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (52202 ^ _780205) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (52204 ^ _780205) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (52206 ^ _780205) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (52208 ^ _780205) ^ [_1833543] : [class_Lazy__Sequence_Osmall__lazy(_1833543), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1833543)))], (52214 ^ _780205) ^ [_1833618] : [-(class_Nat_Osize(tc_List_Olist(_1833618)))], (52216 ^ _780205) ^ [_1833642, _1833644] : [-(class_Finite__Set_Ofinite(tc_sum(_1833642, _1833644))), class_Finite__Set_Ofinite(_1833642), class_Finite__Set_Ofinite(_1833644)], (52226 ^ _780205) ^ [_1833771, _1833773] : [-(class_Enum_Oenum(tc_sum(_1833771, _1833773))), class_Enum_Oenum(_1833771), class_Enum_Oenum(_1833773)], (52236 ^ _780205) ^ [_1833900, _1833902] : [-(class_Nat_Osize(tc_sum(_1833900, _1833902)))], (52238 ^ _780205) ^ [_1833927] : [class_Finite__Set_Ofinite(_1833927), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1833927)))], (52244 ^ _780205) ^ [_1834002] : [class_Enum_Oenum(_1834002), -(class_Enum_Oenum(tc_Option_Ooption(_1834002)))], (52250 ^ _780205) ^ [_1834077] : [-(class_Nat_Osize(tc_Option_Ooption(_1834077)))], (52252 ^ _780205) ^ [_1834101, _1834103] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1834101, _1834103)))], (52254 ^ _780205) ^ [_1834128, _1834130] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1834128, _1834130))), class_Lazy__Sequence_Osmall__lazy(_1834128), class_Lazy__Sequence_Osmall__lazy(_1834130)], (52264 ^ _780205) ^ [_1834257, _1834259] : [-(class_Finite__Set_Ofinite(tc_prod(_1834257, _1834259))), class_Finite__Set_Ofinite(_1834257), class_Finite__Set_Ofinite(_1834259)], (52274 ^ _780205) ^ [_1834386, _1834388] : [-(class_Enum_Oenum(tc_prod(_1834386, _1834388))), class_Enum_Oenum(_1834386), class_Enum_Oenum(_1834388)], (52284 ^ _780205) ^ [_1834515, _1834517] : [-(class_Nat_Osize(tc_prod(_1834515, _1834517)))], (52286 ^ _780205) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (52288 ^ _780205) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (52290 ^ _780205) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (52292 ^ _780205) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (52294 ^ _780205) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (52296 ^ _780205) ^ [_1834632] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1834632)))], (52298 ^ _780205) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52300 ^ _780205) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (52302 ^ _780205) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52304 ^ _780205) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52306 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52308 ^ _780205) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52310 ^ _780205) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52312 ^ _780205) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52314 ^ _780205) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (52316 ^ _780205) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (52318 ^ _780205) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52320 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52322 ^ _780205) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (52324 ^ _780205) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (52326 ^ _780205) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (52328 ^ _780205) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52330 ^ _780205) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52332 ^ _780205) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (52334 ^ _780205) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52336 ^ _780205) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (52338 ^ _780205) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (52340 ^ _780205) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (52342 ^ _780205) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (52344 ^ _780205) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (52346 ^ _780205) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (52348 ^ _780205) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (52350 ^ _780205) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (52352 ^ _780205) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (52354 ^ _780205) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (52356 ^ _780205) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (52358 ^ _780205) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (52360 ^ _780205) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (52362 ^ _780205) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (52364 ^ _780205) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (52366 ^ _780205) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (52368 ^ _780205) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (52370 ^ _780205) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (52372 ^ _780205) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (52374 ^ _780205) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (52376 ^ _780205) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (52378 ^ _780205) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (52380 ^ _780205) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (52382 ^ _780205) ^ [_1835412] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1835412)))], (52384 ^ _780205) ^ [_1835436, _1835438] : [-(hAPP(c_COMBI(_1835436), _1835438) = _1835438)], (52386 ^ _780205) ^ [_1835466, _1835468, _1835470, _1835472] : [-(hAPP(hAPP(c_COMBK(_1835466, _1835468), _1835470), _1835472) = _1835470)], (52388 ^ _780205) ^ [_1835504, _1835506, _1835508, _1835510, _1835512, _1835514] : [-(hAPP(hAPP(hAPP(c_COMBB(_1835504, _1835506, _1835508), _1835510), _1835512), _1835514) = hAPP(_1835510, hAPP(_1835512, _1835514)))], (52390 ^ _780205) ^ [_1835556, _1835558, _1835560, _1835562, _1835564, _1835566] : [-(hAPP(hAPP(hAPP(c_COMBC(_1835556, _1835558, _1835560), _1835562), _1835564), _1835566) = hAPP(hAPP(_1835562, _1835566), _1835564))], (52392 ^ _780205) ^ [_1835608, _1835610, _1835612, _1835614, _1835616, _1835618] : [-(hAPP(hAPP(hAPP(c_COMBS(_1835608, _1835610, _1835612), _1835614), _1835616), _1835618) = hAPP(hAPP(_1835614, _1835618), hAPP(_1835616, _1835618)))], (52394 ^ _780205) ^ [_1835663, _1835665] : [hBOOL(hAPP(hAPP(c_fequal, _1835663), _1835665)), -(_1835663 = _1835665)], (52400 ^ _780205) ^ [_1835752, _1835754] : [_1835752 = _1835754, -(hBOOL(hAPP(hAPP(c_fequal, _1835752), _1835754)))], (52406 ^ _780205) ^ [] : [hBOOL(c_fFalse)], (52408 ^ _780205) ^ [] : [-(hBOOL(c_fTrue))], (52410 ^ _780205) ^ [_1835883] : [hBOOL(hAPP(c_fNot, _1835883)), hBOOL(_1835883)], (52416 ^ _780205) ^ [_1835959] : [-(hBOOL(_1835959)), -(hBOOL(hAPP(c_fNot, _1835959)))], (52422 ^ _780205) ^ [_1835994, _1835996] : [hBOOL(_1835994), hBOOL(_1835996), -(hBOOL(hAPP(hAPP(c_fconj, _1835994), _1835996)))], (52432 ^ _780205) ^ [_1836133, _1836135] : [hBOOL(hAPP(hAPP(c_fconj, _1836133), _1836135)), -(hBOOL(_1836133))], (52438 ^ _780205) ^ [_1836220, _1836222] : [hBOOL(hAPP(hAPP(c_fconj, _1836220), _1836222)), -(hBOOL(_1836222))], (52444 ^ _780205) ^ [_1836307, _1836309] : [hBOOL(_1836307), -(hBOOL(hAPP(hAPP(c_fdisj, _1836307), _1836309)))], (52450 ^ _780205) ^ [_1836394, _1836396] : [hBOOL(_1836394), -(hBOOL(hAPP(hAPP(c_fdisj, _1836396), _1836394)))], (52456 ^ _780205) ^ [_1836481, _1836483] : [hBOOL(hAPP(hAPP(c_fdisj, _1836481), _1836483)), -(hBOOL(_1836481)), -(hBOOL(_1836483))], (52466 ^ _780205) ^ [_1836575, _1836577] : [-(hBOOL(_1836575)), -(hBOOL(hAPP(hAPP(c_fimplies, _1836575), _1836577)))], (52472 ^ _780205) ^ [_1836615, _1836617] : [hBOOL(_1836615), -(hBOOL(hAPP(hAPP(c_fimplies, _1836617), _1836615)))], (52478 ^ _780205) ^ [_1836698, _1836700] : [hBOOL(hAPP(hAPP(c_fimplies, _1836698), _1836700)), hBOOL(_1836698), -(hBOOL(_1836700))]], input).
% 1.86/2.50  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), t_a), hAPP(c_COMBK(tc_HOL_Obool, tc_Com_Ostate), c_fFalse))), v_c), _392888)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))],start(52492 ^ 0,bind([[_2083162, _2083164], [_392888, hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), t_a), hAPP(c_COMBK(tc_HOL_Obool, tc_Com_Ostate), c_fFalse))]]))).
% 1.86/2.50  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), t_a), hAPP(c_COMBK(tc_HOL_Obool, tc_Com_Ostate), c_fFalse))), v_c), _392888)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))))],extension(30332 ^ 1,bind([[_1332368, _1332370, _1332372, _1332374], [t_a, v_G, v_c, _392888]]))).
% 1.86/2.50  %-----------------------------------------------------
% 1.86/2.50  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------