%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW358+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n001.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 12:26:01 EDT 2023

% Result   : Theorem 136.17s 131.27s
% Output   : Proof 136.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWW358+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n001.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 22:46:50 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 136.17/131.27  
% 136.17/131.27  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 136.17/131.27  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 136.17/131.27  %-----------------------------------------------------
% 136.17/131.27  ncf(matrix, plain, [(52804 ^ _779300) ^ [] : [v_G = hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)], (2 ^ _779300) ^ [_779330] : [-(_779330 = _779330)], (4 ^ _779300) ^ [_779353, _779355] : [_779355 = _779353, -(_779353 = _779355)], (10 ^ _779300) ^ [_779426, _779428, _779430] : [-(_779430 = _779426), _779430 = _779428, _779428 = _779426], (20 ^ _779300) ^ [_779563, _779565, _779567, _779569] : [-(v_P(_779567, _779563)), v_P(_779569, _779565), _779569 = _779567, _779565 = _779563], (34 ^ _779300) ^ [_779756, _779758, _779760, _779762, _779764, _779766, _779768, _779770, _779772, _779774, _779776, _779778] : [-(c_Nitpick_Ofold__graph_H(_779776, _779772, _779768, _779764, _779760, _779756)), c_Nitpick_Ofold__graph_H(_779778, _779774, _779770, _779766, _779762, _779758), _779778 = _779776, _779774 = _779772, _779770 = _779768, _779766 = _779764, _779762 = _779760, _779758 = _779756], (64 ^ _779300) ^ [_780301, _780303, _780305, _780307, _780309, _780311] : [-(c_Big__Operators_Osemilattice__big(_780309, _780305, _780301)), c_Big__Operators_Osemilattice__big(_780311, _780307, _780303), _780311 = _780309, _780307 = _780305, _780303 = _780301], (82 ^ _779300) ^ [_780570, _780572, _780574, _780576, _780578, _780580, _780582, _780584, _780586, _780588] : [-(c_Big__Operators_Ocomm__monoid__big(_780586, _780582, _780578, _780574, _780570)), c_Big__Operators_Ocomm__monoid__big(_780588, _780584, _780580, _780576, _780572), _780588 = _780586, _780584 = _780582, _780580 = _780578, _780576 = _780574, _780572 = _780570], (108 ^ _779300) ^ [_781015, _781017, _781019, _781021] : [-(c_Int_Oiszero(_781019, _781015)), c_Int_Oiszero(_781021, _781017), _781021 = _781019, _781017 = _781015], (122 ^ _779300) ^ [_781208, _781210] : [-(class_Rings_Odivision__ring__inverse__zero(_781208)), _781210 = _781208, class_Rings_Odivision__ring__inverse__zero(_781210)], (132 ^ _779300) ^ [_781333, _781335] : [-(class_Rings_Odivision__ring(_781333)), _781335 = _781333, class_Rings_Odivision__ring(_781335)], (142 ^ _779300) ^ [_781458, _781460] : [-(class_Fields_Ofield__inverse__zero(_781458)), _781460 = _781458, class_Fields_Ofield__inverse__zero(_781460)], (152 ^ _779300) ^ [_781583, _781585, _781587, _781589] : [-(c_Nitpick_Orefl_H(_781587, _781583)), c_Nitpick_Orefl_H(_781589, _781585), _781589 = _781587, _781585 = _781583], (166 ^ _779300) ^ [_781776, _781778, _781780, _781782, _781784, _781786, _781788, _781790, _781792, _781794, _781796, _781798] : [-(c_Finite__Set_Ofolding__image__simple__idem(_781796, _781792, _781788, _781784, _781780, _781776)), c_Finite__Set_Ofolding__image__simple__idem(_781798, _781794, _781790, _781786, _781782, _781778), _781798 = _781796, _781794 = _781792, _781790 = _781788, _781786 = _781784, _781782 = _781780, _781778 = _781776], (196 ^ _779300) ^ [_782321, _782323] : [-(class_Fields_Ofield(_782321)), _782323 = _782321, class_Fields_Ofield(_782323)], (206 ^ _779300) ^ [_782446, _782448] : [-(c_Nat__Transfer_Ois__nat(_782446)), _782448 = _782446, c_Nat__Transfer_Ois__nat(_782448)], (216 ^ _779300) ^ [_782571, _782573] : [-(class_Fields_Olinordered__field__inverse__zero(_782571)), _782573 = _782571, class_Fields_Olinordered__field__inverse__zero(_782573)], (226 ^ _779300) ^ [_782696, _782698, _782700, _782702, _782704, _782706, _782708, _782710, _782712, _782714, _782716, _782718] : [-(c_Finite__Set_Ofolding__image__simple(_782716, _782712, _782708, _782704, _782700, _782696)), c_Finite__Set_Ofolding__image__simple(_782718, _782714, _782710, _782706, _782702, _782698), _782718 = _782716, _782714 = _782712, _782710 = _782708, _782706 = _782704, _782702 = _782700, _782698 = _782696], (256 ^ _779300) ^ [_783241, _783243, _783245, _783247] : [-(c_FunDef_Oreduction__pair(_783245, _783241)), c_FunDef_Oreduction__pair(_783247, _783243), _783247 = _783245, _783243 = _783241], (270 ^ _779300) ^ [_783434, _783436, _783438, _783440] : [-(c_Nitpick_Owf_H(_783438, _783434)), c_Nitpick_Owf_H(_783440, _783436), _783440 = _783438, _783436 = _783434], (284 ^ _779300) ^ [_783627, _783629] : [-(c_Nitpick_Ounknown(_783627)), _783629 = _783627, c_Nitpick_Ounknown(_783629)], (294 ^ _779300) ^ [_783752, _783754, _783756, _783758] : [-(c_Wellfounded_OwfP(_783756, _783752)), c_Wellfounded_OwfP(_783758, _783754), _783758 = _783756, _783754 = _783752], (308 ^ _779300) ^ [_783945, _783947, _783949, _783951, _783953, _783955, _783957, _783959] : [-(c_Finite__Set_Ofolding__idem(_783957, _783953, _783949, _783945)), c_Finite__Set_Ofolding__idem(_783959, _783955, _783951, _783947), _783959 = _783957, _783955 = _783953, _783951 = _783949, _783947 = _783945], (330 ^ _779300) ^ [_784298, _784300, _784302, _784304] : [-(c_Relation_Oirrefl(_784302, _784298)), c_Relation_Oirrefl(_784304, _784300), _784304 = _784302, _784300 = _784298], (344 ^ _779300) ^ [_784491, _784493, _784495, _784497, _784499, _784501] : [-(c_Relation_Ototal__on(_784499, _784495, _784491)), c_Relation_Ototal__on(_784501, _784497, _784493), _784501 = _784499, _784497 = _784495, _784493 = _784491], (362 ^ _779300) ^ [_784760, _784762, _784764, _784766, _784768, _784770, _784772, _784774] : [-(c_Finite__Set_Ofolding(_784772, _784768, _784764, _784760)), c_Finite__Set_Ofolding(_784774, _784770, _784766, _784762), _784774 = _784772, _784770 = _784768, _784766 = _784764, _784762 = _784760], (384 ^ _779300) ^ [_785113, _785115, _785117, _785119, _785121, _785123] : [-(c_Finite__Set_Ofolding__one__idem(_785121, _785117, _785113)), c_Finite__Set_Ofolding__one__idem(_785123, _785119, _785115), _785123 = _785121, _785119 = _785117, _785115 = _785113], (402 ^ _779300) ^ [_785382, _785384, _785386, _785388, _785390, _785392] : [-(c_Finite__Set_Ofolding__one(_785390, _785386, _785382)), c_Finite__Set_Ofolding__one(_785392, _785388, _785384), _785392 = _785390, _785388 = _785386, _785384 = _785382], (420 ^ _779300) ^ [_785651, _785653, _785655, _785657, _785659, _785661] : [-(c_Relation_Osingle__valued(_785659, _785655, _785651)), c_Relation_Osingle__valued(_785661, _785657, _785653), _785661 = _785659, _785657 = _785655, _785653 = _785651], (438 ^ _779300) ^ [_785920, _785922] : [-(class_Rings_Oinverse(_785920)), _785922 = _785920, class_Rings_Oinverse(_785922)], (448 ^ _779300) ^ [_786045, _786047, _786049, _786051, _786053, _786055] : [-(c_Nitpick_Oless__frac(_786053, _786049, _786045)), c_Nitpick_Oless__frac(_786055, _786051, _786047), _786055 = _786053, _786051 = _786049, _786047 = _786045], (466 ^ _779300) ^ [_786314, _786316, _786318, _786320, _786322, _786324] : [-(c_Nitpick_Oless__eq__frac(_786322, _786318, _786314)), c_Nitpick_Oless__eq__frac(_786324, _786320, _786316), _786324 = _786322, _786320 = _786318, _786316 = _786314], (484 ^ _779300) ^ [_786583, _786585] : [-(c_Nat__Transfer_Onat__set(_786583)), _786585 = _786583, c_Nat__Transfer_Onat__set(_786585)], (494 ^ _779300) ^ [_786708, _786710, _786712, _786714, _786716, _786718, _786720, _786722] : [-(c_List_Olistrelp(_786720, _786716, _786712, _786708)), c_List_Olistrelp(_786722, _786718, _786714, _786710), _786722 = _786720, _786718 = _786716, _786714 = _786712, _786710 = _786708], (516 ^ _779300) ^ [_787061, _787063] : [-(class_Lattices_Oab__semigroup__idem__mult(_787061)), _787063 = _787061, class_Lattices_Oab__semigroup__idem__mult(_787063)], (526 ^ _779300) ^ [_787186, _787188, _787190, _787192, _787194, _787196] : [-(c_Finite__Set_Ofun__left__comm__idem(_787194, _787190, _787186)), c_Finite__Set_Ofun__left__comm__idem(_787196, _787192, _787188), _787196 = _787194, _787192 = _787190, _787188 = _787186], (544 ^ _779300) ^ [_787455, _787457, _787459, _787461, _787463, _787465, _787467, _787469, _787471, _787473] : [-(c_Typedef_Otype__definition(_787471, _787467, _787463, _787459, _787455)), c_Typedef_Otype__definition(_787473, _787469, _787465, _787461, _787457), _787473 = _787471, _787469 = _787467, _787465 = _787463, _787461 = _787459, _787457 = _787455], (570 ^ _779300) ^ [_787900, _787902, _787904, _787906, _787908, _787910] : [-(c_Finite__Set_Ofun__left__comm(_787908, _787904, _787900)), c_Finite__Set_Ofun__left__comm(_787910, _787906, _787902), _787910 = _787908, _787906 = _787904, _787902 = _787900], (588 ^ _779300) ^ [_788169, _788171] : [-(c_List_Onat__list(_788169)), _788171 = _788169, c_List_Onat__list(_788171)], (598 ^ _779300) ^ [_788294, _788296, _788298, _788300, _788302, _788304, _788306, _788308, _788310, _788312] : [-(c_List_Olist__all2(_788310, _788306, _788302, _788298, _788294)), c_List_Olist__all2(_788312, _788308, _788304, _788300, _788296), _788312 = _788310, _788308 = _788306, _788304 = _788302, _788300 = _788298, _788296 = _788294], (624 ^ _779300) ^ [_788739, _788741, _788743, _788745] : [-(c_List_Olinorder__class_Osorted(_788743, _788739)), c_List_Olinorder__class_Osorted(_788745, _788741), _788745 = _788743, _788741 = _788739], (638 ^ _779300) ^ [_788932, _788934, _788936, _788938] : [-(c_FunDef_Ois__measure(_788936, _788932)), c_FunDef_Ois__measure(_788938, _788934), _788938 = _788936, _788934 = _788932], (652 ^ _779300) ^ [_789125, _789127, _789129, _789131, _789133, _789135, _789137, _789139] : [-(c_Nat__Transfer_Otransfer__morphism(_789137, _789133, _789129, _789125)), c_Nat__Transfer_Otransfer__morphism(_789139, _789135, _789131, _789127), _789139 = _789137, _789135 = _789133, _789131 = _789129, _789127 = _789125], (674 ^ _779300) ^ [_789478, _789480] : [-(class_Fields_Olinordered__field(_789478)), _789480 = _789478, class_Fields_Olinordered__field(_789480)], (684 ^ _779300) ^ [_789603, _789605, _789607, _789609, _789611, _789613] : [-(c_List_Olist__ex1(_789611, _789607, _789603)), c_List_Olist__ex1(_789613, _789609, _789605), _789613 = _789611, _789609 = _789607, _789605 = _789603], (702 ^ _779300) ^ [_789872, _789874, _789876, _789878, _789880, _789882] : [-(c_List_Oall__interval__int(_789880, _789876, _789872)), c_List_Oall__interval__int(_789882, _789878, _789874), _789882 = _789880, _789878 = _789876, _789874 = _789872], (720 ^ _779300) ^ [_790141, _790143, _790145, _790147] : [-(c_Predicate_Oreflp(_790145, _790141)), c_Predicate_Oreflp(_790147, _790143), _790147 = _790145, _790143 = _790141], (734 ^ _779300) ^ [_790334, _790336, _790338, _790340, _790342, _790344, _790346, _790348] : [-(c_Wellfounded_Omax__extp(_790346, _790342, _790338, _790334)), c_Wellfounded_Omax__extp(_790348, _790344, _790340, _790336), _790348 = _790346, _790344 = _790342, _790340 = _790338, _790336 = _790334], (756 ^ _779300) ^ [_790687, _790689, _790691, _790693] : [-(c_Wellfounded_Oacyclic(_790691, _790687)), c_Wellfounded_Oacyclic(_790693, _790689), _790693 = _790691, _790689 = _790687], (770 ^ _779300) ^ [_790880, _790882, _790884, _790886] : [-(c_Relation_Oantisym(_790884, _790880)), c_Relation_Oantisym(_790886, _790882), _790886 = _790884, _790882 = _790880], (784 ^ _779300) ^ [_791073, _791075, _791077, _791079] : [-(c_Relation_Otrans(_791077, _791073)), c_Relation_Otrans(_791079, _791075), _791079 = _791077, _791075 = _791073], (798 ^ _779300) ^ [_791266, _791268, _791270, _791272] : [-(c_Relation_Osym(_791270, _791266)), c_Relation_Osym(_791272, _791268), _791272 = _791270, _791268 = _791266], (812 ^ _779300) ^ [_791459, _791461, _791463, _791465] : [-(c_Predicate_Osymp(_791463, _791459)), c_Predicate_Osymp(_791465, _791461), _791465 = _791463, _791461 = _791459], (826 ^ _779300) ^ [_791652, _791654, _791656, _791658] : [-(c_Predicate_Otransp(_791656, _791652)), c_Predicate_Otransp(_791658, _791654), _791658 = _791656, _791654 = _791652], (840 ^ _779300) ^ [_791845, _791847, _791849, _791851] : [-(c_Equiv__Relations_Opart__equivp(_791849, _791845)), c_Equiv__Relations_Opart__equivp(_791851, _791847), _791851 = _791849, _791847 = _791845], (854 ^ _779300) ^ [_792038, _792040, _792042, _792044, _792046, _792048, _792050, _792052] : [-(c_Fun_Oinj__on(_792050, _792046, _792042, _792038)), c_Fun_Oinj__on(_792052, _792048, _792044, _792040), _792052 = _792050, _792048 = _792046, _792044 = _792042, _792040 = _792038], (876 ^ _779300) ^ [_792391, _792393, _792395, _792397, _792399, _792401, _792403, _792405, _792407, _792409] : [-(c_Fun_Obij__betw(_792407, _792403, _792399, _792395, _792391)), c_Fun_Obij__betw(_792409, _792405, _792401, _792397, _792393), _792409 = _792407, _792405 = _792403, _792401 = _792399, _792397 = _792395, _792393 = _792391], (902 ^ _779300) ^ [_792836, _792838, _792840, _792842, _792844, _792846] : [-(c_Relation_Orefl__on(_792844, _792840, _792836)), c_Relation_Orefl__on(_792846, _792842, _792838), _792846 = _792844, _792842 = _792840, _792838 = _792836], (920 ^ _779300) ^ [_793105, _793107, _793109, _793111] : [-(c_Equiv__Relations_Oequivp(_793109, _793105)), c_Equiv__Relations_Oequivp(_793111, _793107), _793111 = _793109, _793107 = _793105], (934 ^ _779300) ^ [_793298, _793300, _793302, _793304] : [-(c_Wellfounded_Owf(_793302, _793298)), c_Wellfounded_Owf(_793304, _793300), _793304 = _793302, _793300 = _793298], (948 ^ _779300) ^ [_793491, _793493, _793495, _793497, _793499, _793501, _793503, _793505, _793507, _793509, _793511, _793513] : [-(c_Equiv__Relations_Ocongruent2(_793511, _793507, _793503, _793499, _793495, _793491)), c_Equiv__Relations_Ocongruent2(_793513, _793509, _793505, _793501, _793497, _793493), _793513 = _793511, _793509 = _793507, _793505 = _793503, _793501 = _793499, _793497 = _793495, _793493 = _793491], (978 ^ _779300) ^ [_794036, _794038, _794040, _794042, _794044, _794046, _794048, _794050] : [-(c_Equiv__Relations_Ocongruent(_794048, _794044, _794040, _794036)), c_Equiv__Relations_Ocongruent(_794050, _794046, _794042, _794038), _794050 = _794048, _794046 = _794044, _794042 = _794040, _794038 = _794036], (1000 ^ _779300) ^ [_794389, _794391, _794393, _794395, _794397, _794399] : [-(c_List_Olist__all(_794397, _794393, _794389)), c_List_Olist__all(_794399, _794395, _794391), _794399 = _794397, _794395 = _794393, _794391 = _794389], (1018 ^ _779300) ^ [_794658, _794660, _794662, _794664, _794666, _794668] : [-(c_List_Olist__ex(_794666, _794662, _794658)), c_List_Olist__ex(_794668, _794664, _794660), _794668 = _794666, _794664 = _794662, _794660 = _794658], (1036 ^ _779300) ^ [_794927, _794929, _794931, _794933, _794935, _794937] : [-(c_List_Oall__interval__nat(_794935, _794931, _794927)), c_List_Oall__interval__nat(_794937, _794933, _794929), _794937 = _794935, _794933 = _794931, _794929 = _794927], (1054 ^ _779300) ^ [_795196, _795198, _795200, _795202, _795204, _795206, _795208, _795210, _795212, _795214] : [-(c_Finite__Set_Ofolding__image(_795212, _795208, _795204, _795200, _795196)), c_Finite__Set_Ofolding__image(_795214, _795210, _795206, _795202, _795198), _795214 = _795212, _795210 = _795208, _795206 = _795204, _795202 = _795200, _795198 = _795196], (1080 ^ _779300) ^ [_795641, _795643, _795645, _795647, _795649, _795651, _795653, _795655] : [-(c_Orderings_Oorder_Ostrict__mono(_795653, _795649, _795645, _795641)), c_Orderings_Oorder_Ostrict__mono(_795655, _795651, _795647, _795643), _795655 = _795653, _795651 = _795649, _795647 = _795645, _795643 = _795641], (1102 ^ _779300) ^ [_795994, _795996, _795998, _796000, _796002, _796004] : [-(c_Equiv__Relations_Oequiv(_796002, _795998, _795994)), c_Equiv__Relations_Oequiv(_796004, _796000, _795996), _796004 = _796002, _796000 = _795998, _795996 = _795994], (1120 ^ _779300) ^ [_796263, _796265] : [-(class_Lattices_Obounded__lattice(_796263)), _796265 = _796263, class_Lattices_Obounded__lattice(_796265)], (1130 ^ _779300) ^ [_796388, _796390] : [-(class_Rings_Olinordered__semiring__1__strict(_796388)), _796390 = _796388, class_Rings_Olinordered__semiring__1__strict(_796390)], (1140 ^ _779300) ^ [_796513, _796515] : [-(class_Groups_Oordered__ab__group__add__abs(_796513)), _796515 = _796513, class_Groups_Oordered__ab__group__add__abs(_796515)], (1150 ^ _779300) ^ [_796638, _796640] : [-(class_Groups_Olinordered__ab__group__add(_796638)), _796640 = _796638, class_Groups_Olinordered__ab__group__add(_796640)], (1160 ^ _779300) ^ [_796763, _796765] : [-(class_Rings_Oring__1__no__zero__divisors(_796763)), _796765 = _796763, class_Rings_Oring__1__no__zero__divisors(_796765)], (1170 ^ _779300) ^ [_796888, _796890] : [-(class_Rings_Olinordered__ring__strict(_796888)), _796890 = _796888, class_Rings_Olinordered__ring__strict(_796890)], (1180 ^ _779300) ^ [_797013, _797015] : [-(class_Rings_Oring__no__zero__divisors(_797013)), _797015 = _797013, class_Rings_Oring__no__zero__divisors(_797015)], (1190 ^ _779300) ^ [_797138, _797140] : [-(class_Rings_Olinordered__semiring__1(_797138)), _797140 = _797138, class_Rings_Olinordered__semiring__1(_797140)], (1200 ^ _779300) ^ [_797263, _797265] : [-(class_Groups_Oordered__ab__group__add(_797263)), _797265 = _797263, class_Groups_Oordered__ab__group__add(_797265)], (1210 ^ _779300) ^ [_797388, _797390] : [-(class_Rings_Oordered__ring__abs(_797388)), _797390 = _797388, class_Rings_Oordered__ring__abs(_797390)], (1220 ^ _779300) ^ [_797513, _797515] : [-(class_Rings_Olinordered__ring(_797513)), _797515 = _797513, class_Rings_Olinordered__ring(_797515)], (1230 ^ _779300) ^ [_797638, _797640] : [-(class_Rings_Olinordered__idom(_797638)), _797640 = _797638, class_Rings_Olinordered__idom(_797640)], (1240 ^ _779300) ^ [_797763, _797765] : [-(class_Groups_Oab__group__add(_797763)), _797765 = _797763, class_Groups_Oab__group__add(_797765)], (1250 ^ _779300) ^ [_797888, _797890] : [-(class_Rings_Oordered__ring(_797888)), _797890 = _797888, class_Rings_Oordered__ring(_797890)], (1260 ^ _779300) ^ [_798013, _798015] : [-(class_Rings_Ocomm__ring__1(_798013)), _798015 = _798013, class_Rings_Ocomm__ring__1(_798015)], (1270 ^ _779300) ^ [_798138, _798140] : [-(class_Groups_Ogroup__add(_798138)), _798140 = _798138, class_Groups_Ogroup__add(_798140)], (1280 ^ _779300) ^ [_798263, _798265] : [-(class_Divides_Oring__div(_798263)), _798265 = _798263, class_Divides_Oring__div(_798265)], (1290 ^ _779300) ^ [_798388, _798390] : [-(class_Rings_Ocomm__ring(_798388)), _798390 = _798388, class_Rings_Ocomm__ring(_798390)], (1300 ^ _779300) ^ [_798513, _798515] : [-(class_Int_Oring__char__0(_798513)), _798515 = _798513, class_Int_Oring__char__0(_798515)], (1310 ^ _779300) ^ [_798638, _798640] : [-(class_Int_Onumber__ring(_798638)), _798640 = _798638, class_Int_Onumber__ring(_798640)], (1320 ^ _779300) ^ [_798763, _798765] : [-(class_Groups_Osgn__if(_798763)), _798765 = _798763, class_Groups_Osgn__if(_798765)], (1330 ^ _779300) ^ [_798888, _798890] : [-(class_Groups_Oabs__if(_798888)), _798890 = _798888, class_Groups_Oabs__if(_798890)], (1340 ^ _779300) ^ [_799013, _799015] : [-(class_Rings_Oring__1(_799013)), _799015 = _799013, class_Rings_Oring__1(_799015)], (1350 ^ _779300) ^ [_799138, _799140] : [-(class_Rings_Oring(_799138)), _799140 = _799138, class_Rings_Oring(_799140)], (1360 ^ _779300) ^ [_799263, _799265] : [-(class_Rings_Oidom(_799263)), _799265 = _799263, class_Rings_Oidom(_799265)], (1370 ^ _779300) ^ [_799388, _799390] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799388)), _799390 = _799388, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799390)], (1380 ^ _779300) ^ [_799513, _799515] : [-(class_Orderings_Owellorder(_799513)), _799515 = _799513, class_Orderings_Owellorder(_799515)], (1390 ^ _779300) ^ [_799638, _799640] : [-(class_Complete__Lattice_Ocomplete__lattice(_799638)), _799640 = _799638, class_Complete__Lattice_Ocomplete__lattice(_799640)], (1400 ^ _779300) ^ [_799763, _799765] : [-(class_Lattices_Obounded__lattice__top(_799763)), _799765 = _799763, class_Lattices_Obounded__lattice__top(_799765)], (1410 ^ _779300) ^ [_799888, _799890] : [-(class_Lattices_Obounded__lattice__bot(_799888)), _799890 = _799888, class_Lattices_Obounded__lattice__bot(_799890)], (1420 ^ _779300) ^ [_800013, _800015] : [-(class_Lattices_Osemilattice__sup(_800013)), _800015 = _800013, class_Lattices_Osemilattice__sup(_800015)], (1430 ^ _779300) ^ [_800138, _800140] : [-(class_Lattices_Osemilattice__inf(_800138)), _800140 = _800138, class_Lattices_Osemilattice__inf(_800140)], (1440 ^ _779300) ^ [_800263, _800265] : [-(class_Lattices_Odistrib__lattice(_800263)), _800265 = _800263, class_Lattices_Odistrib__lattice(_800265)], (1450 ^ _779300) ^ [_800388, _800390] : [-(class_Lattices_Oboolean__algebra(_800388)), _800390 = _800388, class_Lattices_Oboolean__algebra(_800390)], (1460 ^ _779300) ^ [_800513, _800515] : [-(class_Lattices_Olattice(_800513)), _800515 = _800513, class_Lattices_Olattice(_800515)], (1470 ^ _779300) ^ [_800638, _800640] : [-(class_Orderings_Otop(_800638)), _800640 = _800638, class_Orderings_Otop(_800640)], (1480 ^ _779300) ^ [_800763, _800765] : [-(class_Orderings_Obot(_800763)), _800765 = _800763, class_Orderings_Obot(_800765)], (1490 ^ _779300) ^ [_800888, _800890] : [-(class_Groups_Ouminus(_800888)), _800890 = _800888, class_Groups_Ouminus(_800890)], (1500 ^ _779300) ^ [_801013, _801015] : [-(class_Lazy__Sequence_Osmall__lazy(_801013)), _801015 = _801013, class_Lazy__Sequence_Osmall__lazy(_801015)], (1510 ^ _779300) ^ [_801138, _801140] : [-(class_Finite__Set_Ofinite(_801138)), _801140 = _801138, class_Finite__Set_Ofinite(_801140)], (1520 ^ _779300) ^ [_801263, _801265] : [-(class_Enum_Oenum(_801263)), _801265 = _801263, class_Enum_Oenum(_801265)], (1530 ^ _779300) ^ [_801388, _801390] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_801388)), _801390 = _801388, class_Groups_Oordered__cancel__ab__semigroup__add(_801390)], (1540 ^ _779300) ^ [_801513, _801515] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_801513)), _801515 = _801513, class_Groups_Oordered__ab__semigroup__add__imp__le(_801515)], (1550 ^ _779300) ^ [_801638, _801640] : [-(class_Rings_Olinordered__comm__semiring__strict(_801638)), _801640 = _801638, class_Rings_Olinordered__comm__semiring__strict(_801640)], (1560 ^ _779300) ^ [_801763, _801765] : [-(class_Groups_Olinordered__ab__semigroup__add(_801763)), _801765 = _801763, class_Groups_Olinordered__ab__semigroup__add(_801765)], (1570 ^ _779300) ^ [_801888, _801890] : [-(class_Rings_Olinordered__semiring__strict(_801888)), _801890 = _801888, class_Rings_Olinordered__semiring__strict(_801890)], (1580 ^ _779300) ^ [_802013, _802015] : [-(class_Groups_Oordered__ab__semigroup__add(_802013)), _802015 = _802013, class_Groups_Oordered__ab__semigroup__add(_802015)], (1590 ^ _779300) ^ [_802138, _802140] : [-(class_Groups_Oordered__comm__monoid__add(_802138)), _802140 = _802138, class_Groups_Oordered__comm__monoid__add(_802140)], (1600 ^ _779300) ^ [_802263, _802265] : [-(class_Groups_Ocancel__ab__semigroup__add(_802263)), _802265 = _802263, class_Groups_Ocancel__ab__semigroup__add(_802265)], (1610 ^ _779300) ^ [_802388, _802390] : [-(class_Rings_Oordered__cancel__semiring(_802388)), _802390 = _802388, class_Rings_Oordered__cancel__semiring(_802390)], (1620 ^ _779300) ^ [_802513, _802515] : [-(class_Rings_Oordered__comm__semiring(_802513)), _802515 = _802513, class_Rings_Oordered__comm__semiring(_802515)], (1630 ^ _779300) ^ [_802638, _802640] : [-(class_Groups_Ocancel__semigroup__add(_802638)), _802640 = _802638, class_Groups_Ocancel__semigroup__add(_802640)], (1640 ^ _779300) ^ [_802763, _802765] : [-(class_Rings_Olinordered__semiring(_802763)), _802765 = _802763, class_Rings_Olinordered__semiring(_802765)], (1650 ^ _779300) ^ [_802888, _802890] : [-(class_Rings_Olinordered__semidom(_802888)), _802890 = _802888, class_Rings_Olinordered__semidom(_802890)], (1660 ^ _779300) ^ [_803013, _803015] : [-(class_Groups_Oab__semigroup__mult(_803013)), _803015 = _803013, class_Groups_Oab__semigroup__mult(_803015)], (1670 ^ _779300) ^ [_803138, _803140] : [-(class_Groups_Ocomm__monoid__mult(_803138)), _803140 = _803138, class_Groups_Ocomm__monoid__mult(_803140)], (1680 ^ _779300) ^ [_803263, _803265] : [-(class_Groups_Oab__semigroup__add(_803263)), _803265 = _803263, class_Groups_Oab__semigroup__add(_803265)], (1690 ^ _779300) ^ [_803388, _803390] : [-(class_Rings_Oordered__semiring(_803388)), _803390 = _803388, class_Rings_Oordered__semiring(_803390)], (1700 ^ _779300) ^ [_803513, _803515] : [-(class_Rings_Ono__zero__divisors(_803513)), _803515 = _803513, class_Rings_Ono__zero__divisors(_803515)], (1710 ^ _779300) ^ [_803638, _803640] : [-(class_Groups_Ocomm__monoid__add(_803638)), _803640 = _803638, class_Groups_Ocomm__monoid__add(_803640)], (1720 ^ _779300) ^ [_803763, _803765] : [-(class_Rings_Ocomm__semiring__1(_803763)), _803765 = _803763, class_Rings_Ocomm__semiring__1(_803765)], (1730 ^ _779300) ^ [_803888, _803890] : [-(class_Groups_Osemigroup__add(_803888)), _803890 = _803888, class_Groups_Osemigroup__add(_803890)], (1740 ^ _779300) ^ [_804013, _804015] : [-(class_Divides_Osemiring__div(_804013)), _804015 = _804013, class_Divides_Osemiring__div(_804015)], (1750 ^ _779300) ^ [_804138, _804140] : [-(class_Rings_Ocomm__semiring(_804138)), _804140 = _804138, class_Rings_Ocomm__semiring(_804140)], (1760 ^ _779300) ^ [_804263, _804265] : [-(class_Nat_Osemiring__char__0(_804263)), _804265 = _804263, class_Nat_Osemiring__char__0(_804265)], (1770 ^ _779300) ^ [_804388, _804390] : [-(class_Rings_Ozero__neq__one(_804388)), _804390 = _804388, class_Rings_Ozero__neq__one(_804390)], (1780 ^ _779300) ^ [_804513, _804515] : [-(class_Orderings_Opreorder(_804513)), _804515 = _804513, class_Orderings_Opreorder(_804515)], (1790 ^ _779300) ^ [_804638, _804640] : [-(class_Orderings_Olinorder(_804638)), _804640 = _804638, class_Orderings_Olinorder(_804640)], (1800 ^ _779300) ^ [_804763, _804765] : [-(class_Groups_Omonoid__mult(_804763)), _804765 = _804763, class_Groups_Omonoid__mult(_804765)], (1810 ^ _779300) ^ [_804888, _804890] : [-(class_Groups_Omonoid__add(_804888)), _804890 = _804888, class_Groups_Omonoid__add(_804890)], (1820 ^ _779300) ^ [_805013, _805015] : [-(class_Rings_Osemiring__1(_805013)), _805015 = _805013, class_Rings_Osemiring__1(_805015)], (1830 ^ _779300) ^ [_805138, _805140] : [-(class_Rings_Osemiring__0(_805138)), _805140 = _805138, class_Rings_Osemiring__0(_805140)], (1840 ^ _779300) ^ [_805263, _805265] : [-(class_Rings_Omult__zero(_805263)), _805265 = _805263, class_Rings_Omult__zero(_805265)], (1850 ^ _779300) ^ [_805388, _805390] : [-(class_Orderings_Oorder(_805388)), _805390 = _805388, class_Orderings_Oorder(_805390)], (1860 ^ _779300) ^ [_805513, _805515] : [-(class_Rings_Osemiring(_805513)), _805515 = _805513, class_Rings_Osemiring(_805515)], (1870 ^ _779300) ^ [_805638, _805640] : [-(class_Orderings_Oord(_805638)), _805640 = _805638, class_Orderings_Oord(_805640)], (1880 ^ _779300) ^ [_805763, _805765] : [-(class_Groups_Ominus(_805763)), _805765 = _805763, class_Groups_Ominus(_805765)], (1890 ^ _779300) ^ [_805888, _805890] : [-(class_Power_Opower(_805888)), _805890 = _805888, class_Power_Opower(_805890)], (1900 ^ _779300) ^ [_806013, _806015] : [-(class_Groups_Ozero(_806013)), _806015 = _806013, class_Groups_Ozero(_806015)], (1910 ^ _779300) ^ [_806138, _806140] : [-(class_Int_Onumber(_806138)), _806140 = _806138, class_Int_Onumber(_806140)], (1920 ^ _779300) ^ [_806263, _806265] : [-(class_Groups_Oone(_806263)), _806265 = _806263, class_Groups_Oone(_806265)], (1930 ^ _779300) ^ [_806388, _806390] : [-(class_Rings_Odvd(_806388)), _806390 = _806388, class_Rings_Odvd(_806390)], (1940 ^ _779300) ^ [_806513, _806515] : [-(class_Nat_Osize(_806513)), _806515 = _806513, class_Nat_Osize(_806515)], (1950 ^ _779300) ^ [_806638, _806640] : [-(hBOOL(_806638)), _806640 = _806638, hBOOL(_806640)], (1960 ^ _779300) ^ [_806759, _806761] : [-(v_wt(_806759)), _806761 = _806759, v_wt(_806761)], (1970 ^ _779300) ^ [_807681, _807683] : [_807683 = _807681, -(v_mgt(_807683) = v_mgt(_807681))], (1976 ^ _779300) ^ [_807766, _807768, _807770, _807772] : [-(c_Option_Othe(_807772, _807768) = c_Option_Othe(_807770, _807766)), _807772 = _807770, _807768 = _807766], (1986 ^ _779300) ^ [_807915, _807917] : [_807917 = _807915, -(c_Com_Obody(_807917) = c_Com_Obody(_807915))], (1992 ^ _779300) ^ [_808000, _808002, _808004, _808006, _808008, _808010] : [-(c_Partial__Function_Oflat__lub(_808010, _808006, _808002) = c_Partial__Function_Oflat__lub(_808008, _808004, _808000)), _808010 = _808008, _808006 = _808004, _808002 = _808000], (2006 ^ _779300) ^ [_808221, _808223, _808225, _808227, _808229, _808231, _808233, _808235, _808237, _808239] : [-(c_Nitpick_Opair__box_Opair__box__size(_808239, _808235, _808231, _808227, _808223) = c_Nitpick_Opair__box_Opair__box__size(_808237, _808233, _808229, _808225, _808221)), _808239 = _808237, _808235 = _808233, _808231 = _808229, _808227 = _808225, _808223 = _808221], (2028 ^ _779300) ^ [_808610, _808612, _808614, _808616, _808618, _808620, _808622, _808624, _808626, _808628] : [-(c_Nitpick_Opair__box_Opair__box__rec(_808628, _808624, _808620, _808616, _808612) = c_Nitpick_Opair__box_Opair__box__rec(_808626, _808622, _808618, _808614, _808610)), _808628 = _808626, _808624 = _808622, _808620 = _808618, _808616 = _808614, _808612 = _808610], (2050 ^ _779300) ^ [_808999, _809001, _809003, _809005, _809007, _809009, _809011, _809013, _809015, _809017] : [-(c_Nitpick_Opair__box_Opair__box__case(_809017, _809013, _809009, _809005, _809001) = c_Nitpick_Opair__box_Opair__box__case(_809015, _809011, _809007, _809003, _808999)), _809017 = _809015, _809013 = _809011, _809009 = _809007, _809005 = _809003, _809001 = _808999], (2072 ^ _779300) ^ [_809388, _809390, _809392, _809394, _809396, _809398, _809400, _809402] : [-(c_Nitpick_Opair__box_OPairBox(_809402, _809398, _809394, _809390) = c_Nitpick_Opair__box_OPairBox(_809400, _809396, _809392, _809388)), _809402 = _809400, _809398 = _809396, _809394 = _809392, _809390 = _809388], (2090 ^ _779300) ^ [_809689, _809691, _809693, _809695, _809697, _809699, _809701, _809703] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_809703, _809699, _809695, _809691) = c_Nat_Osemiring__1__class_Oof__nat__aux(_809701, _809697, _809693, _809689)), _809703 = _809701, _809699 = _809697, _809695 = _809693, _809691 = _809689], (2108 ^ _779300) ^ [_809990, _809992, _809994, _809996, _809998, _810000] : [-(c_Finite__Set_Ofold1Set(_810000, _809996, _809992) = c_Finite__Set_Ofold1Set(_809998, _809994, _809990)), _810000 = _809998, _809996 = _809994, _809992 = _809990], (2122 ^ _779300) ^ [_810211, _810213] : [_810213 = _810211, -(c_Nat_Osemiring__1__class_ONats(_810213) = c_Nat_Osemiring__1__class_ONats(_810211))], (2128 ^ _779300) ^ [_810296, _810298, _810300, _810302] : [-(c_Int_Onat__aux(_810302, _810298) = c_Int_Onat__aux(_810300, _810296)), _810302 = _810300, _810298 = _810296], (2138 ^ _779300) ^ [_810445, _810447, _810449, _810451, _810453, _810455] : [-(c_Nat_Onat_Onat__rec(_810455, _810451, _810447) = c_Nat_Onat_Onat__rec(_810453, _810449, _810445)), _810455 = _810453, _810451 = _810449, _810447 = _810445], (2152 ^ _779300) ^ [_810666, _810668, _810670, _810672] : [-(c_SMT_Oz3mod(_810672, _810668) = c_SMT_Oz3mod(_810670, _810666)), _810672 = _810670, _810668 = _810666], (2162 ^ _779300) ^ [_810815, _810817, _810819, _810821, _810823, _810825] : [-(c_Power_Opower_Opower(_810825, _810821, _810817) = c_Power_Opower_Opower(_810823, _810819, _810815)), _810825 = _810823, _810821 = _810819, _810817 = _810815], (2176 ^ _779300) ^ [_811036, _811038, _811040, _811042] : [-(c_SMT_Oz3div(_811042, _811038) = c_SMT_Oz3div(_811040, _811036)), _811042 = _811040, _811038 = _811036], (2186 ^ _779300) ^ [_811185, _811187] : [_811187 = _811185, -(c_Int_Osucc(_811187) = c_Int_Osucc(_811185))], (2192 ^ _779300) ^ [_811270, _811272, _811274, _811276] : [-(c_Nat__Transfer_Otsub(_811276, _811272) = c_Nat__Transfer_Otsub(_811274, _811270)), _811276 = _811274, _811272 = _811270], (2202 ^ _779300) ^ [_811419, _811421] : [_811421 = _811419, -(c_Int_Oring__1__class_OInts(_811421) = c_Int_Oring__1__class_OInts(_811419))], (2208 ^ _779300) ^ [_811504, _811506] : [_811506 = _811504, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_811506) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_811504))], (2214 ^ _779300) ^ [_811589, _811591, _811593, _811595] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_811595, _811591) = c_Code__Numeral_Odiv__mod__code__numeral(_811593, _811589)), _811595 = _811593, _811591 = _811589], (2224 ^ _779300) ^ [_811738, _811740, _811742, _811744] : [-(c_Divides_Odivmod__int__rel(_811744, _811740) = c_Divides_Odivmod__int__rel(_811742, _811738)), _811744 = _811742, _811740 = _811738], (2234 ^ _779300) ^ [_811887, _811889] : [_811889 = _811887, -(c_Divides_Oadjust(_811889) = c_Divides_Oadjust(_811887))], (2240 ^ _779300) ^ [_811972, _811974] : [_811974 = _811972, -(c_Nat_Onat_Onat__size(_811974) = c_Nat_Onat_Onat__size(_811972))], (2246 ^ _779300) ^ [_812057, _812059, _812061, _812063] : [-(c_Divides_OnegDivAlg(_812063, _812059) = c_Divides_OnegDivAlg(_812061, _812057)), _812063 = _812061, _812059 = _812057], (2256 ^ _779300) ^ [_812206, _812208, _812210, _812212, _812214, _812216, _812218, _812220, _812222, _812224] : [-(c_Product__Type_Oprod_Oprod__size(_812224, _812220, _812216, _812212, _812208) = c_Product__Type_Oprod_Oprod__size(_812222, _812218, _812214, _812210, _812206)), _812224 = _812222, _812220 = _812218, _812216 = _812214, _812212 = _812210, _812208 = _812206], (2278 ^ _779300) ^ [_812595, _812597, _812599, _812601, _812603, _812605, _812607, _812609, _812611, _812613] : [-(c_Product__Type_Oprod_Oprod__rec(_812613, _812609, _812605, _812601, _812597) = c_Product__Type_Oprod_Oprod__rec(_812611, _812607, _812603, _812599, _812595)), _812613 = _812611, _812609 = _812607, _812605 = _812603, _812601 = _812599, _812597 = _812595], (2300 ^ _779300) ^ [_812984, _812986, _812988, _812990] : [-(c_Divides_Odivmod__nat(_812990, _812986) = c_Divides_Odivmod__nat(_812988, _812984)), _812990 = _812988, _812986 = _812984], (2310 ^ _779300) ^ [_813133, _813135, _813137, _813139] : [-(c_Divides_Odivmod__nat__rel(_813139, _813135) = c_Divides_Odivmod__nat__rel(_813137, _813133)), _813139 = _813137, _813135 = _813133], (2320 ^ _779300) ^ [_813282, _813284] : [_813284 = _813282, -(c_Int_Opred(_813284) = c_Int_Opred(_813282))], (2326 ^ _779300) ^ [_813367, _813369, _813371, _813373] : [-(c_Orderings_Oord_Omax(_813373, _813369) = c_Orderings_Oord_Omax(_813371, _813367)), _813373 = _813371, _813369 = _813367], (2336 ^ _779300) ^ [_813516, _813518, _813520, _813522] : [-(c_Orderings_Oord_Omin(_813522, _813518) = c_Orderings_Oord_Omin(_813520, _813516)), _813522 = _813520, _813518 = _813516], (2346 ^ _779300) ^ [_813665, _813667, _813669, _813671] : [-(c_FunDef_Orp__inv__image(_813671, _813667) = c_FunDef_Orp__inv__image(_813669, _813665)), _813671 = _813669, _813667 = _813665], (2356 ^ _779300) ^ [_813814, _813816, _813818, _813820, _813822, _813824, _813826, _813828] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_813828, _813824, _813820, _813816) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_813826, _813822, _813818, _813814)), _813828 = _813826, _813824 = _813822, _813820 = _813818, _813816 = _813814], (2374 ^ _779300) ^ [_814115, _814117, _814119, _814121] : [-(c_Divides_Odivmod__int(_814121, _814117) = c_Divides_Odivmod__int(_814119, _814115)), _814121 = _814119, _814117 = _814115], (2384 ^ _779300) ^ [_814264, _814266, _814268, _814270] : [-(c_Groups_Osgn__class_Osgn(_814270, _814266) = c_Groups_Osgn__class_Osgn(_814268, _814264)), _814270 = _814268, _814266 = _814264], (2394 ^ _779300) ^ [_814413, _814415, _814417, _814419] : [-(c_Divides_OposDivAlg(_814419, _814415) = c_Divides_OposDivAlg(_814417, _814413)), _814419 = _814417, _814415 = _814413], (2404 ^ _779300) ^ [_814562, _814564, _814566, _814568] : [-(c_Divides_Opdivmod(_814568, _814564) = c_Divides_Opdivmod(_814566, _814562)), _814568 = _814566, _814564 = _814562], (2414 ^ _779300) ^ [_814711, _814713, _814715, _814717] : [-(c_Nitpick_Onat__gcd(_814717, _814713) = c_Nitpick_Onat__gcd(_814715, _814711)), _814717 = _814715, _814713 = _814711], (2424 ^ _779300) ^ [_814860, _814862, _814864, _814866] : [-(c_Nitpick_Onat__lcm(_814866, _814862) = c_Nitpick_Onat__lcm(_814864, _814860)), _814866 = _814864, _814862 = _814860], (2434 ^ _779300) ^ [_815009, _815011, _815013, _815015] : [-(c_Set_Othe__elem(_815015, _815011) = c_Set_Othe__elem(_815013, _815009)), _815015 = _815013, _815011 = _815009], (2444 ^ _779300) ^ [_815158, _815160, _815162, _815164, _815166, _815168, _815170, _815172] : [-(c_Sum__Type_OPlus(_815172, _815168, _815164, _815160) = c_Sum__Type_OPlus(_815170, _815166, _815162, _815158)), _815172 = _815170, _815168 = _815166, _815164 = _815162, _815160 = _815158], (2462 ^ _779300) ^ [_815459, _815461] : [_815461 = _815459, -(c_SetInterval_Oord__class_OatLeast(_815461) = c_SetInterval_Oord__class_OatLeast(_815459))], (2468 ^ _779300) ^ [_815544, _815546] : [_815546 = _815544, -(c_Int_OBit0(_815546) = c_Int_OBit0(_815544))], (2474 ^ _779300) ^ [_815629, _815631] : [_815631 = _815629, -(c_Nitpick_Ozero__frac(_815631) = c_Nitpick_Ozero__frac(_815629))], (2480 ^ _779300) ^ [_815714, _815716] : [_815716 = _815714, -(c_Nitpick_Oone__frac(_815716) = c_Nitpick_Oone__frac(_815714))], (2486 ^ _779300) ^ [_815799, _815801, _815803, _815805] : [-(c_Nitpick_Onumber__of__frac(_815805, _815801) = c_Nitpick_Onumber__of__frac(_815803, _815799)), _815805 = _815803, _815801 = _815799], (2496 ^ _779300) ^ [_815948, _815950, _815952, _815954] : [-(c_Nitpick_Onorm__frac(_815954, _815950) = c_Nitpick_Onorm__frac(_815952, _815948)), _815954 = _815952, _815950 = _815948], (2506 ^ _779300) ^ [_816097, _816099, _816101, _816103, _816105, _816107, _816109, _816111] : [-(c_Nitpick_Oprod(_816111, _816107, _816103, _816099) = c_Nitpick_Oprod(_816109, _816105, _816101, _816097)), _816111 = _816109, _816107 = _816105, _816103 = _816101, _816099 = _816097], (2524 ^ _779300) ^ [_816398, _816400] : [_816400 = _816398, -(c_Wellfounded_Omeasure(_816400) = c_Wellfounded_Omeasure(_816398))], (2530 ^ _779300) ^ [_816483, _816485, _816487, _816489] : [-(c_Wellfounded_Omin__ext(_816489, _816485) = c_Wellfounded_Omin__ext(_816487, _816483)), _816489 = _816487, _816485 = _816483], (2540 ^ _779300) ^ [_816632, _816634, _816636, _816638, _816640, _816642] : [-(c_Wellfounded_Omlex__prod(_816642, _816638, _816634) = c_Wellfounded_Omlex__prod(_816640, _816636, _816632)), _816642 = _816640, _816638 = _816636, _816634 = _816632], (2554 ^ _779300) ^ [_816853, _816855] : [_816855 = _816853, -(c_Int_Oint__ge__less__than(_816855) = c_Int_Oint__ge__less__than(_816853))], (2560 ^ _779300) ^ [_816938, _816940] : [_816940 = _816938, -(c_Int_Oint__ge__less__than2(_816940) = c_Int_Oint__ge__less__than2(_816938))], (2566 ^ _779300) ^ [_817023, _817025, _817027, _817029, _817031, _817033, _817035, _817037] : [-(c_Recdef_Osame__fst(_817037, _817033, _817029, _817025) = c_Recdef_Osame__fst(_817035, _817031, _817027, _817023)), _817037 = _817035, _817033 = _817031, _817029 = _817027, _817025 = _817023], (2584 ^ _779300) ^ [_817324, _817326, _817328, _817330, _817332, _817334] : [-(c_FunDef_Oin__rel(_817334, _817330, _817326) = c_FunDef_Oin__rel(_817332, _817328, _817324)), _817334 = _817332, _817330 = _817328, _817326 = _817324], (2598 ^ _779300) ^ [_817545, _817547, _817549, _817551] : [-(c_Predicate_OPowp(_817551, _817547) = c_Predicate_OPowp(_817549, _817545)), _817551 = _817549, _817547 = _817545], (2608 ^ _779300) ^ [_817694, _817696, _817698, _817700, _817702, _817704] : [-(c_Predicate_ODomainP(_817704, _817700, _817696) = c_Predicate_ODomainP(_817702, _817698, _817694)), _817704 = _817702, _817700 = _817698, _817696 = _817694], (2622 ^ _779300) ^ [_817915, _817917, _817919, _817921, _817923, _817925] : [-(c_Predicate_ORangeP(_817925, _817921, _817917) = c_Predicate_ORangeP(_817923, _817919, _817915)), _817925 = _817923, _817921 = _817919, _817917 = _817915], (2636 ^ _779300) ^ [_818136, _818138, _818140, _818142, _818144, _818146, _818148, _818150] : [-(c_Product__Type_Oapfst(_818150, _818146, _818142, _818138) = c_Product__Type_Oapfst(_818148, _818144, _818140, _818136)), _818150 = _818148, _818146 = _818144, _818142 = _818140, _818138 = _818136], (2654 ^ _779300) ^ [_818437, _818439, _818441, _818443, _818445, _818447, _818449, _818451] : [-(c_Product__Type_Oapsnd(_818451, _818447, _818443, _818439) = c_Product__Type_Oapsnd(_818449, _818445, _818441, _818437)), _818451 = _818449, _818447 = _818445, _818443 = _818441, _818439 = _818437], (2672 ^ _779300) ^ [_818738, _818740, _818742, _818744] : [-(c_Wellfounded_Omax__ext(_818744, _818740) = c_Wellfounded_Omax__ext(_818742, _818738)), _818744 = _818742, _818740 = _818738], (2682 ^ _779300) ^ [_818887, _818889, _818891, _818893, _818895, _818897, _818899, _818901] : [-(c_Random_Oiterate(_818901, _818897, _818893, _818889) = c_Random_Oiterate(_818899, _818895, _818891, _818887)), _818901 = _818899, _818897 = _818895, _818893 = _818891, _818889 = _818887], (2700 ^ _779300) ^ [_819188, _819190, _819192, _819194] : [-(c_Random_Olog(_819194, _819190) = c_Random_Olog(_819192, _819188)), _819194 = _819192, _819190 = _819188], (2710 ^ _779300) ^ [_819337, _819339, _819341, _819343, _819345, _819347] : [-(c_Random_Ominus__shift(_819347, _819343, _819339) = c_Random_Ominus__shift(_819345, _819341, _819337)), _819347 = _819345, _819343 = _819341, _819339 = _819337], (2724 ^ _779300) ^ [_819558, _819560, _819562, _819564] : [-(c_Random_Oinc__shift(_819564, _819560) = c_Random_Oinc__shift(_819562, _819558)), _819564 = _819562, _819560 = _819558], (2734 ^ _779300) ^ [_819707, _819709] : [_819709 = _819707, -(c_Nat_Ofunpow(_819709) = c_Nat_Ofunpow(_819707))], (2740 ^ _779300) ^ [_819792, _819794] : [_819794 = _819792, -(c_Set_OBall(_819794) = c_Set_OBall(_819792))], (2746 ^ _779300) ^ [_819877, _819879] : [_819879 = _819877, -(c_SetInterval_Oord__class_OgreaterThan(_819879) = c_SetInterval_Oord__class_OgreaterThan(_819877))], (2752 ^ _779300) ^ [_819962, _819964] : [_819964 = _819962, -(c_Relation_OField(_819964) = c_Relation_OField(_819962))], (2758 ^ _779300) ^ [_820047, _820049, _820051, _820053] : [-(c_Relation_ORange(_820053, _820049) = c_Relation_ORange(_820051, _820047)), _820053 = _820051, _820049 = _820047], (2768 ^ _779300) ^ [_820196, _820198, _820200, _820202] : [-(c_Relation_ODomain(_820202, _820198) = c_Relation_ODomain(_820200, _820196)), _820202 = _820200, _820198 = _820196], (2778 ^ _779300) ^ [_820345, _820347] : [_820347 = _820345, -(c_HOL_OAll(_820347) = c_HOL_OAll(_820345))], (2784 ^ _779300) ^ [_820430, _820432, _820434, _820436, _820438, _820440, _820442, _820444, _820446, _820448] : [-(c_Finite__Set_Ofold__graph(_820448, _820444, _820440, _820436, _820432) = c_Finite__Set_Ofold__graph(_820446, _820442, _820438, _820434, _820430)), _820448 = _820446, _820444 = _820442, _820440 = _820438, _820436 = _820434, _820432 = _820430], (2806 ^ _779300) ^ [_820819, _820821, _820823, _820825] : [-(c_Nitpick_Oint__lcm(_820825, _820821) = c_Nitpick_Oint__lcm(_820823, _820819)), _820825 = _820823, _820821 = _820819], (2816 ^ _779300) ^ [_820968, _820970, _820972, _820974, _820976, _820978] : [-(c_Nitpick_Otimes__frac(_820978, _820974, _820970) = c_Nitpick_Otimes__frac(_820976, _820972, _820968)), _820978 = _820976, _820974 = _820972, _820970 = _820968], (2830 ^ _779300) ^ [_821189, _821191, _821193, _821195, _821197, _821199] : [-(c_Nitpick_Oof__frac(_821199, _821195, _821191) = c_Nitpick_Oof__frac(_821197, _821193, _821189)), _821199 = _821197, _821195 = _821193, _821191 = _821189], (2844 ^ _779300) ^ [_821410, _821412] : [_821412 = _821410, -(c_Rings_Oinverse__class_Odivide(_821412) = c_Rings_Oinverse__class_Odivide(_821410))], (2850 ^ _779300) ^ [_821495, _821497] : [_821497 = _821495, -(c_Int_Oring__1__class_Oof__int(_821497) = c_Int_Oring__1__class_Oof__int(_821495))], (2856 ^ _779300) ^ [_821580, _821582, _821584, _821586] : [-(c_Nitpick_Oinverse__frac(_821586, _821582) = c_Nitpick_Oinverse__frac(_821584, _821580)), _821586 = _821584, _821582 = _821580], (2866 ^ _779300) ^ [_821729, _821731] : [_821731 = _821729, -(c_Nitpick_Ofrac(_821731) = c_Nitpick_Ofrac(_821729))], (2872 ^ _779300) ^ [_821814, _821816, _821818, _821820] : [-(c_Nitpick_OAbs__Frac(_821820, _821816) = c_Nitpick_OAbs__Frac(_821818, _821814)), _821820 = _821818, _821816 = _821814], (2882 ^ _779300) ^ [_821963, _821965, _821967, _821969, _821971, _821973] : [-(c_Nitpick_Oplus__frac(_821973, _821969, _821965) = c_Nitpick_Oplus__frac(_821971, _821967, _821963)), _821973 = _821971, _821969 = _821967, _821965 = _821963], (2896 ^ _779300) ^ [_822184, _822186, _822188, _822190] : [-(c_Nitpick_Ouminus__frac(_822190, _822186) = c_Nitpick_Ouminus__frac(_822188, _822184)), _822190 = _822188, _822186 = _822184], (2906 ^ _779300) ^ [_822333, _822335] : [_822335 = _822333, -(c_Nitpick_Odenom(_822335) = c_Nitpick_Odenom(_822333))], (2912 ^ _779300) ^ [_822418, _822420] : [_822420 = _822418, -(c_Nitpick_Onum(_822420) = c_Nitpick_Onum(_822418))], (2918 ^ _779300) ^ [_822503, _822505] : [_822505 = _822503, -(c_Nitpick_ORep__Frac(_822505) = c_Nitpick_ORep__Frac(_822503))], (2924 ^ _779300) ^ [_822588, _822590, _822592, _822594, _822596, _822598] : [-(c_Product__Type_Ointernal__split(_822598, _822594, _822590) = c_Product__Type_Ointernal__split(_822596, _822592, _822588)), _822598 = _822596, _822594 = _822592, _822590 = _822588], (2938 ^ _779300) ^ [_822809, _822811] : [_822811 = _822809, -(c_HOL_Obool_Obool__size(_822811) = c_HOL_Obool_Obool__size(_822809))], (2944 ^ _779300) ^ [_822894, _822896, _822898, _822900] : [-(c_List_Olenlex(_822900, _822896) = c_List_Olenlex(_822898, _822894)), _822900 = _822898, _822896 = _822894], (2954 ^ _779300) ^ [_823043, _823045, _823047, _823049, _823051, _823053, _823055, _823057, _823059, _823061, _823063, _823065] : [-(c_Product__Type_Omap__pair(_823065, _823061, _823057, _823053, _823049, _823045) = c_Product__Type_Omap__pair(_823063, _823059, _823055, _823051, _823047, _823043)), _823065 = _823063, _823061 = _823059, _823057 = _823055, _823053 = _823051, _823049 = _823047, _823045 = _823043], (2980 ^ _779300) ^ [_823528, _823530, _823532, _823534] : [-(c_List_Olexn(_823534, _823530) = c_List_Olexn(_823532, _823528)), _823534 = _823532, _823530 = _823528], (2990 ^ _779300) ^ [_823677, _823679, _823681, _823683] : [-(c_Wellfounded_Oacc(_823683, _823679) = c_Wellfounded_Oacc(_823681, _823677)), _823683 = _823681, _823679 = _823677], (3000 ^ _779300) ^ [_823826, _823828, _823830, _823832] : [-(c_Nitpick_Ocard_H(_823832, _823828) = c_Nitpick_Ocard_H(_823830, _823826)), _823832 = _823830, _823828 = _823826], (3010 ^ _779300) ^ [_823975, _823977, _823979, _823981, _823983, _823985] : [-(c_List_Oset__Cons(_823985, _823981, _823977) = c_List_Oset__Cons(_823983, _823979, _823975)), _823985 = _823983, _823981 = _823979, _823977 = _823975], (3024 ^ _779300) ^ [_824196, _824198, _824200, _824202] : [-(c_List_Olistset(_824202, _824198) = c_List_Olistset(_824200, _824196)), _824202 = _824200, _824198 = _824196], (3034 ^ _779300) ^ [_824345, _824347, _824349, _824351] : [-(c_List_Olistrel1(_824351, _824347) = c_List_Olistrel1(_824349, _824345)), _824351 = _824349, _824347 = _824345], (3044 ^ _779300) ^ [_824494, _824496, _824498, _824500, _824502, _824504, _824506, _824508] : [-(c_Nat_Onat_Onat__case(_824508, _824504, _824500, _824496) = c_Nat_Onat_Onat__case(_824506, _824502, _824498, _824494)), _824508 = _824506, _824504 = _824502, _824500 = _824498, _824496 = _824494], (3062 ^ _779300) ^ [_824795, _824797, _824799, _824801] : [-(c_Nat_Ocompow(_824801, _824797) = c_Nat_Ocompow(_824799, _824795)), _824801 = _824799, _824797 = _824795], (3072 ^ _779300) ^ [_824944, _824946] : [_824946 = _824944, -(c_List_Orotate1(_824946) = c_List_Orotate1(_824944))], (3078 ^ _779300) ^ [_825029, _825031, _825033, _825035] : [-(c_Finite__Set_Ofold1(_825035, _825031) = c_Finite__Set_Ofold1(_825033, _825029)), _825035 = _825033, _825031 = _825029], (3088 ^ _779300) ^ [_825178, _825180, _825182, _825184] : [-(c_Big__Operators_Olattice__class_OSup__fin(_825184, _825180) = c_Big__Operators_Olattice__class_OSup__fin(_825182, _825178)), _825184 = _825182, _825180 = _825178], (3098 ^ _779300) ^ [_825327, _825329, _825331, _825333] : [-(c_Big__Operators_Olattice__class_OInf__fin(_825333, _825329) = c_Big__Operators_Olattice__class_OInf__fin(_825331, _825327)), _825333 = _825331, _825329 = _825327], (3108 ^ _779300) ^ [_825476, _825478, _825480, _825482] : [-(c_Big__Operators_Olinorder__class_OMin(_825482, _825478) = c_Big__Operators_Olinorder__class_OMin(_825480, _825476)), _825482 = _825480, _825478 = _825476], (3118 ^ _779300) ^ [_825625, _825627, _825629, _825631] : [-(c_Big__Operators_Olinorder__class_OMax(_825631, _825627) = c_Big__Operators_Olinorder__class_OMax(_825629, _825625)), _825631 = _825629, _825627 = _825625], (3128 ^ _779300) ^ [_825774, _825776, _825778, _825780, _825782, _825784] : [-(c_Big__Operators_Olattice_OInf__fin(_825784, _825780, _825776) = c_Big__Operators_Olattice_OInf__fin(_825782, _825778, _825774)), _825784 = _825782, _825780 = _825778, _825776 = _825774], (3142 ^ _779300) ^ [_825995, _825997, _825999, _826001, _826003, _826005] : [-(c_Big__Operators_Olattice_OSup__fin(_826005, _826001, _825997) = c_Big__Operators_Olattice_OSup__fin(_826003, _825999, _825995)), _826005 = _826003, _826001 = _825999, _825997 = _825995], (3156 ^ _779300) ^ [_826216, _826218, _826220, _826222, _826224, _826226, _826228, _826230, _826232, _826234] : [-(c_Fun_Ofun__upd(_826234, _826230, _826226, _826222, _826218) = c_Fun_Ofun__upd(_826232, _826228, _826224, _826220, _826216)), _826234 = _826232, _826230 = _826228, _826226 = _826224, _826222 = _826220, _826218 = _826216], (3178 ^ _779300) ^ [_826605, _826607, _826609, _826611, _826613, _826615, _826617, _826619] : [-(c_Nitpick_Osetsum_H(_826619, _826615, _826611, _826607) = c_Nitpick_Osetsum_H(_826617, _826613, _826609, _826605)), _826619 = _826617, _826615 = _826613, _826611 = _826609, _826607 = _826605], (3196 ^ _779300) ^ [_826906, _826908, _826910, _826912, _826914, _826916] : [-(c_List_Olist_Olist__size(_826916, _826912, _826908) = c_List_Olist_Olist__size(_826914, _826910, _826906)), _826916 = _826914, _826912 = _826910, _826908 = _826906], (3210 ^ _779300) ^ [_827127, _827129, _827131, _827133] : [-(c_Random_Oselect(_827133, _827129) = c_Random_Oselect(_827131, _827127)), _827133 = _827131, _827129 = _827127], (3220 ^ _779300) ^ [_827276, _827278] : [_827278 = _827276, -(c_Random_Orange(_827278) = c_Random_Orange(_827276))], (3226 ^ _779300) ^ [_827361, _827363, _827365, _827367] : [-(c_Code__Numeral_Onat__of__aux(_827367, _827363) = c_Code__Numeral_Onat__of__aux(_827365, _827361)), _827367 = _827365, _827363 = _827361], (3236 ^ _779300) ^ [_827510, _827512] : [_827512 = _827510, -(c_Lazy__Sequence_Ohb__not__seq(_827512) = c_Lazy__Sequence_Ohb__not__seq(_827510))], (3242 ^ _779300) ^ [_827595, _827597] : [_827597 = _827595, -(c_Int_OBit1(_827597) = c_Int_OBit1(_827595))], (3248 ^ _779300) ^ [_827680, _827682, _827684, _827686] : [-(c_List_Olists(_827686, _827682) = c_List_Olists(_827684, _827680)), _827686 = _827684, _827682 = _827680], (3258 ^ _779300) ^ [_827829, _827831, _827833, _827835] : [-(c_List_Olistsp(_827835, _827831) = c_List_Olistsp(_827833, _827829)), _827835 = _827833, _827831 = _827829], (3268 ^ _779300) ^ [_827978, _827980, _827982, _827984, _827986, _827988, _827990, _827992] : [-(c_Enum_Oproduct(_827992, _827988, _827984, _827980) = c_Enum_Oproduct(_827990, _827986, _827982, _827978)), _827992 = _827990, _827988 = _827986, _827984 = _827982, _827980 = _827978], (3286 ^ _779300) ^ [_828279, _828281, _828283, _828285] : [-(c_Product__Type_OSigma(_828285, _828281) = c_Product__Type_OSigma(_828283, _828279)), _828285 = _828283, _828281 = _828279], (3296 ^ _779300) ^ [_828428, _828430] : [_828430 = _828428, -(c_Set_OPow(_828430) = c_Set_OPow(_828428))], (3302 ^ _779300) ^ [_828513, _828515, _828517, _828519] : [-(c_HOL_OLet(_828519, _828515) = c_HOL_OLet(_828517, _828513)), _828519 = _828517, _828515 = _828513], (3312 ^ _779300) ^ [_828662, _828664, _828666, _828668] : [-(c_Enum_Osublists(_828668, _828664) = c_Enum_Osublists(_828666, _828662)), _828668 = _828666, _828664 = _828662], (3322 ^ _779300) ^ [_828811, _828813, _828815, _828817] : [-(c_Enum_Oenum__the(_828817, _828813) = c_Enum_Oenum__the(_828815, _828811)), _828817 = _828815, _828813 = _828811], (3332 ^ _779300) ^ [_828960, _828962, _828964, _828966, _828968, _828970] : [-(c_Finite__Set_Ofold(_828970, _828966, _828962) = c_Finite__Set_Ofold(_828968, _828964, _828960)), _828970 = _828968, _828966 = _828964, _828962 = _828960], (3346 ^ _779300) ^ [_829181, _829183, _829185, _829187, _829189, _829191] : [-(c_Enum_On__lists(_829191, _829187, _829183) = c_Enum_On__lists(_829189, _829185, _829181)), _829191 = _829189, _829187 = _829185, _829183 = _829181], (3360 ^ _779300) ^ [_829402, _829404, _829406, _829408, _829410, _829412] : [-(c_List_Opartition(_829412, _829408, _829404) = c_List_Opartition(_829410, _829406, _829402)), _829412 = _829410, _829408 = _829406, _829404 = _829402], (3374 ^ _779300) ^ [_829623, _829625, _829627, _829629] : [-(c_List_OremoveAll(_829629, _829625) = c_List_OremoveAll(_829627, _829623)), _829629 = _829627, _829625 = _829623], (3384 ^ _779300) ^ [_829772, _829774, _829776, _829778, _829780, _829782, _829784, _829786] : [-(c_List_Olist_Olist__case(_829786, _829782, _829778, _829774) = c_List_Olist_Olist__case(_829784, _829780, _829776, _829772)), _829786 = _829784, _829782 = _829780, _829778 = _829776, _829774 = _829772], (3402 ^ _779300) ^ [_830073, _830075, _830077, _830079] : [-(c_Random_Oselect__weight(_830079, _830075) = c_Random_Oselect__weight(_830077, _830073)), _830079 = _830077, _830075 = _830073], (3412 ^ _779300) ^ [_830222, _830224, _830226, _830228] : [-(c_Random_Opick(_830228, _830224) = c_Random_Opick(_830226, _830222)), _830228 = _830226, _830224 = _830222], (3422 ^ _779300) ^ [_830371, _830373] : [_830373 = _830371, -(c_List_Otranspose__rel(_830373) = c_List_Otranspose__rel(_830371))], (3428 ^ _779300) ^ [_830456, _830458, _830460, _830462, _830464, _830466] : [-(c_List_Osublist(_830466, _830462, _830458) = c_List_Osublist(_830464, _830460, _830456)), _830466 = _830464, _830462 = _830460, _830458 = _830456], (3442 ^ _779300) ^ [_830677, _830679] : [_830679 = _830677, -(c_SetInterval_Oord__class_OlessThan(_830679) = c_SetInterval_Oord__class_OlessThan(_830677))], (3448 ^ _779300) ^ [_830762, _830764, _830766, _830768, _830770, _830772] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_830772, _830768, _830764) = c_SetInterval_Oord__class_OgreaterThanAtMost(_830770, _830766, _830762)), _830772 = _830770, _830768 = _830766, _830764 = _830762], (3462 ^ _779300) ^ [_830983, _830985, _830987, _830989, _830991, _830993] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_830993, _830989, _830985) = c_SetInterval_Oord__class_OgreaterThanLessThan(_830991, _830987, _830983)), _830993 = _830991, _830989 = _830987, _830985 = _830983], (3476 ^ _779300) ^ [_831204, _831206] : [_831206 = _831204, -(c_SetInterval_Oord__class_OatMost(_831206) = c_SetInterval_Oord__class_OatMost(_831204))], (3482 ^ _779300) ^ [_831289, _831291, _831293, _831295, _831297, _831299, _831301, _831303] : [-(c_List_Olinorder__class_Osort__key(_831303, _831299, _831295, _831291) = c_List_Olinorder__class_Osort__key(_831301, _831297, _831293, _831289)), _831303 = _831301, _831299 = _831297, _831295 = _831293, _831291 = _831289], (3500 ^ _779300) ^ [_831590, _831592, _831594, _831596, _831598, _831600, _831602, _831604, _831606, _831608] : [-(c_List_Olinorder__class_Oinsort__insert__key(_831608, _831604, _831600, _831596, _831592) = c_List_Olinorder__class_Oinsort__insert__key(_831606, _831602, _831598, _831594, _831590)), _831608 = _831606, _831604 = _831602, _831600 = _831598, _831596 = _831594, _831592 = _831590], (3522 ^ _779300) ^ [_831979, _831981, _831983, _831985] : [-(c_List_Olinorder__class_Osorted__list__of__set(_831985, _831981) = c_List_Olinorder__class_Osorted__list__of__set(_831983, _831979)), _831985 = _831983, _831981 = _831979], (3532 ^ _779300) ^ [_832128, _832130, _832132, _832134, _832136, _832138] : [-(c_List_Oremove1(_832138, _832134, _832130) = c_List_Oremove1(_832136, _832132, _832128)), _832138 = _832136, _832134 = _832132, _832130 = _832128], (3546 ^ _779300) ^ [_832349, _832351, _832353, _832355] : [-(c_List_Orotate(_832355, _832351) = c_List_Orotate(_832353, _832349)), _832355 = _832353, _832351 = _832349], (3556 ^ _779300) ^ [_832498, _832500, _832502, _832504] : [-(c_List_Olist__update(_832504, _832500) = c_List_Olist__update(_832502, _832498)), _832504 = _832502, _832500 = _832498], (3566 ^ _779300) ^ [_832647, _832649, _832651, _832653, _832655, _832657, _832659, _832661, _832663, _832665] : [-(c_List_Ofoldr(_832665, _832661, _832657, _832653, _832649) = c_List_Ofoldr(_832663, _832659, _832655, _832651, _832647)), _832665 = _832663, _832661 = _832659, _832657 = _832655, _832653 = _832651, _832649 = _832647], (3588 ^ _779300) ^ [_833036, _833038] : [_833038 = _833036, -(c_Orderings_Oord__class_Omax(_833038) = c_Orderings_Oord__class_Omax(_833036))], (3594 ^ _779300) ^ [_833121, _833123, _833125, _833127] : [-(c_List_Otranspose(_833127, _833123) = c_List_Otranspose(_833125, _833121)), _833127 = _833125, _833123 = _833121], (3604 ^ _779300) ^ [_833270, _833272, _833274, _833276] : [-(c_List_Obutlast(_833276, _833272) = c_List_Obutlast(_833274, _833270)), _833276 = _833274, _833272 = _833270], (3614 ^ _779300) ^ [_833419, _833421] : [_833421 = _833419, -(c_List_Oreturn__list(_833421) = c_List_Oreturn__list(_833419))], (3620 ^ _779300) ^ [_833504, _833506] : [_833506 = _833504, -(c_List_Oembed__list(_833506) = c_List_Oembed__list(_833504))], (3626 ^ _779300) ^ [_833589, _833591] : [_833591 = _833589, -(c_List_Omonoid__add__class_Olistsum(_833591) = c_List_Omonoid__add__class_Olistsum(_833589))], (3632 ^ _779300) ^ [_833674, _833676, _833678, _833680] : [-(c_List_Oremdups(_833680, _833676) = c_List_Oremdups(_833678, _833674)), _833680 = _833678, _833676 = _833674], (3642 ^ _779300) ^ [_833823, _833825, _833827, _833829, _833831, _833833] : [-(c_List_Oinsert(_833833, _833829, _833825) = c_List_Oinsert(_833831, _833827, _833823)), _833833 = _833831, _833829 = _833827, _833825 = _833823], (3656 ^ _779300) ^ [_834044, _834046, _834048, _834050, _834052, _834054, _834056, _834058] : [-(c_List_Omaps(_834058, _834054, _834050, _834046) = c_List_Omaps(_834056, _834052, _834048, _834044)), _834058 = _834056, _834054 = _834052, _834050 = _834048, _834046 = _834044], (3674 ^ _779300) ^ [_834345, _834347, _834349, _834351] : [-(c_List_Olex(_834351, _834347) = c_List_Olex(_834349, _834345)), _834351 = _834349, _834347 = _834345], (3684 ^ _779300) ^ [_834494, _834496, _834498, _834500] : [-(c_List_Omeasures(_834500, _834496) = c_List_Omeasures(_834498, _834494)), _834500 = _834498, _834496 = _834494], (3694 ^ _779300) ^ [_834643, _834645, _834647, _834649, _834651, _834653, _834655, _834657] : [-(c_List_Ofoldl(_834657, _834653, _834649, _834645) = c_List_Ofoldl(_834655, _834651, _834647, _834643)), _834657 = _834655, _834653 = _834651, _834649 = _834647, _834645 = _834643], (3712 ^ _779300) ^ [_834944, _834946] : [_834946 = _834944, -(c_Enum_Oenum__class_Oenum__ex(_834946) = c_Enum_Oenum__class_Oenum__ex(_834944))], (3718 ^ _779300) ^ [_835029, _835031, _835033, _835035, _835037, _835039, _835041, _835043] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_835043, _835039, _835035, _835031) = c_New__Random__Sequence_Opos__not__random__dseq(_835041, _835037, _835033, _835029)), _835043 = _835041, _835039 = _835037, _835035 = _835033, _835031 = _835029], (3736 ^ _779300) ^ [_835330, _835332] : [_835332 = _835330, -(c_New__DSequence_Opos__not__seq(_835332) = c_New__DSequence_Opos__not__seq(_835330))], (3742 ^ _779300) ^ [_835415, _835417, _835419, _835421, _835423, _835425] : [-(c_List_OdropWhile(_835425, _835421, _835417) = c_List_OdropWhile(_835423, _835419, _835415)), _835425 = _835423, _835421 = _835419, _835417 = _835415], (3756 ^ _779300) ^ [_835636, _835638] : [_835638 = _835636, -(c_List_Odistinct(_835638) = c_List_Odistinct(_835636))], (3762 ^ _779300) ^ [_835721, _835723, _835725, _835727, _835729, _835731] : [-(c_List_OtakeWhile(_835731, _835727, _835723) = c_List_OtakeWhile(_835729, _835725, _835721)), _835731 = _835729, _835727 = _835725, _835723 = _835721], (3776 ^ _779300) ^ [_835942, _835944, _835946, _835948, _835950, _835952] : [-(c_List_Olinorder__class_Oinsort__key(_835952, _835948, _835944) = c_List_Olinorder__class_Oinsort__key(_835950, _835946, _835942)), _835952 = _835950, _835948 = _835946, _835944 = _835942], (3790 ^ _779300) ^ [_836163, _836165] : [_836165 = _836163, -(c_Enum_Oenum__class_Oenum__all(_836165) = c_Enum_Oenum__class_Oenum__all(_836163))], (3796 ^ _779300) ^ [_836248, _836250] : [_836250 = _836248, -(c_Nat_Osemiring__1__class_Oof__nat(_836250) = c_Nat_Osemiring__1__class_Oof__nat(_836248))], (3802 ^ _779300) ^ [_836333, _836335] : [_836335 = _836333, -(c_Lazy__Sequence_Ohit__bound(_836335) = c_Lazy__Sequence_Ohit__bound(_836333))], (3808 ^ _779300) ^ [_836418, _836420, _836422, _836424, _836426, _836428, _836430, _836432, _836434, _836436, _836438, _836440, _836442, _836444] : [-(c_New__Random__Sequence_Opos__decr__bind(_836444, _836440, _836436, _836432, _836428, _836424, _836420) = c_New__Random__Sequence_Opos__decr__bind(_836442, _836438, _836434, _836430, _836426, _836422, _836418)), _836444 = _836442, _836440 = _836438, _836436 = _836434, _836432 = _836430, _836428 = _836426, _836424 = _836422, _836420 = _836418], (3838 ^ _779300) ^ [_837007, _837009, _837011, _837013, _837015, _837017, _837019, _837021] : [-(c_New__DSequence_Opos__decr__bind(_837021, _837017, _837013, _837009) = c_New__DSequence_Opos__decr__bind(_837019, _837015, _837011, _837007)), _837021 = _837019, _837017 = _837015, _837013 = _837011, _837009 = _837007], (3856 ^ _779300) ^ [_837308, _837310, _837312, _837314, _837316, _837318, _837320, _837322, _837324, _837326, _837328, _837330, _837332, _837334] : [-(c_New__Random__Sequence_Oneg__decr__bind(_837334, _837330, _837326, _837322, _837318, _837314, _837310) = c_New__Random__Sequence_Oneg__decr__bind(_837332, _837328, _837324, _837320, _837316, _837312, _837308)), _837334 = _837332, _837330 = _837328, _837326 = _837324, _837322 = _837320, _837318 = _837316, _837314 = _837312, _837310 = _837308], (3886 ^ _779300) ^ [_837897, _837899, _837901, _837903, _837905, _837907, _837909, _837911] : [-(c_New__DSequence_Oneg__decr__bind(_837911, _837907, _837903, _837899) = c_New__DSequence_Oneg__decr__bind(_837909, _837905, _837901, _837897)), _837911 = _837909, _837907 = _837905, _837903 = _837901, _837899 = _837897], (3904 ^ _779300) ^ [_838198, _838200, _838202, _838204, _838206, _838208, _838210, _838212] : [-(c_Lazy__Sequence_Ohb__bind(_838212, _838208, _838204, _838200) = c_Lazy__Sequence_Ohb__bind(_838210, _838206, _838202, _838198)), _838212 = _838210, _838208 = _838206, _838204 = _838202, _838200 = _838198], (3922 ^ _779300) ^ [_838499, _838501, _838503, _838505, _838507, _838509, _838511, _838513] : [-(c_New__Random__Sequence_Opos__empty(_838513, _838509, _838505, _838501) = c_New__Random__Sequence_Opos__empty(_838511, _838507, _838503, _838499)), _838513 = _838511, _838509 = _838507, _838505 = _838503, _838501 = _838499], (3940 ^ _779300) ^ [_838800, _838802] : [_838802 = _838800, -(c_New__DSequence_Opos__empty(_838802) = c_New__DSequence_Opos__empty(_838800))], (3946 ^ _779300) ^ [_838885, _838887, _838889, _838891, _838893, _838895, _838897, _838899] : [-(c_New__DSequence_Oneg__bind(_838899, _838895, _838891, _838887) = c_New__DSequence_Oneg__bind(_838897, _838893, _838889, _838885)), _838899 = _838897, _838895 = _838893, _838891 = _838889, _838887 = _838885], (3964 ^ _779300) ^ [_839186, _839188, _839190, _839192, _839194, _839196, _839198, _839200] : [-(c_New__Random__Sequence_Oneg__map(_839200, _839196, _839192, _839188) = c_New__Random__Sequence_Oneg__map(_839198, _839194, _839190, _839186)), _839200 = _839198, _839196 = _839194, _839192 = _839190, _839188 = _839186], (3982 ^ _779300) ^ [_839487, _839489, _839491, _839493, _839495, _839497, _839499, _839501] : [-(c_New__Random__Sequence_Oneg__bind(_839501, _839497, _839493, _839489) = c_New__Random__Sequence_Oneg__bind(_839499, _839495, _839491, _839487)), _839501 = _839499, _839497 = _839495, _839493 = _839491, _839489 = _839487], (4000 ^ _779300) ^ [_839788, _839790] : [_839790 = _839788, -(c_New__Random__Sequence_Oneg__single(_839790) = c_New__Random__Sequence_Oneg__single(_839788))], (4006 ^ _779300) ^ [_839873, _839875, _839877, _839879, _839881, _839883, _839885, _839887] : [-(c_New__DSequence_Opos__bind(_839887, _839883, _839879, _839875) = c_New__DSequence_Opos__bind(_839885, _839881, _839877, _839873)), _839887 = _839885, _839883 = _839881, _839879 = _839877, _839875 = _839873], (4024 ^ _779300) ^ [_840174, _840176, _840178, _840180] : [-(c_New__DSequence_Oneg__single(_840180, _840176) = c_New__DSequence_Oneg__single(_840178, _840174)), _840180 = _840178, _840176 = _840174], (4034 ^ _779300) ^ [_840323, _840325, _840327, _840329] : [-(c_Lazy__Sequence_Ohb__single(_840329, _840325) = c_Lazy__Sequence_Ohb__single(_840327, _840323)), _840329 = _840327, _840325 = _840323], (4044 ^ _779300) ^ [_840472, _840474, _840476, _840478, _840480, _840482, _840484, _840486] : [-(c_New__Random__Sequence_Opos__map(_840486, _840482, _840478, _840474) = c_New__Random__Sequence_Opos__map(_840484, _840480, _840476, _840472)), _840486 = _840484, _840482 = _840480, _840478 = _840476, _840474 = _840472], (4062 ^ _779300) ^ [_840773, _840775, _840777, _840779, _840781, _840783, _840785, _840787] : [-(c_New__Random__Sequence_Opos__bind(_840787, _840783, _840779, _840775) = c_New__Random__Sequence_Opos__bind(_840785, _840781, _840777, _840773)), _840787 = _840785, _840783 = _840781, _840779 = _840777, _840775 = _840773], (4080 ^ _779300) ^ [_841074, _841076] : [_841076 = _841074, -(c_New__Random__Sequence_Opos__single(_841076) = c_New__Random__Sequence_Opos__single(_841074))], (4086 ^ _779300) ^ [_841159, _841161, _841163, _841165, _841167, _841169] : [-(c_List_Osplice(_841169, _841165, _841161) = c_List_Osplice(_841167, _841163, _841159)), _841169 = _841167, _841165 = _841163, _841161 = _841159], (4100 ^ _779300) ^ [_841380, _841382, _841384, _841386] : [-(c_New__DSequence_Opos__single(_841386, _841382) = c_New__DSequence_Opos__single(_841384, _841380)), _841386 = _841384, _841382 = _841380], (4110 ^ _779300) ^ [_841529, _841531, _841533, _841535, _841537, _841539] : [-(c_Predicate_Oconversep(_841539, _841535, _841531) = c_Predicate_Oconversep(_841537, _841533, _841529)), _841539 = _841537, _841535 = _841533, _841531 = _841529], (4124 ^ _779300) ^ [_841750, _841752] : [_841752 = _841750, -(c_List_Otl(_841752) = c_List_Otl(_841750))], (4130 ^ _779300) ^ [_841835, _841837] : [_841837 = _841835, -(c_List_Orev(_841837) = c_List_Orev(_841835))], (4136 ^ _779300) ^ [_841920, _841922] : [_841922 = _841920, -(c_List_Odrop(_841922) = c_List_Odrop(_841920))], (4142 ^ _779300) ^ [_842005, _842007] : [_842007 = _842005, -(c_List_Ohd(_842007) = c_List_Ohd(_842005))], (4148 ^ _779300) ^ [_842090, _842092, _842094, _842096] : [-(c_List_Olast(_842096, _842092) = c_List_Olast(_842094, _842090)), _842096 = _842094, _842092 = _842090], (4158 ^ _779300) ^ [_842239, _842241] : [_842241 = _842239, -(c_List_Otake(_842241) = c_List_Otake(_842239))], (4164 ^ _779300) ^ [_842324, _842326, _842328, _842330] : [-(c_List_Ozip(_842330, _842326) = c_List_Ozip(_842328, _842324)), _842330 = _842328, _842326 = _842324], (4174 ^ _779300) ^ [_842473, _842475] : [_842475 = _842473, -(c_Orderings_Oord__class_Omin(_842475) = c_Orderings_Oord__class_Omin(_842473))], (4180 ^ _779300) ^ [_842558, _842560] : [_842560 = _842558, -(c_List_Onth(_842560) = c_List_Onth(_842558))], (4186 ^ _779300) ^ [_842643, _842645, _842647, _842649] : [-(c_List_Ofilter(_842649, _842645) = c_List_Ofilter(_842647, _842643)), _842649 = _842647, _842645 = _842643], (4196 ^ _779300) ^ [_842792, _842794, _842796, _842798] : [-(c_List_Oconcat(_842798, _842794) = c_List_Oconcat(_842796, _842792)), _842798 = _842796, _842794 = _842792], (4206 ^ _779300) ^ [_842941, _842943] : [_842943 = _842941, -(c_List_Oappend(_842943) = c_List_Oappend(_842941))], (4212 ^ _779300) ^ [_843026, _843028, _843030, _843032] : [-(c_List_Omap(_843032, _843028) = c_List_Omap(_843030, _843026)), _843032 = _843030, _843028 = _843026], (4222 ^ _779300) ^ [_843175, _843177, _843179, _843181, _843183, _843185] : [-(c_List_Oreplicate(_843185, _843181, _843177) = c_List_Oreplicate(_843183, _843179, _843175)), _843185 = _843183, _843181 = _843179, _843177 = _843175], (4236 ^ _779300) ^ [_843396, _843398] : [_843398 = _843396, -(c_If(_843398) = c_If(_843396))], (4242 ^ _779300) ^ [_843481, _843483, _843485, _843487, _843489, _843491, _843493, _843495, _843497, _843499] : [-(c_Predicate_Opred__comp(_843499, _843495, _843491, _843487, _843483) = c_Predicate_Opred__comp(_843497, _843493, _843489, _843485, _843481)), _843499 = _843497, _843495 = _843493, _843491 = _843489, _843487 = _843485, _843483 = _843481], (4264 ^ _779300) ^ [_843870, _843872, _843874, _843876, _843878, _843880, _843882, _843884] : [-(c_Lazy__Sequence_Oproduct(_843884, _843880, _843876, _843872) = c_Lazy__Sequence_Oproduct(_843882, _843878, _843874, _843870)), _843884 = _843882, _843880 = _843878, _843876 = _843874, _843872 = _843870], (4282 ^ _779300) ^ [_844171, _844173, _844175, _844177, _844179, _844181, _844183, _844185, _844187, _844189, _844191, _844193] : [-(c_New__Random__Sequence_Opos__union(_844193, _844189, _844185, _844181, _844177, _844173) = c_New__Random__Sequence_Opos__union(_844191, _844187, _844183, _844179, _844175, _844171)), _844193 = _844191, _844189 = _844187, _844185 = _844183, _844181 = _844179, _844177 = _844175, _844173 = _844171], (4308 ^ _779300) ^ [_844656, _844658, _844660, _844662, _844664, _844666] : [-(c_New__DSequence_Opos__union(_844666, _844662, _844658) = c_New__DSequence_Opos__union(_844664, _844660, _844656)), _844666 = _844664, _844662 = _844660, _844658 = _844656], (4322 ^ _779300) ^ [_844877, _844879, _844881, _844883] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_844883, _844879) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_844881, _844877)), _844883 = _844881, _844879 = _844877], (4332 ^ _779300) ^ [_845026, _845028] : [_845028 = _845026, -(c_Lazy__Sequence_Oempty(_845028) = c_Lazy__Sequence_Oempty(_845026))], (4338 ^ _779300) ^ [_845111, _845113] : [_845113 = _845111, -(c_Lazy__Sequence_Osingle(_845113) = c_Lazy__Sequence_Osingle(_845111))], (4344 ^ _779300) ^ [_845196, _845198, _845200, _845202] : [-(c_Lazy__Sequence_Osmall__lazy_H(_845202, _845198) = c_Lazy__Sequence_Osmall__lazy_H(_845200, _845196)), _845202 = _845200, _845198 = _845196], (4354 ^ _779300) ^ [_845345, _845347, _845349, _845351] : [-(c_Wellfounded_Oaccp(_845351, _845347) = c_Wellfounded_Oaccp(_845349, _845345)), _845351 = _845349, _845347 = _845345], (4364 ^ _779300) ^ [_845494, _845496, _845498, _845500, _845502, _845504, _845506, _845508, _845510, _845512] : [-(c_Option_Ooption_Ooption__case(_845512, _845508, _845504, _845500, _845496) = c_Option_Ooption_Ooption__case(_845510, _845506, _845502, _845498, _845494)), _845512 = _845510, _845508 = _845506, _845504 = _845502, _845500 = _845498, _845496 = _845494], (4386 ^ _779300) ^ [_845883, _845885] : [_845885 = _845883, -(c_Lazy__Sequence_Oyieldn(_845885) = c_Lazy__Sequence_Oyieldn(_845883))], (4392 ^ _779300) ^ [_845968, _845970, _845972, _845974, _845976, _845978] : [-(c_Lazy__Sequence_Oanamorph(_845978, _845974, _845970) = c_Lazy__Sequence_Oanamorph(_845976, _845972, _845968)), _845978 = _845976, _845974 = _845972, _845970 = _845968], (4406 ^ _779300) ^ [_846189, _846191] : [_846191 = _846189, -(c_Lazy__Sequence_Oyield(_846191) = c_Lazy__Sequence_Oyield(_846189))], (4412 ^ _779300) ^ [_846274, _846276] : [_846276 = _846274, -(c_List_Olist_OCons(_846276) = c_List_Olist_OCons(_846274))], (4418 ^ _779300) ^ [_846359, _846361] : [_846361 = _846359, -(c_List_Olist_ONil(_846361) = c_List_Olist_ONil(_846359))], (4424 ^ _779300) ^ [_846444, _846446] : [_846446 = _846444, -(c_List_Omember(_846446) = c_List_Omember(_846444))], (4430 ^ _779300) ^ [_846529, _846531, _846533, _846535] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846535, _846531) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846533, _846529)), _846535 = _846533, _846531 = _846529], (4440 ^ _779300) ^ [_846678, _846680, _846682, _846684] : [-(c_HOL_OThe(_846684, _846680) = c_HOL_OThe(_846682, _846678)), _846684 = _846682, _846680 = _846678], (4450 ^ _779300) ^ [_846827, _846829, _846831, _846833, _846835, _846837] : [-(c_FunDef_OTHE__default(_846837, _846833, _846829) = c_FunDef_OTHE__default(_846835, _846831, _846827)), _846837 = _846835, _846833 = _846831, _846829 = _846827], (4464 ^ _779300) ^ [_847048, _847050, _847052, _847054] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_847054, _847050) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_847052, _847048)), _847054 = _847052, _847050 = _847048], (4474 ^ _779300) ^ [_847197, _847199] : [_847199 = _847197, -(c_Nat_Osize__class_Osize(_847199) = c_Nat_Osize__class_Osize(_847197))], (4480 ^ _779300) ^ [_847282, _847284, _847286, _847288, _847290, _847292, _847294, _847296, _847298, _847300] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_847300, _847296, _847292, _847288, _847284) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_847298, _847294, _847290, _847286, _847282)), _847300 = _847298, _847296 = _847294, _847292 = _847290, _847288 = _847286, _847284 = _847282], (4502 ^ _779300) ^ [_847671, _847673, _847675, _847677] : [-(c_List_Oupto(_847677, _847673) = c_List_Oupto(_847675, _847671)), _847677 = _847675, _847673 = _847671], (4512 ^ _779300) ^ [_847820, _847822] : [_847822 = _847820, -(c_Code__Numeral_OSuc__code__numeral(_847822) = c_Code__Numeral_OSuc__code__numeral(_847820))], (4518 ^ _779300) ^ [_847905, _847907, _847909, _847911, _847913, _847915, _847917, _847919] : [-(c_Product__Type_Oscomp(_847919, _847915, _847911, _847907) = c_Product__Type_Oscomp(_847917, _847913, _847909, _847905)), _847919 = _847917, _847915 = _847913, _847911 = _847909, _847907 = _847905], (4536 ^ _779300) ^ [_848206, _848208, _848210, _848212, _848214, _848216, _848218, _848220] : [-(c_Random__Sequence_ORandom(_848220, _848216, _848212, _848208) = c_Random__Sequence_ORandom(_848218, _848214, _848210, _848206)), _848220 = _848218, _848216 = _848214, _848212 = _848210, _848208 = _848206], (4554 ^ _779300) ^ [_848507, _848509] : [_848509 = _848507, -(c_DSequence_Ounion(_848509) = c_DSequence_Ounion(_848507))], (4560 ^ _779300) ^ [_848592, _848594, _848596, _848598, _848600, _848602, _848604, _848606] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_848606, _848602, _848598, _848594) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_848604, _848600, _848596, _848592)), _848606 = _848604, _848602 = _848600, _848598 = _848596, _848594 = _848592], (4578 ^ _779300) ^ [_848893, _848895, _848897, _848899, _848901, _848903] : [-(c_Random__Sequence_Oempty(_848903, _848899, _848895) = c_Random__Sequence_Oempty(_848901, _848897, _848893)), _848903 = _848901, _848899 = _848897, _848895 = _848893], (4592 ^ _779300) ^ [_849114, _849116] : [_849116 = _849114, -(c_DSequence_Oempty(_849116) = c_DSequence_Oempty(_849114))], (4598 ^ _779300) ^ [_849199, _849201] : [_849201 = _849199, -(c_DSequence_Osingle(_849201) = c_DSequence_Osingle(_849199))], (4604 ^ _779300) ^ [_849284, _849286, _849288, _849290, _849292, _849294, _849296, _849298] : [-(c_Random__Sequence_Omap(_849298, _849294, _849290, _849286) = c_Random__Sequence_Omap(_849296, _849292, _849288, _849284)), _849298 = _849296, _849294 = _849292, _849290 = _849288, _849286 = _849284], (4622 ^ _779300) ^ [_849585, _849587, _849589, _849591, _849593, _849595, _849597, _849599] : [-(c_Random__Sequence_Obind(_849599, _849595, _849591, _849587) = c_Random__Sequence_Obind(_849597, _849593, _849589, _849585)), _849599 = _849597, _849595 = _849593, _849591 = _849589, _849587 = _849585], (4640 ^ _779300) ^ [_849886, _849888] : [_849888 = _849886, -(c_Random__Sequence_Osingle(_849888) = c_Random__Sequence_Osingle(_849886))], (4646 ^ _779300) ^ [_849971, _849973, _849975, _849977] : [-(c_Product__Type_Osnd(_849977, _849973) = c_Product__Type_Osnd(_849975, _849971)), _849977 = _849975, _849973 = _849971], (4656 ^ _779300) ^ [_850120, _850122, _850124, _850126] : [-(c_Product__Type_Ofst(_850126, _850122) = c_Product__Type_Ofst(_850124, _850120)), _850126 = _850124, _850122 = _850120], (4666 ^ _779300) ^ [_850269, _850271, _850273, _850275, _850277, _850279] : [-(c_Relation_OImage(_850279, _850275, _850271) = c_Relation_OImage(_850277, _850273, _850269)), _850279 = _850277, _850275 = _850273, _850271 = _850269], (4680 ^ _779300) ^ [_850490, _850492, _850494, _850496, _850498, _850500, _850502, _850504] : [-(c_Wellfounded_Olex__prod(_850504, _850500, _850496, _850492) = c_Wellfounded_Olex__prod(_850502, _850498, _850494, _850490)), _850504 = _850502, _850500 = _850498, _850496 = _850494, _850492 = _850490], (4698 ^ _779300) ^ [_850791, _850793] : [_850793 = _850791, -(c_Set_OBex(_850793) = c_Set_OBex(_850791))], (4704 ^ _779300) ^ [_850876, _850878, _850880, _850882] : [-(c_List_Olexord(_850882, _850878) = c_List_Olexord(_850880, _850876)), _850882 = _850880, _850878 = _850876], (4714 ^ _779300) ^ [_851025, _851027] : [_851027 = _851025, -(c_Wellfounded_Ofinite__psubset(_851027) = c_Wellfounded_Ofinite__psubset(_851025))], (4720 ^ _779300) ^ [_851110, _851112] : [_851112 = _851110, -(c_List_Oset(_851112) = c_List_Oset(_851110))], (4726 ^ _779300) ^ [_851195, _851197, _851199, _851201] : [-(c_Complete__Lattice_OSup__class_OSup(_851201, _851197) = c_Complete__Lattice_OSup__class_OSup(_851199, _851195)), _851201 = _851199, _851197 = _851195], (4736 ^ _779300) ^ [_851344, _851346, _851348, _851350] : [-(c_Complete__Lattice_OInf__class_OInf(_851350, _851346) = c_Complete__Lattice_OInf__class_OInf(_851348, _851344)), _851350 = _851348, _851346 = _851344], (4746 ^ _779300) ^ [_851493, _851495, _851497, _851499, _851501, _851503, _851505, _851507, _851509, _851511, _851513, _851515] : [-(c_Partial__Function_Ofun__lub(_851515, _851511, _851507, _851503, _851499, _851495) = c_Partial__Function_Ofun__lub(_851513, _851509, _851505, _851501, _851497, _851493)), _851515 = _851513, _851511 = _851509, _851507 = _851505, _851503 = _851501, _851499 = _851497, _851495 = _851493], (4772 ^ _779300) ^ [_851978, _851980, _851982, _851984, _851986, _851988] : [-(c_Relation_Orel__comp(_851988, _851984, _851980) = c_Relation_Orel__comp(_851986, _851982, _851978)), _851988 = _851986, _851984 = _851982, _851980 = _851978], (4786 ^ _779300) ^ [_852199, _852201, _852203, _852205] : [-(c_Relation_Oinv__image(_852205, _852201) = c_Relation_Oinv__image(_852203, _852199)), _852205 = _852203, _852201 = _852199], (4796 ^ _779300) ^ [_852348, _852350, _852352, _852354] : [-(c_List_Olistrel(_852354, _852350) = c_List_Olistrel(_852352, _852348)), _852354 = _852352, _852350 = _852348], (4806 ^ _779300) ^ [_852497, _852499] : [_852499 = _852497, -(c_Relation_OId(_852499) = c_Relation_OId(_852497))], (4812 ^ _779300) ^ [_852582, _852584, _852586, _852588] : [-(c_Relation_OId__on(_852588, _852584) = c_Relation_OId__on(_852586, _852582)), _852588 = _852586, _852584 = _852582], (4822 ^ _779300) ^ [_852731, _852733, _852735, _852737] : [-(c_Relation_Oconverse(_852737, _852733) = c_Relation_Oconverse(_852735, _852731)), _852737 = _852735, _852733 = _852731], (4832 ^ _779300) ^ [_852880, _852882] : [_852882 = _852880, -(c_HOL_OEx(_852882) = c_HOL_OEx(_852880))], (4838 ^ _779300) ^ [_852965, _852967, _852969, _852971] : [-(c_Hilbert__Choice_OEps(_852971, _852967) = c_Hilbert__Choice_OEps(_852969, _852965)), _852971 = _852969, _852967 = _852965], (4848 ^ _779300) ^ [_853114, _853116, _853118, _853120, _853122, _853124] : [-(c_Finite__Set_Ofold__image(_853124, _853120, _853116) = c_Finite__Set_Ofold__image(_853122, _853118, _853114)), _853124 = _853122, _853120 = _853118, _853116 = _853114], (4862 ^ _779300) ^ [_853335, _853337, _853339, _853341] : [-(c_Quickcheck_Obeyond(_853341, _853337) = c_Quickcheck_Obeyond(_853339, _853335)), _853341 = _853339, _853337 = _853335], (4872 ^ _779300) ^ [_853484, _853486, _853488, _853490, _853492, _853494, _853496, _853498, _853500, _853502] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_853502, _853498, _853494, _853490, _853486) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_853500, _853496, _853492, _853488, _853484)), _853502 = _853500, _853498 = _853496, _853494 = _853492, _853490 = _853488, _853486 = _853484], (4894 ^ _779300) ^ [_853873, _853875] : [_853875 = _853873, -(c_Set_OCollect(_853875) = c_Set_OCollect(_853873))], (4900 ^ _779300) ^ [_853958, _853960] : [_853960 = _853958, -(c_Lattices_Osemilattice__inf__class_Oinf(_853960) = c_Lattices_Osemilattice__inf__class_Oinf(_853958))], (4906 ^ _779300) ^ [_854043, _854045] : [_854045 = _854043, -(c_Lattices_Osemilattice__sup__class_Osup(_854045) = c_Lattices_Osemilattice__sup__class_Osup(_854043))], (4912 ^ _779300) ^ [_854128, _854130] : [_854130 = _854128, -(c_Fun_Oid(_854130) = c_Fun_Oid(_854128))], (4918 ^ _779300) ^ [_854213, _854215, _854217, _854219, _854221, _854223, _854225, _854227] : [-(c_Fun_Othe__inv__into(_854227, _854223, _854219, _854215) = c_Fun_Othe__inv__into(_854225, _854221, _854217, _854213)), _854227 = _854225, _854223 = _854221, _854219 = _854217, _854215 = _854213], (4936 ^ _779300) ^ [_854514, _854516, _854518, _854520, _854522, _854524, _854526, _854528] : [-(c_Product__Type_Ocurry(_854528, _854524, _854520, _854516) = c_Product__Type_Ocurry(_854526, _854522, _854518, _854514)), _854528 = _854526, _854524 = _854522, _854520 = _854518, _854516 = _854514], (4954 ^ _779300) ^ [_854815, _854817, _854819, _854821, _854823, _854825] : [-(c_Product__Type_Oprod_Oprod__case(_854825, _854821, _854817) = c_Product__Type_Oprod_Oprod__case(_854823, _854819, _854815)), _854825 = _854823, _854821 = _854819, _854817 = _854815], (4968 ^ _779300) ^ [_855036, _855038, _855040, _855042, _855044, _855046] : [-(c_Set_Ovimage(_855046, _855042, _855038) = c_Set_Ovimage(_855044, _855040, _855036)), _855046 = _855044, _855042 = _855040, _855038 = _855036], (4982 ^ _779300) ^ [_855257, _855259, _855261, _855263, _855265, _855267, _855269, _855271] : [-(c_Hilbert__Choice_Oinv__into(_855271, _855267, _855263, _855259) = c_Hilbert__Choice_Oinv__into(_855269, _855265, _855261, _855257)), _855271 = _855269, _855267 = _855265, _855263 = _855261, _855259 = _855257], (5000 ^ _779300) ^ [_855558, _855560] : [_855560 = _855558, -(c_Orderings_Otop__class_Otop(_855560) = c_Orderings_Otop__class_Otop(_855558))], (5006 ^ _779300) ^ [_855643, _855645, _855647, _855649, _855651, _855653] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_855653, _855649, _855645) = c_SetInterval_Oord__class_OatLeastAtMost(_855651, _855647, _855643)), _855653 = _855651, _855649 = _855647, _855645 = _855643], (5020 ^ _779300) ^ [_855864, _855866, _855868, _855870] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855870, _855866) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855868, _855864)), _855870 = _855868, _855866 = _855864], (5030 ^ _779300) ^ [_856013, _856015, _856017, _856019] : [-(c_Quotient_ORespects(_856019, _856015) = c_Quotient_ORespects(_856017, _856013)), _856019 = _856017, _856015 = _856013], (5040 ^ _779300) ^ [_856162, _856164, _856166, _856168, _856170, _856172, _856174, _856176] : [-(c_Quotient_OBabs(_856176, _856172, _856168, _856164) = c_Quotient_OBabs(_856174, _856170, _856166, _856162)), _856176 = _856174, _856172 = _856170, _856168 = _856166, _856164 = _856162], (5058 ^ _779300) ^ [_856463, _856465, _856467, _856469] : [-(c_Transitive__Closure_Otrancl(_856469, _856465) = c_Transitive__Closure_Otrancl(_856467, _856463)), _856469 = _856467, _856465 = _856463], (5068 ^ _779300) ^ [_856612, _856614, _856616, _856618] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856618, _856614) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856616, _856612)), _856618 = _856616, _856614 = _856612], (5078 ^ _779300) ^ [_856761, _856763, _856765, _856767] : [-(c_Transitive__Closure_Ortrancl(_856767, _856763) = c_Transitive__Closure_Ortrancl(_856765, _856761)), _856767 = _856765, _856763 = _856761], (5088 ^ _779300) ^ [_856910, _856912, _856914, _856916] : [-(c_Product__Type_OPair(_856916, _856912) = c_Product__Type_OPair(_856914, _856910)), _856916 = _856914, _856912 = _856910], (5098 ^ _779300) ^ [_857059, _857061, _857063, _857065, _857067, _857069] : [-(c_Lazy__Sequence_Oappend(_857069, _857065, _857061) = c_Lazy__Sequence_Oappend(_857067, _857063, _857059)), _857069 = _857067, _857065 = _857063, _857061 = _857059], (5112 ^ _779300) ^ [_857280, _857282, _857284, _857286] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_857286, _857282) = c_SetInterval_Oord__class_OatLeastLessThan(_857284, _857280)), _857286 = _857284, _857282 = _857280], (5122 ^ _779300) ^ [_857429, _857431, _857433, _857435] : [-(c_List_Oupt(_857435, _857431) = c_List_Oupt(_857433, _857429)), _857435 = _857433, _857431 = _857429], (5132 ^ _779300) ^ [_857578, _857580, _857582, _857584, _857586, _857588, _857590, _857592] : [-(c_Fun_Ocomp(_857592, _857588, _857584, _857580) = c_Fun_Ocomp(_857590, _857586, _857582, _857578)), _857592 = _857590, _857588 = _857586, _857584 = _857582, _857580 = _857578], (5150 ^ _779300) ^ [_857879, _857881, _857883, _857885, _857887, _857889] : [-(c_Lazy__Sequence_Obind(_857889, _857885, _857881) = c_Lazy__Sequence_Obind(_857887, _857883, _857879)), _857889 = _857887, _857885 = _857883, _857881 = _857879], (5164 ^ _779300) ^ [_858100, _858102, _858104, _858106] : [-(c_Lazy__Sequence_Oflat(_858106, _858102) = c_Lazy__Sequence_Oflat(_858104, _858100)), _858106 = _858104, _858102 = _858100], (5174 ^ _779300) ^ [_858249, _858251, _858253, _858255, _858257, _858259] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_858259, _858255, _858251) = c_Lazy__Sequence_Olazy__sequence_OInsert(_858257, _858253, _858249)), _858259 = _858257, _858255 = _858253, _858251 = _858249], (5188 ^ _779300) ^ [_858470, _858472] : [_858472 = _858470, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_858472) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_858470))], (5194 ^ _779300) ^ [_858555, _858557, _858559, _858561, _858563, _858565, _858567, _858569, _858571, _858573] : [-(c_New__DSequence_Opos__map(_858573, _858569, _858565, _858561, _858557) = c_New__DSequence_Opos__map(_858571, _858567, _858563, _858559, _858555)), _858573 = _858571, _858569 = _858567, _858565 = _858563, _858561 = _858559, _858557 = _858555], (5216 ^ _779300) ^ [_858944, _858946, _858948, _858950, _858952, _858954, _858956, _858958] : [-(c_Lazy__Sequence_Omap(_858958, _858954, _858950, _858946) = c_Lazy__Sequence_Omap(_858956, _858952, _858948, _858944)), _858958 = _858956, _858954 = _858952, _858950 = _858948, _858946 = _858944], (5234 ^ _779300) ^ [_859245, _859247] : [_859247 = _859245, -(c_Int_Onumber__class_Onumber__of(_859247) = c_Int_Onumber__class_Onumber__of(_859245))], (5240 ^ _779300) ^ [_859330, _859332, _859334, _859336, _859338, _859340] : [-(c_SetInterval_Oord_OatMost(_859340, _859336, _859332) = c_SetInterval_Oord_OatMost(_859338, _859334, _859330)), _859340 = _859338, _859336 = _859334, _859332 = _859330], (5254 ^ _779300) ^ [_859551, _859553, _859555, _859557, _859559, _859561] : [-(c_SetInterval_Oord_OatLeast(_859561, _859557, _859553) = c_SetInterval_Oord_OatLeast(_859559, _859555, _859551)), _859561 = _859559, _859557 = _859555, _859553 = _859551], (5268 ^ _779300) ^ [_859772, _859774, _859776, _859778, _859780, _859782] : [-(c_SetInterval_Oord_OgreaterThan(_859782, _859778, _859774) = c_SetInterval_Oord_OgreaterThan(_859780, _859776, _859772)), _859782 = _859780, _859778 = _859776, _859774 = _859772], (5282 ^ _779300) ^ [_859993, _859995, _859997, _859999, _860001, _860003] : [-(c_SetInterval_Oord_OlessThan(_860003, _859999, _859995) = c_SetInterval_Oord_OlessThan(_860001, _859997, _859993)), _860003 = _860001, _859999 = _859997, _859995 = _859993], (5296 ^ _779300) ^ [_860214, _860216] : [_860216 = _860214, -(c_Groups_Oabs__class_Oabs(_860216) = c_Groups_Oabs__class_Oabs(_860214))], (5302 ^ _779300) ^ [_860299, _860301, _860303, _860305, _860307, _860309] : [-(c_Divides_Odiv__class_Omod(_860309, _860305, _860301) = c_Divides_Odiv__class_Omod(_860307, _860303, _860299)), _860309 = _860307, _860305 = _860303, _860301 = _860299], (5316 ^ _779300) ^ [_860520, _860522] : [_860522 = _860520, -(c_Groups_Ouminus__class_Ouminus(_860522) = c_Groups_Ouminus__class_Ouminus(_860520))], (5322 ^ _779300) ^ [_860605, _860607, _860609, _860611, _860613, _860615, _860617, _860619] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_860619, _860615, _860611, _860607) = c_SetInterval_Oord_OgreaterThanLessThan(_860617, _860613, _860609, _860605)), _860619 = _860617, _860615 = _860613, _860611 = _860609, _860607 = _860605], (5340 ^ _779300) ^ [_860906, _860908, _860910, _860912, _860914, _860916, _860918, _860920, _860922, _860924] : [-(c_SetInterval_Oord_OatLeastLessThan(_860924, _860920, _860916, _860912, _860908) = c_SetInterval_Oord_OatLeastLessThan(_860922, _860918, _860914, _860910, _860906)), _860924 = _860922, _860920 = _860918, _860916 = _860914, _860912 = _860910, _860908 = _860906], (5362 ^ _779300) ^ [_861295, _861297, _861299, _861301, _861303, _861305, _861307, _861309, _861311, _861313] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_861313, _861309, _861305, _861301, _861297) = c_SetInterval_Oord_OgreaterThanAtMost(_861311, _861307, _861303, _861299, _861295)), _861313 = _861311, _861309 = _861307, _861305 = _861303, _861301 = _861299, _861297 = _861295], (5384 ^ _779300) ^ [_861684, _861686, _861688, _861690, _861692, _861694, _861696, _861698] : [-(c_SetInterval_Oord_OatLeastAtMost(_861698, _861694, _861690, _861686) = c_SetInterval_Oord_OatLeastAtMost(_861696, _861692, _861688, _861684)), _861698 = _861696, _861694 = _861692, _861690 = _861688, _861686 = _861684], (5402 ^ _779300) ^ [_861985, _861987] : [_861987 = _861985, -(c_Set_Oinsert(_861987) = c_Set_Oinsert(_861985))], (5408 ^ _779300) ^ [_862070, _862072] : [_862072 = _862070, -(c_Orderings_Obot__class_Obot(_862072) = c_Orderings_Obot__class_Obot(_862070))], (5414 ^ _779300) ^ [_862155, _862157] : [_862157 = _862155, -(c_Groups_Ominus__class_Ominus(_862157) = c_Groups_Ominus__class_Ominus(_862155))], (5420 ^ _779300) ^ [_862240, _862242] : [_862242 = _862240, -(c_Divides_Odiv__class_Odiv(_862242) = c_Divides_Odiv__class_Odiv(_862240))], (5426 ^ _779300) ^ [_862325, _862327] : [_862327 = _862325, -(c_Groups_Oplus__class_Oplus(_862327) = c_Groups_Oplus__class_Oplus(_862325))], (5432 ^ _779300) ^ [_862410, _862412, _862414, _862416] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862416, _862412) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862414, _862410)), _862416 = _862414, _862412 = _862410], (5442 ^ _779300) ^ [_862559, _862561] : [_862561 = _862559, -(c_Power_Opower__class_Opower(_862561) = c_Power_Opower__class_Opower(_862559))], (5448 ^ _779300) ^ [_862644, _862646] : [_862646 = _862644, -(c_Groups_Otimes__class_Otimes(_862646) = c_Groups_Otimes__class_Otimes(_862644))], (5454 ^ _779300) ^ [_862729, _862731] : [_862731 = _862729, -(c_Groups_Oone__class_Oone(_862731) = c_Groups_Oone__class_Oone(_862729))], (5460 ^ _779300) ^ [_862814, _862816] : [_862816 = _862814, -(c_member(_862816) = c_member(_862814))], (5466 ^ _779300) ^ [_862899, _862901] : [_862901 = _862899, -(c_Equiv__Relations_Oquotient(_862901) = c_Equiv__Relations_Oquotient(_862899))], (5472 ^ _779300) ^ [_862984, _862986] : [_862986 = _862984, -(c_Rings_Odvd__class_Odvd(_862986) = c_Rings_Odvd__class_Odvd(_862984))], (5478 ^ _779300) ^ [_863069, _863071] : [_863071 = _863069, -(c_Orderings_Oord__class_Oless(_863071) = c_Orderings_Oord__class_Oless(_863069))], (5484 ^ _779300) ^ [_863154, _863156] : [_863156 = _863154, -(c_Groups_Ozero__class_Ozero(_863156) = c_Groups_Ozero__class_Ozero(_863154))], (5490 ^ _779300) ^ [_863239, _863241] : [_863241 = _863239, -(tc_List_Olist(_863241) = tc_List_Olist(_863239))], (5496 ^ _779300) ^ [_863324, _863326, _863328, _863330] : [-(tc_sum(_863330, _863326) = tc_sum(_863328, _863324)), _863330 = _863328, _863326 = _863324], (5506 ^ _779300) ^ [_863473, _863475] : [_863475 = _863473, -(tc_Option_Ooption(_863475) = tc_Option_Ooption(_863473))], (5512 ^ _779300) ^ [_863558, _863560, _863562, _863564] : [-(tc_Nitpick_Opair__box(_863564, _863560) = tc_Nitpick_Opair__box(_863562, _863558)), _863564 = _863562, _863560 = _863558], (5522 ^ _779300) ^ [_863707, _863709, _863711, _863713] : [-(tc_prod(_863713, _863709) = tc_prod(_863711, _863707)), _863713 = _863711, _863709 = _863707], (5532 ^ _779300) ^ [_863856, _863858] : [_863858 = _863856, -(tc_Lazy__Sequence_Olazy__sequence(_863858) = tc_Lazy__Sequence_Olazy__sequence(_863856))], (5538 ^ _779300) ^ [_863941, _863943] : [_863943 = _863941, -(c_COMBI(_863943) = c_COMBI(_863941))], (5544 ^ _779300) ^ [_864026, _864028, _864030, _864032] : [-(c_COMBK(_864032, _864028) = c_COMBK(_864030, _864026)), _864032 = _864030, _864028 = _864026], (5554 ^ _779300) ^ [_864175, _864177, _864179, _864181, _864183, _864185] : [-(c_COMBB(_864185, _864181, _864177) = c_COMBB(_864183, _864179, _864175)), _864185 = _864183, _864181 = _864179, _864177 = _864175], (5568 ^ _779300) ^ [_864396, _864398, _864400, _864402, _864404, _864406] : [-(c_COMBC(_864406, _864402, _864398) = c_COMBC(_864404, _864400, _864396)), _864406 = _864404, _864402 = _864400, _864398 = _864396], (5582 ^ _779300) ^ [_864617, _864619, _864621, _864623, _864625, _864627] : [-(c_COMBS(_864627, _864623, _864619) = c_COMBS(_864625, _864621, _864617)), _864627 = _864625, _864623 = _864621, _864619 = _864617], (5596 ^ _779300) ^ [_864838, _864840] : [_864840 = _864838, -(c_Finite__Set_Ofinite(_864840) = c_Finite__Set_Ofinite(_864838))], (5602 ^ _779300) ^ [_864923, _864925] : [_864925 = _864923, -(c_Orderings_Oord__class_Oless__eq(_864925) = c_Orderings_Oord__class_Oless__eq(_864923))], (5608 ^ _779300) ^ [_865008, _865010, _865012, _865014] : [-(tc_fun(_865014, _865010) = tc_fun(_865012, _865008)), _865014 = _865012, _865010 = _865008], (5618 ^ _779300) ^ [_865157, _865159] : [_865159 = _865157, -(c_Finite__Set_Ocard(_865159) = c_Finite__Set_Ocard(_865157))], (5624 ^ _779300) ^ [_865242, _865244, _865246, _865248] : [-(hAPP(_865248, _865244) = hAPP(_865246, _865242)), _865248 = _865246, _865244 = _865242], (5634 ^ _779300) ^ [_865387, _865389, _865391, _865393, _865395, _865397] : [-(c_Set_Oimage(_865397, _865393, _865389) = c_Set_Oimage(_865395, _865391, _865387)), _865397 = _865395, _865393 = _865391, _865389 = _865387], (5648 ^ _779300) ^ [_868377, _868379] : [hAPP(_868377, 5649 ^ [_868377, _868379]) = hAPP(_868379, 5649 ^ [_868377, _868379]), -(_868377 = _868379)], (5655 ^ _779300) ^ [_868503, _868505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), _868503), _868505)), -(v_P(_868505, _868503))], (5661 ^ _779300) ^ [_868590, _868592, _868594, _868596] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_868590), _868592)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_868594), hAPP(c_Set_Oimage(_868590, _868594, _868596), _868592))))], (5667 ^ _779300) ^ [_868701, _868703, _868705, _868707, _868709] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_868701), _868703)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_868705, tc_HOL_Obool)), _868707), hAPP(c_Set_Oimage(_868701, _868705, _868709), _868703))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_868705), _868707)))], (5677 ^ _779300) ^ [_868892, _868894, _868896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_868892, tc_HOL_Obool)), _868894), _868896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_868892, tc_HOL_Obool)), _868896), _868894)), -(_868894 = _868896)], (5687 ^ _779300) ^ [_869065, _869067] : [class_Orderings_Opreorder(_869065), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_869065), _869067), _869067)))], (5693 ^ _779300) ^ [_869178, _869180, _869182, _869184, _869186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869178, tc_HOL_Obool)), _869180), hAPP(c_Set_Oimage(_869182, _869178, _869184), _869186))), 5697 ^ _779300 : [(5698 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869182, tc_HOL_Obool)), 5696 ^ [_869178, _869180, _869182, _869184, _869186]), _869186)))], (5700 ^ _779300) ^ [] : [-(_869180 = hAPP(c_Set_Oimage(_869182, _869178, _869184), 5696 ^ [_869178, _869180, _869182, _869184, _869186]))]]], (5702 ^ _779300) ^ [_869382, _869384, _869386, _869388, _869390] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869382, tc_HOL_Obool)), _869384), hAPP(c_Set_Oimage(_869386, _869382, _869388), _869390)))), 5703 ^ _779300 : [(5704 ^ _779300) ^ [_869462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869386, tc_HOL_Obool)), _869462), _869390)), _869384 = hAPP(c_Set_Oimage(_869386, _869382, _869388), _869462)]]], (5712 ^ _779300) ^ [_869627, _869629, _869631, _869633, _869635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869627, tc_HOL_Obool)), _869629), _869631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869633, tc_HOL_Obool)), hAPP(c_Set_Oimage(_869627, _869633, _869635), _869629)), hAPP(c_Set_Oimage(_869627, _869633, _869635), _869631))))], (5718 ^ _779300) ^ [_869778, _869780, _869782] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_869778), _869780)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869778, tc_HOL_Obool)), _869782), _869780)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_869778), _869782)))], (5728 ^ _779300) ^ [_869947, _869949, _869951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869947, tc_HOL_Obool)), _869949), _869951)), hBOOL(hAPP(c_Finite__Set_Ofinite(_869947), _869951)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_869947), _869949)))], (5738 ^ _779300) ^ [_870116, _870118, _870120, _870122] : [class_Orderings_Oord(_870116), 5741 ^ _779300 : [(5742 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870118, _870116)), _870120), _870122)), 5745 ^ _779300 : [(5746 ^ _779300) ^ [_870273] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870116), hAPP(_870120, _870273)), hAPP(_870122, _870273))))]]], (5748 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870116), hAPP(_870120, 5749 ^ [_870116, _870118, _870120, _870122])), hAPP(_870122, 5749 ^ [_870116, _870118, _870120, _870122]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870118, _870116)), _870120), _870122)))]]], (5755 ^ _779300) ^ [_870462, _870464, _870466, _870468, _870470] : [class_Orderings_Oord(_870462), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870464, _870462)), _870466), _870468)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870462), hAPP(_870466, _870470)), hAPP(_870468, _870470))))], (5765 ^ _779300) ^ [_870647, _870649, _870651, _870653, _870655] : [class_Orderings_Oord(_870647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870649, _870647)), _870651), _870653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870647), hAPP(_870651, _870655)), hAPP(_870653, _870655))))], (5775 ^ _779300) ^ [_870832, _870834, _870836] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_870832), _870834)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870832, tc_HOL_Obool)), _870836), _870834)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_870832), _870834)), hAPP(c_Finite__Set_Ocard(_870832), _870836))), -(_870836 = _870834)], (5789 ^ _779300) ^ [_871077, _871079, _871081] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_871077), _871079)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871077, tc_HOL_Obool)), _871081), _871079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_871077), _871081)), hAPP(c_Finite__Set_Ocard(_871077), _871079))))], (5799 ^ _779300) ^ [_871268, _871270, _871272, _871274] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_871268), _871270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_871272), hAPP(c_Set_Oimage(_871268, _871272, _871274), _871270))), hAPP(c_Finite__Set_Ocard(_871268), _871270))))], (5805 ^ _779300) ^ [_871401, _871403, _871405] : [class_Orderings_Olinorder(_871401), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871401), _871403), _871405))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871401), _871405), _871403)))], (5815 ^ _779300) ^ [_871521, _871523, _871525, _871527] : [class_Orderings_Oorder(_871521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871521), _871523), _871525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871521), _871527), _871523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871521), _871527), _871525)))], (5829 ^ _779300) ^ [_871754, _871756, _871758] : [class_Orderings_Oorder(_871754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871754), _871756), _871758)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871754), _871758), _871756)), -(_871758 = _871756)], (5843 ^ _779300) ^ [_871967, _871969, _871971, _871973] : [class_Orderings_Opreorder(_871967), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871967), _871969), _871971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871967), _871971), _871973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871967), _871969), _871973)))], (5857 ^ _779300) ^ [_872200, _872202, _872204] : [class_Orderings_Oorder(_872200), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872200), _872202), _872204)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872200), _872204), _872202)), -(_872202 = _872204)], (5871 ^ _779300) ^ [_872413, _872415, _872417, _872419] : [class_Orderings_Oorder(_872413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872413), _872415), _872417)), _872415 = _872419, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872413), _872419), _872417)))], (5885 ^ _779300) ^ [_872632, _872634, _872636, _872638] : [class_Orderings_Oord(_872632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872632), _872634), _872636)), _872636 = _872638, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872632), _872634), _872638)))], (5899 ^ _779300) ^ [_872851, _872853, _872855, _872857] : [class_Orderings_Oorder(_872851), _872853 = _872855, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872851), _872857), _872855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872851), _872857), _872853)))], (5913 ^ _779300) ^ [_873070, _873072, _873074, _873076] : [class_Orderings_Oord(_873070), _873072 = _873074, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873070), _873074), _873076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873070), _873072), _873076)))], (5927 ^ _779300) ^ [_873289, _873291, _873293] : [class_Orderings_Oorder(_873289), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873289), _873291), _873293)), 5934 ^ _779300 : [(5935 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873289), _873293), _873291)), -(_873293 = _873291)], (5941 ^ _779300) ^ [] : [_873293 = _873291, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873289), _873293), _873291)))]]], (5947 ^ _779300) ^ [_873589, _873591, _873593] : [class_Orderings_Opreorder(_873589), _873591 = _873593, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873589), _873591), _873593)))], (5957 ^ _779300) ^ [_873734, _873736, _873738] : [class_Orderings_Oorder(_873734), 5960 ^ _779300 : [(5961 ^ _779300) ^ [] : [_873736 = _873738, 5964 ^ _779300 : [(5965 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873734), _873736), _873738)))], (5967 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873734), _873738), _873736)))]]], (5969 ^ _779300) ^ [] : [-(_873736 = _873738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873734), _873736), _873738)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873734), _873738), _873736))]]], (5979 ^ _779300) ^ [_874061, _874063, _874065] : [class_Orderings_Olinorder(_874061), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874061), _874063), _874065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874061), _874065), _874063)))], (5989 ^ _779300) ^ [_874179, _874181] : [class_Finite__Set_Ofinite(_874179), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_874179), _874181)))], (5995 ^ _779300) ^ [_874262, _874264] : [class_Finite__Set_Ofinite(_874262), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_874262), _874264)))], (6001 ^ _779300) ^ [_874345, _874347, _874349] : [_874345 = _874347, 6004 ^ _779300 : [(6005 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874349, tc_HOL_Obool)), _874345), _874347)))], (6007 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874349, tc_HOL_Obool)), _874347), _874345)))]]], (6009 ^ _779300) ^ [_874494, _874496, _874498, _874500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874494, tc_HOL_Obool)), _874496), _874498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874494, tc_HOL_Obool)), _874498), _874500)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874494, tc_HOL_Obool)), _874496), _874500)))], (6019 ^ _779300) ^ [_874691, _874693, _874695] : [_874691 = _874693, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874695, tc_HOL_Obool)), _874693), _874691)))], (6025 ^ _779300) ^ [_874790, _874792, _874794] : [_874790 = _874792, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874794, tc_HOL_Obool)), _874790), _874792)))], (6031 ^ _779300) ^ [_874907, _874909, _874911] : [_874907 = _874909, 6034 ^ _779300 : [(6035 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874911, tc_HOL_Obool)), _874907), _874909)))], (6037 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874911, tc_HOL_Obool)), _874909), _874907)))]]], (6039 ^ _779300) ^ [_875048, _875050, _875052] : [-(_875048 = _875050), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875052, tc_HOL_Obool)), _875048), _875050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875052, tc_HOL_Obool)), _875050), _875048))], (6049 ^ _779300) ^ [_875223, _875225] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875223, tc_HOL_Obool)), _875225), _875225)))], (6051 ^ _779300) ^ [_875258, _875260, _875262, _875264, _875266, _875268] : [-(hAPP(c_Set_Oimage(_875258, _875260, _875262), hAPP(c_Set_Oimage(_875264, _875258, _875266), _875268)) = hAPP(c_Set_Oimage(_875264, _875260, hAPP(hAPP(c_COMBB(_875258, _875260, _875264), _875262), _875266)), _875268))], (6053 ^ _779300) ^ [_875322, _875324, _875326, _875328, _875330, _875332, _875334, _875336] : [c_Finite__Set_Ofolding__image__simple__idem(_875322, _875324, _875326, _875328, _875330, _875332), hBOOL(hAPP(c_Finite__Set_Ofinite(_875324), _875334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875324, tc_HOL_Obool)), _875336), _875334)), -(hAPP(hAPP(_875326, hAPP(_875332, _875336)), hAPP(_875332, _875334)) = hAPP(_875332, _875334))], (6067 ^ _779300) ^ [_875605, _875607] : [-(hAPP(c_Set_Oimage(_875605, _875605, c_COMBI(_875605)), _875607) = _875607)], (6069 ^ _779300) ^ [_875639, _875641] : [v_wt(_875639), 6075 ^ _779300 : [(6076 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), 6074 ^ [_875639, _875641]), v_U)))], (6078 ^ _779300) ^ [] : [v_P(_875641, hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, 6074 ^ [_875639, _875641])), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))))]], -(v_P(_875641, hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(_875639)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))], (6082 ^ _779300) ^ [_875882, _875884, _875886, _875888, _875890] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_875882), _875884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875882, tc_HOL_Obool)), _875884), hAPP(c_Set_Oimage(_875886, _875882, _875888), _875890))), 6090 ^ _779300 : [(6091 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875886, tc_HOL_Obool)), 6089 ^ [_875882, _875884, _875886, _875888, _875890]), _875890)))], (6093 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_875886), 6089 ^ [_875882, _875884, _875886, _875888, _875890])))], (6095 ^ _779300) ^ [] : [-(_875884 = hAPP(c_Set_Oimage(_875886, _875882, _875888), 6089 ^ [_875882, _875884, _875886, _875888, _875890]))]]], (6097 ^ _779300) ^ [_876201, _876203, _876205, _876207, _876209] : [c_Fun_Oinj__on(_876201, _876203, _876205, _876207), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876203, tc_HOL_Obool)), hAPP(c_Set_Oimage(_876201, _876203, _876205), _876207)), _876209)), hBOOL(hAPP(c_Finite__Set_Ofinite(_876203), _876209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_876201), _876207)), hAPP(c_Finite__Set_Ocard(_876203), _876209))))], (6111 ^ _779300) ^ [_876476, _876478, _876480, _876482, _876484, _876486] : [c_Fun_Oinj__on(_876476, _876478, _876480, _876482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876478, tc_HOL_Obool)), hAPP(c_Set_Oimage(_876476, _876478, _876480), _876482)), _876484)), c_Fun_Oinj__on(_876478, _876476, _876486, _876484), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876476, tc_HOL_Obool)), hAPP(c_Set_Oimage(_876478, _876476, _876486), _876484)), _876482)), hBOOL(hAPP(c_Finite__Set_Ofinite(_876476), _876482)), hBOOL(hAPP(c_Finite__Set_Ofinite(_876478), _876484)), -(hAPP(c_Finite__Set_Ocard(_876476), _876482) = hAPP(c_Finite__Set_Ocard(_876478), _876484))], (6137 ^ _779300) ^ [_876973, _876975, _876977, _876979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876973, tc_HOL_Obool)), _876975), _876977)), hBOOL(hAPP(_876975, _876979)), -(hBOOL(hAPP(_876977, _876979)))], (6147 ^ _779300) ^ [_877138, _877140, _877142, _877144] : [hBOOL(hAPP(_877138, _877140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877142, tc_HOL_Obool)), _877138), _877144)), -(hBOOL(hAPP(_877144, _877140)))], (6157 ^ _779300) ^ [_877303] : [hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _877303), v_U)), -(v_wt(c_Option_Othe(tc_Com_Ocom, c_Com_Obody(_877303))))], (6163 ^ _779300) ^ [_877396, _877398, _877400, _877402, _877404, _877406, _877408, _877410] : [c_Finite__Set_Ofolding__image(_877396, _877398, _877400, _877402, _877404), hBOOL(hAPP(c_Finite__Set_Ofinite(_877398), _877406)), -(hAPP(hAPP(_877404, hAPP(hAPP(c_COMBS(_877398, _877396, _877396), hAPP(hAPP(c_COMBB(_877396, tc_fun(_877396, _877396), _877398), _877400), _877408)), _877410)), _877406) = hAPP(hAPP(_877400, hAPP(hAPP(_877404, _877408), _877406)), hAPP(hAPP(_877404, _877410), _877406)))], (6173 ^ _779300) ^ [_877657, _877659, _877661, _877663] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_877657), _877659)), hAPP(c_Finite__Set_Ocard(_877661), hAPP(c_Set_Oimage(_877657, _877661, _877663), _877659)) = hAPP(c_Finite__Set_Ocard(_877657), _877659), -(c_Fun_Oinj__on(_877657, _877661, _877663, _877659))], (6183 ^ _779300) ^ [_877840, _877842, _877844, _877846] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_877840), _877842)), 6186 ^ _779300 : [(6187 ^ _779300) ^ [] : [c_Fun_Oinj__on(_877840, _877844, _877846, _877842), -(hAPP(c_Finite__Set_Ocard(_877844), hAPP(c_Set_Oimage(_877840, _877844, _877846), _877842)) = hAPP(c_Finite__Set_Ocard(_877840), _877842))], (6193 ^ _779300) ^ [] : [hAPP(c_Finite__Set_Ocard(_877844), hAPP(c_Set_Oimage(_877840, _877844, _877846), _877842)) = hAPP(c_Finite__Set_Ocard(_877840), _877842), -(c_Fun_Oinj__on(_877840, _877844, _877846, _877842))]]], (6199 ^ _779300) ^ [_878124, _878126, _878128, _878130] : [_878124 = _878126, 6204 ^ _779300 : [(6205 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_878128), _878130), _878124)))], (6207 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_878128), _878130), _878126)))]], 6208 ^ _779300 : [(6209 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_878128), _878130), _878124))], (6211 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_878128), _878130), _878126))]]], (6213 ^ _779300) ^ [_878399, _878401] : [hBOOL(hAPP(hAPP(c_member(_878399), _878401), c_Orderings_Obot__class_Obot(tc_fun(_878399, tc_HOL_Obool))))], (6215 ^ _779300) ^ [_878436, _878438, _878440, _878442] : [hBOOL(hAPP(hAPP(c_member(_878436), _878438), hAPP(hAPP(c_Set_Oinsert(_878436), _878440), _878442))), -(_878438 = _878440), -(hBOOL(hAPP(hAPP(c_member(_878436), _878438), _878442)))], (6225 ^ _779300) ^ [_878576, _878578, _878580, _878582] : [6226 ^ _779300 : [(6227 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_878576), _878578), _878580))], (6229 ^ _779300) ^ [] : [_878578 = _878582]], -(hBOOL(hAPP(hAPP(c_member(_878576), _878578), hAPP(hAPP(c_Set_Oinsert(_878576), _878582), _878580))))], (6233 ^ _779300) ^ [_878741, _878743, _878745, _878747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878741, tc_HOL_Obool)), _878743), _878745)), hBOOL(hAPP(hAPP(c_member(_878741), _878747), _878743)), -(hBOOL(hAPP(hAPP(c_member(_878741), _878747), _878745)))], (6243 ^ _779300) ^ [_878926, _878928, _878930, _878932, _878934, _878936] : [_878926 = hAPP(_878928, _878930), hBOOL(hAPP(hAPP(c_member(_878932), _878930), _878934)), -(hBOOL(hAPP(hAPP(c_member(_878936), _878926), hAPP(c_Set_Oimage(_878932, _878936, _878928), _878934))))], (6253 ^ _779300) ^ [_879119] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_879119), c_Orderings_Obot__class_Obot(tc_fun(_879119, tc_HOL_Obool)))))], (6255 ^ _779300) ^ [_879151, _879153, _879155] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_879151), _879153)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_879151), hAPP(hAPP(c_Set_Oinsert(_879151), _879155), _879153))))], (6261 ^ _779300) ^ [_879262, _879264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879262, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_879262, tc_HOL_Obool))), _879264)))], (6263 ^ _779300) ^ [_879302, _879304, _879306] : [-(c_Fun_Oinj__on(_879302, _879304, _879306, c_Orderings_Obot__class_Obot(tc_fun(_879302, tc_HOL_Obool))))], (6265 ^ _779300) ^ [_879336, _879338] : [v_P(hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, _879336)), _879338), hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(c_Option_Othe(tc_Com_Ocom, c_Com_Obody(_879336)))), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), -(v_P(_879338, hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, _879336)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))], (6271 ^ _779300) ^ [_879490, _879492, _879494] : [c_Orderings_Obot__class_Obot(tc_fun(_879490, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_879490), _879492), _879494)], (6273 ^ _779300) ^ [_879545, _879547, _879549] : [hAPP(hAPP(c_Set_Oinsert(_879545), _879547), _879549) = c_Orderings_Obot__class_Obot(tc_fun(_879545, tc_HOL_Obool))], (6275 ^ _779300) ^ [_879585, _879587, _879589] : [class_Orderings_Obot(_879585), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_879587, _879585)), _879589) = c_Orderings_Obot__class_Obot(_879585))], (6281 ^ _779300) ^ [_879682, _879684, _879686] : [-(hBOOL(hAPP(hAPP(c_member(_879682), _879684), hAPP(hAPP(c_Set_Oinsert(_879682), _879684), _879686))))], (6283 ^ _779300) ^ [_879724, _879726, _879728] : [class_Orderings_Obot(_879724), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_879726, _879724)), _879728) = c_Orderings_Obot__class_Obot(_879724))], (6289 ^ _779300) ^ [_879830, _879832] : [-(hBOOL(hAPP(hAPP(c_member(_879830), 6290 ^ [_879830, _879832]), _879832))), -(_879832 = c_Orderings_Obot__class_Obot(tc_fun(_879830, tc_HOL_Obool)))], (6296 ^ _779300) ^ [_879881, _879883] : [_879883 = c_Orderings_Obot__class_Obot(tc_fun(_879881, tc_HOL_Obool)), 6299 ^ _779300 : [(6300 ^ _779300) ^ [_879961] : [hBOOL(hAPP(hAPP(c_member(_879881), _879961), _879883))]]], (6302 ^ _779300) ^ [_880012, _880014] : [6303 ^ _779300 : [(6304 ^ _779300) ^ [_880065] : [hBOOL(hAPP(hAPP(c_member(_880012), _880065), _880014))]], _880014 = c_Orderings_Obot__class_Obot(tc_fun(_880012, tc_HOL_Obool))], (6308 ^ _779300) ^ [_880121, _880123] : [-(_880123 = c_Orderings_Obot__class_Obot(tc_fun(_880121, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_880121), 6311 ^ [_880121, _880123]), _880123)))], (6315 ^ _779300) ^ [_880190, _880192] : [hBOOL(hAPP(hAPP(c_member(_880190), _880192), c_Orderings_Obot__class_Obot(tc_fun(_880190, tc_HOL_Obool))))], (6317 ^ _779300) ^ [_880245, _880247, _880249] : [hBOOL(hAPP(hAPP(c_member(_880245), _880247), _880249)), -(hBOOL(hAPP(_880249, _880247)))], (6323 ^ _779300) ^ [_880338, _880340, _880342] : [hBOOL(hAPP(_880342, _880340)), -(hBOOL(hAPP(hAPP(c_member(_880338), _880340), _880342)))], (6329 ^ _779300) ^ [_880455, _880457, _880459] : [hBOOL(hAPP(hAPP(c_member(_880455), _880457), hAPP(hAPP(c_Set_Oinsert(_880455), _880459), c_Orderings_Obot__class_Obot(tc_fun(_880455, tc_HOL_Obool))))), -(_880457 = _880459)], (6335 ^ _779300) ^ [_880570, _880572, _880574] : [_880572 = _880574, -(hBOOL(hAPP(hAPP(c_member(_880570), _880572), hAPP(hAPP(c_Set_Oinsert(_880570), _880574), c_Orderings_Obot__class_Obot(tc_fun(_880570, tc_HOL_Obool))))))], (6341 ^ _779300) ^ [_880691, _880693, _880695] : [-(hAPP(hAPP(c_Set_Oinsert(_880691), _880693), hAPP(hAPP(c_Set_Oinsert(_880691), _880693), _880695)) = hAPP(hAPP(c_Set_Oinsert(_880691), _880693), _880695))], (6343 ^ _779300) ^ [_880742, _880744, _880746, _880748] : [-(hAPP(hAPP(c_Set_Oinsert(_880742), _880744), hAPP(hAPP(c_Set_Oinsert(_880742), _880746), _880748)) = hAPP(hAPP(c_Set_Oinsert(_880742), _880746), hAPP(hAPP(c_Set_Oinsert(_880742), _880744), _880748)))], (6355 ^ _779300) ^ [_880958, _880960, _880962, _880964] : [6356 ^ _779300 : [(6357 ^ _779300) ^ [] : [_880960 = _880962], (6359 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_880958), _880960), _880964))]], -(hBOOL(hAPP(hAPP(c_member(_880958), _880960), hAPP(hAPP(c_Set_Oinsert(_880958), _880962), _880964))))], (6345 ^ _779300) ^ [_880824, _880826, _880828, _880830] : [hBOOL(hAPP(hAPP(c_member(_880824), _880826), hAPP(hAPP(c_Set_Oinsert(_880824), _880828), _880830))), -(_880826 = _880828), -(hBOOL(hAPP(hAPP(c_member(_880824), _880826), _880830)))], (6363 ^ _779300) ^ [_881147, _881149, _881151, _881153, _881155] : [hAPP(hAPP(c_Set_Oinsert(_881147), _881149), hAPP(hAPP(c_Set_Oinsert(_881147), _881151), c_Orderings_Obot__class_Obot(tc_fun(_881147, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_881147), _881153), hAPP(hAPP(c_Set_Oinsert(_881147), _881155), c_Orderings_Obot__class_Obot(tc_fun(_881147, tc_HOL_Obool)))), 6368 ^ _779300 : [(6369 ^ _779300) ^ [] : [-(_881149 = _881153)], (6371 ^ _779300) ^ [] : [-(_881151 = _881155)]], 6372 ^ _779300 : [(6373 ^ _779300) ^ [] : [-(_881149 = _881155)], (6375 ^ _779300) ^ [] : [-(_881151 = _881153)]]], (6377 ^ _779300) ^ [_881409, _881411, _881413, _881415, _881417] : [-(hAPP(hAPP(c_Set_Oinsert(_881409), _881411), hAPP(hAPP(c_Set_Oinsert(_881409), _881413), c_Orderings_Obot__class_Obot(tc_fun(_881409, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_881409), _881415), hAPP(hAPP(c_Set_Oinsert(_881409), _881417), c_Orderings_Obot__class_Obot(tc_fun(_881409, tc_HOL_Obool))))), 6378 ^ _779300 : [(6379 ^ _779300) ^ [] : [_881411 = _881415, _881413 = _881417], (6385 ^ _779300) ^ [] : [_881411 = _881417, _881413 = _881415]]], (6403 ^ _779300) ^ [_881860, _881862, _881864, _881866] : [6404 ^ _779300 : [(6405 ^ _779300) ^ [] : [_881862 = _881866], (6407 ^ _779300) ^ [] : [hBOOL(hAPP(_881864, _881866))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_881860), _881862), _881864), _881866)))], (6393 ^ _779300) ^ [_881746, _881748, _881750, _881752] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_881746), _881748), _881750), _881752)), -(_881748 = _881752), -(hBOOL(hAPP(_881750, _881752)))], (6411 ^ _779300) ^ [_882004, _882006, _882008, _882010] : [-(hBOOL(hAPP(hAPP(c_member(_882004), _882006), _882008))), -(hBOOL(hAPP(hAPP(c_member(_882004), _882006), _882010))), 6418 ^ _779300 : [(6419 ^ _779300) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_882004), _882006), _882008) = hAPP(hAPP(c_Set_Oinsert(_882004), _882006), _882010), -(_882008 = _882010)], (6425 ^ _779300) ^ [] : [_882008 = _882010, -(hAPP(hAPP(c_Set_Oinsert(_882004), _882006), _882008) = hAPP(hAPP(c_Set_Oinsert(_882004), _882006), _882010))]]], (6431 ^ _779300) ^ [_882349, _882351, _882353] : [_882349 = c_Orderings_Obot__class_Obot(tc_fun(_882351, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_882351), _882353), _882349))], (6437 ^ _779300) ^ [_882453, _882455, _882457, _882459] : [hBOOL(hAPP(hAPP(c_member(_882453), _882455), _882457)), -(hBOOL(hAPP(hAPP(c_member(_882453), _882455), hAPP(hAPP(c_Set_Oinsert(_882453), _882459), _882457))))], (6443 ^ _779300) ^ [_882578, _882580, _882582] : [hBOOL(hAPP(hAPP(c_member(_882578), _882580), _882582)), -(hAPP(hAPP(c_Set_Oinsert(_882578), _882580), _882582) = _882582)], (6449 ^ _779300) ^ [_882687, _882689, _882691, _882693] : [_882687 = _882689, 6452 ^ _779300 : [(6453 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_882691), _882693), _882687)), -(hBOOL(hAPP(hAPP(c_member(_882691), _882693), _882689)))], (6459 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_882691), _882693), _882689)), -(hBOOL(hAPP(hAPP(c_member(_882691), _882693), _882687)))]]], (6465 ^ _779300) ^ [_882948, _882950, _882952, _882954] : [_882948 = _882950, 6468 ^ _779300 : [(6469 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_882952), _882948), _882954)), -(hBOOL(hAPP(hAPP(c_member(_882952), _882950), _882954)))], (6475 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_882952), _882950), _882954)), -(hBOOL(hAPP(hAPP(c_member(_882952), _882948), _882954)))]]], (6481 ^ _779300) ^ [_883209, _883211, _883213, _883215] : [_883209 = _883211, hBOOL(hAPP(hAPP(c_member(_883213), _883211), _883215)), -(hBOOL(hAPP(hAPP(c_member(_883213), _883209), _883215)))], (6491 ^ _779300) ^ [_883374, _883376, _883378] : [hBOOL(hAPP(hAPP(c_member(_883374), _883376), hAPP(hAPP(c_Set_Oinsert(_883374), _883378), c_Orderings_Obot__class_Obot(tc_fun(_883374, tc_HOL_Obool))))), -(_883376 = _883378)], (6497 ^ _779300) ^ [_883493, _883495, _883497] : [hAPP(hAPP(c_Set_Oinsert(_883493), _883495), c_Orderings_Obot__class_Obot(tc_fun(_883493, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_883493), _883497), c_Orderings_Obot__class_Obot(tc_fun(_883493, tc_HOL_Obool))), -(_883495 = _883497)], (6503 ^ _779300) ^ [_883624, _883626, _883628, _883630, _883632, _883634] : [c_Fun_Oinj__on(_883624, _883626, _883628, _883630), hAPP(_883628, _883632) = hAPP(_883628, _883634), hBOOL(hAPP(hAPP(c_member(_883624), _883632), _883630)), hBOOL(hAPP(hAPP(c_member(_883624), _883634), _883630)), -(_883632 = _883634)], (6521 ^ _779300) ^ [_883933, _883935, _883937, _883939, _883941, _883943] : [c_Fun_Oinj__on(_883933, _883935, _883937, _883939), hBOOL(hAPP(hAPP(c_member(_883933), _883941), _883939)), hBOOL(hAPP(hAPP(c_member(_883933), _883943), _883939)), 6532 ^ _779300 : [(6533 ^ _779300) ^ [] : [hAPP(_883937, _883941) = hAPP(_883937, _883943), -(_883941 = _883943)], (6539 ^ _779300) ^ [] : [_883941 = _883943, -(hAPP(_883937, _883941) = hAPP(_883937, _883943))]]], (6545 ^ _779300) ^ [_884334, _884336, _884338, _884340, _884342, _884344] : [c_Fun_Oinj__on(_884334, _884336, _884338, _884340), -(_884342 = _884344), hBOOL(hAPP(hAPP(c_member(_884334), _884342), _884340)), hBOOL(hAPP(hAPP(c_member(_884334), _884344), _884340)), hAPP(_884338, _884342) = hAPP(_884338, _884344)], (6563 ^ _779300) ^ [_884665, _884667, _884669] : [hAPP(hAPP(c_COMBC(_884665, tc_fun(_884665, tc_HOL_Obool), tc_HOL_Obool), c_member(_884665)), _884667) = hAPP(hAPP(c_COMBC(_884665, tc_fun(_884665, tc_HOL_Obool), tc_HOL_Obool), c_member(_884665)), _884669), -(_884667 = _884669)], (6569 ^ _779300) ^ [_884800, _884802, _884804] : [_884802 = _884804, -(hAPP(hAPP(c_COMBC(_884800, tc_fun(_884800, tc_HOL_Obool), tc_HOL_Obool), c_member(_884800)), _884802) = hAPP(hAPP(c_COMBC(_884800, tc_fun(_884800, tc_HOL_Obool), tc_HOL_Obool), c_member(_884800)), _884804))], (6575 ^ _779300) ^ [_884959, _884961, _884963] : [hBOOL(hAPP(hAPP(c_member(_884959), _884961), hAPP(c_fequal, _884963))), -(_884961 = _884963)], (6581 ^ _779300) ^ [_885054, _885056, _885058] : [_885056 = _885058, -(hBOOL(hAPP(hAPP(c_member(_885054), _885056), hAPP(c_fequal, _885058))))], (6605 ^ _779300) ^ [_885561, _885563, _885565, _885567] : [6607 ^ _779300 : [(6608 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885561), 6606 ^ [_885561, _885563, _885565, _885567]), _885567)))], (6611 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885561), 6609 ^ [_885561, _885563, _885565, _885567]), _885567)))], (6613 ^ _779300) ^ [] : [-(hAPP(_885565, 6606 ^ [_885561, _885563, _885565, _885567]) = hAPP(_885565, 6609 ^ [_885561, _885563, _885565, _885567]))], (6615 ^ _779300) ^ [] : [6606 ^ [_885561, _885563, _885565, _885567] = 6609 ^ [_885561, _885563, _885565, _885567]]], -(c_Fun_Oinj__on(_885561, _885563, _885565, _885567))], (6587 ^ _779300) ^ [_885176, _885178, _885180, _885182] : [c_Fun_Oinj__on(_885176, _885178, _885180, _885182), 6590 ^ _779300 : [(6591 ^ _779300) ^ [_885284] : [hBOOL(hAPP(hAPP(c_member(_885176), _885284), _885182)), 6594 ^ _779300 : [(6595 ^ _779300) ^ [_885386] : [hBOOL(hAPP(hAPP(c_member(_885176), _885386), _885182)), hAPP(_885180, _885284) = hAPP(_885180, _885386), -(_885284 = _885386)]]]]], (6619 ^ _779300) ^ [_885953, _885955] : [-(c_Fun_Oinj__on(_885953, _885953, c_COMBI(_885953), _885955))], (6621 ^ _779300) ^ [_885997, _885999] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_885997, tc_HOL_Obool)), _885999)), -(hBOOL(hAPP(hAPP(c_member(_885997), _885999), c_Orderings_Obot__class_Obot(tc_fun(_885997, tc_HOL_Obool)))))], (6627 ^ _779300) ^ [_886108, _886110] : [hBOOL(hAPP(hAPP(c_member(_886108), _886110), c_Orderings_Obot__class_Obot(tc_fun(_886108, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_886108, tc_HOL_Obool)), _886110)))], (6633 ^ _779300) ^ [_886225, _886227, _886229, _886231, _886233] : [hBOOL(hAPP(hAPP(c_member(_886225), _886227), _886229)), -(hAPP(c_Set_Oimage(_886225, _886231, hAPP(c_COMBK(_886231, _886225), _886233)), _886229) = hAPP(hAPP(c_Set_Oinsert(_886231), _886233), c_Orderings_Obot__class_Obot(tc_fun(_886231, tc_HOL_Obool))))], (6639 ^ _779300) ^ [_886373, _886375, _886377, _886379] : [-(hBOOL(hAPP(hAPP(c_member(_886373), _886375), _886377))), 6642 ^ _779300 : [(6643 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886373, tc_HOL_Obool)), _886377), hAPP(hAPP(c_Set_Oinsert(_886373), _886375), _886379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886373, tc_HOL_Obool)), _886377), _886379)))], (6649 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886373, tc_HOL_Obool)), _886377), _886379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886373, tc_HOL_Obool)), _886377), hAPP(hAPP(c_Set_Oinsert(_886373), _886375), _886379))))]]], (6655 ^ _779300) ^ [_886702, _886704, _886706, _886708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886702, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_886702), _886704), _886706)), _886708)), 6658 ^ _779300 : [(6659 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886702), _886704), _886708)))], (6661 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886702, tc_HOL_Obool)), _886706), _886708)))]]], (6663 ^ _779300) ^ [_886875, _886877, _886879, _886881] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886875, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_886875), _886877), _886879)), _886881))), hBOOL(hAPP(hAPP(c_member(_886875), _886877), _886881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886875, tc_HOL_Obool)), _886879), _886881))], (6673 ^ _779300) ^ [_887084, _887086, _887088, _887090, _887092] : [hBOOL(hAPP(hAPP(c_member(_887084), _887086), _887088)), -(hAPP(hAPP(c_Set_Oinsert(_887090), hAPP(_887092, _887086)), hAPP(c_Set_Oimage(_887084, _887090, _887092), _887088)) = hAPP(c_Set_Oimage(_887084, _887090, _887092), _887088))], (6679 ^ _779300) ^ [_887231, _887233, _887235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887231, tc_HOL_Obool)), _887233), hAPP(hAPP(c_Set_Oinsert(_887231), _887235), c_Orderings_Obot__class_Obot(tc_fun(_887231, tc_HOL_Obool))))), -(_887233 = c_Orderings_Obot__class_Obot(tc_fun(_887231, tc_HOL_Obool))), -(_887233 = hAPP(hAPP(c_Set_Oinsert(_887231), _887235), c_Orderings_Obot__class_Obot(tc_fun(_887231, tc_HOL_Obool))))], (6689 ^ _779300) ^ [_887405, _887407, _887409, _887411, _887413] : [c_Fun_Oinj__on(_887405, _887407, _887409, _887411), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887405, tc_HOL_Obool)), _887413), _887411)), -(c_Fun_Oinj__on(_887405, _887407, _887409, _887413))], (6699 ^ _779300) ^ [_887574, _887576, _887578, _887580, _887582, _887584, _887586] : [c_Finite__Set_Ofolding__image__simple__idem(_887574, _887576, _887578, _887580, _887582, _887584), -(hAPP(hAPP(_887578, _887586), _887586) = _887586)], (6705 ^ _779300) ^ [_887696, _887698, _887700, _887702] : [_887696 = c_Orderings_Obot__class_Obot(tc_fun(_887698, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_887698, _887700, hAPP(c_COMBK(_887700, _887698), _887702)), _887696) = c_Orderings_Obot__class_Obot(tc_fun(_887700, tc_HOL_Obool)))], (6711 ^ _779300) ^ [_887817, _887819, _887821, _887823] : [-(_887817 = c_Orderings_Obot__class_Obot(tc_fun(_887819, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_887819, _887821, hAPP(c_COMBK(_887821, _887819), _887823)), _887817) = hAPP(hAPP(c_Set_Oinsert(_887821), _887823), c_Orderings_Obot__class_Obot(tc_fun(_887821, tc_HOL_Obool))))], (6717 ^ _779300) ^ [_887890, _887892, _887894, _887896, _887898, _887900, _887902, _887904] : [c_Finite__Set_Ofolding__image__simple__idem(_887890, _887892, _887894, _887896, _887898, _887900), hBOOL(hAPP(c_Finite__Set_Ofinite(_887892), _887902)), -(hAPP(_887900, hAPP(hAPP(c_Set_Oinsert(_887892), _887904), _887902)) = hAPP(hAPP(_887894, hAPP(_887898, _887904)), hAPP(_887900, _887902)))], (6727 ^ _779300) ^ [_888105, _888107, _888109, _888111, _888113, _888115, _888117, _888119] : [c_Finite__Set_Ofolding__image__simple__idem(_888105, _888107, _888109, _888111, _888113, _888115), hBOOL(hAPP(c_Finite__Set_Ofinite(_888107), _888117)), hBOOL(hAPP(hAPP(c_member(_888107), _888119), _888117)), -(hAPP(hAPP(_888109, hAPP(_888113, _888119)), hAPP(_888115, _888117)) = hAPP(_888115, _888117))], (6741 ^ _779300) ^ [_888400, _888402, _888404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888400, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_888400, tc_fun(_888400, tc_HOL_Obool), tc_HOL_Obool), c_member(_888400)), _888402)), hAPP(hAPP(c_COMBC(_888400, tc_fun(_888400, tc_HOL_Obool), tc_HOL_Obool), c_member(_888400)), _888404))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888400, tc_HOL_Obool)), _888402), _888404)))], (6747 ^ _779300) ^ [_888575, _888577, _888579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888575, tc_HOL_Obool)), _888577), _888579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888575, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_888575, tc_fun(_888575, tc_HOL_Obool), tc_HOL_Obool), c_member(_888575)), _888577)), hAPP(hAPP(c_COMBC(_888575, tc_fun(_888575, tc_HOL_Obool), tc_HOL_Obool), c_member(_888575)), _888579))))], (6753 ^ _779300) ^ [_888774, _888776, _888778] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_888774), hAPP(hAPP(c_Set_Oinsert(_888774), _888776), _888778))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_888774), _888778)))], (6759 ^ _779300) ^ [_888881, _888883, _888885] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_888881), _888885)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_888881), hAPP(hAPP(c_Set_Oinsert(_888881), _888883), _888885))))], (6765 ^ _779300) ^ [_888994, _888996, _888998] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888994, tc_HOL_Obool)), _888996), hAPP(hAPP(c_Set_Oinsert(_888994), _888998), _888996))))], (6767 ^ _779300) ^ [_889039, _889041, _889043, _889045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889039, tc_HOL_Obool)), _889041), _889043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889039, tc_HOL_Obool)), _889041), hAPP(hAPP(c_Set_Oinsert(_889039), _889045), _889043))))], (6773 ^ _779300) ^ [_889176, _889178, _889180, _889182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889176, tc_HOL_Obool)), _889178), _889180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889176, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_889176), _889182), _889178)), hAPP(hAPP(c_Set_Oinsert(_889176), _889182), _889180))))], (6779 ^ _779300) ^ [_889329, _889331, _889333, _889335, _889337] : [-(hAPP(c_Set_Oimage(_889329, _889331, _889333), hAPP(hAPP(c_Set_Oinsert(_889329), _889335), _889337)) = hAPP(hAPP(c_Set_Oinsert(_889331), hAPP(_889333, _889335)), hAPP(c_Set_Oimage(_889329, _889331, _889333), _889337)))], (6781 ^ _779300) ^ [_889393, _889395, _889397, _889399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889393, tc_HOL_Obool)), _889395), _889397)), hBOOL(hAPP(hAPP(c_member(_889393), _889399), _889395)), -(hBOOL(hAPP(hAPP(c_member(_889393), _889399), _889397)))], (6791 ^ _779300) ^ [_889578, _889580, _889582, _889584] : [hBOOL(hAPP(hAPP(c_member(_889578), _889580), _889582)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889578, tc_HOL_Obool)), _889582), _889584)), -(hBOOL(hAPP(hAPP(c_member(_889578), _889580), _889584)))], (6801 ^ _779300) ^ [_889763, _889765, _889767, _889769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889763, tc_HOL_Obool)), _889765), _889767)), hBOOL(hAPP(hAPP(c_member(_889763), _889769), _889765)), -(hBOOL(hAPP(hAPP(c_member(_889763), _889769), _889767)))], (6811 ^ _779300) ^ [_889972, _889974, _889976, _889978, _889980] : [hBOOL(hAPP(hAPP(c_member(_889972), _889974), hAPP(c_Set_Oimage(_889976, _889972, _889978), _889980))), 6815 ^ _779300 : [(6816 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889976), 6814 ^ [_889972, _889974, _889976, _889978, _889980]), _889980)))], (6818 ^ _779300) ^ [] : [-(_889974 = hAPP(_889978, 6814 ^ [_889972, _889974, _889976, _889978, _889980]))]]], (6820 ^ _779300) ^ [_890156, _890158, _890160, _890162, _890164] : [-(hBOOL(hAPP(hAPP(c_member(_890156), _890158), hAPP(c_Set_Oimage(_890160, _890156, _890162), _890164)))), 6821 ^ _779300 : [(6822 ^ _779300) ^ [_890226] : [hBOOL(hAPP(hAPP(c_member(_890160), _890226), _890164)), _890158 = hAPP(_890162, _890226)]]], (6830 ^ _779300) ^ [_890374, _890376, _890378, _890380, _890382] : [hBOOL(hAPP(hAPP(c_member(_890374), _890376), _890378)), -(hBOOL(hAPP(hAPP(c_member(_890380), hAPP(_890382, _890376)), hAPP(c_Set_Oimage(_890374, _890380, _890382), _890378))))], (6836 ^ _779300) ^ [_890505, _890507, _890509, _890511, _890513, _890515] : [hBOOL(hAPP(hAPP(c_member(_890505), _890507), _890509)), _890511 = hAPP(_890513, _890507), -(hBOOL(hAPP(hAPP(c_member(_890515), _890511), hAPP(c_Set_Oimage(_890505, _890515, _890513), _890509))))], (6846 ^ _779300) ^ [_890698] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_890698), c_Orderings_Obot__class_Obot(tc_fun(_890698, tc_HOL_Obool)))))], (6848 ^ _779300) ^ [_890745, _890747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890745, tc_HOL_Obool)), _890747), c_Orderings_Obot__class_Obot(tc_fun(_890745, tc_HOL_Obool)))), -(_890747 = c_Orderings_Obot__class_Obot(tc_fun(_890745, tc_HOL_Obool)))], (6854 ^ _779300) ^ [_890858, _890860] : [_890860 = c_Orderings_Obot__class_Obot(tc_fun(_890858, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890858, tc_HOL_Obool)), _890860), c_Orderings_Obot__class_Obot(tc_fun(_890858, tc_HOL_Obool)))))], (6860 ^ _779300) ^ [_890998, _891000, _891002, _891004] : [c_Orderings_Obot__class_Obot(tc_fun(_890998, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_891000, _890998, _891002), _891004), -(_891004 = c_Orderings_Obot__class_Obot(tc_fun(_891000, tc_HOL_Obool)))], (6866 ^ _779300) ^ [_891109, _891111, _891113, _891115] : [_891115 = c_Orderings_Obot__class_Obot(tc_fun(_891111, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_891109, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_891111, _891109, _891113), _891115))], (6872 ^ _779300) ^ [_891226, _891228, _891230] : [-(hAPP(c_Set_Oimage(_891226, _891228, _891230), c_Orderings_Obot__class_Obot(tc_fun(_891226, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_891228, tc_HOL_Obool)))], (6874 ^ _779300) ^ [_891291, _891293, _891295, _891297] : [hAPP(c_Set_Oimage(_891291, _891293, _891295), _891297) = c_Orderings_Obot__class_Obot(tc_fun(_891293, tc_HOL_Obool)), -(_891297 = c_Orderings_Obot__class_Obot(tc_fun(_891291, tc_HOL_Obool)))], (6880 ^ _779300) ^ [_891402, _891404, _891406, _891408] : [_891408 = c_Orderings_Obot__class_Obot(tc_fun(_891402, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_891402, _891404, _891406), _891408) = c_Orderings_Obot__class_Obot(tc_fun(_891404, tc_HOL_Obool)))], (6886 ^ _779300) ^ [_891519, _891521] : [class_Orderings_Obot(_891519), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891519), c_Orderings_Obot__class_Obot(_891519)), _891521)))], (6892 ^ _779300) ^ [_891612, _891614, _891616, _891618] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_891612), hAPP(c_Set_Oimage(_891614, _891612, _891616), _891618))), c_Fun_Oinj__on(_891614, _891612, _891616, _891618), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_891614), _891618)))], (6902 ^ _779300) ^ [_891783, _891785, _891787, _891789] : [c_Fun_Oinj__on(_891783, _891785, _891787, _891789), -(hAPP(c_Finite__Set_Ocard(_891785), hAPP(c_Set_Oimage(_891783, _891785, _891787), _891789)) = hAPP(c_Finite__Set_Ocard(_891783), _891789))], (6908 ^ _779300) ^ [_891902, _891904, _891906] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_891902), _891904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_891902), _891904)), hAPP(c_Finite__Set_Ocard(_891902), hAPP(hAPP(c_Set_Oinsert(_891902), _891906), _891904)))))], (6914 ^ _779300) ^ [_892035, _892037, _892039] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_892035), _892037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892035, tc_HOL_Obool)), _892037), hAPP(c_Set_Oimage(_892035, _892035, _892039), _892037))), -(c_Fun_Oinj__on(_892035, _892035, _892039, _892037))], (6924 ^ _779300) ^ [_892214, _892216, _892218] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_892214), _892216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892214, tc_HOL_Obool)), hAPP(c_Set_Oimage(_892214, _892214, _892218), _892216)), _892216)), c_Fun_Oinj__on(_892214, _892214, _892218, _892216), -(hAPP(c_Set_Oimage(_892214, _892214, _892218), _892216) = _892216)], (6938 ^ _779300) ^ [_892461, _892463, _892465, _892467] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_892461), _892463)), hBOOL(hAPP(c_Finite__Set_Ofinite(_892465), _892467)), 6945 ^ _779300 : [(6956 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_892461), _892463)), hAPP(c_Finite__Set_Ocard(_892465), _892467))), 6960 ^ _779300 : [(6961 ^ _779300) ^ [] : [-(c_Fun_Oinj__on(_892461, _892465, 6959 ^ [_892461, _892463, _892465, _892467], _892463))], (6963 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892465, tc_HOL_Obool)), hAPP(c_Set_Oimage(_892461, _892465, 6959 ^ [_892461, _892463, _892465, _892467]), _892463)), _892467)))]]], (6946 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_892461), _892463)), hAPP(c_Finite__Set_Ocard(_892465), _892467)))), 6947 ^ _779300 : [(6948 ^ _779300) ^ [_892672] : [c_Fun_Oinj__on(_892461, _892465, _892672, _892463), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892465, tc_HOL_Obool)), hAPP(c_Set_Oimage(_892461, _892465, _892672), _892463)), _892467))]]]]], (6965 ^ _779300) ^ [_892987, _892989, _892991, _892993] : [-(_892987 = c_Orderings_Obot__class_Obot(tc_fun(_892989, tc_HOL_Obool))), 6968 ^ _779300 : [(6980 ^ _779300) ^ [] : [6981 ^ _779300 : [(6982 ^ _779300) ^ [_893320] : [hAPP(c_Set_Oimage(_892991, _892989, _893320), _892993) = _892987]], 6984 ^ _779300 : [(6985 ^ _779300) ^ [] : [-(c_Fun_Oinj__on(_892989, _892991, 6983 ^ [_892987, _892989, _892991, _892993], _892987))], (6987 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892991, tc_HOL_Obool)), hAPP(c_Set_Oimage(_892989, _892991, 6983 ^ [_892987, _892989, _892991, _892993]), _892987)), _892993)))]]], (6969 ^ _779300) ^ [] : [-(hAPP(c_Set_Oimage(_892991, _892989, 6976 ^ [_892987, _892989, _892991, _892993]), _892993) = _892987), 6970 ^ _779300 : [(6971 ^ _779300) ^ [_893128] : [c_Fun_Oinj__on(_892989, _892991, _893128, _892987), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892991, tc_HOL_Obool)), hAPP(c_Set_Oimage(_892989, _892991, _893128), _892987)), _892993))]]]]], (6989 ^ _779300) ^ [_893445, _893447] : [-(c_Set_Othe__elem(_893445, hAPP(hAPP(c_Set_Oinsert(_893445), _893447), c_Orderings_Obot__class_Obot(tc_fun(_893445, tc_HOL_Obool)))) = _893447)], (6991 ^ _779300) ^ [_893486, _893488, _893490, _893492, _893494] : [c_Finite__Set_Ofolding__one(_893486, _893488, _893490), hBOOL(hAPP(c_Finite__Set_Ofinite(_893486), _893492)), -(hBOOL(hAPP(hAPP(c_member(_893486), _893494), _893492))), -(_893492 = c_Orderings_Obot__class_Obot(tc_fun(_893486, tc_HOL_Obool))), -(hAPP(_893490, hAPP(hAPP(c_Set_Oinsert(_893486), _893494), _893492)) = hAPP(hAPP(_893488, _893494), hAPP(_893490, _893492)))], (7009 ^ _779300) ^ [_893731, _893733, _893735, _893737, _893739, _893741] : [c_Fun_Oinj__on(_893731, _893733, _893735, _893737), hBOOL(hAPP(hAPP(c_member(_893733), _893739), hAPP(c_Set_Oimage(_893731, _893733, _893735), _893737))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893731, tc_HOL_Obool)), _893737), _893741)), -(hBOOL(hAPP(hAPP(c_member(_893731), hAPP(c_Fun_Othe__inv__into(_893731, _893733, _893737, _893735), _893739)), _893741)))], (7023 ^ _779300) ^ [_894018, _894020, _894022, _894024, _894026] : [c_Finite__Set_Ofolding__one__idem(_894018, _894020, _894022), hBOOL(hAPP(c_Finite__Set_Ofinite(_894018), _894024)), -(_894026 = c_Orderings_Obot__class_Obot(tc_fun(_894018, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894018, tc_HOL_Obool)), _894026), _894024)), -(hAPP(hAPP(_894020, hAPP(_894022, _894026)), hAPP(_894022, _894024)) = hAPP(_894022, _894024))], (7041 ^ _779300) ^ [_894348, _894350, _894352, _894354] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_894348), _894350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894348, tc_HOL_Obool)), _894350), _894352)), hBOOL(hAPP(_894354, c_Orderings_Obot__class_Obot(tc_fun(_894348, tc_HOL_Obool)))), 7056 ^ _779300 : [(7057 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_894348), 7055 ^ [_894348, _894350, _894352, _894354])))], (7059 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894348), 7054 ^ [_894348, _894350, _894352, _894354]), _894352)))], (7061 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894348), 7054 ^ [_894348, _894350, _894352, _894354]), 7055 ^ [_894348, _894350, _894352, _894354]))], (7063 ^ _779300) ^ [] : [-(hBOOL(hAPP(_894354, 7055 ^ [_894348, _894350, _894352, _894354])))], (7065 ^ _779300) ^ [] : [hBOOL(hAPP(_894354, hAPP(hAPP(c_Set_Oinsert(_894348), 7054 ^ [_894348, _894350, _894352, _894354]), 7055 ^ [_894348, _894350, _894352, _894354])))]], -(hBOOL(hAPP(_894354, _894350)))], (7069 ^ _779300) ^ [_895013, _895015, _895017, _895019, _895021] : [c_Finite__Set_Ofolding__one__idem(_895013, _895015, _895017), hBOOL(hAPP(c_Finite__Set_Ofinite(_895013), _895019)), -(_895019 = c_Orderings_Obot__class_Obot(tc_fun(_895013, tc_HOL_Obool))), -(hAPP(_895017, hAPP(hAPP(c_Set_Oinsert(_895013), _895021), _895019)) = hAPP(hAPP(_895015, _895021), hAPP(_895017, _895019)))], (7083 ^ _779300) ^ [_895229, _895231, _895233, _895235, _895237, _895239, _895241, _895243] : [c_Finite__Set_Ofolding__image__simple(_895229, _895231, _895233, _895235, _895237, _895239), hBOOL(hAPP(c_Finite__Set_Ofinite(_895231), _895241)), -(hBOOL(hAPP(hAPP(c_member(_895231), _895243), _895241))), -(hAPP(_895239, hAPP(hAPP(c_Set_Oinsert(_895231), _895243), _895241)) = hAPP(hAPP(_895233, hAPP(_895237, _895243)), hAPP(_895239, _895241)))], (7097 ^ _779300) ^ [_895473, _895475, _895477, _895479, _895481] : [c_Fun_Oinj__on(_895473, _895475, _895477, _895479), hBOOL(hAPP(hAPP(c_member(_895475), _895481), hAPP(c_Set_Oimage(_895473, _895475, _895477), _895479))), -(hAPP(_895477, hAPP(c_Fun_Othe__inv__into(_895473, _895475, _895479, _895477), _895481)) = _895481)], (7107 ^ _779300) ^ [_895668, _895670, _895672] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895668), _895670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_895668), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895668, tc_HOL_Obool)), _895670), hAPP(hAPP(c_Set_Oinsert(_895668), _895672), c_Orderings_Obot__class_Obot(tc_fun(_895668, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_895668), _895670))))], (7113 ^ _779300) ^ [_895833, _895835, _895837] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895833), _895835)), hBOOL(hAPP(_895837, c_Orderings_Obot__class_Obot(tc_fun(_895833, tc_HOL_Obool)))), 7124 ^ _779300 : [(7125 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_895833), 7123 ^ [_895833, _895835, _895837])))], (7127 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895833), 7122 ^ [_895833, _895835, _895837]), 7123 ^ [_895833, _895835, _895837]))], (7129 ^ _779300) ^ [] : [-(hBOOL(hAPP(_895837, 7123 ^ [_895833, _895835, _895837])))], (7131 ^ _779300) ^ [] : [hBOOL(hAPP(_895837, hAPP(hAPP(c_Set_Oinsert(_895833), 7122 ^ [_895833, _895835, _895837]), 7123 ^ [_895833, _895835, _895837])))]], -(hBOOL(hAPP(_895837, _895835)))], (7135 ^ _779300) ^ [_896320, _896322, _896324, _896326] : [hBOOL(hAPP(hAPP(c_member(_896320), _896322), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896320, tc_HOL_Obool)), _896324), _896326))), 7138 ^ _779300 : [(7139 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_896320), _896322), _896324)))], (7141 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_896320), _896322), _896326))]]], (7143 ^ _779300) ^ [_896499, _896501, _896503, _896505] : [hBOOL(hAPP(hAPP(c_member(_896499), _896501), _896503)), -(hBOOL(hAPP(hAPP(c_member(_896499), _896501), _896505))), -(hBOOL(hAPP(hAPP(c_member(_896499), _896501), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896499, tc_HOL_Obool)), _896503), _896505))))], (7153 ^ _779300) ^ [_896659, _896661, _896663] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_896659), _896661)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_896659), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896659, tc_HOL_Obool)), _896661), _896663))))], (7159 ^ _779300) ^ [_896776, _896778, _896780] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896776, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896776, tc_HOL_Obool)), _896778), _896780)), _896780) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896776, tc_HOL_Obool)), _896778), _896780))], (7161 ^ _779300) ^ [_896836, _896838, _896840, _896842] : [c_Finite__Set_Ofolding__one__idem(_896836, _896838, _896840), -(hAPP(hAPP(_896838, _896842), _896842) = _896842)], (7167 ^ _779300) ^ [_896931, _896933, _896935, _896937] : [hBOOL(hAPP(hAPP(c_member(_896931), _896933), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896931, tc_HOL_Obool)), _896935), _896937))), hBOOL(hAPP(hAPP(c_member(_896931), _896933), _896937))], (7173 ^ _779300) ^ [_897063, _897065, _897067, _897069] : [hBOOL(hAPP(hAPP(c_member(_897063), _897065), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897063, tc_HOL_Obool)), _897067), _897069))), -(hBOOL(hAPP(hAPP(c_member(_897063), _897065), _897067)))], (7179 ^ _779300) ^ [_897215, _897217, _897219, _897221] : [hBOOL(hAPP(hAPP(c_member(_897215), _897217), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897215, tc_HOL_Obool)), _897219), _897221))), 7182 ^ _779300 : [(7183 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_897215), _897217), _897219)))], (7185 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_897215), _897217), _897221))]]], (7187 ^ _779300) ^ [_897390, _897392, _897394, _897396] : [-(hBOOL(hAPP(hAPP(c_member(_897390), _897392), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897390, tc_HOL_Obool)), _897394), _897396)))), hBOOL(hAPP(hAPP(c_member(_897390), _897392), _897394)), -(hBOOL(hAPP(hAPP(c_member(_897390), _897392), _897396)))], (7197 ^ _779300) ^ [_897596, _897598] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897596, tc_HOL_Obool)), _897598), _897598) = c_Orderings_Obot__class_Obot(tc_fun(_897596, tc_HOL_Obool)))], (7199 ^ _779300) ^ [_897637, _897639] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897637, tc_HOL_Obool)), _897639), c_Orderings_Obot__class_Obot(tc_fun(_897637, tc_HOL_Obool))) = _897639)], (7201 ^ _779300) ^ [_897678, _897680] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897678, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_897678, tc_HOL_Obool))), _897680) = c_Orderings_Obot__class_Obot(tc_fun(_897678, tc_HOL_Obool)))], (7203 ^ _779300) ^ [_897724, _897726, _897728] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_897724), _897726)), 7206 ^ _779300 : [(7207 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_897724), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897724, tc_HOL_Obool)), _897728), _897726))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_897724), _897728)))], (7213 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_897724), _897728)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_897724), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897724, tc_HOL_Obool)), _897728), _897726))))]]], (7219 ^ _779300) ^ [_898002, _898004, _898006, _898008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898002, tc_HOL_Obool)), _898004), _898006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898002, tc_HOL_Obool)), _898006), _898008)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898002, tc_HOL_Obool)), _898006), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898002, tc_HOL_Obool)), _898008), _898004)) = _898004)], (7229 ^ _779300) ^ [_898223, _898225, _898227, _898229, _898231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898223, tc_HOL_Obool)), _898225), _898227)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898223, tc_HOL_Obool)), _898229), _898231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898223, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898223, tc_HOL_Obool)), _898225), _898231)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898223, tc_HOL_Obool)), _898227), _898229))))], (7239 ^ _779300) ^ [_898468, _898470, _898472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898468, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898468, tc_HOL_Obool)), _898470), _898472)), _898470)))], (7241 ^ _779300) ^ [_898516, _898518, _898520, _898522, _898524] : [c_Fun_Oinj__on(_898516, _898518, _898520, _898522), -(c_Fun_Oinj__on(_898516, _898518, _898520, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898516, tc_HOL_Obool)), _898522), _898524)))], (7247 ^ _779300) ^ [_898629, _898631, _898633, _898635, _898637, _898639, _898641, _898643] : [c_Finite__Set_Ofolding__image__simple(_898629, _898631, _898633, _898635, _898637, _898639), hBOOL(hAPP(c_Finite__Set_Ofinite(_898631), _898641)), -(hAPP(_898639, hAPP(hAPP(c_Set_Oinsert(_898631), _898643), _898641)) = hAPP(hAPP(_898633, hAPP(_898637, _898643)), hAPP(_898639, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898631, tc_HOL_Obool)), _898641), hAPP(hAPP(c_Set_Oinsert(_898631), _898643), c_Orderings_Obot__class_Obot(tc_fun(_898631, tc_HOL_Obool)))))))], (7257 ^ _779300) ^ [_898892, _898894, _898896, _898898, _898900] : [c_Finite__Set_Ofolding__one(_898892, _898894, _898896), hBOOL(hAPP(c_Finite__Set_Ofinite(_898892), _898898)), 7264 ^ _779300 : [(7265 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898892, tc_HOL_Obool)), _898898), hAPP(hAPP(c_Set_Oinsert(_898892), _898900), c_Orderings_Obot__class_Obot(tc_fun(_898892, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_898892, tc_HOL_Obool)), -(hAPP(_898896, hAPP(hAPP(c_Set_Oinsert(_898892), _898900), _898898)) = _898900)], (7271 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898892, tc_HOL_Obool)), _898898), hAPP(hAPP(c_Set_Oinsert(_898892), _898900), c_Orderings_Obot__class_Obot(tc_fun(_898892, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_898892, tc_HOL_Obool))), -(hAPP(_898896, hAPP(hAPP(c_Set_Oinsert(_898892), _898900), _898898)) = hAPP(hAPP(_898894, _898900), hAPP(_898896, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898892, tc_HOL_Obool)), _898898), hAPP(hAPP(c_Set_Oinsert(_898892), _898900), c_Orderings_Obot__class_Obot(tc_fun(_898892, tc_HOL_Obool)))))))]]], (7277 ^ _779300) ^ [_899374, _899376, _899378, _899380] : [hBOOL(hAPP(hAPP(c_member(_899374), _899376), _899378)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899374, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_899374), _899376), _899380)), _899378) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899374, tc_HOL_Obool)), _899380), _899378))], (7283 ^ _779300) ^ [_899544, _899546, _899548, _899550] : [hBOOL(hAPP(hAPP(c_member(_899544), _899546), _899548)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899544, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_899544), _899546), _899550)), _899548) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899544, tc_HOL_Obool)), _899550), _899548))], (7289 ^ _779300) ^ [_899693, _899695, _899697, _899699] : [-(hBOOL(hAPP(hAPP(c_member(_899693), _899695), _899697))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899693, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_899693), _899695), _899699)), _899697) = hAPP(hAPP(c_Set_Oinsert(_899693), _899695), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899693, tc_HOL_Obool)), _899699), _899697)))], (7295 ^ _779300) ^ [_899780, _899782, _899784] : [-(hAPP(hAPP(c_Set_Oinsert(_899780), _899782), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899780, tc_HOL_Obool)), _899784), hAPP(hAPP(c_Set_Oinsert(_899780), _899782), c_Orderings_Obot__class_Obot(tc_fun(_899780, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_899780), _899782), _899784))], (7297 ^ _779300) ^ [_899847, _899849, _899851, _899853] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899847, tc_HOL_Obool)), _899849), hAPP(hAPP(c_Set_Oinsert(_899847), _899851), _899853)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899847, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899847, tc_HOL_Obool)), _899849), hAPP(hAPP(c_Set_Oinsert(_899847), _899851), c_Orderings_Obot__class_Obot(tc_fun(_899847, tc_HOL_Obool))))), _899853))], (7299 ^ _779300) ^ [_899930, _899932, _899934, _899936] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899930, tc_HOL_Obool)), _899932), hAPP(hAPP(c_Set_Oinsert(_899930), _899934), _899936)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899930, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899930, tc_HOL_Obool)), _899932), _899936)), hAPP(hAPP(c_Set_Oinsert(_899930), _899934), c_Orderings_Obot__class_Obot(tc_fun(_899930, tc_HOL_Obool)))))], (7301 ^ _779300) ^ [_900034, _900036, _900038, _900040] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_900034), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900034, tc_HOL_Obool)), _900036), hAPP(hAPP(c_Set_Oinsert(_900034), _900038), _900040)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_900034), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900034, tc_HOL_Obool)), _900036), _900040))))], (7307 ^ _779300) ^ [_900187, _900189, _900191, _900193] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_900187), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900187, tc_HOL_Obool)), _900189), _900193))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_900187), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900187, tc_HOL_Obool)), _900189), hAPP(hAPP(c_Set_Oinsert(_900187), _900191), _900193)))))], (7313 ^ _779300) ^ [_900346, _900348, _900350, _900352, _900354] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900346, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900346, tc_HOL_Obool)), hAPP(c_Set_Oimage(_900348, _900346, _900350), _900352)), hAPP(c_Set_Oimage(_900348, _900346, _900350), _900354))), hAPP(c_Set_Oimage(_900348, _900346, _900350), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900348, tc_HOL_Obool)), _900352), _900354)))))], (7315 ^ _779300) ^ [_900430, _900432, _900434, _900436, _900438, _900440] : [c_Finite__Set_Ofolding__image__simple(_900430, _900432, _900434, _900436, _900438, _900440), -(hAPP(_900440, c_Orderings_Obot__class_Obot(tc_fun(_900432, tc_HOL_Obool))) = _900436)], (7321 ^ _779300) ^ [_900539, _900541, _900543, _900545, _900547, _900549, _900551, _900553] : [c_Finite__Set_Ofolding__image__simple(_900539, _900541, _900543, _900545, _900547, _900549), hBOOL(hAPP(c_Finite__Set_Ofinite(_900541), _900551)), hBOOL(hAPP(hAPP(c_member(_900541), _900553), _900551)), -(hAPP(_900549, _900551) = hAPP(hAPP(_900543, hAPP(_900547, _900553)), hAPP(_900549, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900541, tc_HOL_Obool)), _900551), hAPP(hAPP(c_Set_Oinsert(_900541), _900553), c_Orderings_Obot__class_Obot(tc_fun(_900541, tc_HOL_Obool)))))))], (7335 ^ _779300) ^ [_900864, _900866, _900868, _900870, _900872] : [c_Finite__Set_Ofolding__one(_900864, _900866, _900868), hBOOL(hAPP(c_Finite__Set_Ofinite(_900864), _900870)), hBOOL(hAPP(hAPP(c_member(_900864), _900872), _900870)), 7346 ^ _779300 : [(7347 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900864, tc_HOL_Obool)), _900870), hAPP(hAPP(c_Set_Oinsert(_900864), _900872), c_Orderings_Obot__class_Obot(tc_fun(_900864, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_900864, tc_HOL_Obool)), -(hAPP(_900868, _900870) = _900872)], (7353 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900864, tc_HOL_Obool)), _900870), hAPP(hAPP(c_Set_Oinsert(_900864), _900872), c_Orderings_Obot__class_Obot(tc_fun(_900864, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_900864, tc_HOL_Obool))), -(hAPP(_900868, _900870) = hAPP(hAPP(_900866, _900872), hAPP(_900868, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900864, tc_HOL_Obool)), _900870), hAPP(hAPP(c_Set_Oinsert(_900864), _900872), c_Orderings_Obot__class_Obot(tc_fun(_900864, tc_HOL_Obool)))))))]]], (7359 ^ _779300) ^ [_901386, _901388, _901390] : [hBOOL(hAPP(hAPP(c_member(_901386), _901388), _901390)), -(hAPP(hAPP(c_Set_Oinsert(_901386), _901388), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901386, tc_HOL_Obool)), _901390), hAPP(hAPP(c_Set_Oinsert(_901386), _901388), c_Orderings_Obot__class_Obot(tc_fun(_901386, tc_HOL_Obool))))) = _901390)], (7365 ^ _779300) ^ [_901539, _901541, _901543] : [-(hBOOL(hAPP(hAPP(c_member(_901539), _901541), _901543))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901539, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_901539), _901541), _901543)), hAPP(hAPP(c_Set_Oinsert(_901539), _901541), c_Orderings_Obot__class_Obot(tc_fun(_901539, tc_HOL_Obool)))) = _901543)], (7371 ^ _779300) ^ [_901616, _901618, _901620, _901622, _901624, _901626] : [c_Fun_Oinj__on(_901616, _901618, _901620, _901622), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901616, tc_HOL_Obool)), _901624), _901622)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901616, tc_HOL_Obool)), _901626), _901622)), -(hAPP(c_Set_Oimage(_901616, _901618, _901620), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901616, tc_HOL_Obool)), _901624), _901626)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901618, tc_HOL_Obool)), hAPP(c_Set_Oimage(_901616, _901618, _901620), _901624)), hAPP(c_Set_Oimage(_901616, _901618, _901620), _901626)))], (7385 ^ _779300) ^ [_901951, _901953, _901955, _901957, _901959] : [c_Fun_Oinj__on(_901951, _901953, _901955, _901957), hBOOL(hAPP(hAPP(c_member(_901951), _901959), _901957)), -(hAPP(c_Fun_Othe__inv__into(_901951, _901953, _901957, _901955), hAPP(_901955, _901959)) = _901959)], (7395 ^ _779300) ^ [_902132, _902134, _902136, _902138, _902140, _902142] : [c_Fun_Oinj__on(_902132, _902134, _902136, _902138), hAPP(_902136, _902140) = _902142, hBOOL(hAPP(hAPP(c_member(_902132), _902140), _902138)), -(hAPP(c_Fun_Othe__inv__into(_902132, _902134, _902138, _902136), _902142) = _902140)], (7420 ^ _779300) ^ [_902576] : [7422 ^ _779300 : [(7423 ^ _779300) ^ [_902652] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 7421 ^ [_902576, _902652]), _902576)))], (7425 ^ _779300) ^ [_902686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 7421 ^ [_902576, _902686]), _902686))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _902576)))], (7409 ^ _779300) ^ [_902389] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _902389)), 7413 ^ _779300 : [(7414 ^ _779300) ^ [_902469] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _902469), _902389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _902469), 7412 ^ [_902389])))]]], (7429 ^ _779300) ^ [_902755, _902757, _902759, _902761] : [c_Fun_Oinj__on(_902755, _902757, _902759, _902761), -(hAPP(c_Set_Oimage(_902757, _902755, c_Fun_Othe__inv__into(_902755, _902757, _902761, _902759)), hAPP(c_Set_Oimage(_902755, _902757, _902759), _902761)) = _902761)], (7435 ^ _779300) ^ [_902878, _902880, _902882, _902884] : [c_Fun_Oinj__on(_902878, _902880, _902882, _902884), -(c_Fun_Oinj__on(_902880, _902878, c_Fun_Othe__inv__into(_902878, _902880, _902884, _902882), hAPP(c_Set_Oimage(_902878, _902880, _902882), _902884)))], (7441 ^ _779300) ^ [_902991, _902993, _902995, _902997] : [c_Finite__Set_Ofolding__one(_902991, _902993, _902995), -(hAPP(_902995, hAPP(hAPP(c_Set_Oinsert(_902991), _902997), c_Orderings_Obot__class_Obot(tc_fun(_902991, tc_HOL_Obool)))) = _902997)], (7447 ^ _779300) ^ [_903106, _903108, _903110, _903112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903106, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903106, tc_HOL_Obool)), _903108), hAPP(hAPP(c_Set_Oinsert(_903106), _903110), c_Orderings_Obot__class_Obot(tc_fun(_903106, tc_HOL_Obool))))), _903112)), hBOOL(hAPP(hAPP(c_member(_903106), _903110), _903108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903106, tc_HOL_Obool)), _903108), hAPP(hAPP(c_Set_Oinsert(_903106), _903110), _903112))))], (7473 ^ _779300) ^ [_903714, _903716, _903718, _903720] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903714, tc_HOL_Obool)), _903716), hAPP(hAPP(c_Set_Oinsert(_903714), _903718), _903720)))), 7476 ^ _779300 : [(7477 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_903714), _903718), _903716)))], (7479 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903714, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903714, tc_HOL_Obool)), _903716), hAPP(hAPP(c_Set_Oinsert(_903714), _903718), c_Orderings_Obot__class_Obot(tc_fun(_903714, tc_HOL_Obool))))), _903720))]], 7480 ^ _779300 : [(7481 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_903714), _903718), _903716))], (7483 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903714, tc_HOL_Obool)), _903716), _903720))]]], (7457 ^ _779300) ^ [_903382, _903384, _903386, _903388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903382, tc_HOL_Obool)), _903384), hAPP(hAPP(c_Set_Oinsert(_903382), _903386), _903388))), 7460 ^ _779300 : [(7461 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_903382), _903386), _903384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903382, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903382, tc_HOL_Obool)), _903384), hAPP(hAPP(c_Set_Oinsert(_903382), _903386), c_Orderings_Obot__class_Obot(tc_fun(_903382, tc_HOL_Obool))))), _903388)))], (7467 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_903382), _903386), _903384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903382, tc_HOL_Obool)), _903384), _903388)))]]], (7487 ^ _779300) ^ [_904078, _904080, _904082, _904084, _904086] : [c_Finite__Set_Ofolding__one__idem(_904078, _904080, _904082), hBOOL(hAPP(c_Finite__Set_Ofinite(_904078), _904084)), hBOOL(hAPP(hAPP(c_member(_904078), _904086), _904084)), -(hAPP(hAPP(_904080, _904086), hAPP(_904082, _904084)) = hAPP(_904082, _904084))], (7501 ^ _779300) ^ [_904349, _904351, _904353, _904355, _904357] : [c_Fun_Oinj__on(_904349, _904351, _904353, hAPP(hAPP(c_Set_Oinsert(_904349), _904355), _904357)), 7504 ^ _779300 : [(7505 ^ _779300) ^ [] : [-(c_Fun_Oinj__on(_904349, _904351, _904353, _904357))], (7507 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_904351), hAPP(_904353, _904355)), hAPP(c_Set_Oimage(_904349, _904351, _904353), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904349, tc_HOL_Obool)), _904357), hAPP(hAPP(c_Set_Oinsert(_904349), _904355), c_Orderings_Obot__class_Obot(tc_fun(_904349, tc_HOL_Obool)))))))]]], (7509 ^ _779300) ^ [_904568, _904570, _904572, _904574, _904576] : [-(c_Fun_Oinj__on(_904568, _904570, _904572, hAPP(hAPP(c_Set_Oinsert(_904568), _904574), _904576))), c_Fun_Oinj__on(_904568, _904570, _904572, _904576), -(hBOOL(hAPP(hAPP(c_member(_904570), hAPP(_904572, _904574)), hAPP(c_Set_Oimage(_904568, _904570, _904572), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904568, tc_HOL_Obool)), _904576), hAPP(hAPP(c_Set_Oinsert(_904568), _904574), c_Orderings_Obot__class_Obot(tc_fun(_904568, tc_HOL_Obool))))))))], (7519 ^ _779300) ^ [_904820, _904822, _904824, _904826, _904828] : [class_Groups_Ominus(_904820), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904822, _904820)), _904824), _904826), _904828) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_904820), hAPP(_904824, _904828)), hAPP(_904826, _904828)))], (7525 ^ _779300) ^ [_904978, _904980, _904982, _904984] : [hBOOL(hAPP(hAPP(c_member(_904978), _904980), c_SetInterval_Oord_OatMost(_904978, _904982, _904984))), -(hBOOL(hAPP(hAPP(_904982, _904980), _904984)))], (7531 ^ _779300) ^ [_905087, _905089, _905091, _905093] : [hBOOL(hAPP(hAPP(_905091, _905089), _905093)), -(hBOOL(hAPP(hAPP(c_member(_905087), _905089), c_SetInterval_Oord_OatMost(_905087, _905091, _905093))))], (7537 ^ _779300) ^ [_905223, _905225, _905227, _905229] : [hBOOL(hAPP(hAPP(c_member(_905223), _905225), c_SetInterval_Oord_OatLeast(_905223, _905227, _905229))), -(hBOOL(hAPP(hAPP(_905227, _905229), _905225)))], (7543 ^ _779300) ^ [_905332, _905334, _905336, _905338] : [hBOOL(hAPP(hAPP(_905336, _905338), _905334)), -(hBOOL(hAPP(hAPP(c_member(_905332), _905334), c_SetInterval_Oord_OatLeast(_905332, _905336, _905338))))], (7549 ^ _779300) ^ [_905468, _905470, _905472, _905474] : [hBOOL(hAPP(hAPP(c_member(_905468), _905470), c_SetInterval_Oord_OlessThan(_905468, _905472, _905474))), -(hBOOL(hAPP(hAPP(_905472, _905470), _905474)))], (7555 ^ _779300) ^ [_905577, _905579, _905581, _905583] : [hBOOL(hAPP(hAPP(_905581, _905579), _905583)), -(hBOOL(hAPP(hAPP(c_member(_905577), _905579), c_SetInterval_Oord_OlessThan(_905577, _905581, _905583))))], (7561 ^ _779300) ^ [_905713, _905715, _905717, _905719] : [hBOOL(hAPP(hAPP(c_member(_905713), _905715), c_SetInterval_Oord_OgreaterThan(_905713, _905717, _905719))), -(hBOOL(hAPP(hAPP(_905717, _905719), _905715)))], (7567 ^ _779300) ^ [_905822, _905824, _905826, _905828] : [hBOOL(hAPP(hAPP(_905826, _905828), _905824)), -(hBOOL(hAPP(hAPP(c_member(_905822), _905824), c_SetInterval_Oord_OgreaterThan(_905822, _905826, _905828))))], (7573 ^ _779300) ^ [_905961, _905963, _905965, _905967, _905969] : [hBOOL(hAPP(hAPP(c_member(_905961), _905963), c_SetInterval_Oord_OatLeastAtMost(_905961, _905965, _905967, _905969))), 7576 ^ _779300 : [(7577 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_905965, _905967), _905963)))], (7579 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_905965, _905963), _905969)))]]], (7581 ^ _779300) ^ [_906110, _906112, _906114, _906116, _906118] : [-(hBOOL(hAPP(hAPP(c_member(_906110), _906112), c_SetInterval_Oord_OatLeastAtMost(_906110, _906114, _906116, _906118)))), hBOOL(hAPP(hAPP(_906114, _906116), _906112)), hBOOL(hAPP(hAPP(_906114, _906112), _906118))], (7591 ^ _779300) ^ [_906321, _906323, _906325, _906327, _906329] : [hBOOL(hAPP(hAPP(c_member(_906321), _906323), c_SetInterval_Oord_OgreaterThanLessThan(_906321, _906325, _906327, _906329))), 7594 ^ _779300 : [(7595 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_906325, _906327), _906323)))], (7597 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_906325, _906323), _906329)))]]], (7599 ^ _779300) ^ [_906470, _906472, _906474, _906476, _906478] : [-(hBOOL(hAPP(hAPP(c_member(_906470), _906472), c_SetInterval_Oord_OgreaterThanLessThan(_906470, _906474, _906476, _906478)))), hBOOL(hAPP(hAPP(_906474, _906476), _906472)), hBOOL(hAPP(hAPP(_906474, _906472), _906478))], (7609 ^ _779300) ^ [_906684, _906686, _906688, _906690, _906692, _906694] : [hBOOL(hAPP(hAPP(c_member(_906684), _906686), c_SetInterval_Oord_OatLeastLessThan(_906684, _906688, _906690, _906692, _906694))), 7612 ^ _779300 : [(7613 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_906688, _906692), _906686)))], (7615 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_906690, _906686), _906694)))]]], (7617 ^ _779300) ^ [_906837, _906839, _906841, _906843, _906845, _906847] : [-(hBOOL(hAPP(hAPP(c_member(_906837), _906839), c_SetInterval_Oord_OatLeastLessThan(_906837, _906841, _906843, _906845, _906847)))), hBOOL(hAPP(hAPP(_906841, _906845), _906839)), hBOOL(hAPP(hAPP(_906843, _906839), _906847))], (7627 ^ _779300) ^ [_907057, _907059, _907061, _907063, _907065, _907067] : [hBOOL(hAPP(hAPP(c_member(_907057), _907059), c_SetInterval_Oord_OgreaterThanAtMost(_907057, _907061, _907063, _907065, _907067))), 7630 ^ _779300 : [(7631 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_907063, _907065), _907059)))], (7633 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_907061, _907059), _907067)))]]], (7635 ^ _779300) ^ [_907210, _907212, _907214, _907216, _907218, _907220] : [-(hBOOL(hAPP(hAPP(c_member(_907210), _907212), c_SetInterval_Oord_OgreaterThanAtMost(_907210, _907214, _907216, _907218, _907220)))), hBOOL(hAPP(hAPP(_907216, _907218), _907212)), hBOOL(hAPP(hAPP(_907214, _907212), _907220))], (7645 ^ _779300) ^ [_907403, _907405, _907407, _907409, _907411] : [class_Groups_Ominus(_907403), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907405, _907403)), _907407), _907409), _907411) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_907403), hAPP(_907407, _907411)), hAPP(_907409, _907411)))], (7651 ^ _779300) ^ [_907540, _907542, _907544, _907546, _907548] : [class_Groups_Oordered__ab__group__add(_907540), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_907540), _907542), _907544) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_907540), _907546), _907548), 7658 ^ _779300 : [(7659 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907540), _907542), _907544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907540), _907546), _907548)))], (7665 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907540), _907546), _907548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907540), _907542), _907544)))]]], (7671 ^ _779300) ^ [_907895, _907897, _907899, _907901, _907903] : [class_Groups_Oab__group__add(_907895), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_907895), _907897), _907899) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_907895), _907901), _907903), 7678 ^ _779300 : [(7679 ^ _779300) ^ [] : [_907897 = _907899, -(_907901 = _907903)], (7685 ^ _779300) ^ [] : [_907901 = _907903, -(_907897 = _907899)]]], (7691 ^ _779300) ^ [_908208, _908210, _908212] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_908208), _908210)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908208, tc_HOL_Obool)), _908210), _908212)), -(hAPP(c_Finite__Set_Ocard(_908208), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908208, tc_HOL_Obool)), _908212), _908210)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_908208), _908212)), hAPP(c_Finite__Set_Ocard(_908208), _908210)))], (7701 ^ _779300) ^ [_908433, _908435, _908437] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_908433), _908435)), -(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(_908433), _908437)), hAPP(c_Finite__Set_Ocard(_908433), _908435))), hAPP(c_Finite__Set_Ocard(_908433), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908433, tc_HOL_Obool)), _908437), _908435)))))], (7707 ^ _779300) ^ [_908594, _908596, _908598, _908600] : [c_Finite__Set_Ofolding__one(_908594, _908596, _908598), hBOOL(hAPP(c_Finite__Set_Ofinite(_908594), _908600)), -(_908600 = c_Orderings_Obot__class_Obot(tc_fun(_908594, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_908594), hAPP(hAPP(_908596, 7720 ^ [_908594, _908596, _908598, _908600]), 7721 ^ [_908594, _908596, _908598, _908600])), hAPP(hAPP(c_Set_Oinsert(_908594), 7720 ^ [_908594, _908596, _908598, _908600]), hAPP(hAPP(c_Set_Oinsert(_908594), 7721 ^ [_908594, _908596, _908598, _908600]), c_Orderings_Obot__class_Obot(tc_fun(_908594, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_908594), hAPP(_908598, _908600)), _908600)))], (7727 ^ _779300) ^ [_909101, _909103, _909105, _909107, _909109, _909111] : [hBOOL(hAPP(hAPP(c_member(_909101), _909103), _909105)), -(hAPP(c_Set_Oimage(_909101, _909107, c_Fun_Ofun__upd(_909101, _909107, _909109, _909103, _909111)), _909105) = hAPP(hAPP(c_Set_Oinsert(_909107), _909111), hAPP(c_Set_Oimage(_909101, _909107, _909109), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909101, tc_HOL_Obool)), _909105), hAPP(hAPP(c_Set_Oinsert(_909101), _909103), c_Orderings_Obot__class_Obot(tc_fun(_909101, tc_HOL_Obool)))))))], (7733 ^ _779300) ^ [_909298, _909300, _909302, _909304, _909306, _909308] : [-(hBOOL(hAPP(hAPP(c_member(_909298), _909300), _909302))), -(hAPP(c_Set_Oimage(_909298, _909304, c_Fun_Ofun__upd(_909298, _909304, _909306, _909300, _909308)), _909302) = hAPP(c_Set_Oimage(_909298, _909304, _909306), _909302))], (7739 ^ _779300) ^ [_909371, _909373, _909375] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_909371), _909373)), 7742 ^ _779300 : [(7743 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_909371), _909375), _909373)), -(hAPP(c_Finite__Set_Ocard(_909371), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909371, tc_HOL_Obool)), _909373), hAPP(hAPP(c_Set_Oinsert(_909371), _909375), c_Orderings_Obot__class_Obot(tc_fun(_909371, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_909371), _909373)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7749 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_909371), _909375), _909373))), -(hAPP(c_Finite__Set_Ocard(_909371), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909371, tc_HOL_Obool)), _909373), hAPP(hAPP(c_Set_Oinsert(_909371), _909375), c_Orderings_Obot__class_Obot(tc_fun(_909371, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_909371), _909373))]]], (7755 ^ _779300) ^ [_909735, _909737, _909739] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_909735), _909737)), hBOOL(hAPP(hAPP(c_member(_909735), _909739), _909737)), -(hAPP(c_Finite__Set_Ocard(_909735), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909735, tc_HOL_Obool)), _909737), hAPP(hAPP(c_Set_Oinsert(_909735), _909739), c_Orderings_Obot__class_Obot(tc_fun(_909735, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_909735), _909737)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7765 ^ _779300) ^ [_909970, _909972, _909974] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_909970), _909972)), hBOOL(hAPP(hAPP(c_member(_909970), _909974), _909972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_909970), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909970, tc_HOL_Obool)), _909972), hAPP(hAPP(c_Set_Oinsert(_909970), _909974), c_Orderings_Obot__class_Obot(tc_fun(_909970, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_909970), _909972))))], (7775 ^ _779300) ^ [_910203, _910205, _910207, _910209] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_910203), _910205)), hBOOL(hAPP(hAPP(c_member(_910203), _910207), _910205)), hBOOL(hAPP(hAPP(c_member(_910203), _910209), _910205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_910203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910203, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910203, tc_HOL_Obool)), _910205), hAPP(hAPP(c_Set_Oinsert(_910203), _910207), c_Orderings_Obot__class_Obot(tc_fun(_910203, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_910203), _910209), c_Orderings_Obot__class_Obot(tc_fun(_910203, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_910203), _910205))))], (7789 ^ _779300) ^ [_910558, _910560, _910562] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_910558), _910560)), hBOOL(hAPP(_910562, _910560)), 7800 ^ _779300 : [(7801 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_910558), 7799 ^ [_910558, _910560, _910562])))], (7803 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910558), 7798 ^ [_910558, _910560, _910562]), 7799 ^ [_910558, _910560, _910562])))], (7805 ^ _779300) ^ [] : [-(hBOOL(hAPP(_910562, 7799 ^ [_910558, _910560, _910562])))], (7807 ^ _779300) ^ [] : [hBOOL(hAPP(_910562, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910558, tc_HOL_Obool)), 7799 ^ [_910558, _910560, _910562]), hAPP(hAPP(c_Set_Oinsert(_910558), 7798 ^ [_910558, _910560, _910562]), c_Orderings_Obot__class_Obot(tc_fun(_910558, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_910562, c_Orderings_Obot__class_Obot(tc_fun(_910558, tc_HOL_Obool)))))], (7811 ^ _779300) ^ [_911083, _911085, _911087] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_911083), _911085)), hBOOL(hAPP(hAPP(c_member(_911083), _911087), _911085)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_911083), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911083, tc_HOL_Obool)), _911085), hAPP(hAPP(c_Set_Oinsert(_911083), _911087), c_Orderings_Obot__class_Obot(tc_fun(_911083, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_911083), _911085))], (7821 ^ _779300) ^ [_911312, _911314] : [-(c_Set_Othe__elem(_911312, _911314) = c_HOL_OThe(_911312, hAPP(hAPP(c_COMBB(tc_fun(_911312, tc_HOL_Obool), tc_HOL_Obool, _911312), hAPP(c_fequal, _911314)), hAPP(hAPP(c_COMBC(_911312, tc_fun(_911312, tc_HOL_Obool), tc_fun(_911312, tc_HOL_Obool)), c_Set_Oinsert(_911312)), c_Orderings_Obot__class_Obot(tc_fun(_911312, tc_HOL_Obool))))))], (7823 ^ _779300) ^ [_911382, _911384, _911386, _911388, _911390] : [c_Finite__Set_Ofolding__one__idem(_911382, _911384, _911386), hAPP(_911388, hAPP(hAPP(_911384, 7828 ^ [_911382, _911384, _911386, _911388, _911390]), 7829 ^ [_911382, _911384, _911386, _911388, _911390])) = hAPP(hAPP(_911384, hAPP(_911388, 7828 ^ [_911382, _911384, _911386, _911388, _911390])), hAPP(_911388, 7829 ^ [_911382, _911384, _911386, _911388, _911390])), hBOOL(hAPP(c_Finite__Set_Ofinite(_911382), _911390)), -(_911390 = c_Orderings_Obot__class_Obot(tc_fun(_911382, tc_HOL_Obool))), -(hAPP(_911388, hAPP(_911386, _911390)) = hAPP(_911386, hAPP(c_Set_Oimage(_911382, _911382, _911388), _911390)))], (7843 ^ _779300) ^ [_911817] : [-(c_Finite__Set_Ofun__left__comm__idem(_911817, tc_fun(_911817, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_911817, tc_HOL_Obool), tc_fun(tc_fun(_911817, tc_HOL_Obool), tc_fun(_911817, tc_HOL_Obool)), _911817), hAPP(c_COMBC(tc_fun(_911817, tc_HOL_Obool), tc_fun(_911817, tc_HOL_Obool), tc_fun(_911817, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_911817, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_911817, tc_fun(_911817, tc_HOL_Obool), tc_fun(_911817, tc_HOL_Obool)), c_Set_Oinsert(_911817)), c_Orderings_Obot__class_Obot(tc_fun(_911817, tc_HOL_Obool))))))], (7845 ^ _779300) ^ [_911910, _911912, _911914, _911916] : [-(c_Fun_Ofun__upd(_911910, _911912, _911914, _911916, hAPP(_911914, _911916)) = _911914)], (7847 ^ _779300) ^ [_911948, _911950] : [class_Groups_Oone(_911948), 7850 ^ _779300 : [(7851 ^ _779300) ^ [] : [c_Groups_Oone__class_Oone(_911948) = _911950, -(_911950 = c_Groups_Oone__class_Oone(_911948))], (7857 ^ _779300) ^ [] : [_911950 = c_Groups_Oone__class_Oone(_911948), -(c_Groups_Oone__class_Oone(_911948) = _911950)]]], (7863 ^ _779300) ^ [_912165, _912167, _912169, _912171, _912173] : [c_Finite__Set_Ofun__left__comm__idem(_912165, _912167, _912169), -(hAPP(hAPP(_912169, _912171), hAPP(hAPP(_912169, _912171), _912173)) = hAPP(hAPP(_912169, _912171), _912173))], (7869 ^ _779300) ^ [_912286, _912288, _912290, _912292, _912294] : [hAPP(_912286, _912288) = _912290, -(c_Fun_Ofun__upd(_912292, _912294, _912286, _912288, _912290) = _912286)], (7875 ^ _779300) ^ [_912383, _912385, _912387, _912389, _912391, _912393] : [-(_912383 = _912385), -(hAPP(c_Fun_Ofun__upd(_912387, _912389, _912391, _912385, _912393), _912383) = hAPP(_912391, _912383))], (7881 ^ _779300) ^ [_912435, _912437, _912439, _912441, _912443, _912445, _912447] : [-(_912435 = _912437), -(c_Fun_Ofun__upd(_912439, _912441, c_Fun_Ofun__upd(_912439, _912441, _912443, _912435, _912445), _912437, _912447) = c_Fun_Ofun__upd(_912439, _912441, c_Fun_Ofun__upd(_912439, _912441, _912443, _912437, _912447), _912435, _912445))], (7887 ^ _779300) ^ [_912526, _912528, _912530, _912532, _912534, _912536] : [_912526 = _912528, -(hAPP(c_Fun_Ofun__upd(_912530, _912532, _912534, _912528, _912536), _912526) = _912536)], (7893 ^ _779300) ^ [_912623, _912625, _912627, _912629, _912631, _912633] : [-(_912623 = _912625), -(hAPP(c_Fun_Ofun__upd(_912627, _912629, _912631, _912625, _912633), _912623) = hAPP(_912631, _912623))], (7899 ^ _779300) ^ [_912681, _912683, _912685, _912687, _912689] : [-(hAPP(c_Fun_Ofun__upd(_912681, _912683, _912685, _912687, _912689), _912687) = _912689)], (7901 ^ _779300) ^ [_912721, _912723, _912725, _912727, _912729, _912731] : [-(c_Fun_Ofun__upd(_912721, _912723, c_Fun_Ofun__upd(_912721, _912723, _912725, _912727, _912729), _912727, _912731) = c_Fun_Ofun__upd(_912721, _912723, _912725, _912727, _912731))], (7903 ^ _779300) ^ [_912796, _912798, _912800, _912802, _912804] : [c_Fun_Ofun__upd(_912796, _912798, _912800, _912802, _912804) = _912800, -(hAPP(_912800, _912802) = _912804)], (7909 ^ _779300) ^ [_912893, _912895, _912897, _912899, _912901] : [hAPP(_912897, _912899) = _912901, -(c_Fun_Ofun__upd(_912893, _912895, _912897, _912899, _912901) = _912897)], (7915 ^ _779300) ^ [_912996, _912998, _913000] : [class_Orderings_Olinorder(_912996), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912996), _912998), _913000))), -(_912998 = _913000), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912996), _913000), _912998)))], (7929 ^ _779300) ^ [_913131, _913133, _913135] : [class_Orderings_Opreorder(_913131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913131), _913133), _913135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913131), _913135), _913133))], (7939 ^ _779300) ^ [_913291, _913293, _913295, _913297] : [class_Orderings_Oorder(_913291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913291), _913293), _913295)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913291), _913297), _913293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913291), _913297), _913295)))], (7953 ^ _779300) ^ [_913524, _913526, _913528, _913530] : [class_Orderings_Opreorder(_913524), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913524), _913526), _913528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913524), _913528), _913530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913524), _913526), _913530)))], (7967 ^ _779300) ^ [_913757, _913759, _913761, _913763] : [class_Orderings_Oorder(_913757), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913757), _913759), _913761)), _913759 = _913763, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913757), _913763), _913761)))], (7981 ^ _779300) ^ [_913976, _913978, _913980, _913982] : [class_Orderings_Oord(_913976), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913976), _913978), _913980)), _913980 = _913982, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913976), _913978), _913982)))], (7995 ^ _779300) ^ [_914195, _914197, _914199, _914201] : [class_Orderings_Oorder(_914195), _914197 = _914199, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914195), _914201), _914199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914195), _914201), _914197)))], (8009 ^ _779300) ^ [_914414, _914416, _914418, _914420] : [class_Orderings_Oord(_914414), _914416 = _914418, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914414), _914418), _914420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914414), _914416), _914420)))], (8023 ^ _779300) ^ [_914633, _914635, _914637] : [class_Orderings_Oorder(_914633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914633), _914635), _914637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914633), _914637), _914635))], (8033 ^ _779300) ^ [_914793, _914795, _914797] : [class_Orderings_Opreorder(_914793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914793), _914795), _914797)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914793), _914797), _914795))], (8043 ^ _779300) ^ [_914953, _914955, _914957] : [class_Orderings_Oorder(_914953), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914953), _914955), _914957)), _914957 = _914955], (8053 ^ _779300) ^ [_915099, _915101, _915103] : [class_Orderings_Oorder(_915099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915099), _915101), _915103)), _915101 = _915103], (8063 ^ _779300) ^ [_915245, _915247, _915249] : [class_Orderings_Opreorder(_915245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915245), _915247), _915249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915245), _915249), _915247))], (8073 ^ _779300) ^ [_915405, _915407, _915409] : [class_Orderings_Opreorder(_915405), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915405), _915407), _915409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915405), _915409), _915407))], (8083 ^ _779300) ^ [_915565, _915567, _915569] : [class_Orderings_Oorder(_915565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915565), _915567), _915569)), _915567 = _915569], (8093 ^ _779300) ^ [_915711, _915713, _915715] : [class_Orderings_Olinorder(_915711), -(_915713 = _915715), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915711), _915713), _915715))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915711), _915715), _915713)))], (8107 ^ _779300) ^ [_915846, _915848, _915850] : [class_Orderings_Olinorder(_915846), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915846), _915848), _915850))), 8114 ^ _779300 : [(8115 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915846), _915850), _915848))), -(_915850 = _915848)], (8121 ^ _779300) ^ [] : [_915850 = _915848, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915846), _915850), _915848))]]], (8127 ^ _779300) ^ [_916105, _916107, _916109] : [class_Orderings_Olinorder(_916105), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916105), _916107), _916109))), -(_916107 = _916109), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916105), _916109), _916107)))], (8141 ^ _779300) ^ [_916236, _916238, _916240] : [class_Orderings_Olinorder(_916236), 8144 ^ _779300 : [(8155 ^ _779300) ^ [] : [8156 ^ _779300 : [(8157 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916236), _916240), _916238))], (8159 ^ _779300) ^ [] : [_916238 = _916240]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916236), _916238), _916240))], (8145 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916236), _916238), _916240))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916236), _916240), _916238))), -(_916238 = _916240)]]], (8163 ^ _779300) ^ [_916490, _916492, _916494] : [class_Orderings_Olinorder(_916490), 8166 ^ _779300 : [(8177 ^ _779300) ^ [] : [8178 ^ _779300 : [(8179 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916490), _916492), _916494))], (8181 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916490), _916494), _916492))]], _916492 = _916494], (8167 ^ _779300) ^ [] : [-(_916492 = _916494), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916490), _916492), _916494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916490), _916494), _916492)))]]], (8185 ^ _779300) ^ [_916744, _916746] : [class_Orderings_Opreorder(_916744), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916744), _916746), _916746))], (8191 ^ _779300) ^ [_916855, _916857, _916859, _916861, _916863, _916865] : [_916855 = _916857, -(hAPP(c_Fun_Ofun__upd(_916859, _916861, _916863, _916857, _916865), _916855) = _916865)], (8197 ^ _779300) ^ [_916952, _916954, _916956, _916958, _916960, _916962] : [-(_916952 = _916954), -(hAPP(c_Fun_Ofun__upd(_916956, _916958, _916960, _916954, _916962), _916952) = hAPP(_916960, _916952))], (8203 ^ _779300) ^ [_917010, _917012, _917014, _917016, _917018] : [c_Finite__Set_Ofun__left__comm__idem(_917010, _917012, _917014), -(c_Finite__Set_Ofun__left__comm__idem(_917016, _917012, hAPP(hAPP(c_COMBB(_917010, tc_fun(_917012, _917012), _917016), _917014), _917018)))], (8209 ^ _779300) ^ [_917123, _917125, _917127, _917129] : [class_Orderings_Oorder(_917123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917123), _917125), _917127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917123), _917129), _917125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917123), _917129), _917127)))], (8223 ^ _779300) ^ [_917356, _917358, _917360, _917362] : [class_Orderings_Opreorder(_917356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917356), _917358), _917360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917356), _917360), _917362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917356), _917358), _917362)))], (8237 ^ _779300) ^ [_917589, _917591, _917593, _917595] : [class_Orderings_Oorder(_917589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917589), _917591), _917593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917589), _917595), _917591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917589), _917595), _917593)))], (8251 ^ _779300) ^ [_917822, _917824, _917826, _917828] : [class_Orderings_Opreorder(_917822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917822), _917824), _917826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917822), _917826), _917828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917822), _917824), _917828)))], (8265 ^ _779300) ^ [_918055, _918057, _918059] : [class_Orderings_Oorder(_918055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918055), _918057), _918059)), -(_918059 = _918057), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918055), _918057), _918059)))], (8279 ^ _779300) ^ [_918229, _918231, _918233] : [class_Orderings_Oorder(_918229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918229), _918231), _918233)), -(_918231 = _918233), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918229), _918231), _918233)))], (8293 ^ _779300) ^ [_918403, _918405, _918407] : [class_Orderings_Oorder(_918403), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918403), _918405), _918407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918403), _918405), _918407))), -(_918405 = _918407)], (8307 ^ _779300) ^ [_918575, _918577, _918579] : [class_Orderings_Olinorder(_918575), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918575), _918577), _918579)), 8314 ^ _779300 : [(8315 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918575), _918577), _918579))), -(_918577 = _918579)], (8321 ^ _779300) ^ [] : [_918577 = _918579, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918575), _918577), _918579))]]], (8327 ^ _779300) ^ [_918831, _918833, _918835] : [class_Orderings_Opreorder(_918831), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918831), _918833), _918835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918831), _918833), _918835)))], (8337 ^ _779300) ^ [_918990, _918992, _918994] : [class_Orderings_Olinorder(_918990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918990), _918992), _918994)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918990), _918994), _918992))], (8347 ^ _779300) ^ [_919150, _919152, _919154] : [class_Orderings_Oorder(_919150), -(_919152 = _919154), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919150), _919154), _919152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919150), _919154), _919152)))], (8361 ^ _779300) ^ [_919366, _919368, _919370] : [class_Orderings_Oorder(_919366), -(_919368 = _919370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919366), _919368), _919370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919366), _919368), _919370)))], (8375 ^ _779300) ^ [_919582, _919584, _919586] : [class_Orderings_Olinorder(_919582), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919582), _919584), _919586))), 8382 ^ _779300 : [(8383 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919582), _919584), _919586)), -(_919584 = _919586)], (8389 ^ _779300) ^ [] : [_919584 = _919586, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919582), _919584), _919586)))]]], (8395 ^ _779300) ^ [_919885, _919887, _919889] : [class_Orderings_Olinorder(_919885), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919885), _919887), _919889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919885), _919889), _919887)))], (8405 ^ _779300) ^ [_920005, _920007, _920009] : [class_Orderings_Olinorder(_920005), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920005), _920007), _920009))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920005), _920009), _920007)))], (8415 ^ _779300) ^ [_920125, _920127, _920129] : [class_Orderings_Oorder(_920125), 8418 ^ _779300 : [(8429 ^ _779300) ^ [] : [8430 ^ _779300 : [(8431 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920125), _920127), _920129))], (8433 ^ _779300) ^ [] : [_920127 = _920129]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920125), _920127), _920129)))], (8419 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920125), _920127), _920129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920125), _920127), _920129))), -(_920127 = _920129)]]], (8437 ^ _779300) ^ [_920423, _920425, _920427] : [class_Orderings_Opreorder(_920423), 8440 ^ _779300 : [(8441 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920423), _920425), _920427)), 8444 ^ _779300 : [(8445 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920423), _920425), _920427)))], (8447 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920423), _920427), _920425))]]], (8449 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920423), _920425), _920427))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920423), _920425), _920427)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920423), _920427), _920425)))]]], (8459 ^ _779300) ^ [_920780, _920782, _920784] : [class_Orderings_Oorder(_920780), 8462 ^ _779300 : [(8463 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920780), _920782), _920784)), 8466 ^ _779300 : [(8467 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920780), _920782), _920784)))], (8469 ^ _779300) ^ [] : [_920782 = _920784]]], (8471 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920780), _920782), _920784))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920780), _920782), _920784)), -(_920782 = _920784)]]], (8481 ^ _779300) ^ [_921116, _921118, _921120] : [class_Orderings_Olinorder(_921116), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921116), _921118), _921120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921116), _921120), _921118)))], (8491 ^ _779300) ^ [_921234, _921236, _921238] : [class_Orderings_Olinorder(_921234), 8494 ^ _779300 : [(8495 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921234), _921236), _921238))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921234), _921238), _921236)))], (8501 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921234), _921238), _921236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921234), _921236), _921238))]]], (8507 ^ _779300) ^ [_921443, _921445, _921447] : [class_Orderings_Olinorder(_921443), 8510 ^ _779300 : [(8511 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921443), _921445), _921447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921443), _921447), _921445)))], (8517 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921443), _921447), _921445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921443), _921445), _921447))]]], (8523 ^ _779300) ^ [_921652, _921654, _921656, _921658, _921660] : [class_Groups_Oordered__ab__group__add(_921652), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_921652), _921654), _921656) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_921652), _921658), _921660), 8530 ^ _779300 : [(8531 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921652), _921654), _921656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921652), _921658), _921660)))], (8537 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921652), _921658), _921660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921652), _921654), _921656)))]]], (8554 ^ _779300) ^ [_922206] : [8556 ^ _779300 : [(8557 ^ _779300) ^ [_922282] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 8555 ^ [_922206, _922282]), _922206)))], (8559 ^ _779300) ^ [_922316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 8555 ^ [_922206, _922316]), _922316))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _922206)))], (8543 ^ _779300) ^ [_922019] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _922019)), 8547 ^ _779300 : [(8548 ^ _779300) ^ [_922099] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _922099), _922019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _922099), 8546 ^ [_922019])))]]], (8563 ^ _779300) ^ [_922385] : [-(c_Finite__Set_Ofun__left__comm__idem(_922385, tc_fun(_922385, tc_HOL_Obool), c_Set_Oinsert(_922385)))], (8565 ^ _779300) ^ [_922414, _922416, _922418, _922420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_922414), hAPP(c_Set_Oimage(_922416, _922414, _922418), _922420))), hAPP(c_Finite__Set_Ocard(_922416), _922420))), c_Fun_Oinj__on(_922416, _922414, _922418, _922420)], (8571 ^ _779300) ^ [_922544, _922546, _922548, _922550, _922552] : [-(hAPP(c_Fun_Othe__inv__into(_922544, _922546, _922548, _922550), _922552) = c_HOL_OThe(_922544, hAPP(hAPP(c_COMBS(_922544, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _922544), c_fconj), hAPP(hAPP(c_COMBC(_922544, tc_fun(_922544, tc_HOL_Obool), tc_HOL_Obool), c_member(_922544)), _922548))), hAPP(hAPP(c_COMBC(_922544, _922546, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_922546, tc_fun(_922546, tc_HOL_Obool), _922544), c_fequal), _922550)), _922552))))], (8573 ^ _779300) ^ [_922644, _922646, _922648] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_922644), _922646)), -(hBOOL(hAPP(hAPP(c_member(_922644), _922648), _922646))), -(hAPP(c_Finite__Set_Ocard(_922644), hAPP(hAPP(c_Set_Oinsert(_922644), _922648), _922646)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_922644), _922646)))], (8583 ^ _779300) ^ [_922802, _922804, _922806] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_922802), _922804)), 8586 ^ _779300 : [(8587 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_922802), _922806), _922804)), -(hAPP(c_Finite__Set_Ocard(_922802), hAPP(hAPP(c_Set_Oinsert(_922802), _922806), _922804)) = hAPP(c_Finite__Set_Ocard(_922802), _922804))], (8593 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_922802), _922806), _922804))), -(hAPP(c_Finite__Set_Ocard(_922802), hAPP(hAPP(c_Set_Oinsert(_922802), _922806), _922804)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_922802), _922804)))]]], (8599 ^ _779300) ^ [_923096, _923098, _923100, _923102, _923104, _923106] : [c_Fun_Oinj__on(_923096, _923098, _923100, _923102), -(hBOOL(hAPP(hAPP(c_member(_923098), _923104), hAPP(c_Set_Oimage(_923096, _923098, _923100), _923102)))), -(c_Fun_Oinj__on(_923096, _923098, c_Fun_Ofun__upd(_923096, _923098, _923100, _923106, _923104), _923102))], (8609 ^ _779300) ^ [_923244, _923246, _923248] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_923244), _923246)), -(hAPP(c_Finite__Set_Ocard(_923244), hAPP(hAPP(c_Set_Oinsert(_923244), _923248), _923246)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_923244), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923244, tc_HOL_Obool)), _923246), hAPP(hAPP(c_Set_Oinsert(_923244), _923248), c_Orderings_Obot__class_Obot(tc_fun(_923244, tc_HOL_Obool)))))))], (8615 ^ _779300) ^ [_923421, _923423, _923425, _923427] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_923421), _923423)), hBOOL(hAPP(hAPP(c_member(_923421), _923425), _923423)), -(hBOOL(hAPP(hAPP(c_member(_923421), _923425), _923427))), -(hAPP(c_Finite__Set_Ocard(_923421), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923421, tc_HOL_Obool)), _923423), hAPP(hAPP(c_Set_Oinsert(_923421), _923425), _923427))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_923421), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923421, tc_HOL_Obool)), _923423), _923427))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8629 ^ _779300) ^ [_923701] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _923701), hAPP(c_Nat_OSuc, _923701))))], (8631 ^ _779300) ^ [_923732, _923734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _923732), _923734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _923732)), hAPP(c_Nat_OSuc, _923734))))], (8637 ^ _779300) ^ [_923841] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _923841) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _923841)))], (8639 ^ _779300) ^ [_923873, _923875] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _923873), hAPP(c_Nat_OSuc, _923875)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _923873), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _923875))], (8641 ^ _779300) ^ [_923919] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _923919)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _923919)], (8643 ^ _779300) ^ [_923951, _923953, _923955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _923951), _923953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _923951), _923955)), 8650 ^ _779300 : [(8651 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _923953), _923951)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _923955), _923951))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _923953), _923955)))], (8657 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _923953), _923955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _923953), _923951)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _923955), _923951))))]]], (8663 ^ _779300) ^ [_924304, _924306, _924308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _924304), _924306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _924308), _924304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _924304), _924308)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _924306), _924308))))], (8673 ^ _779300) ^ [_924491, _924493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _924491), _924493)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _924493)), _924491) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _924493), _924491)))], (8679 ^ _779300) ^ [_924614, _924616] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _924614), _924616)), hAPP(c_Nat_OSuc, _924614))))], (8681 ^ _779300) ^ [_924668, _924670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _924668), _924670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _924668)), _924670)))], (8687 ^ _779300) ^ [_924767, _924769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _924767)), _924769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _924767), _924769)))], (8693 ^ _779300) ^ [_924887, _924889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _924887), hAPP(c_Nat_OSuc, _924889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _924887), _924889)))], (8699 ^ _779300) ^ [_924986, _924988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _924986), _924988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _924986), hAPP(c_Nat_OSuc, _924988))))], (8705 ^ _779300) ^ [_925091, _925093, _925095, _925097] : [class_Orderings_Oord(_925091), 8708 ^ _779300 : [(8709 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_925093, _925091)), _925095), _925097)), 8712 ^ _779300 : [(8713 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925093, _925091)), _925095), _925097)))], (8715 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925093, _925091)), _925097), _925095))]]], (8717 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_925093, _925091)), _925095), _925097))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925093, _925091)), _925095), _925097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925093, _925091)), _925097), _925095)))]]], (8727 ^ _779300) ^ [_925483, _925485, _925487, _925489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_925483, tc_HOL_Obool)), _925485), _925487)), hBOOL(hAPP(hAPP(c_member(_925483), _925489), _925485)), -(hBOOL(hAPP(hAPP(c_member(_925483), _925489), _925487)))], (8737 ^ _779300) ^ [_925680, _925682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_925680, tc_HOL_Obool)), _925682), c_Orderings_Obot__class_Obot(tc_fun(_925680, tc_HOL_Obool))))], (8739 ^ _779300) ^ [_925738, _925740, _925742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_925738, tc_HOL_Obool)), _925740), _925742)), 8742 ^ _779300 : [(8743 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925738, tc_HOL_Obool)), _925740), _925742)))], (8745 ^ _779300) ^ [] : [_925740 = _925742]]], (8747 ^ _779300) ^ [_925887, _925889, _925891] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_925887, tc_HOL_Obool)), _925889), _925891))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925887, tc_HOL_Obool)), _925889), _925891)), -(_925889 = _925891)], (8767 ^ _779300) ^ [_926211, _926213, _926215] : [8768 ^ _779300 : [(8769 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926211, tc_HOL_Obool)), _926213), _926215))], (8771 ^ _779300) ^ [] : [_926213 = _926215]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926211, tc_HOL_Obool)), _926213), _926215)))], (8757 ^ _779300) ^ [_926083, _926085, _926087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926083, tc_HOL_Obool)), _926085), _926087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926083, tc_HOL_Obool)), _926085), _926087))), -(_926085 = _926087)], (8775 ^ _779300) ^ [_926370, _926372, _926374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926370, tc_HOL_Obool)), _926372), _926374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926370, tc_HOL_Obool)), _926372), _926374)))], (8781 ^ _779300) ^ [_926489, _926491, _926493, _926495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926489, tc_HOL_Obool)), _926491), _926493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926489, tc_HOL_Obool)), _926493), _926495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926489, tc_HOL_Obool)), _926491), _926495)))], (8791 ^ _779300) ^ [_926686, _926688, _926690, _926692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926686, tc_HOL_Obool)), _926688), _926690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926686, tc_HOL_Obool)), _926690), _926692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926686, tc_HOL_Obool)), _926688), _926692)))], (8801 ^ _779300) ^ [_926883, _926885, _926887, _926889, _926891] : [c_Fun_Oinj__on(_926883, _926885, _926887, _926889), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926883, tc_HOL_Obool)), _926891), _926889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926885, tc_HOL_Obool)), hAPP(c_Set_Oimage(_926883, _926885, _926887), _926891)), hAPP(c_Set_Oimage(_926883, _926885, _926887), _926889))))], (8811 ^ _779300) ^ [_927096, _927098, _927100] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_927096), _927098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927096, tc_HOL_Obool)), _927100), _927098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_927096), _927100)), hAPP(c_Finite__Set_Ocard(_927096), _927098))))], (8821 ^ _779300) ^ [_927287, _927289] : [hAPP(c_Nat_OSuc, _927287) = hAPP(c_Nat_OSuc, _927289), -(_927287 = _927289)], (8827 ^ _779300) ^ [_927391, _927393] : [hAPP(c_Nat_OSuc, _927391) = hAPP(c_Nat_OSuc, _927393), -(_927391 = _927393)], (8833 ^ _779300) ^ [_927476, _927478] : [_927476 = _927478, -(hAPP(c_Nat_OSuc, _927476) = hAPP(c_Nat_OSuc, _927478))], (8839 ^ _779300) ^ [_927576] : [hAPP(c_Nat_OSuc, _927576) = _927576], (8841 ^ _779300) ^ [_927611] : [_927611 = hAPP(c_Nat_OSuc, _927611)], (8843 ^ _779300) ^ [_927637] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _927637))], (8845 ^ _779300) ^ [_927662, _927664, _927666] : [8846 ^ _779300 : [(8847 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _927662), _927664)))], (8849 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_927666, _927664), _927662))]], 8852 ^ _779300 : [(8853 ^ _779300) ^ [] : [-(_927662 = _927664)], (8855 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_927666, _927664), _927662))]], 8858 ^ _779300 : [(8859 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _927664), _927662)))], (8861 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_927666, _927664), _927662))]], -(hBOOL(hAPP(hAPP(_927666, _927664), _927662)))], (8865 ^ _779300) ^ [_928008, _928010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928008), _928010)), _928008 = _928010], (8871 ^ _779300) ^ [_928096, _928098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928096), _928098)), _928098 = _928096], (8877 ^ _779300) ^ [_928193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928193), _928193))], (8879 ^ _779300) ^ [_928217, _928219] : [-(_928217 = _928219), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928217), _928219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928219), _928217)))], (8899 ^ _779300) ^ [_928328, _928330] : [8900 ^ _779300 : [(8901 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928328), _928330))], (8903 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928330), _928328))]], _928328 = _928330], (8889 ^ _779300) ^ [_928279, _928281] : [-(_928279 = _928281), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928279), _928281))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928281), _928279)))], (8907 ^ _779300) ^ [_928475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928475), _928475))], (8909 ^ _779300) ^ [_928503] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928503), _928503)))], (8911 ^ _779300) ^ [_928527, _928529] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928527), _928529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928529), _928527)))], (8917 ^ _779300) ^ [_928573, _928575] : [_928573 = _928575, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928573), _928575)))], (8923 ^ _779300) ^ [_928660, _928662, _928664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928660), _928662)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928662), _928664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928660), _928664)))], (8933 ^ _779300) ^ [_928823, _928825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928823), _928825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928825), _928823)), -(_928823 = _928825)], (8943 ^ _779300) ^ [_928972, _928974, _928976] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _928972), _928974)), _928976) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _928972), _928976)), _928974))], (8945 ^ _779300) ^ [_929023, _929025, _929027] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_929023), _929025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929023, tc_HOL_Obool)), _929027), _929025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_929023), _929027)), hAPP(c_Finite__Set_Ocard(_929023), _929025))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929023, tc_HOL_Obool)), _929027), _929025)))], (8985 ^ _779300) ^ [_929836, _929838, _929840, _929842] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929836, tc_HOL_Obool)), _929838), hAPP(hAPP(c_Set_Oinsert(_929836), _929840), _929842)))), 8988 ^ _779300 : [(8989 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929836), _929840), _929842)))], (8991 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929836, tc_HOL_Obool)), _929838), _929842))]], 8992 ^ _779300 : [(8993 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929836), _929840), _929842))], (8995 ^ _779300) ^ [] : [8996 ^ _779300 : [(8997 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929836), _929840), _929838)))], (8999 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929836, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929836, tc_HOL_Obool)), _929838), hAPP(hAPP(c_Set_Oinsert(_929836), _929840), c_Orderings_Obot__class_Obot(tc_fun(_929836, tc_HOL_Obool))))), _929842))]], 9000 ^ _779300 : [(9001 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929836), _929840), _929838))], (9003 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929836, tc_HOL_Obool)), _929838), _929842))]]]]], (8959 ^ _779300) ^ [_929309, _929311, _929313, _929315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929309, tc_HOL_Obool)), _929311), hAPP(hAPP(c_Set_Oinsert(_929309), _929313), _929315))), 8962 ^ _779300 : [(8963 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929309), _929313), _929315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929309, tc_HOL_Obool)), _929311), _929315)))], (8969 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929309), _929313), _929315))), 8972 ^ _779300 : [(8973 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929309), _929313), _929311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929309, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929309, tc_HOL_Obool)), _929311), hAPP(hAPP(c_Set_Oinsert(_929309), _929313), c_Orderings_Obot__class_Obot(tc_fun(_929309, tc_HOL_Obool))))), _929315)))], (8979 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929309), _929313), _929311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929309, tc_HOL_Obool)), _929311), _929315)))]]]]], (9007 ^ _779300) ^ [_930375, _930377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _930375)), hAPP(c_Nat_OSuc, _930377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930375), _930377)))], (9013 ^ _779300) ^ [_930484, _930486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _930484)), _930486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930484), _930486)))], (9019 ^ _779300) ^ [_930587, _930589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930587), hAPP(c_Nat_OSuc, _930589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930587), _930589))), -(_930587 = _930589)], (9029 ^ _779300) ^ [_930705, _930707, _930709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930705), _930707)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930707), _930709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _930705)), _930709)))], (9039 ^ _779300) ^ [_930874, _930876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930874), _930876)), -(hAPP(c_Nat_OSuc, _930874) = _930876), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _930874)), _930876)))], (9049 ^ _779300) ^ [_930998, _931000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930998), _931000)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930998), hAPP(c_Nat_OSuc, _931000))))], (9055 ^ _779300) ^ [_931100, _931102] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931100), _931102))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931100), hAPP(c_Nat_OSuc, _931102))), -(_931102 = _931100)], (9065 ^ _779300) ^ [_931247, _931249] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931247), _931249))), 9068 ^ _779300 : [(9069 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931247), hAPP(c_Nat_OSuc, _931249))), -(_931247 = _931249)], (9075 ^ _779300) ^ [] : [_931247 = _931249, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931247), hAPP(c_Nat_OSuc, _931249))))]]], (9081 ^ _779300) ^ [_931496, _931498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _931496)), hAPP(c_Nat_OSuc, _931498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931496), _931498)))], (9087 ^ _779300) ^ [_931601, _931603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931601), _931603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _931601)), hAPP(c_Nat_OSuc, _931603))))], (9103 ^ _779300) ^ [_931839, _931841] : [9104 ^ _779300 : [(9105 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931839), _931841))], (9107 ^ _779300) ^ [] : [_931839 = _931841]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931839), hAPP(c_Nat_OSuc, _931841))))], (9093 ^ _779300) ^ [_931727, _931729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931727), hAPP(c_Nat_OSuc, _931729))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931727), _931729))), -(_931727 = _931729)], (9111 ^ _779300) ^ [_931991, _931993] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931991), _931993))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931993), hAPP(c_Nat_OSuc, _931991))))], (9117 ^ _779300) ^ [_932036, _932038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _932038), hAPP(c_Nat_OSuc, _932036))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _932036), _932038))], (9123 ^ _779300) ^ [_932151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _932151)), _932151))], (9125 ^ _779300) ^ [_932191, _932193] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932191), _932193))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _932193)), _932191)))], (9131 ^ _779300) ^ [_932236, _932238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _932238)), _932236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932236), _932238))], (9147 ^ _779300) ^ [_932475, _932477] : [9148 ^ _779300 : [(9149 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932475), _932477))], (9151 ^ _779300) ^ [] : [_932475 = hAPP(c_Nat_OSuc, _932477)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932475), hAPP(c_Nat_OSuc, _932477))))], (9137 ^ _779300) ^ [_932357, _932359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932357), hAPP(c_Nat_OSuc, _932359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932357), _932359))), -(_932357 = hAPP(c_Nat_OSuc, _932359))], (9155 ^ _779300) ^ [_932639, _932641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _932639)), hAPP(c_Nat_OSuc, _932641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932639), _932641)))], (9161 ^ _779300) ^ [_932744, _932746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932744), _932746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _932744)), hAPP(c_Nat_OSuc, _932746))))], (9167 ^ _779300) ^ [_932855, _932857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932855), _932857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932855), hAPP(c_Nat_OSuc, _932857))))], (9173 ^ _779300) ^ [_932958, _932960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932958), hAPP(c_Nat_OSuc, _932960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932958), _932960))), -(_932958 = hAPP(c_Nat_OSuc, _932960))], (9183 ^ _779300) ^ [_933082, _933084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _933082)), _933084)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933082), _933084)))], (9189 ^ _779300) ^ [_933200, _933202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _933200), _933202)), 9192 ^ _779300 : [(9193 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933200), _933202)))], (9195 ^ _779300) ^ [] : [_933200 = _933202]]], (9197 ^ _779300) ^ [_933327, _933329] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _933327), _933329))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933327), _933329)), -(_933327 = _933329)], (9217 ^ _779300) ^ [_933602, _933604] : [9218 ^ _779300 : [(9219 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _933602), _933604))], (9221 ^ _779300) ^ [] : [_933602 = _933604]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933602), _933604)))], (9207 ^ _779300) ^ [_933496, _933498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933496), _933498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _933496), _933498))), -(_933496 = _933498)], (9225 ^ _779300) ^ [_933739, _933741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _933739), _933741)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933739), _933741)))], (9231 ^ _779300) ^ [_933836, _933838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933836), _933838)), -(_933836 = _933838), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _933836), _933838)))], (9241 ^ _779300) ^ [_933948, _933950] : [9242 ^ _779300 : [(9243 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _933948), _933950))], (9245 ^ _779300) ^ [] : [_933948 = _933950]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933948), _933950)))], (9249 ^ _779300) ^ [_934083, _934085, _934087] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _934083)), _934085)), hAPP(c_Nat_OSuc, _934087)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934083), _934085)), _934087))], (9251 ^ _779300) ^ [_934140, _934142] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _934140)), hAPP(c_Nat_OSuc, _934142)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934140), _934142))], (9253 ^ _779300) ^ [_934183, _934185, _934187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _934183), _934185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _934183), _934187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934187), _934185)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934187), _934183))))], (9263 ^ _779300) ^ [_934370, _934372, _934374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _934370), _934372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934370), _934374)), _934372)))], (9269 ^ _779300) ^ [_934481, _934483] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934481), _934483)), _934481)))], (9271 ^ _779300) ^ [_934517, _934519, _934521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _934517), _934519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934521), _934519)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934521), _934517))))], (9277 ^ _779300) ^ [_934640, _934642, _934644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _934640), _934642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934640), _934644)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934642), _934644))))], (9283 ^ _779300) ^ [_934763, _934765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _934763), _934765)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934765), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934765), _934763)) = _934763)], (9289 ^ _779300) ^ [_934874, _934876, _934878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _934874), _934876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _934874), _934878)), 9296 ^ _779300 : [(9297 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934876), _934874) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934878), _934874), -(_934876 = _934878)], (9303 ^ _779300) ^ [] : [_934876 = _934878, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934876), _934874) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934878), _934874))]]], (9309 ^ _779300) ^ [_935197, _935199, _935201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935197), _935199)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935197), _935201)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935199), _935197)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935201), _935197)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935199), _935201))], (9319 ^ _779300) ^ [_935398, _935400, _935402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935398), _935400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935398), _935402)), 9326 ^ _779300 : [(9327 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935400), _935398)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935402), _935398))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935400), _935402)))], (9333 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935400), _935402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935400), _935398)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935402), _935398))))]]], (9339 ^ _779300) ^ [_935751, _935753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _935751)), _935753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935751), _935753)))], (9345 ^ _779300) ^ [_935854, _935856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935854), _935856)), 9348 ^ _779300 : [(9349 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935856), hAPP(c_Nat_OSuc, _935854))), -(_935856 = _935854)], (9355 ^ _779300) ^ [] : [_935856 = _935854, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935856), hAPP(c_Nat_OSuc, _935854))))]]], (9361 ^ _779300) ^ [_936095, _936097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _936095), _936097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _936095)), _936097)))], (9367 ^ _779300) ^ [_936198, _936200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936198), _936200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _936198), hAPP(c_Nat_OSuc, _936200))))], (9373 ^ _779300) ^ [_936316, _936318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _936316)), _936318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _936316), _936318)))], (9379 ^ _779300) ^ [_936415, _936417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _936415), _936417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _936415)), _936417)))], (9385 ^ _779300) ^ [_936532, _936534, _936536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936532, tc_HOL_Obool)), _936534), hAPP(hAPP(c_Set_Oinsert(_936532), _936536), c_Orderings_Obot__class_Obot(tc_fun(_936532, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_936532, _936536, _936534) = _936536)], (9391 ^ _779300) ^ [_936659, _936661, _936663] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936659, tc_HOL_Obool)), _936661), hAPP(hAPP(c_Set_Oinsert(_936659), _936663), c_Orderings_Obot__class_Obot(tc_fun(_936659, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_936659, _936663, _936661) = c_HOL_OThe(_936659, hAPP(hAPP(c_COMBC(_936659, tc_fun(_936659, tc_HOL_Obool), tc_HOL_Obool), c_member(_936659)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936659, tc_HOL_Obool)), _936661), hAPP(hAPP(c_Set_Oinsert(_936659), _936663), c_Orderings_Obot__class_Obot(tc_fun(_936659, tc_HOL_Obool)))))))], (9397 ^ _779300) ^ [_936768, _936770, _936772] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_936768), _936770)), hBOOL(hAPP(hAPP(c_member(_936768), _936772), _936770)), -(hAPP(c_Finite__Set_Ocard(_936768), _936770) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_936768), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936768, tc_HOL_Obool)), _936770), hAPP(hAPP(c_Set_Oinsert(_936768), _936772), c_Orderings_Obot__class_Obot(tc_fun(_936768, tc_HOL_Obool)))))))], (9407 ^ _779300) ^ [_936997, _936999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _936997), _936999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936997), _936999)))], (9413 ^ _779300) ^ [_937094, _937096, _937098] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_937094), _937096)), -(hAPP(c_Finite__Set_Ocard(_937094), hAPP(hAPP(c_Set_Oinsert(_937094), _937098), _937096)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_937094), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937094, tc_HOL_Obool)), _937096), hAPP(hAPP(c_Set_Oinsert(_937094), _937098), c_Orderings_Obot__class_Obot(tc_fun(_937094, tc_HOL_Obool)))))))], (9419 ^ _779300) ^ [_937271, _937273] : [-(c_HOL_OThe(_937271, hAPP(hAPP(c_COMBC(_937271, _937271, tc_HOL_Obool), c_fequal), _937273)) = _937273)], (9421 ^ _779300) ^ [_937309, _937311] : [-(c_HOL_OThe(_937309, hAPP(c_fequal, _937311)) = _937311)], (9423 ^ _779300) ^ [_937355, _937357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _937355)), _937357)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937355), _937357)))], (9429 ^ _779300) ^ [_937458, _937460] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937458), _937460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _937458)), _937460)))], (9435 ^ _779300) ^ [_937567, _937569, _937571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_937567), _937569)), -(hBOOL(hAPP(hAPP(c_member(_937567), _937571), _937569))), -(hAPP(c_Finite__Set_Ocard(_937567), hAPP(hAPP(c_Set_Oinsert(_937567), _937571), _937569)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_937567), _937569)))], (9445 ^ _779300) ^ [_937725, _937727, _937729, _937731, _937733, _937735, _937737] : [hBOOL(hAPP(hAPP(c_member(_937725), _937727), _937729)), c_Nitpick_Ofold__graph_H(_937725, _937731, _937733, _937735, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937725, tc_HOL_Obool)), _937729), hAPP(hAPP(c_Set_Oinsert(_937725), _937727), c_Orderings_Obot__class_Obot(tc_fun(_937725, tc_HOL_Obool)))), _937737), -(c_Nitpick_Ofold__graph_H(_937725, _937731, _937733, _937735, _937729, hAPP(hAPP(_937733, _937727), _937737)))], (9455 ^ _779300) ^ [_937964, _937966, _937968, _937970, _937972, _937974, _937976] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_937964, _937966, _937968, _937970, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937964, tc_HOL_Obool)), _937972), hAPP(hAPP(c_Set_Oinsert(_937964), _937974), c_Orderings_Obot__class_Obot(tc_fun(_937964, tc_HOL_Obool))))), _937976)), hBOOL(hAPP(hAPP(c_member(_937964), _937974), _937972)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_937964, _937966, _937968, _937970, _937972), hAPP(hAPP(_937968, _937974), _937976))))], (9465 ^ _779300) ^ [_938219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _938219)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _938219), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _938219)], (9471 ^ _779300) ^ [_938325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938325), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9473 ^ _779300) ^ [_938353] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _938353)))], (9475 ^ _779300) ^ [_938378] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _938378))))], (9477 ^ _779300) ^ [_938406, _938408, _938410, _938412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938406, tc_HOL_Obool)), _938408), _938410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938406, tc_HOL_Obool)), _938410), _938412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938406, tc_HOL_Obool)), _938408), _938412)))], (9487 ^ _779300) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9489 ^ _779300) ^ [_938621, _938623] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938621), _938623) = _938621, -(_938623 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9495 ^ _779300) ^ [_938710, _938712, _938714] : [-(c_Nat_Onat_Onat__case(_938710, _938712, _938714, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _938712)], (9497 ^ _779300) ^ [_938760, _938762, _938764] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938760), _938762) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938764), _938762), -(_938760 = _938764)], (9503 ^ _779300) ^ [_938859, _938861, _938863] : [_938859 = _938863, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938859), _938861) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938863), _938861))], (9509 ^ _779300) ^ [_938982, _938984, _938986] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938982), _938984) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938982), _938986), -(_938984 = _938986)], (9515 ^ _779300) ^ [_939081, _939083, _939085] : [_939083 = _939085, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939081), _939083) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939081), _939085))], (9521 ^ _779300) ^ [_939186, _939188, _939190] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939186), _939188)), _939190) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939186), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939188), _939190)))], (9523 ^ _779300) ^ [_939252, _939254] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939252), _939254) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 9526 ^ _779300 : [(9527 ^ _779300) ^ [] : [-(_939252 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9529 ^ _779300) ^ [] : [-(_939254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9531 ^ _779300) ^ [_939363, _939365] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939363), _939365) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _939363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _939365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9541 ^ _779300) ^ [_939506, _939508, _939510] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939506), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939508), _939510)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939506), _939510)))], (9543 ^ _779300) ^ [_939557, _939559] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939557), _939559) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939559), _939557))], (9545 ^ _779300) ^ [_939594] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939594), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _939594)], (9547 ^ _779300) ^ [_939623] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _939623) = _939623)], (9549 ^ _779300) ^ [_939649, _939651, _939653, _939655] : [class_Groups_Ocancel__semigroup__add(_939649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939649), _939651), _939653) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939649), _939655), _939653), -(_939651 = _939655)], (9559 ^ _779300) ^ [_939816, _939818, _939820, _939822] : [class_Groups_Ocancel__ab__semigroup__add(_939816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939816), _939818), _939820) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939816), _939818), _939822), -(_939820 = _939822)], (9569 ^ _779300) ^ [_939983, _939985, _939987, _939989] : [class_Groups_Ocancel__semigroup__add(_939983), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939983), _939985), _939987) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939983), _939985), _939989), -(_939987 = _939989)], (9579 ^ _779300) ^ [_940150, _940152, _940154, _940156] : [class_Groups_Ocancel__semigroup__add(_940150), 9582 ^ _779300 : [(9583 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940150), _940152), _940154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940150), _940156), _940154), -(_940152 = _940156)], (9589 ^ _779300) ^ [] : [_940152 = _940156, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940150), _940152), _940154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940150), _940156), _940154))]]], (9595 ^ _779300) ^ [_940415, _940417, _940419, _940421] : [class_Groups_Ocancel__semigroup__add(_940415), 9598 ^ _779300 : [(9599 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940415), _940417), _940419) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940415), _940417), _940421), -(_940419 = _940421)], (9605 ^ _779300) ^ [] : [_940419 = _940421, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940415), _940417), _940419) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940415), _940417), _940421))]]], (9611 ^ _779300) ^ [_940680, _940682, _940684, _940686] : [class_Groups_Oab__semigroup__add(_940680), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940680), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940680), _940682), _940684)), _940686) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940680), _940682), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940680), _940684), _940686)))], (9617 ^ _779300) ^ [_940823, _940825] : [class_Groups_Ocomm__monoid__add(_940823), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940823), _940825), c_Groups_Ozero__class_Ozero(_940823)) = _940825)], (9623 ^ _779300) ^ [_940918, _940920] : [class_Groups_Omonoid__add(_940918), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940918), _940920), c_Groups_Ozero__class_Ozero(_940918)) = _940920)], (9629 ^ _779300) ^ [_941013, _941015] : [class_Groups_Olinordered__ab__group__add(_941013), 9632 ^ _779300 : [(9633 ^ _779300) ^ [] : [c_Groups_Ozero__class_Ozero(_941013) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941013), _941015), _941015), -(_941015 = c_Groups_Ozero__class_Ozero(_941013))], (9639 ^ _779300) ^ [] : [_941015 = c_Groups_Ozero__class_Ozero(_941013), -(c_Groups_Ozero__class_Ozero(_941013) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941013), _941015), _941015))]]], (9645 ^ _779300) ^ [_941254, _941256] : [class_Groups_Ozero(_941254), 9648 ^ _779300 : [(9649 ^ _779300) ^ [] : [c_Groups_Ozero__class_Ozero(_941254) = _941256, -(_941256 = c_Groups_Ozero__class_Ozero(_941254))], (9655 ^ _779300) ^ [] : [_941256 = c_Groups_Ozero__class_Ozero(_941254), -(c_Groups_Ozero__class_Ozero(_941254) = _941256)]]], (9661 ^ _779300) ^ [_941471, _941473] : [class_Groups_Ocomm__monoid__add(_941471), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941471), c_Groups_Ozero__class_Ozero(_941471)), _941473) = _941473)], (9667 ^ _779300) ^ [_941566, _941568] : [class_Groups_Omonoid__add(_941566), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941566), c_Groups_Ozero__class_Ozero(_941566)), _941568) = _941568)], (9673 ^ _779300) ^ [_941661, _941663] : [class_Groups_Olinordered__ab__group__add(_941661), 9676 ^ _779300 : [(9677 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941661), c_Groups_Ozero__class_Ozero(_941661)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941661), _941663), _941663))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941661), c_Groups_Ozero__class_Ozero(_941661)), _941663)))], (9683 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941661), c_Groups_Ozero__class_Ozero(_941661)), _941663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941661), c_Groups_Ozero__class_Ozero(_941661)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941661), _941663), _941663))))]]], (9689 ^ _779300) ^ [_941944, _941946] : [class_Groups_Olinordered__ab__group__add(_941944), 9692 ^ _779300 : [(9693 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941944), _941946), _941946)), c_Groups_Ozero__class_Ozero(_941944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941944), _941946), c_Groups_Ozero__class_Ozero(_941944))))], (9699 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941944), _941946), c_Groups_Ozero__class_Ozero(_941944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941944), _941946), _941946)), c_Groups_Ozero__class_Ozero(_941944))))]]], (9705 ^ _779300) ^ [_942227, _942229, _942231] : [class_Groups_Oordered__comm__monoid__add(_942227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942227), c_Groups_Ozero__class_Ozero(_942227)), _942229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942227), c_Groups_Ozero__class_Ozero(_942227)), _942231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942227), c_Groups_Ozero__class_Ozero(_942227)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942227), _942229), _942231))))], (9719 ^ _779300) ^ [_942482, _942484, _942486] : [class_Groups_Oordered__comm__monoid__add(_942482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942482), c_Groups_Ozero__class_Ozero(_942482)), _942484)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942482), c_Groups_Ozero__class_Ozero(_942482)), _942486)), 9730 ^ _779300 : [(9731 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942482), _942484), _942486) = c_Groups_Ozero__class_Ozero(_942482), 9734 ^ _779300 : [(9735 ^ _779300) ^ [] : [-(_942484 = c_Groups_Ozero__class_Ozero(_942482))], (9737 ^ _779300) ^ [] : [-(_942486 = c_Groups_Ozero__class_Ozero(_942482))]]], (9739 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942482), _942484), _942486) = c_Groups_Ozero__class_Ozero(_942482)), _942484 = c_Groups_Ozero__class_Ozero(_942482), _942486 = c_Groups_Ozero__class_Ozero(_942482)]]], (9749 ^ _779300) ^ [_942953, _942955, _942957, _942959] : [class_Groups_Oordered__comm__monoid__add(_942953), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942953), c_Groups_Ozero__class_Ozero(_942953)), _942955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942953), _942957), _942959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942953), _942957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942953), _942955), _942959))))], (9763 ^ _779300) ^ [_943206, _943208, _943210, _943212] : [class_Groups_Oordered__comm__monoid__add(_943206), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943206), c_Groups_Ozero__class_Ozero(_943206)), _943208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943206), _943210), _943212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943206), _943210), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943206), _943212), _943208))))], (9777 ^ _779300) ^ [_943459, _943461, _943463] : [class_Groups_Oordered__comm__monoid__add(_943459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943459), _943461), c_Groups_Ozero__class_Ozero(_943459))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943459), _943463), c_Groups_Ozero__class_Ozero(_943459))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943459), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943459), _943461), _943463)), c_Groups_Ozero__class_Ozero(_943459))))], (9791 ^ _779300) ^ [_943714, _943716, _943718] : [class_Groups_Oordered__comm__monoid__add(_943714), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943714), _943716), c_Groups_Ozero__class_Ozero(_943714))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943714), _943718), c_Groups_Ozero__class_Ozero(_943714))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943714), _943716), _943718)), c_Groups_Ozero__class_Ozero(_943714))))], (9805 ^ _779300) ^ [_943969, _943971, _943973] : [class_Groups_Oordered__comm__monoid__add(_943969), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943969), c_Groups_Ozero__class_Ozero(_943969)), _943971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943969), c_Groups_Ozero__class_Ozero(_943969)), _943973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943969), c_Groups_Ozero__class_Ozero(_943969)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943969), _943971), _943973))))], (9819 ^ _779300) ^ [_944224, _944226] : [class_Groups_Olinordered__ab__group__add(_944224), 9822 ^ _779300 : [(9823 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944224), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944224), _944226), _944226)), c_Groups_Ozero__class_Ozero(_944224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944224), _944226), c_Groups_Ozero__class_Ozero(_944224))))], (9829 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944224), _944226), c_Groups_Ozero__class_Ozero(_944224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944224), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944224), _944226), _944226)), c_Groups_Ozero__class_Ozero(_944224))))]]], (9835 ^ _779300) ^ [_944507, _944509] : [class_Groups_Olinordered__ab__group__add(_944507), 9838 ^ _779300 : [(9839 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944507), c_Groups_Ozero__class_Ozero(_944507)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944507), _944509), _944509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944507), c_Groups_Ozero__class_Ozero(_944507)), _944509)))], (9845 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944507), c_Groups_Ozero__class_Ozero(_944507)), _944509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944507), c_Groups_Ozero__class_Ozero(_944507)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944507), _944509), _944509))))]]], (9851 ^ _779300) ^ [_944805, _944807] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _944805), _944807) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9856 ^ _779300 : [(9857 ^ _779300) ^ [] : [-(_944805 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9859 ^ _779300) ^ [] : [-(_944807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 9860 ^ _779300 : [(9861 ^ _779300) ^ [] : [-(_944805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9863 ^ _779300) ^ [] : [-(_944807 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (9865 ^ _779300) ^ [_944989, _944991] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _944989), _944991) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 9866 ^ _779300 : [(9867 ^ _779300) ^ [] : [_944989 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _944991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9873 ^ _779300) ^ [] : [_944989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _944991 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9881 ^ _779300) ^ [_945230, _945232] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945230), _945232), 9886 ^ _779300 : [(9887 ^ _779300) ^ [] : [-(_945230 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9889 ^ _779300) ^ [] : [-(_945232 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 9890 ^ _779300 : [(9891 ^ _779300) ^ [] : [-(_945230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9893 ^ _779300) ^ [] : [-(_945232 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (9895 ^ _779300) ^ [_945414, _945416] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945414), _945416)), 9896 ^ _779300 : [(9897 ^ _779300) ^ [] : [_945414 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _945416 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9903 ^ _779300) ^ [] : [_945414 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _945416 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9921 ^ _779300) ^ [_945765, _945767] : [9922 ^ _779300 : [(9923 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _945765))], (9925 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _945767))]], -(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), _945765), _945767))))], (9911 ^ _779300) ^ [_945655, _945657] : [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), _945655), _945657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _945655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _945657)))], (9929 ^ _779300) ^ [_945906, _945908] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945906), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945906), _945908)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9931 ^ _779300) ^ [_945943, _945945] : [-(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)), _945943), _945945))], (9933 ^ _779300) ^ [_945973, _945975, _945977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945973), _945975)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945973), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _945975), _945977))))], (9939 ^ _779300) ^ [_946084, _946086, _946088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _946084), _946086)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _946084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _946088), _946086))))], (9945 ^ _779300) ^ [_946195, _946197, _946199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946195), _946197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946195), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _946199), _946197))))], (9951 ^ _779300) ^ [_946306, _946308, _946310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946306), _946308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946306), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _946308), _946310))))], (9957 ^ _779300) ^ [_946417, _946419, _946421] : [class_Groups_Oordered__comm__monoid__add(_946417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946417), _946419), c_Groups_Ozero__class_Ozero(_946417))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946417), _946421), c_Groups_Ozero__class_Ozero(_946417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946417), _946419), _946421)), c_Groups_Ozero__class_Ozero(_946417))))], (9971 ^ _779300) ^ [_946672, _946674, _946676] : [class_Groups_Oordered__comm__monoid__add(_946672), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946672), _946674), c_Groups_Ozero__class_Ozero(_946672))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946672), _946676), c_Groups_Ozero__class_Ozero(_946672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946672), _946674), _946676)), c_Groups_Ozero__class_Ozero(_946672))))], (9985 ^ _779300) ^ [_946927, _946929, _946931, _946933] : [class_Groups_Oordered__comm__monoid__add(_946927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946927), c_Groups_Ozero__class_Ozero(_946927)), _946929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946927), _946931), _946933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946927), _946931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946927), _946929), _946933))))], (9999 ^ _779300) ^ [_947180, _947182, _947184, _947186] : [class_Groups_Oordered__comm__monoid__add(_947180), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947180), c_Groups_Ozero__class_Ozero(_947180)), _947182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947180), _947184), _947186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947180), _947184), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947180), _947182), _947186))))], (10013 ^ _779300) ^ [_947433, _947435, _947437] : [class_Groups_Oordered__comm__monoid__add(_947433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947433), c_Groups_Ozero__class_Ozero(_947433)), _947435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947433), c_Groups_Ozero__class_Ozero(_947433)), _947437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947433), c_Groups_Ozero__class_Ozero(_947433)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947433), _947435), _947437))))], (10027 ^ _779300) ^ [_947688, _947690, _947692] : [class_Groups_Oordered__comm__monoid__add(_947688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947688), c_Groups_Ozero__class_Ozero(_947688)), _947690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947688), c_Groups_Ozero__class_Ozero(_947688)), _947692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947688), c_Groups_Ozero__class_Ozero(_947688)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947688), _947690), _947692))))], (10057 ^ _779300) ^ [_948253, _948255, _948257] : [-(hBOOL(hAPP(_948253, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948255), _948257)))), 10060 ^ _779300 : [(10061 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948255), _948257)))], (10063 ^ _779300) ^ [] : [hBOOL(hAPP(_948253, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10065 ^ _779300 : [(10066 ^ _779300) ^ [] : [-(_948255 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _948257), 10064 ^ [_948253, _948255, _948257]))], (10068 ^ _779300) ^ [] : [hBOOL(hAPP(_948253, 10064 ^ [_948253, _948255, _948257]))]]], (10041 ^ _779300) ^ [_947961, _947963, _947965] : [hBOOL(hAPP(_947961, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947963), _947965))), 10044 ^ _779300 : [(10045 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947963), _947965)), -(hBOOL(hAPP(_947961, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10051 ^ _779300) ^ [_948152] : [_947963 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947965), _948152), -(hBOOL(hAPP(_947961, _948152)))]]], (10088 ^ _779300) ^ [_948848, _948850, _948852] : [-(hBOOL(hAPP(_948848, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948850), _948852)))), 10091 ^ _779300 : [(10092 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948850), _948852)))], (10094 ^ _779300) ^ [] : [hBOOL(hAPP(_948848, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10096 ^ _779300 : [(10097 ^ _779300) ^ [] : [-(_948850 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _948852), 10095 ^ [_948848, _948850, _948852]))], (10099 ^ _779300) ^ [] : [hBOOL(hAPP(_948848, 10095 ^ [_948848, _948850, _948852]))]]], (10072 ^ _779300) ^ [_948564, _948566, _948568] : [hBOOL(hAPP(_948564, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948566), _948568))), 10075 ^ _779300 : [(10076 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948566), _948568)), -(hBOOL(hAPP(_948564, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10082 ^ _779300) ^ [_948749] : [_948566 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _948568), _948749), -(hBOOL(hAPP(_948564, _948749)))]]], (10103 ^ _779300) ^ [_949133, _949135, _949137, _949139] : [-(c_Nitpick_Ofold__graph_H(_949133, _949135, _949137, _949139, c_Orderings_Obot__class_Obot(tc_fun(_949133, tc_HOL_Obool)), _949139))], (10105 ^ _779300) ^ [_949171, _949173, _949175, _949177] : [-(c_Nitpick_Ofold__graph_H(_949171, _949173, _949175, _949177, c_Orderings_Obot__class_Obot(tc_fun(_949171, tc_HOL_Obool)), _949177))], (10107 ^ _779300) ^ [_949209, _949211, _949213, _949215] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_949209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949209), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949209), _949211), _949213)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949209), _949211), _949215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949209), _949213), _949215)))], (10117 ^ _779300) ^ [_949404, _949406, _949408, _949410] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_949404), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949404), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949404), _949406), _949408)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949404), _949410), _949408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949404), _949406), _949410)))], (10127 ^ _779300) ^ [_949599, _949601, _949603, _949605, _949607] : [class_Groups_Oordered__ab__semigroup__add(_949599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949599), _949601), _949603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949599), _949605), _949607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949599), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949599), _949601), _949605)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949599), _949603), _949607))))], (10141 ^ _779300) ^ [_949870, _949872, _949874, _949876] : [class_Groups_Oordered__ab__semigroup__add(_949870), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949870), _949872), _949874)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949870), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949870), _949876), _949872)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949870), _949876), _949874))))], (10151 ^ _779300) ^ [_950065, _950067, _950069, _950071] : [class_Groups_Oordered__ab__semigroup__add(_950065), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950065), _950067), _950069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950065), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950065), _950067), _950071)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950065), _950069), _950071))))], (10161 ^ _779300) ^ [_950260, _950262, _950264, _950266] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_950260), 10164 ^ _779300 : [(10165 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950260), _950262), _950264)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950260), _950262), _950266))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950260), _950264), _950266)))], (10171 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950260), _950264), _950266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950260), _950262), _950264)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950260), _950262), _950266))))]]], (10177 ^ _779300) ^ [_950567, _950569, _950571, _950573] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_950567), 10180 ^ _779300 : [(10181 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950567), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950567), _950569), _950571)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950567), _950573), _950571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950567), _950569), _950573)))], (10187 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950567), _950569), _950573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950567), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950567), _950569), _950571)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950567), _950573), _950571))))]]], (10193 ^ _779300) ^ [_950874, _950876, _950878, _950880] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_950874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950874), _950876), _950878)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950874), _950876), _950880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950874), _950878), _950880)))], (10203 ^ _779300) ^ [_951069, _951071, _951073, _951075] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_951069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951069), _951071), _951073)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951069), _951075), _951073))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951069), _951071), _951075)))], (10213 ^ _779300) ^ [_951264, _951266, _951268, _951270, _951272] : [class_Groups_Oordered__cancel__ab__semigroup__add(_951264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951264), _951266), _951268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951264), _951270), _951272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951264), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951264), _951266), _951270)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951264), _951268), _951272))))], (10227 ^ _779300) ^ [_951535, _951537, _951539, _951541] : [class_Groups_Oordered__cancel__ab__semigroup__add(_951535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951535), _951537), _951539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951535), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951535), _951541), _951537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951535), _951541), _951539))))], (10237 ^ _779300) ^ [_951730, _951732, _951734, _951736] : [class_Groups_Oordered__cancel__ab__semigroup__add(_951730), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951730), _951732), _951734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951730), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951730), _951732), _951736)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951730), _951734), _951736))))], (10247 ^ _779300) ^ [_951925, _951927, _951929, _951931] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_951925), 10250 ^ _779300 : [(10251 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951925), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951925), _951927), _951929)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951925), _951927), _951931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951925), _951929), _951931)))], (10257 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951925), _951929), _951931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951925), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951925), _951927), _951929)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951925), _951927), _951931))))]]], (10263 ^ _779300) ^ [_952232, _952234, _952236, _952238] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_952232), 10266 ^ _779300 : [(10267 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952232), _952234), _952236)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952232), _952238), _952236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952232), _952234), _952238)))], (10273 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952232), _952234), _952238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952232), _952234), _952236)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952232), _952238), _952236))))]]], (10279 ^ _779300) ^ [_952539, _952541, _952543] : [class_Groups_Ogroup__add(_952539), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952539), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_952539), _952541), _952543)), _952543) = _952541)], (10285 ^ _779300) ^ [_952648, _952650, _952652] : [class_Groups_Ogroup__add(_952648), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_952648), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952648), _952650), _952652)), _952652) = _952650)], (10291 ^ _779300) ^ [_952757, _952759] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952757), hAPP(c_Nat_OSuc, _952759)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952757), _952759)))], (10293 ^ _779300) ^ [_952800, _952802] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _952800)), _952802) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952800), _952802)))], (10295 ^ _779300) ^ [_952843, _952845] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _952843)), _952845) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952843), hAPP(c_Nat_OSuc, _952845)))], (10297 ^ _779300) ^ [_952898, _952900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952898), _952900)), _952898))], (10299 ^ _779300) ^ [_952946, _952948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952946), _952948)), _952948))], (10301 ^ _779300) ^ [_953000, _953002, _953004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953000), _953002)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953000), _953004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953002), _953004)))], (10307 ^ _779300) ^ [_953119, _953121, _953123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953121), _953123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953119), _953121)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953119), _953123))))], (10313 ^ _779300) ^ [_953244, _953246, _953248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953244), _953246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953246), _953248))))], (10319 ^ _779300) ^ [_953355, _953357, _953359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953355), _953357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953355), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953359), _953357))))], (10325 ^ _779300) ^ [_953466, _953468, _953470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953466), _953468)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953466), _953470)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953468), _953470))))], (10331 ^ _779300) ^ [_953589, _953591, _953593, _953595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953589), _953591)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953593), _953595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953589), _953593)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953591), _953595))))], (10341 ^ _779300) ^ [_953780, _953782, _953784, _953786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953780), _953782)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953784), _953782) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953780), _953786), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953784), _953786)))], (10351 ^ _779300) ^ [_953961, _953963, _953965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953961), _953963)), _953965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _953961), _953965)))], (10357 ^ _779300) ^ [_954072, _954074, _954076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954072), _954074)), _954076)), 10360 ^ _779300 : [(10361 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954072), _954076)))], (10363 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954074), _954076)))]]], (10365 ^ _779300) ^ [_954223, _954225, _954227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954223), _954225)), _954227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954223), _954227)))], (10371 ^ _779300) ^ [_954334, _954336, _954338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954334), _954336)), _954338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954336), _954338)))], (10377 ^ _779300) ^ [_954445, _954447, _954449, _954451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954445), _954447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954449), _954451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954445), _954449)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954447), _954451))))], (10387 ^ _779300) ^ [_954636, _954638, _954640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954636), _954638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954636), _954640)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954638), _954640))))], (10393 ^ _779300) ^ [_954759, _954761, _954763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954759), _954761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954759), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954763), _954761))))], (10399 ^ _779300) ^ [_954870, _954872, _954874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954870), _954872)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954870), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954872), _954874))))], (10405 ^ _779300) ^ [_954999, _955001, _955003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954999), _955001)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954999), _955003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955001), _955003)))], (10411 ^ _779300) ^ [_955118, _955120, _955122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955120), _955122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955118), _955120)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955118), _955122))))], (10417 ^ _779300) ^ [_955258, _955260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955258), _955260)), -(_955260 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955258), 10420 ^ [_955258, _955260]))], (10424 ^ _779300) ^ [_955365, _955367] : [10425 ^ _779300 : [(10426 ^ _779300) ^ [_955415] : [_955367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955365), _955415)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955365), _955367)))], (10430 ^ _779300) ^ [_955479, _955481] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955479), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955479), _955481))))], (10432 ^ _779300) ^ [_955515, _955517] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955515), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955517), _955515))))], (10434 ^ _779300) ^ [_955551, _955553] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955551), _955553)), _955553) = _955551)], (10436 ^ _779300) ^ [_955588, _955590] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955588), _955590)), _955588) = _955590)], (10438 ^ _779300) ^ [_955625, _955627, _955629] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _955625), _955627)), _955629) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _955625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955627), _955629)))], (10440 ^ _779300) ^ [_955676, _955678, _955680] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955676), _955678)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955676), _955680)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _955678), _955680))], (10442 ^ _779300) ^ [_955727, _955729, _955731] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955727), _955729)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955731), _955729)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _955727), _955731))], (10444 ^ _779300) ^ [_955778, _955780] : [class_Groups_Ogroup__add(_955778), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_955778), _955780), c_Groups_Ozero__class_Ozero(_955778)) = _955780)], (10450 ^ _779300) ^ [_955873, _955875] : [class_Groups_Ogroup__add(_955873), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_955873), _955875), _955875) = c_Groups_Ozero__class_Ozero(_955873))], (10456 ^ _779300) ^ [_955968, _955970, _955972] : [class_Groups_Oab__group__add(_955968), 10459 ^ _779300 : [(10460 ^ _779300) ^ [] : [_955970 = _955972, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_955968), _955970), _955972) = c_Groups_Ozero__class_Ozero(_955968))], (10466 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_955968), _955970), _955972) = c_Groups_Ozero__class_Ozero(_955968), -(_955970 = _955972)]]], (10472 ^ _779300) ^ [_956209, _956211, _956213] : [class_Groups_Ogroup__add(_956209), 10475 ^ _779300 : [(10476 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_956209), _956211), _956213) = c_Groups_Ozero__class_Ozero(_956209), -(_956211 = _956213)], (10482 ^ _779300) ^ [] : [_956211 = _956213, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_956209), _956211), _956213) = c_Groups_Ozero__class_Ozero(_956209))]]], (10488 ^ _779300) ^ [_956459] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _956459)], (10490 ^ _779300) ^ [_956494] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _956494)], (10492 ^ _779300) ^ [_956529] : [hAPP(c_Nat_OSuc, _956529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10494 ^ _779300) ^ [_956564] : [hAPP(c_Nat_OSuc, _956564) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10496 ^ _779300) ^ [_956599] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _956599)], (10498 ^ _779300) ^ [_956634] : [hAPP(c_Nat_OSuc, _956634) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10500 ^ _779300) ^ [_956669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956669), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10502 ^ _779300) ^ [_956703] : [-(_956703 = 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)), _956703)))], (10508 ^ _779300) ^ [_956735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _956735)), _956735 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10514 ^ _779300) ^ [_956826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956826), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10516 ^ _779300) ^ [_956854, _956856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956854), _956856)), _956856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10522 ^ _779300) ^ [_956938] : [-(_956938 = 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)), _956938)))], (10528 ^ _779300) ^ [_956986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956986), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_956986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10534 ^ _779300) ^ [_957067] : [_957067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957067), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10540 ^ _779300) ^ [_957154] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957154)))], (10542 ^ _779300) ^ [_957179] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957179) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10544 ^ _779300) ^ [_957205] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957205), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _957205)], (10546 ^ _779300) ^ [_957234] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957234), _957234) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10548 ^ _779300) ^ [_957263, _957265] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957263), _957265) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957265), _957263) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_957263 = _957265)], (10558 ^ _779300) ^ [_957416, _957418, _957420, _957422, _957424] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_957416, _957418, _957420, _957422, c_Orderings_Obot__class_Obot(tc_fun(_957416, tc_HOL_Obool))), _957424)), -(_957424 = _957422)], (10564 ^ _779300) ^ [_957525, _957527, _957529, _957531] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_957525, _957527, _957529, _957531, c_Orderings_Obot__class_Obot(tc_fun(_957525, tc_HOL_Obool))), _957531)))], (10566 ^ _779300) ^ [_957567, _957569, _957571, _957573] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_957567, _957569, _957571, _957573, c_Orderings_Obot__class_Obot(tc_fun(_957567, tc_HOL_Obool))), _957573)))], (10568 ^ _779300) ^ [_957609, _957611, _957613, _957615, _957617, _957619] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_957609, _957611, _957613, _957615, _957617), _957619)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_957609), _957617)))], (10574 ^ _779300) ^ [_957727, _957729] : [_957727 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957727), _957729) = _957729)], (10580 ^ _779300) ^ [_957810, _957812] : [-(_957810 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957810), _957812) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957810), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _957812)))], (10586 ^ _779300) ^ [_957869, _957871, _957873, _957875, _957877] : [class_Groups_Oordered__cancel__ab__semigroup__add(_957869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957869), _957871), _957873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957869), _957875), _957877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957869), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957869), _957871), _957875)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957869), _957873), _957877))))], (10600 ^ _779300) ^ [_958140, _958142, _958144, _958146, _958148] : [class_Groups_Oordered__cancel__ab__semigroup__add(_958140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958140), _958142), _958144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958140), _958146), _958148)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958140), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958140), _958142), _958146)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958140), _958144), _958148))))], (10614 ^ _779300) ^ [_958411, _958413] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958411), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958411), _958413)))))], (10616 ^ _779300) ^ [_958450, _958452] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958450), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958452), _958450)))))], (10618 ^ _779300) ^ [_958504, _958506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958504), _958506)), -(_958506 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958504), 10621 ^ [_958504, _958506])))], (10625 ^ _779300) ^ [_958617, _958619] : [10626 ^ _779300 : [(10627 ^ _779300) ^ [_958670] : [_958619 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958617), _958670))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958617), _958619)))], (10631 ^ _779300) ^ [_958755, _958757, _958759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958755), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _958757), _958759))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958755), _958759)), _958757)))], (10637 ^ _779300) ^ [_958874, _958876, _958878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958874), _958878)), _958876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958874), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _958876), _958878))))], (10643 ^ _779300) ^ [_958995, _958997] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958995), _958997))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958997), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _958995), _958997)) = _958995)], (10649 ^ _779300) ^ [_959048, _959050, _959052] : [class_Groups_Oordered__ab__group__add(_959048), 10652 ^ _779300 : [(10653 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959048), _959050), _959052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959048), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959048), _959050), _959052)), c_Groups_Ozero__class_Ozero(_959048))))], (10659 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959048), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959048), _959050), _959052)), c_Groups_Ozero__class_Ozero(_959048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959048), _959050), _959052)))]]], (10665 ^ _779300) ^ [_959331, _959333, _959335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959331), _959333)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959333), _959335)), _959331) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959333), _959331)), _959335))], (10671 ^ _779300) ^ [_959468, _959470, _959472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959468), _959470)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959470), _959468)), _959472) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959470), _959472)), _959468))], (10677 ^ _779300) ^ [_959605, _959607, _959609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959605), _959607)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959609), _959607)), _959605) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959609), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959607), _959605)))], (10683 ^ _779300) ^ [_959742, _959744, _959746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _959742), _959744)), 10686 ^ _779300 : [(10687 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959744), _959742) = _959746, -(_959744 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959746), _959742))], (10693 ^ _779300) ^ [] : [_959744 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _959746), _959742), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _959744), _959742) = _959746)]]], (10699 ^ _779300) ^ [_960001, _960003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960001), _960003)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _960003), _960001)), _960001) = _960003)], (10705 ^ _779300) ^ [_960112, _960114, _960116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960112), _960114)), 10708 ^ _779300 : [(10709 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960116), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _960114), _960112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _960116), _960112)), _960114)))], (10715 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _960116), _960112)), _960114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960116), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _960114), _960112))))]]], (10721 ^ _779300) ^ [_960401, _960403, _960405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960401), _960403)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _960405), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _960403), _960401)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _960405), _960403)), _960401))], (10727 ^ _779300) ^ [_960538, _960540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960538), _960540)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _960538), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _960540), _960538)) = _960540)], (10733 ^ _779300) ^ [_960649, _960651, _960653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960649), _960651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960653), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _960651), _960653)), _960649))))], (10739 ^ _779300) ^ [_960790, _960792, _960794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _960790), _960792)), _960794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _960794), _960792))))], (10745 ^ _779300) ^ [_960909, _960911, _960913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960909), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _960913), _960911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _960909), _960911)), _960913)))], (10751 ^ _779300) ^ [_961034, _961036, _961038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961034), _961036)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _961038), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _961036), _961034)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961038), _961034)), _961036))], (10757 ^ _779300) ^ [_961171, _961173, _961175] : [class_Groups_Oordered__ab__group__add(_961171), 10760 ^ _779300 : [(10761 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961171), _961173), _961175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961171), _961173), _961175)), c_Groups_Ozero__class_Ozero(_961171))))], (10767 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961171), _961173), _961175)), c_Groups_Ozero__class_Ozero(_961171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961171), _961173), _961175)))]]], (10773 ^ _779300) ^ [_961454] : [-(hAPP(c_Nat_OSuc, _961454) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _961454))], (10775 ^ _779300) ^ [_961483] : [-(hAPP(c_Nat_OSuc, _961483) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961483), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10777 ^ _779300) ^ [_961527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961527)), -(_961527 = hAPP(c_Nat_OSuc, 10780 ^ [_961527]))], (10784 ^ _779300) ^ [_961618] : [10785 ^ _779300 : [(10786 ^ _779300) ^ [_961660] : [_961618 = hAPP(c_Nat_OSuc, _961660)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961618)))], (10790 ^ _779300) ^ [_961730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961730), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_961730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10796 ^ _779300) ^ [_961811] : [_961811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961811), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (10802 ^ _779300) ^ [_961913, _961915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _961913), hAPP(c_Nat_OSuc, _961915))), -(_961913 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10810 ^ _779300 : [(10811 ^ _779300) ^ [] : [-(_961913 = hAPP(c_Nat_OSuc, 10809 ^ [_961913, _961915]))], (10813 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 10809 ^ [_961913, _961915]), _961915)))]]], (10815 ^ _779300) ^ [_962093, _962095] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962093), hAPP(c_Nat_OSuc, _962095)))), 10816 ^ _779300 : [(10817 ^ _779300) ^ [] : [_962093 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10819 ^ _779300) ^ [_962181] : [_962093 = hAPP(c_Nat_OSuc, _962181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962181), _962095))]]], (10827 ^ _779300) ^ [_962315] : [-(hAPP(c_Finite__Set_Ocard(_962315), c_Orderings_Obot__class_Obot(tc_fun(_962315, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10829 ^ _779300) ^ [_962344, _962346] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_962344), _962346))), -(hAPP(c_Finite__Set_Ocard(_962344), _962346) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10835 ^ _779300) ^ [_962404, _962406] : [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), _962404), _962406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962406), _962404)))], (10841 ^ _779300) ^ [_962503, _962505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962505), _962503)), -(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), _962503), _962505))))], (10847 ^ _779300) ^ [_962608, _962610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962610), _962608)), _962610)))], (10857 ^ _779300) ^ [_962767, _962769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962767), _962769)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962767), _962769) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10863 ^ _779300) ^ [_962881, _962883] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962881), _962883) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962881), _962883)))], (10869 ^ _779300) ^ [_962976, _962978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962976), _962978)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962976), _962978) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10875 ^ _779300) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10877 ^ _779300) ^ [_963094, _963096, _963098, _963100, _963102, _963104, _963106] : [-(hBOOL(hAPP(hAPP(c_member(_963094), _963096), _963098))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_963094, _963100, _963102, _963104, _963098), _963106)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_963094, _963100, _963102, _963104, hAPP(hAPP(c_Set_Oinsert(_963094), _963096), _963098)), hAPP(hAPP(_963102, _963096), _963106))))], (10887 ^ _779300) ^ [_963308, _963310, _963312, _963314] : [-(c_Nat_Onat_Onat__case(_963308, _963310, _963312, hAPP(c_Nat_OSuc, _963314)) = hAPP(_963312, _963314))], (10889 ^ _779300) ^ [_963348, _963350, _963352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963348), _963350)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963352), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963350), _963348))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963352), _963348)), hAPP(c_Nat_OSuc, _963350)))], (10895 ^ _779300) ^ [_963497, _963499, _963501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963497), _963499)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963499), _963497))), _963501) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963499)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963497), _963501)))], (10911 ^ _779300) ^ [_963816, _963818] : [10912 ^ _779300 : [(10913 ^ _779300) ^ [] : [_963818 = c_Orderings_Obot__class_Obot(tc_fun(_963816, tc_HOL_Obool))], (10915 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_963816), _963818)))]], -(hAPP(c_Finite__Set_Ocard(_963816), _963818) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10901 ^ _779300) ^ [_963661, _963663] : [hAPP(c_Finite__Set_Ocard(_963661), _963663) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_963663 = c_Orderings_Obot__class_Obot(tc_fun(_963661, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_963661), _963663))], (10919 ^ _779300) ^ [_963960, _963962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_963960), _963962))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_963960), _963962)))], (10925 ^ _779300) ^ [_964059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _964059)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964059), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _964059)], (10931 ^ _779300) ^ [_964156, _964158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _964156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964156), hAPP(c_Nat_OSuc, _964158))), _964156)))], (10937 ^ _779300) ^ [_964280, _964282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_964280), _964282))), 10940 ^ _779300 : [(10941 ^ _779300) ^ [] : [_964282 = c_Orderings_Obot__class_Obot(tc_fun(_964280, tc_HOL_Obool))], (10943 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_964280), _964282)))]]], (10945 ^ _779300) ^ [_964421, _964423] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_964421), _964423)))), -(_964423 = c_Orderings_Obot__class_Obot(tc_fun(_964421, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_964421), _964423))], (10955 ^ _779300) ^ [_964587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _964587)), -(_964587 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964587), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (10961 ^ _779300) ^ [_964684] : [class_Rings_Olinordered__semidom(_964684), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964684), c_Groups_Ozero__class_Ozero(_964684)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964684), c_Groups_Oone__class_Oone(_964684)), c_Groups_Oone__class_Oone(_964684)))))], (10967 ^ _779300) ^ [_964799, _964801] : [class_Rings_Olinordered__semidom(_964799), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964799), _964801), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964799), _964801), c_Groups_Oone__class_Oone(_964799)))))], (10973 ^ _779300) ^ [_964908] : [class_Rings_Olinordered__semidom(_964908), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964908), c_Groups_Oone__class_Oone(_964908)), c_Groups_Ozero__class_Ozero(_964908)))], (10979 ^ _779300) ^ [_965004] : [class_Rings_Olinordered__semidom(_965004), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965004), c_Groups_Ozero__class_Ozero(_965004)), c_Groups_Oone__class_Oone(_965004))))], (10985 ^ _779300) ^ [_965099] : [class_Rings_Olinordered__semidom(_965099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965099), c_Groups_Oone__class_Oone(_965099)), c_Groups_Ozero__class_Ozero(_965099)))], (10991 ^ _779300) ^ [_965195] : [class_Rings_Olinordered__semidom(_965195), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965195), c_Groups_Ozero__class_Ozero(_965195)), c_Groups_Oone__class_Oone(_965195))))], (10997 ^ _779300) ^ [_965290, _965292] : [class_Rings_Olinordered__idom(_965290), 11000 ^ _779300 : [(11001 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965290), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965290), _965292), _965292)), c_Groups_Ozero__class_Ozero(_965290))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965290), _965292), c_Groups_Ozero__class_Ozero(_965290))))], (11007 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965290), _965292), c_Groups_Ozero__class_Ozero(_965290))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965290), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965290), _965292), _965292)), c_Groups_Ozero__class_Ozero(_965290))))]]], (11013 ^ _779300) ^ [_965573, _965575, _965577, _965579] : [class_Rings_Olinordered__semidom(_965573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965573), c_Groups_Ozero__class_Ozero(_965573)), _965575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965573), _965577), _965579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965573), _965577), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965573), _965575), _965579))))], (11027 ^ _779300) ^ [_965826, _965828, _965830, _965832, _965834] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_965826, _965826, _965828, _965830, _965832), _965834)), -(hBOOL(hAPP(hAPP(c_member(_965826), _965830), _965832))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_965826, _965828, hAPP(hAPP(c_Set_Oinsert(_965826), _965830), _965832)), _965834)))], (11037 ^ _779300) ^ [_966000, _966002, _966004] : [hAPP(c_Finite__Set_Ocard(_966000), _966002) = hAPP(c_Nat_OSuc, _966004), 11042 ^ _779300 : [(11043 ^ _779300) ^ [] : [-(_966002 = hAPP(hAPP(c_Set_Oinsert(_966000), 11040 ^ [_966000, _966002, _966004]), 11041 ^ [_966000, _966002, _966004]))], (11045 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_966000), 11040 ^ [_966000, _966002, _966004]), 11041 ^ [_966000, _966002, _966004]))], (11047 ^ _779300) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_966000), 11041 ^ [_966000, _966002, _966004]) = _966004)], (11049 ^ _779300) ^ [] : [_966004 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(11041 ^ [_966000, _966002, _966004] = c_Orderings_Obot__class_Obot(tc_fun(_966000, tc_HOL_Obool)))]]], (11055 ^ _779300) ^ [_966418, _966420, _966422] : [-(hAPP(c_Finite__Set_Ocard(_966418), _966420) = hAPP(c_Nat_OSuc, _966422)), 11056 ^ _779300 : [(11057 ^ _779300) ^ [_966518, _966520] : [_966420 = hAPP(hAPP(c_Set_Oinsert(_966418), _966520), _966518), -(hBOOL(hAPP(hAPP(c_member(_966418), _966520), _966518))), hAPP(c_Finite__Set_Ocard(_966418), _966518) = _966422, 11068 ^ _779300 : [(11069 ^ _779300) ^ [] : [-(_966422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11071 ^ _779300) ^ [] : [_966518 = c_Orderings_Obot__class_Obot(tc_fun(_966418, tc_HOL_Obool))]]]]], (11075 ^ _779300) ^ [_966855, _966857, _966859] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_966855, _966857, c_Orderings_Obot__class_Obot(tc_fun(_966855, tc_HOL_Obool))), _966859))], (11077 ^ _779300) ^ [_966893, _966895, _966897, _966899] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_966893, _966895, _966897), _966899)), _966897 = c_Orderings_Obot__class_Obot(tc_fun(_966893, tc_HOL_Obool))], (11083 ^ _779300) ^ [_966997, _966999, _967001] : [class_Rings_Olinordered__idom(_966997), -(_966999 = _967001), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966997), _966999), _967001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966997), _967001), _966999)))], (11097 ^ _779300) ^ [_967153, _967155, _967157, _967159] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_967153, _967155, hAPP(hAPP(c_Set_Oinsert(_967153), _967157), c_Orderings_Obot__class_Obot(tc_fun(_967153, tc_HOL_Obool)))), _967159)), -(_967157 = _967159)], (11103 ^ _779300) ^ [_967268, _967270, _967272, _967274] : [_967272 = _967274, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_967268, _967270, hAPP(hAPP(c_Set_Oinsert(_967268), _967272), c_Orderings_Obot__class_Obot(tc_fun(_967268, tc_HOL_Obool)))), _967274)))], (11109 ^ _779300) ^ [_967389, _967391] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967389), hAPP(c_Nat_OSuc, _967391)) = 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), _967389), _967391)))], (11111 ^ _779300) ^ [_967434, _967436] : [class_Groups_Olinordered__ab__group__add(_967434), 11114 ^ _779300 : [(11115 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967434), _967436), _967436) = c_Groups_Ozero__class_Ozero(_967434), -(_967436 = c_Groups_Ozero__class_Ozero(_967434))], (11121 ^ _779300) ^ [] : [_967436 = c_Groups_Ozero__class_Ozero(_967434), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967434), _967436), _967436) = c_Groups_Ozero__class_Ozero(_967434))]]], (11127 ^ _779300) ^ [_967675] : [class_Rings_Ozero__neq__one(_967675), c_Groups_Ozero__class_Ozero(_967675) = c_Groups_Oone__class_Oone(_967675)], (11133 ^ _779300) ^ [_967757] : [class_Rings_Ozero__neq__one(_967757), c_Groups_Oone__class_Oone(_967757) = c_Groups_Ozero__class_Ozero(_967757)], (11139 ^ _779300) ^ [_967839, _967841] : [class_Rings_Olinordered__idom(_967839), hBOOL(hAPP(hAPP(c_member(_967839), _967841), c_Int_Oring__1__class_OInts(_967839))), 11146 ^ _779300 : [(11147 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967839), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967839), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967839), c_Groups_Oone__class_Oone(_967839)), _967841)), _967841)), c_Groups_Ozero__class_Ozero(_967839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967839), _967841), c_Groups_Ozero__class_Ozero(_967839))))], (11153 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967839), _967841), c_Groups_Ozero__class_Ozero(_967839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967839), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967839), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967839), c_Groups_Oone__class_Oone(_967839)), _967841)), _967841)), c_Groups_Ozero__class_Ozero(_967839))))]]], (11159 ^ _779300) ^ [_968252, _968254, _968256, _968258, _968260, _968262, _968264] : [c_Nitpick_Ofold__graph_H(_968252, _968254, _968256, _968258, _968260, hAPP(hAPP(_968256, _968262), _968264)), 11164 ^ _779300 : [(11165 ^ _779300) ^ [] : [-(_968260 = c_Orderings_Obot__class_Obot(tc_fun(_968252, tc_HOL_Obool)))], (11167 ^ _779300) ^ [] : [-(hAPP(hAPP(_968256, _968262), _968264) = _968258)]], 11170 ^ _779300 : [(11171 ^ _779300) ^ [] : [-(hAPP(hAPP(_968256, _968262), _968264) = hAPP(hAPP(_968256, 11168 ^ [_968252, _968254, _968256, _968258, _968260, _968262, _968264]), 11169 ^ [_968252, _968254, _968256, _968258, _968260, _968262, _968264]))], (11173 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_968252), 11168 ^ [_968252, _968254, _968256, _968258, _968260, _968262, _968264]), _968260)))], (11175 ^ _779300) ^ [] : [-(c_Nitpick_Ofold__graph_H(_968252, _968254, _968256, _968258, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968252, tc_HOL_Obool)), _968260), hAPP(hAPP(c_Set_Oinsert(_968252), 11168 ^ [_968252, _968254, _968256, _968258, _968260, _968262, _968264]), c_Orderings_Obot__class_Obot(tc_fun(_968252, tc_HOL_Obool)))), 11169 ^ [_968252, _968254, _968256, _968258, _968260, _968262, _968264]))]]], (11177 ^ _779300) ^ [_968689, _968691, _968693, _968695, _968697, _968699, _968701] : [-(c_Nitpick_Ofold__graph_H(_968689, _968691, _968693, _968695, _968697, hAPP(hAPP(_968693, _968699), _968701))), 11178 ^ _779300 : [(11179 ^ _779300) ^ [] : [_968697 = c_Orderings_Obot__class_Obot(tc_fun(_968689, tc_HOL_Obool)), hAPP(hAPP(_968693, _968699), _968701) = _968695], (11185 ^ _779300) ^ [_968918, _968920] : [hAPP(hAPP(_968693, _968699), _968701) = hAPP(hAPP(_968693, _968920), _968918), hBOOL(hAPP(hAPP(c_member(_968689), _968920), _968697)), c_Nitpick_Ofold__graph_H(_968689, _968691, _968693, _968695, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968689, tc_HOL_Obool)), _968697), hAPP(hAPP(c_Set_Oinsert(_968689), _968920), c_Orderings_Obot__class_Obot(tc_fun(_968689, tc_HOL_Obool)))), _968918)]]], (11197 ^ _779300) ^ [_969210, _969212, _969214] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_969210), 11200 ^ _779300 : [(11201 ^ _779300) ^ [] : [_969212 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969210), _969212), _969214), -(_969214 = c_Groups_Ozero__class_Ozero(_969210))], (11207 ^ _779300) ^ [] : [_969214 = c_Groups_Ozero__class_Ozero(_969210), -(_969212 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969210), _969212), _969214))]]], (11213 ^ _779300) ^ [_969451, _969453] : [class_Rings_Ocomm__semiring__1(_969451), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969451), _969453), c_Groups_Ozero__class_Ozero(_969451)) = _969453)], (11219 ^ _779300) ^ [_969546, _969548] : [class_Rings_Ocomm__semiring__1(_969546), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969546), c_Groups_Ozero__class_Ozero(_969546)), _969548) = _969548)], (11235 ^ _779300) ^ [_969861, _969863, _969865, _969867] : [11236 ^ _779300 : [(11237 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_969861), _969863)))], (11239 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_969865), _969867)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_969861, _969865)), c_Sum__Type_OPlus(_969861, _969865, _969863, _969867)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11225 ^ _779300) ^ [_969656, _969658, _969660, _969662] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_969656, _969660)), c_Sum__Type_OPlus(_969656, _969660, _969658, _969662)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_969656), _969658)), hAPP(c_Finite__Set_Ocard(_969660), _969662))), hBOOL(hAPP(c_Finite__Set_Ofinite(_969656), _969658)), hBOOL(hAPP(c_Finite__Set_Ofinite(_969660), _969662))], (11243 ^ _779300) ^ [_969960, _969962] : [-(hBOOL(hAPP(_969960, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_969960, _969962)), 11251 ^ _779300 : [(11252 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 11250 ^ [_969960, _969962]), _969962)))], (11260 ^ _779300) ^ [] : [-(hBOOL(hAPP(_969960, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 11250 ^ [_969960, _969962]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (11254 ^ _779300) ^ [_970198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970198), 11250 ^ [_969960, _969962])), hBOOL(hAPP(_969960, _970198))]]], (11262 ^ _779300) ^ [_970359, _970361] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_970359), _970361)), -(hAPP(c_Finite__Set_Ocard(_970359), _970361) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _970359, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _970359), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970361))], (11268 ^ _779300) ^ [_970486, _970488] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_970486), _970488))), -(hAPP(c_Finite__Set_Ocard(_970486), _970488) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11274 ^ _779300) ^ [_970533, _970535] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_970533), _970535)), -(hAPP(c_Finite__Set_Ocard(_970533), _970535) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _970533, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _970533), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970535))], (11280 ^ _779300) ^ [_970666, _970668, _970670, _970672, _970674] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_970666, _970668, _970670), _970672), _970674), c_Orderings_Obot__class_Obot(tc_fun(_970668, tc_HOL_Obool))) = _970674)], (11282 ^ _779300) ^ [_970715, _970717, _970719, _970721] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_970715, _970717)), c_Sum__Type_OPlus(_970715, _970717, _970719, _970721))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_970717), _970721)))], (11288 ^ _779300) ^ [_970828, _970830, _970832, _970834] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_970828, _970830)), c_Sum__Type_OPlus(_970828, _970830, _970832, _970834))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_970828), _970832)))], (11294 ^ _779300) ^ [_970941, _970943, _970945, _970947] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_970941), _970943)), hBOOL(hAPP(c_Finite__Set_Ofinite(_970945), _970947)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_970941, _970945)), c_Sum__Type_OPlus(_970941, _970945, _970943, _970947))))], (11304 ^ _779300) ^ [_971139, _971141, _971143, _971145] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_971139, _971141)), c_Sum__Type_OPlus(_971139, _971141, _971143, _971145))), 11307 ^ _779300 : [(11308 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_971139), _971143)))], (11310 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_971141), _971145)))]]], (11312 ^ _779300) ^ [_971282, _971284, _971286, _971288] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_971282, _971284)), c_Sum__Type_OPlus(_971282, _971284, _971286, _971288)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_971282), _971286)), hBOOL(hAPP(c_Finite__Set_Ofinite(_971284), _971288))], (11322 ^ _779300) ^ [_971461, _971463, _971465, _971467, _971469, _971471, _971473] : [c_Finite__Set_Ofolding__image__simple(_971461, _971463, _971465, _971467, _971469, _971471), hBOOL(hAPP(c_Finite__Set_Ofinite(_971463), _971473)), -(hAPP(_971471, _971473) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_971461, _971463, _971465), _971469), _971467), _971473))], (11332 ^ _779300) ^ [_971658, _971660, _971662, _971664, _971666, _971668, _971670] : [c_Finite__Set_Ofolding__image(_971658, _971660, _971662, _971664, _971666), hBOOL(hAPP(c_Finite__Set_Ofinite(_971660), _971668)), -(hAPP(hAPP(_971666, _971670), _971668) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_971658, _971660, _971662), _971670), _971664), _971668))], (11342 ^ _779300) ^ [_971859] : [class_Rings_Oring__1(_971859), -(hBOOL(hAPP(hAPP(c_member(_971859), c_Groups_Ozero__class_Ozero(_971859)), c_Int_Oring__1__class_OInts(_971859))))], (11348 ^ _779300) ^ [_971954, _971956, _971958] : [class_Rings_Oring__1(_971954), hBOOL(hAPP(hAPP(c_member(_971954), _971956), c_Int_Oring__1__class_OInts(_971954))), hBOOL(hAPP(hAPP(c_member(_971954), _971958), c_Int_Oring__1__class_OInts(_971954))), -(hBOOL(hAPP(hAPP(c_member(_971954), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971954), _971956), _971958)), c_Int_Oring__1__class_OInts(_971954))))], (11362 ^ _779300) ^ [_972209, _972211, _972213] : [class_Rings_Oring__1(_972209), hBOOL(hAPP(hAPP(c_member(_972209), _972211), c_Int_Oring__1__class_OInts(_972209))), hBOOL(hAPP(hAPP(c_member(_972209), _972213), c_Int_Oring__1__class_OInts(_972209))), -(hBOOL(hAPP(hAPP(c_member(_972209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_972209), _972211), _972213)), c_Int_Oring__1__class_OInts(_972209))))], (11376 ^ _779300) ^ [_972464] : [class_Rings_Oring__1(_972464), -(hBOOL(hAPP(hAPP(c_member(_972464), c_Groups_Oone__class_Oone(_972464)), c_Int_Oring__1__class_OInts(_972464))))], (11382 ^ _779300) ^ [_972559, _972561, _972563] : [class_Rings_Ocomm__semiring__1(_972559), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972559), _972561), _972563) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972559), _972563), _972561))], (11388 ^ _779300) ^ [_972668, _972670, _972672, _972674] : [class_Rings_Ocomm__semiring__1(_972668), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972668), _972670), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972668), _972672), _972674)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972668), _972672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972668), _972670), _972674)))], (11394 ^ _779300) ^ [_972811, _972813, _972815, _972817] : [class_Rings_Ocomm__semiring__1(_972811), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972811), _972813), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972811), _972815), _972817)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972811), _972813), _972815)), _972817))], (11400 ^ _779300) ^ [_972954, _972956, _972958, _972960] : [class_Rings_Ocomm__semiring__1(_972954), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972954), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972954), _972956), _972958)), _972960) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972954), _972956), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972954), _972958), _972960)))], (11406 ^ _779300) ^ [_973097, _973099, _973101, _973103] : [class_Rings_Ocomm__semiring__1(_973097), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973097), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973097), _973099), _973101)), _973103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973097), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973097), _973099), _973103)), _973101))], (11412 ^ _779300) ^ [_973240, _973242, _973244, _973246, _973248] : [class_Rings_Ocomm__semiring__1(_973240), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973240), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973240), _973242), _973244)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973240), _973246), _973248)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973240), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973240), _973242), _973246)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973240), _973244), _973248)))], (11418 ^ _779300) ^ [_973417, _973419] : [class_Int_Oring__char__0(_973417), hBOOL(hAPP(hAPP(c_member(_973417), _973419), c_Int_Oring__1__class_OInts(_973417))), 11425 ^ _779300 : [(11426 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973417), _973419), _973419) = c_Groups_Ozero__class_Ozero(_973417), -(_973419 = c_Groups_Ozero__class_Ozero(_973417))], (11432 ^ _779300) ^ [] : [_973419 = c_Groups_Ozero__class_Ozero(_973417), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973417), _973419), _973419) = c_Groups_Ozero__class_Ozero(_973417))]]], (11438 ^ _779300) ^ [_973728, _973730, _973732, _973734] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_973728), _973730)), hBOOL(hAPP(c_Finite__Set_Ofinite(_973732), _973734)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_973728, _973732)), c_Sum__Type_OPlus(_973728, _973732, _973730, _973734)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_973728), _973730)), hAPP(c_Finite__Set_Ocard(_973732), _973734)))], (11448 ^ _779300) ^ [_973939, _973941] : [class_Int_Oring__char__0(_973939), hBOOL(hAPP(hAPP(c_member(_973939), _973941), c_Int_Oring__1__class_OInts(_973939))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973939), c_Groups_Oone__class_Oone(_973939)), _973941)), _973941) = c_Groups_Ozero__class_Ozero(_973939)], (11458 ^ _779300) ^ [_974146, _974148, _974150, _974152] : [c_Sum__Type_OPlus(_974146, _974148, _974150, _974152) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_974146, _974148), tc_HOL_Obool)), 11461 ^ _779300 : [(11462 ^ _779300) ^ [] : [-(_974150 = c_Orderings_Obot__class_Obot(tc_fun(_974146, tc_HOL_Obool)))], (11464 ^ _779300) ^ [] : [-(_974152 = c_Orderings_Obot__class_Obot(tc_fun(_974148, tc_HOL_Obool)))]]], (11466 ^ _779300) ^ [_974295, _974297, _974299, _974301] : [-(c_Sum__Type_OPlus(_974295, _974297, _974299, _974301) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_974295, _974297), tc_HOL_Obool))), _974299 = c_Orderings_Obot__class_Obot(tc_fun(_974295, tc_HOL_Obool)), _974301 = c_Orderings_Obot__class_Obot(tc_fun(_974297, tc_HOL_Obool))], (11476 ^ _779300) ^ [_974480, _974482, _974484, _974486, _974488] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974480, _974482, hAPP(hAPP(c_Set_Oinsert(_974480), _974484), _974486)), _974488)), 11481 ^ _779300 : [(11482 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_974480), _974484), _974486) = hAPP(hAPP(c_Set_Oinsert(_974480), 11479 ^ [_974480, _974482, _974484, _974486, _974488]), 11480 ^ [_974480, _974482, _974484, _974486, _974488]))], (11484 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974480, _974480, _974482, 11479 ^ [_974480, _974482, _974484, _974486, _974488], 11480 ^ [_974480, _974482, _974484, _974486, _974488]), _974488)))], (11486 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_974480), 11479 ^ [_974480, _974482, _974484, _974486, _974488]), 11480 ^ [_974480, _974482, _974484, _974486, _974488]))]]], (11488 ^ _779300) ^ [_974897, _974899, _974901, _974903, _974905] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974897, _974899, hAPP(hAPP(c_Set_Oinsert(_974897), _974901), _974903)), _974905)), 11493 ^ _779300 : [(11494 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_974897), _974901), _974903) = hAPP(hAPP(c_Set_Oinsert(_974897), 11491 ^ [_974897, _974899, _974901, _974903, _974905]), 11492 ^ [_974897, _974899, _974901, _974903, _974905]))], (11496 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974897, _974897, _974899, 11491 ^ [_974897, _974899, _974901, _974903, _974905], 11492 ^ [_974897, _974899, _974901, _974903, _974905]), _974905)))], (11498 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_974897), 11491 ^ [_974897, _974899, _974901, _974903, _974905]), 11492 ^ [_974897, _974899, _974901, _974903, _974905]))]]], (11500 ^ _779300) ^ [_975288, _975290, _975292, _975294, _975296] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_975288, _975290, hAPP(hAPP(c_Set_Oinsert(_975288), _975292), _975294)), _975296))), 11501 ^ _779300 : [(11502 ^ _779300) ^ [_975392, _975394] : [hAPP(hAPP(c_Set_Oinsert(_975288), _975292), _975294) = hAPP(hAPP(c_Set_Oinsert(_975288), _975394), _975392), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975288, _975288, _975290, _975394, _975392), _975296)), -(hBOOL(hAPP(hAPP(c_member(_975288), _975394), _975392)))]]], (11514 ^ _779300) ^ [_975649, _975651] : [11516 ^ _779300 : [(11517 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 11515 ^ [_975649, _975651]), _975649)))], (11519 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _975651), 11515 ^ [_975649, _975651]))]], -(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)), _975651), _975649))], (11523 ^ _779300) ^ [_975824, _975826, _975828, _975830, _975832] : [class_Groups_Oab__semigroup__mult(_975824), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975824, _975824, c_Groups_Otimes__class_Otimes(_975824), _975826, _975828), _975830)), hBOOL(hAPP(hAPP(c_member(_975824), _975832), _975828)), -(hBOOL(hAPP(hAPP(c_member(_975824), _975826), _975828))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975824, _975824, c_Groups_Otimes__class_Otimes(_975824), _975832, hAPP(hAPP(c_Set_Oinsert(_975824), _975826), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975824, tc_HOL_Obool)), _975828), hAPP(hAPP(c_Set_Oinsert(_975824), _975832), c_Orderings_Obot__class_Obot(tc_fun(_975824, tc_HOL_Obool)))))), _975830)))], (11541 ^ _779300) ^ [_976168, _976170] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976168), _976170)), 11547 ^ _779300 : [(11548 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_976168), 11546 ^ [_976168, _976170]), _976170)))], (11550 ^ _779300) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_976168), _976170) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11554 ^ _779300) ^ [_976368] : [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), _976368))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _976368) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _976368)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (11560 ^ _779300) ^ [_976483, _976485, _976487, _976489, _976491, _976493] : [class_Rings_Olinordered__semiring__1__strict(_976483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976483), _976485), _976487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976483), _976489), _976487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976483), c_Groups_Ozero__class_Ozero(_976483)), _976491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976483), c_Groups_Ozero__class_Ozero(_976483)), _976493)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976483), _976491), _976493) = c_Groups_Oone__class_Oone(_976483), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976483), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976483), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976483), _976491), _976485)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976483), _976493), _976489))), _976487)))], (11586 ^ _779300) ^ [_977012, _977014, _977016, _977018, _977020, _977022] : [-(c_Nitpick_Opair__box_Opair__box__size(_977012, _977014, _977016, _977018, c_Nitpick_Opair__box_OPairBox(_977012, _977014, _977020, _977022)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_977016, _977020)), hAPP(_977018, _977022))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11588 ^ _779300) ^ [_977074, _977076, _977078] : [class_Rings_Ocomm__semiring__1(_977074), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977074), _977076), _977078) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977074), _977078), _977076))], (11594 ^ _779300) ^ [_977183, _977185, _977187, _977189] : [class_Rings_Ocomm__semiring__1(_977183), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977183), _977185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977183), _977187), _977189)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977183), _977187), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977183), _977185), _977189)))], (11600 ^ _779300) ^ [_977326, _977328, _977330, _977332] : [class_Rings_Ocomm__semiring__1(_977326), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977326), _977328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977326), _977330), _977332)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977326), _977328), _977330)), _977332))], (11606 ^ _779300) ^ [_977469, _977471, _977473, _977475] : [class_Rings_Ocomm__semiring__1(_977469), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977469), _977471), _977473)), _977475) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977469), _977471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977469), _977473), _977475)))], (11612 ^ _779300) ^ [_977612, _977614, _977616, _977618] : [class_Rings_Ocomm__semiring__1(_977612), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977612), _977614), _977616)), _977618) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977612), _977614), _977618)), _977616))], (11618 ^ _779300) ^ [_977755, _977757, _977759, _977761, _977763] : [class_Rings_Ocomm__semiring__1(_977755), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977755), _977757), _977759)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977755), _977761), _977763)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977755), _977757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977755), _977759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977755), _977761), _977763))))], (11624 ^ _779300) ^ [_977932, _977934, _977936, _977938, _977940] : [class_Rings_Ocomm__semiring__1(_977932), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977932), _977934), _977936)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977932), _977938), _977940)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977932), _977938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977932), _977934), _977936)), _977940)))], (11630 ^ _779300) ^ [_978109, _978111, _978113, _978115, _978117] : [class_Rings_Ocomm__semiring__1(_978109), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978109), _978111), _978113)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978109), _978115), _978117)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978109), _978111), _978115)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978109), _978113), _978117)))], (11636 ^ _779300) ^ [_978286, _978288] : [class_Lattices_Oab__semigroup__idem__mult(_978286), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978286), _978288), _978288) = _978288)], (11642 ^ _779300) ^ [_978377, _978379] : [class_Lattices_Oab__semigroup__idem__mult(_978377), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978377), _978379), _978379) = _978379)], (11648 ^ _779300) ^ [_978468, _978470, _978472] : [class_Lattices_Oab__semigroup__idem__mult(_978468), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978468), _978470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978468), _978470), _978472)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978468), _978470), _978472))], (11654 ^ _779300) ^ [_978593, _978595, _978597, _978599] : [class_Groups_Oab__semigroup__mult(_978593), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978593), _978595), _978597)), _978599) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978593), _978595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978593), _978597), _978599)))], (11660 ^ _779300) ^ [_978736, _978738, _978740] : [class_Int_Onumber__ring(_978736), -(hAPP(c_Int_Onumber__class_Onumber__of(_978736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _978738), _978740)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978736), hAPP(c_Int_Onumber__class_Onumber__of(_978736), _978738)), hAPP(c_Int_Onumber__class_Onumber__of(_978736), _978740)))], (11666 ^ _779300) ^ [_978871, _978873, _978875] : [class_Int_Onumber(_978871), 11669 ^ _779300 : [(11670 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_978871), _978873) = _978875, -(_978875 = hAPP(c_Int_Onumber__class_Onumber__of(_978871), _978873))], (11676 ^ _779300) ^ [] : [_978875 = hAPP(c_Int_Onumber__class_Onumber__of(_978871), _978873), -(hAPP(c_Int_Onumber__class_Onumber__of(_978871), _978873) = _978875)]]], (11682 ^ _779300) ^ [_979112, _979114, _979116] : [class_Int_Onumber__ring(_979112), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979112), hAPP(c_Int_Onumber__class_Onumber__of(_979112), _979114)), hAPP(c_Int_Onumber__class_Onumber__of(_979112), _979116)) = hAPP(c_Int_Onumber__class_Onumber__of(_979112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _979114), _979116)))], (11688 ^ _779300) ^ [_979247, _979249, _979251] : [class_Int_Onumber__ring(_979247), class_Int_Oring__char__0(_979247), 11695 ^ _779300 : [(11696 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_979247), _979249) = hAPP(c_Int_Onumber__class_Onumber__of(_979247), _979251), -(_979249 = _979251)], (11702 ^ _779300) ^ [] : [_979249 = _979251, -(hAPP(c_Int_Onumber__class_Onumber__of(_979247), _979249) = hAPP(c_Int_Onumber__class_Onumber__of(_979247), _979251))]]], (11708 ^ _779300) ^ [_979542, _979544, _979546, _979548] : [class_Int_Onumber__ring(_979542), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979542), hAPP(c_Int_Onumber__class_Onumber__of(_979542), _979544)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979542), hAPP(c_Int_Onumber__class_Onumber__of(_979542), _979546)), _979548)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979542), hAPP(c_Int_Onumber__class_Onumber__of(_979542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _979544), _979546))), _979548))], (11714 ^ _779300) ^ [_979711, _979713, _979715, _979717] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979711), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_979711), _979713), _979715)), hAPP(c_Int_Onumber__class_Onumber__of(_979711), _979717)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_979711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979711), _979713), hAPP(c_Int_Onumber__class_Onumber__of(_979711), _979717))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979711), _979715), hAPP(c_Int_Onumber__class_Onumber__of(_979711), _979717)))), class_Int_Onumber(_979711), class_Rings_Oring(_979711)], (11724 ^ _779300) ^ [_979954, _979956, _979958, _979960] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979954), hAPP(c_Int_Onumber__class_Onumber__of(_979954), _979956)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_979954), _979958), _979960)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_979954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979954), hAPP(c_Int_Onumber__class_Onumber__of(_979954), _979956)), _979958)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979954), hAPP(c_Int_Onumber__class_Onumber__of(_979954), _979956)), _979960))), class_Int_Onumber(_979954), class_Rings_Oring(_979954)], (11734 ^ _779300) ^ [_980197, _980199, _980201, _980203] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980197), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980197), _980199), _980201)), hAPP(c_Int_Onumber__class_Onumber__of(_980197), _980203)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980197), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980197), _980199), hAPP(c_Int_Onumber__class_Onumber__of(_980197), _980203))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980197), _980201), hAPP(c_Int_Onumber__class_Onumber__of(_980197), _980203)))), class_Int_Onumber(_980197), class_Rings_Osemiring(_980197)], (11744 ^ _779300) ^ [_980440, _980442, _980444, _980446] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980440), hAPP(c_Int_Onumber__class_Onumber__of(_980440), _980442)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980440), _980444), _980446)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980440), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980440), hAPP(c_Int_Onumber__class_Onumber__of(_980440), _980442)), _980444)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980440), hAPP(c_Int_Onumber__class_Onumber__of(_980440), _980442)), _980446))), class_Int_Onumber(_980440), class_Rings_Osemiring(_980440)], (11754 ^ _779300) ^ [_980710, _980712, _980714, _980716, _980718, _980720] : [c_Nitpick_Opair__box_OPairBox(_980710, _980712, _980714, _980716) = c_Nitpick_Opair__box_OPairBox(_980710, _980712, _980718, _980720), 11757 ^ _779300 : [(11758 ^ _779300) ^ [] : [-(_980714 = _980718)], (11760 ^ _779300) ^ [] : [-(_980716 = _980720)]]], (11762 ^ _779300) ^ [_980837, _980839, _980841, _980843, _980845, _980847] : [-(c_Nitpick_Opair__box_OPairBox(_980837, _980839, _980841, _980843) = c_Nitpick_Opair__box_OPairBox(_980837, _980839, _980845, _980847)), _980841 = _980845, _980843 = _980847], (11772 ^ _779300) ^ [_981004, _981006, _981008] : [class_Int_Onumber__ring(_981004), class_Rings_Olinordered__idom(_981004), 11779 ^ _779300 : [(11780 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981004), hAPP(c_Int_Onumber__class_Onumber__of(_981004), _981006)), hAPP(c_Int_Onumber__class_Onumber__of(_981004), _981008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981006), _981008)))], (11786 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981006), _981008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981004), hAPP(c_Int_Onumber__class_Onumber__of(_981004), _981006)), hAPP(c_Int_Onumber__class_Onumber__of(_981004), _981008))))]]], (11792 ^ _779300) ^ [_981335, _981337, _981339] : [class_Int_Onumber__ring(_981335), class_Rings_Olinordered__idom(_981335), 11799 ^ _779300 : [(11800 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981335), hAPP(c_Int_Onumber__class_Onumber__of(_981335), _981337)), hAPP(c_Int_Onumber__class_Onumber__of(_981335), _981339))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _981337), _981339)))], (11806 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _981337), _981339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981335), hAPP(c_Int_Onumber__class_Onumber__of(_981335), _981337)), hAPP(c_Int_Onumber__class_Onumber__of(_981335), _981339))))]]], (11812 ^ _779300) ^ [_981666, _981668, _981670, _981672] : [class_Int_Onumber__ring(_981666), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981666), hAPP(c_Int_Onumber__class_Onumber__of(_981666), _981668)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981666), hAPP(c_Int_Onumber__class_Onumber__of(_981666), _981670)), _981672)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981666), hAPP(c_Int_Onumber__class_Onumber__of(_981666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _981668), _981670))), _981672))], (11818 ^ _779300) ^ [_981835, _981837, _981839] : [class_Int_Onumber__ring(_981835), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981835), hAPP(c_Int_Onumber__class_Onumber__of(_981835), _981837)), hAPP(c_Int_Onumber__class_Onumber__of(_981835), _981839)) = hAPP(c_Int_Onumber__class_Onumber__of(_981835), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _981837), _981839)))], (11824 ^ _779300) ^ [_981970, _981972, _981974] : [class_Int_Onumber__ring(_981970), -(hAPP(c_Int_Onumber__class_Onumber__of(_981970), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _981972), _981974)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981970), hAPP(c_Int_Onumber__class_Onumber__of(_981970), _981972)), hAPP(c_Int_Onumber__class_Onumber__of(_981970), _981974)))], (11830 ^ _779300) ^ [_982105, _982107, _982109] : [class_Int_Onumber__ring(_982105), -(hAPP(c_Int_Onumber__class_Onumber__of(_982105), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _982107), _982109)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_982105), hAPP(c_Int_Onumber__class_Onumber__of(_982105), _982107)), hAPP(c_Int_Onumber__class_Onumber__of(_982105), _982109)))], (11836 ^ _779300) ^ [_982240, _982242, _982244] : [class_Rings_Ono__zero__divisors(_982240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982240), _982242), _982244) = c_Groups_Ozero__class_Ozero(_982240), -(_982242 = c_Groups_Ozero__class_Ozero(_982240)), -(_982244 = c_Groups_Ozero__class_Ozero(_982240))], (11850 ^ _779300) ^ [_982412, _982414, _982416] : [class_Rings_Ono__zero__divisors(_982412), -(_982414 = c_Groups_Ozero__class_Ozero(_982412)), -(_982416 = c_Groups_Ozero__class_Ozero(_982412)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982412), _982414), _982416) = c_Groups_Ozero__class_Ozero(_982412)], (11864 ^ _779300) ^ [_982632, _982634, _982636] : [class_Rings_Oring__no__zero__divisors(_982632), 11867 ^ _779300 : [(11878 ^ _779300) ^ [] : [11879 ^ _779300 : [(11880 ^ _779300) ^ [] : [_982634 = c_Groups_Ozero__class_Ozero(_982632)], (11882 ^ _779300) ^ [] : [_982636 = c_Groups_Ozero__class_Ozero(_982632)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982632), _982634), _982636) = c_Groups_Ozero__class_Ozero(_982632))], (11868 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982632), _982634), _982636) = c_Groups_Ozero__class_Ozero(_982632), -(_982634 = c_Groups_Ozero__class_Ozero(_982632)), -(_982636 = c_Groups_Ozero__class_Ozero(_982632))]]], (11886 ^ _779300) ^ [_982930, _982932] : [class_Rings_Omult__zero(_982930), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982930), _982932), c_Groups_Ozero__class_Ozero(_982930)) = c_Groups_Ozero__class_Ozero(_982930))], (11892 ^ _779300) ^ [_983029, _983031] : [class_Rings_Omult__zero(_983029), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983029), c_Groups_Ozero__class_Ozero(_983029)), _983031) = c_Groups_Ozero__class_Ozero(_983029))], (11898 ^ _779300) ^ [_983128, _983130] : [class_Rings_Ocomm__semiring__1(_983128), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983128), c_Groups_Ozero__class_Ozero(_983128)), _983130) = c_Groups_Ozero__class_Ozero(_983128))], (11904 ^ _779300) ^ [_983227, _983229] : [class_Rings_Ocomm__semiring__1(_983227), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983227), _983229), c_Groups_Ozero__class_Ozero(_983227)) = c_Groups_Ozero__class_Ozero(_983227))], (11910 ^ _779300) ^ [_983326, _983328, _983330, _983332, _983334] : [class_Rings_Osemiring(_983326), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983326), _983328), _983330)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983326), _983332), _983330)), _983334)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983326), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983326), _983328), _983332)), _983330)), _983334))], (11916 ^ _779300) ^ [_983519, _983521, _983523, _983525] : [class_Rings_Ocomm__semiring(_983519), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983519), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983519), _983521), _983523)), _983525) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983519), _983521), _983525)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983519), _983523), _983525)))], (11922 ^ _779300) ^ [_983678, _983680, _983682, _983684, _983686] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_983678), 11925 ^ _779300 : [(11936 ^ _779300) ^ [] : [11937 ^ _779300 : [(11938 ^ _779300) ^ [] : [_983680 = _983684], (11940 ^ _779300) ^ [] : [_983682 = _983686]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983678), _983680), _983682)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983678), _983684), _983686)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983678), _983680), _983686)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983678), _983684), _983682)))], (11926 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983678), _983680), _983682)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983678), _983684), _983686)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983678), _983680), _983686)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983678), _983684), _983682)), -(_983680 = _983684), -(_983682 = _983686)]]], (11944 ^ _779300) ^ [_984090, _984092, _984094, _984096] : [class_Rings_Ocomm__semiring__1(_984090), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984090), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984090), _984092), _984094)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984090), _984096), _984094)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984090), _984092), _984096)), _984094))], (11950 ^ _779300) ^ [_984249, _984251, _984253, _984255] : [class_Rings_Ocomm__semiring__1(_984249), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984249), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984249), _984251), _984253)), _984255) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984249), _984251), _984255)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984249), _984253), _984255)))], (11956 ^ _779300) ^ [_984408, _984410, _984412, _984414, _984416] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_984408), 11959 ^ _779300 : [(11970 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984408), _984410), _984414)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984408), _984412), _984416)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984408), _984410), _984416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984408), _984412), _984414))), 11973 ^ _779300 : [(11974 ^ _779300) ^ [] : [_984410 = _984412], (11976 ^ _779300) ^ [] : [_984414 = _984416]]], (11960 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984408), _984410), _984414)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984408), _984412), _984416)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984408), _984410), _984416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984408), _984412), _984414)), -(_984410 = _984412), -(_984414 = _984416)]]], (11978 ^ _779300) ^ [_984826, _984828, _984830, _984832] : [class_Rings_Ocomm__semiring__1(_984826), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984826), _984828), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984826), _984830), _984832)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984826), _984828), _984830)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984826), _984828), _984832)))], (11984 ^ _779300) ^ [_984985, _984987] : [class_Groups_Omonoid__mult(_984985), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984985), c_Groups_Oone__class_Oone(_984985)), _984987) = _984987)], (11990 ^ _779300) ^ [_985080, _985082] : [class_Groups_Ocomm__monoid__mult(_985080), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985080), c_Groups_Oone__class_Oone(_985080)), _985082) = _985082)], (11996 ^ _779300) ^ [_985175, _985177] : [class_Groups_Omonoid__mult(_985175), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985175), _985177), c_Groups_Oone__class_Oone(_985175)) = _985177)], (12002 ^ _779300) ^ [_985270, _985272] : [class_Groups_Ocomm__monoid__mult(_985270), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985270), _985272), c_Groups_Oone__class_Oone(_985270)) = _985272)], (12008 ^ _779300) ^ [_985365, _985367] : [class_Rings_Ocomm__semiring__1(_985365), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985365), _985367), c_Groups_Oone__class_Oone(_985365)) = _985367)], (12014 ^ _779300) ^ [_985460, _985462] : [class_Rings_Ocomm__semiring__1(_985460), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985460), c_Groups_Oone__class_Oone(_985460)), _985462) = _985462)], (12020 ^ _779300) ^ [_985555] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _985555) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12022 ^ _779300) ^ [_985581] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985581), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12034 ^ _779300) ^ [_985723, _985725] : [12035 ^ _779300 : [(12036 ^ _779300) ^ [] : [_985723 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12038 ^ _779300) ^ [] : [_985725 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985723), _985725) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12024 ^ _779300) ^ [_985625, _985627] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985625), _985627) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_985625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_985627 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12052 ^ _779300) ^ [_985982, _985984, _985986] : [12053 ^ _779300 : [(12054 ^ _779300) ^ [] : [_985984 = _985986], (12056 ^ _779300) ^ [] : [_985982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985982), _985984) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985982), _985986))], (12042 ^ _779300) ^ [_985870, _985872, _985874] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985870), _985872) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985870), _985874), -(_985872 = _985874), -(_985870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12070 ^ _779300) ^ [_986255, _986257, _986259] : [12071 ^ _779300 : [(12072 ^ _779300) ^ [] : [_986255 = _986259], (12074 ^ _779300) ^ [] : [_986257 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986255), _986257) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986259), _986257))], (12060 ^ _779300) ^ [_986143, _986145, _986147] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986143), _986145) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986147), _986145), -(_986143 = _986147), -(_986145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12078 ^ _779300) ^ [_986416, _986418, _986420] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _986416)), _986418) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _986416)), _986420), -(_986418 = _986420)], (12084 ^ _779300) ^ [_986527, _986529, _986531] : [_986529 = _986531, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _986527)), _986529) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _986527)), _986531))], (12090 ^ _779300) ^ [_986644, _986646, _986648] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986644), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986646), _986648)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986644), _986646)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986644), _986648)))], (12092 ^ _779300) ^ [_986701, _986703, _986705] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986701), _986703)), _986705) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986701), _986705)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986703), _986705)))], (12094 ^ _779300) ^ [_986758] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986758), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986758), _986758))))], (12096 ^ _779300) ^ [_986792] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986792), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986792), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986792), _986792)))))], (12098 ^ _779300) ^ [_986832, _986834, _986836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986832), _986834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986832), _986836)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986834), _986836))))], (12104 ^ _779300) ^ [_986955, _986957, _986959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _986955), _986957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986959), _986955)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986959), _986957))))], (12110 ^ _779300) ^ [_987078, _987080, _987082, _987084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987078), _987080)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987082), _987084)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987078), _987082)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987080), _987084))))], (12120 ^ _779300) ^ [_987269, _987271, _987273] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _987269), _987271)), _987273) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987269), _987273)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987271), _987273)))], (12122 ^ _779300) ^ [_987326, _987328, _987330] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987326), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _987328), _987330)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987326), _987328)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987326), _987330)))], (12124 ^ _779300) ^ [_987398, _987400] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987398), _987400) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 12127 ^ _779300 : [(12128 ^ _779300) ^ [] : [-(_987398 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12130 ^ _779300) ^ [] : [-(_987400 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12132 ^ _779300) ^ [_987509, _987511] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987509), _987511) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _987509 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _987511 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12142 ^ _779300) ^ [_987652] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987652), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _987652)], (12144 ^ _779300) ^ [_987696, _987698] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987696), _987698), 12147 ^ _779300 : [(12148 ^ _779300) ^ [] : [-(_987696 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12150 ^ _779300) ^ [] : [-(_987698 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12152 ^ _779300) ^ [_987807, _987809] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _987807), _987809)), _987807 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _987809 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12162 ^ _779300) ^ [_987950] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _987950) = _987950)], (12164 ^ _779300) ^ [_987976] : [class_Lattices_Oab__semigroup__idem__mult(_987976), -(c_Finite__Set_Ofun__left__comm__idem(_987976, _987976, c_Groups_Otimes__class_Otimes(_987976)))], (12170 ^ _779300) ^ [_988055, _988057, _988059] : [class_Int_Onumber(_988055), class_Orderings_Olinorder(_988055), 12177 ^ _779300 : [(12178 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988055), hAPP(c_Int_Onumber__class_Onumber__of(_988055), _988057)), hAPP(c_Int_Onumber__class_Onumber__of(_988055), _988059))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988055), hAPP(c_Int_Onumber__class_Onumber__of(_988055), _988059)), hAPP(c_Int_Onumber__class_Onumber__of(_988055), _988057)))], (12184 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988055), hAPP(c_Int_Onumber__class_Onumber__of(_988055), _988059)), hAPP(c_Int_Onumber__class_Onumber__of(_988055), _988057)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988055), hAPP(c_Int_Onumber__class_Onumber__of(_988055), _988057)), hAPP(c_Int_Onumber__class_Onumber__of(_988055), _988059))))]]], (12190 ^ _779300) ^ [_988382, _988384, _988386, _988388] : [class_Int_Onumber__ring(_988382), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988382), hAPP(c_Int_Onumber__class_Onumber__of(_988382), _988384)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_988382), hAPP(c_Int_Onumber__class_Onumber__of(_988382), _988386)), _988388)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_988382), hAPP(c_Int_Onumber__class_Onumber__of(_988382), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _988384), _988386))), _988388))], (12196 ^ _779300) ^ [_988551, _988553, _988555] : [class_Rings_Oordered__cancel__semiring(_988551), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988551), _988553), _988555)), c_Groups_Ozero__class_Ozero(_988551)))), 12201 ^ _779300 : [(12202 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988551), c_Groups_Ozero__class_Ozero(_988551)), _988553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988551), _988555), c_Groups_Ozero__class_Ozero(_988551)))], (12208 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988551), _988553), c_Groups_Ozero__class_Ozero(_988551))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988551), c_Groups_Ozero__class_Ozero(_988551)), _988555))]]], (12216 ^ _779300) ^ [_988927, _988929, _988931] : [class_Rings_Oordered__ring(_988927), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988927), c_Groups_Ozero__class_Ozero(_988927)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988927), _988929), _988931)))), 12221 ^ _779300 : [(12222 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988927), c_Groups_Ozero__class_Ozero(_988927)), _988929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988927), c_Groups_Ozero__class_Ozero(_988927)), _988931))], (12228 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988927), _988929), c_Groups_Ozero__class_Ozero(_988927))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988927), _988931), c_Groups_Ozero__class_Ozero(_988927)))]]], (12236 ^ _779300) ^ [_989303, _989305, _989307, _989309, _989311] : [class_Rings_Oordered__semiring(_989303), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989303), _989305), _989307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989303), _989309), _989311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989303), c_Groups_Ozero__class_Ozero(_989303)), _989307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989303), c_Groups_Ozero__class_Ozero(_989303)), _989309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989303), _989305), _989309)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989303), _989307), _989311))))], (12258 ^ _779300) ^ [_989726, _989728, _989730, _989732, _989734] : [class_Rings_Oordered__semiring(_989726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989726), _989728), _989730)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989726), _989732), _989734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989726), c_Groups_Ozero__class_Ozero(_989726)), _989728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989726), c_Groups_Ozero__class_Ozero(_989726)), _989732)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989726), _989728), _989732)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989726), _989730), _989734))))], (12280 ^ _779300) ^ [_990149, _990151, _990153, _990155] : [class_Rings_Oordered__ring(_990149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990149), _990151), _990153)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990149), _990155), c_Groups_Ozero__class_Ozero(_990149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990149), _990155), _990153)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990149), _990155), _990151))))], (12294 ^ _779300) ^ [_990418, _990420, _990422, _990424] : [class_Rings_Oordered__ring(_990418), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990418), _990420), _990422)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990418), _990424), c_Groups_Ozero__class_Ozero(_990418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990418), _990422), _990424)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990418), _990420), _990424))))], (12308 ^ _779300) ^ [_990687, _990689, _990691, _990693] : [class_Rings_Oordered__comm__semiring(_990687), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990687), _990689), _990691)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990687), c_Groups_Ozero__class_Ozero(_990687)), _990693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990687), _990693), _990689)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990687), _990693), _990691))))], (12322 ^ _779300) ^ [_990956, _990958, _990960, _990962] : [class_Rings_Oordered__semiring(_990956), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990956), _990958), _990960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990956), c_Groups_Ozero__class_Ozero(_990956)), _990962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990956), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990956), _990962), _990958)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_990956), _990962), _990960))))], (12336 ^ _779300) ^ [_991225, _991227, _991229, _991231] : [class_Rings_Oordered__semiring(_991225), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991225), _991227), _991229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991225), c_Groups_Ozero__class_Ozero(_991225)), _991231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991225), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991225), _991227), _991231)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991225), _991229), _991231))))], (12350 ^ _779300) ^ [_991494, _991496, _991498] : [class_Rings_Oordered__ring(_991494), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991494), _991496), c_Groups_Ozero__class_Ozero(_991494))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991494), _991498), c_Groups_Ozero__class_Ozero(_991494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991494), c_Groups_Ozero__class_Ozero(_991494)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991494), _991496), _991498))))], (12364 ^ _779300) ^ [_991749, _991751, _991753] : [class_Rings_Oordered__cancel__semiring(_991749), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991749), _991751), c_Groups_Ozero__class_Ozero(_991749))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991749), c_Groups_Ozero__class_Ozero(_991749)), _991753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991749), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_991749), _991751), _991753)), c_Groups_Ozero__class_Ozero(_991749))))], (12378 ^ _779300) ^ [_992004, _992006, _992008] : [class_Rings_Oordered__cancel__semiring(_992004), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992004), c_Groups_Ozero__class_Ozero(_992004)), _992006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992004), _992008), c_Groups_Ozero__class_Ozero(_992004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992004), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992004), _992008), _992006)), c_Groups_Ozero__class_Ozero(_992004))))], (12392 ^ _779300) ^ [_992259, _992261, _992263] : [class_Rings_Oordered__cancel__semiring(_992259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992259), c_Groups_Ozero__class_Ozero(_992259)), _992261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992259), _992263), c_Groups_Ozero__class_Ozero(_992259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992259), _992261), _992263)), c_Groups_Ozero__class_Ozero(_992259))))], (12406 ^ _779300) ^ [_992514, _992516, _992518] : [class_Rings_Oordered__cancel__semiring(_992514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992514), c_Groups_Ozero__class_Ozero(_992514)), _992516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992514), c_Groups_Ozero__class_Ozero(_992514)), _992518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992514), c_Groups_Ozero__class_Ozero(_992514)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992514), _992516), _992518))))], (12420 ^ _779300) ^ [_992769, _992771, _992773] : [class_Rings_Olinordered__ring__strict(_992769), 12423 ^ _779300 : [(12424 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992769), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992769), _992771), _992773)), c_Groups_Ozero__class_Ozero(_992769))), 12429 ^ _779300 : [(12430 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992769), c_Groups_Ozero__class_Ozero(_992769)), _992771)))], (12432 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992769), _992773), c_Groups_Ozero__class_Ozero(_992769))))]], 12433 ^ _779300 : [(12434 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992769), _992771), c_Groups_Ozero__class_Ozero(_992769))))], (12436 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992769), c_Groups_Ozero__class_Ozero(_992769)), _992773)))]]], (12438 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992769), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992769), _992771), _992773)), c_Groups_Ozero__class_Ozero(_992769)))), 12439 ^ _779300 : [(12440 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992769), c_Groups_Ozero__class_Ozero(_992769)), _992771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992769), _992773), c_Groups_Ozero__class_Ozero(_992769)))], (12446 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992769), _992771), c_Groups_Ozero__class_Ozero(_992769))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992769), c_Groups_Ozero__class_Ozero(_992769)), _992773))]]]]], (12454 ^ _779300) ^ [_993359, _993361, _993363] : [class_Rings_Olinordered__ring__strict(_993359), 12457 ^ _779300 : [(12458 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993359), c_Groups_Ozero__class_Ozero(_993359)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993359), _993361), _993363))), 12463 ^ _779300 : [(12464 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993359), c_Groups_Ozero__class_Ozero(_993359)), _993361)))], (12466 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993359), c_Groups_Ozero__class_Ozero(_993359)), _993363)))]], 12467 ^ _779300 : [(12468 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993359), _993361), c_Groups_Ozero__class_Ozero(_993359))))], (12470 ^ _779300) ^ [] : 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000240), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1000240), _1000248), _1000242)), _1000244)), _1000250), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000240), _1000242), _1000244)), _1000246) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000240), _1000248), _1000244)), _1000250))]]], (12846 ^ _779300) ^ [_1000637, _1000639, _1000641, _1000643, _1000645, _1000647] : [class_Rings_Oring(_1000637), 12849 ^ _779300 : [(12850 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000637), _1000639), _1000641)), _1000643) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000637), _1000645), _1000641)), _1000647), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000637), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1000637), _1000639), _1000645)), _1000641)), _1000643) = _1000647)], (12856 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000637), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1000637), _1000639), _1000645)), _1000641)), _1000643) = _1000647, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000637), _1000639), _1000641)), _1000643) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000637), _1000645), _1000641)), _1000647))]]], (12862 ^ _779300) ^ [_1001034, _1001036, _1001038] : [class_Rings_Ocomm__semiring__1(_1001034), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001034), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001034), _1001036), _1001038)), _1001038) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001034), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001034), _1001036), c_Groups_Oone__class_Oone(_1001034))), _1001038))], (12868 ^ _779300) ^ [_1001179, _1001181, _1001183] : [class_Rings_Ocomm__semiring__1(_1001179), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001179), _1001181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001179), _1001183), _1001181)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001179), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001179), _1001183), c_Groups_Oone__class_Oone(_1001179))), _1001181))], (12874 ^ _779300) ^ [_1001324, _1001326] : [class_Rings_Ocomm__semiring__1(_1001324), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001324), _1001326), _1001326) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001324), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001324), c_Groups_Oone__class_Oone(_1001324)), c_Groups_Oone__class_Oone(_1001324))), _1001326))], (12880 ^ _779300) ^ [_1001470, _1001472] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001470), _1001472) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 12883 ^ _779300 : [(12884 ^ _779300) ^ [] : [-(_1001470 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12886 ^ _779300) ^ [] : [-(_1001472 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (12888 ^ _779300) ^ [_1001581, _1001583] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001581), _1001583) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1001581 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001583 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12898 ^ _779300) ^ [_1001739, _1001741] : [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), _1001739), _1001741))), 12901 ^ _779300 : [(12902 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001739)))], (12904 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001741)))]]], (12906 ^ _779300) ^ [_1001862, _1001864] : [-(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), _1001862), _1001864)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001864))], (12916 ^ _779300) ^ [_1002035, _1002037, _1002039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002035), _1002037)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002035), _1002039))), 12919 ^ _779300 : [(12920 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1002035)))], (12922 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002037), _1002039)))]]], (12924 ^ _779300) ^ [_1002184, _1002186, _1002188] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002184), _1002186)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002184), _1002188)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1002184)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002186), _1002188))], (12934 ^ _779300) ^ [_1002385, _1002387, _1002389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002385), _1002387)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002389), _1002387))), 12937 ^ _779300 : [(12938 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1002387)))], (12940 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002385), _1002389)))]]], (12942 ^ _779300) ^ [_1002534, _1002536, _1002538] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002534), _1002536)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002538), _1002536)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1002536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002534), _1002538))], (12952 ^ _779300) ^ [_1002717, _1002719, _1002721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002717), _1002719)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1002721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002717), _1002721)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002719), _1002721))))], (12962 ^ _779300) ^ [_1002898, _1002900, _1002902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002898), _1002900)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1002902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002902), _1002898)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002902), _1002900))))], (12972 ^ _779300) ^ [_1003097, _1003099, _1003101] : [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, _1003097)), _1003099)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1003097)), _1003101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003099), _1003101)))], (12978 ^ _779300) ^ [_1003228, _1003230, _1003232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003230), _1003232)), -(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, _1003228)), _1003230)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1003228)), _1003232))))], (12984 ^ _779300) ^ [_1003365, _1003367] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1003365), hAPP(c_Nat_OSuc, _1003367)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003365), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1003365), _1003367)))], (12986 ^ _779300) ^ [_1003411, _1003413] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1003411)), _1003413) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003413), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1003411), _1003413)))], (12988 ^ _779300) ^ [_1003475, _1003477, _1003479] : [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, _1003475)), _1003477)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1003475)), _1003479))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003477), _1003479)))], (12994 ^ _779300) ^ [_1003606, _1003608, _1003610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003608), _1003610)), -(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, _1003606)), _1003608)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1003606)), _1003610))))], (13000 ^ _779300) ^ [_1003743, _1003745] : [class_Int_Onumber__ring(_1003743), -(hBOOL(hAPP(hAPP(c_member(_1003743), hAPP(c_Int_Onumber__class_Onumber__of(_1003743), _1003745)), c_Int_Oring__1__class_OInts(_1003743))))], (13006 ^ _779300) ^ [_1003846, _1003848] : [_1003846 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1003846), _1003848), -(_1003848 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1003846 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13016 ^ _779300) ^ [_1003948, _1003950, _1003952] : [class_Rings_Oring__1(_1003948), hBOOL(hAPP(hAPP(c_member(_1003948), _1003950), c_Int_Oring__1__class_OInts(_1003948))), hBOOL(hAPP(hAPP(c_member(_1003948), _1003952), c_Int_Oring__1__class_OInts(_1003948))), -(hBOOL(hAPP(hAPP(c_member(_1003948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003948), _1003950), _1003952)), c_Int_Oring__1__class_OInts(_1003948))))], (13030 ^ _779300) ^ [_1004203, _1004205, _1004207, _1004209] : [class_Rings_Olinordered__semiring__strict(_1004203), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004203), _1004205), _1004207)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004203), _1004205), _1004209))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004203), c_Groups_Ozero__class_Ozero(_1004203)), _1004205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004203), _1004207), _1004209)))], (13044 ^ _779300) ^ [_1004472, _1004474, _1004476, _1004478] : [class_Rings_Olinordered__semiring__strict(_1004472), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004472), _1004474), _1004476)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004472), _1004478), _1004476))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004472), c_Groups_Ozero__class_Ozero(_1004472)), _1004476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004472), _1004474), _1004478)))], (13058 ^ _779300) ^ [_1004741, _1004743, _1004745, _1004747] : [class_Rings_Olinordered__semiring__strict(_1004741), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004741), _1004743), _1004745)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004741), _1004743), _1004747))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004741), c_Groups_Ozero__class_Ozero(_1004741)), _1004743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004741), _1004745), _1004747)))], (13072 ^ _779300) ^ [_1005010, _1005012, _1005014, _1005016] : [class_Rings_Olinordered__semiring(_1005010), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005010), _1005012), _1005014)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005010), _1005012), _1005016))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1005010), c_Groups_Ozero__class_Ozero(_1005010)), _1005012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005010), _1005014), _1005016)))], (13086 ^ _779300) ^ [_1005279, _1005281, _1005283, _1005285] : [class_Rings_Olinordered__semiring__strict(_1005279), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005279), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005279), _1005281), _1005283)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005279), _1005285), _1005283))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1005279), c_Groups_Ozero__class_Ozero(_1005279)), _1005283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005279), _1005281), _1005285)))], (13100 ^ _779300) ^ [_1005548, _1005550, _1005552, _1005554] : [class_Rings_Olinordered__semiring(_1005548), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005548), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005548), _1005550), _1005552)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005548), _1005554), _1005552))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1005548), c_Groups_Ozero__class_Ozero(_1005548)), _1005552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005548), _1005550), _1005554)))], (13114 ^ _779300) ^ [_1005817, _1005819, _1005821, _1005823, _1005825] : [class_Rings_Olinordered__semiring__strict(_1005817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1005817), _1005819), _1005821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005817), _1005823), _1005825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005817), c_Groups_Ozero__class_Ozero(_1005817)), _1005819)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1005817), c_Groups_Ozero__class_Ozero(_1005817)), _1005823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005817), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005817), _1005819), _1005823)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005817), _1005821), _1005825))))], (13136 ^ _779300) ^ [_1006240, _1006242, _1006244, _1006246, _1006248] : [class_Rings_Olinordered__semiring__strict(_1006240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006240), _1006242), _1006244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006240), _1006246), _1006248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006240), c_Groups_Ozero__class_Ozero(_1006240)), _1006242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006240), c_Groups_Ozero__class_Ozero(_1006240)), _1006246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006240), _1006242), _1006246)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006240), _1006244), _1006248))))], (13158 ^ _779300) ^ [_1006663, _1006665, _1006667, _1006669, _1006671] : [class_Rings_Olinordered__semiring__strict(_1006663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006663), _1006665), _1006667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006663), _1006669), _1006671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006663), c_Groups_Ozero__class_Ozero(_1006663)), _1006665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006663), c_Groups_Ozero__class_Ozero(_1006663)), _1006669)), 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012517), _1012515))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1012515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1012513), _1012517)))], (13474 ^ _779300) ^ [_1013047, _1013049, _1013051] : [13475 ^ _779300 : [(13476 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1013047)))], (13478 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1013049), _1013051))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013047), _1013049)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013047), _1013051))))], (13464 ^ _779300) ^ [_1012870, _1012872, _1012874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012870), _1012872)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012870), _1012874))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1012870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1012872), _1012874)))], (13482 ^ _779300) ^ [_1013209, _1013211, _1013213, _1013215, _1013217] : [class_Groups_Oab__semigroup__mult(_1013209), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1013209, _1013209, c_Groups_Otimes__class_Otimes(_1013209), _1013211, _1013213), _1013215)), -(hBOOL(hAPP(hAPP(c_member(_1013209), _1013211), _1013213))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1013209, _1013209, c_Groups_Otimes__class_Otimes(_1013209), _1013217, hAPP(hAPP(c_Set_Oinsert(_1013209), _1013211), _1013213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013209), _1013217), _1013215))))], (13496 ^ _779300) ^ [_1013449, _1013451, _1013453, _1013455, _1013457] : [class_Groups_Ocomm__monoid__mult(_1013449), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013451), _1013453)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1013449, _1013451, c_Groups_Otimes__class_Otimes(_1013449)), hAPP(hAPP(c_COMBS(_1013451, _1013449, _1013449), hAPP(hAPP(c_COMBB(_1013449, tc_fun(_1013449, _1013449), _1013451), c_Groups_Otimes__class_Otimes(_1013449)), _1013455)), _1013457)), c_Groups_Oone__class_Oone(_1013449)), _1013453) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013449), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1013449, _1013451, c_Groups_Otimes__class_Otimes(_1013449)), _1013455), c_Groups_Oone__class_Oone(_1013449)), _1013453)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1013449, _1013451, c_Groups_Otimes__class_Otimes(_1013449)), _1013457), c_Groups_Oone__class_Oone(_1013449)), _1013453)))], (13506 ^ _779300) ^ [_1013764, _1013766, _1013768, _1013770, _1013772, _1013774] : [class_Rings_Olinordered__semiring__1(_1013764), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013764), _1013766), _1013768)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013764), _1013770), _1013768)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013764), c_Groups_Ozero__class_Ozero(_1013764)), _1013772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013764), c_Groups_Ozero__class_Ozero(_1013764)), _1013774)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013764), _1013772), _1013774) = c_Groups_Oone__class_Oone(_1013764), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013764), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013764), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013764), _1013772), _1013766)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013764), _1013774), _1013770))), _1013768)))], (13532 ^ _779300) ^ [_1014293, _1014295, _1014297, _1014299, _1014301, _1014303] : [class_Groups_Oab__semigroup__mult(_1014293), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014295), _1014297)), -(hBOOL(hAPP(hAPP(c_member(_1014295), _1014299), _1014297))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1014293, _1014295, c_Groups_Otimes__class_Otimes(_1014293)), _1014301), _1014303), hAPP(hAPP(c_Set_Oinsert(_1014295), _1014299), _1014297)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014293), hAPP(_1014301, _1014299)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1014293, _1014295, c_Groups_Otimes__class_Otimes(_1014293)), _1014301), _1014303), _1014297)))], (13546 ^ _779300) ^ [_1014580, _1014582] : [_1014580 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014580), _1014582) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13552 ^ _779300) ^ [_1014663, _1014665] : [-(_1014663 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014663), _1014665) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1014665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014663), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1014665)))], (13558 ^ _779300) ^ [_1014725, _1014727, _1014729, _1014731, _1014733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014725), _1014727)), 13561 ^ _779300 : [(13562 ^ _779300) ^ [] : [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), _1014727), _1014729)), _1014731)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014725), _1014729)), _1014733))), -(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), _1014727), _1014725)), _1014729)), _1014731)), _1014733)))], (13568 ^ _779300) ^ [] : [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), _1014727), _1014725)), _1014729)), _1014731)), _1014733)), -(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), _1014727), _1014729)), _1014731)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014725), _1014729)), _1014733))))]]], (13574 ^ _779300) ^ [_1015116, _1015118, _1015120, _1015122, _1015124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015116), _1015118)), 13577 ^ _779300 : [(13578 ^ _779300) ^ [] : [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), _1015116), _1015120)), _1015122)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015118), _1015120)), _1015124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015122), 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), _1015118), _1015116)), _1015120)), _1015124))))], (13584 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015122), 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), _1015118), _1015116)), _1015120)), _1015124))), -(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), _1015116), _1015120)), _1015122)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015118), _1015120)), _1015124))))]]], (13590 ^ _779300) ^ [_1015507, _1015509, _1015511, _1015513, _1015515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015507), _1015509)), 13593 ^ _779300 : [(13594 ^ _779300) ^ [] : [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), _1015509), _1015511)), _1015513)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015507), _1015511)), _1015515))), -(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), _1015509), _1015507)), _1015511)), _1015513)), _1015515)))], (13600 ^ _779300) ^ [] : [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), _1015509), _1015507)), _1015511)), _1015513)), _1015515)), -(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), _1015509), _1015511)), _1015513)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015507), _1015511)), _1015515))))]]], (13606 ^ _779300) ^ [_1015898, _1015900, _1015902, _1015904, _1015906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015898), _1015900)), -(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), _1015900), _1015902)), _1015904)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015898), _1015902)), _1015906)) = 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), _1015900), _1015898)), _1015902)), _1015904)), _1015906))], (13612 ^ _779300) ^ [_1016099, _1016101, _1016103, _1016105, _1016107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016099), _1016101)), 13615 ^ _779300 : [(13616 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016101), _1016103)), _1016105) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016099), _1016103)), _1016107), -(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), _1016101), _1016099)), _1016103)), _1016105) = _1016107)], (13622 ^ _779300) ^ [] : [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), _1016101), _1016099)), _1016103)), _1016105) = _1016107, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016101), _1016103)), _1016105) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016099), _1016103)), _1016107))]]], (13628 ^ _779300) ^ [_1016460, _1016462, _1016464, _1016466, _1016468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016460), _1016462)), 13631 ^ _779300 : [(13632 ^ _779300) ^ [] : [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), _1016460), _1016464)), _1016466)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016462), _1016464)), _1016468))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016466), 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), _1016462), _1016460)), _1016464)), _1016468))))], (13638 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016466), 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), _1016462), _1016460)), _1016464)), _1016468))), -(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), _1016460), _1016464)), _1016466)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016462), _1016464)), _1016468))))]]], (13644 ^ _779300) ^ [_1016851, _1016853, _1016855, _1016857, _1016859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016851), _1016853)), -(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), _1016851), _1016855)), _1016857)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016853), _1016855)), _1016859)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016857), 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), _1016853), _1016851)), _1016855)), _1016859)))], (13650 ^ _779300) ^ [_1017052, _1017054, _1017056, _1017058, _1017060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1017052), _1017054)), 13653 ^ _779300 : [(13654 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017052), _1017056)), _1017058) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017054), _1017056)), _1017060), -(_1017058 = 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), _1017054), _1017052)), _1017056)), _1017060))], (13660 ^ _779300) ^ [] : [_1017058 = 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), _1017054), _1017052)), _1017056)), _1017060), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017052), _1017056)), _1017058) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017054), _1017056)), _1017060))]]], (13666 ^ _779300) ^ [_1017413, _1017415, _1017417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1017413)), 13669 ^ _779300 : [(13670 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017413), _1017415)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017413), _1017417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1017415), _1017417)))], (13676 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1017415), _1017417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017413), _1017415)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017413), _1017417))))]]], (13682 ^ _779300) ^ [_1017696, _1017698] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017696), _1017698) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017698), _1017696))], (13684 ^ _779300) ^ [_1017733, _1017735, _1017737] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017733), _1017735)), _1017737) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017735), _1017737)))], (13686 ^ _779300) ^ [_1017784] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1017784) = _1017784)], (13688 ^ _779300) ^ [_1017810] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017810), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1017810)], (13690 ^ _779300) ^ [_1017854, _1017856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017854)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017856))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017854), _1017856)))], (13696 ^ _779300) ^ [_1017959, _1017961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017959), _1017961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017959)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017961))))], (13702 ^ _779300) ^ [_1018070, _1018072] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018070), _1018072) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018072), _1018070))], (13704 ^ _779300) ^ [_1018107, _1018109] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1018107)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1018109)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018107), _1018109)))], (13706 ^ _779300) ^ [_1018153, _1018155, _1018157] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018153), _1018155)), _1018157) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018155), _1018157)))], (13708 ^ _779300) ^ [_1018204, _1018206, _1018208] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018204), _1018206)), _1018208) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018204), _1018208)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018206), _1018208)))], (13710 ^ _779300) ^ [_1018261, _1018263, _1018265] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018261), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018263), _1018265)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018261), _1018263)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018261), _1018265)))], (13712 ^ _779300) ^ [_1018318, _1018320, _1018322] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018318), _1018320)), _1018322) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018318), _1018322)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018320), _1018322)))], (13714 ^ _779300) ^ [_1018375, _1018377] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1018375)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1018377)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018375), _1018377)))], (13716 ^ _779300) ^ [_1018421, _1018423, _1018425] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018421), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018423), _1018425)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018421), _1018423)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018421), _1018425)))], (13718 ^ _779300) ^ [_1018478, _1018480, _1018482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018478), _1018480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018482), _1018478)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018482), _1018480))))], (13728 ^ _779300) ^ [_1018659, _1018661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018659)), 13731 ^ _779300 : [(13732 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018659), _1018661) = c_Groups_Oone__class_Oone(tc_Int_Oint), 13735 ^ _779300 : [(13736 ^ _779300) ^ [] : [-(_1018659 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (13738 ^ _779300) ^ [] : [-(_1018661 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (13740 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018659), _1018661) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1018659 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1018661 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (13750 ^ _779300) ^ [_1018975, _1018977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1018975)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1018977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018975), _1018977)))], (13756 ^ _779300) ^ [_1019080, _1019082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019080), _1019082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1019080)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1019082))))], (13762 ^ _779300) ^ [_1019206, _1019208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019206), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1019208), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019206), _1019208)))], (13768 ^ _779300) ^ [_1019311, _1019313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019311), _1019313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019311), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1019313), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (13774 ^ _779300) ^ [_1019437, _1019439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019437), _1019439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1019437), _1019439)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13780 ^ _779300) ^ [_1019542, _1019544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1019542), _1019544)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019542), _1019544)))], (13786 ^ _779300) ^ [_1019665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1019665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019665)))], (13792 ^ _779300) ^ [_1019744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1019744)))], (13798 ^ _779300) ^ [_1019844, _1019846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019844), _1019846)), 13801 ^ _779300 : [(13802 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019844), _1019846)))], (13804 ^ _779300) ^ [] : [_1019844 = _1019846]]], (13806 ^ _779300) ^ [_1019971, _1019973] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019971), _1019973))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019971), _1019973)), -(_1019971 = _1019973)], (13816 ^ _779300) ^ [_1020140, _1020142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020140), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020142), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1020140), _1020142)))], (13822 ^ _779300) ^ [_1020245, _1020247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1020245), _1020247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020245), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020247), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (13828 ^ _779300) ^ [_1020371, _1020373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020371), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1020373)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020371), _1020373)))], (13834 ^ _779300) ^ [_1020476, _1020478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020476), _1020478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020476), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1020478)))], (13840 ^ _779300) ^ [_1020587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020587)), -(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)), _1020587))))], (13846 ^ _779300) ^ [_1020676, _1020678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020676), _1020678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020676), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1020678)))], (13852 ^ _779300) ^ [_1020785, _1020787, _1020789, _1020791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020785), _1020787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1020789), _1020791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020785), _1020789)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020787), _1020791))))], (13862 ^ _779300) ^ [_1020985] : [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)), _1020985)), _1020985) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (13864 ^ _779300) ^ [] : [-(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))))], (13866 ^ _779300) ^ [_1021031, _1021033] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021031), _1021033))), -(_1021031 = _1021033), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021033), _1021031)))], (13886 ^ _779300) ^ [_1021217, _1021219] : [13887 ^ _779300 : [(13888 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021217), _1021219))], (13890 ^ _779300) ^ [] : [_1021217 = _1021219]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021219), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (13876 ^ _779300) ^ [_1021099, _1021101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021099), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021101), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021099), _1021101))), -(_1021099 = _1021101)], (13894 ^ _779300) ^ [_1021378] : [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)), _1021378)), _1021378)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021378), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13900 ^ _779300) ^ [_1021487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021487), 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)), _1021487)), _1021487)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13906 ^ _779300) ^ [_1021602, _1021604, _1021606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021602), _1021604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021602), _1021606)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021604), _1021606))))], (13912 ^ _779300) ^ [_1021725, _1021727, _1021729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021725), _1021727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021729), _1021725)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021729), _1021727))))], (13918 ^ _779300) ^ [_1021848] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021848) = _1021848)], (13920 ^ _779300) ^ [_1021874] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021874), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1021874)], (13922 ^ _779300) ^ [_1021903, _1021905] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021903), _1021905) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021905), _1021903))], (13924 ^ _779300) ^ [_1021940, _1021942, _1021944] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021940), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021942), _1021944)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021942), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021940), _1021944)))], (13926 ^ _779300) ^ [_1021991, _1021993, _1021995] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021991), _1021993)), _1021995) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021991), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021993), _1021995)))], (13928 ^ _779300) ^ [_1022042, _1022044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022042), _1022044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022044), _1022042)), -(_1022042 = _1022044)], (13938 ^ _779300) ^ [_1022191, _1022193, _1022195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022191), _1022193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022193), _1022195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022191), _1022195)))], (13948 ^ _779300) ^ [_1022350, _1022352] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022350), _1022352))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022352), _1022350)))], (13954 ^ _779300) ^ [_1022396] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022396), _1022396)))], (13966 ^ _779300) ^ [_1022554, _1022556, _1022558] : [13967 ^ _779300 : [(13968 ^ _779300) ^ [] : [_1022554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13970 ^ _779300) ^ [] : [_1022556 = _1022558]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022554), _1022556) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022554), _1022558))], (13956 ^ _779300) ^ [_1022442, _1022444, _1022446] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022442), _1022444) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022442), _1022446), -(_1022442 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1022444 = _1022446)], (13974 ^ _779300) ^ [_1022697, _1022699, _1022701, _1022703] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022697), _1022699)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022701), _1022699)), _1022703)) = 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), _1022697), _1022701)), _1022699)), _1022703))], (13976 ^ _779300) ^ [_1022768, _1022770, _1022772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1022768)), 13979 ^ _779300 : [(13980 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022768), _1022770) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022768), _1022772), -(_1022770 = _1022772)], (13986 ^ _779300) ^ [] : [_1022770 = _1022772, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022768), _1022770) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022768), _1022772))]]], (13992 ^ _779300) ^ [_1023021, _1023023, _1023025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1023021)), 13995 ^ _779300 : [(13996 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023021), _1023023)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023021), _1023025))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1023023), _1023025)))], (14002 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1023023), _1023025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023021), _1023023)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023021), _1023025))))]]], (14008 ^ _779300) ^ [_1023304, _1023306, _1023308, _1023310, _1023312, _1023314] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023304), _1023306)), _1023308) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023310), _1023312)), _1023314), 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), _1023310), _1023312)), _1023314)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023308), _1023304)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023310), _1023304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023312), _1023306)))], (14034 ^ _779300) ^ [_1023809, _1023811, _1023813, _1023815, _1023817] : [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), _1023809), _1023811)), _1023813)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023809), _1023815)), _1023817))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023817), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023809), _1023817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023809), _1023813)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023815), _1023811)))], (14052 ^ _779300) ^ [_1024164, _1024166, _1024168, _1024170, _1024172, _1024174] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024164), _1024166)), _1024168) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024170), _1024172)), _1024174), 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), _1024170), _1024172)), _1024174))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024174), _1024170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1024170), _1024164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1024166), _1024172)))], (14078 ^ _779300) ^ [_1024663, _1024665, _1024667, _1024669, _1024671] : [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), _1024663), _1024665)), _1024667)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024663), _1024669)), _1024671))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024667), _1024663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024671), _1024663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1024665), _1024669)))], (14096 ^ _779300) ^ [_1025012, _1025014, _1025016] : [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), _1025012), _1025014)), _1025016)), 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)), _1025016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1025014), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14110 ^ _779300) ^ [_1025251, _1025253, _1025255] : [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), _1025251), _1025253)), _1025255))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1025255), _1025251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025253)))], (14124 ^ _779300) ^ [_1025484, _1025486, _1025488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025484)), _1025484 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1025486), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1025484), _1025488)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1025486), _1025484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1025488)))], (14138 ^ _779300) ^ [_1025713, _1025715, _1025717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025713)), _1025713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1025715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1025713), _1025717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1025717), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (14152 ^ _779300) ^ [_1025942] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1025942) = _1025942)], (14154 ^ _779300) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (14156 ^ _779300) ^ [_1025992, _1025994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025992)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025994)), -(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), _1025992), _1025994))))], (14166 ^ _779300) ^ [] : [-(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))))], (14168 ^ _779300) ^ [_1026163, _1026165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026165)), -(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), _1026163), _1026165))))], (14178 ^ _779300) ^ [_1026316, _1026318, _1026320, _1026322] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1026316, _1026318)), c_Nitpick_Opair__box_OPairBox(_1026316, _1026318, _1026320, _1026322)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14180 ^ _779300) ^ [_1026358, _1026360, _1026362, _1026364, _1026366, _1026368] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1026358, _1026360, _1026362, _1026364, c_Nitpick_Opair__box_OPairBox(_1026358, _1026360, _1026366, _1026368)) = hAPP(hAPP(_1026364, _1026366), _1026368))], (14182 ^ _779300) ^ [_1026408, _1026410, _1026412, _1026414, _1026416, _1026418] : [-(c_Nitpick_Opair__box_Opair__box__case(_1026408, _1026410, _1026412, _1026414, c_Nitpick_Opair__box_OPairBox(_1026408, _1026410, _1026416, _1026418)) = hAPP(hAPP(_1026414, _1026416), _1026418))], (14184 ^ _779300) ^ [] : [-(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))))], (14186 ^ _779300) ^ [_1026476, _1026478] : [class_Int_Onumber__ring(_1026476), 14189 ^ _779300 : [(14190 ^ _779300) ^ [] : [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), _1026478))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1026476), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1026478)) = hAPP(c_Int_Onumber__class_Onumber__of(_1026476), _1026478))], (14196 ^ _779300) ^ [] : [-(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), _1026478)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1026476), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1026478)) = c_Groups_Ozero__class_Ozero(_1026476))]]], (14202 ^ _779300) ^ [_1026716, _1026718, _1026720] : [class_Nat_Osemiring__char__0(_1026716), 14205 ^ _779300 : [(14206 ^ _779300) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1026716), _1026718) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1026716), _1026720), -(_1026718 = _1026720)], (14212 ^ _779300) ^ [] : [_1026718 = _1026720, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1026716), _1026718) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1026716), _1026720))]]], (14218 ^ _779300) ^ [_1026969] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1026969)), -(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)), _1026969))))], (14224 ^ _779300) ^ [_1027054] : [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)), _1027054))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1027054)))], (14230 ^ _779300) ^ [] : [-(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)))], (14232 ^ _779300) ^ [_1027175] : [14234 ^ _779300 : [(14235 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14233 ^ [_1027175])))], (14237 ^ _779300) ^ [] : [hBOOL(hAPP(_1027175, 14233 ^ [_1027175]))]], 14238 ^ _779300 : [(14239 ^ _779300) ^ [_1027302] : [-(hBOOL(hAPP(_1027175, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027302))))]]], (14241 ^ _779300) ^ [_1027332] : [hBOOL(hAPP(_1027332, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 14242 ^ [_1027332]))), 14245 ^ _779300 : [(14246 ^ _779300) ^ [_1027432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027432)), -(hBOOL(hAPP(_1027332, _1027432)))]]], (14263 ^ _779300) ^ [_1027705] : [14264 ^ _779300 : [(14265 ^ _779300) ^ [_1027762] : [hBOOL(hAPP(_1027705, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027762)))]], 14267 ^ _779300 : [(14268 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14266 ^ [_1027705])))], (14270 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1027705, 14266 ^ [_1027705])))]]], (14252 ^ _779300) ^ [_1027535] : [-(hBOOL(hAPP(_1027535, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 14259 ^ [_1027535])))), 14253 ^ _779300 : [(14254 ^ _779300) ^ [_1027587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027587)), hBOOL(hAPP(_1027535, _1027587))]]], (14272 ^ _779300) ^ [_1027854] : [-(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), _1027854))))], (14274 ^ _779300) ^ [_1027897, _1027899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027897)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027899))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027897), _1027899)))], (14280 ^ _779300) ^ [_1028002, _1028004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028002), _1028004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028002)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028004))))], (14286 ^ _779300) ^ [_1028128, _1028130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028128)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028128), _1028130)))], (14292 ^ _779300) ^ [_1028233, _1028235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028233), _1028235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028233)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028235))))], (14298 ^ _779300) ^ [_1028344, _1028346] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028344)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028346)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028344), _1028346)))], (14300 ^ _779300) ^ [_1028390, _1028392] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028390)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028392)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028390), _1028392)))], (14302 ^ _779300) ^ [] : [-(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)))], (14304 ^ _779300) ^ [_1028466] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028466) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1028466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14310 ^ _779300) ^ [_1028543] : [_1028543 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028543) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14316 ^ _779300) ^ [] : [-(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))], (14318 ^ _779300) ^ [_1028644] : [-(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), _1028644))))], (14320 ^ _779300) ^ [_1028681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028681)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14322 ^ _779300) ^ [_1028727, _1028729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028727)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028729))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028727), _1028729)))], (14328 ^ _779300) ^ [_1028832, _1028834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028832), _1028834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028832)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028834))))], (14334 ^ _779300) ^ [_1028958, _1028960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028958)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028958), _1028960)))], (14340 ^ _779300) ^ [_1029063, _1029065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029063), _1029065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029063)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029065))))], (14346 ^ _779300) ^ [_1029174, _1029176, _1029178] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029174)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029176)), _1029178)) = 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), _1029174), _1029176))), _1029178))], (14348 ^ _779300) ^ [_1029234, _1029236] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029234)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029236)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029234), _1029236)))], (14350 ^ _779300) ^ [_1029295, _1029297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029295), _1029297)), -(_1029297 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1029295), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 14353 ^ [_1029295, _1029297])))], (14357 ^ _779300) ^ [_1029408, _1029410] : [14358 ^ _779300 : [(14359 ^ _779300) ^ [_1029461] : [_1029410 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1029408), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029461))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029408), _1029410)))], (14363 ^ _779300) ^ [_1029528, _1029530] : [class_Rings_Olinordered__semidom(_1029528), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029528), c_Groups_Ozero__class_Ozero(_1029528)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029528), _1029530))))], (14369 ^ _779300) ^ [_1029631, _1029633] : [class_Rings_Olinordered__semidom(_1029631), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029631), c_Groups_Ozero__class_Ozero(_1029631)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029631), _1029633))))], (14375 ^ _779300) ^ [_1029734, _1029736] : [class_Rings_Olinordered__semidom(_1029734), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029734), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029734), _1029736)), c_Groups_Ozero__class_Ozero(_1029734)))], (14381 ^ _779300) ^ [_1029838, _1029840] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029838), _1029840)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029838)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029840)))], (14383 ^ _779300) ^ [_1029884, _1029886] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029884)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029886)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029884), _1029886)))], (14385 ^ _779300) ^ [_1029930] : [class_Rings_Osemiring__1(_1029930), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029930), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1029930))], (14391 ^ _779300) ^ [_1030017, _1030019, _1030021] : [class_Rings_Olinordered__semidom(_1030017), 14394 ^ _779300 : [(14395 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030017), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030017), _1030019)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030017), _1030021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030019), _1030021)))], (14401 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030019), _1030021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030017), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030017), _1030019)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030017), _1030021))))]]], (14407 ^ _779300) ^ [_1030294, _1030296, _1030298] : [class_Rings_Olinordered__semidom(_1030294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030296), _1030298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030294), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030294), _1030296)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030294), _1030298))))], (14417 ^ _779300) ^ [_1030469, _1030471, _1030473] : [class_Rings_Olinordered__semidom(_1030469), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030469), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030469), _1030471)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030469), _1030473))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030471), _1030473)))], (14427 ^ _779300) ^ [] : [-(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))], (14429 ^ _779300) ^ [_1030662, _1030664, _1030666] : [class_Rings_Olinordered__semidom(_1030662), 14432 ^ _779300 : [(14433 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030662), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030662), _1030664)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030662), _1030666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030664), _1030666)))], (14439 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030664), _1030666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030662), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030662), _1030664)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030662), _1030666))))]]], (14445 ^ _779300) ^ [_1030939, _1030941, _1030943] : [class_Rings_Osemiring__1(_1030939), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030941), _1030943)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030939), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030939), _1030941)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030939), _1030943)))], (14451 ^ _779300) ^ [_1031074, _1031076, _1031078] : [class_Rings_Osemiring__1(_1031074), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031076), _1031078)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031074), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031074), _1031076)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031074), _1031078)))], (14457 ^ _779300) ^ [_1031209] : [class_Rings_Osemiring__1(_1031209), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031209), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1031209))], (14463 ^ _779300) ^ [_1031296, _1031298] : [class_Rings_Oring__1(_1031296), -(hBOOL(hAPP(hAPP(c_member(_1031296), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031296), _1031298)), c_Int_Oring__1__class_OInts(_1031296))))], (14469 ^ _779300) ^ [_1031411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031411)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1031411 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14475 ^ _779300) ^ [_1031498] : [_1031498 = 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), _1031498)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14481 ^ _779300) ^ [] : [-(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))], (14483 ^ _779300) ^ [_1031624, _1031626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1031624), _1031626)), -(_1031626 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1031624), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 14486 ^ [_1031624, _1031626]))))], (14490 ^ _779300) ^ [_1031743, _1031745] : [14491 ^ _779300 : [(14492 ^ _779300) ^ [_1031799] : [_1031745 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1031743), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1031799)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1031743), _1031745)))], (14496 ^ _779300) ^ [_1031869] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1031869)) = 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), _1031869)))], (14498 ^ _779300) ^ [_1031904, _1031906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031904), _1031906)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031906)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031904)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031906), _1031904)))], (14504 ^ _779300) ^ [_1032033, _1032035] : [class_Rings_Osemiring__1(_1032033), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032033), hAPP(c_Nat_OSuc, _1032035)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032033), c_Groups_Oone__class_Oone(_1032033)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032033), _1032035)))], (14510 ^ _779300) ^ [_1032154, _1032156, _1032158] : [class_Rings_Oring__1(_1032154), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032156), _1032158)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032154), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1032158), _1032156)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032154), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032154), _1032158)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032154), _1032156)))], (14520 ^ _779300) ^ [_1032365] : [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), _1032365))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032365)))], (14526 ^ _779300) ^ [_1032450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032450)), -(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), _1032450))))], (14532 ^ _779300) ^ [_1032541, _1032543, _1032545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1032541), _1032543)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032545)), -(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), _1032545)), _1032541)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032545)), _1032543))))], (14542 ^ _779300) ^ [_1032734, _1032736] : [class_Rings_Olinordered__semidom(_1032734), 14545 ^ _779300 : [(14546 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032734), c_Groups_Ozero__class_Ozero(_1032734)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032734), _1032736))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032736)))], (14552 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032734), c_Groups_Ozero__class_Ozero(_1032734)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032734), _1032736))))]]], (14574 ^ _779300) ^ [_1033294, _1033296, _1033298] : [-(hBOOL(hAPP(_1033294, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033296), _1033298))))), 14577 ^ _779300 : [(14578 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1033298), _1033296)))], (14580 ^ _779300) ^ [] : [hBOOL(hAPP(_1033294, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1033296)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1033298))))]], 14581 ^ _779300 : [(14582 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033296), _1033298)))], (14584 ^ _779300) ^ [] : [hBOOL(hAPP(_1033294, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (14558 ^ _779300) ^ [_1033005, _1033007, _1033009] : [hBOOL(hAPP(_1033005, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033007), _1033009)))), 14561 ^ _779300 : [(14562 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1033009), _1033007)), -(hBOOL(hAPP(_1033005, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1033007)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1033009)))))], (14568 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1033007), _1033009)), -(hBOOL(hAPP(_1033005, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (14588 ^ _779300) ^ [_1033569, _1033571] : [class_Rings_Osemiring__1(_1033569), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1033569), _1033571) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1033569, hAPP(hAPP(c_COMBC(_1033569, _1033569, _1033569), c_Groups_Oplus__class_Oplus(_1033569)), c_Groups_Oone__class_Oone(_1033569)), _1033571, c_Groups_Ozero__class_Ozero(_1033569)))], (14594 ^ _779300) ^ [_1033705, _1033707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033705), _1033707)), -(c_Nat__Transfer_Otsub(_1033707, _1033705) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1033707), _1033705))], (14600 ^ _779300) ^ [_1033804, _1033806] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033804), _1033806))), -(c_Nat__Transfer_Otsub(_1033806, _1033804) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14606 ^ _779300) ^ [_1033850, _1033852] : [class_Int_Onumber__ring(_1033850), 14609 ^ _779300 : [(14610 ^ _779300) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1033852))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1033850), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033852)) = c_Groups_Ozero__class_Ozero(_1033850))], (14616 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1033852)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1033850), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033852)) = hAPP(c_Int_Onumber__class_Onumber__of(_1033850), _1033852))]]], (14622 ^ _779300) ^ [_1034090, _1034092, _1034094] : [class_Groups_Oab__semigroup__mult(_1034090), -(_1034092 = c_Orderings_Obot__class_Obot(tc_fun(_1034090, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034090), _1034092)), -(hBOOL(hAPP(hAPP(c_member(_1034090), _1034094), _1034092))), -(hAPP(c_Finite__Set_Ofold1(_1034090, c_Groups_Otimes__class_Otimes(_1034090)), hAPP(hAPP(c_Set_Oinsert(_1034090), _1034094), _1034092)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034090), _1034094), hAPP(c_Finite__Set_Ofold1(_1034090, c_Groups_Otimes__class_Otimes(_1034090)), _1034092)))], (14640 ^ _779300) ^ [_1034398, _1034400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1034398), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034398)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034400)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14646 ^ _779300) ^ [_1034503, _1034505] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1034503), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034503)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034505)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1034503), _1034505)))], (14652 ^ _779300) ^ [_1034579, _1034581, _1034583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1034579), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034579)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034581)), _1034583)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14658 ^ _779300) ^ [_1034698, _1034700, _1034702] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1034698), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034698)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034700)), _1034702)) = 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), _1034698), _1034700))), _1034702))], (14664 ^ _779300) ^ [_1034776, _1034778, _1034780, _1034782] : [class_Groups_Ocomm__monoid__mult(_1034776), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034778), _1034780)), 14674 ^ _779300 : [(14675 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1034778), 14673 ^ [_1034776, _1034778, _1034780, _1034782]), _1034780)))], (14677 ^ _779300) ^ [] : [hAPP(_1034782, 14673 ^ [_1034776, _1034778, _1034780, _1034782]) = c_Groups_Oone__class_Oone(_1034776)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1034776, _1034778, c_Groups_Otimes__class_Otimes(_1034776)), _1034782), c_Groups_Oone__class_Oone(_1034776)), _1034780) = c_Groups_Oone__class_Oone(_1034776))], (14681 ^ _779300) ^ [] : [-(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))))], (14683 ^ _779300) ^ [_1035150, _1035152] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035150) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035152), -(_1035150 = _1035152)], (14689 ^ _779300) ^ [_1035235, _1035237] : [_1035235 = _1035237, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035235) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035237))], (14695 ^ _779300) ^ [_1035335] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035335)))], (14697 ^ _779300) ^ [_1035378, _1035380] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035378) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035380), -(_1035378 = _1035380)], (14703 ^ _779300) ^ [_1035463, _1035465] : [_1035463 = _1035465, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035463) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035465))], (14709 ^ _779300) ^ [_1035569, _1035571] : [_1035569 = _1035571, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035569) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035571))], (14715 ^ _779300) ^ [_1035654, _1035656] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035654) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035656), -(_1035654 = _1035656)], (14721 ^ _779300) ^ [_1035760, _1035762] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1035760), _1035762)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035760)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035762))))], (14727 ^ _779300) ^ [_1035865, _1035867] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035865)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035867))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1035865), _1035867)))], (14733 ^ _779300) ^ [_1035976] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1035976) = 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)), _1035976)))], (14735 ^ _779300) ^ [_1036023, _1036025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1036023), _1036025)), -(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)), _1036023)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1036025))))], (14741 ^ _779300) ^ [_1036128, _1036130] : [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)), _1036128)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1036130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1036128), _1036130)))], (14747 ^ _779300) ^ [_1036254, _1036256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1036254), _1036256)), -(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)), _1036254)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1036256))))], (14753 ^ _779300) ^ [_1036359, _1036361] : [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)), _1036359)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1036361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1036359), _1036361)))], (14759 ^ _779300) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (14761 ^ _779300) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14763 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (14765 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (14767 ^ _779300) ^ [_1036554] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1036554), c_Int_OPls) = _1036554)], (14769 ^ _779300) ^ [_1036583] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1036583) = _1036583)], (14771 ^ _779300) ^ [_1036609] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1036609) = c_Int_OPls)], (14773 ^ _779300) ^ [_1036635] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1036635), c_Int_OPls) = _1036635)], (14775 ^ _779300) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14777 ^ _779300) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (14779 ^ _779300) ^ [_1036712] : [class_Int_Onumber__ring(_1036712), -(hAPP(c_Int_Onumber__class_Onumber__of(_1036712), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1036712))], (14785 ^ _779300) ^ [_1036799] : [class_Int_Onumber__ring(_1036799), -(c_Groups_Ozero__class_Ozero(_1036799) = hAPP(c_Int_Onumber__class_Onumber__of(_1036799), c_Int_OPls))], (14791 ^ _779300) ^ [_1036886, _1036888] : [class_Int_Onumber__ring(_1036886), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036886), hAPP(c_Int_Onumber__class_Onumber__of(_1036886), c_Int_OPls)), _1036888) = _1036888)], (14797 ^ _779300) ^ [_1036987, _1036989] : [class_Int_Onumber__ring(_1036987), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036987), _1036989), hAPP(c_Int_Onumber__class_Onumber__of(_1036987), c_Int_OPls)) = _1036989)], (14803 ^ _779300) ^ [] : [-(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))))], (14805 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14807 ^ _779300) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (14809 ^ _779300) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14811 ^ _779300) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (14813 ^ _779300) ^ [_1037184, _1037186, _1037188] : [-(hAPP(c_Finite__Set_Ofold1(_1037184, _1037186), hAPP(hAPP(c_Set_Oinsert(_1037184), _1037188), c_Orderings_Obot__class_Obot(tc_fun(_1037184, tc_HOL_Obool)))) = _1037188)], (14815 ^ _779300) ^ [_1037230, _1037232, _1037234, _1037236] : [_1037230 = c_Finite__Set_Ofold1(_1037232, _1037234), -(hAPP(_1037230, hAPP(hAPP(c_Set_Oinsert(_1037232), _1037236), c_Orderings_Obot__class_Obot(tc_fun(_1037232, tc_HOL_Obool)))) = _1037236)], (14821 ^ _779300) ^ [_1037355] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1037355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1037355)))], (14827 ^ _779300) ^ [_1037389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1037389)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1037389))], (14833 ^ _779300) ^ [_1037487] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1037487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1037487), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14839 ^ _779300) ^ [_1037572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1037572), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1037572)))], (14845 ^ _779300) ^ [_1037663, _1037665] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037663), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037665)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037663), _1037665)))], (14847 ^ _779300) ^ [_1037706, _1037708, _1037710, _1037712] : [c_Finite__Set_Ofolding__one(_1037706, _1037708, _1037710), hBOOL(hAPP(c_Finite__Set_Ofinite(_1037706), _1037712)), -(hAPP(_1037710, _1037712) = hAPP(c_Finite__Set_Ofold1(_1037706, _1037708), _1037712))], (14857 ^ _779300) ^ [_1037871, _1037873, _1037875] : [class_Rings_Osemiring__1(_1037871), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1037871, _1037873, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1037875) = _1037875)], (14863 ^ _779300) ^ [_1037958, _1037960, _1037962, _1037964] : [class_Rings_Osemiring__1(_1037958), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1037958, _1037960, hAPP(c_Nat_OSuc, _1037962), _1037964) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1037958, _1037960, _1037962, hAPP(_1037960, _1037964)))], (14869 ^ _779300) ^ [_1038081] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038081), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038081), c_Int_OPls)))], (14875 ^ _779300) ^ [_1038168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038168), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038168))], (14881 ^ _779300) ^ [_1038273] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038273) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038273), c_Int_OPls)))], (14887 ^ _779300) ^ [_1038360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038360), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038360) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14893 ^ _779300) ^ [_1038468, _1038470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038468)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038470))), 14896 ^ _779300 : [(14903 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1038468), _1038470)))], (14897 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1038468), _1038470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1038470)))]]], (14905 ^ _779300) ^ [_1038671, _1038673] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038671)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038673)))), 14908 ^ _779300 : [(14909 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1038671), _1038673)))], (14911 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1038673))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1038671), _1038673))], (14927 ^ _779300) ^ [_1039026, _1039028] : [14928 ^ _779300 : [(14929 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1039026), _1039028))], (14931 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1039026), 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), _1039026)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1039028))))], (14917 ^ _779300) ^ [_1038896, _1038898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038896)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038898))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038896), _1038898))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038896), c_Int_OPls)))], (14935 ^ _779300) ^ [_1039187, _1039189, _1039191] : [-(hAPP(c_Finite__Set_Ofold1(_1039187, _1039189), _1039191) = c_HOL_OThe(_1039187, c_Finite__Set_Ofold1Set(_1039187, _1039189, _1039191)))], (14937 ^ _779300) ^ [_1039227] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1039227))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1039227) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14943 ^ _779300) ^ [_1039324] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1039324))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1039324)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14949 ^ _779300) ^ [_1039415] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1039415)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1039415)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1039415))], (14955 ^ _779300) ^ [_1039465, _1039467] : [class_Int_Onumber__ring(_1039465), class_Rings_Olinordered__idom(_1039465), 14962 ^ _779300 : [(14963 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039465), hAPP(c_Int_Onumber__class_Onumber__of(_1039465), _1039467)), c_Groups_Ozero__class_Ozero(_1039465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1039467), c_Int_OPls)))], (14969 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1039467), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039465), hAPP(c_Int_Onumber__class_Onumber__of(_1039465), _1039467)), c_Groups_Ozero__class_Ozero(_1039465))))]]], (14975 ^ _779300) ^ [_1039779, _1039781] : [class_Int_Onumber__ring(_1039779), class_Rings_Olinordered__idom(_1039779), 14982 ^ _779300 : [(14983 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039779), c_Groups_Ozero__class_Ozero(_1039779)), hAPP(c_Int_Onumber__class_Onumber__of(_1039779), _1039781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1039781)))], (14989 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1039781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039779), c_Groups_Ozero__class_Ozero(_1039779)), hAPP(c_Int_Onumber__class_Onumber__of(_1039779), _1039781))))]]], (14995 ^ _779300) ^ [_1040084, _1040086] : [class_Int_Onumber__ring(_1040084), class_Rings_Olinordered__idom(_1040084), 15002 ^ _779300 : [(15003 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040084), hAPP(c_Int_Onumber__class_Onumber__of(_1040084), _1040086)), c_Groups_Ozero__class_Ozero(_1040084))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040086), c_Int_OPls)))], (15009 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040086), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040084), hAPP(c_Int_Onumber__class_Onumber__of(_1040084), _1040086)), c_Groups_Ozero__class_Ozero(_1040084))))]]], (15015 ^ _779300) ^ [_1040398, _1040400] : [class_Int_Onumber__ring(_1040398), class_Rings_Olinordered__idom(_1040398), 15022 ^ _779300 : [(15023 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040398), c_Groups_Ozero__class_Ozero(_1040398)), hAPP(c_Int_Onumber__class_Onumber__of(_1040398), _1040400))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1040400)))], (15029 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1040400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040398), c_Groups_Ozero__class_Ozero(_1040398)), hAPP(c_Int_Onumber__class_Onumber__of(_1040398), _1040400))))]]], (15035 ^ _779300) ^ [_1040715] : [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), _1040715))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1040715)))], (15041 ^ _779300) ^ [_1040800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1040800)), -(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), _1040800))))], (15047 ^ _779300) ^ [_1040900, _1040902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040900), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040902)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040902))], (15053 ^ _779300) ^ [_1041012, _1041014] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1041012), c_Int_OPls))), 15056 ^ _779300 : [(15057 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1041014), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041012)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041014)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041012))], (15063 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1041014), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041012)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041014)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1041012), _1041014)))]]], (15069 ^ _779300) ^ [_1041285, _1041287, _1041289] : [class_Lattices_Oab__semigroup__idem__mult(_1041285), -(_1041287 = c_Orderings_Obot__class_Obot(tc_fun(_1041285, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1041285), _1041287)), -(hAPP(c_Finite__Set_Ofold1(_1041285, c_Groups_Otimes__class_Otimes(_1041285)), hAPP(hAPP(c_Set_Oinsert(_1041285), _1041289), _1041287)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041285), _1041289), hAPP(c_Finite__Set_Ofold1(_1041285, c_Groups_Otimes__class_Otimes(_1041285)), _1041287)))], (15109 ^ _779300) ^ [_1041955, _1041957] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041955) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041957)), 15112 ^ _779300 : [(15113 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041955))))], (15115 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041957)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 15116 ^ _779300 : [(15117 ^ _779300) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041955)))], (15119 ^ _779300) ^ [] : [15120 ^ _779300 : [(15121 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041957))))], (15123 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041955) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 15124 ^ _779300 : [(15125 ^ _779300) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041957)))], (15127 ^ _779300) ^ [] : [_1041955 = _1041957]]]]], (15083 ^ _779300) ^ [_1041570, _1041572] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041570) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041572), 15086 ^ _779300 : [(15087 ^ _779300) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041570))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041572)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15093 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041570)))), 15096 ^ _779300 : [(15097 ^ _779300) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041572))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041570) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15103 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041572)))), -(_1041570 = _1041572)]]]]], (15131 ^ _779300) ^ [_1042368, _1042370, _1042372] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042368))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042368)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042370)), _1042372)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042370)), _1042372))], (15137 ^ _779300) ^ [_1042506, _1042508, _1042510] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042506)))), 15140 ^ _779300 : [(15141 ^ _779300) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042508))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042506)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042508)), _1042510)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042506)), _1042510))], (15147 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042508)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042506)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042508)), _1042510)) = 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), _1042506), _1042508))), _1042510))]]], (15153 ^ _779300) ^ [_1042831, _1042833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1042831, _1042833))))], (15163 ^ _779300) ^ [_1042978, _1042980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1042978), _1042980)), -(c_Nat__Transfer_Otsub(_1042980, _1042978) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042980), _1042978))], (15169 ^ _779300) ^ [_1043092, _1043094] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1043092))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043092)), _1043094)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1043094))], (15175 ^ _779300) ^ [_1043203, _1043205] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1043203)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043203)), _1043205)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1043203))), _1043205))], (15181 ^ _779300) ^ [_1043275] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1043275))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043275)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15187 ^ _779300) ^ [_1043366] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1043366)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043366)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1043366)))], (15193 ^ _779300) ^ [_1043424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1043424), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043424)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15199 ^ _779300) ^ [_1043521] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1043521), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043521)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1043521)))], (15205 ^ _779300) ^ [_1043582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1043582), 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), _1043582)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15211 ^ _779300) ^ [_1043673] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1043673), 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), _1043673)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1043673)))], (15217 ^ _779300) ^ [_1043731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1043731), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043731)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15223 ^ _779300) ^ [_1043828] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1043828), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043828)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1043828)))], (15229 ^ _779300) ^ [_1043883, _1043885] : [class_Groups_Oab__semigroup__mult(_1043883), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043883), _1043885)), -(_1043885 = c_Orderings_Obot__class_Obot(tc_fun(_1043883, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1043883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043883), 15242 ^ [_1043883, _1043885]), 15243 ^ [_1043883, _1043885])), hAPP(hAPP(c_Set_Oinsert(_1043883), 15242 ^ [_1043883, _1043885]), hAPP(hAPP(c_Set_Oinsert(_1043883), 15243 ^ [_1043883, _1043885]), c_Orderings_Obot__class_Obot(tc_fun(_1043883, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1043883), hAPP(c_Finite__Set_Ofold1(_1043883, c_Groups_Otimes__class_Otimes(_1043883)), _1043885)), _1043885)))], (15249 ^ _779300) ^ [_1044337, _1044339] : [class_Int_Onumber__ring(_1044337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1044339)), -(hBOOL(hAPP(hAPP(c_member(_1044337), hAPP(c_Int_Onumber__class_Onumber__of(_1044337), _1044339)), c_Nat_Osemiring__1__class_ONats(_1044337))))], (15259 ^ _779300) ^ [_1044496, _1044498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1044496)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1044498)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1044496)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044498), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1044496))))], (15265 ^ _779300) ^ [_1044623] : [-(c_Int_Osucc(c_Int_Opred(_1044623)) = _1044623)], (15267 ^ _779300) ^ [_1044665, _1044667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1044665), _1044667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1044665)), _1044667)))], (15273 ^ _779300) ^ [_1044762, _1044764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1044762)), _1044764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1044762), _1044764)))], (15279 ^ _779300) ^ [_1044865] : [-(c_Int_Opred(_1044865) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044865), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15281 ^ _779300) ^ [_1044896] : [-(c_Int_Osucc(_1044896) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1044896), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15283 ^ _779300) ^ [_1044927] : [class_Rings_Osemiring__1(_1044927), -(hBOOL(hAPP(hAPP(c_member(_1044927), c_Groups_Ozero__class_Ozero(_1044927)), c_Nat_Osemiring__1__class_ONats(_1044927))))], (15289 ^ _779300) ^ [_1045022, _1045024, _1045026] : [class_Rings_Osemiring__1(_1045022), hBOOL(hAPP(hAPP(c_member(_1045022), _1045024), c_Nat_Osemiring__1__class_ONats(_1045022))), hBOOL(hAPP(hAPP(c_member(_1045022), _1045026), c_Nat_Osemiring__1__class_ONats(_1045022))), -(hBOOL(hAPP(hAPP(c_member(_1045022), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045022), _1045024), _1045026)), c_Nat_Osemiring__1__class_ONats(_1045022))))], (15303 ^ _779300) ^ [_1045277, _1045279, _1045281] : [class_Rings_Osemiring__1(_1045277), hBOOL(hAPP(hAPP(c_member(_1045277), _1045279), c_Nat_Osemiring__1__class_ONats(_1045277))), hBOOL(hAPP(hAPP(c_member(_1045277), _1045281), c_Nat_Osemiring__1__class_ONats(_1045277))), -(hBOOL(hAPP(hAPP(c_member(_1045277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045277), _1045279), _1045281)), c_Nat_Osemiring__1__class_ONats(_1045277))))], (15317 ^ _779300) ^ [_1045532] : [class_Rings_Osemiring__1(_1045532), -(hBOOL(hAPP(hAPP(c_member(_1045532), c_Groups_Oone__class_Oone(_1045532)), c_Nat_Osemiring__1__class_ONats(_1045532))))], (15323 ^ _779300) ^ [_1045627, _1045629] : [class_Rings_Osemiring__1(_1045627), -(hBOOL(hAPP(hAPP(c_member(_1045627), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1045627), _1045629)), c_Nat_Osemiring__1__class_ONats(_1045627))))], (15329 ^ _779300) ^ [_1045730, _1045732] : [class_Int_Onumber__ring(_1045730), -(hAPP(c_Int_Onumber__class_Onumber__of(_1045730), c_Int_Osucc(_1045732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045730), c_Groups_Oone__class_Oone(_1045730)), hAPP(c_Int_Onumber__class_Onumber__of(_1045730), _1045732)))], (15335 ^ _779300) ^ [_1045861] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1045861)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1045861) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15341 ^ _779300) ^ [_1045952] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1045952) = 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(_1045952)))))], (15347 ^ _779300) ^ [_1046049, _1046051, _1046053, _1046055, _1046057] : [-(c_Nat_Onat_Onat__case(_1046049, _1046051, _1046053, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1046055)), _1046057)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1046049), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1046055))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1046049, _1046049), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1046049, tc_fun(_1046049, _1046049)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1046049, tc_fun(_1046049, _1046049)), tc_Int_Oint), c_If(_1046049)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1046049, _1046051, _1046053, _1046057))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1046049, tc_Int_Oint), _1046053), 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)), _1046057)))))], (15349 ^ _779300) ^ [_1046182, _1046184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1046182)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1046184))), -(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(_1046184))), 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), _1046182)), c_Int_Onat))))))], (15355 ^ _779300) ^ [_1046327, _1046329] : [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(_1046329))), 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), _1046327)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1046327)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1046329))))], (15361 ^ _779300) ^ [_1046493, _1046495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1046493)), hAPP(c_Nat_OSuc, _1046495))), -(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(_1046493))), 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)), _1046495)))))], (15367 ^ _779300) ^ [_1046620, _1046622] : [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(_1046620))), 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)), _1046622)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1046620)), hAPP(c_Nat_OSuc, _1046622))))], (15373 ^ _779300) ^ [_1046768, _1046770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1046768)), hAPP(c_Nat_OSuc, _1046770))), -(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(_1046768))), 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)), _1046770)))))], (15379 ^ _779300) ^ [_1046895, _1046897] : [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(_1046895))), 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)), _1046897)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1046895)), hAPP(c_Nat_OSuc, _1046897))))], (15385 ^ _779300) ^ [_1047043, _1047045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1047043)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1047045))), -(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(_1047045))), 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), _1047043)), c_Int_Onat))))))], (15391 ^ _779300) ^ [_1047188, _1047190] : [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(_1047190))), 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), _1047188)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1047188)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1047190))))], (15397 ^ _779300) ^ [_1047339, _1047341, _1047343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1047339)), 15403 ^ _779300 : [(15404 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1047341, 15402 ^ [_1047339, _1047341, _1047343])))], (15406 ^ _779300) ^ [] : [hBOOL(hAPP(_1047341, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 15402 ^ [_1047339, _1047341, _1047343]), _1047339)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1047343)), 15411 ^ _779300 : [(15412 ^ _779300) ^ [_1047628] : [hBOOL(hAPP(_1047341, _1047628)), -(hBOOL(hAPP(_1047341, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1047628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1047343), _1047339)))))]]], (15418 ^ _779300) ^ [_1047757] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047757))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1047757)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15424 ^ _779300) ^ [_1047846] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047846)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1047846)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1047846)), 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)))))], (15430 ^ _779300) ^ [_1047901, _1047903, _1047905] : [class_Lattices_Oab__semigroup__idem__mult(_1047901), hAPP(_1047903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047901), 15435 ^ [_1047901, _1047903, _1047905]), 15436 ^ [_1047901, _1047903, _1047905])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047901), hAPP(_1047903, 15435 ^ [_1047901, _1047903, _1047905])), hAPP(_1047903, 15436 ^ [_1047901, _1047903, _1047905])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047901), _1047905)), -(_1047905 = c_Orderings_Obot__class_Obot(tc_fun(_1047901, tc_HOL_Obool))), -(hAPP(_1047903, hAPP(c_Finite__Set_Ofold1(_1047901, c_Groups_Otimes__class_Otimes(_1047901)), _1047905)) = hAPP(c_Finite__Set_Ofold1(_1047901, c_Groups_Otimes__class_Otimes(_1047901)), hAPP(c_Set_Oimage(_1047901, _1047901, _1047903), _1047905)))], (15450 ^ _779300) ^ [_1048339, _1048341] : [c_Int_OBit1(_1048339) = c_Int_OBit1(_1048341), -(_1048339 = _1048341)], (15456 ^ _779300) ^ [_1048420, _1048422] : [_1048420 = _1048422, -(c_Int_OBit1(_1048420) = c_Int_OBit1(_1048422))], (15462 ^ _779300) ^ [_1048522, _1048524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1048522)), c_Int_OBit1(_1048524))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1048522), _1048524)))], (15468 ^ _779300) ^ [_1048623, _1048625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1048623), _1048625)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1048623)), c_Int_OBit1(_1048625))))], (15474 ^ _779300) ^ [_1048745, _1048747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1048745)), c_Int_OBit1(_1048747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1048745), _1048747)))], (15480 ^ _779300) ^ [_1048846, _1048848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1048846), _1048848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1048846)), c_Int_OBit1(_1048848))))], (15486 ^ _779300) ^ [_1048968, _1048970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1048968)), c_Int_OBit1(_1048970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1048968), _1048970)))], (15492 ^ _779300) ^ [_1049069, _1049071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049069), _1049071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1049069)), c_Int_OBit1(_1049071))))], (15498 ^ _779300) ^ [_1049191, _1049193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1049191)), c_Int_OBit1(_1049193))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049191), _1049193)))], (15504 ^ _779300) ^ [_1049292, _1049294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1049292), _1049294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1049292)), c_Int_OBit1(_1049294))))], (15510 ^ _779300) ^ [_1049399] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049399)) = _1049399)], (15512 ^ _779300) ^ [_1049437] : [c_Int_OPls = c_Int_OBit1(_1049437)], (15514 ^ _779300) ^ [_1049471] : [c_Int_OBit1(_1049471) = c_Int_OPls], (15516 ^ _779300) ^ [] : [-(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)))))], (15518 ^ _779300) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15520 ^ _779300) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15522 ^ _779300) ^ [_1049550, _1049552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1049550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1049552)), 15529 ^ _779300 : [(15530 ^ _779300) ^ [] : [hAPP(c_Int_Onat, _1049550) = hAPP(c_Int_Onat, _1049552), -(_1049550 = _1049552)], (15536 ^ _779300) ^ [] : [_1049550 = _1049552, -(hAPP(c_Int_Onat, _1049550) = hAPP(c_Int_Onat, _1049552))]]], (15542 ^ _779300) ^ [_1049847] : [15543 ^ _779300 : [(15544 ^ _779300) ^ [_1049904] : [hBOOL(hAPP(_1049847, _1049904))]], 15546 ^ _779300 : [(15547 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15545 ^ [_1049847])))], (15549 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1049847, hAPP(c_Int_Onat, 15545 ^ [_1049847]))))]]], (15551 ^ _779300) ^ [_1049990] : [-(hBOOL(hAPP(_1049990, 15558 ^ [_1049990]))), 15552 ^ _779300 : [(15553 ^ _779300) ^ [_1050042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1050042)), hBOOL(hAPP(_1049990, hAPP(c_Int_Onat, _1050042)))]]], (15573 ^ _779300) ^ [_1050366] : [15575 ^ _779300 : [(15576 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15574 ^ [_1050366])))], (15578 ^ _779300) ^ [] : [hBOOL(hAPP(_1050366, hAPP(c_Int_Onat, 15574 ^ [_1050366])))]], 15579 ^ _779300 : [(15580 ^ _779300) ^ [_1050499] : [-(hBOOL(hAPP(_1050366, _1050499)))]]], (15562 ^ _779300) ^ [_1050181] : [hBOOL(hAPP(_1050181, 15563 ^ [_1050181])), 15566 ^ _779300 : [(15567 ^ _779300) ^ [_1050275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1050275)), -(hBOOL(hAPP(_1050181, hAPP(c_Int_Onat, _1050275))))]]], (15582 ^ _779300) ^ [_1050532, _1050534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1050532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1050534)), 15589 ^ _779300 : [(15590 ^ _779300) ^ [] : [hAPP(c_Int_Onat, _1050532) = hAPP(c_Int_Onat, _1050534), -(_1050532 = _1050534)], (15596 ^ _779300) ^ [] : [_1050532 = _1050534, -(hAPP(c_Int_Onat, _1050532) = hAPP(c_Int_Onat, _1050534))]]], (15602 ^ _779300) ^ [_1050829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1050829)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050829), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15608 ^ _779300) ^ [_1050924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050924), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1050924)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15614 ^ _779300) ^ [_1051025] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1051025)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1051025))], (15616 ^ _779300) ^ [_1051057] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1051057) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1051057)))], (15618 ^ _779300) ^ [_1051101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1051101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1051101)))], (15624 ^ _779300) ^ [_1051184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1051184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1051184))))], (15630 ^ _779300) ^ [_1051285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1051285)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051285), c_Int_OPls)))], (15636 ^ _779300) ^ [_1051380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051380), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1051380)), c_Int_OPls)))], (15642 ^ _779300) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15644 ^ _779300) ^ [_1051499] : [-(c_Int_OBit1(_1051499) = 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)), _1051499)), _1051499))], (15646 ^ _779300) ^ [_1051533] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1051533)), -(hAPP(c_Int_Onat, _1051533) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15652 ^ _779300) ^ [_1051614] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1051614))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1051614)) = _1051614)], (15658 ^ _779300) ^ [_1051668] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1051668)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1051668))))], (15664 ^ _779300) ^ [_1051763] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1051763))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1051763)))))], (15670 ^ _779300) ^ [_1051864] : [-(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)), _1051864)) = _1051864)], (15672 ^ _779300) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (15674 ^ _779300) ^ [] : [-(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))))], (15676 ^ _779300) ^ [_1051941] : [hAPP(c_Int_Onat, _1051941) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051941), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15682 ^ _779300) ^ [_1052028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052028), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1052028) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15688 ^ _779300) ^ [_1052121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052121), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1052121) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15694 ^ _779300) ^ [_1052227, _1052229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1052227)), hAPP(c_Int_Onat, _1052229))), 15697 ^ _779300 : [(15698 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052229)))], (15700 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052227), _1052229)))]]], (15702 ^ _779300) ^ [_1052362, _1052364] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1052362)), hAPP(c_Int_Onat, _1052364)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052362), _1052364))], (15712 ^ _779300) ^ [_1052529, _1052531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052529)), 15715 ^ _779300 : [(15716 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1052531)), hAPP(c_Int_Onat, _1052529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052531), _1052529)))], (15722 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052531), _1052529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1052531)), hAPP(c_Int_Onat, _1052529))))]]], (15728 ^ _779300) ^ [_1052788, _1052790] : [class_Int_Onumber__ring(_1052788), -(hAPP(c_Int_Onumber__class_Onumber__of(_1052788), c_Int_OBit1(_1052790)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052788), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052788), c_Groups_Oone__class_Oone(_1052788)), hAPP(c_Int_Onumber__class_Onumber__of(_1052788), _1052790))), hAPP(c_Int_Onumber__class_Onumber__of(_1052788), _1052790)))], (15734 ^ _779300) ^ [_1052933, _1052935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052935)), 15741 ^ _779300 : [(15742 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1052933)), hAPP(c_Int_Onat, _1052935))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052933), _1052935)))], (15748 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052933), _1052935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1052933)), hAPP(c_Int_Onat, _1052935))))]]], (15754 ^ _779300) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15756 ^ _779300) ^ [_1053266, _1053268] : [class_Int_Onumber__ring(_1053266), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053266), _1053268), hAPP(c_Int_Onumber__class_Onumber__of(_1053266), c_Int_OBit1(c_Int_OPls))) = _1053268)], (15762 ^ _779300) ^ [_1053367, _1053369] : [class_Int_Onumber__ring(_1053367), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053367), hAPP(c_Int_Onumber__class_Onumber__of(_1053367), c_Int_OBit1(c_Int_OPls))), _1053369) = _1053369)], (15768 ^ _779300) ^ [_1053474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053474)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1053474)) = _1053474)], (15774 ^ _779300) ^ [_1053559] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053559))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1053559)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15780 ^ _779300) ^ [_1053618, _1053620] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1053618) = _1053620, 15783 ^ _779300 : [(15784 ^ _779300) ^ [] : [-(_1053618 = hAPP(c_Int_Onat, _1053620))], (15786 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053620)))]]], (15788 ^ _779300) ^ [_1053733, _1053735] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1053733) = _1053735), _1053733 = hAPP(c_Int_Onat, _1053735), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053735))], (15798 ^ _779300) ^ [_1053880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053880)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1053880)) = _1053880)], (15804 ^ _779300) ^ [_1053986, _1053988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1053986), hAPP(c_Int_Onat, _1053988))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1053986)), _1053988)))], (15810 ^ _779300) ^ [_1054091, _1054093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1054091)), _1054093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1054091), hAPP(c_Int_Onat, _1054093))))], (15816 ^ _779300) ^ [_1054202] : [class_Int_Onumber__ring(_1054202), -(c_Groups_Oone__class_Oone(_1054202) = hAPP(c_Int_Onumber__class_Onumber__of(_1054202), c_Int_OBit1(c_Int_OPls)))], (15822 ^ _779300) ^ [_1054289] : [class_Int_Onumber__ring(_1054289), -(hAPP(c_Int_Onumber__class_Onumber__of(_1054289), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1054289))], (15828 ^ _779300) ^ [_1054388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1054388)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1054388), c_Int_OPls)))], (15834 ^ _779300) ^ [_1054483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1054483), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1054483)), c_Int_OPls)))], (15840 ^ _779300) ^ [_1054596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1054596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1054596)))], (15846 ^ _779300) ^ [_1054679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1054679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1054679))))], (15852 ^ _779300) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (15854 ^ _779300) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15856 ^ _779300) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (15858 ^ _779300) ^ [_1054834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1054834))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054834)))], (15864 ^ _779300) ^ [_1054919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1054919))))], (15870 ^ _779300) ^ [_1055010, _1055012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055010)), 15873 ^ _779300 : [(15874 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1055010)), hAPP(c_Int_Onat, _1055012))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1055010), _1055012)))], (15880 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1055010), _1055012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1055010)), hAPP(c_Int_Onat, _1055012))))]]], (15886 ^ _779300) ^ [_1055269, _1055271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055269)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055271)), 15893 ^ _779300 : [(15894 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1055269)), hAPP(c_Int_Onat, _1055271))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1055269), _1055271)))], (15900 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1055269), _1055271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1055269)), hAPP(c_Int_Onat, _1055271))))]]], (15922 ^ _779300) ^ [_1055791, _1055793] : [-(hAPP(c_Int_Onat, _1055791) = _1055793), 15925 ^ _779300 : [(15926 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055791)))], (15928 ^ _779300) ^ [] : [_1055791 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1055793)]], 15929 ^ _779300 : [(15930 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055791))], (15932 ^ _779300) ^ [] : [_1055793 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (15906 ^ _779300) ^ [_1055599, _1055601] : [hAPP(c_Int_Onat, _1055599) = _1055601, 15909 ^ _779300 : [(15910 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055599)), -(_1055599 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1055601))], (15916 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055599))), -(_1055601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (15952 ^ _779300) ^ [_1056222, _1056224] : [-(_1056222 = hAPP(c_Int_Onat, _1056224)), 15955 ^ _779300 : [(15956 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1056224)))], (15958 ^ _779300) ^ [] : [_1056224 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1056222)]], 15959 ^ _779300 : [(15960 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1056224))], (15962 ^ _779300) ^ [] : [_1056222 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (15936 ^ _779300) ^ [_1056030, _1056032] : [_1056030 = hAPP(c_Int_Onat, _1056032), 15939 ^ _779300 : [(15940 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1056032)), -(_1056032 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1056030))], (15946 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1056032))), -(_1056030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (15966 ^ _779300) ^ [_1056446, _1056448] : [15967 ^ _779300 : [(15968 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1056446))], (15970 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1056448))]], 15971 ^ _779300 : [(15972 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1056446)), hAPP(c_Int_Onat, _1056448))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1056446), _1056448)))], (15978 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1056446), _1056448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1056446)), hAPP(c_Int_Onat, _1056448))))]]], (16000 ^ _779300) ^ [_1057025, _1057027] : [-(hBOOL(hAPP(_1057025, hAPP(c_Int_Onat, _1057027)))), 16004 ^ _779300 : [(16005 ^ _779300) ^ [] : [-(_1057027 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 16003 ^ [_1057025, _1057027]))], (16007 ^ _779300) ^ [] : [hBOOL(hAPP(_1057025, 16003 ^ [_1057025, _1057027]))]], 16008 ^ _779300 : [(16009 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057027), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16011 ^ _779300) ^ [] : [hBOOL(hAPP(_1057025, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (15984 ^ _779300) ^ [_1056762, _1056764] : [hBOOL(hAPP(_1056762, hAPP(c_Int_Onat, _1056764))), 15987 ^ _779300 : [(15988 ^ _779300) ^ [_1056862] : [_1056764 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1056862), -(hBOOL(hAPP(_1056762, _1056862)))], (15994 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1056764), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1056762, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (16015 ^ _779300) ^ [_1057288, _1057290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057290)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1057288), _1057290)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1057288)), hAPP(c_Int_Onat, _1057290)))], (16025 ^ _779300) ^ [_1057467, _1057469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057467)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057469)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1057467)), hAPP(c_Int_Onat, _1057469)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1057467), _1057469)))], (16035 ^ _779300) ^ [_1057661, _1057663] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1057661) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1057663), 16038 ^ _779300 : [(16039 ^ _779300) ^ [] : [-(_1057661 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1057663)))], (16041 ^ _779300) ^ [] : [-(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), _1057663))))]]], (16043 ^ _779300) ^ [_1057794, _1057796] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1057794) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1057796)), _1057794 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1057796)), 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), _1057796)))], (16053 ^ _779300) ^ [_1057959, _1057961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057959)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1057959), _1057961)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1057959)), hAPP(c_Int_Onat, _1057961)))], (16059 ^ _779300) ^ [_1058082, _1058084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058084)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1058082)), hAPP(c_Int_Onat, _1058084)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1058082), _1058084)))], (16069 ^ _779300) ^ [_1058261, _1058263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1058261), _1058263)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1058263), _1058261)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1058263)), hAPP(c_Int_Onat, _1058261)))], (16079 ^ _779300) ^ [] : [-(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)))))], (16081 ^ _779300) ^ [] : [-(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)))], (16083 ^ _779300) ^ [] : [-(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))))))], (16085 ^ _779300) ^ [_1058500] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1058500))) = 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)))), _1058500))], (16087 ^ _779300) ^ [] : [-(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)))))], (16089 ^ _779300) ^ [_1058553, _1058555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058555)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1058553)), hAPP(c_Int_Onat, _1058555)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1058553, _1058555)))], (16099 ^ _779300) ^ [_1058735, _1058737] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1058735)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1058737)), hAPP(c_Int_Onat, _1058735)) = hAPP(c_Int_Onat, _1058737))], (16105 ^ _779300) ^ [_1058840, _1058842] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1058840))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1058842)), hAPP(c_Int_Onat, _1058840)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1058842), _1058840)), 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)))], (16111 ^ _779300) ^ [_1058916] : [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, _1058916))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1058916)))], (16117 ^ _779300) ^ [_1059001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1059001)), -(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, _1059001))))], (16123 ^ _779300) ^ [_1059092, _1059094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1059092)), 16126 ^ _779300 : [(16127 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1059092)), _1059094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059092), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1059094))))], (16133 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059092), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1059094))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1059092)), _1059094)))]]], (16139 ^ _779300) ^ [_1059351, _1059353] : [class_Int_Onumber__ring(_1059351), class_Rings_Olinordered__idom(_1059351), 16146 ^ _779300 : [(16147 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059351), c_Groups_Oone__class_Oone(_1059351)), hAPP(c_Int_Onumber__class_Onumber__of(_1059351), _1059353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1059353)))], (16153 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1059353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059351), c_Groups_Oone__class_Oone(_1059351)), hAPP(c_Int_Onumber__class_Onumber__of(_1059351), _1059353))))]]], (16159 ^ _779300) ^ [_1059656, _1059658] : [class_Int_Onumber__ring(_1059656), class_Rings_Olinordered__idom(_1059656), 16166 ^ _779300 : [(16167 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059656), hAPP(c_Int_Onumber__class_Onumber__of(_1059656), _1059658)), c_Groups_Oone__class_Oone(_1059656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059658), c_Int_OBit1(c_Int_OPls))))], (16173 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059658), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059656), hAPP(c_Int_Onumber__class_Onumber__of(_1059656), _1059658)), c_Groups_Oone__class_Oone(_1059656))))]]], (16179 ^ _779300) ^ [_1059970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1059970)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1059970)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1059970)))], (16185 ^ _779300) ^ [_1060073, _1060075] : [class_Int_Onumber__ring(_1060073), class_Rings_Olinordered__idom(_1060073), 16192 ^ _779300 : [(16193 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060073), hAPP(c_Int_Onumber__class_Onumber__of(_1060073), _1060075)), c_Groups_Oone__class_Oone(_1060073))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1060075), c_Int_OBit1(c_Int_OPls))))], (16199 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1060075), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060073), hAPP(c_Int_Onumber__class_Onumber__of(_1060073), _1060075)), c_Groups_Oone__class_Oone(_1060073))))]]], (16205 ^ _779300) ^ [_1060387, _1060389] : [class_Int_Onumber__ring(_1060387), class_Rings_Olinordered__idom(_1060387), 16212 ^ _779300 : [(16213 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060387), c_Groups_Oone__class_Oone(_1060387)), hAPP(c_Int_Onumber__class_Onumber__of(_1060387), _1060389))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1060389)))], (16219 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1060389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060387), c_Groups_Oone__class_Oone(_1060387)), hAPP(c_Int_Onumber__class_Onumber__of(_1060387), _1060389))))]]], (16225 ^ _779300) ^ [_1060692, _1060694] : [class_Int_Onumber__ring(_1060692), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060692), c_Groups_Oone__class_Oone(_1060692)), hAPP(c_Int_Onumber__class_Onumber__of(_1060692), _1060694)) = hAPP(c_Int_Onumber__class_Onumber__of(_1060692), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1060694)))], (16231 ^ _779300) ^ [_1060813, _1060815] : [class_Int_Onumber__ring(_1060813), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060813), hAPP(c_Int_Onumber__class_Onumber__of(_1060813), _1060815)), c_Groups_Oone__class_Oone(_1060813)) = hAPP(c_Int_Onumber__class_Onumber__of(_1060813), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1060815), c_Int_OBit1(c_Int_OPls))))], (16237 ^ _779300) ^ [_1060940, _1060942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1060940)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060942)), _1060940) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060942), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060940), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (16243 ^ _779300) ^ [_1061078, _1061080] : [hAPP(c_Nat_OSuc, _1061078) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061080), -(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(_1061080))), 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)), _1061078))))))], (16249 ^ _779300) ^ [_1061201, _1061203] : [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(_1061203))), 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)), _1061201))))), -(hAPP(c_Nat_OSuc, _1061201) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061203))], (16255 ^ _779300) ^ [_1061345, _1061347] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061345) = hAPP(c_Nat_OSuc, _1061347), -(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(_1061345))), 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)), _1061347))))))], (16261 ^ _779300) ^ [_1061468, _1061470] : [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(_1061468))), 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)), _1061470))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061468) = hAPP(c_Nat_OSuc, _1061470))], (16267 ^ _779300) ^ [_1061597, _1061599, _1061601, _1061603] : [-(c_Nat_Onat_Onat__case(_1061597, _1061599, _1061601, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061603)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1061597), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1061603))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1061597, _1061597), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1061597, tc_fun(_1061597, _1061597)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1061597, tc_fun(_1061597, _1061597)), tc_Int_Oint), c_If(_1061597)), c_Nat__Numeral_Oneg)), _1061599)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1061597, tc_Int_Oint), _1061601), c_Int_Onat))))], (16269 ^ _779300) ^ [_1061699, _1061701] : [-(c_Int_Onat__aux(_1061699, _1061701) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1061699)), _1061701))], (16271 ^ _779300) ^ [_1061736, _1061738, _1061740, _1061742, _1061744] : [-(hAPP(c_Nat_Onat_Onat__rec(_1061736, _1061738, _1061740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061742)), _1061744)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1061736), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1061742))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1061736, _1061736), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1061736, tc_fun(_1061736, _1061736)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1061736, tc_fun(_1061736, _1061736)), tc_Int_Oint), c_If(_1061736)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1061736, _1061738, _1061740), _1061744))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1061736, _1061736), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1061736, _1061736), tc_Int_Oint), _1061740), 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)), _1061744))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1061736, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1061736, _1061738, _1061740)), 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)), _1061744))))))], (16273 ^ _779300) ^ [_1061888, _1061890, _1061892, _1061894] : [-(hAPP(c_Nat_Onat_Onat__rec(_1061888, _1061890, _1061892), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061894)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1061888), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1061894))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1061888, _1061888), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1061888, tc_fun(_1061888, _1061888)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1061888, tc_fun(_1061888, _1061888)), tc_Int_Oint), c_If(_1061888)), c_Nat__Numeral_Oneg)), _1061890)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1061888, _1061888), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1061888, _1061888), tc_Int_Oint), _1061892), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1061888, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1061888, _1061890, _1061892)), c_Int_Onat)))))], (16275 ^ _779300) ^ [] : [-(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))))], (16277 ^ _779300) ^ [_1062046, _1062048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1062046), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062048)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062046)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062048))], (16283 ^ _779300) ^ [_1062157, _1062159] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1062157), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062159)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062157)) = 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), _1062159), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1062157)))), 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)))], (16289 ^ _779300) ^ [_1062230, _1062232] : [class_Rings_Osemiring__1(_1062230), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1062232)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1062230), 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)))), _1062232))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062230), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1062230), hAPP(c_Int_Onat, _1062232))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1062230), hAPP(c_Int_Onat, _1062232))))], (16299 ^ _779300) ^ [_1062431, _1062433, _1062435] : [class_Int_Onumber__ring(_1062431), 16302 ^ _779300 : [(16303 ^ _779300) ^ [] : [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), _1062433))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1062431), hAPP(c_Int_Onumber__class_Onumber__of(_1062431), _1062435)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1062433))) = hAPP(hAPP(c_HOL_OLet(_1062431, _1062431), hAPP(hAPP(c_Power_Opower__class_Opower(_1062431), hAPP(c_Int_Onumber__class_Onumber__of(_1062431), _1062435)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062433))), hAPP(hAPP(c_COMBS(_1062431, _1062431, _1062431), hAPP(hAPP(c_COMBB(_1062431, tc_fun(_1062431, _1062431), _1062431), c_Groups_Otimes__class_Otimes(_1062431)), hAPP(c_Groups_Otimes__class_Otimes(_1062431), hAPP(c_Int_Onumber__class_Onumber__of(_1062431), _1062435)))), c_COMBI(_1062431))))], (16309 ^ _779300) ^ [] : [-(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), _1062433)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1062431), hAPP(c_Int_Onumber__class_Onumber__of(_1062431), _1062435)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1062433))) = c_Groups_Oone__class_Oone(_1062431))]]], (16315 ^ _779300) ^ [_1062829, _1062831] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062829)), hAPP(c_Nat_OSuc, _1062831)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1062829))), 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)), _1062831)))))], (16317 ^ _779300) ^ [_1062886, _1062888] : [class_Groups_Oordered__ab__group__add(_1062886), -(c_Fun_Oinj__on(_1062886, _1062886, c_Groups_Ouminus__class_Ouminus(_1062886), _1062888))], (16323 ^ _779300) ^ [_1062969, _1062971] : [-(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), _1062969))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062971))))], (16325 ^ _779300) ^ [_1063008, _1063010] : [-(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, _1063008)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1063010))))], (16327 ^ _779300) ^ [_1063050, _1063052] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1063050)), _1063052) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1063050), _1063052)))], (16329 ^ _779300) ^ [_1063093, _1063095] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1063093), _1063095)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1063093)), _1063095))], (16331 ^ _779300) ^ [_1063136, _1063138] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1063136)), _1063138) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1063136), _1063138)))], (16333 ^ _779300) ^ [_1063179, _1063181] : [class_Int_Onumber__ring(_1063179), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1063179), hAPP(c_Int_Onumber__class_Onumber__of(_1063179), _1063181)) = hAPP(c_Int_Onumber__class_Onumber__of(_1063179), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1063181)))], (16339 ^ _779300) ^ [_1063290, _1063292] : [class_Int_Onumber__ring(_1063290), -(hAPP(c_Int_Onumber__class_Onumber__of(_1063290), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1063292)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1063290), hAPP(c_Int_Onumber__class_Onumber__of(_1063290), _1063292)))], (16345 ^ _779300) ^ [_1063416, _1063418] : [c_Int_OBit0(_1063416) = c_Int_OBit0(_1063418), -(_1063416 = _1063418)], (16351 ^ _779300) ^ [_1063497, _1063499] : [_1063497 = _1063499, -(c_Int_OBit0(_1063497) = c_Int_OBit0(_1063499))], (16357 ^ _779300) ^ [_1063584] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1063584)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1063584)))], (16359 ^ _779300) ^ [_1063617] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1063617)) = _1063617)], (16361 ^ _779300) ^ [_1063646, _1063648, _1063650, _1063652] : [class_Orderings_Olinorder(_1063646), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063646), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063646), _1063648), _1063650)), _1063652) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063646), _1063648), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063646), _1063650), _1063652)))], (16367 ^ _779300) ^ [_1063789, _1063791, _1063793, _1063795] : [class_Orderings_Olinorder(_1063789), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063789), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063789), _1063791), _1063793)), _1063795) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063789), _1063791), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063789), _1063793), _1063795)))], (16373 ^ _779300) ^ [_1063932, _1063934, _1063936] : [class_Lattices_Oboolean__algebra(_1063932), 16376 ^ _779300 : [(16377 ^ _779300) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1063932), _1063934) = hAPP(c_Groups_Ouminus__class_Ouminus(_1063932), _1063936), -(_1063934 = _1063936)], (16383 ^ _779300) ^ [] : [_1063934 = _1063936, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1063932), _1063934) = hAPP(c_Groups_Ouminus__class_Ouminus(_1063932), _1063936))]]], (16389 ^ _779300) ^ [_1064173, _1064175, _1064177] : [class_Groups_Ogroup__add(_1064173), 16392 ^ _779300 : [(16393 ^ _779300) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1064173), _1064175) = hAPP(c_Groups_Ouminus__class_Ouminus(_1064173), _1064177), -(_1064175 = _1064177)], (16399 ^ _779300) ^ [] : [_1064175 = _1064177, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1064173), _1064175) = hAPP(c_Groups_Ouminus__class_Ouminus(_1064173), _1064177))]]], (16405 ^ _779300) ^ [_1064414, _1064416, _1064418] : [class_Groups_Ogroup__add(_1064414), 16408 ^ _779300 : [(16409 ^ _779300) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1064414), _1064416) = _1064418, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1064414), _1064418) = _1064416)], (16415 ^ _779300) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1064414), _1064418) = _1064416, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1064414), _1064416) = _1064418)]]], (16421 ^ _779300) ^ [_1064655, _1064657, _1064659, _1064661] : [class_Orderings_Olinorder(_1064655), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064655), _1064657), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064655), _1064659), _1064661)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064655), _1064659), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064655), _1064657), _1064661)))], (16427 ^ _779300) ^ [_1064798, _1064800, _1064802, _1064804] : [class_Orderings_Olinorder(_1064798), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064798), _1064800), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064798), _1064802), _1064804)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064798), _1064802), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064798), _1064800), _1064804)))], (16433 ^ _779300) ^ [_1064941, _1064943, _1064945] : [class_Orderings_Olinorder(_1064941), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064941), _1064943), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064941), _1064943), _1064945)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064941), _1064943), _1064945))], (16439 ^ _779300) ^ [_1065066, _1065068, _1065070] : [class_Orderings_Olinorder(_1065066), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065066), _1065068), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065066), _1065068), _1065070)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065066), _1065068), _1065070))], (16445 ^ _779300) ^ [_1065191, _1065193, _1065195] : [class_Groups_Ogroup__add(_1065191), 16448 ^ _779300 : [(16449 ^ _779300) ^ [] : [_1065193 = hAPP(c_Groups_Ouminus__class_Ouminus(_1065191), _1065195), -(_1065195 = hAPP(c_Groups_Ouminus__class_Ouminus(_1065191), _1065193))], (16455 ^ _779300) ^ [] : [_1065195 = hAPP(c_Groups_Ouminus__class_Ouminus(_1065191), _1065193), -(_1065193 = hAPP(c_Groups_Ouminus__class_Ouminus(_1065191), _1065195))]]], (16461 ^ _779300) ^ [_1065432, _1065434, _1065436] : [class_Orderings_Olinorder(_1065432), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065432), _1065434), _1065436) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065432), _1065436), _1065434))], (16467 ^ _779300) ^ [_1065541, _1065543, _1065545] : [class_Orderings_Olinorder(_1065541), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065541), _1065543), _1065545) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065541), _1065545), _1065543))], (16473 ^ _779300) ^ [_1065650, _1065652, _1065654, _1065656] : [class_Groups_Ouminus(_1065650), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1065652, _1065650)), _1065654), _1065656) = hAPP(c_Groups_Ouminus__class_Ouminus(_1065650), hAPP(_1065654, _1065656)))], (16479 ^ _779300) ^ [_1065767, _1065769] : [class_Orderings_Olinorder(_1065767), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065767), _1065769), _1065769) = _1065769)], (16485 ^ _779300) ^ [_1065858, _1065860] : [class_Lattices_Oboolean__algebra(_1065858), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1065858), hAPP(c_Groups_Ouminus__class_Ouminus(_1065858), _1065860)) = _1065860)], (16491 ^ _779300) ^ [_1065953, _1065955] : [class_Groups_Ogroup__add(_1065953), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1065953), hAPP(c_Groups_Ouminus__class_Ouminus(_1065953), _1065955)) = _1065955)], (16497 ^ _779300) ^ [_1066048, _1066050, _1066052, _1066054] : [class_Groups_Ouminus(_1066048), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1066050, _1066048)), _1066052), _1066054) = hAPP(c_Groups_Ouminus__class_Ouminus(_1066048), hAPP(_1066052, _1066054)))], (16503 ^ _779300) ^ [_1066165, _1066167] : [class_Rings_Oring__1(_1066165), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1066165), hAPP(c_Groups_Ouminus__class_Ouminus(_1066165), _1066167)), 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(_1066165), _1066167), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (16509 ^ _779300) ^ [_1066282, _1066284, _1066286] : [class_Int_Onumber__ring(_1066282), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066282), hAPP(c_Groups_Ouminus__class_Ouminus(_1066282), hAPP(c_Int_Onumber__class_Onumber__of(_1066282), _1066284))), _1066286) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066282), hAPP(c_Int_Onumber__class_Onumber__of(_1066282), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1066284))), _1066286))], (16515 ^ _779300) ^ [_1066427, _1066429, _1066431] : [class_Lattices_Oboolean__algebra(_1066427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066427), _1066429), _1066431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066427), hAPP(c_Groups_Ouminus__class_Ouminus(_1066427), _1066431)), hAPP(c_Groups_Ouminus__class_Ouminus(_1066427), _1066429))))], (16525 ^ _779300) ^ [_1066606, _1066608, _1066610] : [class_Groups_Oordered__ab__group__add(_1066606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066606), _1066608), _1066610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066606), hAPP(c_Groups_Ouminus__class_Ouminus(_1066606), _1066610)), hAPP(c_Groups_Ouminus__class_Ouminus(_1066606), _1066608))))], (16535 ^ _779300) ^ [_1066785, _1066787, _1066789] : [class_Lattices_Oboolean__algebra(_1066785), 16538 ^ _779300 : [(16539 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066785), hAPP(c_Groups_Ouminus__class_Ouminus(_1066785), _1066787)), hAPP(c_Groups_Ouminus__class_Ouminus(_1066785), _1066789))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066785), _1066789), _1066787)))], (16545 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066785), _1066789), _1066787)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066785), hAPP(c_Groups_Ouminus__class_Ouminus(_1066785), _1066787)), hAPP(c_Groups_Ouminus__class_Ouminus(_1066785), _1066789))))]]], (16551 ^ _779300) ^ [_1067068, _1067070, _1067072] : [class_Groups_Oordered__ab__group__add(_1067068), 16554 ^ _779300 : [(16555 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067068), hAPP(c_Groups_Ouminus__class_Ouminus(_1067068), _1067070)), hAPP(c_Groups_Ouminus__class_Ouminus(_1067068), _1067072))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067068), _1067072), _1067070)))], (16561 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067068), _1067072), _1067070)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067068), hAPP(c_Groups_Ouminus__class_Ouminus(_1067068), _1067070)), hAPP(c_Groups_Ouminus__class_Ouminus(_1067068), _1067072))))]]], (16567 ^ _779300) ^ [_1067351, _1067353, _1067355] : [class_Groups_Oordered__ab__group__add(_1067351), 16570 ^ _779300 : [(16571 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067351), hAPP(c_Groups_Ouminus__class_Ouminus(_1067351), _1067353)), _1067355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067351), hAPP(c_Groups_Ouminus__class_Ouminus(_1067351), _1067355)), _1067353)))], (16577 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067351), hAPP(c_Groups_Ouminus__class_Ouminus(_1067351), _1067355)), _1067353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067351), hAPP(c_Groups_Ouminus__class_Ouminus(_1067351), _1067353)), _1067355)))]]], (16583 ^ _779300) ^ [_1067634, _1067636, _1067638] : [class_Groups_Oordered__ab__group__add(_1067634), 16586 ^ _779300 : [(16587 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067634), _1067636), hAPP(c_Groups_Ouminus__class_Ouminus(_1067634), _1067638))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067634), _1067638), hAPP(c_Groups_Ouminus__class_Ouminus(_1067634), _1067636))))], (16593 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067634), _1067638), hAPP(c_Groups_Ouminus__class_Ouminus(_1067634), _1067636))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067634), _1067636), hAPP(c_Groups_Ouminus__class_Ouminus(_1067634), _1067638))))]]], (16599 ^ _779300) ^ [_1067917, _1067919, _1067921, _1067923] : [class_Orderings_Olinorder(_1067917), 16602 ^ _779300 : [(16613 ^ _779300) ^ [] : [16614 ^ _779300 : [(16615 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067917), _1067919), _1067923))], (16617 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067917), _1067921), _1067923))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067917), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067917), _1067919), _1067921)), _1067923)))], (16603 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067917), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067917), _1067919), _1067921)), _1067923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067917), _1067919), _1067923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067917), _1067921), _1067923)))]]], (16621 ^ _779300) ^ [_1068266, _1068268, _1068270, _1068272] : [class_Orderings_Olinorder(_1068266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068266), _1068268), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1068266), _1068270), _1068272))), 16628 ^ _779300 : [(16629 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068266), _1068268), _1068270)))], (16631 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068266), _1068268), _1068272)))]]], (16633 ^ _779300) ^ [_1068489, _1068491, _1068493, _1068495, _1068497] : [class_Orderings_Olinorder(_1068489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068489), _1068491), _1068493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068489), _1068495), _1068497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068489), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1068489), _1068491), _1068495)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1068489), _1068493), _1068497))))], (16647 ^ _779300) ^ [_1068760, _1068762, _1068764, _1068766] : [class_Orderings_Olinorder(_1068760), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068760), _1068762), _1068764)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068760), _1068762), _1068766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068760), _1068762), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1068760), _1068764), _1068766))))], (16661 ^ _779300) ^ [_1069009, _1069011, _1069013, _1069015] : [class_Orderings_Olinorder(_1069009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069009), _1069011), _1069013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069009), _1069011), _1069015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069009), _1069011), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069009), _1069013), _1069015))))], (16675 ^ _779300) ^ [_1069258, _1069260, _1069262] : [class_Orderings_Olinorder(_1069258), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069258), _1069260), _1069262)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069258), _1069262), _1069260) = _1069260)], (16685 ^ _779300) ^ [_1069419, _1069421, _1069423] : [class_Orderings_Olinorder(_1069419), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069419), _1069421), _1069423)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069419), _1069421), _1069423) = _1069421)], (16695 ^ _779300) ^ [_1069580, _1069582, _1069584, _1069586] : [class_Orderings_Olinorder(_1069580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069580), _1069582), _1069584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069580), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069580), _1069586), _1069582)), _1069584)))], (16705 ^ _779300) ^ [_1069759, _1069761, _1069763, _1069765] : [class_Orderings_Olinorder(_1069759), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069759), _1069761), _1069763)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069759), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069759), _1069761), _1069765)), _1069763)))], (16715 ^ _779300) ^ [_1069938, _1069940, _1069942, _1069944] : [class_Orderings_Olinorder(_1069938), 16718 ^ _779300 : [(16719 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069938), _1069940), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069938), _1069942), _1069944))), 16722 ^ _779300 : [(16723 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069938), _1069940), _1069942)))], (16725 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069938), _1069940), _1069944)))]]], (16727 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069938), _1069940), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069938), _1069942), _1069944)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069938), _1069940), _1069942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069938), _1069940), _1069944))]]], (16737 ^ _779300) ^ [_1070318, _1070320, _1070322] : [class_Orderings_Olinorder(_1070318), 16740 ^ _779300 : [(16741 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070318), _1070320), _1070322)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1070318), _1070320), _1070322) = _1070320)], (16747 ^ _779300) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1070318), _1070320), _1070322) = _1070320, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070318), _1070320), _1070322)))]]], (16753 ^ _779300) ^ [_1070574, _1070576, _1070578] : [class_Orderings_Olinorder(_1070574), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070574), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1070574), _1070576), _1070578)), _1070578)))], (16759 ^ _779300) ^ [_1070681, _1070683, _1070685] : [class_Orderings_Olinorder(_1070681), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070681), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1070681), _1070683), _1070685)), _1070683)))], (16765 ^ _779300) ^ [_1070788, _1070790] : [class_Groups_Olinordered__ab__group__add(_1070788), 16768 ^ _779300 : [(16769 ^ _779300) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1070788), _1070790) = _1070790, -(_1070790 = c_Groups_Ozero__class_Ozero(_1070788))], (16775 ^ _779300) ^ [] : [_1070790 = c_Groups_Ozero__class_Ozero(_1070788), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1070788), _1070790) = _1070790)]]], (16781 ^ _779300) ^ [_1071014, _1071016] : [class_Groups_Ogroup__add(_1071014), 16784 ^ _779300 : [(16785 ^ _779300) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1071014), _1071016) = c_Groups_Ozero__class_Ozero(_1071014), -(_1071016 = c_Groups_Ozero__class_Ozero(_1071014))], (16791 ^ _779300) ^ [] : [_1071016 = c_Groups_Ozero__class_Ozero(_1071014), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1071014), _1071016) = c_Groups_Ozero__class_Ozero(_1071014))]]], (16797 ^ _779300) ^ [_1071246, _1071248] : [class_Groups_Olinordered__ab__group__add(_1071246), 16800 ^ _779300 : [(16801 ^ _779300) ^ [] : [_1071248 = hAPP(c_Groups_Ouminus__class_Ouminus(_1071246), _1071248), -(_1071248 = c_Groups_Ozero__class_Ozero(_1071246))], (16807 ^ _779300) ^ [] : [_1071248 = c_Groups_Ozero__class_Ozero(_1071246), -(_1071248 = hAPP(c_Groups_Ouminus__class_Ouminus(_1071246), _1071248))]]], (16813 ^ _779300) ^ [_1071472, _1071474] : [class_Groups_Ogroup__add(_1071472), 16816 ^ _779300 : [(16817 ^ _779300) ^ [] : [c_Groups_Ozero__class_Ozero(_1071472) = hAPP(c_Groups_Ouminus__class_Ouminus(_1071472), _1071474), -(c_Groups_Ozero__class_Ozero(_1071472) = _1071474)], (16823 ^ _779300) ^ [] : [c_Groups_Ozero__class_Ozero(_1071472) = _1071474, -(c_Groups_Ozero__class_Ozero(_1071472) = hAPP(c_Groups_Ouminus__class_Ouminus(_1071472), _1071474))]]], (16829 ^ _779300) ^ [_1071704] : [class_Groups_Ogroup__add(_1071704), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1071704), c_Groups_Ozero__class_Ozero(_1071704)) = c_Groups_Ozero__class_Ozero(_1071704))], (16835 ^ _779300) ^ [_1071795, _1071797, _1071799] : [class_Groups_Oordered__ab__group__add(_1071795), 16838 ^ _779300 : [(16839 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071795), hAPP(c_Groups_Ouminus__class_Ouminus(_1071795), _1071797)), hAPP(c_Groups_Ouminus__class_Ouminus(_1071795), _1071799))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071795), _1071799), _1071797)))], (16845 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071795), _1071799), _1071797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071795), hAPP(c_Groups_Ouminus__class_Ouminus(_1071795), _1071797)), hAPP(c_Groups_Ouminus__class_Ouminus(_1071795), _1071799))))]]], (16851 ^ _779300) ^ [_1072078, _1072080, _1072082] : [class_Groups_Oordered__ab__group__add(_1072078), 16854 ^ _779300 : [(16855 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072078), hAPP(c_Groups_Ouminus__class_Ouminus(_1072078), _1072080)), _1072082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072078), hAPP(c_Groups_Ouminus__class_Ouminus(_1072078), _1072082)), _1072080)))], (16861 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072078), hAPP(c_Groups_Ouminus__class_Ouminus(_1072078), _1072082)), _1072080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072078), hAPP(c_Groups_Ouminus__class_Ouminus(_1072078), _1072080)), _1072082)))]]], (16867 ^ _779300) ^ [_1072361, _1072363, _1072365] : [class_Groups_Oordered__ab__group__add(_1072361), 16870 ^ _779300 : [(16871 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), _1072363), hAPP(c_Groups_Ouminus__class_Ouminus(_1072361), _1072365))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), _1072365), hAPP(c_Groups_Ouminus__class_Ouminus(_1072361), _1072363))))], (16877 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), _1072365), hAPP(c_Groups_Ouminus__class_Ouminus(_1072361), _1072363))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072361), _1072363), hAPP(c_Groups_Ouminus__class_Ouminus(_1072361), _1072365))))]]], (16883 ^ _779300) ^ [_1072644, _1072646, _1072648, _1072650] : [class_Orderings_Olinorder(_1072644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072644), _1072646), _1072648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072644), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1072644), _1072650), _1072646)), _1072648)))], (16893 ^ _779300) ^ [_1072823, _1072825, _1072827, _1072829] : [class_Orderings_Olinorder(_1072823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072823), _1072825), _1072827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072823), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1072823), _1072825), _1072829)), _1072827)))], (16903 ^ _779300) ^ [_1073002, _1073004, _1073006, _1073008] : [class_Orderings_Olinorder(_1073002), 16906 ^ _779300 : [(16917 ^ _779300) ^ [] : [16918 ^ _779300 : [(16919 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073002), _1073004), _1073008))], (16921 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073002), _1073006), _1073008))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073002), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1073002), _1073004), _1073006)), _1073008)))], (16907 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073002), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1073002), _1073004), _1073006)), _1073008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073002), _1073004), _1073008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073002), _1073006), _1073008)))]]], (16925 ^ _779300) ^ [_1073351, _1073353, _1073355, _1073357] : [class_Orderings_Olinorder(_1073351), 16928 ^ _779300 : [(16929 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073351), _1073353), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1073351), _1073355), _1073357))), 16932 ^ _779300 : [(16933 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073351), _1073353), _1073355)))], (16935 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073351), _1073353), _1073357)))]]], (16937 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073351), _1073353), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1073351), _1073355), _1073357)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073351), _1073353), _1073355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073351), _1073353), _1073357))]]], (16947 ^ _779300) ^ [_1073731, _1073733, _1073735] : [class_Groups_Ogroup__add(_1073731), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073731), hAPP(c_Groups_Ouminus__class_Ouminus(_1073731), _1073733)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073731), _1073733), _1073735)) = _1073735)], (16953 ^ _779300) ^ [_1073850, _1073852, _1073854] : [class_Groups_Ogroup__add(_1073850), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073850), _1073852), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073850), hAPP(c_Groups_Ouminus__class_Ouminus(_1073850), _1073852)), _1073854)) = _1073854)], (16959 ^ _779300) ^ [_1073969, _1073971, _1073973] : [class_Groups_Ogroup__add(_1073969), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1073969), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073969), _1073971), _1073973)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073969), hAPP(c_Groups_Ouminus__class_Ouminus(_1073969), _1073973)), hAPP(c_Groups_Ouminus__class_Ouminus(_1073969), _1073971)))], (16965 ^ _779300) ^ [_1074108, _1074110, _1074112] : [class_Groups_Oab__group__add(_1074108), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1074108), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074108), _1074110), _1074112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074108), hAPP(c_Groups_Ouminus__class_Ouminus(_1074108), _1074110)), hAPP(c_Groups_Ouminus__class_Ouminus(_1074108), _1074112)))], (16971 ^ _779300) ^ [_1074247, _1074249, _1074251] : [class_Rings_Oidom(_1074247), 16974 ^ _779300 : [(16985 ^ _779300) ^ [] : [16986 ^ _779300 : [(16987 ^ _779300) ^ [] : [_1074249 = _1074251], (16989 ^ _779300) ^ [] : [_1074249 = hAPP(c_Groups_Ouminus__class_Ouminus(_1074247), _1074251)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074247), _1074249), _1074249) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074247), _1074251), _1074251))], (16975 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074247), _1074249), _1074249) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074247), _1074251), _1074251), -(_1074249 = _1074251), -(_1074249 = hAPP(c_Groups_Ouminus__class_Ouminus(_1074247), _1074251))]]], (16993 ^ _779300) ^ [_1074566, _1074568, _1074570] : [class_Rings_Oring(_1074566), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074566), hAPP(c_Groups_Ouminus__class_Ouminus(_1074566), _1074568)), hAPP(c_Groups_Ouminus__class_Ouminus(_1074566), _1074570)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074566), _1074568), _1074570))], (16999 ^ _779300) ^ [_1074695, _1074697, _1074699] : [class_Rings_Oring(_1074695), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074695), hAPP(c_Groups_Ouminus__class_Ouminus(_1074695), _1074697)), _1074699) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074695), _1074697), hAPP(c_Groups_Ouminus__class_Ouminus(_1074695), _1074699)))], (17005 ^ _779300) ^ [_1074824, _1074826, _1074828] : [class_Rings_Oring(_1074824), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1074824), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074824), _1074826), _1074828)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074824), hAPP(c_Groups_Ouminus__class_Ouminus(_1074824), _1074826)), _1074828))], (17011 ^ _779300) ^ [_1074953, _1074955, _1074957] : [class_Rings_Oring(_1074953), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1074953), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074953), _1074955), _1074957)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074953), _1074955), hAPP(c_Groups_Ouminus__class_Ouminus(_1074953), _1074957)))], (17017 ^ _779300) ^ [_1075082, _1075084, _1075086, _1075088] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1075082), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075082), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1075082), _1075084), _1075086)), _1075088) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1075082), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075082), _1075084), _1075088)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075082), _1075086), _1075088)))], (17023 ^ _779300) ^ [_1075241, _1075243, _1075245, _1075247] : [class_Rings_Ocomm__semiring__1(_1075241), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1075241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075241), _1075243), _1075245)), _1075247) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075241), hAPP(hAPP(c_Power_Opower__class_Opower(_1075241), _1075243), _1075247)), hAPP(hAPP(c_Power_Opower__class_Opower(_1075241), _1075245), _1075247)))], (17029 ^ _779300) ^ [_1075400, _1075402, _1075404] : [class_Groups_Oab__group__add(_1075400), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1075400), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1075400), _1075402), _1075404)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1075400), _1075404), _1075402))], (17035 ^ _779300) ^ [_1075519, _1075521, _1075523, _1075525] : [class_Groups_Oordered__ab__group__add(_1075519), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1075519), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1075519), _1075521), _1075523)), _1075525) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1075519), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1075519), _1075521), _1075525)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1075519), _1075523), _1075525)))], (17041 ^ _779300) ^ [_1075678] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1075678), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17043 ^ _779300) ^ [_1075707] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1075707) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17045 ^ _779300) ^ [_1075733, _1075735] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1075733)), hAPP(c_Nat_OSuc, _1075735)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1075733), _1075735)))], (17047 ^ _779300) ^ [_1075779, _1075781, _1075783] : [class_Int_Onumber__ring(_1075779), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1075779), _1075781), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1075783))) = hAPP(hAPP(c_HOL_OLet(_1075779, _1075779), hAPP(hAPP(c_Power_Opower__class_Opower(_1075779), _1075781), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075783))), hAPP(hAPP(c_COMBS(_1075779, _1075779, _1075779), c_Groups_Otimes__class_Otimes(_1075779)), c_COMBI(_1075779))))], (17053 ^ _779300) ^ [_1075965, _1075967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1075965)), c_Int_OBit0(_1075967))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075965), _1075967)))], (17059 ^ _779300) ^ [_1076066, _1076068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1076066), _1076068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1076066)), c_Int_OBit0(_1076068))))], (17065 ^ _779300) ^ [_1076188, _1076190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1076188)), c_Int_OBit0(_1076190))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1076188), _1076190)))], (17071 ^ _779300) ^ [_1076289, _1076291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1076289), _1076291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1076289)), c_Int_OBit0(_1076291))))], (17077 ^ _779300) ^ [_1076411, _1076413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1076411)), c_Int_OBit0(_1076413))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076411), _1076413)))], (17083 ^ _779300) ^ [_1076512, _1076514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076512), _1076514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1076512)), c_Int_OBit0(_1076514))))], (17089 ^ _779300) ^ [_1076634, _1076636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1076634)), c_Int_OBit0(_1076636))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076634), _1076636)))], (17095 ^ _779300) ^ [_1076735, _1076737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076735), _1076737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1076735)), c_Int_OBit0(_1076737))))], (17101 ^ _779300) ^ [] : [-(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))], (17103 ^ _779300) ^ [_1076872] : [c_Int_OBit0(_1076872) = c_Int_OPls, -(_1076872 = c_Int_OPls)], (17109 ^ _779300) ^ [_1076947] : [_1076947 = c_Int_OPls, -(c_Int_OBit0(_1076947) = c_Int_OPls)], (17115 ^ _779300) ^ [_1077040] : [c_Int_OPls = c_Int_OBit0(_1077040), -(c_Int_OPls = _1077040)], (17121 ^ _779300) ^ [_1077115] : [c_Int_OPls = _1077115, -(c_Int_OPls = c_Int_OBit0(_1077115))], (17127 ^ _779300) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (17129 ^ _779300) ^ [_1077226, _1077228] : [c_Int_OBit1(_1077226) = c_Int_OBit0(_1077228)], (17131 ^ _779300) ^ [_1077267, _1077269] : [c_Int_OBit0(_1077267) = c_Int_OBit1(_1077269)], (17133 ^ _779300) ^ [_1077296] : [-(c_Int_OBit0(_1077296) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1077296), _1077296))], (17135 ^ _779300) ^ [_1077327, _1077329] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1077327)), c_Int_OBit0(_1077329)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1077327), _1077329)))], (17137 ^ _779300) ^ [_1077370, _1077372, _1077374, _1077376] : [class_Rings_Ocomm__semiring__1(_1077370), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1077370), hAPP(hAPP(c_Power_Opower__class_Opower(_1077370), _1077372), _1077374)), _1077376) = hAPP(hAPP(c_Power_Opower__class_Opower(_1077370), _1077372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077374), _1077376)))], (17143 ^ _779300) ^ [_1077509, _1077511, _1077513] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1077509), _1077511)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1077513), _1077511)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1077509), _1077513)), _1077511))], (17145 ^ _779300) ^ [_1077566, _1077568, _1077570] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1077566), _1077568)), _1077570) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1077566), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077568), _1077570)))], (17147 ^ _779300) ^ [_1077617, _1077619] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1077617), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1077619))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1077617), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1077619))), 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))))], (17149 ^ _779300) ^ [_1077668, _1077670] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1077668)), _1077670) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1077668), _1077670)))], (17151 ^ _779300) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (17153 ^ _779300) ^ [_1077727, _1077729] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1077727), _1077729)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1077727)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1077729)))], (17155 ^ _779300) ^ [_1077773] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077773)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1077773)))], (17157 ^ _779300) ^ [_1077808, _1077810] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1077808)), c_Int_OBit0(_1077810)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1077808), _1077810)))], (17159 ^ _779300) ^ [_1077851, _1077853] : [class_Rings_Ocomm__semiring__1(_1077851), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1077851), _1077853), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1077853)], (17165 ^ _779300) ^ [_1077942, _1077944] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1077942)), _1077944) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1077942), _1077944)))], (17167 ^ _779300) ^ [_1077985, _1077987] : [class_Rings_Oring__1__no__zero__divisors(_1077985), 17170 ^ _779300 : [(17181 ^ _779300) ^ [] : [17182 ^ _779300 : [(17183 ^ _779300) ^ [] : [_1077987 = c_Groups_Oone__class_Oone(_1077985)], (17185 ^ _779300) ^ [] : [_1077987 = hAPP(c_Groups_Ouminus__class_Ouminus(_1077985), c_Groups_Oone__class_Oone(_1077985))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1077985), _1077987), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1077985))], (17171 ^ _779300) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1077985), _1077987), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1077985), -(_1077987 = c_Groups_Oone__class_Oone(_1077985)), -(_1077987 = hAPP(c_Groups_Ouminus__class_Ouminus(_1077985), c_Groups_Oone__class_Oone(_1077985)))]]], (17189 ^ _779300) ^ [_1078292, _1078294, _1078296] : [class_Rings_Oring__1(_1078292), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078292), hAPP(c_Groups_Ouminus__class_Ouminus(_1078292), _1078294)), 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)))), _1078296)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1078292), _1078294), 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)))), _1078296)))], (17195 ^ _779300) ^ [_1078423] : [class_Orderings_Olinorder(_1078423), -(c_Finite__Set_Ofun__left__comm__idem(_1078423, _1078423, c_Orderings_Oord__class_Omin(_1078423)))], (17201 ^ _779300) ^ [_1078502, _1078504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078502)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1078502)), _1078504) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1078502), _1078504)))], (17207 ^ _779300) ^ [_1078619, _1078621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078619)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1078619), _1078621)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1078619)), _1078621))], (17213 ^ _779300) ^ [_1078736, _1078738] : [class_Rings_Oring__1(_1078736), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078736), hAPP(c_Groups_Ouminus__class_Ouminus(_1078736), c_Groups_Oone__class_Oone(_1078736))), 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)))), _1078738)) = c_Groups_Oone__class_Oone(_1078736))], (17219 ^ _779300) ^ [_1078851, _1078853, _1078855] : [class_Int_Onumber__ring(_1078851), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078851), hAPP(c_Int_Onumber__class_Onumber__of(_1078851), _1078853)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1078855))) = hAPP(hAPP(c_HOL_OLet(_1078851, _1078851), hAPP(hAPP(c_Power_Opower__class_Opower(_1078851), hAPP(c_Int_Onumber__class_Onumber__of(_1078851), _1078853)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078855))), hAPP(hAPP(c_COMBS(_1078851, _1078851, _1078851), c_Groups_Otimes__class_Otimes(_1078851)), c_COMBI(_1078851))))], (17225 ^ _779300) ^ [_1079042, _1079044] : [class_Rings_Oring__1(_1079042), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079042), hAPP(c_Groups_Ouminus__class_Ouminus(_1079042), c_Groups_Oone__class_Oone(_1079042))), 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)))), _1079044))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1079042), c_Groups_Oone__class_Oone(_1079042)))], (17231 ^ _779300) ^ [_1079173] : [class_Rings_Osemiring__1(_1079173), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079173), c_Groups_Ozero__class_Ozero(_1079173)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1079173))], (17237 ^ _779300) ^ [_1079270, _1079272] : [class_Rings_Oring__1__no__zero__divisors(_1079270), 17240 ^ _779300 : [(17241 ^ _779300) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1079270), _1079272), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1079270), -(_1079272 = c_Groups_Ozero__class_Ozero(_1079270))], (17247 ^ _779300) ^ [] : [_1079272 = c_Groups_Ozero__class_Ozero(_1079270), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079270), _1079272), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1079270))]]], (17253 ^ _779300) ^ [_1079511, _1079513] : [class_Rings_Ocomm__semiring__1(_1079511), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079511), _1079513), _1079513) = hAPP(hAPP(c_Power_Opower__class_Opower(_1079511), _1079513), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (17259 ^ _779300) ^ [_1079618, _1079620] : [class_Groups_Omonoid__mult(_1079618), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079618), _1079620), 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(_1079618), _1079620), _1079620))], (17265 ^ _779300) ^ [_1079725] : [class_Rings_Osemiring__1(_1079725), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079725), c_Groups_Oone__class_Oone(_1079725)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1079725))], (17271 ^ _779300) ^ [_1079822, _1079824, _1079826] : [class_Groups_Omonoid__mult(_1079822), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079822), _1079824), 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)))), _1079826)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1079822), hAPP(hAPP(c_Power_Opower__class_Opower(_1079822), _1079824), _1079826)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (17277 ^ _779300) ^ [_1079953, _1079955] : [class_Groups_Oordered__ab__group__add(_1079953), 17280 ^ _779300 : [(17281 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079953), c_Groups_Ozero__class_Ozero(_1079953)), hAPP(c_Groups_Ouminus__class_Ouminus(_1079953), _1079955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079953), _1079955), c_Groups_Ozero__class_Ozero(_1079953))))], (17287 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079953), _1079955), c_Groups_Ozero__class_Ozero(_1079953))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079953), c_Groups_Ozero__class_Ozero(_1079953)), hAPP(c_Groups_Ouminus__class_Ouminus(_1079953), _1079955))))]]], (17293 ^ _779300) ^ [_1080227, _1080229] : [class_Groups_Olinordered__ab__group__add(_1080227), 17296 ^ _779300 : [(17297 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080227), _1080229), hAPP(c_Groups_Ouminus__class_Ouminus(_1080227), _1080229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080227), _1080229), c_Groups_Ozero__class_Ozero(_1080227))))], (17303 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080227), _1080229), c_Groups_Ozero__class_Ozero(_1080227))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080227), _1080229), hAPP(c_Groups_Ouminus__class_Ouminus(_1080227), _1080229))))]]], (17309 ^ _779300) ^ [_1080495, _1080497] : [class_Groups_Oordered__ab__group__add(_1080495), 17312 ^ _779300 : [(17313 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080495), hAPP(c_Groups_Ouminus__class_Ouminus(_1080495), _1080497)), c_Groups_Ozero__class_Ozero(_1080495))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080495), c_Groups_Ozero__class_Ozero(_1080495)), _1080497)))], (17319 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080495), c_Groups_Ozero__class_Ozero(_1080495)), _1080497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080495), hAPP(c_Groups_Ouminus__class_Ouminus(_1080495), _1080497)), c_Groups_Ozero__class_Ozero(_1080495))))]]], (17325 ^ _779300) ^ [_1080769, _1080771] : [class_Groups_Olinordered__ab__group__add(_1080769), 17328 ^ _779300 : [(17329 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080769), hAPP(c_Groups_Ouminus__class_Ouminus(_1080769), _1080771)), _1080771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080769), c_Groups_Ozero__class_Ozero(_1080769)), _1080771)))], (17335 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080769), c_Groups_Ozero__class_Ozero(_1080769)), _1080771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080769), hAPP(c_Groups_Ouminus__class_Ouminus(_1080769), _1080771)), _1080771)))]]], (17341 ^ _779300) ^ [_1081037, _1081039] : [class_Groups_Olinordered__ab__group__add(_1081037), 17344 ^ _779300 : [(17345 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081037), hAPP(c_Groups_Ouminus__class_Ouminus(_1081037), _1081039)), _1081039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081037), c_Groups_Ozero__class_Ozero(_1081037)), _1081039)))], (17351 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081037), c_Groups_Ozero__class_Ozero(_1081037)), _1081039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081037), hAPP(c_Groups_Ouminus__class_Ouminus(_1081037), _1081039)), _1081039)))]]], (17357 ^ _779300) ^ [_1081305, _1081307] : [class_Groups_Oordered__ab__group__add(_1081305), 17360 ^ _779300 : [(17361 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081305), hAPP(c_Groups_Ouminus__class_Ouminus(_1081305), _1081307)), c_Groups_Ozero__class_Ozero(_1081305))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081305), c_Groups_Ozero__class_Ozero(_1081305)), _1081307)))], (17367 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081305), c_Groups_Ozero__class_Ozero(_1081305)), _1081307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081305), hAPP(c_Groups_Ouminus__class_Ouminus(_1081305), _1081307)), c_Groups_Ozero__class_Ozero(_1081305))))]]], (17373 ^ _779300) ^ [_1081579, _1081581] : [class_Groups_Oordered__ab__group__add(_1081579), 17376 ^ _779300 : [(17377 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081579), c_Groups_Ozero__class_Ozero(_1081579)), hAPP(c_Groups_Ouminus__class_Ouminus(_1081579), _1081581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081579), _1081581), c_Groups_Ozero__class_Ozero(_1081579))))], (17383 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081579), _1081581), c_Groups_Ozero__class_Ozero(_1081579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081579), c_Groups_Ozero__class_Ozero(_1081579)), hAPP(c_Groups_Ouminus__class_Ouminus(_1081579), _1081581))))]]], (17389 ^ _779300) ^ [_1081853, _1081855] : [class_Rings_Olinordered__idom(_1081853), 17392 ^ _779300 : [(17393 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081853), _1081855), hAPP(c_Groups_Ouminus__class_Ouminus(_1081853), _1081855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081853), _1081855), c_Groups_Ozero__class_Ozero(_1081853))))], (17399 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081853), _1081855), c_Groups_Ozero__class_Ozero(_1081853))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081853), _1081855), hAPP(c_Groups_Ouminus__class_Ouminus(_1081853), _1081855))))]]], (17405 ^ _779300) ^ [_1082121, _1082123, _1082125] : [class_Groups_Ogroup__add(_1082121), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082121), _1082123), _1082125) = c_Groups_Ozero__class_Ozero(_1082121), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1082121), _1082123) = _1082125)], (17415 ^ _779300) ^ [_1082282, _1082284] : [class_Groups_Oab__group__add(_1082282), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082282), hAPP(c_Groups_Ouminus__class_Ouminus(_1082282), _1082284)), _1082284) = c_Groups_Ozero__class_Ozero(_1082282))], (17421 ^ _779300) ^ [_1082387, _1082389] : [class_Groups_Ogroup__add(_1082387), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082387), hAPP(c_Groups_Ouminus__class_Ouminus(_1082387), _1082389)), _1082389) = c_Groups_Ozero__class_Ozero(_1082387))], (17427 ^ _779300) ^ [_1082492, _1082494, _1082496] : [class_Groups_Ogroup__add(_1082492), 17430 ^ _779300 : [(17431 ^ _779300) ^ [] : [_1082494 = hAPP(c_Groups_Ouminus__class_Ouminus(_1082492), _1082496), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082492), _1082494), _1082496) = c_Groups_Ozero__class_Ozero(_1082492))], (17437 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082492), _1082494), _1082496) = c_Groups_Ozero__class_Ozero(_1082492), -(_1082494 = hAPP(c_Groups_Ouminus__class_Ouminus(_1082492), _1082496))]]], (17443 ^ _779300) ^ [_1082748, _1082750] : [class_Groups_Ogroup__add(_1082748), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082748), _1082750), hAPP(c_Groups_Ouminus__class_Ouminus(_1082748), _1082750)) = c_Groups_Ozero__class_Ozero(_1082748))], (17449 ^ _779300) ^ [_1082853, _1082855] : [class_Groups_Ogroup__add(_1082853), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082853), c_Groups_Ozero__class_Ozero(_1082853)), _1082855) = hAPP(c_Groups_Ouminus__class_Ouminus(_1082853), _1082855))], (17455 ^ _779300) ^ [_1082958, _1082960, _1082962] : [class_Int_Onumber(_1082958), class_Orderings_Oord(_1082958), 17462 ^ _779300 : [(17463 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082958), hAPP(c_Int_Onumber__class_Onumber__of(_1082958), _1082960)), hAPP(c_Int_Onumber__class_Onumber__of(_1082958), _1082962))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1082958), hAPP(c_Int_Onumber__class_Onumber__of(_1082958), _1082960)), hAPP(c_Int_Onumber__class_Onumber__of(_1082958), _1082962)) = hAPP(c_Int_Onumber__class_Onumber__of(_1082958), _1082960))], (17469 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082958), hAPP(c_Int_Onumber__class_Onumber__of(_1082958), _1082960)), hAPP(c_Int_Onumber__class_Onumber__of(_1082958), _1082962)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1082958), hAPP(c_Int_Onumber__class_Onumber__of(_1082958), _1082960)), hAPP(c_Int_Onumber__class_Onumber__of(_1082958), _1082962)) = hAPP(c_Int_Onumber__class_Onumber__of(_1082958), _1082962))]]], (17475 ^ _779300) ^ [_1083350, _1083352, _1083354] : [class_Rings_Ocomm__ring__1(_1083350), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083350), _1083352), _1083354) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1083350), _1083352), hAPP(c_Groups_Ouminus__class_Ouminus(_1083350), _1083354)))], (17481 ^ _779300) ^ [_1083469, _1083471, _1083473] : [class_Groups_Ogroup__add(_1083469), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083469), _1083471), _1083473) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1083469), _1083471), hAPP(c_Groups_Ouminus__class_Ouminus(_1083469), _1083473)))], (17487 ^ _779300) ^ [_1083588, _1083590, _1083592] : [class_Groups_Oab__group__add(_1083588), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083588), _1083590), _1083592) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1083588), _1083590), hAPP(c_Groups_Ouminus__class_Ouminus(_1083588), _1083592)))], (17493 ^ _779300) ^ [_1083707, _1083709, _1083711] : [class_Groups_Ogroup__add(_1083707), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083707), _1083709), hAPP(c_Groups_Ouminus__class_Ouminus(_1083707), _1083711)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1083707), _1083709), _1083711))], (17499 ^ _779300) ^ [_1083826, _1083828] : [class_Rings_Oring__1__no__zero__divisors(_1083826), 17502 ^ _779300 : [(17513 ^ _779300) ^ [] : [17514 ^ _779300 : [(17515 ^ _779300) ^ [] : [_1083828 = c_Groups_Oone__class_Oone(_1083826)], (17517 ^ _779300) ^ [] : [_1083828 = hAPP(c_Groups_Ouminus__class_Ouminus(_1083826), c_Groups_Oone__class_Oone(_1083826))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083826), _1083828), _1083828) = c_Groups_Oone__class_Oone(_1083826))], (17503 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083826), _1083828), _1083828) = c_Groups_Oone__class_Oone(_1083826), -(_1083828 = c_Groups_Oone__class_Oone(_1083826)), -(_1083828 = hAPP(c_Groups_Ouminus__class_Ouminus(_1083826), c_Groups_Oone__class_Oone(_1083826)))]]], (17521 ^ _779300) ^ [_1084133, _1084135] : [class_Rings_Ocomm__ring__1(_1084133), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1084133), _1084135) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084133), hAPP(c_Groups_Ouminus__class_Ouminus(_1084133), c_Groups_Oone__class_Oone(_1084133))), _1084135))], (17527 ^ _779300) ^ [_1084248, _1084250, _1084252] : [class_Rings_Ocomm__semiring__1(_1084248), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084248), _1084250), hAPP(c_Nat_OSuc, _1084252)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084248), _1084250), hAPP(hAPP(c_Power_Opower__class_Opower(_1084248), _1084250), _1084252)))], (17533 ^ _779300) ^ [_1084379, _1084381, _1084383] : [class_Rings_Ocomm__semiring__1(_1084379), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084379), _1084381), hAPP(hAPP(c_Power_Opower__class_Opower(_1084379), _1084381), _1084383)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1084379), _1084381), hAPP(c_Nat_OSuc, _1084383)))], (17539 ^ _779300) ^ [_1084510, _1084512, _1084514] : [class_Rings_Ocomm__semiring__1(_1084510), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084510), hAPP(hAPP(c_Power_Opower__class_Opower(_1084510), _1084512), _1084514)), _1084512) = hAPP(hAPP(c_Power_Opower__class_Opower(_1084510), _1084512), hAPP(c_Nat_OSuc, _1084514)))], (17545 ^ _779300) ^ [_1084641, _1084643] : [class_Rings_Ocomm__semiring__1(_1084641), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084641), _1084643), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1084641))], (17551 ^ _779300) ^ [_1084736, _1084738, _1084740, _1084742] : [class_Rings_Ocomm__semiring__1(_1084736), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084736), hAPP(hAPP(c_Power_Opower__class_Opower(_1084736), _1084738), _1084740)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084736), _1084738), _1084742)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1084736), _1084738), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084740), _1084742)))], (17557 ^ _779300) ^ [_1084903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1084903)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084903), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17563 ^ _779300) ^ [_1084998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084998), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1084998)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17569 ^ _779300) ^ [_1085099, _1085101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1085099)), -(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), _1085099), _1085101))))], (17575 ^ _779300) ^ [_1085196, _1085198, _1085200] : [-(hAPP(c_Nat_Onat_Onat__rec(_1085196, _1085198, _1085200), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1085198)], (17577 ^ _779300) ^ [_1085230, _1085232, _1085234, _1085236] : [-(hAPP(c_Nat_Onat_Onat__rec(_1085230, _1085232, _1085234), hAPP(c_Nat_OSuc, _1085236)) = hAPP(hAPP(_1085234, _1085236), hAPP(c_Nat_Onat_Onat__rec(_1085230, _1085232, _1085234), _1085236)))], (17579 ^ _779300) ^ [_1085294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1085294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1085294)))], (17585 ^ _779300) ^ [_1085377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1085377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1085377))))], (17591 ^ _779300) ^ [_1085478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085478)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085478), c_Int_OPls)))], (17597 ^ _779300) ^ [_1085573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085573), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085573)), c_Int_OPls)))], (17603 ^ _779300) ^ [_1085689, _1085691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085689)), c_Int_OBit1(_1085691))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085689), _1085691)))], (17609 ^ _779300) ^ [_1085790, _1085792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085790), _1085792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085790)), c_Int_OBit1(_1085792))))], (17615 ^ _779300) ^ [_1085912, _1085914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085912)), c_Int_OBit1(_1085914))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085912), _1085914)))], (17621 ^ _779300) ^ [_1086013, _1086015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086013), _1086015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1086013)), c_Int_OBit1(_1086015))))], (17627 ^ _779300) ^ [_1086132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1086132)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086132), c_Int_OPls)))], (17633 ^ _779300) ^ [_1086227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086227), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1086227)), c_Int_OPls)))], (17639 ^ _779300) ^ [_1086340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1086340))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1086340)))], (17645 ^ _779300) ^ [_1086423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1086423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1086423))))], (17651 ^ _779300) ^ [_1086527, _1086529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1086527)), c_Int_OBit0(_1086529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086527), _1086529)))], (17657 ^ _779300) ^ [_1086628, _1086630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086628), _1086630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1086628)), c_Int_OBit0(_1086630))))], (17663 ^ _779300) ^ [_1086750, _1086752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1086750)), c_Int_OBit0(_1086752))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086750), _1086752)))], (17669 ^ _779300) ^ [_1086851, _1086853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086851), _1086853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1086851)), c_Int_OBit0(_1086853))))], (17675 ^ _779300) ^ [_1086958, _1086960] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1086958)), c_Int_OBit0(_1086960)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086958), _1086960)))], (17677 ^ _779300) ^ [_1087001, _1087003] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1087001)), c_Int_OBit1(_1087003)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1087001), _1087003)))], (17679 ^ _779300) ^ [_1087044, _1087046, _1087048] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1087044), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1087046), _1087048)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1087044), _1087046)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1087044), _1087048)))], (17681 ^ _779300) ^ [_1087101] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1087101)), _1087101) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17683 ^ _779300) ^ [_1087148, _1087150] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1087148)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1087150), 17686 ^ _779300 : [(17687 ^ _779300) ^ [] : [-(_1087148 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17689 ^ _779300) ^ [] : [-(_1087150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (17691 ^ _779300) ^ [_1087265, _1087267] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1087265)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1087267)), _1087265 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1087267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17701 ^ _779300) ^ [_1087414] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1087414)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1087414)))], (17703 ^ _779300) ^ [_1087447, _1087449] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1087447)), c_Int_OBit1(_1087449)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1087447), _1087449)))], (17705 ^ _779300) ^ [_1087490, _1087492] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1087490)), c_Int_OBit0(_1087492)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1087490), _1087492)))], (17707 ^ _779300) ^ [_1087545, _1087547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1087545)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1087547))))], (17709 ^ _779300) ^ [_1087584, _1087586] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1087584), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1087586)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1087584), _1087586))], (17711 ^ _779300) ^ [_1087624, _1087626] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1087624), _1087626) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1087624), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1087626)))], (17713 ^ _779300) ^ [_1087664, _1087666] : [class_Rings_Oring__1(_1087664), hBOOL(hAPP(hAPP(c_member(_1087664), _1087666), c_Int_Oring__1__class_OInts(_1087664))), -(hBOOL(hAPP(hAPP(c_member(_1087664), hAPP(c_Groups_Ouminus__class_Ouminus(_1087664), _1087666)), c_Int_Oring__1__class_OInts(_1087664))))], (17723 ^ _779300) ^ [_1087837, _1087839, _1087841] : [class_Rings_Oring__1(_1087837), hBOOL(hAPP(hAPP(c_member(_1087837), _1087839), c_Int_Oring__1__class_OInts(_1087837))), -(hBOOL(hAPP(hAPP(c_member(_1087837), hAPP(hAPP(c_Power_Opower__class_Opower(_1087837), _1087839), _1087841)), c_Int_Oring__1__class_OInts(_1087837))))], (17733 ^ _779300) ^ [_1088032] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1088032)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088032))))], (17739 ^ _779300) ^ [_1088127] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1088127))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1088127)))))], (17745 ^ _779300) ^ [_1088228] : [-(c_Int_Opred(c_Int_OBit1(_1088228)) = c_Int_OBit0(_1088228))], (17747 ^ _779300) ^ [_1088257] : [-(c_Int_Opred(c_Int_OBit0(_1088257)) = c_Int_OBit1(c_Int_Opred(_1088257)))], (17749 ^ _779300) ^ [_1088288] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1088288)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1088288))))], (17751 ^ _779300) ^ [_1088323, _1088325, _1088327] : [class_Rings_Olinordered__semidom(_1088323), hAPP(hAPP(c_Power_Opower__class_Opower(_1088323), _1088325), 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(_1088323), _1088327), 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(_1088323), c_Groups_Ozero__class_Ozero(_1088323)), _1088325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088323), c_Groups_Ozero__class_Ozero(_1088323)), _1088327)), -(_1088325 = _1088327)], (17769 ^ _779300) ^ [_1088630, _1088632, _1088634] : [class_Rings_Olinordered__semidom(_1088630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088630), hAPP(hAPP(c_Power_Opower__class_Opower(_1088630), _1088632), 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(_1088630), _1088634), 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(_1088630), c_Groups_Ozero__class_Ozero(_1088630)), _1088634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088630), _1088632), _1088634)))], (17783 ^ _779300) ^ [_1088893, _1088895] : [class_Rings_Olinordered__idom(_1088893), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088893), c_Groups_Ozero__class_Ozero(_1088893)), hAPP(hAPP(c_Power_Opower__class_Opower(_1088893), _1088895), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (17789 ^ _779300) ^ [_1089002, _1089004] : [class_Rings_Olinordered__idom(_1089002), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089002), hAPP(hAPP(c_Power_Opower__class_Opower(_1089002), _1089004), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1089002)))], (17795 ^ _779300) ^ [_1089112, _1089114] : [class_Rings_Olinordered__idom(_1089112), 17798 ^ _779300 : [(17799 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089112), c_Groups_Ozero__class_Ozero(_1089112)), hAPP(hAPP(c_Power_Opower__class_Opower(_1089112), _1089114), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1089114 = c_Groups_Ozero__class_Ozero(_1089112)], (17805 ^ _779300) ^ [] : [-(_1089114 = c_Groups_Ozero__class_Ozero(_1089112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089112), c_Groups_Ozero__class_Ozero(_1089112)), hAPP(hAPP(c_Power_Opower__class_Opower(_1089112), _1089114), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (17811 ^ _779300) ^ [_1089336, _1089338, _1089340] : [class_Rings_Olinordered__idom(_1089336), 17814 ^ _779300 : [(17815 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089336), hAPP(hAPP(c_Power_Opower__class_Opower(_1089336), _1089338), 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(_1089336), _1089340), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1089336), 17818 ^ _779300 : [(17819 ^ _779300) ^ [] : [-(_1089338 = c_Groups_Ozero__class_Ozero(_1089336))], (17821 ^ _779300) ^ [] : [-(_1089340 = c_Groups_Ozero__class_Ozero(_1089336))]]], (17823 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089336), hAPP(hAPP(c_Power_Opower__class_Opower(_1089336), _1089338), 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(_1089336), _1089340), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1089336)), _1089338 = c_Groups_Ozero__class_Ozero(_1089336), _1089340 = c_Groups_Ozero__class_Ozero(_1089336)]]], (17833 ^ _779300) ^ [_1089711, _1089713] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1089711), hAPP(c_Int_Onumber__class_Onumber__of(_1089711), _1089713)), 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(_1089711), hAPP(c_Int_Onumber__class_Onumber__of(_1089711), _1089713)), hAPP(c_Int_Onumber__class_Onumber__of(_1089711), _1089713))), class_Groups_Omonoid__mult(_1089711), class_Int_Onumber(_1089711)], (17843 ^ _779300) ^ [_1089898] : [-(c_Int_Osucc(c_Int_OBit0(_1089898)) = c_Int_OBit1(_1089898))], (17845 ^ _779300) ^ [_1089927] : [-(c_Int_Osucc(c_Int_OBit1(_1089927)) = c_Int_OBit0(c_Int_Osucc(_1089927)))], (17847 ^ _779300) ^ [_1089958, _1089960, _1089962] : [class_Rings_Ocomm__semiring__1(_1089958), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1089958), _1089960), 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)))), _1089962)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089958), hAPP(hAPP(c_Power_Opower__class_Opower(_1089958), _1089960), _1089962)), hAPP(hAPP(c_Power_Opower__class_Opower(_1089958), _1089960), _1089962)))], (17853 ^ _779300) ^ [_1090105] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1090105)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090105)), 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))))], (17855 ^ _779300) ^ [_1090151, _1090153] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090151))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090151)), _1090153) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1090153))], (17861 ^ _779300) ^ [_1090256, _1090258] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090256)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090256)), _1090258) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090256)), _1090258)))], (17867 ^ _779300) ^ [_1090329, _1090331] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090329))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090329)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090331)) = 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), _1090331)))], (17873 ^ _779300) ^ [_1090446, _1090448] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090446)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090446)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090448)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1090446)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090448))))], (17879 ^ _779300) ^ [_1090516, _1090518, _1090520] : [class_Rings_Olinordered__semidom(_1090516), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090516), hAPP(hAPP(c_Power_Opower__class_Opower(_1090516), _1090518), 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(_1090516), _1090520), 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(_1090516), c_Groups_Ozero__class_Ozero(_1090516)), _1090520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090516), _1090518), _1090520)))], (17893 ^ _779300) ^ [_1090779, _1090781, _1090783] : [class_Rings_Olinordered__idom(_1090779), 17896 ^ _779300 : [(17897 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090779), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090779), hAPP(hAPP(c_Power_Opower__class_Opower(_1090779), _1090781), 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(_1090779), _1090783), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1090779))), 17900 ^ _779300 : [(17901 ^ _779300) ^ [] : [-(_1090781 = c_Groups_Ozero__class_Ozero(_1090779))], (17903 ^ _779300) ^ [] : [-(_1090783 = c_Groups_Ozero__class_Ozero(_1090779))]]], (17905 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090779), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090779), hAPP(hAPP(c_Power_Opower__class_Opower(_1090779), _1090781), 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(_1090779), _1090783), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1090779)))), _1090781 = c_Groups_Ozero__class_Ozero(_1090779), _1090783 = c_Groups_Ozero__class_Ozero(_1090779)]]], (17915 ^ _779300) ^ [_1091175, _1091177, _1091179] : [class_Rings_Olinordered__idom(_1091175), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091175), c_Groups_Ozero__class_Ozero(_1091175)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091175), hAPP(hAPP(c_Power_Opower__class_Opower(_1091175), _1091177), 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(_1091175), _1091179), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (17921 ^ _779300) ^ [_1091318, _1091320, _1091322] : [class_Rings_Olinordered__idom(_1091318), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091318), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091318), hAPP(hAPP(c_Power_Opower__class_Opower(_1091318), _1091320), 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(_1091318), _1091322), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1091318)))], (17927 ^ _779300) ^ [_1091462, _1091464, _1091466] : [class_Rings_Olinordered__idom(_1091462), 17930 ^ _779300 : [(17941 ^ _779300) ^ [] : [17942 ^ _779300 : [(17943 ^ _779300) ^ [] : [-(_1091464 = c_Groups_Ozero__class_Ozero(_1091462))], (17945 ^ _779300) ^ [] : [-(_1091466 = c_Groups_Ozero__class_Ozero(_1091462))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091462), c_Groups_Ozero__class_Ozero(_1091462)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091462), hAPP(hAPP(c_Power_Opower__class_Opower(_1091462), _1091464), 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(_1091462), _1091466), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (17931 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091462), c_Groups_Ozero__class_Ozero(_1091462)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091462), hAPP(hAPP(c_Power_Opower__class_Opower(_1091462), _1091464), 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(_1091462), _1091466), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1091464 = c_Groups_Ozero__class_Ozero(_1091462), _1091466 = c_Groups_Ozero__class_Ozero(_1091462)]]], (17949 ^ _779300) ^ [_1091837, _1091839, _1091841] : [class_Int_Onumber__ring(_1091837), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1091837), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091837), _1091839), _1091841)), 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(_1091837), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091837), hAPP(hAPP(c_Power_Opower__class_Opower(_1091837), _1091839), 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(_1091837), _1091841), 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(_1091837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091837), hAPP(c_Int_Onumber__class_Onumber__of(_1091837), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1091839)), _1091841)))], (17955 ^ _779300) ^ [_1092052, _1092054, _1092056] : [class_Rings_Olinordered__idom(_1092052), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092052), c_Groups_Ozero__class_Ozero(_1092052)), hAPP(hAPP(c_Power_Opower__class_Opower(_1092052), _1092054), 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)))), _1092056)))))], (17961 ^ _779300) ^ [_1092169, _1092171, _1092173] : [class_Groups_Omonoid__mult(_1092169), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1092169), _1092171), 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)))), _1092173))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092169), _1092171), hAPP(hAPP(c_Power_Opower__class_Opower(_1092169), hAPP(hAPP(c_Power_Opower__class_Opower(_1092169), _1092171), _1092173)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (17967 ^ _779300) ^ [_1092322, _1092324, _1092326] : [class_Rings_Ocomm__semiring__1(_1092322), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1092322), _1092324), 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)))), _1092326))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092322), _1092324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092322), hAPP(hAPP(c_Power_Opower__class_Opower(_1092322), _1092324), _1092326)), hAPP(hAPP(c_Power_Opower__class_Opower(_1092322), _1092324), _1092326))))], (17973 ^ _779300) ^ [_1092491, _1092493] : [class_Int_Onumber__ring(_1092491), -(hAPP(c_Int_Onumber__class_Onumber__of(_1092491), c_Int_OBit0(_1092493)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092491), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092491), c_Groups_Ozero__class_Ozero(_1092491)), hAPP(c_Int_Onumber__class_Onumber__of(_1092491), _1092493))), hAPP(c_Int_Onumber__class_Onumber__of(_1092491), _1092493)))], (17979 ^ _779300) ^ [_1092651, _1092653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1092651)), c_Int_OBit1(_1092653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092651), _1092653)))], (17985 ^ _779300) ^ [_1092752, _1092754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092752), _1092754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1092752)), c_Int_OBit1(_1092754))))], (17991 ^ _779300) ^ [_1092874, _1092876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1092874)), c_Int_OBit1(_1092876))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092874), _1092876)))], (17997 ^ _779300) ^ [_1092975, _1092977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092975), _1092977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1092975)), c_Int_OBit1(_1092977))))], (18003 ^ _779300) ^ [_1093097, _1093099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1093097)), c_Int_OBit0(_1093099))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093097), _1093099)))], (18009 ^ _779300) ^ [_1093198, _1093200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093198), _1093200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1093198)), c_Int_OBit0(_1093200))))], (18015 ^ _779300) ^ [_1093320, _1093322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1093320)), c_Int_OBit0(_1093322))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093320), _1093322)))], (18021 ^ _779300) ^ [_1093421, _1093423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093421), _1093423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1093421)), c_Int_OBit0(_1093423))))], (18027 ^ _779300) ^ [_1093528, _1093530, _1093532] : [class_Int_Onumber__ring(_1093528), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1093528), hAPP(c_Int_Onumber__class_Onumber__of(_1093528), _1093530)), hAPP(c_Int_Onumber__class_Onumber__of(_1093528), _1093532)) = hAPP(c_Int_Onumber__class_Onumber__of(_1093528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093530), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1093532))))], (18033 ^ _779300) ^ [_1093669, _1093671] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1093669)), _1093671) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1093669), _1093671))), _1093671))], (18035 ^ _779300) ^ [_1093731, _1093733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1093731)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1093733)))), 18038 ^ _779300 : [(18039 ^ _779300) ^ [] : [-(_1093731 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18041 ^ _779300) ^ [] : [-(_1093733 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18043 ^ _779300) ^ [_1093858, _1093860] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1093858)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1093860))))), _1093858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1093860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18053 ^ _779300) ^ [_1094017] : [-(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), _1094017))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18055 ^ _779300) ^ [_1094051] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1094051))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18057 ^ _779300) ^ [_1094083, _1094085] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094083)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094085)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094083), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094085))))], (18059 ^ _779300) ^ [_1094132] : [-(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, _1094132))))))], (18061 ^ _779300) ^ [_1094166, _1094168] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1094166)), c_Int_OBit1(_1094168)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1094166)), _1094168)))], (18063 ^ _779300) ^ [_1094211, _1094213, _1094215] : [class_Int_Onumber__ring(_1094211), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1094211), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1094211), _1094213), _1094215)), 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(_1094211), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094211), hAPP(hAPP(c_Power_Opower__class_Opower(_1094211), _1094213), 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(_1094211), _1094215), 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(_1094211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094211), hAPP(c_Int_Onumber__class_Onumber__of(_1094211), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1094213)), _1094215)))], (18069 ^ _779300) ^ [_1094426, _1094428, _1094430] : [class_Rings_Olinordered__idom(_1094426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094426), c_Groups_Ozero__class_Ozero(_1094426)), hAPP(hAPP(c_Power_Opower__class_Opower(_1094426), _1094428), 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)))), _1094430))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094426), c_Groups_Ozero__class_Ozero(_1094426)), _1094428)))], (18079 ^ _779300) ^ [_1094621, _1094623, _1094625] : [class_Rings_Olinordered__idom(_1094621), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094621), _1094623), c_Groups_Ozero__class_Ozero(_1094621))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094621), hAPP(hAPP(c_Power_Opower__class_Opower(_1094621), _1094623), 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)))), _1094625)))), c_Groups_Ozero__class_Ozero(_1094621))))], (18089 ^ _779300) ^ [_1094816, _1094818] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1094816)), c_Int_OBit1(_1094818)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094816), c_Int_Osucc(_1094818))))], (18091 ^ _779300) ^ [_1094861, _1094863] : [class_Int_Onumber__ring(_1094861), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094861), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094861), c_Groups_Oone__class_Oone(_1094861)), c_Groups_Oone__class_Oone(_1094861))), hAPP(c_Int_Onumber__class_Onumber__of(_1094861), _1094863)) = hAPP(c_Int_Onumber__class_Onumber__of(_1094861), c_Int_OBit0(_1094863)))], (18097 ^ _779300) ^ [_1095000, _1095002] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1095000)), _1095002) = 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), _1095000)), _1095002))], (18099 ^ _779300) ^ [_1095045, _1095047] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1095045), hAPP(c_Nat_OSuc, _1095047)) = 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)), _1095047)), _1095045))], (18101 ^ _779300) ^ [_1095090, _1095092] : [class_Groups_Omonoid__mult(_1095090), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095090), _1095092), 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(_1095090), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095090), _1095092), _1095092)), _1095092))], (18107 ^ _779300) ^ [_1095213, _1095215, _1095217, _1095219] : [class_Int_Onumber__ring(_1095213), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095213), hAPP(c_Int_Onumber__class_Onumber__of(_1095213), _1095215)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1095213), _1095217), hAPP(c_Int_Onumber__class_Onumber__of(_1095213), _1095219))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095213), hAPP(c_Int_Onumber__class_Onumber__of(_1095213), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1095215), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1095219)))), _1095217))], (18113 ^ _779300) ^ [_1095388] : [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), _1095388))), 18116 ^ _779300 : [(18117 ^ _779300) ^ [] : [-(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(_1095388)))))], (18119 ^ _779300) ^ [] : [-(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(_1095388)))))]]], (18121 ^ _779300) ^ [_1095527, _1095529] : [class_Int_Onumber__ring(_1095527), -(hAPP(c_Int_Onumber__class_Onumber__of(_1095527), c_Int_Opred(_1095529)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095527), hAPP(c_Groups_Ouminus__class_Ouminus(_1095527), c_Groups_Oone__class_Oone(_1095527))), hAPP(c_Int_Onumber__class_Onumber__of(_1095527), _1095529)))], (18127 ^ _779300) ^ [_1095665] : [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, _1095665)))))], (18129 ^ _779300) ^ [_1095699] : [-(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, _1095699)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18131 ^ _779300) ^ [_1095745, _1095747] : [_1095745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1095747), _1095745) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18137 ^ _779300) ^ [_1095828, _1095830] : [-(_1095828 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1095830), _1095828) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1095830), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1095830), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1095828), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (18143 ^ _779300) ^ [_1095890, _1095892] : [class_Int_Onumber__ring(_1095890), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095890), _1095892), hAPP(c_Int_Onumber__class_Onumber__of(_1095890), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095890), _1095892), _1095892))], (18149 ^ _779300) ^ [_1096007, _1096009] : [class_Int_Onumber__ring(_1096007), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096007), hAPP(c_Int_Onumber__class_Onumber__of(_1096007), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1096009) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096007), _1096009), _1096009))], (18155 ^ _779300) ^ [_1096124] : [class_Int_Onumber__ring(_1096124), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096124), c_Groups_Oone__class_Oone(_1096124)), c_Groups_Oone__class_Oone(_1096124)) = hAPP(c_Int_Onumber__class_Onumber__of(_1096124), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (18161 ^ _779300) ^ [] : [-(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))))], (18163 ^ _779300) ^ [] : [-(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))))], (18165 ^ _779300) ^ [] : [-(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))))))], (18167 ^ _779300) ^ [_1096285] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1096285), 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, _1096285)))], (18169 ^ _779300) ^ [_1096320] : [-(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)))), _1096320) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1096320)))], (18171 ^ _779300) ^ [_1096352] : [-(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)))), _1096352) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1096352), _1096352))], (18173 ^ _779300) ^ [_1096384] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1096384), 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), _1096384), _1096384))], (18175 ^ _779300) ^ [] : [-(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)))))], (18177 ^ _779300) ^ [] : [-(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)))))], (18179 ^ _779300) ^ [] : [-(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))))], (18181 ^ _779300) ^ [_1096473, _1096475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096473), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1096473), _1096475)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1096473))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1096475))))], (18187 ^ _779300) ^ [_1096614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1096614), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1096614 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1096614 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18197 ^ _779300) ^ [] : [-(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))))], (18199 ^ _779300) ^ [_1096730, _1096732] : [class_Int_Onumber__ring(_1096730), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1096730), c_Groups_Oone__class_Oone(_1096730)), hAPP(c_Int_Onumber__class_Onumber__of(_1096730), _1096732)) = hAPP(c_Int_Onumber__class_Onumber__of(_1096730), 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), _1096732))))], (18205 ^ _779300) ^ [_1096857, _1096859] : [class_Int_Onumber__ring(_1096857), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1096857), hAPP(c_Int_Onumber__class_Onumber__of(_1096857), _1096859)), c_Groups_Oone__class_Oone(_1096857)) = hAPP(c_Int_Onumber__class_Onumber__of(_1096857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1096859), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (18211 ^ _779300) ^ [_1096984, _1096986, _1096988] : [class_Int_Onumber__ring(_1096984), 18214 ^ _779300 : [(18215 ^ _779300) ^ [] : [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), _1096986))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096984), _1096988), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1096986))) = hAPP(hAPP(c_HOL_OLet(_1096984, _1096984), hAPP(hAPP(c_Power_Opower__class_Opower(_1096984), _1096988), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096986))), hAPP(hAPP(c_COMBS(_1096984, _1096984, _1096984), hAPP(hAPP(c_COMBB(_1096984, tc_fun(_1096984, _1096984), _1096984), c_Groups_Otimes__class_Otimes(_1096984)), hAPP(c_Groups_Otimes__class_Otimes(_1096984), _1096988))), c_COMBI(_1096984))))], (18221 ^ _779300) ^ [] : [-(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), _1096986)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096984), _1096988), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1096986))) = c_Groups_Oone__class_Oone(_1096984))]]], (18227 ^ _779300) ^ [_1097351, _1097353] : [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), _1097351))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1097353), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1097351))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1097353), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097351))), 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), _1097353))), c_COMBI(tc_Int_Oint))))], (18233 ^ _779300) ^ [_1097508, _1097510] : [-(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), _1097508)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1097510), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1097508))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (18239 ^ _779300) ^ [_1097562, _1097564] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1097562)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1097564)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1097564))), 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), _1097562)), c_Int_Onat)))))], (18241 ^ _779300) ^ [_1097625, _1097627, _1097629] : [class_Orderings_Olinorder(_1097625), -(_1097627 = c_Orderings_Obot__class_Obot(tc_fun(_1097625, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097625, tc_HOL_Obool)), _1097627), _1097629)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097625), _1097629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097625), hAPP(c_Finite__Set_Ofold1(_1097625, c_Orderings_Oord__class_Omin(_1097625)), _1097629)), hAPP(c_Finite__Set_Ofold1(_1097625, c_Orderings_Oord__class_Omin(_1097625)), _1097627))))], (18259 ^ _779300) ^ [_1097951, _1097953, _1097955, _1097957] : [class_Rings_Olinordered__semidom(_1097951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097951), _1097953), _1097955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097951), c_Groups_Ozero__class_Ozero(_1097951)), _1097953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1097957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097951), hAPP(hAPP(c_Power_Opower__class_Opower(_1097951), _1097953), _1097957)), hAPP(hAPP(c_Power_Opower__class_Opower(_1097951), _1097955), _1097957))))], (18277 ^ _779300) ^ [_1098280, _1098282, _1098284] : [class_Orderings_Olinorder(_1098280), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098280), _1098282)), -(_1098282 = c_Orderings_Obot__class_Obot(tc_fun(_1098280, tc_HOL_Obool))), 18288 ^ _779300 : [(18289 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098280), hAPP(c_Finite__Set_Ofold1(_1098280, c_Orderings_Oord__class_Omin(_1098280)), _1098282)), _1098284)), 18293 ^ _779300 : [(18294 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098280), 18292 ^ [_1098280, _1098282, _1098284]), _1098282)))], (18296 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098280), 18292 ^ [_1098280, _1098282, _1098284]), _1098284)))]]], (18298 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098280), hAPP(c_Finite__Set_Ofold1(_1098280, c_Orderings_Oord__class_Omin(_1098280)), _1098282)), _1098284))), 18299 ^ _779300 : [(18300 ^ _779300) ^ [_1098669] : [hBOOL(hAPP(hAPP(c_member(_1098280), _1098669), _1098282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098280), _1098669), _1098284))]]]]], (18308 ^ _779300) ^ [_1098830, _1098832, _1098834] : [class_Orderings_Olinorder(_1098830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098830), _1098832)), -(_1098832 = c_Orderings_Obot__class_Obot(tc_fun(_1098830, tc_HOL_Obool))), 18319 ^ _779300 : [(18330 ^ _779300) ^ [] : [18332 ^ _779300 : [(18333 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098830), 18331 ^ [_1098830, _1098832, _1098834]), _1098832)))], (18335 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098830), _1098834), 18331 ^ [_1098830, _1098832, _1098834]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098830), _1098834), hAPP(c_Finite__Set_Ofold1(_1098830, c_Orderings_Oord__class_Omin(_1098830)), _1098832))))], (18320 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098830), _1098834), hAPP(c_Finite__Set_Ofold1(_1098830, c_Orderings_Oord__class_Omin(_1098830)), _1098832))), 18323 ^ _779300 : [(18324 ^ _779300) ^ [_1099123] : [hBOOL(hAPP(hAPP(c_member(_1098830), _1099123), _1098832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098830), _1098834), _1099123)))]]]]], (18339 ^ _779300) ^ [_1099408, _1099410, _1099412] : [class_Orderings_Olinorder(_1099408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099408), _1099410)), -(_1099410 = c_Orderings_Obot__class_Obot(tc_fun(_1099408, tc_HOL_Obool))), 18350 ^ _779300 : [(18351 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099408), hAPP(c_Finite__Set_Ofold1(_1099408, c_Orderings_Oord__class_Omin(_1099408)), _1099410)), _1099412)), 18355 ^ _779300 : [(18356 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099408), 18354 ^ [_1099408, _1099410, _1099412]), _1099410)))], (18358 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099408), 18354 ^ [_1099408, _1099410, _1099412]), _1099412)))]]], (18360 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099408), hAPP(c_Finite__Set_Ofold1(_1099408, c_Orderings_Oord__class_Omin(_1099408)), _1099410)), _1099412))), 18361 ^ _779300 : [(18362 ^ _779300) ^ [_1099797] : [hBOOL(hAPP(hAPP(c_member(_1099408), _1099797), _1099410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099408), _1099797), _1099412))]]]]], (18370 ^ _779300) ^ [_1099958, _1099960, _1099962] : [class_Orderings_Olinorder(_1099958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099958), _1099960)), -(_1099960 = c_Orderings_Obot__class_Obot(tc_fun(_1099958, tc_HOL_Obool))), 18381 ^ _779300 : [(18392 ^ _779300) ^ [] : [18394 ^ _779300 : [(18395 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099958), 18393 ^ [_1099958, _1099960, _1099962]), _1099960)))], (18397 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099958), _1099962), 18393 ^ [_1099958, _1099960, _1099962]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099958), _1099962), hAPP(c_Finite__Set_Ofold1(_1099958, c_Orderings_Oord__class_Omin(_1099958)), _1099960))))], (18382 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099958), _1099962), hAPP(c_Finite__Set_Ofold1(_1099958, c_Orderings_Oord__class_Omin(_1099958)), _1099960))), 18385 ^ _779300 : [(18386 ^ _779300) ^ [_1100251] : [hBOOL(hAPP(hAPP(c_member(_1099958), _1100251), _1099960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099958), _1099962), _1100251)))]]]]], (18401 ^ _779300) ^ [_1100536, _1100538, _1100540] : [class_Orderings_Olinorder(_1100536), hBOOL(hAPP(c_Finite__Set_Ofinite(_1100536), _1100538)), hBOOL(hAPP(hAPP(c_member(_1100536), _1100540), _1100538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100536), hAPP(c_Finite__Set_Ofold1(_1100536, c_Orderings_Oord__class_Omin(_1100536)), _1100538)), _1100540)))], (18415 ^ _779300) ^ [_1100769, _1100771, _1100773] : [-(hBOOL(hAPP(hAPP(c_member(_1100769), _1100771), _1100773))), -(hBOOL(hAPP(hAPP(c_member(_1100769), _1100771), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100769, tc_HOL_Obool)), _1100773))))], (18421 ^ _779300) ^ [_1100847, _1100849, _1100851] : [hBOOL(hAPP(hAPP(c_member(_1100847), _1100849), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100847, tc_HOL_Obool)), _1100851))), hBOOL(hAPP(hAPP(c_member(_1100847), _1100849), _1100851))], (18427 ^ _779300) ^ [_1100965, _1100967, _1100969] : [-(hBOOL(hAPP(hAPP(c_member(_1100965), _1100967), _1100969))), -(hBOOL(hAPP(hAPP(c_member(_1100965), _1100967), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100965, tc_HOL_Obool)), _1100969))))], (18433 ^ _779300) ^ [_1101027, _1101029, _1101031] : [hBOOL(hAPP(hAPP(c_member(_1101027), _1101029), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101027, tc_HOL_Obool)), _1101031))), hBOOL(hAPP(hAPP(c_member(_1101027), _1101029), _1101031))], (18439 ^ _779300) ^ [_1101151, _1101153, _1101155] : [hBOOL(hAPP(hAPP(c_member(_1101151), _1101153), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101151, tc_HOL_Obool)), _1101155))), hBOOL(hAPP(hAPP(c_member(_1101151), _1101153), _1101155))], (18445 ^ _779300) ^ [_1101293, _1101295, _1101297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101293, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101293, tc_HOL_Obool)), _1101295)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101293, tc_HOL_Obool)), _1101297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101293, tc_HOL_Obool)), _1101297), _1101295)))], (18451 ^ _779300) ^ [_1101440, _1101442, _1101444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101440, tc_HOL_Obool)), _1101444), _1101442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101440, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101440, tc_HOL_Obool)), _1101442)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101440, tc_HOL_Obool)), _1101444))))], (18457 ^ _779300) ^ [_1101593, _1101595, _1101597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101593, tc_HOL_Obool)), _1101595), _1101597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101593, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101593, tc_HOL_Obool)), _1101597)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101593, tc_HOL_Obool)), _1101595))))], (18463 ^ _779300) ^ [_1101759, _1101761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101759, tc_HOL_Obool)), _1101761), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101759, tc_HOL_Obool)), _1101761))), -(_1101761 = c_Orderings_Obot__class_Obot(tc_fun(_1101759, tc_HOL_Obool)))], (18469 ^ _779300) ^ [_1101878, _1101880] : [_1101880 = c_Orderings_Obot__class_Obot(tc_fun(_1101878, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101878, tc_HOL_Obool)), _1101880), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101878, tc_HOL_Obool)), _1101880))))], (18475 ^ _779300) ^ [_1102003, _1102005] : [class_Orderings_Olinorder(_1102003), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1102003), _1102005), _1102005) = _1102005)], (18481 ^ _779300) ^ [_1102094, _1102096, _1102098] : [class_Rings_Oring__1__no__zero__divisors(_1102094), -(_1102096 = c_Groups_Ozero__class_Ozero(_1102094)), hAPP(hAPP(c_Power_Opower__class_Opower(_1102094), _1102096), _1102098) = c_Groups_Ozero__class_Ozero(_1102094)], (18491 ^ _779300) ^ [_1102253] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1102253) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18503 ^ _779300) ^ [_1102392, _1102394] : [18504 ^ _779300 : [(18505 ^ _779300) ^ [] : [_1102394 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18507 ^ _779300) ^ [] : [_1102392 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1102392), _1102394) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18493 ^ _779300) ^ [_1102294, _1102296] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1102294), _1102296) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1102296 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1102294 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18511 ^ _779300) ^ [_1102521, _1102523, _1102525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1102521), _1102523)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1102521), _1102525))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1102523), _1102525)))], (18531 ^ _779300) ^ [_1102823, _1102825] : [18532 ^ _779300 : [(18533 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102823))], (18535 ^ _779300) ^ [] : [_1102825 = 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), _1102823), _1102825))))], (18521 ^ _779300) ^ [_1102717, _1102719] : [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), _1102717), _1102719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102717))), -(_1102719 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18539 ^ _779300) ^ [_1102960, _1102962, _1102964, _1102966] : [class_Groups_Ocomm__monoid__mult(_1102960), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1102960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102960), _1102962), _1102964)), _1102966) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102960), hAPP(hAPP(c_Power_Opower__class_Opower(_1102960), _1102962), _1102966)), hAPP(hAPP(c_Power_Opower__class_Opower(_1102960), _1102964), _1102966)))], (18545 ^ _779300) ^ [_1103119, _1103121, _1103123] : [class_Groups_Omonoid__mult(_1103119), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103119), hAPP(hAPP(c_Power_Opower__class_Opower(_1103119), _1103121), _1103123)), _1103121) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103119), _1103121), hAPP(hAPP(c_Power_Opower__class_Opower(_1103119), _1103121), _1103123)))], (18551 ^ _779300) ^ [_1103260, _1103262] : [class_Groups_Omonoid__mult(_1103260), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1103260), c_Groups_Oone__class_Oone(_1103260)), _1103262) = c_Groups_Oone__class_Oone(_1103260))], (18557 ^ _779300) ^ [_1103359, _1103361, _1103363] : [class_Rings_Osemiring__1(_1103359), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103359), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1103361), _1103363)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1103359), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103359), _1103361)), _1103363))], (18563 ^ _779300) ^ [_1103484, _1103486, _1103488, _1103490] : [class_Groups_Omonoid__mult(_1103484), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1103484), _1103486), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103488), _1103490)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1103484), hAPP(hAPP(c_Power_Opower__class_Opower(_1103484), _1103486), _1103488)), _1103490))], (18569 ^ _779300) ^ [_1103623, _1103625] : [class_Groups_Omonoid__mult(_1103623), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1103623), _1103625), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1103625)], (18575 ^ _779300) ^ [_1103714, _1103716, _1103718, _1103720] : [class_Rings_Olinordered__semidom(_1103714), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103714), _1103716), _1103718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103714), c_Groups_Ozero__class_Ozero(_1103714)), _1103716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103714), hAPP(hAPP(c_Power_Opower__class_Opower(_1103714), _1103716), _1103720)), hAPP(hAPP(c_Power_Opower__class_Opower(_1103714), _1103718), _1103720))))], (18589 ^ _779300) ^ [_1103983, _1103985, _1103987] : [class_Rings_Olinordered__semidom(_1103983), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103983), c_Groups_Ozero__class_Ozero(_1103983)), _1103985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103983), c_Groups_Ozero__class_Ozero(_1103983)), hAPP(hAPP(c_Power_Opower__class_Opower(_1103983), _1103985), _1103987))))], (18599 ^ _779300) ^ [_1104166, _1104168, _1104170] : [class_Rings_Olinordered__semidom(_1104166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104166), c_Groups_Ozero__class_Ozero(_1104166)), _1104168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104166), c_Groups_Ozero__class_Ozero(_1104166)), hAPP(hAPP(c_Power_Opower__class_Opower(_1104166), _1104168), _1104170))))], (18609 ^ _779300) ^ [_1104349, _1104351, _1104353] : [class_Power_Opower(_1104349), class_Rings_Omult__zero(_1104349), class_Rings_Ono__zero__divisors(_1104349), class_Rings_Ozero__neq__one(_1104349), 18624 ^ _779300 : [(18625 ^ _779300) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1104349), _1104351), _1104353) = c_Groups_Ozero__class_Ozero(_1104349), 18628 ^ _779300 : [(18629 ^ _779300) ^ [] : [-(_1104351 = c_Groups_Ozero__class_Ozero(_1104349))], (18631 ^ _779300) ^ [] : [_1104353 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (18633 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1104349), _1104351), _1104353) = c_Groups_Ozero__class_Ozero(_1104349)), _1104351 = c_Groups_Ozero__class_Ozero(_1104349), -(_1104353 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18643 ^ _779300) ^ [_1104841, _1104843, _1104845] : [class_Rings_Olinordered__semidom(_1104841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104841), c_Groups_Oone__class_Oone(_1104841)), _1104843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104841), c_Groups_Oone__class_Oone(_1104841)), hAPP(hAPP(c_Power_Opower__class_Opower(_1104841), _1104843), _1104845))))], (18653 ^ _779300) ^ [_1105024, _1105026] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1105024), c_Groups_Ozero__class_Ozero(_1105024)), hAPP(c_Nat_OSuc, _1105026)) = c_Groups_Ozero__class_Ozero(_1105024)), class_Power_Opower(_1105024), class_Rings_Osemiring__0(_1105024)], (18663 ^ _779300) ^ [_1105179, _1105181, _1105183, _1105185] : [class_Rings_Olinordered__semidom(_1105179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105179), c_Groups_Oone__class_Oone(_1105179)), _1105181)), 18670 ^ _779300 : [(18671 ^ _779300) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1105179), _1105181), _1105183) = hAPP(hAPP(c_Power_Opower__class_Opower(_1105179), _1105181), _1105185), -(_1105183 = _1105185)], (18677 ^ _779300) ^ [] : [_1105183 = _1105185, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1105179), _1105181), _1105183) = hAPP(hAPP(c_Power_Opower__class_Opower(_1105179), _1105181), _1105185))]]], (18683 ^ _779300) ^ [_1105518, _1105520, _1105522] : [class_Power_Opower(_1105518), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1105518), _1105520), hAPP(c_Nat_OSuc, _1105522)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105518), _1105520), hAPP(hAPP(c_Power_Opower__class_Opower(_1105518), _1105520), _1105522)))], (18689 ^ _779300) ^ [_1105649, _1105651, _1105653] : [class_Groups_Omonoid__mult(_1105649), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1105649), _1105651), hAPP(c_Nat_OSuc, _1105653)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105649), hAPP(hAPP(c_Power_Opower__class_Opower(_1105649), _1105651), _1105653)), _1105651))], (18695 ^ _779300) ^ [_1105780, _1105782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1105780)), -(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), _1105780), _1105782))))], (18701 ^ _779300) ^ [_1105877, _1105879] : [class_Power_Opower(_1105877), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1105877), _1105879), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1105877))], (18707 ^ _779300) ^ [_1105972, _1105974, _1105976, _1105978] : [class_Groups_Omonoid__mult(_1105972), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1105972), _1105974), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1105976), _1105978)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105972), hAPP(hAPP(c_Power_Opower__class_Opower(_1105972), _1105974), _1105976)), hAPP(hAPP(c_Power_Opower__class_Opower(_1105972), _1105974), _1105978)))], (18713 ^ _779300) ^ [_1106127, _1106129, _1106131, _1106133] : [class_Rings_Olinordered__semidom(_1106127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106127), hAPP(hAPP(c_Power_Opower__class_Opower(_1106127), _1106129), _1106131)), hAPP(hAPP(c_Power_Opower__class_Opower(_1106127), _1106133), _1106131))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106127), c_Groups_Ozero__class_Ozero(_1106127)), _1106133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106127), _1106129), _1106133)))], (18727 ^ _779300) ^ [_1106396, _1106398, _1106400, _1106402] : [class_Rings_Olinordered__semidom(_1106396), hAPP(hAPP(c_Power_Opower__class_Opower(_1106396), _1106398), hAPP(c_Nat_OSuc, _1106400)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1106396), _1106402), hAPP(c_Nat_OSuc, _1106400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106396), c_Groups_Ozero__class_Ozero(_1106396)), _1106398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106396), c_Groups_Ozero__class_Ozero(_1106396)), _1106402)), -(_1106398 = _1106402)], (18745 ^ _779300) ^ [_1106723, _1106725, _1106727, _1106729] : [class_Rings_Olinordered__semidom(_1106723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106723), hAPP(hAPP(c_Power_Opower__class_Opower(_1106723), _1106725), hAPP(c_Nat_OSuc, _1106727))), hAPP(hAPP(c_Power_Opower__class_Opower(_1106723), _1106729), hAPP(c_Nat_OSuc, _1106727)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106723), c_Groups_Ozero__class_Ozero(_1106723)), _1106729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106723), _1106725), _1106729)))], (18759 ^ _779300) ^ [_1107004, _1107006, _1107008] : [class_Rings_Olinordered__semidom(_1107004), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107004), c_Groups_Oone__class_Oone(_1107004)), _1107006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107004), hAPP(hAPP(c_Power_Opower__class_Opower(_1107004), _1107006), _1107008)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107004), _1107006), hAPP(hAPP(c_Power_Opower__class_Opower(_1107004), _1107006), _1107008)))))], (18769 ^ _779300) ^ [_1107215, _1107217, _1107219] : [class_Rings_Olinordered__semidom(_1107215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107215), c_Groups_Oone__class_Oone(_1107215)), _1107217)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107215), c_Groups_Oone__class_Oone(_1107215)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107215), _1107217), hAPP(hAPP(c_Power_Opower__class_Opower(_1107215), _1107217), _1107219)))))], (18779 ^ _779300) ^ [_1107414, _1107416] : [class_Power_Opower(_1107414), class_Rings_Osemiring__0(_1107414), 18786 ^ _779300 : [(18787 ^ _779300) ^ [] : [_1107416 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1107414), c_Groups_Ozero__class_Ozero(_1107414)), _1107416) = c_Groups_Oone__class_Oone(_1107414))], (18793 ^ _779300) ^ [] : [-(_1107416 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1107414), c_Groups_Ozero__class_Ozero(_1107414)), _1107416) = c_Groups_Ozero__class_Ozero(_1107414))]]], (18799 ^ _779300) ^ [_1107688, _1107690, _1107692] : [class_Rings_Olinordered__semidom(_1107688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107688), c_Groups_Oone__class_Oone(_1107688)), _1107690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107688), c_Groups_Oone__class_Oone(_1107688)), hAPP(hAPP(c_Power_Opower__class_Opower(_1107688), _1107690), hAPP(c_Nat_OSuc, _1107692)))))], (18809 ^ _779300) ^ [_1107877, _1107879, _1107881, _1107883] : [class_Rings_Olinordered__semidom(_1107877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1107879), _1107881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107877), c_Groups_Oone__class_Oone(_1107877)), _1107883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107877), hAPP(hAPP(c_Power_Opower__class_Opower(_1107877), _1107883), _1107879)), hAPP(hAPP(c_Power_Opower__class_Opower(_1107877), _1107883), _1107881))))], (18823 ^ _779300) ^ [_1108142, _1108144, _1108146, _1108148] : [class_Rings_Olinordered__semidom(_1108142), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108142), c_Groups_Oone__class_Oone(_1108142)), _1108144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108142), hAPP(hAPP(c_Power_Opower__class_Opower(_1108142), _1108144), _1108146)), hAPP(hAPP(c_Power_Opower__class_Opower(_1108142), _1108144), _1108148))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108146), _1108148)))], (18837 ^ _779300) ^ [_1108407, _1108409, _1108411, _1108413] : [class_Rings_Olinordered__semidom(_1108407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108407), c_Groups_Oone__class_Oone(_1108407)), _1108409)), 18844 ^ _779300 : [(18845 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108407), hAPP(hAPP(c_Power_Opower__class_Opower(_1108407), _1108409), _1108411)), hAPP(hAPP(c_Power_Opower__class_Opower(_1108407), _1108409), _1108413))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108411), _1108413)))], (18851 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108411), _1108413)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108407), hAPP(hAPP(c_Power_Opower__class_Opower(_1108407), _1108409), _1108411)), hAPP(hAPP(c_Power_Opower__class_Opower(_1108407), _1108409), _1108413))))]]], (18857 ^ _779300) ^ [_1108782, _1108784, _1108786, _1108788] : [class_Rings_Olinordered__semidom(_1108782), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1108784), _1108786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108782), c_Groups_Oone__class_Oone(_1108782)), _1108788)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108782), hAPP(hAPP(c_Power_Opower__class_Opower(_1108782), _1108788), _1108784)), hAPP(hAPP(c_Power_Opower__class_Opower(_1108782), _1108788), _1108786))))], (18871 ^ _779300) ^ [_1109047, _1109049, _1109051] : [class_Rings_Oring__1(_1109047), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1109047), hAPP(c_Groups_Ouminus__class_Ouminus(_1109047), _1109049)), _1109051) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109047), hAPP(hAPP(c_Power_Opower__class_Opower(_1109047), hAPP(c_Groups_Ouminus__class_Ouminus(_1109047), c_Groups_Oone__class_Oone(_1109047))), _1109051)), hAPP(hAPP(c_Power_Opower__class_Opower(_1109047), _1109049), _1109051)))], (18877 ^ _779300) ^ [_1109212, _1109214, _1109216] : [class_Rings_Olinordered__semidom(_1109212), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109212), c_Groups_Ozero__class_Ozero(_1109212)), _1109214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109212), _1109214), c_Groups_Oone__class_Oone(_1109212))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109212), _1109214), hAPP(hAPP(c_Power_Opower__class_Opower(_1109212), _1109214), _1109216))), hAPP(hAPP(c_Power_Opower__class_Opower(_1109212), _1109214), _1109216))))], (18891 ^ _779300) ^ [_1109495, _1109497, _1109499, _1109501] : [class_Rings_Olinordered__semidom(_1109495), hAPP(hAPP(c_Power_Opower__class_Opower(_1109495), _1109497), _1109499) = hAPP(hAPP(c_Power_Opower__class_Opower(_1109495), _1109501), _1109499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109495), c_Groups_Ozero__class_Ozero(_1109495)), _1109497)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109495), c_Groups_Ozero__class_Ozero(_1109495)), _1109501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1109499)), -(_1109497 = _1109501)], (18913 ^ _779300) ^ [_1109870, _1109872, _1109874] : [class_Rings_Olinordered__semidom(_1109870), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109870), c_Groups_Ozero__class_Ozero(_1109870)), _1109872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109870), _1109872), c_Groups_Oone__class_Oone(_1109870))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109870), hAPP(hAPP(c_Power_Opower__class_Opower(_1109870), _1109872), hAPP(c_Nat_OSuc, _1109874))), c_Groups_Oone__class_Oone(_1109870))))], (18927 ^ _779300) ^ [_1110131, _1110133, _1110135, _1110137] : [class_Rings_Olinordered__semidom(_1110131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110133), _1110135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110131), c_Groups_Ozero__class_Ozero(_1110131)), _1110137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110131), _1110137), c_Groups_Oone__class_Oone(_1110131))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110131), hAPP(hAPP(c_Power_Opower__class_Opower(_1110131), _1110137), _1110135)), hAPP(hAPP(c_Power_Opower__class_Opower(_1110131), _1110137), _1110133))))], (18945 ^ _779300) ^ [_1110470, _1110472, _1110474, _1110476] : [class_Rings_Olinordered__semidom(_1110470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110472), _1110474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110470), c_Groups_Ozero__class_Ozero(_1110470)), _1110476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110470), _1110476), c_Groups_Oone__class_Oone(_1110470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110470), hAPP(hAPP(c_Power_Opower__class_Opower(_1110470), _1110476), _1110474)), hAPP(hAPP(c_Power_Opower__class_Opower(_1110470), _1110476), _1110472))))], (18963 ^ _779300) ^ [_1110809, _1110811, _1110813, _1110815] : [class_Rings_Olinordered__semidom(_1110809), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110809), c_Groups_Oone__class_Oone(_1110809)), _1110811)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110809), hAPP(hAPP(c_Power_Opower__class_Opower(_1110809), _1110811), _1110813)), hAPP(hAPP(c_Power_Opower__class_Opower(_1110809), _1110811), _1110815))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110813), _1110815)))], (18977 ^ _779300) ^ [_1111074, _1111076, _1111078, _1111080] : [class_Rings_Olinordered__semidom(_1111074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111074), c_Groups_Oone__class_Oone(_1111074)), _1111076)), 18984 ^ _779300 : [(18985 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111074), hAPP(hAPP(c_Power_Opower__class_Opower(_1111074), _1111076), _1111078)), hAPP(hAPP(c_Power_Opower__class_Opower(_1111074), _1111076), _1111080))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111078), _1111080)))], (18991 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111078), _1111080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111074), hAPP(hAPP(c_Power_Opower__class_Opower(_1111074), _1111076), _1111078)), hAPP(hAPP(c_Power_Opower__class_Opower(_1111074), _1111076), _1111080))))]]], (18997 ^ _779300) ^ [_1111449, _1111451, _1111453] : [class_Rings_Olinordered__semidom(_1111449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111449), c_Groups_Oone__class_Oone(_1111449)), _1111451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1111453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111449), c_Groups_Oone__class_Oone(_1111449)), hAPP(hAPP(c_Power_Opower__class_Opower(_1111449), _1111451), _1111453))))], (19011 ^ _779300) ^ [_1111690, _1111692, _1111694, _1111696] : [c_Big__Operators_Osemilattice__big(_1111690, _1111692, _1111694), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111690), _1111696)), -(hAPP(_1111694, _1111696) = hAPP(c_Finite__Set_Ofold1(_1111690, _1111692), _1111696))], (19021 ^ _779300) ^ [_1111855, _1111857] : [class_Int_Onumber__ring(_1111855), 19024 ^ _779300 : [(19025 ^ _779300) ^ [] : [c_Groups_Oone__class_Oone(_1111855) = hAPP(c_Int_Onumber__class_Onumber__of(_1111855), _1111857), -(c_Int_Oiszero(_1111855, hAPP(c_Int_Onumber__class_Onumber__of(_1111855), 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), _1111857)))))], (19031 ^ _779300) ^ [] : [c_Int_Oiszero(_1111855, hAPP(c_Int_Onumber__class_Onumber__of(_1111855), 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), _1111857)))), -(c_Groups_Oone__class_Oone(_1111855) = hAPP(c_Int_Onumber__class_Onumber__of(_1111855), _1111857))]]], (19037 ^ _779300) ^ [_1112114, _1112116] : [class_Int_Onumber__ring(_1112114), 19040 ^ _779300 : [(19041 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1112114), _1112116) = c_Groups_Oone__class_Oone(_1112114), -(c_Int_Oiszero(_1112114, hAPP(c_Int_Onumber__class_Onumber__of(_1112114), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1112116), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (19047 ^ _779300) ^ [] : [c_Int_Oiszero(_1112114, hAPP(c_Int_Onumber__class_Onumber__of(_1112114), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1112116), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1112114), _1112116) = c_Groups_Oone__class_Oone(_1112114))]]], (19053 ^ _779300) ^ [_1112382, _1112384] : [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), _1112382))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1112384)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1112382))) = 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), _1112384), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1112382)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19059 ^ _779300) ^ [_1112529, _1112531] : [-(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), _1112529)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1112531)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1112529))) = 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), _1112531)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1112529)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19065 ^ _779300) ^ [_1112611, _1112613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1112611), 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)))), _1112613)), 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)))), _1112611)) = 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), _1112613), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1112611))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19071 ^ _779300) ^ [_1112762] : [class_Orderings_Olinorder(_1112762), -(c_Orderings_Oord_Omax(_1112762, hAPP(c_COMBC(_1112762, _1112762, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1112762))) = c_Orderings_Oord__class_Omin(_1112762))], (19077 ^ _779300) ^ [_1112863, _1112865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1112863)), -(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)))), _1112865)), 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)))), _1112863)) = 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, _1112865, _1112863))))], (19083 ^ _779300) ^ [_1113008, _1113010, _1113012] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1113008, tc_HOL_Obool)), _1113010) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1113008, tc_HOL_Obool)), _1113012), -(_1113010 = _1113012)], (19089 ^ _779300) ^ [_1113115, _1113117, _1113119] : [_1113117 = _1113119, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1113115, tc_HOL_Obool)), _1113117) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1113115, tc_HOL_Obool)), _1113119))], (19095 ^ _779300) ^ [_1113228, _1113230] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1113228, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1113228, tc_HOL_Obool)), _1113230)) = _1113230)], (19097 ^ _779300) ^ [_1113269, _1113271, _1113273] : [class_Divides_Osemiring__div(_1113269), -(c_Divides_Odiv__class_Omod(_1113269, c_Divides_Odiv__class_Omod(_1113269, _1113271, _1113273), _1113273) = c_Divides_Odiv__class_Omod(_1113269, _1113271, _1113273))], (19103 ^ _779300) ^ [_1113370, _1113372] : [class_Divides_Osemiring__div(_1113370), -(c_Divides_Odiv__class_Omod(_1113370, _1113372, _1113372) = c_Groups_Ozero__class_Ozero(_1113370))], (19109 ^ _779300) ^ [_1113457, _1113459] : [class_Divides_Osemiring__div(_1113457), -(c_Divides_Odiv__class_Omod(_1113457, _1113459, c_Groups_Ozero__class_Ozero(_1113457)) = _1113459)], (19115 ^ _779300) ^ [_1113544, _1113546] : [class_Divides_Osemiring__div(_1113544), -(c_Divides_Odiv__class_Omod(_1113544, c_Groups_Ozero__class_Ozero(_1113544), _1113546) = c_Groups_Ozero__class_Ozero(_1113544))], (19121 ^ _779300) ^ [_1113635, _1113637, _1113639] : [class_Divides_Osemiring__div(_1113635), -(c_Divides_Odiv__class_Omod(_1113635, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113635), _1113637), _1113639), _1113639) = c_Divides_Odiv__class_Omod(_1113635, _1113637, _1113639))], (19127 ^ _779300) ^ [_1113744, _1113746, _1113748] : [class_Divides_Osemiring__div(_1113744), -(c_Divides_Odiv__class_Omod(_1113744, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113744), _1113746), _1113748), _1113746) = c_Divides_Odiv__class_Omod(_1113744, _1113748, _1113746))], (19133 ^ _779300) ^ [_1113853, _1113855, _1113857, _1113859] : [class_Divides_Osemiring__div(_1113853), -(c_Divides_Odiv__class_Omod(_1113853, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113853), _1113855), _1113857), _1113859) = c_Divides_Odiv__class_Omod(_1113853, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113853), _1113855), c_Divides_Odiv__class_Omod(_1113853, _1113857, _1113859)), _1113859))], (19139 ^ _779300) ^ [_1113988, _1113990, _1113992, _1113994] : [class_Divides_Osemiring__div(_1113988), -(c_Divides_Odiv__class_Omod(_1113988, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113988), _1113990), _1113992), _1113994) = c_Divides_Odiv__class_Omod(_1113988, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113988), c_Divides_Odiv__class_Omod(_1113988, _1113990, _1113994)), _1113992), _1113994))], (19145 ^ _779300) ^ [_1114123, _1114125, _1114127, _1114129] : [class_Divides_Osemiring__div(_1114123), -(c_Divides_Odiv__class_Omod(_1114123, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114123), _1114125), _1114127), _1114129) = c_Divides_Odiv__class_Omod(_1114123, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114123), c_Divides_Odiv__class_Omod(_1114123, _1114125, _1114129)), c_Divides_Odiv__class_Omod(_1114123, _1114127, _1114129)), _1114129))], (19151 ^ _779300) ^ [_1114266, _1114268, _1114270, _1114272] : [class_Divides_Osemiring__div(_1114266), -(c_Divides_Odiv__class_Omod(_1114266, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114266), _1114268), c_Divides_Odiv__class_Omod(_1114266, _1114270, _1114272)), _1114272) = c_Divides_Odiv__class_Omod(_1114266, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114266), _1114268), _1114270), _1114272))], (19157 ^ _779300) ^ [_1114401, _1114403, _1114405, _1114407] : [class_Divides_Osemiring__div(_1114401), -(c_Divides_Odiv__class_Omod(_1114401, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114401), c_Divides_Odiv__class_Omod(_1114401, _1114403, _1114405)), _1114407), _1114405) = c_Divides_Odiv__class_Omod(_1114401, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114401), _1114403), _1114407), _1114405))], (19163 ^ _779300) ^ [_1114536, _1114538, _1114540, _1114542, _1114544, _1114546] : [class_Divides_Osemiring__div(_1114536), c_Divides_Odiv__class_Omod(_1114536, _1114538, _1114540) = c_Divides_Odiv__class_Omod(_1114536, _1114542, _1114540), c_Divides_Odiv__class_Omod(_1114536, _1114544, _1114540) = c_Divides_Odiv__class_Omod(_1114536, _1114546, _1114540), -(c_Divides_Odiv__class_Omod(_1114536, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114536), _1114538), _1114544), _1114540) = c_Divides_Odiv__class_Omod(_1114536, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114536), _1114542), _1114546), _1114540))], (19177 ^ _779300) ^ [_1114819, _1114821, _1114823, _1114825] : [class_Divides_Osemiring__div(_1114819), -(c_Divides_Odiv__class_Omod(_1114819, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114819), _1114821), _1114823), _1114825) = c_Divides_Odiv__class_Omod(_1114819, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114819), _1114821), c_Divides_Odiv__class_Omod(_1114819, _1114823, _1114825)), _1114825))], (19183 ^ _779300) ^ [_1114954, _1114956, _1114958, _1114960] : [class_Divides_Osemiring__div(_1114954), -(c_Divides_Odiv__class_Omod(_1114954, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114954), _1114956), _1114958), _1114960) = c_Divides_Odiv__class_Omod(_1114954, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114954), c_Divides_Odiv__class_Omod(_1114954, _1114956, _1114960)), _1114958), _1114960))], (19189 ^ _779300) ^ [_1115089, _1115091, _1115093, _1115095] : [class_Divides_Osemiring__div(_1115089), -(c_Divides_Odiv__class_Omod(_1115089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115089), _1115091), _1115093), _1115095) = c_Divides_Odiv__class_Omod(_1115089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115089), c_Divides_Odiv__class_Omod(_1115089, _1115091, _1115095)), c_Divides_Odiv__class_Omod(_1115089, _1115093, _1115095)), _1115095))], (19195 ^ _779300) ^ [_1115232, _1115234, _1115236, _1115238] : [class_Divides_Osemiring__div(_1115232), -(c_Divides_Odiv__class_Omod(_1115232, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115232), _1115234), _1115236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115232), _1115234), _1115238)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115232), _1115234), c_Divides_Odiv__class_Omod(_1115232, _1115236, _1115238)))], (19201 ^ _779300) ^ [_1115375, _1115377, _1115379, _1115381] : [class_Divides_Osemiring__div(_1115375), -(c_Divides_Odiv__class_Omod(_1115375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115375), _1115377), _1115379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115375), _1115381), _1115379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115375), c_Divides_Odiv__class_Omod(_1115375, _1115377, _1115381)), _1115379))], (19207 ^ _779300) ^ [_1115518, _1115520, _1115522, _1115524] : [class_Divides_Osemiring__div(_1115518), -(c_Divides_Odiv__class_Omod(_1115518, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115518), c_Divides_Odiv__class_Omod(_1115518, _1115520, _1115522)), _1115524), _1115522) = c_Divides_Odiv__class_Omod(_1115518, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115518), _1115520), _1115524), _1115522))], (19213 ^ _779300) ^ [_1115653, _1115655, _1115657, _1115659, _1115661, _1115663] : [class_Divides_Osemiring__div(_1115653), c_Divides_Odiv__class_Omod(_1115653, _1115655, _1115657) = c_Divides_Odiv__class_Omod(_1115653, _1115659, _1115657), c_Divides_Odiv__class_Omod(_1115653, _1115661, _1115657) = c_Divides_Odiv__class_Omod(_1115653, _1115663, _1115657), -(c_Divides_Odiv__class_Omod(_1115653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115653), _1115655), _1115661), _1115657) = c_Divides_Odiv__class_Omod(_1115653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115653), _1115659), _1115663), _1115657))], (19227 ^ _779300) ^ [_1115936, _1115938, _1115940, _1115942] : [class_Divides_Oring__div(_1115936), -(c_Divides_Odiv__class_Omod(_1115936, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115936), _1115938), _1115940), _1115942) = c_Divides_Odiv__class_Omod(_1115936, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115936), _1115938), c_Divides_Odiv__class_Omod(_1115936, _1115940, _1115942)), _1115942))], (19233 ^ _779300) ^ [_1116071, _1116073, _1116075, _1116077] : [class_Divides_Oring__div(_1116071), -(c_Divides_Odiv__class_Omod(_1116071, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1116071), _1116073), _1116075), _1116077) = c_Divides_Odiv__class_Omod(_1116071, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1116071), c_Divides_Odiv__class_Omod(_1116071, _1116073, _1116077)), _1116075), _1116077))], (19239 ^ _779300) ^ [_1116206, _1116208, _1116210, _1116212] : [class_Divides_Oring__div(_1116206), -(c_Divides_Odiv__class_Omod(_1116206, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1116206), _1116208), _1116210), _1116212) = c_Divides_Odiv__class_Omod(_1116206, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1116206), c_Divides_Odiv__class_Omod(_1116206, _1116208, _1116212)), c_Divides_Odiv__class_Omod(_1116206, _1116210, _1116212)), _1116212))], (19245 ^ _779300) ^ [_1116349, _1116351, _1116353, _1116355, _1116357, _1116359] : [class_Divides_Oring__div(_1116349), c_Divides_Odiv__class_Omod(_1116349, _1116351, _1116353) = c_Divides_Odiv__class_Omod(_1116349, _1116355, _1116353), c_Divides_Odiv__class_Omod(_1116349, _1116357, _1116353) = c_Divides_Odiv__class_Omod(_1116349, _1116359, _1116353), -(c_Divides_Odiv__class_Omod(_1116349, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1116349), _1116351), _1116357), _1116353) = c_Divides_Odiv__class_Omod(_1116349, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1116349), _1116355), _1116359), _1116353))], (19259 ^ _779300) ^ [_1116632, _1116634, _1116636, _1116638] : [class_Divides_Oring__div(_1116632), c_Divides_Odiv__class_Omod(_1116632, _1116634, _1116636) = c_Divides_Odiv__class_Omod(_1116632, _1116638, _1116636), -(c_Divides_Odiv__class_Omod(_1116632, hAPP(c_Groups_Ouminus__class_Ouminus(_1116632), _1116634), _1116636) = c_Divides_Odiv__class_Omod(_1116632, hAPP(c_Groups_Ouminus__class_Ouminus(_1116632), _1116638), _1116636))], (19269 ^ _779300) ^ [_1116819, _1116821, _1116823] : [class_Divides_Oring__div(_1116819), -(c_Divides_Odiv__class_Omod(_1116819, hAPP(c_Groups_Ouminus__class_Ouminus(_1116819), _1116821), _1116823) = c_Divides_Odiv__class_Omod(_1116819, hAPP(c_Groups_Ouminus__class_Ouminus(_1116819), c_Divides_Odiv__class_Omod(_1116819, _1116821, _1116823)), _1116823))], (19275 ^ _779300) ^ [_1116940] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1116940) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19277 ^ _779300) ^ [_1116967] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116967, _1116967) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19279 ^ _779300) ^ [_1116994, _1116996, _1116998] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116994), _1116996), _1116998) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116994), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116996, _1116998)), _1116998))], (19281 ^ _779300) ^ [_1117045, _1117047, _1117049] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1117045), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1117047, _1117049)), _1117049) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1117045), _1117047), _1117049))], (19283 ^ _779300) ^ [_1117096, _1117098, _1117100] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1117096), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1117098, _1117100)), _1117100) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1117096), _1117098), _1117100))], (19285 ^ _779300) ^ [_1117147, _1117149, _1117151] : [-(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, _1117147, _1117149)), _1117151), _1117149) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1117147), _1117151), _1117149))], (19287 ^ _779300) ^ [_1117198, _1117200] : [-(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, _1117198, _1117200)), _1117200) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1117198), _1117200))], (19289 ^ _779300) ^ [_1117241, _1117243] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1117241), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1117243)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1117241, _1117243)))], (19291 ^ _779300) ^ [_1117283, _1117285] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1117283, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1117285)) = 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), _1117283), _1117285)))], (19293 ^ _779300) ^ [_1117325, _1117327, _1117329] : [-(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, _1117325, _1117327)), _1117329), _1117327) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1117325), _1117329), _1117327))], (19295 ^ _779300) ^ [_1117376, _1117378, _1117380] : [class_Divides_Osemiring__div(_1117376), -(c_Divides_Odiv__class_Omod(_1117376, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117376), _1117378), _1117380), _1117380) = c_Groups_Ozero__class_Ozero(_1117376))], (19301 ^ _779300) ^ [_1117481, _1117483, _1117485] : [class_Divides_Osemiring__div(_1117481), -(c_Divides_Odiv__class_Omod(_1117481, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117481), _1117483), _1117485), _1117483) = c_Groups_Ozero__class_Ozero(_1117481))], (19307 ^ _779300) ^ [_1117586, _1117588, _1117590, _1117592] : [class_Divides_Osemiring__div(_1117586), -(c_Divides_Odiv__class_Omod(_1117586, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117586), _1117588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117586), _1117590), _1117592)), _1117590) = c_Divides_Odiv__class_Omod(_1117586, _1117588, _1117590))], (19313 ^ _779300) ^ [_1117713, _1117715, _1117717, _1117719] : [class_Divides_Osemiring__div(_1117713), -(c_Divides_Odiv__class_Omod(_1117713, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117713), _1117715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117713), _1117717), _1117719)), _1117719) = c_Divides_Odiv__class_Omod(_1117713, _1117715, _1117719))], (19319 ^ _779300) ^ [_1117840, _1117842] : [class_Divides_Osemiring__div(_1117840), -(c_Divides_Odiv__class_Omod(_1117840, _1117842, c_Groups_Oone__class_Oone(_1117840)) = c_Groups_Ozero__class_Ozero(_1117840))], (19325 ^ _779300) ^ [_1117931] : [class_Rings_Osemiring__1(_1117931), -(c_Int_Oiszero(_1117931, c_Groups_Ozero__class_Ozero(_1117931)))], (19331 ^ _779300) ^ [_1118008, _1118010] : [class_Rings_Osemiring__1(_1118008), 19334 ^ _779300 : [(19335 ^ _779300) ^ [] : [c_Int_Oiszero(_1118008, _1118010), -(_1118010 = c_Groups_Ozero__class_Ozero(_1118008))], (19341 ^ _779300) ^ [] : [_1118010 = c_Groups_Ozero__class_Ozero(_1118008), -(c_Int_Oiszero(_1118008, _1118010))]]], (19347 ^ _779300) ^ [_1118219] : [class_Rings_Osemiring__1(_1118219), c_Int_Oiszero(_1118219, c_Groups_Oone__class_Oone(_1118219))], (19353 ^ _779300) ^ [_1118297, _1118299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118299)), -(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, _1118297, _1118299))))], (19363 ^ _779300) ^ [_1118446, _1118448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118446, _1118448)), _1118446)))], (19369 ^ _779300) ^ [_1118545, _1118547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118545), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118545), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118547, _1118545))))], (19375 ^ _779300) ^ [_1118650, _1118652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118652, _1118650)), _1118650)))], (19381 ^ _779300) ^ [_1118764, _1118766] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118764, _1118766) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1118764 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1118766), 19384 ^ [_1118764, _1118766]))], (19388 ^ _779300) ^ [_1118869, _1118871] : [19389 ^ _779300 : [(19390 ^ _779300) ^ [_1118918] : [_1118869 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1118871), _1118918)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118869, _1118871) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19394 ^ _779300) ^ [_1118980, _1118982] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1118980), _1118982) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118980, _1118982) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (19400 ^ _779300) ^ [_1119070, _1119072] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119070, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1119072)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119070, _1119072) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (19406 ^ _779300) ^ [_1119161, _1119163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1119161)), -(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, _1119163, _1119161))))], (19412 ^ _779300) ^ [_1119254, _1119256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1119254)), 19415 ^ _779300 : [(19416 ^ _779300) ^ [] : [-(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, _1119256, _1119254))))], (19418 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119256, _1119254)), _1119254)))]]], (19420 ^ _779300) ^ [_1119391, _1119393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1119391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119391), _1119393)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119391, _1119393) = _1119391)], (19430 ^ _779300) ^ [_1119542, _1119544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119542), 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, _1119544, _1119542)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19436 ^ _779300) ^ [_1119647, _1119649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119647), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19439 ^ _779300 : [(19440 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119649, _1119647)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19442 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119647), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119649, _1119647))))]]], (19444 ^ _779300) ^ [_1119796, _1119798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1119796), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119798), _1119796)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119796, _1119798) = _1119796)], (19454 ^ _779300) ^ [_1119962, _1119964] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119962, _1119964) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119962, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1119964)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19460 ^ _779300) ^ [_1120055, _1120057] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120055, _1120057) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120055, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1120057)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120055, _1120057)), _1120057))], (19466 ^ _779300) ^ [_1120123, _1120125] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120123, _1120125) = 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), _1120123), _1120125) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19472 ^ _779300) ^ [_1120216, _1120218] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120216, _1120218) = 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), _1120216), _1120218) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1120218), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120216, _1120218)))], (19478 ^ _779300) ^ [_1120275] : [class_Int_Onumber__ring(_1120275), -(c_Int_Oiszero(_1120275, hAPP(c_Int_Onumber__class_Onumber__of(_1120275), c_Int_OPls)))], (19484 ^ _779300) ^ [_1120358, _1120360] : [c_Int_Oiszero(_1120358, hAPP(c_Int_Onumber__class_Onumber__of(_1120358), c_Int_OBit1(_1120360))), class_Int_Onumber__ring(_1120358), class_Int_Oring__char__0(_1120358)], (19494 ^ _779300) ^ [_1120498, _1120500] : [class_Int_Onumber__ring(_1120498), class_Int_Oring__char__0(_1120498), 19501 ^ _779300 : [(19502 ^ _779300) ^ [] : [c_Int_Oiszero(_1120498, hAPP(c_Int_Onumber__class_Onumber__of(_1120498), c_Int_OBit0(_1120500))), -(c_Int_Oiszero(_1120498, hAPP(c_Int_Onumber__class_Onumber__of(_1120498), _1120500)))], (19508 ^ _779300) ^ [] : [c_Int_Oiszero(_1120498, hAPP(c_Int_Onumber__class_Onumber__of(_1120498), _1120500)), -(c_Int_Oiszero(_1120498, hAPP(c_Int_Onumber__class_Onumber__of(_1120498), c_Int_OBit0(_1120500))))]]], (19514 ^ _779300) ^ [_1120791, _1120793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120791), _1120793)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120791, _1120793) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120791), _1120793))], (19524 ^ _779300) ^ [_1120966, _1120968, _1120970, _1120972] : [_1120966 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1120968), _1120970)), _1120972), -(_1120968 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120966, _1120968) = _1120972), 19531 ^ _779300 : [(19532 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120968)))], (19534 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120972), _1120968))]], 19539 ^ _779300 : [(19540 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120968))], (19542 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120968), _1120972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120972), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (19554 ^ _779300) ^ [_1121431, _1121433, _1121435, _1121437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121433), _1121435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121435), 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), _1121433), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1121437, _1121431))), _1121435)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19568 ^ _779300) ^ [_1121690, _1121692, _1121694, _1121696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121692), _1121694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121694), 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), _1121692), _1121690)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121692), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1121696, _1121690))), _1121694))))], (19582 ^ _779300) ^ [_1121961, _1121963, _1121965, _1121967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121963), _1121965)), -(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), _1121965), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1121967, _1121961))), _1121963)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121965), _1121961))))], (19596 ^ _779300) ^ [_1122226, _1122228, _1122230, _1122232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122226)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122228)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122228), _1122230)), -(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), _1122230), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1122232, _1122226))), _1122228))))], (19656 ^ _779300) ^ [_1123368, _1123370, _1123372] : [-(hBOOL(hAPP(_1123368, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1123370, _1123372)))), 19659 ^ _779300 : [(19660 ^ _779300) ^ [] : [-(_1123372 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19662 ^ _779300) ^ [] : [hBOOL(hAPP(_1123368, _1123370))]], 19665 ^ _779300 : [(19666 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1123372)))], (19670 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19668 ^ [_1123368, _1123370, _1123372])))], (19672 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 19668 ^ [_1123368, _1123370, _1123372]), _1123372)))], (19674 ^ _779300) ^ [] : [-(_1123370 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123372), 19667 ^ [_1123368, _1123370, _1123372])), 19668 ^ [_1123368, _1123370, _1123372]))], (19676 ^ _779300) ^ [] : [hBOOL(hAPP(_1123368, 19668 ^ [_1123368, _1123370, _1123372]))]], 19677 ^ _779300 : [(19678 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123372), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19682 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123372), 19680 ^ [_1123368, _1123370, _1123372])))], (19684 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 19680 ^ [_1123368, _1123370, _1123372]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19686 ^ _779300) ^ [] : [-(_1123370 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123372), 19679 ^ [_1123368, _1123370, _1123372])), 19680 ^ [_1123368, _1123370, _1123372]))], (19688 ^ _779300) ^ [] : [hBOOL(hAPP(_1123368, 19680 ^ [_1123368, _1123370, _1123372]))]]], (19610 ^ _779300) ^ [_1122491, _1122493, _1122495] : [hBOOL(hAPP(_1122491, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1122493, _1122495))), 19613 ^ _779300 : [(19614 ^ _779300) ^ [] : [_1122495 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1122491, _1122493)))], (19620 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122495)), 19623 ^ _779300 : [(19624 ^ _779300) ^ [_1122821, _1122823] : [-(hBOOL(hAPP(_1122491, _1122821))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122821), _1122495)), _1122493 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122495), _1122823)), _1122821)]]], (19638 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122495), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19641 ^ _779300 : [(19642 ^ _779300) ^ [_1123113, _1123115] : [-(hBOOL(hAPP(_1122491, _1123113))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122495), _1123113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123113), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1122493 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122495), _1123115)), _1123113)]]]]], (19692 ^ _779300) ^ [_1124080, _1124082] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1124080)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1124082))) = 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), _1124080), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1124082))))], (19694 ^ _779300) ^ [_1124132] : [class_Int_Onumber__ring(_1124132), c_Int_Oiszero(_1124132, hAPP(c_Int_Onumber__class_Onumber__of(_1124132), c_Int_OBit1(c_Int_OPls)))], (19700 ^ _779300) ^ [_1124216, _1124218, _1124220] : [class_Int_Onumber__ring(_1124216), 19703 ^ _779300 : [(19704 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1124216), _1124218) = hAPP(c_Int_Onumber__class_Onumber__of(_1124216), _1124220), -(c_Int_Oiszero(_1124216, hAPP(c_Int_Onumber__class_Onumber__of(_1124216), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124218), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1124220)))))], (19710 ^ _779300) ^ [] : [c_Int_Oiszero(_1124216, hAPP(c_Int_Onumber__class_Onumber__of(_1124216), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124218), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1124220)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1124216), _1124218) = hAPP(c_Int_Onumber__class_Onumber__of(_1124216), _1124220))]]], (19716 ^ _779300) ^ [_1124499, _1124501] : [class_Int_Onumber__ring(_1124499), 19719 ^ _779300 : [(19720 ^ _779300) ^ [] : [c_Groups_Ozero__class_Ozero(_1124499) = hAPP(c_Int_Onumber__class_Onumber__of(_1124499), _1124501), -(c_Int_Oiszero(_1124499, hAPP(c_Int_Onumber__class_Onumber__of(_1124499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1124501)))))], (19726 ^ _779300) ^ [] : [c_Int_Oiszero(_1124499, hAPP(c_Int_Onumber__class_Onumber__of(_1124499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1124501)))), -(c_Groups_Ozero__class_Ozero(_1124499) = hAPP(c_Int_Onumber__class_Onumber__of(_1124499), _1124501))]]], (19732 ^ _779300) ^ [_1124758, _1124760] : [class_Int_Onumber__ring(_1124758), 19735 ^ _779300 : [(19736 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1124758), _1124760) = c_Groups_Ozero__class_Ozero(_1124758), -(c_Int_Oiszero(_1124758, hAPP(c_Int_Onumber__class_Onumber__of(_1124758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124760), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (19742 ^ _779300) ^ [] : [c_Int_Oiszero(_1124758, hAPP(c_Int_Onumber__class_Onumber__of(_1124758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124760), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1124758), _1124760) = c_Groups_Ozero__class_Ozero(_1124758))]]], (19748 ^ _779300) ^ [_1125026, _1125028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125026)), -(c_SMT_Oz3mod(_1125028, _1125026) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1125028, _1125026))], (19754 ^ _779300) ^ [_1125115, _1125117] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125115))), -(c_SMT_Oz3mod(_1125117, _1125115) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1125117, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1125115)))], (19760 ^ _779300) ^ [_1125165, _1125167, _1125169, _1125171, _1125173, _1125175, _1125177] : [c_Big__Operators_Ocomm__monoid__big(_1125165, _1125167, _1125169, _1125171, _1125173), 19763 ^ _779300 : [(19764 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1125167), _1125175)), -(hAPP(hAPP(_1125173, _1125177), _1125175) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1125165, _1125167, _1125169), _1125177), _1125171), _1125175))], (19770 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1125167), _1125175))), -(hAPP(hAPP(_1125173, _1125177), _1125175) = _1125171)]]], (19776 ^ _779300) ^ [_1125433, _1125435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125433)), -(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)))), _1125435))), 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)))), _1125433)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1125435), _1125433))], (19782 ^ _779300) ^ [_1125556, _1125558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125556), 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)))), _1125558))), 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)))), _1125556)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1125558), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1125556))], (19788 ^ _779300) ^ [_1125697] : [class_Orderings_Oord(_1125697), -(c_Orderings_Oord__class_Omin(_1125697) = c_Orderings_Oord_Omin(_1125697, c_Orderings_Oord__class_Oless__eq(_1125697)))], (19794 ^ _779300) ^ [_1125784] : [class_Power_Opower(_1125784), -(c_Power_Opower__class_Opower(_1125784) = c_Power_Opower_Opower(_1125784, c_Groups_Oone__class_Oone(_1125784), c_Groups_Otimes__class_Otimes(_1125784)))], (19800 ^ _779300) ^ [_1125877] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125877) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19802 ^ _779300) ^ [_1125903, _1125905] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1125903), _1125905) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125903, _1125905)), _1125905))], (19804 ^ _779300) ^ [_1125946, _1125948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125946), _1125948)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125946, _1125948) = _1125946)], (19810 ^ _779300) ^ [_1126041, _1126043] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1126041, _1126043)), _1126041)))], (19812 ^ _779300) ^ [_1126075, _1126077, _1126079] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1126075, _1126077)), _1126079) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126075), _1126079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126077), _1126079)))], (19814 ^ _779300) ^ [_1126128, _1126130, _1126132] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126128), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1126130, _1126132)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126128), _1126130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126128), _1126132)))], (19816 ^ _779300) ^ [_1126181, _1126183] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126181), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1126183)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1126181)), _1126183))], (19818 ^ _779300) ^ [_1126224, _1126226] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1126224)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1126226)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126224), _1126226))], (19820 ^ _779300) ^ [_1126267, _1126269] : [class_Divides_Osemiring__div(_1126267), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1126267), c_Groups_Ozero__class_Ozero(_1126267)), _1126269) = c_Groups_Ozero__class_Ozero(_1126267))], (19826 ^ _779300) ^ [_1126366, _1126368] : [class_Divides_Osemiring__div(_1126366), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1126366), _1126368), c_Groups_Ozero__class_Ozero(_1126366)) = c_Groups_Ozero__class_Ozero(_1126366))], (19832 ^ _779300) ^ [_1126465, _1126467] : [class_Divides_Osemiring__div(_1126465), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1126465), _1126467), c_Groups_Oone__class_Oone(_1126465)) = _1126467)], (19838 ^ _779300) ^ [_1126560] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1126560, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19840 ^ _779300) ^ [_1126596, _1126598] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1126596, _1126598)) = _1126598, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1126596), _1126598) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19846 ^ _779300) ^ [_1126695, _1126697] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1126695, _1126697)) = _1126697), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1126695), _1126697) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1126695, _1126697)))], (19852 ^ _779300) ^ [_1126754, _1126756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126754)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126756)), -(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), _1126754), _1126756))))], (19862 ^ _779300) ^ [_1126907, _1126909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1126907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1126909, _1126907)), _1126907)))], (19868 ^ _779300) ^ [_1127006, _1127008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127006)), 19871 ^ _779300 : [(19872 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127008), _1127006)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1127008), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19878 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1127008), 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), _1127008), _1127006)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (19884 ^ _779300) ^ [_1127265, _1127267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1127265), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19887 ^ _779300 : [(19888 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127267), _1127265)), 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)), _1127267)))], (19894 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1127267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127267), _1127265)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (19900 ^ _779300) ^ [_1127521, _1127523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1127521), 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)), _1127523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127521), _1127523)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19910 ^ _779300) ^ [_1127682] : [-(_1127682 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127682), _1127682) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (19916 ^ _779300) ^ [_1127737, _1127739] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127737, _1127739) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1127737 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127739), 19919 ^ [_1127737, _1127739]))], (19923 ^ _779300) ^ [_1127842, _1127844] : [19924 ^ _779300 : [(19925 ^ _779300) ^ [_1127891] : [_1127842 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127844), _1127891)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127842, _1127844) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19929 ^ _779300) ^ [_1127950, _1127952] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127950), _1127952))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127950, _1127952) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1127950), _1127952), _1127952))], (19935 ^ _779300) ^ [_1128014, _1128016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1128014), _1128016)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1128014, _1128016) = _1128014)], (19941 ^ _779300) ^ [_1128103, _1128105] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1128103), _1128105))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1128103, _1128105) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128103), _1128105), _1128105))], (19947 ^ _779300) ^ [_1128160, _1128162] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1128160))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1128162))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1128160)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1128162)))], (19949 ^ _779300) ^ [_1128211] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1128211), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19951 ^ _779300) ^ [_1128237] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1128237, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1128237)], (19953 ^ _779300) ^ [_1128266, _1128268] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1128266, _1128268)), _1128268) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19955 ^ _779300) ^ [_1128301, _1128303, _1128305] : [-(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), _1128301), _1128303)), _1128305), _1128303) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1128305, _1128303))], (19957 ^ _779300) ^ [_1128348, _1128350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128348), _1128350)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1128350, _1128348) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128350), _1128348), _1128348))], (19963 ^ _779300) ^ [_1128463, _1128465, _1128467] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1128463), _1128465)), _1128467) = 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), _1128463), _1128467)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1128465), _1128467))), 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, _1128463, _1128467)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1128465, _1128467))), _1128467)))], (19965 ^ _779300) ^ [_1128546, _1128548] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1128546, _1128548)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1128546), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1128548)))], (19967 ^ _779300) ^ [_1128588, _1128590] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1128588), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1128590)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1128588, _1128590)))], (19969 ^ _779300) ^ [_1128630, _1128632, _1128634, _1128636] : [class_Divides_Osemiring__div(_1128630), -(_1128632 = c_Groups_Ozero__class_Ozero(_1128630)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128630), _1128632), _1128634)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128630), _1128632), _1128636)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128630), _1128634), _1128636))], (19979 ^ _779300) ^ [_1128792, _1128794, _1128796, _1128798] : [class_Divides_Osemiring__div(_1128792), -(_1128794 = c_Groups_Ozero__class_Ozero(_1128792)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128792), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128792), _1128796), _1128794)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128792), _1128798), _1128794)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128792), _1128796), _1128798))], (19989 ^ _779300) ^ [_1128954, _1128956, _1128958] : [class_Divides_Osemiring__div(_1128954), -(_1128956 = c_Groups_Ozero__class_Ozero(_1128954)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128954), _1128956), _1128958)), _1128956) = _1128958)], (19999 ^ _779300) ^ [_1129082, _1129084, _1129086] : [class_Divides_Osemiring__div(_1129082), -(_1129084 = c_Groups_Ozero__class_Ozero(_1129082)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129082), _1129086), _1129084)), _1129084) = _1129086)], (20009 ^ _779300) ^ [_1129210, _1129212, _1129214, _1129216] : [class_Divides_Osemiring__div(_1129210), 20012 ^ _779300 : [(20013 ^ _779300) ^ [] : [_1129212 = c_Groups_Ozero__class_Ozero(_1129210), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129210), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129210), _1129212), _1129214)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129210), _1129212), _1129216)) = c_Groups_Ozero__class_Ozero(_1129210))], (20019 ^ _779300) ^ [] : [-(_1129212 = c_Groups_Ozero__class_Ozero(_1129210)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129210), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129210), _1129212), _1129214)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129210), _1129212), _1129216)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129210), _1129214), _1129216))]]], (20025 ^ _779300) ^ [_1129516, _1129518] : [class_Divides_Osemiring__div(_1129516), -(_1129518 = c_Groups_Ozero__class_Ozero(_1129516)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129516), _1129518), _1129518) = c_Groups_Oone__class_Oone(_1129516))], (20035 ^ _779300) ^ [_1129630, _1129632, _1129634] : [class_Divides_Osemiring__div(_1129630), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1129630), c_Divides_Odiv__class_Omod(_1129630, _1129632, _1129634)), _1129634) = c_Groups_Ozero__class_Ozero(_1129630))], (20041 ^ _779300) ^ [_1129735, _1129737, _1129739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129735), _1129737)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129739), 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), _1129737), _1129739)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129735), _1129739))))], (20051 ^ _779300) ^ [_1129922, _1129924, _1129926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129922), _1129924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129922), _1129926)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129924), _1129926))))], (20061 ^ _779300) ^ [_1130103, _1130105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130103), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130105), _1130103)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130103), _1130105) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20071 ^ _779300) ^ [_1130264, _1130266, _1130268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130264), 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)), _1130266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130266), _1130268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130264), _1130266)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130264), _1130268))))], (20085 ^ _779300) ^ [_1130509, _1130511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130509), 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)), _1130511)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130509), _1130511)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20095 ^ _779300) ^ [_1130674, _1130676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130674), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 20098 ^ _779300 : [(20099 ^ _779300) ^ [] : [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), _1130676), _1130674))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130676), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20105 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130676), 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), _1130676), _1130674))))]]], (20111 ^ _779300) ^ [_1130930, _1130932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130930), _1130932)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130930), _1130932) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20121 ^ _779300) ^ [_1131085, _1131087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131085)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1131087), 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), _1131085), _1131087)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20131 ^ _779300) ^ [_1131250, _1131252, _1131254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131252), _1131254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131250), _1131254)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131250), _1131252))))], (20145 ^ _779300) ^ [_1131489, _1131491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131489)), 20148 ^ _779300 : [(20149 ^ _779300) ^ [] : [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), _1131489), _1131491))), 20152 ^ _779300 : [(20153 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131491), _1131489)))], (20155 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131491)))]]], (20157 ^ _779300) ^ [] : [-(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), _1131489), _1131491)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131491), _1131489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131491))]]], (20167 ^ _779300) ^ [_1131817, _1131819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131817)), 20170 ^ _779300 : [(20171 ^ _779300) ^ [] : [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), _1131819), _1131817))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131817), _1131819)))], (20177 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131817), _1131819)), -(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), _1131819), _1131817))))]]], (20183 ^ _779300) ^ [_1132067, _1132069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132067)), 20186 ^ _779300 : [(20187 ^ _779300) ^ [] : [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), _1132069), _1132067))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132069)))], (20193 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132069)), -(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), _1132069), _1132067))))]]], (20199 ^ _779300) ^ [_1132323, _1132325] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132323), _1132325) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1132325 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20208 ^ _779300 : [(20209 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132323)))], (20211 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132323), _1132325)))]], 20212 ^ _779300 : [(20213 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132323), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20215 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132325), _1132323)))]]], (20217 ^ _779300) ^ [_1132554, _1132556] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132554), _1132556) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20218 ^ _779300 : [(20219 ^ _779300) ^ [] : [_1132556 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (20221 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132554), _1132556))], (20227 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132554), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1132556), _1132554))]]], (20235 ^ _779300) ^ [_1132849, _1132851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1132849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1132851, _1132849)), _1132849)))], (20241 ^ _779300) ^ [_1132948, _1132950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1132950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132948), _1132950)), _1132948)))], (20251 ^ _779300) ^ [_1133107, _1133109, _1133111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1133107)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1133109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133111), _1133107)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1133109), _1133111)), _1133107))], (20257 ^ _779300) ^ [_1133238, _1133240, _1133242] : [-(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), _1133238), _1133240)), _1133242)), _1133240) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1133242), _1133240))], (20259 ^ _779300) ^ [_1133291, _1133293] : [-(_1133291 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133293), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1133291), _1133293))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1133291, _1133293)))], (20261 ^ _779300) ^ [_1133338, _1133340, _1133342] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133338), _1133340)), _1133342) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133338), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1133340), _1133342))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133338), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1133340, _1133342))), _1133342)))], (20263 ^ _779300) ^ [_1133411, _1133413, _1133415] : [-(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), _1133411), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1133413), _1133411))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1133413, _1133411))), _1133415) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1133413), _1133415))], (20265 ^ _779300) ^ [_1133472, _1133474, _1133476] : [-(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), _1133472), _1133474)), _1133474)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1133472, _1133474))), _1133476) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1133472), _1133476))], (20267 ^ _779300) ^ [_1133533, _1133535] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1133533), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1133535), _1133533)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1133535), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1133535, _1133533)))], (20269 ^ _779300) ^ [_1133580, _1133582] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1133580, _1133582) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1133580), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1133580), _1133582)), _1133582)))], (20271 ^ _779300) ^ [_1133627, _1133629, _1133631, _1133633] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1133627, _1133629, _1133631), _1133633), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1133629)], (20273 ^ _779300) ^ [_1133666, _1133668, _1133670, _1133672, _1133674] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1133666, _1133668, _1133670), _1133672), hAPP(c_Nat_OSuc, _1133674)) = hAPP(hAPP(_1133670, _1133672), hAPP(hAPP(c_Power_Opower_Opower(_1133666, _1133668, _1133670), _1133672), _1133674)))], (20275 ^ _779300) ^ [_1133726, _1133728, _1133730, _1133732] : [class_Divides_Osemiring__div(_1133726), -(_1133728 = c_Groups_Ozero__class_Ozero(_1133726)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133726), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133726), _1133730), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133726), _1133732), _1133728))), _1133728) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133726), _1133732), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133726), _1133730), _1133728)))], (20285 ^ _779300) ^ [_1133904, _1133906, _1133908, _1133910] : [class_Divides_Osemiring__div(_1133904), -(_1133906 = c_Groups_Ozero__class_Ozero(_1133904)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133904), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133904), _1133908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133904), _1133906), _1133910))), _1133906) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133904), _1133910), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133904), _1133908), _1133906)))], (20295 ^ _779300) ^ [_1134082, _1134084, _1134086] : [class_Divides_Osemiring__div(_1134082), -(_1134084 = c_Groups_Ozero__class_Ozero(_1134082)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1134082), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134082), _1134084), _1134086)), _1134084) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134082), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1134082), _1134086), _1134084)), c_Groups_Oone__class_Oone(_1134082)))], (20305 ^ _779300) ^ [_1134246, _1134248, _1134250] : [class_Divides_Osemiring__div(_1134246), -(_1134248 = c_Groups_Ozero__class_Ozero(_1134246)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1134246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134246), _1134250), _1134248)), _1134248) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134246), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1134246), _1134250), _1134248)), c_Groups_Oone__class_Oone(_1134246)))], (20315 ^ _779300) ^ [_1134410, _1134412, _1134414, _1134416] : [class_Divides_Osemiring__div(_1134410), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134410), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134410), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1134410), _1134412), _1134414)), _1134414)), c_Divides_Odiv__class_Omod(_1134410, _1134412, _1134414))), _1134416) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134410), _1134412), _1134416))], (20321 ^ _779300) ^ [_1134577, _1134579, _1134581, _1134583] : [class_Divides_Osemiring__div(_1134577), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134577), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134577), _1134579), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1134577), _1134581), _1134579))), c_Divides_Odiv__class_Omod(_1134577, _1134581, _1134579))), _1134583) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134577), _1134581), _1134583))], (20327 ^ _779300) ^ [_1134744, _1134746, _1134748] : [class_Divides_Osemiring__div(_1134744), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134744), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1134744), _1134746), _1134748)), _1134748)), c_Divides_Odiv__class_Omod(_1134744, _1134746, _1134748)) = _1134746)], (20333 ^ _779300) ^ [_1134877, _1134879, _1134881] : [class_Divides_Osemiring__div(_1134877), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134877), _1134879), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1134877), _1134881), _1134879))), c_Divides_Odiv__class_Omod(_1134877, _1134881, _1134879)) = _1134881)], (20339 ^ _779300) ^ [_1135010, _1135012, _1135014] : [class_Divides_Osemiring__div(_1135010), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135010), c_Divides_Odiv__class_Omod(_1135010, _1135012, _1135014)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135010), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1135010), _1135012), _1135014)), _1135014)) = _1135012)], (20345 ^ _779300) ^ [_1135143, _1135145, _1135147, _1135149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1135143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135145), _1135147)), -(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), _1135147), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1135149, _1135143))), _1135145)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1135147), _1135143))))], (20379 ^ _779300) ^ [_1135799, _1135801, _1135803] : [-(hBOOL(hAPP(_1135799, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1135801, _1135803)))), 20382 ^ _779300 : [(20383 ^ _779300) ^ [] : [-(_1135803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20385 ^ _779300) ^ [] : [hBOOL(hAPP(_1135799, _1135801))]], 20386 ^ _779300 : [(20387 ^ _779300) ^ [] : [_1135803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20391 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20389 ^ [_1135799, _1135801, _1135803]), _1135803)))], (20393 ^ _779300) ^ [] : [-(_1135801 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1135803), 20388 ^ [_1135799, _1135801, _1135803])), 20389 ^ [_1135799, _1135801, _1135803]))], (20395 ^ _779300) ^ [] : [hBOOL(hAPP(_1135799, 20389 ^ [_1135799, _1135801, _1135803]))]]], (20355 ^ _779300) ^ [_1135366, _1135368, _1135370] : [hBOOL(hAPP(_1135366, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1135368, _1135370))), 20358 ^ _779300 : [(20359 ^ _779300) ^ [] : [_1135370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1135366, _1135368)))], (20365 ^ _779300) ^ [] : [-(_1135370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20368 ^ _779300 : [(20369 ^ _779300) ^ [_1135614, _1135616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135614), _1135370)), _1135368 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1135370), _1135616)), _1135614), -(hBOOL(hAPP(_1135366, _1135614)))]]]]], (20399 ^ _779300) ^ [_1136208, _1136210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1136208)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1136208), _1136210)), _1136208) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20405 ^ _779300) ^ [_1136315, _1136317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136315)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136317)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1136315, _1136317)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1136315), hAPP(c_Int_Onat, _1136317)))], (20415 ^ _779300) ^ [_1136486, _1136488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136486)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136488)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1136486), hAPP(c_Int_Onat, _1136488)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1136486, _1136488)))], (20425 ^ _779300) ^ [_1136657, _1136659, _1136661, _1136663, _1136665, _1136667, _1136669] : [c_Big__Operators_Ocomm__monoid__big(_1136657, _1136659, _1136661, _1136663, _1136665), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1136659), _1136667))), -(hAPP(hAPP(_1136665, _1136669), _1136667) = _1136663)], (20481 ^ _779300) ^ [_1137763, _1137765, _1137767] : [-(hBOOL(hAPP(_1137763, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1137765), _1137767)))), 20484 ^ _779300 : [(20485 ^ _779300) ^ [] : [-(_1137767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20487 ^ _779300) ^ [] : [hBOOL(hAPP(_1137763, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 20490 ^ _779300 : [(20491 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137767)))], (20495 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20493 ^ [_1137763, _1137765, _1137767])))], (20497 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 20493 ^ [_1137763, _1137765, _1137767]), _1137767)))], (20499 ^ _779300) ^ [] : [-(_1137765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1137767), 20492 ^ [_1137763, _1137765, _1137767])), 20493 ^ [_1137763, _1137765, _1137767]))], (20501 ^ _779300) ^ [] : [hBOOL(hAPP(_1137763, 20492 ^ [_1137763, _1137765, _1137767]))]], 20502 ^ _779300 : [(20503 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137767), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20507 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137767), 20505 ^ [_1137763, _1137765, _1137767])))], (20509 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 20505 ^ [_1137763, _1137765, _1137767]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20511 ^ _779300) ^ [] : [-(_1137765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1137767), 20504 ^ [_1137763, _1137765, _1137767])), 20505 ^ [_1137763, _1137765, _1137767]))], (20513 ^ _779300) ^ [] : [hBOOL(hAPP(_1137763, 20504 ^ [_1137763, _1137765, _1137767]))]]], (20435 ^ _779300) ^ [_1136803, _1136805, _1136807] : [hBOOL(hAPP(_1136803, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1136805), _1136807))), 20438 ^ _779300 : [(20439 ^ _779300) ^ [] : [_1136807 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1136803, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20445 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136807)), 20448 ^ _779300 : [(20449 ^ _779300) ^ [_1137137] : [-(hBOOL(hAPP(_1136803, _1137137))), 20450 ^ _779300 : [(20451 ^ _779300) ^ [_1137208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137208), _1136807)), _1136805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1136807), _1137137)), _1137208)]]]]], (20463 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136807), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 20466 ^ _779300 : [(20467 ^ _779300) ^ [_1137467] : [-(hBOOL(hAPP(_1136803, _1137467))), 20468 ^ _779300 : [(20469 ^ _779300) ^ [_1137541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136807), _1137541)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137541), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1136805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1136807), _1137467)), _1137541)]]]]]]], (20517 ^ _779300) ^ [_1138477, _1138479, _1138481, _1138483] : [_1138477 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1138479), _1138481)), _1138483), -(_1138479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1138477), _1138479) = _1138481), 20524 ^ _779300 : [(20525 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138479)))], (20527 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138483), _1138479))]], 20532 ^ _779300 : [(20533 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138479))], (20535 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1138479), _1138483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1138483), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (20547 ^ _779300) ^ [_1138946, _1138948] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1138946, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1138948)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1138946, 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)))), _1138948)))], (20549 ^ _779300) ^ [_1138991, _1138993] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1138991))), _1138993) = 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)))), _1138991), _1138993))], (20551 ^ _779300) ^ [_1139036, _1139038] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1139036))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139038)) = 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)))), _1139036), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139038)))], (20553 ^ _779300) ^ [_1139087, _1139089, _1139091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139087)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139091), _1139087)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139091), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139089), _1139091), _1139087))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139089, _1139091)))], (20559 ^ _779300) ^ [_1139242] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1139242)), 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, _1139242, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (20561 ^ _779300) ^ [_1139278, _1139280] : [-(_1139278 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20564 ^ _779300 : [(20565 ^ _779300) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139280, _1139278) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139280), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1139278)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139280), _1139278)))], (20571 ^ _779300) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139280, _1139278) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139280), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1139278)) = 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), _1139280), _1139278))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (20577 ^ _779300) ^ [_1139551, _1139553] : [-(_1139551 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20580 ^ _779300 : [(20581 ^ _779300) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139553, _1139551) = 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), _1139553)), _1139551) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139553), _1139551)))], (20587 ^ _779300) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139553, _1139551) = 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), _1139553)), _1139551) = 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), _1139553), _1139551))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (20593 ^ _779300) ^ [_1139825, _1139827, _1139829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139825)), 20596 ^ _779300 : [(20615 ^ _779300) ^ [] : [20618 ^ _779300 : [(20619 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20617 ^ [_1139825, _1139827, _1139829])))], (20621 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 20617 ^ [_1139825, _1139827, _1139829]), _1139825)))], (20623 ^ _779300) ^ [] : [-(_1139829 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139825), 20616 ^ [_1139825, _1139827, _1139829])), 20617 ^ [_1139825, _1139827, _1139829]))], (20625 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1139827, 20616 ^ [_1139825, _1139827, _1139829]), 20617 ^ [_1139825, _1139827, _1139829]))]], -(hBOOL(hAPP(hAPP(_1139827, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139829), _1139825)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139829, _1139825))))], (20597 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1139827, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139829), _1139825)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139829, _1139825))), 20600 ^ _779300 : [(20601 ^ _779300) ^ [_1140026, _1140028] : [-(hBOOL(hAPP(hAPP(_1139827, _1140028), _1140026))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1140026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140026), _1139825)), _1139829 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139825), _1140028)), _1140026)]]]]], (20629 ^ _779300) ^ [_1140540, _1140542, _1140544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140540), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 20632 ^ _779300 : [(20651 ^ _779300) ^ [] : [20654 ^ _779300 : [(20655 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140540), 20653 ^ [_1140540, _1140542, _1140544])))], (20657 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 20653 ^ [_1140540, _1140542, _1140544]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20659 ^ _779300) ^ [] : [-(_1140544 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140540), 20652 ^ [_1140540, _1140542, _1140544])), 20653 ^ [_1140540, _1140542, _1140544]))], (20661 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1140542, 20652 ^ [_1140540, _1140542, _1140544]), 20653 ^ [_1140540, _1140542, _1140544]))]], -(hBOOL(hAPP(hAPP(_1140542, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1140544), _1140540)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1140544, _1140540))))], (20633 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1140542, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1140544), _1140540)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1140544, _1140540))), 20636 ^ _779300 : [(20637 ^ _779300) ^ [_1140750, _1140752] : [-(hBOOL(hAPP(hAPP(_1140542, _1140752), _1140750))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1140540), _1140750)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1140750), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1140544 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1140540), _1140752)), _1140750)]]]]], (20665 ^ _779300) ^ [_1141282, _1141284] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141282))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141282), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141284)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20671 ^ _779300) ^ [_1141384, _1141386] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141384)))), 20674 ^ _779300 : [(20675 ^ _779300) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141386))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141384), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141386)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141384))], (20681 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141386)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141384), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141386)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141384), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141386))))]]], (20687 ^ _779300) ^ [_1141666, _1141668] : [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), _1141666))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1141668))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1141666))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141668)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141666)))], (20693 ^ _779300) ^ [_1141803, _1141805] : [-(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), _1141803)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1141805))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1141803))) = 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), _1141805)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141803)))], (20699 ^ _779300) ^ [_1141880, _1141882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1141880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141882)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1141882), _1141880)), _1141882) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1141882), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1141880), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (20709 ^ _779300) ^ [_1142077] : [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, _1142077, 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, _1142077, 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))], (20715 ^ _779300) ^ [_1142168] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1142168, 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, _1142168, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20721 ^ _779300) ^ [_1142271] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1142271))), -(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), _1142271)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20727 ^ _779300) ^ [_1142364] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1142364)))), -(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), _1142364)) = 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), _1142364))))], (20733 ^ _779300) ^ [_1142431, _1142433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1142431)), -(c_SMT_Oz3div(_1142433, _1142431) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1142433), _1142431))], (20739 ^ _779300) ^ [_1142524, _1142526] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1142524))), -(c_SMT_Oz3div(_1142526, _1142524) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1142526), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1142524))))], (20745 ^ _779300) ^ [_1142579, _1142581] : [class_Int_Onumber__ring(_1142579), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1142579), hAPP(c_Int_Onumber__class_Onumber__of(_1142579), 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)))), _1142581))) = hAPP(c_Int_Onumber__class_Onumber__of(_1142579), c_Int_OMin))], (20751 ^ _779300) ^ [_1142702, _1142704] : [class_Int_Onumber__ring(_1142702), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1142702), hAPP(c_Int_Onumber__class_Onumber__of(_1142702), 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)))), _1142704)) = c_Groups_Oone__class_Oone(_1142702))], (20757 ^ _779300) ^ [_1142813, _1142815] : [c_Nat__Transfer_Onat__set(_1142813), c_Nat__Transfer_Onat__set(_1142815), 20764 ^ _779300 : [(20765 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1142813), _1142815)), -(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), _1142813)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1142815))))], (20771 ^ _779300) ^ [] : [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), _1142813)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1142815))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1142813), _1142815)))]]], (20777 ^ _779300) ^ [_1143116, _1143118] : [c_Nat__Transfer_Onat__set(_1143116), c_Nat__Transfer_Onat__set(_1143118), 20784 ^ _779300 : [(20785 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1143116), _1143118)), -(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), _1143116)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1143118))))], (20791 ^ _779300) ^ [] : [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), _1143116)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1143118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1143116), _1143118)))]]], (20797 ^ _779300) ^ [_1143419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1143419)), -(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), _1143419), 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)))))))], (20803 ^ _779300) ^ [_1143526, _1143528, _1143530] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1143526), _1143528)), _1143530) = 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), _1143526), _1143530)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143528), _1143530))), 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, _1143526, _1143530)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1143528, _1143530))), _1143530)))], (20805 ^ _779300) ^ [_1143609, _1143611, _1143613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1143609), _1143611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143609), _1143613)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143611), _1143613))))], (20811 ^ _779300) ^ [_1143732, _1143734] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143732), _1143734)), _1143732)))], (20813 ^ _779300) ^ [_1143768, _1143770, _1143772] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143770), _1143772)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143768), _1143770)), _1143772))], (20815 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (20817 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (20819 ^ _779300) ^ [] : [c_Int_OPls = c_Int_OMin], (20821 ^ _779300) ^ [] : [c_Int_OMin = c_Int_OPls], (20823 ^ _779300) ^ [_1143921] : [c_Int_OBit1(_1143921) = c_Int_OMin, -(_1143921 = c_Int_OMin)], (20829 ^ _779300) ^ [_1143996] : [_1143996 = c_Int_OMin, -(c_Int_OBit1(_1143996) = c_Int_OMin)], (20835 ^ _779300) ^ [_1144089] : [c_Int_OMin = c_Int_OBit1(_1144089), -(c_Int_OMin = _1144089)], (20841 ^ _779300) ^ [_1144164] : [c_Int_OMin = _1144164, -(c_Int_OMin = c_Int_OBit1(_1144164))], (20847 ^ _779300) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (20849 ^ _779300) ^ [_1144272] : [c_Int_OBit0(_1144272) = c_Int_OMin], (20851 ^ _779300) ^ [_1144306] : [c_Int_OMin = c_Int_OBit0(_1144306)], (20853 ^ _779300) ^ [_1144331] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144331), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1144331)], (20855 ^ _779300) ^ [_1144360, _1144362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144360), _1144362)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144360), _1144362) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20861 ^ _779300) ^ [_1144471, _1144473, _1144475] : [_1144471 = 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), _1144471), _1144473)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144471), _1144475)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20867 ^ _779300) ^ [_1144580, _1144582, _1144584] : [-(_1144580 = 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), _1144580), _1144582)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144580), _1144584)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144582), _1144584))], (20873 ^ _779300) ^ [_1144644, _1144646, _1144648] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144644), _1144646)), _1144648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144644), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144646), _1144648))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144644), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144646, _1144648))), _1144648)))], (20875 ^ _779300) ^ [_1144717, _1144719, _1144721] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144717, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144719), _1144721)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144719), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144717), _1144719), _1144721))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144717, _1144719)))], (20877 ^ _779300) ^ [_1144780, _1144782] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144780, _1144782) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144780), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144780), _1144782)), _1144782)))], (20879 ^ _779300) ^ [_1144827, _1144829] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144827), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144829), _1144827)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144829), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144829, _1144827)))], (20881 ^ _779300) ^ [_1144874, _1144876] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144874), _1144876)), _1144876) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144874), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144874, _1144876)))], (20883 ^ _779300) ^ [_1144921, _1144923] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144921)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144923)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144921), _1144923)))], (20885 ^ _779300) ^ [_1144967, _1144969] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144967), _1144969)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144967)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144969)))], (20887 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20889 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (20891 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (20893 ^ _779300) ^ [_1145085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1145085)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145085), c_Int_OMin)))], (20899 ^ _779300) ^ [_1145180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145180), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1145180)), c_Int_OMin)))], (20905 ^ _779300) ^ [_1145293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1145293))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1145293)))], (20911 ^ _779300) ^ [_1145376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1145376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1145376))))], (20917 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (20919 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (20921 ^ _779300) ^ [_1145519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1145519))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1145519)))], (20927 ^ _779300) ^ [_1145602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1145602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1145602))))], (20933 ^ _779300) ^ [_1145703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1145703)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145703), c_Int_OMin)))], (20939 ^ _779300) ^ [_1145798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145798), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1145798)), c_Int_OMin)))], (20945 ^ _779300) ^ [_1145911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1145911)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145911), c_Int_OMin)))], (20951 ^ _779300) ^ [_1146006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146006), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1146006)), c_Int_OMin)))], (20957 ^ _779300) ^ [_1146119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1146119))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1146119)))], (20963 ^ _779300) ^ [_1146202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1146202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1146202))))], (20969 ^ _779300) ^ [] : [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)], (20971 ^ _779300) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20973 ^ _779300) ^ [_1146333] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1146333) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1146333))], (20975 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (20977 ^ _779300) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (20979 ^ _779300) ^ [_1146398] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1146398), c_Int_OMin) = c_Int_Opred(_1146398))], (20981 ^ _779300) ^ [_1146429] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1146429) = c_Int_Opred(_1146429))], (20983 ^ _779300) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (20985 ^ _779300) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (20987 ^ _779300) ^ [_1146493] : [class_Int_Onumber__ring(_1146493), c_Int_Oiszero(_1146493, hAPP(c_Int_Onumber__class_Onumber__of(_1146493), c_Int_OMin))], (20993 ^ _779300) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (20995 ^ _779300) ^ [_1146595] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1146595), c_Int_OMin) = c_Int_Osucc(_1146595))], (21007 ^ _779300) ^ [_1146795] : [21009 ^ _779300 : [(21010 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21008 ^ [_1146795]), _1146795)))], (21012 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21008 ^ [_1146795]))]], -(c_Nat__Transfer_Onat__set(_1146795))], (20997 ^ _779300) ^ [_1146638] : [c_Nat__Transfer_Onat__set(_1146638), 21000 ^ _779300 : [(21001 ^ _779300) ^ [_1146704] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1146704), _1146638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146704)))]]], (21016 ^ _779300) ^ [_1146943, _1146945, _1146947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1146943), _1146945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1146947), _1146945)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1146947), _1146943))))], (21026 ^ _779300) ^ [_1147124, _1147126, _1147128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147124)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147124), _1147126)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147124), _1147128)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1147126), _1147128))], (21032 ^ _779300) ^ [_1147255, _1147257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147255)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147257), _1147255)), _1147255) = _1147257)], (21038 ^ _779300) ^ [_1147360, _1147362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147360)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147360), _1147362)), _1147360) = _1147362)], (21044 ^ _779300) ^ [_1147465, _1147467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1147465)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1147467), _1147465)), _1147467)))], (21054 ^ _779300) ^ [_1147624, _1147626] : [class_Int_Onumber__ring(_1147624), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147624), hAPP(c_Int_Onumber__class_Onumber__of(_1147624), c_Int_OMin)), _1147626) = hAPP(c_Groups_Ouminus__class_Ouminus(_1147624), _1147626))], (21060 ^ _779300) ^ [_1147735, _1147737] : [class_Int_Onumber__ring(_1147735), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147735), _1147737), hAPP(c_Int_Onumber__class_Onumber__of(_1147735), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1147735), _1147737))], (21066 ^ _779300) ^ [_1147846] : [-(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)), _1147846)))], (21068 ^ _779300) ^ [_1147871] : [class_Int_Onumber__ring(_1147871), -(hAPP(c_Int_Onumber__class_Onumber__of(_1147871), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1147871), c_Groups_Oone__class_Oone(_1147871)))], (21074 ^ _779300) ^ [_1147968] : [class_Int_Onumber__ring(_1147968), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1147968), c_Groups_Oone__class_Oone(_1147968)) = hAPP(c_Int_Onumber__class_Onumber__of(_1147968), c_Int_OMin))], (21080 ^ _779300) ^ [_1148065, _1148067] : [c_Nat__Transfer_Onat__set(_1148065), c_Nat__Transfer_Onat__set(_1148067), 21087 ^ _779300 : [(21088 ^ _779300) ^ [] : [_1148065 = _1148067, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1148065) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1148067))], (21094 ^ _779300) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1148065) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1148067), -(_1148065 = _1148067)]]], (21100 ^ _779300) ^ [_1148350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1148350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1148350)))], (21106 ^ _779300) ^ [_1148433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1148433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1148433))))], (21112 ^ _779300) ^ [_1148534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1148534)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1148534), c_Int_OMin)))], (21118 ^ _779300) ^ [_1148629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1148629), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1148629)), c_Int_OMin)))], (21124 ^ _779300) ^ [_1148730] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1148730, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21126 ^ _779300) ^ [_1148757] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1148757)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1148757)))], (21128 ^ _779300) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (21130 ^ _779300) ^ [_1148823, _1148825] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1148823), _1148825) = c_Groups_Oone__class_Oone(tc_Int_Oint), 21135 ^ _779300 : [(21136 ^ _779300) ^ [] : [-(_1148823 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (21138 ^ _779300) ^ [] : [-(_1148825 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 21139 ^ _779300 : [(21140 ^ _779300) ^ [] : [-(_1148823 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (21142 ^ _779300) ^ [] : [-(_1148825 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (21144 ^ _779300) ^ [_1149007, _1149009] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1149007), _1149009) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 21145 ^ _779300 : [(21146 ^ _779300) ^ [] : [_1149007 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1149009 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (21152 ^ _779300) ^ [] : [_1149007 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1149009 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (21160 ^ _779300) ^ [_1149233, _1149235] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1149233), _1149235) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1149233 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1149233 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (21170 ^ _779300) ^ [_1149335] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1149335)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1149335)))], (21172 ^ _779300) ^ [_1149368] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1149368)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1149368)))], (21174 ^ _779300) ^ [_1149401] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1149401), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1149401))], (21176 ^ _779300) ^ [_1149433, _1149435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1149433)), 21179 ^ _779300 : [(21180 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1149435), _1149433)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1149435), _1149433) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21186 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1149435), _1149433))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1149435), _1149433) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1149435), _1149433)), _1149433)))]]], (21192 ^ _779300) ^ [_1149687, _1149689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1149687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1149689), _1149687))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1149689), _1149687) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1149689), _1149687)), _1149687)))], (21226 ^ _779300) ^ [_1150290, _1150292, _1150294] : [-(hBOOL(hAPP(_1150290, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1150292), _1150294)))), 21229 ^ _779300 : [(21230 ^ _779300) ^ [] : [-(_1150294 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21232 ^ _779300) ^ [] : [hBOOL(hAPP(_1150290, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 21233 ^ _779300 : [(21234 ^ _779300) ^ [] : [_1150294 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21238 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21236 ^ [_1150290, _1150292, _1150294]), _1150294)))], (21240 ^ _779300) ^ [] : [-(_1150292 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150294), 21235 ^ [_1150290, _1150292, _1150294])), 21236 ^ [_1150290, _1150292, _1150294]))], (21242 ^ _779300) ^ [] : [hBOOL(hAPP(_1150290, 21235 ^ [_1150290, _1150292, _1150294]))]]], (21202 ^ _779300) ^ [_1149853, _1149855, _1149857] : [hBOOL(hAPP(_1149853, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1149855), _1149857))), 21205 ^ _779300 : [(21206 ^ _779300) ^ [] : [_1149857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1149853, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21212 ^ _779300) ^ [] : [-(_1149857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21215 ^ _779300 : [(21216 ^ _779300) ^ [_1150105, _1150107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150105), _1149857)), _1149855 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1149857), _1150107)), _1150105), -(hBOOL(hAPP(_1149853, _1150107)))]]]]], (21246 ^ _779300) ^ [_1150712, _1150714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150714)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1150712)), hAPP(c_Int_Onat, _1150714)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1150712), _1150714)))], (21256 ^ _779300) ^ [_1150891, _1150893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150891)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1150891), _1150893)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1150891)), hAPP(c_Int_Onat, _1150893)))], (21262 ^ _779300) ^ [_1151014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1151014)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1151014) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (21268 ^ _779300) ^ [_1151099, _1151101] : [c_Nat__Transfer_Onat__set(_1151099), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1151101), _1151099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1151101)))], (21278 ^ _779300) ^ [_1151240, _1151242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1151240), _1151242)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1151242), _1151240) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1151242), _1151240)), _1151240)))], (21288 ^ _779300) ^ [_1151443, _1151445, _1151447] : [hBOOL(hAPP(_1151443, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1151445), _1151447))), 21293 ^ _779300 : [(21294 ^ _779300) ^ [] : [-(_1151447 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21296 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1151443, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 21298 ^ _779300 : [(21299 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151447), 21297 ^ [_1151443, _1151445, _1151447])), _1151445)))], (21301 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151445), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151447), hAPP(c_Nat_OSuc, 21297 ^ [_1151443, _1151445, _1151447])))))], (21303 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1151443, 21297 ^ [_1151443, _1151445, _1151447])))]]], (21305 ^ _779300) ^ [_1151747, _1151749, _1151751] : [-(hBOOL(hAPP(_1151747, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1151749), _1151751)))), 21306 ^ _779300 : [(21307 ^ _779300) ^ [] : [_1151751 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1151747, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21313 ^ _779300) ^ [_1151915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151751), _1151915)), _1151749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151749), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151751), hAPP(c_Nat_OSuc, _1151915)))), hBOOL(hAPP(_1151747, _1151915))]]], (21325 ^ _779300) ^ [_1152145, _1152147, _1152149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152145)), 21328 ^ _779300 : [(21339 ^ _779300) ^ [] : [_1152147 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1152149), _1152145), 21342 ^ _779300 : [(21343 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152145), _1152147)), _1152149)))], (21345 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152145), hAPP(c_Nat_OSuc, _1152147)))))]]], (21329 ^ _779300) ^ [] : [-(_1152147 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1152149), _1152145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152145), _1152147)), _1152149)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152145), hAPP(c_Nat_OSuc, _1152147))))]]], (21347 ^ _779300) ^ [_1152529, _1152531] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1152529)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152531)) = 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)))), _1152529)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152531)))], (21349 ^ _779300) ^ [_1152584, _1152586] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1152584)))), _1152586) = 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)))), _1152584)), _1152586))], (21351 ^ _779300) ^ [_1152633, _1152635] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1152633), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1152635)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1152633), 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)))), _1152635)))], (21353 ^ _779300) ^ [_1152682] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1152682))), 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), _1152682), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (21355 ^ _779300) ^ [_1152726] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1152726), _1152726)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1152726)], (21357 ^ _779300) ^ [_1152761] : [c_Nat__Transfer_Onat__set(_1152761), -(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), _1152761)) = _1152761)], (21363 ^ _779300) ^ [_1152855, _1152857] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1152855))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152855)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152857)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21369 ^ _779300) ^ [_1152960, _1152962] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1152960)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152960)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152962)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1152960)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1152962))))], (21375 ^ _779300) ^ [_1153030, _1153032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153030), _1153032)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1153030), _1153032) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (21385 ^ _779300) ^ [_1153197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153197)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1153197) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1153197), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21391 ^ _779300) ^ [_1153296] : [c_Nat__Transfer_Onat__set(_1153296), 21394 ^ _779300 : [(21395 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1153296)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153296))))], (21401 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153296))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1153296)))]]], (21407 ^ _779300) ^ [_1153516] : [c_Nat__Transfer_Onat__set(_1153516), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1153516) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153516)))], (21413 ^ _779300) ^ [_1153607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1153607)), -(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), _1153607), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21419 ^ _779300) ^ [_1153702] : [-(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), _1153702)) = 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), _1153702))))], (21421 ^ _779300) ^ [_1153746] : [_1153746 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1153746) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21427 ^ _779300) ^ [_1153822] : [-(_1153822 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 21430 ^ _779300 : [(21431 ^ _779300) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1153822, 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, _1153822) = 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), _1153822), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21437 ^ _779300) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1153822, 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, _1153822) = 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), _1153822), 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)))]]], (21443 ^ _779300) ^ [_1154082, _1154084] : [c_Nat__Transfer_Ois__nat(_1154082), c_Nat__Transfer_Onat__set(_1154084), 21450 ^ _779300 : [(21451 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1154082), _1154084)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1154082)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1154084))))], (21457 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1154082)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1154084))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1154082), _1154084)))]]], (21463 ^ _779300) ^ [_1154385, _1154387] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1154385, _1154387)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1154387), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1154385), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21465 ^ _779300) ^ [] : [-(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)))], (21467 ^ _779300) ^ [_1154450, _1154452, _1154454] : [class_Orderings_Olinorder(_1154450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1154450), _1154452)), hBOOL(hAPP(hAPP(c_member(_1154450), _1154454), _1154452)), 21478 ^ _779300 : [(21479 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1154450, tc_HOL_Obool)), _1154452), hAPP(hAPP(c_Set_Oinsert(_1154450), _1154454), c_Orderings_Obot__class_Obot(tc_fun(_1154450, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1154450, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1154450, _1154452) = _1154454)], (21485 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1154450, tc_HOL_Obool)), _1154452), hAPP(hAPP(c_Set_Oinsert(_1154450), _1154454), c_Orderings_Obot__class_Obot(tc_fun(_1154450, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1154450, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1154450, _1154452) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1154450), _1154454), c_Big__Operators_Olinorder__class_OMin(_1154450, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1154450, tc_HOL_Obool)), _1154452), hAPP(hAPP(c_Set_Oinsert(_1154450), _1154454), c_Orderings_Obot__class_Obot(tc_fun(_1154450, tc_HOL_Obool)))))))]]], (21491 ^ _779300) ^ [_1154956, _1154958] : [class_Rings_Oring__1(_1154956), 21494 ^ _779300 : [(21495 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154958), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1154956), _1154958) = hAPP(c_Groups_Ouminus__class_Ouminus(_1154956), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1154956), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1154958)))))], (21501 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154958), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1154956), _1154958) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1154956), hAPP(c_Int_Onat, _1154958)))]]], (21507 ^ _779300) ^ [_1155218, _1155220] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1155218, _1155220))))], (21509 ^ _779300) ^ [_1155249, _1155251, _1155253] : [class_Int_Oring__char__0(_1155249), 21512 ^ _779300 : [(21513 ^ _779300) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1155249), _1155251) = hAPP(c_Int_Oring__1__class_Oof__int(_1155249), _1155253), -(_1155251 = _1155253)], (21519 ^ _779300) ^ [] : [_1155251 = _1155253, -(hAPP(c_Int_Oring__1__class_Oof__int(_1155249), _1155251) = hAPP(c_Int_Oring__1__class_Oof__int(_1155249), _1155253))]]], (21525 ^ _779300) ^ [] : [-(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))], (21527 ^ _779300) ^ [_1155508, _1155510] : [class_Int_Onumber__ring(_1155508), -(hAPP(c_Int_Onumber__class_Onumber__of(_1155508), _1155510) = hAPP(c_Int_Oring__1__class_Oof__int(_1155508), _1155510))], (21533 ^ _779300) ^ [_1155603] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1155603) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1155603))], (21535 ^ _779300) ^ [_1155632] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155632)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155632))], (21537 ^ _779300) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21539 ^ _779300) ^ [_1155682, _1155684] : [c_Nat__Transfer_Ois__nat(_1155682), c_Nat__Transfer_Ois__nat(_1155684), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1155682), _1155684)))], (21549 ^ _779300) ^ [_1155817] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155817)))], (21551 ^ _779300) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21553 ^ _779300) ^ [_1155860, _1155862] : [c_Nat__Transfer_Ois__nat(_1155860), c_Nat__Transfer_Ois__nat(_1155862), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1155860), _1155862)))], (21563 ^ _779300) ^ [_1155995, _1155997] : [c_Nat__Transfer_Ois__nat(_1155995), c_Nat__Transfer_Ois__nat(_1155997), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1155995, _1155997)))], (21573 ^ _779300) ^ [_1156126, _1156128] : [c_Nat__Transfer_Ois__nat(_1156126), c_Nat__Transfer_Ois__nat(_1156128), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1156126), _1156128)))], (21583 ^ _779300) ^ [_1156261, _1156263] : [c_Nat__Transfer_Ois__nat(_1156261), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1156261), _1156263)))], (21589 ^ _779300) ^ [_1156346, _1156348] : [c_Nat__Transfer_Ois__nat(_1156346), c_Nat__Transfer_Ois__nat(_1156348), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1156346, _1156348)))], (21599 ^ _779300) ^ [_1156475, _1156477] : [class_Int_Oring__char__0(_1156475), 21602 ^ _779300 : [(21603 ^ _779300) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1156475), _1156477) = c_Groups_Ozero__class_Ozero(_1156475), -(_1156477 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21609 ^ _779300) ^ [] : [_1156477 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1156475), _1156477) = c_Groups_Ozero__class_Ozero(_1156475))]]], (21615 ^ _779300) ^ [_1156701, _1156703] : [class_Int_Oring__char__0(_1156701), 21618 ^ _779300 : [(21619 ^ _779300) ^ [] : [c_Groups_Ozero__class_Ozero(_1156701) = hAPP(c_Int_Oring__1__class_Oof__int(_1156701), _1156703), -(_1156703 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21625 ^ _779300) ^ [] : [_1156703 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1156701) = hAPP(c_Int_Oring__1__class_Oof__int(_1156701), _1156703))]]], (21631 ^ _779300) ^ [_1156927] : [class_Rings_Oring__1(_1156927), -(hAPP(c_Int_Oring__1__class_Oof__int(_1156927), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1156927))], (21637 ^ _779300) ^ [_1157014, _1157016, _1157018] : [class_Rings_Olinordered__idom(_1157014), 21640 ^ _779300 : [(21641 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157014), hAPP(c_Int_Oring__1__class_Oof__int(_1157014), _1157016)), hAPP(c_Int_Oring__1__class_Oof__int(_1157014), _1157018))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1157016), _1157018)))], (21647 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1157016), _1157018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157014), hAPP(c_Int_Oring__1__class_Oof__int(_1157014), _1157016)), hAPP(c_Int_Oring__1__class_Oof__int(_1157014), _1157018))))]]], (21653 ^ _779300) ^ [_1157291, _1157293, _1157295] : [class_Rings_Olinordered__idom(_1157291), 21656 ^ _779300 : [(21657 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157291), hAPP(c_Int_Oring__1__class_Oof__int(_1157291), _1157293)), hAPP(c_Int_Oring__1__class_Oof__int(_1157291), _1157295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157293), _1157295)))], (21663 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157293), _1157295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157291), hAPP(c_Int_Oring__1__class_Oof__int(_1157291), _1157293)), hAPP(c_Int_Oring__1__class_Oof__int(_1157291), _1157295))))]]], (21669 ^ _779300) ^ [_1157568, _1157570, _1157572] : [class_Rings_Oring__1(_1157568), -(hAPP(c_Int_Oring__1__class_Oof__int(_1157568), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1157570), _1157572)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157568), hAPP(c_Int_Oring__1__class_Oof__int(_1157568), _1157570)), hAPP(c_Int_Oring__1__class_Oof__int(_1157568), _1157572)))], (21675 ^ _779300) ^ [_1157703, _1157705] : [class_Int_Onumber__ring(_1157703), -(hAPP(c_Int_Oring__1__class_Oof__int(_1157703), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1157705)) = hAPP(c_Int_Onumber__class_Onumber__of(_1157703), _1157705))], (21681 ^ _779300) ^ [_1157804, _1157806, _1157808] : [class_Rings_Oring__1(_1157804), -(hAPP(c_Int_Oring__1__class_Oof__int(_1157804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1157806), _1157808)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157804), hAPP(c_Int_Oring__1__class_Oof__int(_1157804), _1157806)), hAPP(c_Int_Oring__1__class_Oof__int(_1157804), _1157808)))], (21687 ^ _779300) ^ [_1157939] : [class_Rings_Oring__1(_1157939), -(hAPP(c_Int_Oring__1__class_Oof__int(_1157939), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1157939))], (21693 ^ _779300) ^ [_1158026, _1158028, _1158030] : [class_Rings_Oring__1(_1158026), -(hAPP(c_Int_Oring__1__class_Oof__int(_1158026), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1158028), _1158030)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1158026), hAPP(c_Int_Oring__1__class_Oof__int(_1158026), _1158028)), hAPP(c_Int_Oring__1__class_Oof__int(_1158026), _1158030)))], (21699 ^ _779300) ^ [_1158161, _1158163] : [class_Orderings_Olinorder(_1158161), -(c_Big__Operators_Olinorder__class_OMin(_1158161, hAPP(hAPP(c_Set_Oinsert(_1158161), _1158163), c_Orderings_Obot__class_Obot(tc_fun(_1158161, tc_HOL_Obool)))) = _1158163)], (21705 ^ _779300) ^ [_1158268, _1158270] : [class_Rings_Oring__1(_1158268), -(hAPP(c_Int_Oring__1__class_Oof__int(_1158268), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1158270)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1158268), _1158270))], (21711 ^ _779300) ^ [_1158369, _1158371] : [class_Rings_Oring__1(_1158369), -(hAPP(c_Int_Oring__1__class_Oof__int(_1158369), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1158371)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1158369), hAPP(c_Int_Oring__1__class_Oof__int(_1158369), _1158371)))], (21717 ^ _779300) ^ [_1158480, _1158482] : [class_Rings_Oring__1(_1158480), -(hBOOL(hAPP(hAPP(c_member(_1158480), hAPP(c_Int_Oring__1__class_Oof__int(_1158480), _1158482)), c_Int_Oring__1__class_OInts(_1158480))))], (21723 ^ _779300) ^ [_1158583, _1158585, _1158587] : [class_Rings_Oring__1(_1158583), -(hAPP(c_Int_Oring__1__class_Oof__int(_1158583), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1158585), _1158587)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1158583), hAPP(c_Int_Oring__1__class_Oof__int(_1158583), _1158585)), _1158587))], (21729 ^ _779300) ^ [_1158720] : [c_Nat__Transfer_Ois__nat(_1158720), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1158720)))], (21735 ^ _779300) ^ [_1158793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1158793)), -(c_Nat__Transfer_Ois__nat(_1158793))], (21741 ^ _779300) ^ [_1158872, _1158874, _1158876] : [class_Orderings_Oorder(_1158872), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158872), _1158874), _1158876)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1158872, _1158876, _1158874) = c_Orderings_Obot__class_Obot(tc_fun(_1158872, tc_HOL_Obool)))], (21751 ^ _779300) ^ [_1159035, _1159037, _1159039] : [class_Groups_Oordered__ab__group__add(_1159035), -(hAPP(c_Set_Oimage(_1159035, _1159035, c_Groups_Ouminus__class_Ouminus(_1159035)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1159035, _1159037, _1159039)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1159035, hAPP(c_Groups_Ouminus__class_Ouminus(_1159035), _1159039), hAPP(c_Groups_Ouminus__class_Ouminus(_1159035), _1159037)))], (21757 ^ _779300) ^ [_1159166, _1159168, _1159170] : [class_Orderings_Olinorder(_1159166), hBOOL(hAPP(c_Finite__Set_Ofinite(_1159166), _1159168)), hBOOL(hAPP(hAPP(c_member(_1159166), _1159170), _1159168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159166), c_Big__Operators_Olinorder__class_OMin(_1159166, _1159168)), _1159170)))], (21771 ^ _779300) ^ [_1159393, _1159395] : [c_Nat__Transfer_Onat__set(_1159393), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1159395), _1159393)), -(c_Nat__Transfer_Ois__nat(_1159395))], (21781 ^ _779300) ^ [_1159528, _1159530] : [class_Orderings_Olinorder(_1159528), hBOOL(hAPP(c_Finite__Set_Ofinite(_1159528), _1159530)), -(_1159530 = c_Orderings_Obot__class_Obot(tc_fun(_1159528, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1159528), c_Big__Operators_Olinorder__class_OMin(_1159528, _1159530)), _1159530)))], (21795 ^ _779300) ^ [] : [-(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))], (21797 ^ _779300) ^ [_1159726, _1159728, _1159730] : [class_Orderings_Olinorder(_1159726), hBOOL(hAPP(c_Finite__Set_Ofinite(_1159726), _1159728)), hBOOL(hAPP(hAPP(c_member(_1159726), _1159730), _1159728)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1159726), _1159730), c_Big__Operators_Olinorder__class_OMin(_1159726, _1159728)) = c_Big__Operators_Olinorder__class_OMin(_1159726, _1159728))], (21811 ^ _779300) ^ [_1159961] : [class_Int_Onumber__ring(_1159961), -(hAPP(c_Int_Oring__1__class_Oof__int(_1159961), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1159961), c_Int_OMin))], (21817 ^ _779300) ^ [_1160054, _1160056] : [class_Orderings_Olinorder(_1160054), hBOOL(hAPP(c_Finite__Set_Ofinite(_1160054), _1160056)), -(c_Big__Operators_Olinorder__class_OMin(_1160054, _1160056) = hAPP(c_Finite__Set_Ofold1(_1160054, c_Orderings_Oord__class_Omin(_1160054)), _1160056))], (21827 ^ _779300) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (21829 ^ _779300) ^ [_1160229, _1160231] : [class_Rings_Olinordered__idom(_1160229), 21832 ^ _779300 : [(21833 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160229), hAPP(c_Int_Oring__1__class_Oof__int(_1160229), _1160231)), c_Groups_Ozero__class_Ozero(_1160229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1160231), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21839 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1160231), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160229), hAPP(c_Int_Oring__1__class_Oof__int(_1160229), _1160231)), c_Groups_Ozero__class_Ozero(_1160229))))]]], (21845 ^ _779300) ^ [_1160491, _1160493] : [class_Rings_Olinordered__idom(_1160491), 21848 ^ _779300 : [(21849 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160491), c_Groups_Ozero__class_Ozero(_1160491)), hAPP(c_Int_Oring__1__class_Oof__int(_1160491), _1160493))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1160493)))], (21855 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1160493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160491), c_Groups_Ozero__class_Ozero(_1160491)), hAPP(c_Int_Oring__1__class_Oof__int(_1160491), _1160493))))]]], (21861 ^ _779300) ^ [_1160744, _1160746] : [class_Rings_Olinordered__idom(_1160744), 21864 ^ _779300 : [(21865 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160744), hAPP(c_Int_Oring__1__class_Oof__int(_1160744), _1160746)), c_Groups_Ozero__class_Ozero(_1160744))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160746), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21871 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160746), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160744), hAPP(c_Int_Oring__1__class_Oof__int(_1160744), _1160746)), c_Groups_Ozero__class_Ozero(_1160744))))]]], (21877 ^ _779300) ^ [_1161006, _1161008] : [class_Rings_Olinordered__idom(_1161006), 21880 ^ _779300 : [(21881 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161006), c_Groups_Ozero__class_Ozero(_1161006)), hAPP(c_Int_Oring__1__class_Oof__int(_1161006), _1161008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1161008)))], (21887 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1161008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161006), c_Groups_Ozero__class_Ozero(_1161006)), hAPP(c_Int_Oring__1__class_Oof__int(_1161006), _1161008))))]]], (21893 ^ _779300) ^ [_1161259, _1161261, _1161263] : [class_Orderings_Olinorder(_1161259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1161259, tc_HOL_Obool)), _1161261), _1161263)), -(_1161261 = c_Orderings_Obot__class_Obot(tc_fun(_1161259, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1161259), _1161263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161259), c_Big__Operators_Olinorder__class_OMin(_1161259, _1161263)), c_Big__Operators_Olinorder__class_OMin(_1161259, _1161261))))], (21911 ^ _779300) ^ [_1161565, _1161567] : [class_Rings_Oring__1(_1161565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1161567)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1161565), hAPP(c_Int_Onat, _1161567)) = hAPP(c_Int_Oring__1__class_Oof__int(_1161565), _1161567))], (21921 ^ _779300) ^ [_1161722, _1161724, _1161726] : [class_Orderings_Olinorder(_1161722), hBOOL(hAPP(c_Finite__Set_Ofinite(_1161722), _1161724)), -(_1161724 = c_Orderings_Obot__class_Obot(tc_fun(_1161722, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1161722, hAPP(hAPP(c_Set_Oinsert(_1161722), _1161726), _1161724)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1161722), _1161726), c_Big__Operators_Olinorder__class_OMin(_1161722, _1161724)))], (21935 ^ _779300) ^ [_1161930, _1161932, _1161934] : [class_Orderings_Olinorder(_1161930), hBOOL(hAPP(c_Finite__Set_Ofinite(_1161930), _1161932)), -(_1161934 = c_Orderings_Obot__class_Obot(tc_fun(_1161930, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1161930, tc_HOL_Obool)), _1161934), _1161932)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1161930), c_Big__Operators_Olinorder__class_OMin(_1161930, _1161934)), c_Big__Operators_Olinorder__class_OMin(_1161930, _1161932)) = c_Big__Operators_Olinorder__class_OMin(_1161930, _1161932))], (21953 ^ _779300) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (21955 ^ _779300) ^ [_1162262, _1162264, _1162266] : [class_Orderings_Olinorder(_1162262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1162262), _1162264)), -(hBOOL(hAPP(hAPP(c_member(_1162262), _1162266), _1162264))), -(_1162264 = c_Orderings_Obot__class_Obot(tc_fun(_1162262, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1162262, hAPP(hAPP(c_Set_Oinsert(_1162262), _1162266), _1162264)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162262), _1162266), c_Big__Operators_Olinorder__class_OMin(_1162262, _1162264)))], (21973 ^ _779300) ^ [_1162499, _1162501, _1162503] : [class_Orderings_Olinorder(_1162499), hBOOL(hAPP(c_Finite__Set_Ofinite(_1162499), _1162501)), 21980 ^ _779300 : [(21981 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1162499, tc_HOL_Obool)), _1162501), hAPP(hAPP(c_Set_Oinsert(_1162499), _1162503), c_Orderings_Obot__class_Obot(tc_fun(_1162499, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1162499, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1162499, hAPP(hAPP(c_Set_Oinsert(_1162499), _1162503), _1162501)) = _1162503)], (21987 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1162499, tc_HOL_Obool)), _1162501), hAPP(hAPP(c_Set_Oinsert(_1162499), _1162503), c_Orderings_Obot__class_Obot(tc_fun(_1162499, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1162499, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1162499, hAPP(hAPP(c_Set_Oinsert(_1162499), _1162503), _1162501)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1162499), _1162503), c_Big__Operators_Olinorder__class_OMin(_1162499, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1162499, tc_HOL_Obool)), _1162501), hAPP(hAPP(c_Set_Oinsert(_1162499), _1162503), c_Orderings_Obot__class_Obot(tc_fun(_1162499, tc_HOL_Obool)))))))]]], (21993 ^ _779300) ^ [_1162978, _1162980] : [_1162978 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1162978, _1162980) = _1162980)], (21999 ^ _779300) ^ [_1163055, _1163057] : [-(_1163055 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1163055, _1163057) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1163055), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1163057)))], (22005 ^ _779300) ^ [_1163108, _1163110] : [class_Rings_Oring__1(_1163108), 22008 ^ _779300 : [(22009 ^ _779300) ^ [] : [_1163110 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1163108), _1163110) = c_Groups_Ozero__class_Ozero(_1163108))], (22015 ^ _779300) ^ [] : [-(_1163110 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22018 ^ _779300 : [(22019 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163110), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1163108), _1163110) = hAPP(c_Groups_Ouminus__class_Ouminus(_1163108), hAPP(c_Int_Oring__1__class_Oof__int(_1163108), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1163110))))], (22025 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163110), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1163108), _1163110) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1163108), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1163108, _1163108)), tc_fun(tc_Int_Oint, _1163108)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1163108, _1163108), _1163108), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1163108, _1163108)), tc_fun(tc_Int_Oint, _1163108)), tc_Int_Oint), c_COMBB(tc_fun(_1163108, _1163108), _1163108, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1163108, tc_fun(tc_fun(_1163108, _1163108), _1163108), tc_Int_Oint), c_HOL_OLet(_1163108, _1163108)), c_Int_Oring__1__class_Oof__int(_1163108)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1163108, _1163108), tc_fun(_1163108, _1163108)), hAPP(hAPP(c_COMBB(tc_fun(_1163108, tc_fun(_1163108, _1163108)), tc_fun(tc_fun(_1163108, _1163108), tc_fun(_1163108, _1163108)), tc_Int_Oint), c_COMBS(_1163108, _1163108, _1163108)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1163108, _1163108), tc_fun(_1163108, tc_fun(_1163108, _1163108))), hAPP(hAPP(c_COMBB(tc_fun(_1163108, tc_fun(_1163108, _1163108)), tc_fun(tc_fun(_1163108, _1163108), tc_fun(_1163108, tc_fun(_1163108, _1163108))), tc_Int_Oint), c_COMBB(_1163108, tc_fun(_1163108, _1163108), _1163108)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1163108, tc_fun(_1163108, _1163108)), tc_Int_Oint), c_If(_1163108)), 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(_1163108, _1163108, _1163108), c_Groups_Oplus__class_Oplus(_1163108)), c_COMBI(_1163108))))), hAPP(hAPP(c_COMBC(_1163108, _1163108, _1163108), hAPP(hAPP(c_COMBB(_1163108, tc_fun(_1163108, _1163108), _1163108), c_Groups_Oplus__class_Oplus(_1163108)), hAPP(hAPP(c_COMBS(_1163108, _1163108, _1163108), c_Groups_Oplus__class_Oplus(_1163108)), c_COMBI(_1163108)))), c_Groups_Oone__class_Oone(_1163108))))), c_Divides_Odivmod__int(_1163110, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (22031 ^ _779300) ^ [_1164021, _1164023] : [class_Orderings_Olinorder(_1164021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1164021), _1164023)), -(_1164023 = c_Orderings_Obot__class_Obot(tc_fun(_1164021, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1164021), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1164021), 22044 ^ [_1164021, _1164023]), 22045 ^ [_1164021, _1164023])), hAPP(hAPP(c_Set_Oinsert(_1164021), 22044 ^ [_1164021, _1164023]), hAPP(hAPP(c_Set_Oinsert(_1164021), 22045 ^ [_1164021, _1164023]), c_Orderings_Obot__class_Obot(tc_fun(_1164021, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1164021), c_Big__Operators_Olinorder__class_OMin(_1164021, _1164023)), _1164023)))], (22051 ^ _779300) ^ [] : [-(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))], (22053 ^ _779300) ^ [_1164483, _1164485, _1164487] : [class_Orderings_Olinorder(_1164483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1164483), _1164485)), hBOOL(hAPP(hAPP(c_member(_1164483), _1164487), _1164485)), 22064 ^ _779300 : [(22065 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1164483, tc_HOL_Obool)), _1164485), hAPP(hAPP(c_Set_Oinsert(_1164483), _1164487), c_Orderings_Obot__class_Obot(tc_fun(_1164483, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1164483, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1164483, c_Orderings_Oord__class_Omin(_1164483), _1164485) = _1164487)], (22071 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1164483, tc_HOL_Obool)), _1164485), hAPP(hAPP(c_Set_Oinsert(_1164483), _1164487), c_Orderings_Obot__class_Obot(tc_fun(_1164483, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1164483, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1164483, c_Orderings_Oord__class_Omin(_1164483), _1164485) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1164483), _1164487), c_Big__Operators_Olattice_OInf__fin(_1164483, c_Orderings_Oord__class_Omin(_1164483), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1164483, tc_HOL_Obool)), _1164485), hAPP(hAPP(c_Set_Oinsert(_1164483), _1164487), c_Orderings_Obot__class_Obot(tc_fun(_1164483, tc_HOL_Obool)))))))]]], (22077 ^ _779300) ^ [_1165007, _1165009, _1165011, _1165013, _1165015, _1165017] : [class_Groups_Ocomm__monoid__mult(_1165007), hBOOL(hAPP(c_Finite__Set_Ofinite(_1165009), _1165011)), 22084 ^ _779300 : [(22085 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1165009), _1165013), _1165011)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165009, _1165007), hAPP(hAPP(c_COMBC(_1165009, _1165007, _1165007), hAPP(hAPP(c_COMBS(_1165009, _1165007, tc_fun(_1165007, _1165007)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1165007, tc_fun(_1165007, _1165007)), _1165009), c_If(_1165007)), hAPP(hAPP(c_COMBC(_1165009, _1165009, tc_HOL_Obool), c_fequal), _1165013))), _1165015)), _1165017)), _1165011) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165007), hAPP(_1165015, _1165013)), hAPP(hAPP(c_Power_Opower__class_Opower(_1165007), _1165017), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1165009), _1165011)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (22091 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1165009), _1165013), _1165011))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165009, _1165007), hAPP(hAPP(c_COMBC(_1165009, _1165007, _1165007), hAPP(hAPP(c_COMBS(_1165009, _1165007, tc_fun(_1165007, _1165007)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1165007, tc_fun(_1165007, _1165007)), _1165009), c_If(_1165007)), hAPP(hAPP(c_COMBC(_1165009, _1165009, tc_HOL_Obool), c_fequal), _1165013))), _1165015)), _1165017)), _1165011) = hAPP(hAPP(c_Power_Opower__class_Opower(_1165007), _1165017), hAPP(c_Finite__Set_Ocard(_1165009), _1165011)))]]], (22097 ^ _779300) ^ [_1165619, _1165621] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1165619, _1165621))))], (22099 ^ _779300) ^ [_1165650, _1165652, _1165654, _1165656] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1165650), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165652, tc_Int_Oint), _1165654), _1165656)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165652, _1165650), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1165650, _1165652), c_Int_Oring__1__class_Oof__int(_1165650)), _1165654)), _1165656)), class_Groups_Ocomm__monoid__mult(_1165650), class_Rings_Oring__1(_1165650)], (22109 ^ _779300) ^ [_1165853, _1165855, _1165857] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165853, tc_Nat_Onat), _1165855), _1165857)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165853, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1165853), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1165855)), _1165857))], (22111 ^ _779300) ^ [_1165911, _1165913, _1165915, _1165917] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1165911), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165913, tc_Nat_Onat), _1165915), _1165917)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165913, _1165911), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1165911, _1165913), c_Nat_Osemiring__1__class_Oof__nat(_1165911)), _1165915)), _1165917)), class_Groups_Ocomm__monoid__mult(_1165911), class_Rings_Osemiring__1(_1165911)], (22121 ^ _779300) ^ [_1166114, _1166116, _1166118] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166114, tc_Nat_Onat), _1166116), _1166118) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166114, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1166114), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1166116)), _1166118)))], (22123 ^ _779300) ^ [_1166172, _1166174, _1166176, _1166178, _1166180] : [class_Groups_Ocomm__monoid__mult(_1166172), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166174, _1166172), hAPP(hAPP(c_COMBS(_1166174, _1166172, _1166172), hAPP(hAPP(c_COMBB(_1166172, tc_fun(_1166172, _1166172), _1166174), c_Groups_Otimes__class_Otimes(_1166172)), _1166176)), _1166178)), _1166180) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166172), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166174, _1166172), _1166176), _1166180)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166174, _1166172), _1166178), _1166180)))], (22129 ^ _779300) ^ [_1166373, _1166375, _1166377] : [class_Groups_Ocomm__monoid__mult(_1166373), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166375, _1166373), hAPP(c_COMBK(_1166373, _1166375), c_Groups_Oone__class_Oone(_1166373))), _1166377) = c_Groups_Oone__class_Oone(_1166373))], (22135 ^ _779300) ^ [_1166488, _1166490, _1166492] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1166488), _1166490), _1166492) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1166488), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1166488, tc_Int_Oint), _1166490), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1166492))), class_Groups_Ocomm__monoid__add(_1166488), class_Groups_Ocomm__monoid__mult(_1166488)], (22145 ^ _779300) ^ [_1166679, _1166681, _1166683, _1166685] : [class_Rings_Ocomm__semiring__1(_1166679), class_Rings_Ono__zero__divisors(_1166679), hBOOL(hAPP(c_Finite__Set_Ofinite(_1166681), _1166683)), 22156 ^ _779300 : [(22157 ^ _779300) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166681, _1166679), _1166685), _1166683) = c_Groups_Ozero__class_Ozero(_1166679), 22161 ^ _779300 : [(22162 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1166681), 22160 ^ [_1166679, _1166681, _1166683, _1166685]), _1166683)))], (22164 ^ _779300) ^ [] : [-(hAPP(_1166685, 22160 ^ [_1166679, _1166681, _1166683, _1166685]) = c_Groups_Ozero__class_Ozero(_1166679))]]], (22166 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166681, _1166679), _1166685), _1166683) = c_Groups_Ozero__class_Ozero(_1166679)), 22167 ^ _779300 : [(22168 ^ _779300) ^ [_1167057] : [hBOOL(hAPP(hAPP(c_member(_1166681), _1167057), _1166683)), hAPP(_1166685, _1167057) = c_Groups_Ozero__class_Ozero(_1166679)]]]]], (22176 ^ _779300) ^ [_1167212, _1167214, _1167216, _1167218] : [class_Rings_Ocomm__semiring__1(_1167212), hBOOL(hAPP(c_Finite__Set_Ofinite(_1167214), _1167216)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167214, _1167212), _1167218), _1167216) = c_Groups_Ozero__class_Ozero(_1167212)), 22185 ^ _779300 : [(22186 ^ _779300) ^ [_1167393] : [hBOOL(hAPP(hAPP(c_member(_1167214), _1167393), _1167216)), hAPP(_1167218, _1167393) = c_Groups_Ozero__class_Ozero(_1167212)]]], (22194 ^ _779300) ^ [_1167542, _1167544, _1167546] : [class_Groups_Ocomm__monoid__mult(_1167542), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167544, _1167542), _1167546), c_Orderings_Obot__class_Obot(tc_fun(_1167544, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1167542))], (22200 ^ _779300) ^ [_1167651, _1167653, _1167655] : [class_Groups_Ocomm__monoid__mult(_1167651), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167653, _1167651), _1167655), c_Orderings_Obot__class_Obot(tc_fun(_1167653, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1167651))], (22206 ^ _779300) ^ [_1167760, _1167762, _1167764, _1167766] : [class_Groups_Ocomm__monoid__mult(_1167760), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1167762), _1167764))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167762, _1167760), _1167766), _1167764) = c_Groups_Oone__class_Oone(_1167760))], (22216 ^ _779300) ^ [_1167884, _1167886, _1167888, _1167890] : [class_Groups_Ocomm__monoid__mult(_1167884), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1167886), _1167888))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167886, _1167884), _1167890), _1167888) = c_Groups_Oone__class_Oone(_1167884))], (22226 ^ _779300) ^ [_1168008, _1168010, _1168012] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1168008), _1168010)), 22229 ^ _779300 : [(22240 ^ _779300) ^ [] : [22242 ^ _779300 : [(22243 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1168008), 22241 ^ [_1168008, _1168010, _1168012]), _1168010)))], (22245 ^ _779300) ^ [] : [hAPP(_1168012, 22241 ^ [_1168008, _1168010, _1168012]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168008, tc_Nat_Onat), _1168012), _1168010) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (22230 ^ _779300) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168008, tc_Nat_Onat), _1168012), _1168010) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 22233 ^ _779300 : [(22234 ^ _779300) ^ [_1168170] : [hBOOL(hAPP(hAPP(c_member(_1168008), _1168170), _1168010)), -(hAPP(_1168012, _1168170) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (22249 ^ _779300) ^ [_1168428, _1168430, _1168432] : [class_Groups_Ocomm__monoid__add(_1168428), class_Groups_Ocomm__monoid__mult(_1168428), c_Nat__Transfer_Onat__set(_1168430), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1168428), _1168432), _1168430) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1168428), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1168428, tc_Nat_Onat), _1168432), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1168430)))], (22263 ^ _779300) ^ [_1168673, _1168675, _1168677, _1168679, _1168681] : [class_Groups_Ocomm__monoid__mult(_1168673), hBOOL(hAPP(c_Finite__Set_Ofinite(_1168675), _1168677)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168675, _1168673), hAPP(hAPP(c_COMBS(_1168675, _1168673, _1168673), hAPP(hAPP(c_COMBB(_1168673, tc_fun(_1168673, _1168673), _1168675), c_Groups_Otimes__class_Otimes(_1168673)), _1168679)), _1168681)), _1168677) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168673), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168675, _1168673), _1168679), _1168677)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168675, _1168673), _1168681), _1168677)))], (22273 ^ _779300) ^ [_1168940, _1168942, _1168944] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1168940), _1168942)), 22276 ^ _779300 : [(22287 ^ _779300) ^ [] : [22289 ^ _779300 : [(22290 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1168940), 22288 ^ [_1168940, _1168942, _1168944]), _1168942)))], (22292 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1168944, 22288 ^ [_1168940, _1168942, _1168944])))]], -(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(_1168940, tc_Nat_Onat), _1168944), _1168942))))], (22277 ^ _779300) ^ [] : [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(_1168940, tc_Nat_Onat), _1168944), _1168942))), 22280 ^ _779300 : [(22281 ^ _779300) ^ [_1169108] : [hBOOL(hAPP(hAPP(c_member(_1168940), _1169108), _1168942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1168944, _1169108))))]]]]], (22296 ^ _779300) ^ [_1169376, _1169378, _1169380, _1169382, _1169384] : [class_Groups_Ocomm__monoid__mult(_1169376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169378), _1169380)), 22303 ^ _779300 : [(22304 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1169378), _1169382), _1169380)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169378, _1169376), hAPP(hAPP(c_COMBC(_1169378, _1169376, _1169376), hAPP(hAPP(c_COMBS(_1169378, _1169376, tc_fun(_1169376, _1169376)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1169376, tc_fun(_1169376, _1169376)), _1169378), c_If(_1169376)), hAPP(hAPP(c_COMBC(_1169378, _1169378, tc_HOL_Obool), c_fequal), _1169382))), _1169384)), c_Groups_Oone__class_Oone(_1169376))), _1169380) = hAPP(_1169384, _1169382))], (22310 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1169378), _1169382), _1169380))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169378, _1169376), hAPP(hAPP(c_COMBC(_1169378, _1169376, _1169376), hAPP(hAPP(c_COMBS(_1169378, _1169376, tc_fun(_1169376, _1169376)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1169376, tc_fun(_1169376, _1169376)), _1169378), c_If(_1169376)), hAPP(hAPP(c_COMBC(_1169378, _1169378, tc_HOL_Obool), c_fequal), _1169382))), _1169384)), c_Groups_Oone__class_Oone(_1169376))), _1169380) = c_Groups_Oone__class_Oone(_1169376))]]], (22316 ^ _779300) ^ [_1169914, _1169916, _1169918, _1169920, _1169922] : [class_Groups_Ocomm__monoid__mult(_1169914), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169916), _1169918)), 22323 ^ _779300 : [(22324 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1169916), _1169920), _1169918)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169916, _1169914), hAPP(hAPP(c_COMBC(_1169916, _1169914, _1169914), hAPP(hAPP(c_COMBS(_1169916, _1169914, tc_fun(_1169914, _1169914)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1169914, tc_fun(_1169914, _1169914)), _1169916), c_If(_1169914)), hAPP(c_fequal, _1169920))), _1169922)), c_Groups_Oone__class_Oone(_1169914))), _1169918) = hAPP(_1169922, _1169920))], (22330 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1169916), _1169920), _1169918))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169916, _1169914), hAPP(hAPP(c_COMBC(_1169916, _1169914, _1169914), hAPP(hAPP(c_COMBS(_1169916, _1169914, tc_fun(_1169914, _1169914)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1169914, tc_fun(_1169914, _1169914)), _1169916), c_If(_1169914)), hAPP(c_fequal, _1169920))), _1169922)), c_Groups_Oone__class_Oone(_1169914))), _1169918) = c_Groups_Oone__class_Oone(_1169914))]]], (22336 ^ _779300) ^ [_1170424, _1170426, _1170428, _1170430] : [class_Groups_Ocomm__monoid__mult(_1170424), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170426), _1170428)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1170426, _1170424), hAPP(c_COMBK(_1170424, _1170426), _1170430)), _1170428) = hAPP(hAPP(c_Power_Opower__class_Opower(_1170424), _1170430), hAPP(c_Finite__Set_Ocard(_1170426), _1170428)))], (22346 ^ _779300) ^ [_1170623, _1170625, _1170627] : [class_Orderings_Olinorder(_1170623), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170623), _1170625)), hBOOL(hAPP(hAPP(c_member(_1170623), _1170627), _1170625)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1170623), _1170627), c_Big__Operators_Olattice_OInf__fin(_1170623, c_Orderings_Oord__class_Omin(_1170623), _1170625)) = c_Big__Operators_Olattice_OInf__fin(_1170623, c_Orderings_Oord__class_Omin(_1170623), _1170625))], (22360 ^ _779300) ^ [_1170870, _1170872] : [class_Orderings_Olinorder(_1170870), -(c_Big__Operators_Olattice_OInf__fin(_1170870, c_Orderings_Oord__class_Omin(_1170870), hAPP(hAPP(c_Set_Oinsert(_1170870), _1170872), c_Orderings_Obot__class_Obot(tc_fun(_1170870, tc_HOL_Obool)))) = _1170872)], (22366 ^ _779300) ^ [_1170983, _1170985, _1170987, _1170989, _1170991] : [class_Groups_Ocomm__monoid__mult(_1170983), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170985), _1170987)), -(hBOOL(hAPP(hAPP(c_member(_1170985), _1170989), _1170987))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1170985, _1170983), _1170991), hAPP(hAPP(c_Set_Oinsert(_1170985), _1170989), _1170987)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170983), hAPP(_1170991, _1170989)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1170985, _1170983), _1170991), _1170987)))], (22380 ^ _779300) ^ [_1171233, _1171235, _1171237, _1171239, _1171241] : [class_Groups_Ocomm__monoid__mult(_1171233), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171235), _1171237)), -(hBOOL(hAPP(hAPP(c_member(_1171235), _1171239), _1171237))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1171235, _1171233), _1171241), hAPP(hAPP(c_Set_Oinsert(_1171235), _1171239), _1171237)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171233), hAPP(_1171241, _1171239)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1171235, _1171233), _1171241), _1171237)))], (22394 ^ _779300) ^ [_1171483, _1171485] : [class_Orderings_Olinorder(_1171483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171483), _1171485)), -(c_Big__Operators_Olattice_OInf__fin(_1171483, c_Orderings_Oord__class_Omin(_1171483), _1171485) = hAPP(c_Finite__Set_Ofold1(_1171483, c_Orderings_Oord__class_Omin(_1171483)), _1171485))], (22404 ^ _779300) ^ [_1171646, _1171648, _1171650, _1171652] : [class_Groups_Ocomm__monoid__mult(_1171646), 22407 ^ _779300 : [(22408 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1171648), _1171650)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1171648, _1171646), _1171652), _1171650) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1171646, _1171648, c_Groups_Otimes__class_Otimes(_1171646)), _1171652), c_Groups_Oone__class_Oone(_1171646)), _1171650))], (22414 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1171648), _1171650))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1171648, _1171646), _1171652), _1171650) = c_Groups_Oone__class_Oone(_1171646))]]], (22420 ^ _779300) ^ [_1171918, _1171920, _1171922, _1171924] : [class_Groups_Ocomm__monoid__mult(_1171918), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171920), _1171922)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1171920, _1171918), _1171924), _1171922) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1171918, _1171920, c_Groups_Otimes__class_Otimes(_1171918)), _1171924), c_Groups_Oone__class_Oone(_1171918)), _1171922))], (22430 ^ _779300) ^ [_1172113, _1172115, _1172117, _1172119, _1172121] : [class_Groups_Ocomm__monoid__mult(_1172113), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172115), _1172117)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1172115, _1172113), _1172119), hAPP(hAPP(c_Set_Oinsert(_1172115), _1172121), _1172117)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172113), hAPP(_1172119, _1172121)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1172115, _1172113), _1172119), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172115, tc_HOL_Obool)), _1172117), hAPP(hAPP(c_Set_Oinsert(_1172115), _1172121), c_Orderings_Obot__class_Obot(tc_fun(_1172115, tc_HOL_Obool)))))))], (22440 ^ _779300) ^ [_1172382, _1172384] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1172382, _1172384)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1172384), hAPP(c_Nat_OSuc, _1172382)))], (22442 ^ _779300) ^ [_1172423, _1172425, _1172427] : [class_Orderings_Olinorder(_1172423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172423), _1172425)), -(_1172425 = c_Orderings_Obot__class_Obot(tc_fun(_1172423, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1172423, c_Orderings_Oord__class_Omin(_1172423), hAPP(hAPP(c_Set_Oinsert(_1172423), _1172427), _1172425)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1172423), _1172427), c_Big__Operators_Olattice_OInf__fin(_1172423, c_Orderings_Oord__class_Omin(_1172423), _1172425)))], (22456 ^ _779300) ^ [_1172643, _1172645, _1172647] : [class_Orderings_Olinorder(_1172643), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172643), _1172645)), -(_1172647 = c_Orderings_Obot__class_Obot(tc_fun(_1172643, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1172643, tc_HOL_Obool)), _1172647), _1172645)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1172643), c_Big__Operators_Olattice_OInf__fin(_1172643, c_Orderings_Oord__class_Omin(_1172643), _1172647)), c_Big__Operators_Olattice_OInf__fin(_1172643, c_Orderings_Oord__class_Omin(_1172643), _1172645)) = c_Big__Operators_Olattice_OInf__fin(_1172643, c_Orderings_Oord__class_Omin(_1172643), _1172645))], (22474 ^ _779300) ^ [_1172975, _1172977, _1172979, _1172981, _1172983] : [class_Groups_Ocomm__monoid__mult(_1172975), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172977), _1172979)), hBOOL(hAPP(hAPP(c_member(_1172977), _1172981), _1172979)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1172977, _1172975), _1172983), _1172979) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172975), hAPP(_1172983, _1172981)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1172977, _1172975), _1172983), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172977, tc_HOL_Obool)), _1172979), hAPP(hAPP(c_Set_Oinsert(_1172977), _1172981), c_Orderings_Obot__class_Obot(tc_fun(_1172977, tc_HOL_Obool)))))))], (22488 ^ _779300) ^ [_1173300, _1173302, _1173304] : [class_Orderings_Olinorder(_1173300), hBOOL(hAPP(c_Finite__Set_Ofinite(_1173300), _1173302)), -(hBOOL(hAPP(hAPP(c_member(_1173300), _1173304), _1173302))), -(_1173302 = c_Orderings_Obot__class_Obot(tc_fun(_1173300, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1173300, c_Orderings_Oord__class_Omin(_1173300), hAPP(hAPP(c_Set_Oinsert(_1173300), _1173304), _1173302)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1173300), _1173304), c_Big__Operators_Olattice_OInf__fin(_1173300, c_Orderings_Oord__class_Omin(_1173300), _1173302)))], (22506 ^ _779300) ^ [_1173549, _1173551, _1173553] : [class_Orderings_Olinorder(_1173549), hBOOL(hAPP(c_Finite__Set_Ofinite(_1173549), _1173551)), 22513 ^ _779300 : [(22514 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1173549, tc_HOL_Obool)), _1173551), hAPP(hAPP(c_Set_Oinsert(_1173549), _1173553), c_Orderings_Obot__class_Obot(tc_fun(_1173549, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1173549, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1173549, c_Orderings_Oord__class_Omin(_1173549), hAPP(hAPP(c_Set_Oinsert(_1173549), _1173553), _1173551)) = _1173553)], (22520 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1173549, tc_HOL_Obool)), _1173551), hAPP(hAPP(c_Set_Oinsert(_1173549), _1173553), c_Orderings_Obot__class_Obot(tc_fun(_1173549, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1173549, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1173549, c_Orderings_Oord__class_Omin(_1173549), hAPP(hAPP(c_Set_Oinsert(_1173549), _1173553), _1173551)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1173549), _1173553), c_Big__Operators_Olattice_OInf__fin(_1173549, c_Orderings_Oord__class_Omin(_1173549), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1173549, tc_HOL_Obool)), _1173551), hAPP(hAPP(c_Set_Oinsert(_1173549), _1173553), c_Orderings_Obot__class_Obot(tc_fun(_1173549, tc_HOL_Obool)))))))]]], (22526 ^ _779300) ^ [_1174037] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1174037)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1174037)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22528 ^ _779300) ^ [_1174072, _1174074] : [class_Orderings_Olinorder(_1174072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1174072), _1174074)), -(_1174074 = c_Orderings_Obot__class_Obot(tc_fun(_1174072, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1174072), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1174072), 22541 ^ [_1174072, _1174074]), 22542 ^ [_1174072, _1174074])), hAPP(hAPP(c_Set_Oinsert(_1174072), 22541 ^ [_1174072, _1174074]), hAPP(hAPP(c_Set_Oinsert(_1174072), 22542 ^ [_1174072, _1174074]), c_Orderings_Obot__class_Obot(tc_fun(_1174072, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1174072), c_Big__Operators_Olattice_OInf__fin(_1174072, c_Orderings_Oord__class_Omin(_1174072), _1174074)), _1174074)))], (22548 ^ _779300) ^ [_1174522, _1174524] : [-(c_Divides_Odivmod__int__rel(_1174522, _1174524) = 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, _1174522))), 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), _1174524)))))), 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)), _1174524))), 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)), _1174524))))), 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)), _1174524)))), 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), _1174524))), 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))))))))], (22550 ^ _779300) ^ [] : [-(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)))))], (22552 ^ _779300) ^ [_1174655, _1174657, _1174659, _1174661, _1174663] : [class_Fields_Ofield(_1174655), hBOOL(hAPP(c_Finite__Set_Ofinite(_1174657), _1174659)), -(hAPP(_1174661, _1174663) = c_Groups_Ozero__class_Ozero(_1174655)), 22563 ^ _779300 : [(22564 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1174657), _1174663), _1174659)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1174657, _1174655), _1174661), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1174657, tc_HOL_Obool)), _1174659), hAPP(hAPP(c_Set_Oinsert(_1174657), _1174663), c_Orderings_Obot__class_Obot(tc_fun(_1174657, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174655), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1174657, _1174655), _1174661), _1174659)), hAPP(_1174661, _1174663)))], (22570 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1174657), _1174663), _1174659))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1174657, _1174655), _1174661), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1174657, tc_HOL_Obool)), _1174659), hAPP(hAPP(c_Set_Oinsert(_1174657), _1174663), c_Orderings_Obot__class_Obot(tc_fun(_1174657, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1174657, _1174655), _1174661), _1174659))]]], (22576 ^ _779300) ^ [_1175196] : [-(c_Divides_Oadjust(_1175196) = 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)), _1175196))))), 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)), _1175196))))), 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))))))))], (22578 ^ _779300) ^ [_1175257, _1175259] : [class_Rings_Odivision__ring(_1175257), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175257), c_Groups_Ozero__class_Ozero(_1175257)), _1175259) = c_Groups_Ozero__class_Ozero(_1175257))], (22584 ^ _779300) ^ [_1175356, _1175358] : [class_Rings_Odivision__ring__inverse__zero(_1175356), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175356), _1175358), c_Groups_Ozero__class_Ozero(_1175356)) = c_Groups_Ozero__class_Ozero(_1175356))], (22590 ^ _779300) ^ [_1175476, _1175478, _1175480, _1175482] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1175476, tc_fun(_1175478, tc_HOL_Obool))), _1175480), _1175482)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1175476, _1175478)), hAPP(hAPP(c_Product__Type_OPair(_1175476, _1175478), _1175480), _1175482)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1175476, _1175478), tc_HOL_Obool)))))], (22596 ^ _779300) ^ [_1175633, _1175635, _1175637, _1175639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1175633, _1175635)), hAPP(hAPP(c_Product__Type_OPair(_1175633, _1175635), _1175637), _1175639)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1175633, _1175635), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1175633, tc_fun(_1175635, tc_HOL_Obool))), _1175637), _1175639)))], (22602 ^ _779300) ^ [_1175817, _1175819, _1175821, _1175823] : [hAPP(hAPP(c_COMBC(_1175817, tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_fun(_1175819, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1175819, tc_fun(tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_fun(_1175819, tc_HOL_Obool)), _1175817), c_COMBC(_1175819, tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1175819, tc_prod(_1175817, _1175819)), tc_fun(_1175819, tc_fun(tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_HOL_Obool)), _1175817), hAPP(c_COMBB(tc_prod(_1175817, _1175819), tc_fun(tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_HOL_Obool), _1175819), c_member(tc_prod(_1175817, _1175819)))), c_Product__Type_OPair(_1175817, _1175819)))), _1175821) = hAPP(hAPP(c_COMBC(_1175817, tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_fun(_1175819, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1175819, tc_fun(tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_fun(_1175819, tc_HOL_Obool)), _1175817), c_COMBC(_1175819, tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1175819, tc_prod(_1175817, _1175819)), tc_fun(_1175819, tc_fun(tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_HOL_Obool)), _1175817), hAPP(c_COMBB(tc_prod(_1175817, _1175819), tc_fun(tc_fun(tc_prod(_1175817, _1175819), tc_HOL_Obool), tc_HOL_Obool), _1175819), c_member(tc_prod(_1175817, _1175819)))), c_Product__Type_OPair(_1175817, _1175819)))), _1175823), -(_1175821 = _1175823)], (22608 ^ _779300) ^ [_1176366, _1176368, _1176370, _1176372] : [_1176370 = _1176372, -(hAPP(hAPP(c_COMBC(_1176366, tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_fun(_1176368, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176368, tc_fun(tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_fun(_1176368, tc_HOL_Obool)), _1176366), c_COMBC(_1176368, tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176368, tc_prod(_1176366, _1176368)), tc_fun(_1176368, tc_fun(tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_HOL_Obool)), _1176366), hAPP(c_COMBB(tc_prod(_1176366, _1176368), tc_fun(tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_HOL_Obool), _1176368), c_member(tc_prod(_1176366, _1176368)))), c_Product__Type_OPair(_1176366, _1176368)))), _1176370) = hAPP(hAPP(c_COMBC(_1176366, tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_fun(_1176368, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176368, tc_fun(tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_fun(_1176368, tc_HOL_Obool)), _1176366), c_COMBC(_1176368, tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176368, tc_prod(_1176366, _1176368)), tc_fun(_1176368, tc_fun(tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_HOL_Obool)), _1176366), hAPP(c_COMBB(tc_prod(_1176366, _1176368), tc_fun(tc_fun(tc_prod(_1176366, _1176368), tc_HOL_Obool), tc_HOL_Obool), _1176368), c_member(tc_prod(_1176366, _1176368)))), c_Product__Type_OPair(_1176366, _1176368)))), _1176372))], (22614 ^ _779300) ^ [_1176942, _1176944, _1176946, _1176948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1176942, tc_fun(_1176944, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1176942, tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_fun(_1176944, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176944, tc_fun(tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_fun(_1176944, tc_HOL_Obool)), _1176942), c_COMBC(_1176944, tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176944, tc_prod(_1176942, _1176944)), tc_fun(_1176944, tc_fun(tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_HOL_Obool)), _1176942), hAPP(c_COMBB(tc_prod(_1176942, _1176944), tc_fun(tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_HOL_Obool), _1176944), c_member(tc_prod(_1176942, _1176944)))), c_Product__Type_OPair(_1176942, _1176944)))), _1176946)), hAPP(hAPP(c_COMBC(_1176942, tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_fun(_1176944, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176944, tc_fun(tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_fun(_1176944, tc_HOL_Obool)), _1176942), c_COMBC(_1176944, tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176944, tc_prod(_1176942, _1176944)), tc_fun(_1176944, tc_fun(tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_HOL_Obool)), _1176942), hAPP(c_COMBB(tc_prod(_1176942, _1176944), tc_fun(tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool), tc_HOL_Obool), _1176944), c_member(tc_prod(_1176942, _1176944)))), c_Product__Type_OPair(_1176942, _1176944)))), _1176948))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1176942, _1176944), tc_HOL_Obool)), _1176946), _1176948)))], (22620 ^ _779300) ^ [_1177543, _1177545, _1177547, _1177549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool)), _1177547), _1177549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1177543, tc_fun(_1177545, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1177543, tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_fun(_1177545, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1177545, tc_fun(tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_fun(_1177545, tc_HOL_Obool)), _1177543), c_COMBC(_1177545, tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1177545, tc_prod(_1177543, _1177545)), tc_fun(_1177545, tc_fun(tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_HOL_Obool)), _1177543), hAPP(c_COMBB(tc_prod(_1177543, _1177545), tc_fun(tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_HOL_Obool), _1177545), c_member(tc_prod(_1177543, _1177545)))), c_Product__Type_OPair(_1177543, _1177545)))), _1177547)), hAPP(hAPP(c_COMBC(_1177543, tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_fun(_1177545, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1177545, tc_fun(tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_fun(_1177545, tc_HOL_Obool)), _1177543), c_COMBC(_1177545, tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1177545, tc_prod(_1177543, _1177545)), tc_fun(_1177545, tc_fun(tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_HOL_Obool)), _1177543), hAPP(c_COMBB(tc_prod(_1177543, _1177545), tc_fun(tc_fun(tc_prod(_1177543, _1177545), tc_HOL_Obool), tc_HOL_Obool), _1177545), c_member(tc_prod(_1177543, _1177545)))), c_Product__Type_OPair(_1177543, _1177545)))), _1177549))))], (22626 ^ _779300) ^ [_1178150, _1178152, _1178154, _1178156, _1178158, _1178160] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1178150, _1178152), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1178154), _1178156))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1178150, _1178152), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1178158), _1178160))), -(_1178152 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1178156 = _1178160)], (22640 ^ _779300) ^ [_1178354, _1178356, _1178358, _1178360, _1178362, _1178364] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1178354, _1178356), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1178358), _1178360))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1178354, _1178356), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1178362), _1178364))), -(_1178356 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1178358 = _1178362)], (22654 ^ _779300) ^ [_1178558, _1178560, _1178562] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1178558, _1178558), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1178560), _1178562))), -(_1178558 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1178562 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22664 ^ _779300) ^ [_1178670] : [-(_1178670 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1178670), 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)))))], (22670 ^ _779300) ^ [_1178724, _1178726] : [c_Code__Numeral_OSuc__code__numeral(_1178724) = c_Code__Numeral_OSuc__code__numeral(_1178726), -(_1178724 = _1178726)], (22676 ^ _779300) ^ [_1178805, _1178807] : [_1178805 = _1178807, -(c_Code__Numeral_OSuc__code__numeral(_1178805) = c_Code__Numeral_OSuc__code__numeral(_1178807))], (22682 ^ _779300) ^ [_1178892, _1178894, _1178896, _1178898] : [class_Rings_Odivision__ring(_1178892), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178892), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178892), _1178894), _1178896)), _1178898) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178892), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178892), _1178894), _1178898)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178892), _1178896), _1178898)))], (22688 ^ _779300) ^ [_1179051, _1179053, _1179055, _1179057] : [class_Rings_Odivision__ring(_1179051), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179051), _1179053), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179051), _1179055), _1179057)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179051), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179051), _1179053), _1179055)), _1179057))], (22694 ^ _779300) ^ [_1179194, _1179196, _1179198, _1179200] : [class_Rings_Odivision__ring(_1179194), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179194), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1179194), _1179196), _1179198)), _1179200) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1179194), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179194), _1179196), _1179200)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179194), _1179198), _1179200)))], (22700 ^ _779300) ^ [_1179353, _1179355] : [class_Rings_Odivision__ring(_1179353), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179353), _1179355), c_Groups_Oone__class_Oone(_1179353)) = _1179355)], (22706 ^ _779300) ^ [_1179448, _1179450, _1179452] : [class_Rings_Odivision__ring(_1179448), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1179448), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179448), _1179450), _1179452)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179448), hAPP(c_Groups_Ouminus__class_Ouminus(_1179448), _1179450)), _1179452))], (22712 ^ _779300) ^ [_1179577, _1179579, _1179581, _1179583] : [class_Fields_Ofield__inverse__zero(_1179577), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1179577), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179577), _1179579), _1179581)), _1179583) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179577), hAPP(hAPP(c_Power_Opower__class_Opower(_1179577), _1179579), _1179583)), hAPP(hAPP(c_Power_Opower__class_Opower(_1179577), _1179581), _1179583)))], (22718 ^ _779300) ^ [_1179736, _1179738, _1179740] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1179736, _1179736), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1179738), _1179740))), -(_1179736 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1179738 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22728 ^ _779300) ^ [_1179852, _1179854, _1179856, _1179858] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1179852, _1179854), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1179856), _1179858))), -(_1179854 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179852, _1179854) = _1179858)], (22738 ^ _779300) ^ [_1179978, _1179980, _1179982, _1179984] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1179978, _1179980), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1179982), _1179984))), -(_1179980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179978), _1179980) = _1179982)], (22748 ^ _779300) ^ [_1180104, _1180106] : [-(_1180104 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1180106, _1180104), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180106), _1180104)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1180106, _1180104)))))], (22754 ^ _779300) ^ [_1180161, _1180163, _1180165, _1180167] : [class_Rings_Odivision__ring(_1180161), -(_1180163 = c_Groups_Ozero__class_Ozero(_1180161)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180161), _1180165), _1180163) = _1180167, -(_1180165 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180161), _1180167), _1180163))], (22768 ^ _779300) ^ [_1180391, _1180393, _1180395, _1180397] : [class_Rings_Odivision__ring(_1180391), -(_1180393 = c_Groups_Ozero__class_Ozero(_1180391)), _1180395 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180391), _1180397), _1180393), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180391), _1180395), _1180393) = _1180397)], (22782 ^ _779300) ^ [_1180621, _1180623, _1180625, _1180627] : [class_Rings_Odivision__ring(_1180621), -(_1180623 = c_Groups_Ozero__class_Ozero(_1180621)), 22789 ^ _779300 : [(22790 ^ _779300) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180621), _1180625), _1180623) = _1180627, -(_1180625 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180621), _1180627), _1180623))], (22796 ^ _779300) ^ [] : [_1180625 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180621), _1180627), _1180623), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180621), _1180625), _1180623) = _1180627)]]], (22802 ^ _779300) ^ [_1180949, _1180951, _1180953, _1180955] : [class_Rings_Odivision__ring(_1180949), -(_1180951 = c_Groups_Ozero__class_Ozero(_1180949)), 22809 ^ _779300 : [(22810 ^ _779300) ^ [] : [_1180953 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180949), _1180955), _1180951), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180949), _1180953), _1180951) = _1180955)], (22816 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180949), _1180953), _1180951) = _1180955, -(_1180953 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180949), _1180955), _1180951))]]], (22822 ^ _779300) ^ [_1181277, _1181279, _1181281] : [class_Rings_Odivision__ring(_1181277), -(_1181279 = c_Groups_Ozero__class_Ozero(_1181277)), 22829 ^ _779300 : [(22830 ^ _779300) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181277), _1181281), _1181279) = c_Groups_Oone__class_Oone(_1181277), -(_1181281 = _1181279)], (22836 ^ _779300) ^ [] : [_1181281 = _1181279, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181277), _1181281), _1181279) = c_Groups_Oone__class_Oone(_1181277))]]], (22842 ^ _779300) ^ [_1181579, _1181581] : [class_Rings_Odivision__ring(_1181579), -(_1181581 = c_Groups_Ozero__class_Ozero(_1181579)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181579), _1181581), _1181581) = c_Groups_Oone__class_Oone(_1181579))], (22852 ^ _779300) ^ [_1181693, _1181695] : [class_Rings_Odivision__ring__inverse__zero(_1181693), 22855 ^ _779300 : [(22856 ^ _779300) ^ [] : [_1181695 = c_Groups_Ozero__class_Ozero(_1181693), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181693), _1181695), _1181695) = c_Groups_Ozero__class_Ozero(_1181693))], (22862 ^ _779300) ^ [] : [-(_1181695 = c_Groups_Ozero__class_Ozero(_1181693)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181693), _1181695), _1181695) = c_Groups_Oone__class_Oone(_1181693))]]], (22868 ^ _779300) ^ [_1181915, _1181917, _1181919] : [class_Rings_Odivision__ring(_1181915), -(_1181917 = c_Groups_Ozero__class_Ozero(_1181915)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1181915), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181915), _1181919), _1181917)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181915), _1181919), hAPP(c_Groups_Ouminus__class_Ouminus(_1181915), _1181917)))], (22878 ^ _779300) ^ [_1182063, _1182065, _1182067] : [class_Rings_Odivision__ring(_1182063), -(_1182065 = c_Groups_Ozero__class_Ozero(_1182063)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182063), hAPP(c_Groups_Ouminus__class_Ouminus(_1182063), _1182067)), hAPP(c_Groups_Ouminus__class_Ouminus(_1182063), _1182065)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182063), _1182067), _1182065))], (22888 ^ _779300) ^ [_1182211, _1182213, _1182215, _1182217] : [class_Fields_Ofield(_1182211), -(_1182213 = c_Groups_Ozero__class_Ozero(_1182211)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1182211), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182211), _1182215), _1182213)), _1182217) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182211), hAPP(hAPP(c_Power_Opower__class_Opower(_1182211), _1182215), _1182217)), hAPP(hAPP(c_Power_Opower__class_Opower(_1182211), _1182213), _1182217)))], (22898 ^ _779300) ^ [_1182389, _1182391, _1182393] : [class_Fields_Ofield__inverse__zero(_1182389), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182389), c_Groups_Oone__class_Oone(_1182389)), hAPP(hAPP(c_Power_Opower__class_Opower(_1182389), _1182391), _1182393)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1182389), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182389), c_Groups_Oone__class_Oone(_1182389)), _1182391)), _1182393))], (22904 ^ _779300) ^ [_1182547] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1182547)], (22906 ^ _779300) ^ [_1182581] : [c_Code__Numeral_OSuc__code__numeral(_1182581) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (22908 ^ _779300) ^ [_1182606, _1182608, _1182610, _1182612, _1182614, _1182616, _1182618] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1182606, _1182608), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1182610), _1182612))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1182614, _1182608), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1182616), _1182618))), -(_1182608 = 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), _1182606), _1182614), _1182608), 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), _1182610), _1182616)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1182612), _1182618)), _1182608))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1182612), _1182618), _1182608)))))], (22922 ^ _779300) ^ [_1182916, _1182918, _1182920, _1182922] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1182916, _1182918), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1182920), _1182922))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182916), _1182918), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1182922), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182920)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182920)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1182922), 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), _1182918), _1182922))))))], (22928 ^ _779300) ^ [_1183143, _1183145, _1183147, _1183149, _1183151] : [class_Fields_Ofield__inverse__zero(_1183143), hBOOL(hAPP(c_Finite__Set_Ofinite(_1183145), _1183147)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1183145, _1183143), hAPP(hAPP(c_COMBS(_1183145, _1183143, _1183143), hAPP(hAPP(c_COMBB(_1183143, tc_fun(_1183143, _1183143), _1183145), c_Rings_Oinverse__class_Odivide(_1183143)), _1183149)), _1183151)), _1183147) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183143), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1183145, _1183143), _1183149), _1183147)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1183145, _1183143), _1183151), _1183147)))], (22938 ^ _779300) ^ [_1183410, _1183412, _1183414, _1183416] : [_1183410 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1183412), _1183414)), _1183416), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1183410, _1183412), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1183414), _1183416)))), 22945 ^ _779300 : [(22946 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183412)))], (22948 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183416), _1183412))]], 22953 ^ _779300 : [(22954 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183412))], (22956 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183412), _1183416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1183416), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (22964 ^ _779300) ^ [_1183872, _1183874, _1183876, _1183878] : [class_Fields_Ofield__inverse__zero(_1183872), class_Int_Onumber(_1183872), 22971 ^ _779300 : [(22988 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183872), _1183874), hAPP(c_Int_Onumber__class_Onumber__of(_1183872), _1183876)) = _1183878), 22991 ^ _779300 : [(22992 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1183872), _1183876) = c_Groups_Ozero__class_Ozero(_1183872)], (22994 ^ _779300) ^ [] : [_1183874 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183872), _1183878), hAPP(c_Int_Onumber__class_Onumber__of(_1183872), _1183876))]], 22995 ^ _779300 : [(22996 ^ _779300) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1183872), _1183876) = c_Groups_Ozero__class_Ozero(_1183872))], (22998 ^ _779300) ^ [] : [_1183878 = c_Groups_Ozero__class_Ozero(_1183872)]]], (22972 ^ _779300) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183872), _1183874), hAPP(c_Int_Onumber__class_Onumber__of(_1183872), _1183876)) = _1183878, 22975 ^ _779300 : [(22976 ^ _779300) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1183872), _1183876) = c_Groups_Ozero__class_Ozero(_1183872)), -(_1183874 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183872), _1183878), hAPP(c_Int_Onumber__class_Onumber__of(_1183872), _1183876)))], (22982 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1183872), _1183876) = c_Groups_Ozero__class_Ozero(_1183872), -(_1183878 = c_Groups_Ozero__class_Ozero(_1183872))]]]]], (23002 ^ _779300) ^ [_1184482, _1184484, _1184486, _1184488] : [class_Fields_Ofield__inverse__zero(_1184482), class_Int_Onumber(_1184482), 23009 ^ _779300 : [(23026 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184482), _1184484), _1184486) = hAPP(c_Int_Onumber__class_Onumber__of(_1184482), _1184488)), 23029 ^ _779300 : [(23030 ^ _779300) ^ [] : [_1184486 = c_Groups_Ozero__class_Ozero(_1184482)], (23032 ^ _779300) ^ [] : [_1184484 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184482), hAPP(c_Int_Onumber__class_Onumber__of(_1184482), _1184488)), _1184486)]], 23033 ^ _779300 : [(23034 ^ _779300) ^ [] : [-(_1184486 = c_Groups_Ozero__class_Ozero(_1184482))], (23036 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1184482), _1184488) = c_Groups_Ozero__class_Ozero(_1184482)]]], (23010 ^ _779300) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184482), _1184484), _1184486) = hAPP(c_Int_Onumber__class_Onumber__of(_1184482), _1184488), 23013 ^ _779300 : [(23014 ^ _779300) ^ [] : [-(_1184486 = c_Groups_Ozero__class_Ozero(_1184482)), -(_1184484 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184482), hAPP(c_Int_Onumber__class_Onumber__of(_1184482), _1184488)), _1184486))], (23020 ^ _779300) ^ [] : [_1184486 = c_Groups_Ozero__class_Ozero(_1184482), -(hAPP(c_Int_Onumber__class_Onumber__of(_1184482), _1184488) = c_Groups_Ozero__class_Ozero(_1184482))]]]]], (23040 ^ _779300) ^ [_1185077, _1185079, _1185081, _1185083] : [class_Fields_Ofield__inverse__zero(_1185077), class_Int_Onumber(_1185077), 23047 ^ _779300 : [(23064 ^ _779300) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1185077), _1185079) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1185077), _1185081), _1185083)), 23067 ^ _779300 : [(23068 ^ _779300) ^ [] : [_1185083 = c_Groups_Ozero__class_Ozero(_1185077)], (23070 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185077), hAPP(c_Int_Onumber__class_Onumber__of(_1185077), _1185079)), _1185083) = _1185081]], 23071 ^ _779300 : [(23072 ^ _779300) ^ [] : [-(_1185083 = c_Groups_Ozero__class_Ozero(_1185077))], (23074 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1185077), _1185079) = c_Groups_Ozero__class_Ozero(_1185077)]]], (23048 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1185077), _1185079) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1185077), _1185081), _1185083), 23051 ^ _779300 : [(23052 ^ _779300) ^ [] : [-(_1185083 = c_Groups_Ozero__class_Ozero(_1185077)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185077), hAPP(c_Int_Onumber__class_Onumber__of(_1185077), _1185079)), _1185083) = _1185081)], (23058 ^ _779300) ^ [] : [_1185083 = c_Groups_Ozero__class_Ozero(_1185077), -(hAPP(c_Int_Onumber__class_Onumber__of(_1185077), _1185079) = c_Groups_Ozero__class_Ozero(_1185077))]]]]], (23078 ^ _779300) ^ [_1185672, _1185674, _1185676, _1185678] : [class_Fields_Ofield__inverse__zero(_1185672), class_Int_Onumber(_1185672), 23085 ^ _779300 : [(23102 ^ _779300) ^ [] : [-(_1185674 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1185672), _1185676), hAPP(c_Int_Onumber__class_Onumber__of(_1185672), _1185678))), 23105 ^ _779300 : [(23106 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1185672), _1185678) = c_Groups_Ozero__class_Ozero(_1185672)], (23108 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185672), _1185674), hAPP(c_Int_Onumber__class_Onumber__of(_1185672), _1185678)) = _1185676]], 23109 ^ _779300 : [(23110 ^ _779300) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1185672), _1185678) = c_Groups_Ozero__class_Ozero(_1185672))], (23112 ^ _779300) ^ [] : [_1185674 = c_Groups_Ozero__class_Ozero(_1185672)]]], (23086 ^ _779300) ^ [] : [_1185674 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1185672), _1185676), hAPP(c_Int_Onumber__class_Onumber__of(_1185672), _1185678)), 23089 ^ _779300 : [(23090 ^ _779300) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1185672), _1185678) = c_Groups_Ozero__class_Ozero(_1185672)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185672), _1185674), hAPP(c_Int_Onumber__class_Onumber__of(_1185672), _1185678)) = _1185676)], (23096 ^ _779300) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1185672), _1185678) = c_Groups_Ozero__class_Ozero(_1185672), -(_1185674 = c_Groups_Ozero__class_Ozero(_1185672))]]]]], (23116 ^ _779300) ^ [_1186282, _1186284, _1186286, _1186288, _1186290] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1186282, _1186284), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1186286), _1186288))), -(_1186284 = 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), _1186290), _1186282), _1186284), 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), _1186290), _1186286)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186290), _1186288)), _1186284))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186290), _1186288), _1186284)))))], (23126 ^ _779300) ^ [_1186504, _1186506] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186504), _1186506), hAPP(c_Int_Onumber__class_Onumber__of(_1186504), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1186504)), class_Fields_Ofield__inverse__zero(_1186504), class_Int_Onumber__ring(_1186504)], (23136 ^ _779300) ^ [_1186659, _1186661] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186659), _1186661), hAPP(c_Int_Onumber__class_Onumber__of(_1186659), c_Int_OBit1(c_Int_OPls))) = _1186661), class_Fields_Ofield(_1186659), class_Int_Onumber__ring(_1186659)], (23146 ^ _779300) ^ [_1186810, _1186812] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186810), _1186812), hAPP(c_Int_Onumber__class_Onumber__of(_1186810), c_Int_OBit1(c_Int_OPls))) = _1186812), class_Fields_Ofield(_1186810), class_Int_Onumber__ring(_1186810)], (23156 ^ _779300) ^ [_1186961, _1186963] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186961), _1186963), hAPP(c_Int_Onumber__class_Onumber__of(_1186961), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1186961), _1186963)), class_Fields_Ofield__inverse__zero(_1186961), class_Int_Onumber__ring(_1186961)], (23166 ^ _779300) ^ [_1187118, _1187120] : [-(_1187118 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187120, _1187118), c_Divides_Odivmod__int(_1187120, _1187118))))], (23172 ^ _779300) ^ [_1187162, _1187164, _1187166, _1187168, _1187170] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187162, _1187164), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187166), _1187168))), -(_1187164 = 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)), _1187170)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187162, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1187164), _1187170)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1187166), _1187170)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1187164), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187166, _1187170))), _1187168)))))], (23186 ^ _779300) ^ [_1187468, _1187470] : [-(c_Divides_Odivmod__int(_1187468, _1187470) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1187468), _1187470)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187468, _1187470)))], (23188 ^ _779300) ^ [_1187512, _1187514, _1187516, _1187518] : [class_Fields_Olinordered__field__inverse__zero(_1187512), class_Int_Onumber(_1187512), 23195 ^ _779300 : [(23222 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187512), _1187514), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516))), _1187518))), 23225 ^ _779300 : [(23226 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), c_Groups_Ozero__class_Ozero(_1187512)), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516))))], (23228 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), _1187514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187512), _1187518), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516))))]], 23229 ^ _779300 : [(23230 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), c_Groups_Ozero__class_Ozero(_1187512)), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516)))], (23232 ^ _779300) ^ [] : [23233 ^ _779300 : [(23234 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516)), c_Groups_Ozero__class_Ozero(_1187512))))], (23236 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187512), _1187518), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516))), _1187514))]], 23237 ^ _779300 : [(23238 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516)), c_Groups_Ozero__class_Ozero(_1187512)))], (23240 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), c_Groups_Ozero__class_Ozero(_1187512)), _1187518))]]]]], (23196 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187512), _1187514), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516))), _1187518)), 23199 ^ _779300 : [(23200 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), c_Groups_Ozero__class_Ozero(_1187512)), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), _1187514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187512), _1187518), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516)))))], (23206 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), c_Groups_Ozero__class_Ozero(_1187512)), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516)))), 23209 ^ _779300 : [(23210 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516)), c_Groups_Ozero__class_Ozero(_1187512))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187512), _1187518), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516))), _1187514)))], (23216 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), hAPP(c_Int_Onumber__class_Onumber__of(_1187512), _1187516)), c_Groups_Ozero__class_Ozero(_1187512)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187512), c_Groups_Ozero__class_Ozero(_1187512)), _1187518)))]]]]]]], (23244 ^ _779300) ^ [_1188626, _1188628, _1188630, _1188632] : [class_Fields_Olinordered__field__inverse__zero(_1188626), class_Int_Onumber(_1188626), 23251 ^ _779300 : [(23278 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1188626), _1188628), _1188630)), hAPP(c_Int_Onumber__class_Onumber__of(_1188626), _1188632)))), 23281 ^ _779300 : [(23282 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), c_Groups_Ozero__class_Ozero(_1188626)), _1188630)))], (23284 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), _1188628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188626), hAPP(c_Int_Onumber__class_Onumber__of(_1188626), _1188632)), _1188630)))]], 23285 ^ _779300 : [(23286 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), c_Groups_Ozero__class_Ozero(_1188626)), _1188630))], (23288 ^ _779300) ^ [] : [23289 ^ _779300 : [(23290 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), _1188630), c_Groups_Ozero__class_Ozero(_1188626))))], (23292 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188626), hAPP(c_Int_Onumber__class_Onumber__of(_1188626), _1188632)), _1188630)), _1188628))]], 23293 ^ _779300 : [(23294 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), _1188630), c_Groups_Ozero__class_Ozero(_1188626)))], (23296 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), c_Groups_Ozero__class_Ozero(_1188626)), hAPP(c_Int_Onumber__class_Onumber__of(_1188626), _1188632)))]]]]], (23252 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1188626), _1188628), _1188630)), hAPP(c_Int_Onumber__class_Onumber__of(_1188626), _1188632))), 23255 ^ _779300 : [(23256 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), c_Groups_Ozero__class_Ozero(_1188626)), _1188630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), _1188628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188626), hAPP(c_Int_Onumber__class_Onumber__of(_1188626), _1188632)), _1188630))))], (23262 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), c_Groups_Ozero__class_Ozero(_1188626)), _1188630))), 23265 ^ _779300 : [(23266 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), _1188630), c_Groups_Ozero__class_Ozero(_1188626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188626), hAPP(c_Int_Onumber__class_Onumber__of(_1188626), _1188632)), _1188630)), _1188628)))], (23272 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), _1188630), c_Groups_Ozero__class_Ozero(_1188626)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188626), c_Groups_Ozero__class_Ozero(_1188626)), hAPP(c_Int_Onumber__class_Onumber__of(_1188626), _1188632))))]]]]]]], (23300 ^ _779300) ^ [_1189695, _1189697, _1189699, _1189701] : [class_Fields_Olinordered__field__inverse__zero(_1189695), class_Int_Onumber(_1189695), 23307 ^ _779300 : [(23334 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), hAPP(c_Int_Onumber__class_Onumber__of(_1189695), _1189697)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1189695), _1189699), _1189701)))), 23337 ^ _779300 : [(23338 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), c_Groups_Ozero__class_Ozero(_1189695)), _1189701)))], (23340 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189695), hAPP(c_Int_Onumber__class_Onumber__of(_1189695), _1189697)), _1189701)), _1189699))]], 23341 ^ _779300 : [(23342 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), c_Groups_Ozero__class_Ozero(_1189695)), _1189701))], (23344 ^ _779300) ^ [] : [23345 ^ _779300 : [(23346 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), _1189701), c_Groups_Ozero__class_Ozero(_1189695))))], (23348 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), _1189699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189695), hAPP(c_Int_Onumber__class_Onumber__of(_1189695), _1189697)), _1189701)))]], 23349 ^ _779300 : [(23350 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), _1189701), c_Groups_Ozero__class_Ozero(_1189695)))], (23352 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), hAPP(c_Int_Onumber__class_Onumber__of(_1189695), _1189697)), c_Groups_Ozero__class_Ozero(_1189695)))]]]]], (23308 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), hAPP(c_Int_Onumber__class_Onumber__of(_1189695), _1189697)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1189695), _1189699), _1189701))), 23311 ^ _779300 : [(23312 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), c_Groups_Ozero__class_Ozero(_1189695)), _1189701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189695), hAPP(c_Int_Onumber__class_Onumber__of(_1189695), _1189697)), _1189701)), _1189699)))], (23318 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), c_Groups_Ozero__class_Ozero(_1189695)), _1189701))), 23321 ^ _779300 : [(23322 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), _1189701), c_Groups_Ozero__class_Ozero(_1189695))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), _1189699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189695), hAPP(c_Int_Onumber__class_Onumber__of(_1189695), _1189697)), _1189701))))], (23328 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), _1189701), c_Groups_Ozero__class_Ozero(_1189695)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189695), hAPP(c_Int_Onumber__class_Onumber__of(_1189695), _1189697)), c_Groups_Ozero__class_Ozero(_1189695))))]]]]]]], (23356 ^ _779300) ^ [_1190764, _1190766, _1190768, _1190770] : [class_Fields_Olinordered__field__inverse__zero(_1190764), class_Int_Onumber(_1190764), 23363 ^ _779300 : [(23390 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), _1190766), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1190764), _1190768), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770))))), 23393 ^ _779300 : [(23394 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), c_Groups_Ozero__class_Ozero(_1190764)), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770))))], (23396 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190764), _1190766), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770))), _1190768))]], 23397 ^ _779300 : [(23398 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), c_Groups_Ozero__class_Ozero(_1190764)), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770)))], (23400 ^ _779300) ^ [] : [23401 ^ _779300 : [(23402 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770)), c_Groups_Ozero__class_Ozero(_1190764))))], (23404 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), _1190768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190764), _1190766), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770))))]], 23405 ^ _779300 : [(23406 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770)), c_Groups_Ozero__class_Ozero(_1190764)))], (23408 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), _1190766), c_Groups_Ozero__class_Ozero(_1190764)))]]]]], (23364 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), _1190766), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1190764), _1190768), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770)))), 23367 ^ _779300 : [(23368 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), c_Groups_Ozero__class_Ozero(_1190764)), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190764), _1190766), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770))), _1190768)))], (23374 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), c_Groups_Ozero__class_Ozero(_1190764)), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770)))), 23377 ^ _779300 : [(23378 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770)), c_Groups_Ozero__class_Ozero(_1190764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), _1190768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190764), _1190766), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770)))))], (23384 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), hAPP(c_Int_Onumber__class_Onumber__of(_1190764), _1190770)), c_Groups_Ozero__class_Ozero(_1190764)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190764), _1190766), c_Groups_Ozero__class_Ozero(_1190764))))]]]]]]], (23412 ^ _779300) ^ [_1191878, _1191880, _1191882, _1191884] : [class_Fields_Ofield(_1191878), -(_1191880 = c_Groups_Ozero__class_Ozero(_1191878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1191882), _1191884)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191878), _1191880), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1191884), _1191882)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191878), hAPP(hAPP(c_Power_Opower__class_Opower(_1191878), _1191880), _1191884)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191878), _1191880), _1191882)))], (23426 ^ _779300) ^ [_1192162, _1192164] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192162), hAPP(c_Int_Onumber__class_Onumber__of(_1192162), c_Int_OMin)), _1192164) = hAPP(c_Groups_Ouminus__class_Ouminus(_1192162), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192162), c_Groups_Oone__class_Oone(_1192162)), _1192164))), class_Fields_Ofield__inverse__zero(_1192162), class_Int_Onumber__ring(_1192162)], (23436 ^ _779300) ^ [_1192343] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1192343)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1192343)], (23438 ^ _779300) ^ [_1192374, _1192376, _1192378, _1192380] : [class_Fields_Olinordered__field__inverse__zero(_1192374), class_Int_Onumber(_1192374), 23445 ^ _779300 : [(23472 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192374), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192374), _1192376), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378))), _1192380))), 23475 ^ _779300 : [(23476 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192374), c_Groups_Ozero__class_Ozero(_1192374)), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378))))], (23478 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192374), _1192376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192374), _1192380), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378))))]], 23479 ^ _779300 : [(23480 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192374), c_Groups_Ozero__class_Ozero(_1192374)), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378)))], (23482 ^ _779300) ^ [] : [23483 ^ _779300 : [(23484 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192374), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378)), c_Groups_Ozero__class_Ozero(_1192374))))], (23486 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192374), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192374), _1192380), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378))), _1192376))]], 23487 ^ _779300 : [(23488 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192374), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378)), c_Groups_Ozero__class_Ozero(_1192374)))], (23490 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192374), c_Groups_Ozero__class_Ozero(_1192374)), _1192380))]]]]], (23446 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192374), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192374), _1192376), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378))), _1192380)), 23449 ^ _779300 : [(23450 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192374), c_Groups_Ozero__class_Ozero(_1192374)), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192374), _1192376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192374), _1192380), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378)))))], (23456 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192374), c_Groups_Ozero__class_Ozero(_1192374)), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378)))), 23459 ^ _779300 : [(23460 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192374), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378)), c_Groups_Ozero__class_Ozero(_1192374))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192374), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192374), _1192380), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378))), _1192376)))], (23466 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192374), hAPP(c_Int_Onumber__class_Onumber__of(_1192374), _1192378)), c_Groups_Ozero__class_Ozero(_1192374)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192374), c_Groups_Ozero__class_Ozero(_1192374)), _1192380)))]]]]]]], (23494 ^ _779300) ^ [_1193488, _1193490, _1193492, _1193494] : [class_Fields_Olinordered__field__inverse__zero(_1193488), class_Int_Onumber(_1193488), 23501 ^ _779300 : [(23528 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193488), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1193488), _1193490), _1193492)), hAPP(c_Int_Onumber__class_Onumber__of(_1193488), _1193494)))), 23531 ^ _779300 : [(23532 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193488), c_Groups_Ozero__class_Ozero(_1193488)), _1193492)))], (23534 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193488), _1193490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193488), hAPP(c_Int_Onumber__class_Onumber__of(_1193488), _1193494)), _1193492)))]], 23535 ^ _779300 : [(23536 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193488), c_Groups_Ozero__class_Ozero(_1193488)), _1193492))], (23538 ^ _779300) ^ [] : [23539 ^ _779300 : [(23540 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193488), _1193492), c_Groups_Ozero__class_Ozero(_1193488))))], (23542 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193488), hAPP(c_Int_Onumber__class_Onumber__of(_1193488), _1193494)), _1193492)), _1193490))]], 23543 ^ _779300 : [(23544 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193488), _1193492), c_Groups_Ozero__class_Ozero(_1193488)))], (23546 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193488), c_Groups_Ozero__class_Ozero(_1193488)), hAPP(c_Int_Onumber__class_Onumber__of(_1193488), _1193494)))]]]]], (23502 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193488), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1193488), _1193490), _1193492)), hAPP(c_Int_Onumber__class_Onumber__of(_1193488), _1193494))), 23505 ^ _779300 : [(23506 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193488), c_Groups_Ozero__class_Ozero(_1193488)), _1193492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193488), _1193490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193488), hAPP(c_Int_Onumber__class_Onumber__of(_1193488), _1193494)), _1193492))))], (23512 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193488), c_Groups_Ozero__class_Ozero(_1193488)), _1193492))), 23515 ^ _779300 : [(23516 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193488), _1193492), c_Groups_Ozero__class_Ozero(_1193488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193488), hAPP(c_Int_Onumber__class_Onumber__of(_1193488), _1193494)), _1193492)), _1193490)))], (23522 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193488), _1193492), c_Groups_Ozero__class_Ozero(_1193488)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193488), c_Groups_Ozero__class_Ozero(_1193488)), hAPP(c_Int_Onumber__class_Onumber__of(_1193488), _1193494))))]]]]]]], (23550 ^ _779300) ^ [_1194557, _1194559, _1194561, _1194563] : [class_Fields_Olinordered__field__inverse__zero(_1194557), class_Int_Onumber(_1194557), 23557 ^ _779300 : [(23584 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194557), hAPP(c_Int_Onumber__class_Onumber__of(_1194557), _1194559)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1194557), _1194561), _1194563)))), 23587 ^ _779300 : [(23588 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194557), c_Groups_Ozero__class_Ozero(_1194557)), _1194563)))], (23590 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194557), hAPP(c_Int_Onumber__class_Onumber__of(_1194557), _1194559)), _1194563)), _1194561))]], 23591 ^ _779300 : [(23592 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194557), c_Groups_Ozero__class_Ozero(_1194557)), _1194563))], (23594 ^ _779300) ^ [] : [23595 ^ _779300 : [(23596 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194557), _1194563), c_Groups_Ozero__class_Ozero(_1194557))))], (23598 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194557), _1194561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194557), hAPP(c_Int_Onumber__class_Onumber__of(_1194557), _1194559)), _1194563)))]], 23599 ^ _779300 : [(23600 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194557), _1194563), c_Groups_Ozero__class_Ozero(_1194557)))], (23602 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194557), hAPP(c_Int_Onumber__class_Onumber__of(_1194557), _1194559)), c_Groups_Ozero__class_Ozero(_1194557)))]]]]], (23558 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194557), hAPP(c_Int_Onumber__class_Onumber__of(_1194557), _1194559)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1194557), _1194561), _1194563))), 23561 ^ _779300 : [(23562 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194557), c_Groups_Ozero__class_Ozero(_1194557)), _1194563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194557), hAPP(c_Int_Onumber__class_Onumber__of(_1194557), _1194559)), _1194563)), _1194561)))], (23568 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194557), c_Groups_Ozero__class_Ozero(_1194557)), _1194563))), 23571 ^ _779300 : [(23572 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194557), _1194563), c_Groups_Ozero__class_Ozero(_1194557))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194557), _1194561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194557), hAPP(c_Int_Onumber__class_Onumber__of(_1194557), _1194559)), _1194563))))], (23578 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194557), _1194563), c_Groups_Ozero__class_Ozero(_1194557)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194557), hAPP(c_Int_Onumber__class_Onumber__of(_1194557), _1194559)), c_Groups_Ozero__class_Ozero(_1194557))))]]]]]]], (23606 ^ _779300) ^ [_1195626, _1195628, _1195630, _1195632] : [class_Fields_Olinordered__field__inverse__zero(_1195626), class_Int_Onumber(_1195626), 23613 ^ _779300 : [(23640 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195626), _1195628), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195626), _1195630), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632))))), 23643 ^ _779300 : [(23644 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195626), c_Groups_Ozero__class_Ozero(_1195626)), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632))))], (23646 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195626), _1195628), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632))), _1195630))]], 23647 ^ _779300 : [(23648 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195626), c_Groups_Ozero__class_Ozero(_1195626)), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632)))], (23650 ^ _779300) ^ [] : [23651 ^ _779300 : [(23652 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195626), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632)), c_Groups_Ozero__class_Ozero(_1195626))))], (23654 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195626), _1195630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195626), _1195628), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632))))]], 23655 ^ _779300 : [(23656 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195626), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632)), c_Groups_Ozero__class_Ozero(_1195626)))], (23658 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195626), _1195628), c_Groups_Ozero__class_Ozero(_1195626)))]]]]], (23614 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195626), _1195628), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195626), _1195630), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632)))), 23617 ^ _779300 : [(23618 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195626), c_Groups_Ozero__class_Ozero(_1195626)), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195626), _1195628), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632))), _1195630)))], (23624 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195626), c_Groups_Ozero__class_Ozero(_1195626)), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632)))), 23627 ^ _779300 : [(23628 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195626), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632)), c_Groups_Ozero__class_Ozero(_1195626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195626), _1195630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195626), _1195628), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632)))))], (23634 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195626), hAPP(c_Int_Onumber__class_Onumber__of(_1195626), _1195632)), c_Groups_Ozero__class_Ozero(_1195626)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195626), _1195628), c_Groups_Ozero__class_Ozero(_1195626))))]]]]]]], (23662 ^ _779300) ^ [_1196740, _1196742] : [class_Fields_Olinordered__field__inverse__zero(_1196740), class_Int_Onumber__ring(_1196740), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196740), c_Groups_Ozero__class_Ozero(_1196740)), _1196742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196740), c_Groups_Ozero__class_Ozero(_1196740)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196740), _1196742), hAPP(c_Int_Onumber__class_Onumber__of(_1196740), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (23676 ^ _779300) ^ [_1196981, _1196983] : [class_Fields_Olinordered__field__inverse__zero(_1196981), class_Int_Onumber__ring(_1196981), 23683 ^ _779300 : [(23684 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196981), c_Groups_Ozero__class_Ozero(_1196981)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196981), _1196983), hAPP(c_Int_Onumber__class_Onumber__of(_1196981), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196981), c_Groups_Ozero__class_Ozero(_1196981)), _1196983)))], (23690 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196981), c_Groups_Ozero__class_Ozero(_1196981)), _1196983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196981), c_Groups_Ozero__class_Ozero(_1196981)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196981), _1196983), hAPP(c_Int_Onumber__class_Onumber__of(_1196981), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (23696 ^ _779300) ^ [_1197331, _1197333, _1197335] : [-(hAPP(c_Divides_Oadjust(_1197331), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1197333), _1197335)) = 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), _1197335), _1197331)), 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)))), _1197333)), 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)))), _1197333)), _1197335))))], (23698 ^ _779300) ^ [_1197411, _1197413, _1197415, _1197417, _1197419, _1197421, _1197423] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1197411, _1197413)), hAPP(hAPP(c_Product__Type_OPair(_1197411, _1197413), _1197415), _1197417)), _1197419)), -(hBOOL(hAPP(hAPP(c_member(_1197421), hAPP(hAPP(_1197423, _1197415), _1197417)), hAPP(c_Set_Oimage(tc_prod(_1197411, _1197413), _1197421, hAPP(c_Product__Type_Oprod_Oprod__case(_1197411, _1197413, _1197421), _1197423)), _1197419))))], (23704 ^ _779300) ^ [_1197605, _1197607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197605), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1197607, _1197605) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197607), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197605)))], (23710 ^ _779300) ^ [_1197711, _1197713] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197711), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23713 ^ _779300 : [(23714 ^ _779300) ^ [] : [23715 ^ _779300 : [(23716 ^ _779300) ^ [] : [_1197713 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23718 ^ _779300) ^ [] : [_1197711 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1197713, _1197711) = 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)))], (23722 ^ _779300) ^ [] : [-(c_Nitpick_Onorm__frac(_1197713, _1197711) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1197713), _1197711)), 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), _1197713))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1197711)))), -(_1197713 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1197711 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (23732 ^ _779300) ^ [_1198009] : [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), _1198009))), 23735 ^ _779300 : [(23736 ^ _779300) ^ [] : [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), _1198009)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1198009)) = 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), _1198009))))], (23742 ^ _779300) ^ [] : [-(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), _1198009))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1198009)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1198009)), 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), _1198009)))))]]], (23748 ^ _779300) ^ [_1198299, _1198301, _1198303, _1198305, _1198307] : [hBOOL(hAPP(hAPP(_1198299, _1198301), _1198303)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1198305, _1198307, tc_HOL_Obool), _1198299), hAPP(hAPP(c_Product__Type_OPair(_1198305, _1198307), _1198301), _1198303))))], (23754 ^ _779300) ^ [_1198428, _1198430, _1198432, _1198434, _1198436] : [hBOOL(hAPP(hAPP(_1198428, _1198430), _1198432)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1198434, _1198436, tc_HOL_Obool), _1198428), hAPP(hAPP(c_Product__Type_OPair(_1198434, _1198436), _1198430), _1198432))))], (23760 ^ _779300) ^ [_1198557, _1198559, _1198561, _1198563, _1198565, _1198567, _1198569] : [hBOOL(hAPP(hAPP(c_member(_1198557), _1198559), hAPP(hAPP(_1198561, _1198563), _1198565))), -(hBOOL(hAPP(hAPP(c_member(_1198557), _1198559), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1198567, _1198569, tc_fun(_1198557, tc_HOL_Obool)), _1198561), hAPP(hAPP(c_Product__Type_OPair(_1198567, _1198569), _1198563), _1198565)))))], (23766 ^ _779300) ^ [_1198746, _1198748, _1198750, _1198752] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1198746, tc_fun(_1198748, tc_HOL_Obool))), _1198750), _1198752))], (23768 ^ _779300) ^ [_1198788, _1198790, _1198792, _1198794, _1198796, _1198798, _1198800] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1198788, _1198790, tc_fun(_1198792, tc_HOL_Obool)), _1198794), hAPP(hAPP(c_Product__Type_OPair(_1198788, _1198790), _1198796), _1198798)), _1198800)), -(hBOOL(hAPP(hAPP(hAPP(_1198794, _1198796), _1198798), _1198800)))], (23774 ^ _779300) ^ [_1198939, _1198941, _1198943] : [_1198939 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1198941, _1198941), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1198941, _1198941), tc_HOL_Obool)), _1198939), _1198943)))], (23780 ^ _779300) ^ [_1199060, _1199062, _1199064, _1199066, _1199068, _1199070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199060, tc_fun(_1199062, tc_HOL_Obool))), _1199064), _1199066)), hBOOL(hAPP(hAPP(_1199064, _1199068), _1199070)), -(hBOOL(hAPP(hAPP(_1199066, _1199068), _1199070)))], (23790 ^ _779300) ^ [_1199251, _1199253, _1199255, _1199257, _1199259, _1199261] : [hBOOL(hAPP(hAPP(_1199251, _1199253), _1199255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199257, tc_fun(_1199259, tc_HOL_Obool))), _1199251), _1199261)), -(hBOOL(hAPP(hAPP(_1199261, _1199253), _1199255)))], (23800 ^ _779300) ^ [_1199460, _1199462, _1199464] : [hBOOL(hAPP(_1199460, 23801 ^ [_1199460, _1199462, _1199464])), 23804 ^ _779300 : [(23805 ^ _779300) ^ [_1199571, _1199573] : [-(hBOOL(hAPP(_1199460, hAPP(hAPP(c_Product__Type_OPair(_1199462, _1199464), _1199573), _1199571))))]]], (23807 ^ _779300) ^ [_1199607, _1199609, _1199611] : [hBOOL(hAPP(_1199607, hAPP(hAPP(c_Product__Type_OPair(_1199609, _1199611), 23808 ^ [_1199607, _1199609, _1199611]), 23809 ^ [_1199607, _1199609, _1199611]))), 23812 ^ _779300 : [(23813 ^ _779300) ^ [_1199754] : [-(hBOOL(hAPP(_1199607, _1199754)))]]], (23815 ^ _779300) ^ [_1199812, _1199814, _1199816, _1199818, _1199820, _1199822] : [hAPP(hAPP(c_Product__Type_OPair(_1199812, _1199814), _1199816), _1199818) = hAPP(hAPP(c_Product__Type_OPair(_1199812, _1199814), _1199820), _1199822), 23818 ^ _779300 : [(23819 ^ _779300) ^ [] : [-(_1199816 = _1199820)], (23821 ^ _779300) ^ [] : [-(_1199818 = _1199822)]]], (23823 ^ _779300) ^ [_1199955, _1199957, _1199959, _1199961, _1199963, _1199965] : [-(hAPP(hAPP(c_Product__Type_OPair(_1199955, _1199957), _1199959), _1199961) = hAPP(hAPP(c_Product__Type_OPair(_1199955, _1199957), _1199963), _1199965)), _1199959 = _1199963, _1199961 = _1199965], (23833 ^ _779300) ^ [_1200138, _1200140, _1200142, _1200144, _1200146, _1200148] : [hAPP(hAPP(c_Product__Type_OPair(_1200138, _1200140), _1200142), _1200144) = hAPP(hAPP(c_Product__Type_OPair(_1200138, _1200140), _1200146), _1200148), 23836 ^ _779300 : [(23837 ^ _779300) ^ [] : [-(_1200142 = _1200146)], (23839 ^ _779300) ^ [] : [-(_1200144 = _1200148)]]], (23841 ^ _779300) ^ [_1200289, _1200291, _1200293, _1200295, _1200297, _1200299] : [_1200289 = _1200291, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1200293, _1200295, _1200297), _1200299), _1200289) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1200293, _1200295, _1200297), _1200299), _1200291))], (23847 ^ _779300) ^ [_1200414, _1200416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200414), 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)), _1200416)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1200414, _1200416), c_Divides_OnegDivAlg(_1200414, _1200416))))], (23857 ^ _779300) ^ [_1200573, _1200575, _1200577, _1200579, _1200581, _1200583] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1200573, _1200575, _1200577), _1200579), hAPP(hAPP(c_Product__Type_OPair(_1200573, _1200575), _1200581), _1200583)) = hAPP(hAPP(_1200579, _1200581), _1200583))], (23859 ^ _779300) ^ [_1200631, _1200633, _1200635, _1200637, _1200639, _1200641] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1200631, _1200633, _1200635), _1200637), hAPP(hAPP(c_Product__Type_OPair(_1200631, _1200633), _1200639), _1200641)) = hAPP(hAPP(_1200637, _1200639), _1200641))], (23861 ^ _779300) ^ [_1200689, _1200691, _1200693, _1200695, _1200697] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1200689, _1200691, tc_HOL_Obool), _1200693), hAPP(hAPP(c_Product__Type_OPair(_1200689, _1200691), _1200695), _1200697))), -(hBOOL(hAPP(hAPP(_1200693, _1200695), _1200697)))], (23867 ^ _779300) ^ [_1200818, _1200820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200818), 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)), _1200820)), -(c_Divides_OnegDivAlg(_1200818, _1200820) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1200818), _1200820)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1200818, _1200820)))], (23877 ^ _779300) ^ [_1200999] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1200999) = 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), _1200999), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (23879 ^ _779300) ^ [_1201034, _1201036, _1201038, _1201040] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1201034, _1201036, _1201038), hAPP(hAPP(c_COMBB(tc_fun(_1201036, tc_prod(_1201034, _1201036)), tc_fun(_1201036, _1201038), _1201034), hAPP(c_COMBB(tc_prod(_1201034, _1201036), _1201038, _1201036), _1201040)), c_Product__Type_OPair(_1201034, _1201036))) = _1201040)], (23881 ^ _779300) ^ [_1201102, _1201104, _1201106] : [-(c_HOL_OThe(tc_prod(_1201102, _1201104), _1201106) = c_HOL_OThe(tc_prod(_1201102, _1201104), hAPP(c_Product__Type_Oprod_Oprod__case(_1201102, _1201104, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1201104, tc_prod(_1201102, _1201104)), tc_fun(_1201104, tc_HOL_Obool), _1201102), hAPP(c_COMBB(tc_prod(_1201102, _1201104), tc_HOL_Obool, _1201104), _1201106)), c_Product__Type_OPair(_1201102, _1201104)))))], (23883 ^ _779300) ^ [_1201180, _1201182, _1201184, _1201186] : [-(c_HOL_OThe(tc_prod(_1201180, _1201182), hAPP(c_Product__Type_Oprod_Oprod__case(_1201180, _1201182, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1201180, tc_fun(_1201182, tc_HOL_Obool), tc_fun(_1201182, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1201182, tc_HOL_Obool), tc_fun(_1201182, tc_HOL_Obool)), _1201180), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1201182)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1201180), c_fconj), hAPP(c_fequal, _1201184)))), hAPP(c_fequal, _1201186)))) = hAPP(hAPP(c_Product__Type_OPair(_1201180, _1201182), _1201184), _1201186))], (23885 ^ _779300) ^ [_1201286, _1201288, _1201290] : [-(c_Fun_Oinj__on(tc_prod(_1201286, _1201288), tc_prod(_1201288, _1201286), hAPP(c_Product__Type_Oprod_Oprod__case(_1201286, _1201288, tc_prod(_1201288, _1201286)), hAPP(c_COMBC(_1201288, _1201286, tc_prod(_1201288, _1201286)), c_Product__Type_OPair(_1201288, _1201286))), _1201290))], (23887 ^ _779300) ^ [_1201344, _1201346, _1201348, _1201350, _1201352, _1201354, _1201356, _1201358] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1201344, _1201346, _1201348), _1201350), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1201352, _1201354, tc_prod(_1201344, _1201346)), _1201356), _1201358)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1201352, _1201354, _1201348), hAPP(hAPP(c_COMBB(tc_fun(_1201354, tc_prod(_1201344, _1201346)), tc_fun(_1201354, _1201348), _1201352), hAPP(c_COMBB(tc_prod(_1201344, _1201346), _1201348, _1201354), hAPP(c_Product__Type_Oprod_Oprod__case(_1201344, _1201346, _1201348), _1201350))), _1201356)), _1201358))], (23889 ^ _779300) ^ [_1201459, _1201461] : [23890 ^ _779300 : [(23891 ^ _779300) ^ [] : [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), _1201459), _1201461)))], (23893 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1201461), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1201459, _1201461) = 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), _1201459), _1201461)))], (23897 ^ _779300) ^ [_1201618, _1201620] : [-(c_Divides_OnegDivAlg(_1201618, _1201620) = hAPP(c_Divides_Oadjust(_1201620), c_Divides_OnegDivAlg(_1201618, 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)))), _1201620)))), -(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), _1201618), _1201620)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1201620), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23907 ^ _779300) ^ [_1201690, _1201692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201690)), 23910 ^ _779300 : [(23911 ^ _779300) ^ [] : [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), _1201692), _1201690))), -(c_Divides_OnegDivAlg(_1201692, _1201690) = 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), _1201692), _1201690)))], (23917 ^ _779300) ^ [] : [-(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), _1201692), _1201690)))), -(c_Divides_OnegDivAlg(_1201692, _1201690) = hAPP(c_Divides_Oadjust(_1201690), c_Divides_OnegDivAlg(_1201692, 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)))), _1201690))))]]], (23923 ^ _779300) ^ [_1201954, _1201956] : [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), _1201954))), 23926 ^ _779300 : [(23927 ^ _779300) ^ [] : [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), _1201956)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201954)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201956), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201954)) = 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), _1201956)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201954))))], (23933 ^ _779300) ^ [] : [-(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), _1201956)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201954))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201956), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201954)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201954)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201956), 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), _1201954)))))]]], (23939 ^ _779300) ^ [_1202326, _1202328, _1202330, _1202332, _1202334] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1202326, _1202328, _1202330), _1202332), _1202334)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1202326, _1202328)), hAPP(hAPP(c_Product__Type_OPair(_1202326, _1202328), _1202332), _1202334)), _1202330)))], (23945 ^ _779300) ^ [_1202461, _1202463, _1202465, _1202467, _1202469] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1202461, _1202463)), hAPP(hAPP(c_Product__Type_OPair(_1202461, _1202463), _1202467), _1202469)), _1202465)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1202461, _1202463, _1202465), _1202467), _1202469)))], (23951 ^ _779300) ^ [_1202602, _1202604] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1202602, _1202604) = 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), _1202602), _1202604)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1202602, _1202604)))], (23953 ^ _779300) ^ [_1202646, _1202648, _1202650, _1202652] : [class_Fields_Olinordered__field__inverse__zero(_1202646), 23956 ^ _779300 : [(23983 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202646), _1202648), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202646), _1202650), _1202652)))), 23986 ^ _779300 : [(23987 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202646), c_Groups_Ozero__class_Ozero(_1202646)), _1202652)))], (23989 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202646), _1202648), _1202652)), _1202650))]], 23990 ^ _779300 : [(23991 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202646), c_Groups_Ozero__class_Ozero(_1202646)), _1202652))], (23993 ^ _779300) ^ [] : [23994 ^ _779300 : [(23995 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202646), _1202652), c_Groups_Ozero__class_Ozero(_1202646))))], (23997 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202646), _1202650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202646), _1202648), _1202652)))]], 23998 ^ _779300 : [(23999 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202646), _1202652), c_Groups_Ozero__class_Ozero(_1202646)))], (24001 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202646), _1202648), c_Groups_Ozero__class_Ozero(_1202646)))]]]]], (23957 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202646), _1202648), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202646), _1202650), _1202652))), 23960 ^ _779300 : [(23961 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202646), c_Groups_Ozero__class_Ozero(_1202646)), _1202652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202646), _1202648), _1202652)), _1202650)))], (23967 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202646), c_Groups_Ozero__class_Ozero(_1202646)), _1202652))), 23970 ^ _779300 : [(23971 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202646), _1202652), c_Groups_Ozero__class_Ozero(_1202646))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202646), _1202650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202646), _1202648), _1202652))))], (23977 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202646), _1202652), c_Groups_Ozero__class_Ozero(_1202646)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202646), _1202648), c_Groups_Ozero__class_Ozero(_1202646))))]]]]]]], (24005 ^ _779300) ^ [_1203599, _1203601, _1203603, _1203605] : [class_Fields_Olinordered__field__inverse__zero(_1203599), 24008 ^ _779300 : [(24035 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203599), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203599), _1203601), _1203603)), _1203605))), 24038 ^ _779300 : [(24039 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203599), c_Groups_Ozero__class_Ozero(_1203599)), _1203603)))], (24041 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203599), _1203601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1203599), _1203605), _1203603)))]], 24042 ^ _779300 : [(24043 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203599), c_Groups_Ozero__class_Ozero(_1203599)), _1203603))], (24045 ^ _779300) ^ [] : [24046 ^ _779300 : [(24047 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203599), _1203603), c_Groups_Ozero__class_Ozero(_1203599))))], (24049 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1203599), _1203605), _1203603)), _1203601))]], 24050 ^ _779300 : [(24051 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203599), _1203603), c_Groups_Ozero__class_Ozero(_1203599)))], (24053 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203599), c_Groups_Ozero__class_Ozero(_1203599)), _1203605))]]]]], (24009 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203599), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203599), _1203601), _1203603)), _1203605)), 24012 ^ _779300 : [(24013 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203599), c_Groups_Ozero__class_Ozero(_1203599)), _1203603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203599), _1203601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1203599), _1203605), _1203603))))], (24019 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203599), c_Groups_Ozero__class_Ozero(_1203599)), _1203603))), 24022 ^ _779300 : [(24023 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203599), _1203603), c_Groups_Ozero__class_Ozero(_1203599))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1203599), _1203605), _1203603)), _1203601)))], (24029 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203599), _1203603), c_Groups_Ozero__class_Ozero(_1203599)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203599), c_Groups_Ozero__class_Ozero(_1203599)), _1203605)))]]]]]]], (24057 ^ _779300) ^ [_1204552, _1204554, _1204556, _1204558] : [class_Fields_Olinordered__field(_1204552), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204552), c_Groups_Ozero__class_Ozero(_1204552)), _1204554)), 24064 ^ _779300 : [(24065 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204552), _1204556), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1204552), _1204558), _1204554))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204552), _1204556), _1204554)), _1204558)))], (24071 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204552), _1204556), _1204554)), _1204558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204552), _1204556), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1204552), _1204558), _1204554))))]]], (24077 ^ _779300) ^ [_1204933, _1204935, _1204937, _1204939, _1204941] : [class_Fields_Ofield__inverse__zero(_1204933), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204933), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1204933), _1204935), _1204937)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1204933), _1204939), _1204941)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1204933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204933), _1204935), _1204939)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204933), _1204937), _1204941)))], (24083 ^ _779300) ^ [_1205110, _1205112, _1205114] : [class_Fields_Ofield__inverse__zero(_1205110), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1205110), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205110), _1205112), _1205114)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205110), _1205112), hAPP(c_Groups_Ouminus__class_Ouminus(_1205110), _1205114)))], (24089 ^ _779300) ^ [_1205239, _1205241, _1205243] : [class_Fields_Ofield__inverse__zero(_1205239), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205239), hAPP(c_Groups_Ouminus__class_Ouminus(_1205239), _1205241)), hAPP(c_Groups_Ouminus__class_Ouminus(_1205239), _1205243)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205239), _1205241), _1205243))], (24095 ^ _779300) ^ [_1205368, _1205370, _1205372, _1205374] : [class_Fields_Olinordered__field__inverse__zero(_1205368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205368), _1205370), _1205372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205368), _1205374), c_Groups_Ozero__class_Ozero(_1205368))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205368), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205368), _1205372), _1205374)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205368), _1205370), _1205374))))], (24109 ^ _779300) ^ [_1205637, _1205639, _1205641, _1205643] : [class_Fields_Olinordered__field__inverse__zero(_1205637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205637), _1205639), _1205641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205637), c_Groups_Ozero__class_Ozero(_1205637)), _1205643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205637), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205637), _1205639), _1205643)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205637), _1205641), _1205643))))], (24123 ^ _779300) ^ [_1205906, _1205908, _1205910] : [class_Fields_Olinordered__field__inverse__zero(_1205906), 24126 ^ _779300 : [(24127 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205906), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205906), _1205908), _1205910)), c_Groups_Ozero__class_Ozero(_1205906))), 24132 ^ _779300 : [(24133 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205906), c_Groups_Ozero__class_Ozero(_1205906)), _1205908)))], (24135 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205906), _1205910), c_Groups_Ozero__class_Ozero(_1205906))))]], 24136 ^ _779300 : [(24137 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205906), _1205908), c_Groups_Ozero__class_Ozero(_1205906))))], (24139 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205906), c_Groups_Ozero__class_Ozero(_1205906)), _1205910)))]]], (24141 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205906), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205906), _1205908), _1205910)), c_Groups_Ozero__class_Ozero(_1205906)))), 24142 ^ _779300 : [(24143 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205906), c_Groups_Ozero__class_Ozero(_1205906)), _1205908)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205906), _1205910), c_Groups_Ozero__class_Ozero(_1205906)))], (24149 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205906), _1205908), c_Groups_Ozero__class_Ozero(_1205906))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205906), c_Groups_Ozero__class_Ozero(_1205906)), _1205910))]]]]], (24157 ^ _779300) ^ [_1206496, _1206498, _1206500] : [class_Fields_Olinordered__field__inverse__zero(_1206496), 24160 ^ _779300 : [(24161 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206496), c_Groups_Ozero__class_Ozero(_1206496)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1206496), _1206498), _1206500))), 24166 ^ _779300 : [(24167 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206496), c_Groups_Ozero__class_Ozero(_1206496)), _1206498)))], (24169 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206496), c_Groups_Ozero__class_Ozero(_1206496)), _1206500)))]], 24170 ^ _779300 : [(24171 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206496), _1206498), c_Groups_Ozero__class_Ozero(_1206496))))], (24173 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206496), _1206500), c_Groups_Ozero__class_Ozero(_1206496))))]]], (24175 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206496), c_Groups_Ozero__class_Ozero(_1206496)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1206496), _1206498), _1206500)))), 24176 ^ _779300 : [(24177 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206496), c_Groups_Ozero__class_Ozero(_1206496)), _1206498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206496), c_Groups_Ozero__class_Ozero(_1206496)), _1206500))], (24183 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206496), _1206498), c_Groups_Ozero__class_Ozero(_1206496))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206496), _1206500), c_Groups_Ozero__class_Ozero(_1206496)))]]]]], (24191 ^ _779300) ^ [_1207086, _1207088, _1207090, _1207092] : [class_Fields_Olinordered__field(_1207086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207086), _1207088), _1207090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207086), _1207092), c_Groups_Ozero__class_Ozero(_1207086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207086), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1207086), _1207090), _1207092)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1207086), _1207088), _1207092))))], (24205 ^ _779300) ^ [_1207355, _1207357, _1207359, _1207361] : [class_Fields_Olinordered__field(_1207355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207355), _1207357), _1207359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207355), c_Groups_Ozero__class_Ozero(_1207355)), _1207361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207355), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1207355), _1207357), _1207361)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1207355), _1207359), _1207361))))], (24219 ^ _779300) ^ [_1207624, _1207626, _1207628] : [class_Fields_Olinordered__field(_1207624), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207624), _1207626), c_Groups_Ozero__class_Ozero(_1207624))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207624), _1207628), c_Groups_Ozero__class_Ozero(_1207624))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207624), c_Groups_Ozero__class_Ozero(_1207624)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1207624), _1207626), _1207628))))], (24233 ^ _779300) ^ [_1207879, _1207881, _1207883] : [class_Fields_Olinordered__field(_1207879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207879), _1207881), c_Groups_Ozero__class_Ozero(_1207879))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207879), c_Groups_Ozero__class_Ozero(_1207879)), _1207883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207879), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1207879), _1207881), _1207883)), c_Groups_Ozero__class_Ozero(_1207879))))], (24247 ^ _779300) ^ [_1208134, _1208136, _1208138] : [class_Fields_Olinordered__field(_1208134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208134), c_Groups_Ozero__class_Ozero(_1208134)), _1208136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208134), _1208138), c_Groups_Ozero__class_Ozero(_1208134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1208134), _1208136), _1208138)), c_Groups_Ozero__class_Ozero(_1208134))))], (24261 ^ _779300) ^ [_1208389, _1208391, _1208393] : [class_Fields_Olinordered__field(_1208389), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208389), c_Groups_Ozero__class_Ozero(_1208389)), _1208391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208389), c_Groups_Ozero__class_Ozero(_1208389)), _1208393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208389), c_Groups_Ozero__class_Ozero(_1208389)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1208389), _1208391), _1208393))))], (24275 ^ _779300) ^ [_1208644, _1208646, _1208648] : [class_Fields_Olinordered__field__inverse__zero(_1208644), 24278 ^ _779300 : [(24279 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208644), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1208644), _1208646), _1208648)), c_Groups_Ozero__class_Ozero(_1208644))), 24284 ^ _779300 : [(24285 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208644), c_Groups_Ozero__class_Ozero(_1208644)), _1208646)))], (24287 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208644), _1208648), c_Groups_Ozero__class_Ozero(_1208644))))]], 24288 ^ _779300 : [(24289 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208644), _1208646), c_Groups_Ozero__class_Ozero(_1208644))))], (24291 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208644), c_Groups_Ozero__class_Ozero(_1208644)), _1208648)))]]], (24293 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208644), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1208644), _1208646), _1208648)), c_Groups_Ozero__class_Ozero(_1208644)))), 24294 ^ _779300 : [(24295 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208644), c_Groups_Ozero__class_Ozero(_1208644)), _1208646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208644), _1208648), c_Groups_Ozero__class_Ozero(_1208644)))], (24301 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208644), _1208646), c_Groups_Ozero__class_Ozero(_1208644))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208644), c_Groups_Ozero__class_Ozero(_1208644)), _1208648))]]]]], (24309 ^ _779300) ^ [_1209234, _1209236, _1209238] : [class_Fields_Olinordered__field__inverse__zero(_1209234), 24312 ^ _779300 : [(24313 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209234), c_Groups_Ozero__class_Ozero(_1209234)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209234), _1209236), _1209238))), 24318 ^ _779300 : [(24319 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209234), c_Groups_Ozero__class_Ozero(_1209234)), _1209236)))], (24321 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209234), c_Groups_Ozero__class_Ozero(_1209234)), _1209238)))]], 24322 ^ _779300 : [(24323 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209234), _1209236), c_Groups_Ozero__class_Ozero(_1209234))))], (24325 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209234), _1209238), c_Groups_Ozero__class_Ozero(_1209234))))]]], (24327 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209234), c_Groups_Ozero__class_Ozero(_1209234)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209234), _1209236), _1209238)))), 24328 ^ _779300 : [(24329 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209234), c_Groups_Ozero__class_Ozero(_1209234)), _1209236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209234), c_Groups_Ozero__class_Ozero(_1209234)), _1209238))], (24335 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209234), _1209236), c_Groups_Ozero__class_Ozero(_1209234))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209234), _1209238), c_Groups_Ozero__class_Ozero(_1209234)))]]]]], (24343 ^ _779300) ^ [_1209824, _1209826, _1209828, _1209830, _1209832] : [class_Fields_Ofield(_1209824), -(_1209826 = c_Groups_Ozero__class_Ozero(_1209824)), -(_1209828 = c_Groups_Ozero__class_Ozero(_1209824)), 24354 ^ _779300 : [(24355 ^ _779300) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209824), _1209830), _1209826) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209824), _1209832), _1209828), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209824), _1209830), _1209828) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209824), _1209832), _1209826))], (24361 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209824), _1209830), _1209828) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209824), _1209832), _1209826), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209824), _1209830), _1209826) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209824), _1209832), _1209828))]]], (24367 ^ _779300) ^ [_1210273, _1210275, _1210277, _1210279] : [class_Fields_Ofield__inverse__zero(_1210273), -(_1210275 = c_Groups_Ozero__class_Ozero(_1210273)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210273), _1210275), _1210277)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210273), _1210275), _1210279)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210273), _1210277), _1210279))], (24377 ^ _779300) ^ [_1210435, _1210437, _1210439, _1210441] : [class_Fields_Ofield__inverse__zero(_1210435), -(_1210437 = c_Groups_Ozero__class_Ozero(_1210435)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210435), _1210439), _1210437)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210435), _1210441), _1210437)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210435), _1210439), _1210441))], (24387 ^ _779300) ^ [_1210597, _1210599, _1210601, _1210603] : [class_Fields_Ofield__inverse__zero(_1210597), 24390 ^ _779300 : [(24407 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210597), _1210599), _1210601) = _1210603), 24410 ^ _779300 : [(24411 ^ _779300) ^ [] : [_1210601 = c_Groups_Ozero__class_Ozero(_1210597)], (24413 ^ _779300) ^ [] : [_1210599 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210597), _1210603), _1210601)]], 24414 ^ _779300 : [(24415 ^ _779300) ^ [] : [-(_1210601 = c_Groups_Ozero__class_Ozero(_1210597))], (24417 ^ _779300) ^ [] : [_1210603 = c_Groups_Ozero__class_Ozero(_1210597)]]], (24391 ^ _779300) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210597), _1210599), _1210601) = _1210603, 24394 ^ _779300 : [(24395 ^ _779300) ^ [] : [-(_1210601 = c_Groups_Ozero__class_Ozero(_1210597)), -(_1210599 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210597), _1210603), _1210601))], (24401 ^ _779300) ^ [] : [_1210601 = c_Groups_Ozero__class_Ozero(_1210597), -(_1210603 = c_Groups_Ozero__class_Ozero(_1210597))]]]]], (24421 ^ _779300) ^ [_1211091, _1211093, _1211095, _1211097] : [class_Fields_Ofield__inverse__zero(_1211091), 24424 ^ _779300 : [(24441 ^ _779300) ^ [] : [-(_1211093 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1211091), _1211095), _1211097)), 24444 ^ _779300 : [(24445 ^ _779300) ^ [] : [_1211097 = c_Groups_Ozero__class_Ozero(_1211091)], (24447 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1211091), _1211093), _1211097) = _1211095]], 24448 ^ _779300 : [(24449 ^ _779300) ^ [] : [-(_1211097 = c_Groups_Ozero__class_Ozero(_1211091))], (24451 ^ _779300) ^ [] : [_1211093 = c_Groups_Ozero__class_Ozero(_1211091)]]], (24425 ^ _779300) ^ [] : [_1211093 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1211091), _1211095), _1211097), 24428 ^ _779300 : [(24429 ^ _779300) ^ [] : [-(_1211097 = c_Groups_Ozero__class_Ozero(_1211091)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1211091), _1211093), _1211097) = _1211095)], (24435 ^ _779300) ^ [] : [_1211097 = c_Groups_Ozero__class_Ozero(_1211091), -(_1211093 = c_Groups_Ozero__class_Ozero(_1211091))]]]]], (24455 ^ _779300) ^ [_1211585, _1211587, _1211589] : [class_Fields_Olinordered__field(_1211585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211585), _1211587), c_Groups_Ozero__class_Ozero(_1211585))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211585), _1211589), c_Groups_Ozero__class_Ozero(_1211585))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211585), c_Groups_Ozero__class_Ozero(_1211585)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1211585), _1211587), _1211589))))], (24469 ^ _779300) ^ [_1211840, _1211842, _1211844] : [class_Fields_Olinordered__field(_1211840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211840), _1211842), c_Groups_Ozero__class_Ozero(_1211840))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211840), c_Groups_Ozero__class_Ozero(_1211840)), _1211844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211840), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1211840), _1211842), _1211844)), c_Groups_Ozero__class_Ozero(_1211840))))], (24483 ^ _779300) ^ [_1212095, _1212097, _1212099, _1212101, _1212103] : [class_Fields_Olinordered__field(_1212095), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212095), c_Groups_Ozero__class_Ozero(_1212095)), _1212097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212095), _1212097), _1212099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212095), c_Groups_Ozero__class_Ozero(_1212095)), _1212101)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212095), _1212101), _1212103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212095), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212095), _1212097), _1212103)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212095), _1212099), _1212101))))], (24505 ^ _779300) ^ [_1212518, _1212520, _1212522, _1212524, _1212526] : [class_Fields_Olinordered__field(_1212518), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212518), c_Groups_Ozero__class_Ozero(_1212518)), _1212520)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212518), _1212520), _1212522)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212518), c_Groups_Ozero__class_Ozero(_1212518)), _1212524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212518), _1212524), _1212526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212518), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212518), _1212520), _1212526)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212518), _1212522), _1212524))))], (24527 ^ _779300) ^ [_1212941, _1212943, _1212945, _1212947, _1212949] : [class_Fields_Olinordered__field(_1212941), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212941), c_Groups_Ozero__class_Ozero(_1212941)), _1212943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212941), _1212943), _1212945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212941), c_Groups_Ozero__class_Ozero(_1212941)), _1212947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212941), _1212947), _1212949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212941), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212941), _1212943), _1212949)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212941), _1212945), _1212947))))], (24549 ^ _779300) ^ [_1213364, _1213366, _1213368] : [class_Fields_Olinordered__field(_1213364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213364), c_Groups_Ozero__class_Ozero(_1213364)), _1213366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213364), _1213368), c_Groups_Ozero__class_Ozero(_1213364))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213364), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213364), _1213366), _1213368)), c_Groups_Ozero__class_Ozero(_1213364))))], (24563 ^ _779300) ^ [_1213619, _1213621, _1213623] : [class_Fields_Olinordered__field(_1213619), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213619), c_Groups_Ozero__class_Ozero(_1213619)), _1213621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213619), c_Groups_Ozero__class_Ozero(_1213619)), _1213623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213619), c_Groups_Ozero__class_Ozero(_1213619)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213619), _1213621), _1213623))))], (24577 ^ _779300) ^ [_1213874, _1213876, _1213878, _1213880] : [class_Fields_Olinordered__field(_1213874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213874), _1213876), _1213878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213874), _1213880), c_Groups_Ozero__class_Ozero(_1213874))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213874), c_Groups_Ozero__class_Ozero(_1213874)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213874), _1213876), _1213878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213874), _1213880), _1213876)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213874), _1213880), _1213878))))], (24595 ^ _779300) ^ [_1214233, _1214235, _1214237, _1214239] : [class_Fields_Olinordered__field(_1214233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214233), _1214235), _1214237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214233), c_Groups_Ozero__class_Ozero(_1214233)), _1214239)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214233), c_Groups_Ozero__class_Ozero(_1214233)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214233), _1214237), _1214235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214233), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214233), _1214239), _1214237)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214233), _1214239), _1214235))))], (24613 ^ _779300) ^ [_1214592, _1214594, _1214596, _1214598] : [class_Fields_Olinordered__field(_1214592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214592), _1214594), c_Groups_Ozero__class_Ozero(_1214592))), 24620 ^ _779300 : [(24621 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214592), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214592), _1214596), _1214594)), _1214598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214592), _1214598), _1214594)), _1214596)))], (24627 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214592), _1214598), _1214594)), _1214596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214592), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214592), _1214596), _1214594)), _1214598)))]]], (24633 ^ _779300) ^ [_1214973, _1214975, _1214977, _1214979] : [class_Fields_Olinordered__field(_1214973), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214973), _1214975), c_Groups_Ozero__class_Ozero(_1214973))), 24640 ^ _779300 : [(24641 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214973), _1214977), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214973), _1214979), _1214975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214973), _1214979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214973), _1214977), _1214975))))], (24647 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214973), _1214979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214973), _1214977), _1214975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214973), _1214977), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214973), _1214979), _1214975))))]]], (24653 ^ _779300) ^ [_1215354, _1215356, _1215358, _1215360] : [class_Fields_Olinordered__field(_1215354), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215354), c_Groups_Ozero__class_Ozero(_1215354)), _1215356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215354), _1215358), _1215356)), _1215360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215354), _1215358), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1215354), _1215360), _1215356))))], (24667 ^ _779300) ^ [_1215623, _1215625, _1215627, _1215629] : [class_Fields_Olinordered__field(_1215623), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215623), c_Groups_Ozero__class_Ozero(_1215623)), _1215625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215623), _1215627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215623), _1215629), _1215625))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215623), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1215623), _1215627), _1215625)), _1215629)))], (24681 ^ _779300) ^ [_1215892, _1215894, _1215896, _1215898] : [class_Fields_Olinordered__field(_1215892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215892), c_Groups_Ozero__class_Ozero(_1215892)), _1215894)), 24688 ^ _779300 : [(24689 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215892), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1215892), _1215896), _1215894)), _1215898)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215892), _1215896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215892), _1215898), _1215894))))], (24695 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215892), _1215896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215892), _1215898), _1215894))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215892), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1215892), _1215896), _1215894)), _1215898)))]]], (24701 ^ _779300) ^ [_1216273, _1216275, _1216277, _1216279] : [class_Fields_Olinordered__field(_1216273), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216273), c_Groups_Ozero__class_Ozero(_1216273)), _1216275)), 24708 ^ _779300 : [(24709 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216273), _1216277), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216273), _1216279), _1216275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216273), _1216277), _1216275)), _1216279)))], (24715 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216273), _1216277), _1216275)), _1216279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216273), _1216277), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216273), _1216279), _1216275))))]]], (24721 ^ _779300) ^ [_1216654, _1216656, _1216658, _1216660] : [class_Fields_Olinordered__field__inverse__zero(_1216654), 24724 ^ _779300 : [(24751 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216654), _1216656), _1216658)), _1216660))), 24754 ^ _779300 : [(24755 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), c_Groups_Ozero__class_Ozero(_1216654)), _1216658)))], (24757 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), _1216656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216654), _1216660), _1216658)))]], 24758 ^ _779300 : [(24759 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), c_Groups_Ozero__class_Ozero(_1216654)), _1216658))], (24761 ^ _779300) ^ [] : [24762 ^ _779300 : [(24763 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), _1216658), c_Groups_Ozero__class_Ozero(_1216654))))], (24765 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216654), _1216660), _1216658)), _1216656))]], 24766 ^ _779300 : [(24767 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), _1216658), c_Groups_Ozero__class_Ozero(_1216654)))], (24769 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), c_Groups_Ozero__class_Ozero(_1216654)), _1216660))]]]]], (24725 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216654), _1216656), _1216658)), _1216660)), 24728 ^ _779300 : [(24729 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), c_Groups_Ozero__class_Ozero(_1216654)), _1216658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), _1216656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216654), _1216660), _1216658))))], (24735 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), c_Groups_Ozero__class_Ozero(_1216654)), _1216658))), 24738 ^ _779300 : [(24739 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), _1216658), c_Groups_Ozero__class_Ozero(_1216654))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216654), _1216660), _1216658)), _1216656)))], (24745 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), _1216658), c_Groups_Ozero__class_Ozero(_1216654)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216654), c_Groups_Ozero__class_Ozero(_1216654)), _1216660)))]]]]]]], (24773 ^ _779300) ^ [_1217607, _1217609, _1217611, _1217613] : [class_Fields_Olinordered__field__inverse__zero(_1217607), 24776 ^ _779300 : [(24803 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), _1217609), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217607), _1217611), _1217613)))), 24806 ^ _779300 : [(24807 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), c_Groups_Ozero__class_Ozero(_1217607)), _1217613)))], (24809 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217607), _1217609), _1217613)), _1217611))]], 24810 ^ _779300 : [(24811 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), c_Groups_Ozero__class_Ozero(_1217607)), _1217613))], (24813 ^ _779300) ^ [] : [24814 ^ _779300 : [(24815 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), _1217613), c_Groups_Ozero__class_Ozero(_1217607))))], (24817 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), _1217611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217607), _1217609), _1217613)))]], 24818 ^ _779300 : [(24819 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), _1217613), c_Groups_Ozero__class_Ozero(_1217607)))], (24821 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), _1217609), c_Groups_Ozero__class_Ozero(_1217607)))]]]]], (24777 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), _1217609), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217607), _1217611), _1217613))), 24780 ^ _779300 : [(24781 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), c_Groups_Ozero__class_Ozero(_1217607)), _1217613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217607), _1217609), _1217613)), _1217611)))], (24787 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), c_Groups_Ozero__class_Ozero(_1217607)), _1217613))), 24790 ^ _779300 : [(24791 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), _1217613), c_Groups_Ozero__class_Ozero(_1217607))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), _1217611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217607), _1217609), _1217613))))], (24797 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), _1217613), c_Groups_Ozero__class_Ozero(_1217607)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217607), _1217609), c_Groups_Ozero__class_Ozero(_1217607))))]]]]]]], (24825 ^ _779300) ^ [_1218560, _1218562, _1218564, _1218566, _1218568] : [class_Fields_Ofield(_1218560), -(_1218562 = c_Groups_Ozero__class_Ozero(_1218560)), -(_1218564 = c_Groups_Ozero__class_Ozero(_1218560)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218560), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218560), _1218566), _1218562)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218560), _1218568), _1218564)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218560), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218560), _1218566), _1218564)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218560), _1218568), _1218562))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218560), _1218562), _1218564)))], (24839 ^ _779300) ^ [_1218807, _1218809, _1218811, _1218813] : [class_Fields_Ofield(_1218807), -(_1218809 = c_Groups_Ozero__class_Ozero(_1218807)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218807), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218807), _1218811), _1218809)), _1218813) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218807), _1218811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218807), _1218809), _1218813))), _1218809))], (24849 ^ _779300) ^ [_1218985, _1218987, _1218989, _1218991] : [class_Fields_Ofield__inverse__zero(_1218985), -(_1218987 = c_Groups_Ozero__class_Ozero(_1218985)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218985), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218985), _1218989), _1218987)), _1218991) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218985), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218985), _1218989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218985), _1218991), _1218987))), _1218987))], (24859 ^ _779300) ^ [_1219163, _1219165, _1219167, _1219169] : [class_Fields_Ofield(_1219163), -(_1219165 = c_Groups_Ozero__class_Ozero(_1219163)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219163), _1219167), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219163), _1219169), _1219165)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219163), _1219165), _1219167)), _1219169)), _1219165))], (24869 ^ _779300) ^ [_1219341, _1219343, _1219345, _1219347] : [class_Fields_Ofield__inverse__zero(_1219341), -(_1219343 = c_Groups_Ozero__class_Ozero(_1219341)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219341), _1219345), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219341), _1219347), _1219343)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219341), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219341), _1219347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219341), _1219345), _1219343))), _1219343))], (24879 ^ _779300) ^ [_1219519, _1219521, _1219523, _1219525] : [class_Fields_Ofield(_1219519), -(_1219521 = c_Groups_Ozero__class_Ozero(_1219519)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1219519), _1219523), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219519), _1219525), _1219521)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219519), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1219519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219519), _1219521), _1219523)), _1219525)), _1219521))], (24889 ^ _779300) ^ [_1219697, _1219699, _1219701, _1219703] : [class_Fields_Ofield(_1219697), -(_1219699 = c_Groups_Ozero__class_Ozero(_1219697)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1219697), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219697), _1219701), _1219699)), _1219703) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219697), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1219697), _1219701), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219697), _1219699), _1219703))), _1219699))], (24899 ^ _779300) ^ [_1219875, _1219877, _1219879, _1219881, _1219883] : [class_Fields_Ofield(_1219875), -(_1219877 = c_Groups_Ozero__class_Ozero(_1219875)), -(_1219879 = c_Groups_Ozero__class_Ozero(_1219875)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1219875), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219875), _1219881), _1219877)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219875), _1219883), _1219879)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219875), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1219875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219875), _1219881), _1219879)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219875), _1219883), _1219877))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219875), _1219877), _1219879)))], (24913 ^ _779300) ^ [_1220122, _1220124, _1220126] : [class_Fields_Olinordered__field(_1220122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220122), _1220124), _1220126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220122), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220122), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220122), _1220124), _1220126)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220122), c_Groups_Oone__class_Oone(_1220122)), c_Groups_Oone__class_Oone(_1220122)))), _1220126)))], (24923 ^ _779300) ^ [_1220337, _1220339, _1220341] : [class_Fields_Olinordered__field(_1220337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220337), _1220339), _1220341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220337), _1220339), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220337), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220337), _1220339), _1220341)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220337), c_Groups_Oone__class_Oone(_1220337)), c_Groups_Oone__class_Oone(_1220337))))))], (24933 ^ _779300) ^ [_1220552, _1220554, _1220556, _1220558] : [class_Fields_Olinordered__field__inverse__zero(_1220552), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220552), _1220554), _1220556)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220552), _1220558), c_Groups_Ozero__class_Ozero(_1220552))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220552), c_Groups_Ozero__class_Ozero(_1220552)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220552), _1220554), _1220556))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220552), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220552), _1220558), _1220554)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220552), _1220558), _1220556))))], (24951 ^ _779300) ^ [_1220911, _1220913, _1220915, _1220917] : [class_Fields_Olinordered__field(_1220911), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220911), _1220913), _1220915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220911), c_Groups_Ozero__class_Ozero(_1220911)), _1220917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220911), c_Groups_Ozero__class_Ozero(_1220911)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220911), _1220915), _1220913))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220911), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220911), _1220917), _1220915)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220911), _1220917), _1220913))))], (24969 ^ _779300) ^ [_1221270, _1221272, _1221274, _1221276] : [class_Fields_Olinordered__field(_1221270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221270), _1221272), c_Groups_Ozero__class_Ozero(_1221270))), 24976 ^ _779300 : [(24977 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221270), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221270), _1221274), _1221272)), _1221276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221270), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221270), _1221276), _1221272)), _1221274)))], (24983 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221270), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221270), _1221276), _1221272)), _1221274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221270), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221270), _1221274), _1221272)), _1221276)))]]], (24989 ^ _779300) ^ [_1221651, _1221653, _1221655, _1221657] : [class_Fields_Olinordered__field(_1221651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221651), _1221653), c_Groups_Ozero__class_Ozero(_1221651))), 24996 ^ _779300 : [(24997 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221651), _1221655), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221651), _1221657), _1221653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221651), _1221657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221651), _1221655), _1221653))))], (25003 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221651), _1221657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221651), _1221655), _1221653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221651), _1221655), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221651), _1221657), _1221653))))]]], (25009 ^ _779300) ^ [_1222032, _1222034, _1222036, _1222038] : [class_Fields_Olinordered__field(_1222032), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222032), c_Groups_Ozero__class_Ozero(_1222032)), _1222034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222032), _1222036), _1222034)), _1222038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222032), _1222036), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222032), _1222038), _1222034))))], (25023 ^ _779300) ^ [_1222301, _1222303, _1222305, _1222307] : [class_Fields_Olinordered__field(_1222301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222301), c_Groups_Ozero__class_Ozero(_1222301)), _1222303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222301), _1222305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222301), _1222307), _1222303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222301), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222301), _1222305), _1222303)), _1222307)))], (25037 ^ _779300) ^ [_1222570, _1222572, _1222574, _1222576] : [class_Fields_Olinordered__field(_1222570), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222570), c_Groups_Ozero__class_Ozero(_1222570)), _1222572)), 25044 ^ _779300 : [(25045 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222570), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222570), _1222574), _1222572)), _1222576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222570), _1222574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222570), _1222576), _1222572))))], (25051 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222570), _1222574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222570), _1222576), _1222572))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222570), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222570), _1222574), _1222572)), _1222576)))]]], (25057 ^ _779300) ^ [_1222966, _1222968] : [c_Nitpick_Orefl_H(_1222966, _1222968), 25060 ^ _779300 : [(25061 ^ _779300) ^ [_1223044] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1222966, _1222966)), hAPP(hAPP(c_Product__Type_OPair(_1222966, _1222966), _1223044), _1223044)), _1222968)))]]], (25063 ^ _779300) ^ [_1223086, _1223088] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1223086, _1223086)), hAPP(hAPP(c_Product__Type_OPair(_1223086, _1223086), 25064 ^ [_1223086, _1223088]), 25064 ^ [_1223086, _1223088])), _1223088)), -(c_Nitpick_Orefl_H(_1223086, _1223088))], (25070 ^ _779300) ^ [_1223253] : [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), _1223253))), 25073 ^ _779300 : [(25074 ^ _779300) ^ [] : [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), _1223253))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223253)) = 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)))], (25080 ^ _779300) ^ [] : [-(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), _1223253)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223253)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223253)), 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), _1223253)))))]]], (25086 ^ _779300) ^ [_1223522, _1223524] : [25087 ^ _779300 : [(25088 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223522), _1223524))], (25090 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1223524), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1223522, _1223524) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223522))], (25094 ^ _779300) ^ [_1223663, _1223665] : [-(c_Divides_OposDivAlg(_1223663, _1223665) = hAPP(c_Divides_Oadjust(_1223665), c_Divides_OposDivAlg(_1223663, 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)))), _1223665)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223663), _1223665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1223665), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25104 ^ _779300) ^ [_1223732, _1223734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223732)), 25107 ^ _779300 : [(25108 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223734), _1223732)), -(c_Divides_OposDivAlg(_1223734, _1223732) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223734))], (25114 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223734), _1223732))), -(c_Divides_OposDivAlg(_1223734, _1223732) = hAPP(c_Divides_Oadjust(_1223732), c_Divides_OposDivAlg(_1223734, 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)))), _1223732))))]]], (25120 ^ _779300) ^ [_1223972, _1223974] : [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), _1223972))), 25123 ^ _779300 : [(25124 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223974)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223972))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223974), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223972)) = 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), _1223974)))], (25130 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223974)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223972)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223974), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223972)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223972)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223974), 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), _1223972)))))]]], (25136 ^ _779300) ^ [_1224290] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1224290) = 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)))], (25138 ^ _779300) ^ [_1224316, _1224318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224318)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1224316, _1224318), c_Divides_OposDivAlg(_1224316, _1224318))))], (25148 ^ _779300) ^ [_1224469, _1224471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224471)), -(c_Divides_OposDivAlg(_1224469, _1224471) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1224469), _1224471)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1224469, _1224471)))], (25184 ^ _779300) ^ [_1225023, _1225025] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225023))), 25187 ^ _779300 : [(25188 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225025)), -(c_Divides_Odivmod__int(_1225023, _1225025) = c_Divides_OnegDivAlg(_1225023, _1225025))], (25194 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225025))), -(c_Divides_Odivmod__int(_1225023, _1225025) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1225023), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1225025))))]]], (25158 ^ _779300) ^ [_1224653, _1224655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224653)), 25161 ^ _779300 : [(25162 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224655)), -(c_Divides_Odivmod__int(_1224653, _1224655) = c_Divides_OposDivAlg(_1224653, _1224655))], (25168 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224655))), 25171 ^ _779300 : [(25172 ^ _779300) ^ [] : [_1224653 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1224653, _1224655) = 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)))], (25178 ^ _779300) ^ [] : [-(_1224653 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1224653, _1224655) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1224653), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1224655))))]]]]], (25200 ^ _779300) ^ [_1225251, _1225253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1225251), _1225253)), -(c_Divides_Odivmod__nat(_1225253, _1225251) = 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), _1225253), _1225251)), _1225251))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1225253), _1225251), _1225251)))], (25210 ^ _779300) ^ [_1225462] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1225462)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1225462)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25212 ^ _779300) ^ [_1225499, _1225501] : [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), _1225499), _1225501))), 25215 ^ _779300 : [(25216 ^ _779300) ^ [] : [25217 ^ _779300 : [(25218 ^ _779300) ^ [] : [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), _1225499), _1225501)))], (25220 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225501), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1225499, _1225501) = 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), _1225499), _1225501)))], (25224 ^ _779300) ^ [] : [-(c_Divides_OnegDivAlg(_1225499, _1225501) = hAPP(c_Divides_Oadjust(_1225501), c_Divides_OnegDivAlg(_1225499, 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)))), _1225501)))), -(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), _1225499), _1225501)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225501), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25234 ^ _779300) ^ [_1225846, _1225848, _1225850] : [25236 ^ _779300 : [(25237 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1225846), 25235 ^ [_1225846, _1225848, _1225850]), _1225848)))], (25239 ^ _779300) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1225850, 25235 ^ [_1225846, _1225848, _1225850]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1225846, tc_Int_Oint), _1225850), _1225848) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1225846, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1225846), c_Int_Onat), _1225850)), _1225848)))], (25243 ^ _779300) ^ [_1226076] : [-(c_Divides_Odivmod__nat(_1226076, 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)), _1226076))], (25245 ^ _779300) ^ [_1226105, _1226107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1226105), _1226107)), -(c_Divides_Odivmod__nat(_1226105, _1226107) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1226105))], (25251 ^ _779300) ^ [_1226204, _1226206] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1226204), _1226206)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1226204), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226206)))], (25253 ^ _779300) ^ [_1226247, _1226249] : [-(c_Divides_Odivmod__nat(_1226247, _1226249) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1226247), _1226249)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1226247, _1226249)))], (25255 ^ _779300) ^ [_1226291, _1226293, _1226295] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226291), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226293)), _1226295)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1226291, _1226293), hAPP(c_Divides_OnegateSnd, _1226295))))], (25261 ^ _779300) ^ [] : [-(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))], (25263 ^ _779300) ^ [_1226435, _1226437] : [25264 ^ _779300 : [(25265 ^ _779300) ^ [] : [_1226435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25267 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1226437), _1226435))]], -(c_Divides_Odivmod__nat(_1226437, _1226435) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1226437))], (25271 ^ _779300) ^ [_1226566, _1226568] : [-(c_Divides_Odivmod__nat(_1226568, _1226566) = 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), _1226568), _1226566), _1226566))), -(_1226566 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1226568), _1226566)))], (25281 ^ _779300) ^ [_1226631, _1226633] : [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), _1226631), _1226633))), 25284 ^ _779300 : [(25285 ^ _779300) ^ [] : [25286 ^ _779300 : [(25287 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226631), _1226633))], (25289 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226633), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1226631, _1226633) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226631))], (25293 ^ _779300) ^ [] : [-(c_Divides_OposDivAlg(_1226631, _1226633) = hAPP(c_Divides_Oadjust(_1226633), c_Divides_OposDivAlg(_1226631, 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)))), _1226633)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226631), _1226633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226633), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25303 ^ _779300) ^ [_1226954, _1226956] : [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), _1226954), _1226956))), 25306 ^ _779300 : [(25307 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226956), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1226954, _1226956) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226954), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226956)))], (25313 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226956), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 25316 ^ _779300 : [(25317 ^ _779300) ^ [] : [25318 ^ _779300 : [(25319 ^ _779300) ^ [] : [_1226954 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (25321 ^ _779300) ^ [] : [_1226956 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1226954, _1226956) = 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)))], (25325 ^ _779300) ^ [] : [-(c_Nitpick_Onorm__frac(_1226954, _1226956) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1226954), _1226956)), 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), _1226954))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1226956)))), -(_1226954 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1226956 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (25335 ^ _779300) ^ [_1227446, _1227448, _1227450] : [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), _1227446), _1227448))), -(hBOOL(hAPP(hAPP(_1227450, _1227446), _1227448))), 25342 ^ _779300 : [(25343 ^ _779300) ^ [] : [-(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), 25340 ^ [_1227446, _1227448, _1227450]), 25341 ^ [_1227446, _1227448, _1227450]))))], (25355 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1227450, 25340 ^ [_1227446, _1227448, _1227450]), 25341 ^ [_1227446, _1227448, _1227450]))], (25345 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1227450, 25340 ^ [_1227446, _1227448, _1227450]), 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)))), 25341 ^ [_1227446, _1227448, _1227450])))), -(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), 25340 ^ [_1227446, _1227448, _1227450]), 25341 ^ [_1227446, _1227448, _1227450])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 25341 ^ [_1227446, _1227448, _1227450]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25359 ^ _779300) ^ [_1227941, _1227943, _1227945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1227941, tc_fun(_1227941, tc_HOL_Obool))), _1227943), _1227945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1227941, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1227941, _1227945)), c_Wellfounded_Oaccp(_1227941, _1227943))))], (25365 ^ _779300) ^ [_1228078, _1228080, _1228082, _1228084, _1228086] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1228078, _1228080), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1228082), _1228084))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1228080)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1228086), _1228078), _1228080), 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), _1228086), _1228082)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1228086), _1228084)), _1228080))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1228086), _1228084), _1228080)))))], (25375 ^ _779300) ^ [_1228347, _1228349, _1228351, _1228353] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1228347, _1228349), _1228351)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1228347, _1228349), _1228353)), -(_1228351 = _1228353)], (25385 ^ _779300) ^ [_1228504, _1228506, _1228508] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1228504, _1228506), _1228508)), -(c_Divides_Odivmod__nat(_1228504, _1228506) = _1228508)], (25391 ^ _779300) ^ [_1228599, _1228601] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1228599, _1228601), c_Divides_Odivmod__nat(_1228599, _1228601))))], (25393 ^ _779300) ^ [_1228632, _1228634] : [-(c_Divides_Odivmod__nat(_1228632, _1228634) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1228632, _1228634)))], (25395 ^ _779300) ^ [_1228666, _1228668, _1228670, _1228672] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1228666, _1228668), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1228670), _1228672))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1228666, _1228668) = _1228672)], (25401 ^ _779300) ^ [_1228777, _1228779, _1228781, _1228783] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1228777, _1228779), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1228781), _1228783))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228777), _1228779) = _1228781)], (25417 ^ _779300) ^ [_1229096, _1229098, _1229100] : [25419 ^ _779300 : [(25420 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1229098, 25418 ^ [_1229096, _1229098, _1229100]), _1229100)))], (25422 ^ _779300) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1229096, _1229098), 25418 ^ [_1229096, _1229098, _1229100]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1229096, _1229098), _1229100)))], (25407 ^ _779300) ^ [_1228910, _1228912, _1228914] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1228910, _1228912), _1228914)), 25410 ^ _779300 : [(25411 ^ _779300) ^ [_1228995] : [hBOOL(hAPP(hAPP(_1228912, _1228995), _1228914)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1228910, _1228912), _1228995)))]]], (25436 ^ _779300) ^ [_1229486, _1229488, _1229490] : [25438 ^ _779300 : [(25439 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1229488, 25437 ^ [_1229486, _1229488, _1229490]), _1229490)))], (25441 ^ _779300) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1229486, _1229488), 25437 ^ [_1229486, _1229488, _1229490]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1229486, _1229488), _1229490)))], (25426 ^ _779300) ^ [_1229300, _1229302, _1229304] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1229300, _1229302), _1229304)), 25429 ^ _779300 : [(25430 ^ _779300) ^ [_1229385] : [hBOOL(hAPP(hAPP(_1229302, _1229385), _1229304)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1229300, _1229302), _1229385)))]]], (25445 ^ _779300) ^ [_1229672, _1229674, _1229676, _1229678] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1229672, _1229674), _1229676)), hBOOL(hAPP(hAPP(_1229674, _1229678), _1229676)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1229672, _1229674), _1229678)))], (25455 ^ _779300) ^ [_1229839, _1229841] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1229839, _1229841), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1229839), _1229841)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1229839, _1229841)))))], (25457 ^ _779300) ^ [_1229885, _1229887, _1229889, _1229891, _1229893, _1229895, _1229897] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1229885, _1229887), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1229889), _1229891))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1229893, _1229887), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1229895), _1229897))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1229887)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1229885), _1229893), _1229887), 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), _1229889), _1229895)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1229891), _1229897)), _1229887))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1229891), _1229897), _1229887)))))], (25471 ^ _779300) ^ [_1230246, _1230248, _1230250, _1230252, _1230254] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1230246, _1230248), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1230250), _1230252))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1230248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1230254)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1230246, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1230248), _1230254)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1230250), _1230254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1230248), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1230250, _1230254))), _1230252)))))], (25485 ^ _779300) ^ [_1230553, _1230555, _1230557] : [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), _1230553), _1230555))), -(hBOOL(hAPP(hAPP(_1230557, _1230553), _1230555))), 25492 ^ _779300 : [(25493 ^ _779300) ^ [] : [-(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), 25490 ^ [_1230553, _1230555, _1230557]), 25491 ^ [_1230553, _1230555, _1230557]))))], (25505 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1230557, 25490 ^ [_1230553, _1230555, _1230557]), 25491 ^ [_1230553, _1230555, _1230557]))], (25495 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1230557, 25490 ^ [_1230553, _1230555, _1230557]), 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)))), 25491 ^ [_1230553, _1230555, _1230557])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 25490 ^ [_1230553, _1230555, _1230557]), 25491 ^ [_1230553, _1230555, _1230557]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 25491 ^ [_1230553, _1230555, _1230557]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25509 ^ _779300) ^ [_1231039] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1231039)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1231039)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25511 ^ _779300) ^ [_1231075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1231075)), 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), _1231075)) = 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), _1231075))))))], (25517 ^ _779300) ^ [_1231231, _1231233, _1231235, _1231237] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1231231, _1231231)), hAPP(hAPP(c_Product__Type_OPair(_1231231, _1231231), _1231233), _1231235)), hAPP(c_Wellfounded_Omeasure(_1231231), _1231237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1231237, _1231233)), hAPP(_1231237, _1231235))))], (25523 ^ _779300) ^ [_1231378, _1231380, _1231382, _1231384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1231384, _1231380)), hAPP(_1231384, _1231382))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1231378, _1231378)), hAPP(hAPP(c_Product__Type_OPair(_1231378, _1231378), _1231380), _1231382)), hAPP(c_Wellfounded_Omeasure(_1231378), _1231384))))], (25529 ^ _779300) ^ [_1231531, _1231533, _1231535] : [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), _1231531), _1231533))), -(hBOOL(hAPP(hAPP(_1231535, _1231531), _1231533))), 25536 ^ _779300 : [(25537 ^ _779300) ^ [] : [-(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), 25534 ^ [_1231531, _1231533, _1231535]), 25535 ^ [_1231531, _1231533, _1231535]))))], (25545 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1231535, 25534 ^ [_1231531, _1231533, _1231535]), 25535 ^ [_1231531, _1231533, _1231535]))], (25539 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 25535 ^ [_1231531, _1231533, _1231535]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1231535, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 25534 ^ [_1231531, _1231533, _1231535])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 25535 ^ [_1231531, _1231533, _1231535]))))]]], (25549 ^ _779300) ^ [_1232004, _1232006, _1232008, _1232010] : [-(hAPP(c_Product__Type_Osnd(_1232004, _1232006), hAPP(hAPP(c_Product__Type_OPair(_1232004, _1232006), _1232008), _1232010)) = _1232010)], (25551 ^ _779300) ^ [_1232048, _1232050, _1232052, _1232054, _1232056] : [hAPP(c_Product__Type_Osnd(_1232048, _1232050), hAPP(hAPP(c_Product__Type_OPair(_1232048, _1232050), _1232052), _1232054)) = _1232056, -(_1232054 = _1232056)], (25557 ^ _779300) ^ [_1232161, _1232163, _1232165] : [-(hAPP(c_Product__Type_Osnd(_1232161, _1232163), _1232165) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1232161, _1232163, _1232163), hAPP(c_COMBK(tc_fun(_1232163, _1232163), _1232161), c_COMBI(_1232163))), _1232165))], (25559 ^ _779300) ^ [_1232215, _1232217] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232215, _1232217) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1232215, _1232217)))], (25561 ^ _779300) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25563 ^ _779300) ^ [_1232268, _1232270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232268), 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)), _1232270)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232268, _1232270) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1232268, _1232270)))], (25573 ^ _779300) ^ [_1232431, _1232433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232433)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232431, _1232433) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1232431, _1232433)))], (25583 ^ _779300) ^ [_1232588] : [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), _1232588))), -(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), _1232588)) = 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), _1232588))))], (25589 ^ _779300) ^ [_1232705, _1232707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232705)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232707), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232705, _1232707) = 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), _1232705), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232707)))))], (25599 ^ _779300) ^ [_1232886, _1232888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232886), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232888), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232886, _1232888) = 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), _1232886), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232888)))))], (25609 ^ _779300) ^ [_1233073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233073)), 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), _1233073)) = 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), _1233073))))))], (25615 ^ _779300) ^ [_1233206, _1233208, _1233210, _1233212, _1233214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1233206, _1233208)), hAPP(_1233206, _1233210))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1233212, _1233212)), hAPP(hAPP(c_Product__Type_OPair(_1233212, _1233212), _1233208), _1233210)), _1233214)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1233212, _1233212)), hAPP(hAPP(c_Product__Type_OPair(_1233212, _1233212), _1233208), _1233210)), c_Wellfounded_Omlex__prod(_1233212, _1233206, _1233214))))], (25625 ^ _779300) ^ [_1233453, _1233455, _1233457, _1233459, _1233461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1233453, _1233455)), hAPP(_1233453, _1233457))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1233459, _1233459)), hAPP(hAPP(c_Product__Type_OPair(_1233459, _1233459), _1233455), _1233457)), c_Wellfounded_Omlex__prod(_1233459, _1233453, _1233461))))], (25631 ^ _779300) ^ [_1233604, _1233606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233604), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233606), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233604), _1233606) = 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), _1233604), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1233606)))))], (25641 ^ _779300) ^ [_1233795] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1233795)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1233795)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25643 ^ _779300) ^ [_1233833] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1233833) = _1233833)], (25645 ^ _779300) ^ [_1233859, _1233861, _1233863, _1233865, _1233867] : [hAPP(c_Product__Type_Ofst(_1233859, _1233861), hAPP(hAPP(c_Product__Type_OPair(_1233859, _1233861), _1233863), _1233865)) = _1233867, -(_1233863 = _1233867)], (25651 ^ _779300) ^ [_1233972, _1233974, _1233976, _1233978] : [-(hAPP(c_Product__Type_Ofst(_1233972, _1233974), hAPP(hAPP(c_Product__Type_OPair(_1233972, _1233974), _1233976), _1233978)) = _1233976)], (25653 ^ _779300) ^ [_1234016, _1234018, _1234020, _1234022] : [hAPP(c_Product__Type_Ofst(_1234016, _1234018), _1234020) = hAPP(c_Product__Type_Ofst(_1234016, _1234018), _1234022), hAPP(c_Product__Type_Osnd(_1234016, _1234018), _1234020) = hAPP(c_Product__Type_Osnd(_1234016, _1234018), _1234022), -(_1234020 = _1234022)], (25663 ^ _779300) ^ [_1234222, _1234224, _1234226, _1234228] : [_1234222 = _1234224, 25666 ^ _779300 : [(25667 ^ _779300) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1234226, _1234228), _1234222) = hAPP(c_Product__Type_Ofst(_1234226, _1234228), _1234224))], (25669 ^ _779300) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1234226, _1234228), _1234222) = hAPP(c_Product__Type_Osnd(_1234226, _1234228), _1234224))]]], (25671 ^ _779300) ^ [_1234373, _1234375, _1234377, _1234379] : [-(_1234373 = _1234375), hAPP(c_Product__Type_Ofst(_1234377, _1234379), _1234373) = hAPP(c_Product__Type_Ofst(_1234377, _1234379), _1234375), hAPP(c_Product__Type_Osnd(_1234377, _1234379), _1234373) = hAPP(c_Product__Type_Osnd(_1234377, _1234379), _1234375)], (25681 ^ _779300) ^ [_1234560, _1234562, _1234564] : [-(hAPP(c_Product__Type_Ofst(_1234560, _1234562), _1234564) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1234560, _1234562, _1234560), c_COMBK(_1234560, _1234562)), _1234564))], (25683 ^ _779300) ^ [_1234606, _1234608, _1234610] : [-(_1234606 = hAPP(hAPP(c_Product__Type_OPair(_1234608, _1234610), hAPP(c_Product__Type_Ofst(_1234608, _1234610), _1234606)), hAPP(c_Product__Type_Osnd(_1234608, _1234610), _1234606)))], (25685 ^ _779300) ^ [_1234654, _1234656, _1234658] : [-(hAPP(hAPP(c_Product__Type_OPair(_1234654, _1234656), hAPP(c_Product__Type_Ofst(_1234654, _1234656), _1234658)), hAPP(c_Product__Type_Osnd(_1234654, _1234656), _1234658)) = _1234658)], (25687 ^ _779300) ^ [_1234702, _1234704, _1234706, _1234708, _1234710] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1234702, _1234704, _1234706), _1234708), _1234710) = hAPP(hAPP(_1234708, hAPP(c_Product__Type_Ofst(_1234702, _1234704), _1234710)), hAPP(c_Product__Type_Osnd(_1234702, _1234704), _1234710)))], (25689 ^ _779300) ^ [_1234761, _1234763] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234761), _1234763) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1234761, _1234763)))], (25691 ^ _779300) ^ [_1234798, _1234800] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1234798, _1234800) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1234798, _1234800)))], (25693 ^ _779300) ^ [_1234833, _1234835, _1234837, _1234839, _1234841] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1234833, _1234835, _1234837), _1234839), _1234841) = hAPP(hAPP(_1234839, hAPP(c_Product__Type_Ofst(_1234833, _1234835), _1234841)), hAPP(c_Product__Type_Osnd(_1234833, _1234835), _1234841)))], (25695 ^ _779300) ^ [_1234892, _1234894, _1234896, _1234898, _1234900, _1234902] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1234892, _1234894), _1234894, _1234896), hAPP(hAPP(c_COMBB(_1234898, tc_fun(_1234894, _1234896), tc_prod(_1234892, _1234894)), _1234900), hAPP(hAPP(c_COMBB(_1234892, _1234898, tc_prod(_1234892, _1234894)), _1234902), c_Product__Type_Ofst(_1234892, _1234894)))), c_Product__Type_Osnd(_1234892, _1234894)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1234892, _1234894, _1234896), hAPP(hAPP(c_COMBB(_1234898, tc_fun(_1234894, _1234896), _1234892), _1234900), _1234902)))], (25697 ^ _779300) ^ [] : [-(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))], (25699 ^ _779300) ^ [_1235011, _1235013, _1235015, _1235017, _1235019] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1235011, _1235013, _1235015), _1235017), _1235019) = hAPP(hAPP(_1235017, hAPP(c_Product__Type_Ofst(_1235011, _1235013), _1235019)), hAPP(c_Product__Type_Osnd(_1235011, _1235013), _1235019)))], (25701 ^ _779300) ^ [_1235070, _1235072, _1235074] : [-(c_HOL_OThe(tc_prod(_1235070, _1235072), hAPP(c_Product__Type_Oprod_Oprod__case(_1235070, _1235072, tc_HOL_Obool), _1235074)) = c_HOL_OThe(tc_prod(_1235070, _1235072), hAPP(hAPP(c_COMBS(tc_prod(_1235070, _1235072), _1235072, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1235070, tc_fun(_1235072, tc_HOL_Obool), tc_prod(_1235070, _1235072)), _1235074), c_Product__Type_Ofst(_1235070, _1235072))), c_Product__Type_Osnd(_1235070, _1235072))))], (25703 ^ _779300) ^ [_1235151, _1235153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235151), 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)), _1235153)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235151), _1235153) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1235151, _1235153)))], (25713 ^ _779300) ^ [_1235318, _1235320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235320)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235318), _1235320) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1235318, _1235320)))], (25723 ^ _779300) ^ [_1235479] : [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), _1235479))), -(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), _1235479)) = 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), _1235479))))], (25729 ^ _779300) ^ [_1235594, _1235596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235596), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235594), _1235596) = 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), _1235594), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1235596)))))], (25739 ^ _779300) ^ [_1235779, _1235781, _1235783, _1235785, _1235787] : [-(c_Product__Type_Oprod_Oprod__size(_1235779, _1235781, _1235783, _1235785, _1235787) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1235783, hAPP(c_Product__Type_Ofst(_1235779, _1235781), _1235787))), hAPP(_1235785, hAPP(c_Product__Type_Osnd(_1235779, _1235781), _1235787)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25741 ^ _779300) ^ [_1235846, _1235848, _1235850, _1235852, _1235854, _1235856] : [hBOOL(hAPP(_1235846, _1235848)), hBOOL(hAPP(_1235850, _1235852)), 25748 ^ _779300 : [(25749 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1235846, hAPP(c_Product__Type_Ofst(_1235854, _1235856), hAPP(hAPP(c_Product__Type_OPair(_1235854, _1235856), _1235848), _1235852)))))], (25751 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1235850, hAPP(c_Product__Type_Osnd(_1235854, _1235856), hAPP(hAPP(c_Product__Type_OPair(_1235854, _1235856), _1235848), _1235852)))))]]], (25753 ^ _779300) ^ [_1236093, _1236095, _1236097, _1236099, _1236101] : [hBOOL(hAPP(hAPP(_1236093, _1236095), _1236097)), -(hBOOL(hAPP(hAPP(_1236093, hAPP(c_Product__Type_Osnd(_1236099, _1236101), hAPP(hAPP(c_Product__Type_OPair(_1236099, _1236101), _1236097), _1236095))), hAPP(c_Product__Type_Ofst(_1236099, _1236101), hAPP(hAPP(c_Product__Type_OPair(_1236099, _1236101), _1236097), _1236095)))))], (25759 ^ _779300) ^ [_1236256, _1236258, _1236260, _1236262, _1236264, _1236266] : [-(c_Product__Type_Oprod_Oprod__rec(_1236256, _1236258, _1236260, _1236262, hAPP(hAPP(c_Product__Type_OPair(_1236256, _1236258), _1236264), _1236266)) = hAPP(hAPP(_1236262, _1236264), _1236266))], (25761 ^ _779300) ^ [_1236343, _1236345, _1236347, _1236349, _1236351, _1236353, _1236355, _1236357] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1236343, _1236345), tc_prod(_1236343, _1236345))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1236343, _1236345), tc_prod(_1236343, _1236345)), hAPP(hAPP(c_Product__Type_OPair(_1236343, _1236345), _1236347), _1236349)), hAPP(hAPP(c_Product__Type_OPair(_1236343, _1236345), _1236351), _1236353))), c_Wellfounded_Olex__prod(_1236343, _1236345, _1236355, _1236357))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1236343, _1236343)), hAPP(hAPP(c_Product__Type_OPair(_1236343, _1236343), _1236347), _1236351)), _1236355))), 25768 ^ _779300 : [(25769 ^ _779300) ^ [] : [-(_1236347 = _1236351)], (25771 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1236345, _1236345)), hAPP(hAPP(c_Product__Type_OPair(_1236345, _1236345), _1236349), _1236353)), _1236357)))]]], (25773 ^ _779300) ^ [_1236668, _1236670, _1236672, _1236674, _1236676, _1236678, _1236680, _1236682] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1236668, _1236670), tc_prod(_1236668, _1236670))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1236668, _1236670), tc_prod(_1236668, _1236670)), hAPP(hAPP(c_Product__Type_OPair(_1236668, _1236670), _1236672), _1236674)), hAPP(hAPP(c_Product__Type_OPair(_1236668, _1236670), _1236676), _1236678))), c_Wellfounded_Olex__prod(_1236668, _1236670, _1236680, _1236682)))), 25774 ^ _779300 : [(25775 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1236668, _1236668)), hAPP(hAPP(c_Product__Type_OPair(_1236668, _1236668), _1236672), _1236676)), _1236680))], (25777 ^ _779300) ^ [] : [_1236672 = _1236676, hBOOL(hAPP(hAPP(c_member(tc_prod(_1236670, _1236670)), hAPP(hAPP(c_Product__Type_OPair(_1236670, _1236670), _1236674), _1236678)), _1236682))]]], (25785 ^ _779300) ^ [_1237043, _1237045] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237043), _1237045) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1237043, _1237045)))], (25819 ^ _779300) ^ [_1237634, _1237636, _1237638] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1237634, _1237636), _1237638))), _1237634 = 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), _1237638)), _1237636)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1237638)), 25826 ^ _779300 : [(25827 ^ _779300) ^ [] : [-(_1237636 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25829 ^ _779300) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1237638) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 25830 ^ _779300 : [(25831 ^ _779300) ^ [] : [_1237636 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25833 ^ _779300) ^ [] : [25834 ^ _779300 : [(25835 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1237636)))], (25837 ^ _779300) ^ [] : [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), _1237638))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1237638)), _1237636))]], 25842 ^ _779300 : [(25843 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1237636))], (25845 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237636), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1237638))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1237638)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (25787 ^ _779300) ^ [_1237098, _1237100, _1237102] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1237098, _1237100), _1237102)), 25790 ^ _779300 : [(25791 ^ _779300) ^ [] : [-(_1237098 = 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), _1237102)), _1237100)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1237102)))], (25793 ^ _779300) ^ [] : [_1237100 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1237102) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25799 ^ _779300) ^ [] : [-(_1237100 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25802 ^ _779300 : [(25803 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1237100)), 25806 ^ _779300 : [(25807 ^ _779300) ^ [] : [-(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), _1237102))))], (25809 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1237102)), _1237100)))]]], (25811 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1237100))), 25814 ^ _779300 : [(25815 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237100), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1237102))))], (25817 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1237102)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (25853 ^ _779300) ^ [_1238243, _1238245, _1238247, _1238249, _1238251, _1238253, _1238255] : [hBOOL(hAPP(_1238243, _1238245)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1238247, _1238247)), hAPP(hAPP(c_Product__Type_OPair(_1238247, _1238247), _1238249), _1238251)), hAPP(_1238253, _1238245))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1238255, _1238247), tc_prod(_1238255, _1238247))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1238255, _1238247), tc_prod(_1238255, _1238247)), hAPP(hAPP(c_Product__Type_OPair(_1238255, _1238247), _1238245), _1238249)), hAPP(hAPP(c_Product__Type_OPair(_1238255, _1238247), _1238245), _1238251))), c_Recdef_Osame__fst(_1238255, _1238247, _1238243, _1238253))))], (25863 ^ _779300) ^ [_1238566, _1238568, _1238570] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1238566, tc_HOL_Obool), tc_fun(_1238566, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1238566, tc_HOL_Obool), tc_fun(_1238566, tc_HOL_Obool)), _1238568), _1238570)), c_Wellfounded_Ofinite__psubset(_1238566))), 25866 ^ _779300 : [(25867 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1238566, tc_HOL_Obool)), _1238568), _1238570)))], (25869 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1238566), _1238570)))]]], (25871 ^ _779300) ^ [_1238761, _1238763, _1238765] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1238761, tc_HOL_Obool), tc_fun(_1238761, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1238761, tc_HOL_Obool), tc_fun(_1238761, tc_HOL_Obool)), _1238763), _1238765)), c_Wellfounded_Ofinite__psubset(_1238761)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1238761, tc_HOL_Obool)), _1238763), _1238765)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1238761), _1238765))], (25881 ^ _779300) ^ [_1238990, _1238992] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238990)), hAPP(c_Nat_OSuc, _1238992)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1238990))), 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, _1238992))), 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)), _1238992)))))], (25883 ^ _779300) ^ [_1239056, _1239058] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1239056)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239058)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1239058))), 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, _1239056))), 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), _1239056)), c_Int_Onat)))))], (25885 ^ _779300) ^ [_1239128, _1239130, _1239132, _1239134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1239128), _1239130)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1239132), _1239134)), -(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), _1239128), _1239132)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1239130), _1239134))), c_FunDef_Opair__less)))], (25895 ^ _779300) ^ [_1239331, _1239333, _1239335, _1239337] : [class_Orderings_Olinorder(_1239331), 25898 ^ _779300 : [(25909 ^ _779300) ^ [] : [25910 ^ _779300 : [(25911 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239331), _1239333), _1239335))], (25913 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239331), _1239333), _1239337))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239331), _1239333), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239331), _1239335), _1239337))))], (25899 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239331), _1239333), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239331), _1239335), _1239337))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239331), _1239333), _1239335))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239331), _1239333), _1239337)))]]], (25917 ^ _779300) ^ [_1239680, _1239682, _1239684, _1239686] : [class_Orderings_Olinorder(_1239680), 25920 ^ _779300 : [(25921 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239680), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239680), _1239682), _1239684)), _1239686)), 25924 ^ _779300 : [(25925 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239680), _1239682), _1239686)))], (25927 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239680), _1239684), _1239686)))]]], (25929 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239680), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239680), _1239682), _1239684)), _1239686))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239680), _1239682), _1239686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239680), _1239684), _1239686))]]], (25939 ^ _779300) ^ [_1240060, _1240062, _1240064, _1240066] : [class_Orderings_Olinorder(_1240060), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240060), _1240062), _1240064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240060), _1240062), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240060), _1240064), _1240066))))], (25949 ^ _779300) ^ [_1240239, _1240241, _1240243, _1240245] : [class_Orderings_Olinorder(_1240239), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240239), _1240241), _1240243)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240239), _1240241), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240239), _1240245), _1240243))))], (25959 ^ _779300) ^ [_1240418, _1240420] : [class_Orderings_Olinorder(_1240418), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240418), _1240420), _1240420) = _1240420)], (25965 ^ _779300) ^ [_1240509, _1240511, _1240513, _1240515] : [class_Orderings_Olinorder(_1240509), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240509), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240509), _1240511), _1240513)), _1240515) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240509), _1240511), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240509), _1240513), _1240515)))], (25971 ^ _779300) ^ [_1240652, _1240654, _1240656, _1240658] : [class_Orderings_Olinorder(_1240652), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240652), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240652), _1240654), _1240656)), _1240658) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240652), _1240654), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240652), _1240656), _1240658)))], (25977 ^ _779300) ^ [_1240795, _1240797, _1240799, _1240801] : [class_Orderings_Olinorder(_1240795), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240795), _1240797), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240795), _1240799), _1240801)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240795), _1240799), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240795), _1240797), _1240801)))], (25983 ^ _779300) ^ [_1240938, _1240940, _1240942, _1240944] : [class_Orderings_Olinorder(_1240938), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240938), _1240940), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240938), _1240942), _1240944)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240938), _1240942), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240938), _1240940), _1240944)))], (25989 ^ _779300) ^ [_1241081, _1241083, _1241085] : [class_Orderings_Olinorder(_1241081), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241081), _1241083), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241081), _1241083), _1241085)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241081), _1241083), _1241085))], (25995 ^ _779300) ^ [_1241206, _1241208, _1241210] : [class_Orderings_Olinorder(_1241206), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241206), _1241208), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241206), _1241208), _1241210)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241206), _1241208), _1241210))], (26001 ^ _779300) ^ [_1241331, _1241333, _1241335] : [class_Orderings_Olinorder(_1241331), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241331), _1241333), _1241335) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241331), _1241335), _1241333))], (26007 ^ _779300) ^ [_1241440, _1241442, _1241444] : [class_Orderings_Olinorder(_1241440), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241440), _1241442), _1241444) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241440), _1241444), _1241442))], (26013 ^ _779300) ^ [_1241549, _1241551] : [class_Orderings_Olinorder(_1241549), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241549), _1241551), _1241551) = _1241551)], (26019 ^ _779300) ^ [_1241640, _1241642] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1241640)), hAPP(c_Nat_OSuc, _1241642)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1241640), _1241642)))], (26021 ^ _779300) ^ [_1241686] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1241686) = _1241686)], (26023 ^ _779300) ^ [_1241712] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1241712), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1241712)], (26025 ^ _779300) ^ [_1241741, _1241743, _1241745, _1241747] : [class_Groups_Oordered__ab__group__add(_1241741), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1241741), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241741), _1241743), _1241745)), _1241747) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241741), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1241741), _1241743), _1241747)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1241741), _1241745), _1241747)))], (26031 ^ _779300) ^ [_1241900, _1241902, _1241904, _1241906] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1241900), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1241900), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241900), _1241902), _1241904)), _1241906) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1241900), _1241902), _1241906)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1241900), _1241904), _1241906)))], (26037 ^ _779300) ^ [_1242059, _1242061, _1242063, _1242065] : [class_Orderings_Olinorder(_1242059), 26040 ^ _779300 : [(26051 ^ _779300) ^ [] : [26052 ^ _779300 : [(26053 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242059), _1242061), _1242063))], (26055 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242059), _1242061), _1242065))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242059), _1242061), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242059), _1242063), _1242065))))], (26041 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242059), _1242061), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242059), _1242063), _1242065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242059), _1242061), _1242063))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242059), _1242061), _1242065)))]]], (26059 ^ _779300) ^ [_1242408, _1242410, _1242412, _1242414] : [class_Orderings_Olinorder(_1242408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242408), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242408), _1242410), _1242412)), _1242414)), 26066 ^ _779300 : [(26067 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242408), _1242410), _1242414)))], (26069 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242408), _1242412), _1242414)))]]], (26071 ^ _779300) ^ [_1242631, _1242633, _1242635, _1242637, _1242639] : [class_Orderings_Olinorder(_1242631), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242631), _1242633), _1242635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242631), _1242637), _1242639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242631), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242631), _1242633), _1242637)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242631), _1242635), _1242639))))], (26085 ^ _779300) ^ [_1242902, _1242904, _1242906, _1242908] : [class_Orderings_Olinorder(_1242902), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242902), _1242904), _1242906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242902), _1242908), _1242906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242902), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242902), _1242904), _1242908)), _1242906)))], (26099 ^ _779300) ^ [_1243151, _1243153, _1243155, _1243157] : [class_Orderings_Olinorder(_1243151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243151), _1243153), _1243155)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243151), _1243157), _1243155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243151), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243151), _1243153), _1243157)), _1243155)))], (26113 ^ _779300) ^ [_1243400, _1243402, _1243404] : [class_Orderings_Olinorder(_1243400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243400), _1243402), _1243404)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243400), _1243404), _1243402) = _1243404)], (26123 ^ _779300) ^ [_1243561, _1243563, _1243565] : [class_Orderings_Olinorder(_1243561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243561), _1243563), _1243565)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243561), _1243563), _1243565) = _1243565)], (26133 ^ _779300) ^ [_1243722, _1243724, _1243726, _1243728] : [class_Orderings_Olinorder(_1243722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243722), _1243724), _1243726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243722), _1243724), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243722), _1243728), _1243726))))], (26143 ^ _779300) ^ [_1243901, _1243903, _1243905, _1243907] : [class_Orderings_Olinorder(_1243901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243901), _1243903), _1243905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243901), _1243903), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243901), _1243905), _1243907))))], (26153 ^ _779300) ^ [_1244080, _1244082, _1244084, _1244086] : [class_Orderings_Olinorder(_1244080), 26156 ^ _779300 : [(26157 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244080), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244080), _1244082), _1244084)), _1244086)), 26160 ^ _779300 : [(26161 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244080), _1244082), _1244086)))], (26163 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244080), _1244084), _1244086)))]]], (26165 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244080), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244080), _1244082), _1244084)), _1244086))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244080), _1244082), _1244086)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244080), _1244084), _1244086))]]], (26175 ^ _779300) ^ [_1244460, _1244462, _1244464] : [class_Orderings_Olinorder(_1244460), 26178 ^ _779300 : [(26179 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244460), _1244462), _1244464)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244460), _1244462), _1244464) = _1244464)], (26185 ^ _779300) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244460), _1244462), _1244464) = _1244464, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244460), _1244462), _1244464)))]]], (26191 ^ _779300) ^ [_1244716, _1244718, _1244720] : [class_Orderings_Olinorder(_1244716), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244716), _1244718), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244716), _1244720), _1244718))))], (26197 ^ _779300) ^ [_1244823, _1244825, _1244827] : [class_Orderings_Olinorder(_1244823), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244823), _1244825), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244823), _1244825), _1244827))))], (26203 ^ _779300) ^ [_1244930, _1244932, _1244934] : [class_Orderings_Olinorder(_1244930), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244930), _1244932), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244930), _1244932), _1244934)) = _1244932)], (26209 ^ _779300) ^ [_1245039, _1245041, _1245043] : [class_Orderings_Olinorder(_1245039), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245039), _1245041), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245039), _1245041), _1245043)) = _1245041)], (26215 ^ _779300) ^ [_1245148, _1245150, _1245152, _1245154] : [class_Orderings_Olinorder(_1245148), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245148), _1245150), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245148), _1245152), _1245154)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245148), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245148), _1245150), _1245152)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245148), _1245150), _1245154)))], (26221 ^ _779300) ^ [_1245307, _1245309, _1245311, _1245313] : [class_Orderings_Olinorder(_1245307), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245307), _1245309), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245307), _1245311), _1245313)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245307), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245307), _1245309), _1245311)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245307), _1245309), _1245313)))], (26227 ^ _779300) ^ [_1245466, _1245468, _1245470, _1245472] : [class_Orderings_Olinorder(_1245466), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245466), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245466), _1245468), _1245470)), _1245472) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245466), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245466), _1245468), _1245472)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245466), _1245470), _1245472)))], (26233 ^ _779300) ^ [_1245625, _1245627, _1245629, _1245631] : [class_Orderings_Olinorder(_1245625), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245625), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245625), _1245627), _1245629)), _1245631) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245625), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245625), _1245627), _1245631)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245625), _1245629), _1245631)))], (26239 ^ _779300) ^ [_1245784] : [class_Orderings_Olinorder(_1245784), -(c_Finite__Set_Ofun__left__comm__idem(_1245784, _1245784, c_Orderings_Oord__class_Omax(_1245784)))], (26245 ^ _779300) ^ [_1245863, _1245865, _1245867] : [class_Int_Onumber(_1245863), class_Orderings_Oord(_1245863), 26252 ^ _779300 : [(26253 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245863), hAPP(c_Int_Onumber__class_Onumber__of(_1245863), _1245865)), hAPP(c_Int_Onumber__class_Onumber__of(_1245863), _1245867))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245863), hAPP(c_Int_Onumber__class_Onumber__of(_1245863), _1245865)), hAPP(c_Int_Onumber__class_Onumber__of(_1245863), _1245867)) = hAPP(c_Int_Onumber__class_Onumber__of(_1245863), _1245867))], (26259 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245863), hAPP(c_Int_Onumber__class_Onumber__of(_1245863), _1245865)), hAPP(c_Int_Onumber__class_Onumber__of(_1245863), _1245867)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245863), hAPP(c_Int_Onumber__class_Onumber__of(_1245863), _1245865)), hAPP(c_Int_Onumber__class_Onumber__of(_1245863), _1245867)) = hAPP(c_Int_Onumber__class_Onumber__of(_1245863), _1245865))]]], (26265 ^ _779300) ^ [_1246255, _1246257, _1246259, _1246261] : [class_Orderings_Olinorder(_1246255), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246255), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1246255), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1246255), _1246257), _1246259)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1246255), _1246257), _1246261))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1246255), _1246257), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1246255), _1246259), _1246261)))))], (26271 ^ _779300) ^ [_1246428, _1246430, _1246432, _1246434] : [class_Orderings_Olinorder(_1246428), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246428), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1246428), _1246430), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1246428), _1246432), _1246434))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1246428), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1246428), _1246430), _1246432)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1246428), _1246430), _1246434)))))], (26277 ^ _779300) ^ [_1246601, _1246603, _1246605] : [class_Groups_Olinordered__ab__group__add(_1246601), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1246601), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1246601), _1246603), _1246605)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1246601), hAPP(c_Groups_Ouminus__class_Ouminus(_1246601), _1246603)), hAPP(c_Groups_Ouminus__class_Ouminus(_1246601), _1246605)))], (26283 ^ _779300) ^ [_1246740, _1246742, _1246744] : [class_Groups_Olinordered__ab__group__add(_1246740), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1246740), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1246740), _1246742), _1246744)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1246740), hAPP(c_Groups_Ouminus__class_Ouminus(_1246740), _1246742)), hAPP(c_Groups_Ouminus__class_Ouminus(_1246740), _1246744)))], (26289 ^ _779300) ^ [_1246879, _1246881] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1246879), _1246881)), _1246881) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1246879), _1246881))], (26291 ^ _779300) ^ [_1246922, _1246924] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1246922), hAPP(c_Nat_OSuc, _1246924)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1246924), 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)), _1246924)), _1246922))], (26293 ^ _779300) ^ [_1246970, _1246972] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1246970)), _1246972) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1246970), 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), _1246970)), _1246972))], (26295 ^ _779300) ^ [_1247018] : [class_Orderings_Oord(_1247018), -(c_Orderings_Oord__class_Omax(_1247018) = c_Orderings_Oord_Omax(_1247018, c_Orderings_Oord__class_Oless__eq(_1247018)))], (26301 ^ _779300) ^ [_1247105] : [class_Orderings_Olinorder(_1247105), -(c_Orderings_Oord_Omin(_1247105, hAPP(c_COMBC(_1247105, _1247105, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1247105))) = c_Orderings_Oord__class_Omax(_1247105))], (26307 ^ _779300) ^ [_1247206, _1247208, _1247210] : [class_Orderings_Olinorder(_1247206), hBOOL(hAPP(c_Finite__Set_Ofinite(_1247206), _1247208)), hBOOL(hAPP(hAPP(c_member(_1247206), _1247210), _1247208)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1247206), _1247210), c_Big__Operators_Olattice_OInf__fin(_1247206, c_Orderings_Oord__class_Omin(_1247206), _1247208)) = _1247210)], (26321 ^ _779300) ^ [_1247441, _1247443, _1247445, _1247447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1247441), _1247443)), -(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), _1247441), _1247445)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1247443), _1247447))), c_FunDef_Opair__less)))], (26327 ^ _779300) ^ [_1247578, _1247580, _1247582, _1247584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1247578), _1247580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1247582), _1247584)), -(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), _1247578), _1247582)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1247580), _1247584))), c_FunDef_Opair__leq)))], (26337 ^ _779300) ^ [_1247781, _1247783, _1247785, _1247787] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1247781), _1247783)), 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)), _1247785), _1247781)), 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)), _1247787), _1247783)), 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)), _1247785), _1247787)), _1247783)), c_FunDef_Omax__strict)))], (26351 ^ _779300) ^ [_1248062, _1248064, _1248066, _1248068] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1248062), _1248064)), 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)), _1248062), _1248066)), 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)), _1248064), _1248068)), 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)), _1248064), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1248066), _1248068))), c_FunDef_Omin__strict)))], (26365 ^ _779300) ^ [_1248343, _1248345, _1248347, _1248349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1248343), _1248345)), -(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), _1248343), _1248347)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1248345), _1248349))), c_FunDef_Opair__leq)))], (26371 ^ _779300) ^ [_1248480, _1248482, _1248484] : [class_Orderings_Olinorder(_1248480), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248480), _1248482)), hBOOL(hAPP(hAPP(c_member(_1248480), _1248484), _1248482)), 26382 ^ _779300 : [(26383 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248480, tc_HOL_Obool)), _1248482), hAPP(hAPP(c_Set_Oinsert(_1248480), _1248484), c_Orderings_Obot__class_Obot(tc_fun(_1248480, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1248480, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1248480, _1248482) = _1248484)], (26389 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248480, tc_HOL_Obool)), _1248482), hAPP(hAPP(c_Set_Oinsert(_1248480), _1248484), c_Orderings_Obot__class_Obot(tc_fun(_1248480, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1248480, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1248480, _1248482) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1248480), _1248484), c_Big__Operators_Olinorder__class_OMax(_1248480, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248480, tc_HOL_Obool)), _1248482), hAPP(hAPP(c_Set_Oinsert(_1248480), _1248484), c_Orderings_Obot__class_Obot(tc_fun(_1248480, tc_HOL_Obool)))))))]]], (26395 ^ _779300) ^ [_1248986] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1248986)), -(_1248986 = 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))), _1248986)), c_FunDef_Omax__strict)))], (26405 ^ _779300) ^ [_1249092] : [-(_1249092 = 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)), _1249092), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (26411 ^ _779300) ^ [_1249137, _1249139] : [class_Orderings_Olinorder(_1249137), -(c_Big__Operators_Olinorder__class_OMax(_1249137, hAPP(hAPP(c_Set_Oinsert(_1249137), _1249139), c_Orderings_Obot__class_Obot(tc_fun(_1249137, tc_HOL_Obool)))) = _1249139)], (26417 ^ _779300) ^ [_1249244, _1249246, _1249248] : [class_Orderings_Olinorder(_1249244), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249244), _1249246)), hBOOL(hAPP(hAPP(c_member(_1249244), _1249248), _1249246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249244), _1249248), c_Big__Operators_Olinorder__class_OMax(_1249244, _1249246))))], (26431 ^ _779300) ^ [_1249471, _1249473] : [class_Orderings_Olinorder(_1249471), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249471), _1249473)), -(_1249473 = c_Orderings_Obot__class_Obot(tc_fun(_1249471, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1249471), c_Big__Operators_Olinorder__class_OMax(_1249471, _1249473)), _1249473)))], (26445 ^ _779300) ^ [_1249651, _1249653, _1249655] : [class_Orderings_Olinorder(_1249651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249651), _1249653)), hBOOL(hAPP(hAPP(c_member(_1249651), _1249655), _1249653)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1249651), _1249655), c_Big__Operators_Olinorder__class_OMax(_1249651, _1249653)) = c_Big__Operators_Olinorder__class_OMax(_1249651, _1249653))], (26459 ^ _779300) ^ [_1249886, _1249888] : [class_Orderings_Olinorder(_1249886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249886), _1249888)), -(c_Big__Operators_Olinorder__class_OMax(_1249886, _1249888) = hAPP(c_Finite__Set_Ofold1(_1249886, c_Orderings_Oord__class_Omax(_1249886)), _1249888))], (26469 ^ _779300) ^ [_1250043, _1250045, _1250047] : [class_Orderings_Olinorder(_1250043), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1250043, tc_HOL_Obool)), _1250045), _1250047)), -(_1250045 = c_Orderings_Obot__class_Obot(tc_fun(_1250043, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250043), _1250047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250043), c_Big__Operators_Olinorder__class_OMax(_1250043, _1250045)), c_Big__Operators_Olinorder__class_OMax(_1250043, _1250047))))], (26487 ^ _779300) ^ [_1250349, _1250351, _1250353] : [class_Orderings_Olinorder(_1250349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250349), _1250351)), -(_1250351 = c_Orderings_Obot__class_Obot(tc_fun(_1250349, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1250349, hAPP(hAPP(c_Set_Oinsert(_1250349), _1250353), _1250351)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1250349), _1250353), c_Big__Operators_Olinorder__class_OMax(_1250349, _1250351)))], (26501 ^ _779300) ^ [_1250557, _1250559, _1250561] : [class_Orderings_Olinorder(_1250557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250557), _1250559)), -(_1250561 = c_Orderings_Obot__class_Obot(tc_fun(_1250557, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1250557, tc_HOL_Obool)), _1250561), _1250559)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1250557), c_Big__Operators_Olinorder__class_OMax(_1250557, _1250561)), c_Big__Operators_Olinorder__class_OMax(_1250557, _1250559)) = c_Big__Operators_Olinorder__class_OMax(_1250557, _1250559))], (26519 ^ _779300) ^ [_1250871, _1250873, _1250875] : [class_Orderings_Olinorder(_1250871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250871), _1250873)), -(hBOOL(hAPP(hAPP(c_member(_1250871), _1250875), _1250873))), -(_1250873 = c_Orderings_Obot__class_Obot(tc_fun(_1250871, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1250871, hAPP(hAPP(c_Set_Oinsert(_1250871), _1250875), _1250873)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1250871), _1250875), c_Big__Operators_Olinorder__class_OMax(_1250871, _1250873)))], (26537 ^ _779300) ^ [_1251108, _1251110, _1251112] : [class_Orderings_Olinorder(_1251108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251108), _1251110)), 26544 ^ _779300 : [(26545 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1251108, tc_HOL_Obool)), _1251110), hAPP(hAPP(c_Set_Oinsert(_1251108), _1251112), c_Orderings_Obot__class_Obot(tc_fun(_1251108, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1251108, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1251108, hAPP(hAPP(c_Set_Oinsert(_1251108), _1251112), _1251110)) = _1251112)], (26551 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1251108, tc_HOL_Obool)), _1251110), hAPP(hAPP(c_Set_Oinsert(_1251108), _1251112), c_Orderings_Obot__class_Obot(tc_fun(_1251108, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1251108, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1251108, hAPP(hAPP(c_Set_Oinsert(_1251108), _1251112), _1251110)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1251108), _1251112), c_Big__Operators_Olinorder__class_OMax(_1251108, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1251108, tc_HOL_Obool)), _1251110), hAPP(hAPP(c_Set_Oinsert(_1251108), _1251112), c_Orderings_Obot__class_Obot(tc_fun(_1251108, tc_HOL_Obool)))))))]]], (26557 ^ _779300) ^ [_1251578, _1251580] : [class_Groups_Olinordered__ab__group__add(_1251578), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251578), _1251580)), -(_1251580 = c_Orderings_Obot__class_Obot(tc_fun(_1251578, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1251578), c_Big__Operators_Olinorder__class_OMax(_1251578, _1251580)) = c_Big__Operators_Olinorder__class_OMin(_1251578, hAPP(c_Set_Oimage(_1251578, _1251578, c_Groups_Ouminus__class_Ouminus(_1251578)), _1251580)))], (26571 ^ _779300) ^ [_1251778, _1251780] : [class_Groups_Olinordered__ab__group__add(_1251778), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251778), 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tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1251980), _1251984)), 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)), _1251980), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1251982), _1251984))), c_FunDef_Omin__weak)))], (26599 ^ _779300) ^ [_1252259, _1252261, _1252263, _1252265] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1252259), _1252261)), 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)), _1252263), _1252259)), 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)), _1252265), _1252261)), 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)), _1252263), _1252265)), _1252261)), c_FunDef_Omax__weak)))], (26613 ^ _779300) ^ [_1252540, _1252542] : [class_Orderings_Olinorder(_1252540), hBOOL(hAPP(c_Finite__Set_Ofinite(_1252540), _1252542)), -(_1252542 = c_Orderings_Obot__class_Obot(tc_fun(_1252540, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1252540), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1252540), 26626 ^ [_1252540, _1252542]), 26627 ^ [_1252540, _1252542])), hAPP(hAPP(c_Set_Oinsert(_1252540), 26626 ^ [_1252540, _1252542]), hAPP(hAPP(c_Set_Oinsert(_1252540), 26627 ^ [_1252540, _1252542]), c_Orderings_Obot__class_Obot(tc_fun(_1252540, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1252540), c_Big__Operators_Olinorder__class_OMax(_1252540, _1252542)), _1252542)))], (26633 ^ _779300) ^ [_1252984] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1252984)), -(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))), _1252984)), c_FunDef_Omax__weak)))], (26639 ^ _779300) ^ [_1253079] : [-(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)), _1253079), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (26641 ^ _779300) ^ [] : [-(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)))], (26643 ^ _779300) ^ [] : [-(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)))], (26645 ^ _779300) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (26647 ^ _779300) ^ [_1253182, _1253184] : [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), _1253182), _1253184)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1253182), _1253184)))], (26653 ^ _779300) ^ [_1253287, _1253289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1253287), _1253289)), -(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), _1253287), _1253289)), c_Wellfounded_Oless__than)))], (26659 ^ _779300) ^ [_1253419, _1253421, _1253423, _1253425] : [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), _1253419), _1253421)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1253423), _1253425))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253419), _1253425) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253423), _1253421))], (26665 ^ _779300) ^ [_1253566, _1253568, _1253570, _1253572] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253566), _1253572) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253570), _1253568), -(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), _1253566), _1253568)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1253570), _1253572))), c_Int_Ointrel)))], (26671 ^ _779300) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (26673 ^ _779300) ^ [_1253737, _1253739, _1253741] : [-(c_Wellfounded_Omlex__prod(_1253737, _1253739, _1253741) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1253737), _1253737), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1253737, c_Wellfounded_Oless__than, _1253741)), hAPP(hAPP(c_COMBS(_1253737, _1253737, tc_prod(tc_Nat_Onat, _1253737)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1253737, tc_prod(tc_Nat_Onat, _1253737)), _1253737), c_Product__Type_OPair(tc_Nat_Onat, _1253737)), _1253739)), c_COMBI(_1253737))))], (26675 ^ _779300) ^ [] : [-(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)))))], (26677 ^ _779300) ^ [_1253837, _1253839] : [class_Orderings_Olinorder(_1253837), hBOOL(hAPP(c_Finite__Set_Ofinite(_1253837), _1253839)), -(_1253839 = c_Orderings_Obot__class_Obot(tc_fun(_1253837, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253837), c_Big__Operators_Olattice_OInf__fin(_1253837, c_Orderings_Oord__class_Omin(_1253837), _1253839)), c_Big__Operators_Olattice_OSup__fin(_1253837, c_Orderings_Oord__class_Omax(_1253837), _1253839))))], (26691 ^ _779300) ^ [_1254035, _1254037, _1254039] : [class_Orderings_Olinorder(_1254035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1254035), _1254037)), hBOOL(hAPP(hAPP(c_member(_1254035), _1254039), _1254037)), 26702 ^ _779300 : [(26703 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1254035, tc_HOL_Obool)), _1254037), hAPP(hAPP(c_Set_Oinsert(_1254035), _1254039), c_Orderings_Obot__class_Obot(tc_fun(_1254035, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1254035, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1254035, c_Orderings_Oord__class_Omax(_1254035), _1254037) = _1254039)], (26709 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1254035, tc_HOL_Obool)), _1254037), hAPP(hAPP(c_Set_Oinsert(_1254035), _1254039), c_Orderings_Obot__class_Obot(tc_fun(_1254035, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1254035, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1254035, c_Orderings_Oord__class_Omax(_1254035), _1254037) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1254035), _1254039), c_Big__Operators_Olattice_OSup__fin(_1254035, c_Orderings_Oord__class_Omax(_1254035), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1254035, tc_HOL_Obool)), _1254037), hAPP(hAPP(c_Set_Oinsert(_1254035), _1254039), c_Orderings_Obot__class_Obot(tc_fun(_1254035, tc_HOL_Obool)))))))]]], (26715 ^ _779300) ^ [_1254559, _1254561, _1254563, _1254565] : [c_FunDef_Oreduction__pair(_1254559, _1254561), -(c_FunDef_Oreduction__pair(_1254563, hAPP(hAPP(c_FunDef_Orp__inv__image(_1254559, _1254563), _1254561), _1254565)))], (26721 ^ _779300) ^ [_1254658, _1254660, _1254662, _1254664] : [26722 ^ _779300 : [(26723 ^ _779300) ^ [] : [hBOOL(hAPP(_1254658, _1254660))], (26725 ^ _779300) ^ [] : [hBOOL(hAPP(_1254662, _1254660))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254664, tc_HOL_Obool)), _1254662), _1254658), _1254660)))], (26729 ^ _779300) ^ [_1254813, _1254815, _1254817, _1254819] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254813, tc_HOL_Obool)), _1254815), _1254817), _1254819)), -(hBOOL(hAPP(_1254815, _1254819))), -(hBOOL(hAPP(_1254817, _1254819)))], (26739 ^ _779300) ^ [_1254943, _1254945, _1254947, _1254949] : [26740 ^ _779300 : [(26741 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254943), _1254945), _1254947))], (26743 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254943), _1254945), _1254949))]], -(hBOOL(hAPP(hAPP(c_member(_1254943), _1254945), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254943, tc_HOL_Obool)), _1254949), _1254947))))], (26747 ^ _779300) ^ [_1255128, _1255130, _1255132, _1255134] : [hBOOL(hAPP(hAPP(c_member(_1255128), _1255130), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255128, tc_HOL_Obool)), _1255132), _1255134))), -(hBOOL(hAPP(hAPP(c_member(_1255128), _1255130), _1255132))), -(hBOOL(hAPP(hAPP(c_member(_1255128), _1255130), _1255134)))], (26757 ^ _779300) ^ [_1255288, _1255290, _1255292, _1255294] : [hBOOL(hAPP(hAPP(c_member(_1255288), _1255290), _1255292)), -(hBOOL(hAPP(hAPP(c_member(_1255288), _1255290), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255288, tc_HOL_Obool)), _1255294), _1255292))))], (26763 ^ _779300) ^ [_1255419, _1255421, _1255423, _1255425] : [hBOOL(hAPP(hAPP(c_member(_1255419), _1255421), _1255423)), -(hBOOL(hAPP(hAPP(c_member(_1255419), _1255421), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255419, tc_HOL_Obool)), _1255423), _1255425))))], (26779 ^ _779300) ^ [_1255725, _1255727, _1255729, _1255731] : [26780 ^ _779300 : [(26781 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1255725), _1255727), _1255729))], (26783 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1255725), _1255727), _1255731))]], -(hBOOL(hAPP(hAPP(c_member(_1255725), _1255727), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255725, tc_HOL_Obool)), _1255729), _1255731))))], (26769 ^ _779300) ^ [_1255571, _1255573, _1255575, _1255577] : [hBOOL(hAPP(hAPP(c_member(_1255571), _1255573), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255571, tc_HOL_Obool)), _1255575), _1255577))), -(hBOOL(hAPP(hAPP(c_member(_1255571), _1255573), _1255575))), -(hBOOL(hAPP(hAPP(c_member(_1255571), _1255573), _1255577)))], (26787 ^ _779300) ^ [_1255910] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1255910) = c_Orderings_Oord__class_Omax(_1255910)), class_Lattices_Osemilattice__sup(_1255910), class_Orderings_Olinorder(_1255910)], (26797 ^ _779300) ^ [_1256039, _1256041, _1256043, _1256045] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256039, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1256039), _1256041), _1256043)), _1256045) = hAPP(hAPP(c_Set_Oinsert(_1256039), _1256041), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256039, tc_HOL_Obool)), _1256043), _1256045)))], (26799 ^ _779300) ^ [_1256106, _1256108, _1256110, _1256112] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256106, tc_HOL_Obool)), _1256108), hAPP(hAPP(c_Set_Oinsert(_1256106), _1256110), _1256112)) = hAPP(hAPP(c_Set_Oinsert(_1256106), _1256110), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256106, tc_HOL_Obool)), _1256108), _1256112)))], (26801 ^ _779300) ^ [_1256173, _1256175, _1256177, _1256179, _1256181] : [class_Lattices_Olattice(_1256173), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256175, _1256173)), _1256177), _1256179), _1256181) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256173), hAPP(_1256177, _1256181)), hAPP(_1256179, _1256181)))], (26807 ^ _779300) ^ [_1256310, _1256312, _1256314] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256310, tc_HOL_Obool)), _1256312), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1256310, tc_HOL_Obool)), _1256314), _1256312)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256310, tc_HOL_Obool)), _1256312), _1256314))], (26809 ^ _779300) ^ [_1256370, _1256372, _1256374] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256370, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1256370, tc_HOL_Obool)), _1256372), _1256374)), _1256374) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256370, tc_HOL_Obool)), _1256372), _1256374))], (26811 ^ _779300) ^ [_1256430, _1256432, _1256434, _1256436] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1256430, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256430, tc_HOL_Obool)), _1256432), _1256434)), _1256436) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256430, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1256430, tc_HOL_Obool)), _1256432), _1256436)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1256430, tc_HOL_Obool)), _1256434), _1256436)))], (26813 ^ _779300) ^ [_1256514, _1256516, _1256518] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256514, tc_HOL_Obool)), _1256516), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256514, tc_HOL_Obool)), _1256516), _1256518))))], (26815 ^ _779300) ^ [_1256562, _1256564, _1256566] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256562, tc_HOL_Obool)), _1256564), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256562, tc_HOL_Obool)), _1256566), _1256564))))], (26817 ^ _779300) ^ [_1256628, _1256630, _1256632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256628, tc_HOL_Obool)), _1256630), _1256632)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256628, tc_HOL_Obool)), _1256630), _1256632) = _1256632)], (26823 ^ _779300) ^ [_1256745, _1256747, _1256749] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256745, tc_HOL_Obool)), _1256747), _1256749) = _1256749, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256745, tc_HOL_Obool)), _1256747), _1256749)))], (26829 ^ _779300) ^ [_1256868, _1256870, _1256872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256868, tc_HOL_Obool)), _1256870), _1256872)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256868, tc_HOL_Obool)), _1256870), _1256872) = _1256872)], (26835 ^ _779300) ^ [_1256989, _1256991, _1256993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1256989, tc_HOL_Obool)), _1256991), _1256993)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256989, tc_HOL_Obool)), _1256993), _1256991) = _1256993)], (26841 ^ _779300) ^ [_1257110, _1257112, _1257114, _1257116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257110, tc_HOL_Obool)), _1257112), _1257114)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257110, tc_HOL_Obool)), _1257116), _1257114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257110, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257110, tc_HOL_Obool)), _1257112), _1257116)), _1257114)))], (26851 ^ _779300) ^ [_1257329, _1257331, _1257333, _1257335, _1257337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257329, tc_HOL_Obool)), _1257331), _1257333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257329, tc_HOL_Obool)), _1257335), _1257337)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257329, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257329, tc_HOL_Obool)), _1257331), _1257335)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257329, tc_HOL_Obool)), _1257333), _1257337))))], (26861 ^ _779300) ^ [_1257574, _1257576] : [class_Lattices_Olattice(_1257574), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257574), _1257576), _1257576) = _1257576)], (26867 ^ _779300) ^ [_1257665, _1257667, _1257669, _1257671, _1257673] : [class_Lattices_Olattice(_1257665), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257667, _1257665)), _1257669), _1257671), _1257673) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257665), hAPP(_1257669, _1257673)), hAPP(_1257671, _1257673)))], (26873 ^ _779300) ^ [_1257802, _1257804, _1257806, _1257808] : [class_Lattices_Osemilattice__sup(_1257802), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257802), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257802), _1257804), _1257806)), _1257808) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257802), _1257804), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257802), _1257806), _1257808)))], (26879 ^ _779300) ^ [_1257945, _1257947, _1257949, _1257951] : [class_Lattices_Olattice(_1257945), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257945), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257945), _1257947), _1257949)), _1257951) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257945), _1257947), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257945), _1257949), _1257951)))], (26885 ^ _779300) ^ [_1258088, _1258090, _1258092, _1258094] : [class_Lattices_Osemilattice__sup(_1258088), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258088), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258088), _1258090), _1258092)), _1258094) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258088), _1258090), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258088), _1258092), _1258094)))], (26891 ^ _779300) ^ [_1258231, _1258233, _1258235, _1258237] : [class_Lattices_Osemilattice__sup(_1258231), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258231), _1258233), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258231), _1258235), _1258237)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258231), _1258235), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258231), _1258233), _1258237)))], (26897 ^ _779300) ^ [_1258374, _1258376, _1258378, _1258380] : [class_Lattices_Olattice(_1258374), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258374), _1258376), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258374), _1258378), _1258380)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258374), _1258378), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258374), _1258376), _1258380)))], (26903 ^ _779300) ^ [_1258517, _1258519, _1258521, _1258523] : [class_Lattices_Osemilattice__sup(_1258517), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258517), _1258519), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258517), _1258521), _1258523)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258517), _1258521), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258517), _1258519), _1258523)))], (26909 ^ _779300) ^ [_1258660, _1258662, _1258664] : [class_Lattices_Osemilattice__sup(_1258660), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258660), _1258662), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258660), _1258662), _1258664)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258660), _1258662), _1258664))], (26915 ^ _779300) ^ [_1258785, _1258787, _1258789] : [class_Lattices_Olattice(_1258785), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258785), _1258787), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258785), _1258787), _1258789)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258785), _1258787), _1258789))], (26921 ^ _779300) ^ [_1258910, _1258912, _1258914] : [class_Lattices_Osemilattice__sup(_1258910), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258910), _1258912), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258910), _1258912), _1258914)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258910), _1258912), _1258914))], (26927 ^ _779300) ^ [_1259035, _1259037, _1259039] : [class_Lattices_Osemilattice__sup(_1259035), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259035), _1259037), _1259039) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259035), _1259039), _1259037))], (26933 ^ _779300) ^ [_1259144, _1259146, _1259148] : [class_Lattices_Olattice(_1259144), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259144), _1259146), _1259148) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259144), _1259148), _1259146))], (26939 ^ _779300) ^ [_1259253, _1259255, _1259257] : [class_Lattices_Osemilattice__sup(_1259253), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259253), _1259255), _1259257) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259253), _1259257), _1259255))], (26945 ^ _779300) ^ [_1259362, _1259364] : [class_Lattices_Osemilattice__sup(_1259362), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259362), _1259364), _1259364) = _1259364)], (26951 ^ _779300) ^ [_1259453, _1259455] : [class_Lattices_Osemilattice__sup(_1259453), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259453), _1259455), _1259455) = _1259455)], (26957 ^ _779300) ^ [_1259544, _1259546, _1259548, _1259550] : [hBOOL(hAPP(_1259544, _1259546)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259548, tc_HOL_Obool)), _1259550), _1259544), _1259546)))], (26963 ^ _779300) ^ [_1259655, _1259657, _1259659, _1259661] : [hBOOL(hAPP(_1259655, _1259657)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259659, tc_HOL_Obool)), _1259655), _1259661), _1259657)))], (26988 ^ _779300) ^ [_1260209, _1260211, _1260213, _1260215] : [26992 ^ _779300 : [(26993 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1260209), 26991 ^ [_1260209, _1260211, _1260213, _1260215]), _1260211)))], (26995 ^ _779300) ^ [] : [hBOOL(hAPP(_1260215, 26991 ^ [_1260209, _1260211, _1260213, _1260215]))]], 26997 ^ _779300 : [(26998 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1260209), 26996 ^ [_1260209, _1260211, _1260213, _1260215]), _1260213)))], (27000 ^ _779300) ^ [] : [hBOOL(hAPP(_1260215, 26996 ^ [_1260209, _1260211, _1260213, _1260215]))]], 27001 ^ _779300 : [(27002 ^ _779300) ^ [_1260542] : [hBOOL(hAPP(hAPP(c_member(_1260209), _1260542), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260209, tc_HOL_Obool)), _1260211), _1260213))), -(hBOOL(hAPP(_1260215, _1260542)))]]], (26969 ^ _779300) ^ [_1259787, _1259789, _1259791, _1259793] : [26971 ^ _779300 : [(26972 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1259787), 26970 ^ [_1259787, _1259789, _1259791, _1259793]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259787, tc_HOL_Obool)), _1259789), _1259791))))], (26974 ^ _779300) ^ [] : [hBOOL(hAPP(_1259793, 26970 ^ [_1259787, _1259789, _1259791, _1259793]))]], 26975 ^ _779300 : [(26976 ^ _779300) ^ [_1260007] : [hBOOL(hAPP(hAPP(c_member(_1259787), _1260007), _1259789)), -(hBOOL(hAPP(_1259793, _1260007)))], (26982 ^ _779300) ^ [_1260104] : [hBOOL(hAPP(hAPP(c_member(_1259787), _1260104), _1259791)), -(hBOOL(hAPP(_1259793, _1260104)))]]], (27008 ^ _779300) ^ [_1260694, _1260696, _1260698, _1260700] : [27009 ^ _779300 : [(27010 ^ _779300) ^ [_1260804] : [hBOOL(hAPP(hAPP(c_member(_1260694), _1260804), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260694, tc_HOL_Obool)), _1260696), _1260698))), hBOOL(hAPP(_1260700, _1260804))]], 27018 ^ _779300 : [(27019 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1260694), 27017 ^ [_1260694, _1260696, _1260698, _1260700]), _1260696)))], (27021 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1260700, 27017 ^ [_1260694, _1260696, _1260698, _1260700])))]], 27023 ^ _779300 : [(27024 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1260694), 27022 ^ [_1260694, _1260696, _1260698, _1260700]), _1260698)))], (27026 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1260700, 27022 ^ [_1260694, _1260696, _1260698, _1260700])))]]], (27028 ^ _779300) ^ [_1261093, _1261095, _1261097, _1261099] : [27042 ^ _779300 : [(27043 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1261093), 27041 ^ [_1261093, _1261095, _1261097, _1261099]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261093, tc_HOL_Obool)), _1261095), _1261097))))], (27045 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1261099, 27041 ^ [_1261093, _1261095, _1261097, _1261099])))]], 27029 ^ _779300 : [(27030 ^ _779300) ^ [_1261206] : [hBOOL(hAPP(hAPP(c_member(_1261093), _1261206), _1261095)), hBOOL(hAPP(_1261099, _1261206))], (27036 ^ _779300) ^ [_1261302] : [hBOOL(hAPP(hAPP(c_member(_1261093), _1261302), _1261097)), hBOOL(hAPP(_1261099, _1261302))]]], (27047 ^ _779300) ^ [_1261496, _1261498, _1261500, _1261502] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261496, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261496, tc_HOL_Obool)), _1261498), _1261500)), _1261502) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261496, tc_HOL_Obool)), _1261498), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261496, tc_HOL_Obool)), _1261500), _1261502)))], (27049 ^ _779300) ^ [_1261569, _1261571, _1261573, _1261575] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261569, tc_HOL_Obool)), _1261571), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261569, tc_HOL_Obool)), _1261573), _1261575)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261569, tc_HOL_Obool)), _1261573), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261569, tc_HOL_Obool)), _1261571), _1261575)))], (27051 ^ _779300) ^ [_1261642, _1261644, _1261646] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261642, tc_HOL_Obool)), _1261644), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261642, tc_HOL_Obool)), _1261644), _1261646)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261642, tc_HOL_Obool)), _1261644), _1261646))], (27053 ^ _779300) ^ [_1261702, _1261704, _1261706] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261702, tc_HOL_Obool)), _1261704), _1261706) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261702, tc_HOL_Obool)), _1261706), _1261704))], (27055 ^ _779300) ^ [_1261751, _1261753] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261751, tc_HOL_Obool)), _1261753), _1261753) = _1261753)], (27057 ^ _779300) ^ [_1261787, _1261789, _1261791, _1261793] : [class_Lattices_Osemilattice__sup(_1261787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261787), _1261789), _1261791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261787), _1261789), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1261787), _1261791), _1261793))))], (27067 ^ _779300) ^ [_1261966, _1261968, _1261970, _1261972] : [class_Lattices_Osemilattice__sup(_1261966), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261966), _1261968), _1261970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261966), _1261968), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1261966), _1261972), _1261970))))], (27077 ^ _779300) ^ [_1262145, _1262147, _1262149, _1262151] : [class_Lattices_Osemilattice__sup(_1262145), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262145), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262145), _1262147), _1262149)), _1262151)), 27084 ^ _779300 : [(27085 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262145), _1262147), _1262151)))], (27087 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262145), _1262149), _1262151)))]]], (27089 ^ _779300) ^ [_1262368, _1262370, _1262372, _1262374, _1262376] : [class_Lattices_Osemilattice__sup(_1262368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262368), _1262370), _1262372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262368), _1262374), _1262376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262368), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262368), _1262370), _1262374)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262368), _1262372), _1262376))))], (27103 ^ _779300) ^ [_1262639, _1262641, _1262643, _1262645] : [class_Lattices_Osemilattice__sup(_1262639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262639), _1262641), _1262643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262639), _1262645), _1262643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262639), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262639), _1262641), _1262645)), _1262643)))], (27117 ^ _779300) ^ [_1262888, _1262890, _1262892, _1262894] : [class_Lattices_Osemilattice__sup(_1262888), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262888), _1262890), _1262892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262888), _1262894), _1262892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262888), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262888), _1262890), _1262894)), _1262892)))], (27131 ^ _779300) ^ [_1263137, _1263139, _1263141] : [class_Lattices_Osemilattice__sup(_1263137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263137), _1263139), _1263141)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263137), _1263141), _1263139) = _1263141)], (27141 ^ _779300) ^ [_1263298, _1263300, _1263302] : [class_Lattices_Osemilattice__sup(_1263298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263298), _1263300), _1263302)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263298), _1263300), _1263302) = _1263302)], (27151 ^ _779300) ^ [_1263459, _1263461, _1263463, _1263465] : [class_Lattices_Osemilattice__sup(_1263459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263459), _1263461), _1263463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263459), _1263461), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263459), _1263465), _1263463))))], (27161 ^ _779300) ^ [_1263638, _1263640, _1263642, _1263644] : [class_Lattices_Osemilattice__sup(_1263638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263638), _1263640), _1263642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263638), _1263640), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263638), _1263642), _1263644))))], (27171 ^ _779300) ^ [_1263817, _1263819, _1263821, _1263823] : [class_Lattices_Osemilattice__sup(_1263817), 27174 ^ _779300 : [(27175 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263817), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263817), _1263819), _1263821)), _1263823)), 27178 ^ _779300 : [(27179 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263817), _1263819), _1263823)))], (27181 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263817), _1263821), _1263823)))]]], (27183 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263817), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263817), _1263819), _1263821)), _1263823))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263817), _1263819), _1263823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263817), _1263821), _1263823))]]], (27193 ^ _779300) ^ [_1264197, _1264199, _1264201] : [class_Lattices_Osemilattice__sup(_1264197), 27196 ^ _779300 : [(27197 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264197), _1264199), _1264201)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264197), _1264199), _1264201) = _1264201)], (27203 ^ _779300) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264197), _1264199), _1264201) = _1264201, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264197), _1264199), _1264201)))]]], (27209 ^ _779300) ^ [_1264453, _1264455, _1264457] : [class_Lattices_Osemilattice__sup(_1264453), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264453), _1264455), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264453), _1264457), _1264455))))], (27215 ^ _779300) ^ [_1264560, _1264562, _1264564] : [class_Lattices_Olattice(_1264560), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264560), _1264562), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264560), _1264564), _1264562))))], (27221 ^ _779300) ^ [_1264667, _1264669, _1264671] : [class_Lattices_Osemilattice__sup(_1264667), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264667), _1264669), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264667), _1264669), _1264671))))], (27227 ^ _779300) ^ [_1264774, _1264776, _1264778] : [class_Lattices_Olattice(_1264774), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264774), _1264776), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264774), _1264776), _1264778))))], (27233 ^ _779300) ^ [_1264881, _1264883, _1264885, _1264887, _1264889] : [-(hAPP(c_Set_Oimage(_1264881, _1264883, _1264885), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264881, tc_HOL_Obool)), _1264887), _1264889)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264883, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1264881, _1264883, _1264885), _1264887)), hAPP(c_Set_Oimage(_1264881, _1264883, _1264885), _1264889)))], (27235 ^ _779300) ^ [_1264973, _1264975, _1264977] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264973, tc_HOL_Obool)), _1264975), _1264977) = c_Orderings_Obot__class_Obot(tc_fun(_1264973, tc_HOL_Obool)), 27238 ^ _779300 : [(27239 ^ _779300) ^ [] : [-(_1264975 = c_Orderings_Obot__class_Obot(tc_fun(_1264973, tc_HOL_Obool)))], (27241 ^ _779300) ^ [] : [-(_1264977 = c_Orderings_Obot__class_Obot(tc_fun(_1264973, tc_HOL_Obool)))]]], (27243 ^ _779300) ^ [_1265126, _1265128, _1265130] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265126, tc_HOL_Obool)), _1265128), _1265130) = c_Orderings_Obot__class_Obot(tc_fun(_1265126, tc_HOL_Obool))), _1265128 = c_Orderings_Obot__class_Obot(tc_fun(_1265126, tc_HOL_Obool)), _1265130 = c_Orderings_Obot__class_Obot(tc_fun(_1265126, tc_HOL_Obool))], (27253 ^ _779300) ^ [_1265313, _1265315] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265313, tc_HOL_Obool)), _1265315), c_Orderings_Obot__class_Obot(tc_fun(_1265313, tc_HOL_Obool))) = _1265315)], (27255 ^ _779300) ^ [_1265354, _1265356] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265354, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1265354, tc_HOL_Obool))), _1265356) = _1265356)], (27257 ^ _779300) ^ [_1265395, _1265397, _1265399] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1265395), _1265397)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265395), _1265399)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1265395), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265395, tc_HOL_Obool)), _1265397), _1265399))))], (27267 ^ _779300) ^ [_1265592, _1265594, _1265596] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1265592), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265592, tc_HOL_Obool)), _1265594), _1265596))), 27270 ^ _779300 : [(27271 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1265592), _1265594)))], (27273 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1265592), _1265596)))]]], (27275 ^ _779300) ^ [_1265739, _1265741, _1265743] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1265739), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265739, tc_HOL_Obool)), _1265741), _1265743)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265739), _1265741)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265739), _1265743))], (27285 ^ _779300) ^ [_1265920, _1265922, _1265924] : [class_Lattices_Obounded__lattice__bot(_1265920), 27288 ^ _779300 : [(27289 ^ _779300) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265920), _1265922), _1265924) = c_Orderings_Obot__class_Obot(_1265920), 27292 ^ _779300 : [(27293 ^ _779300) ^ [] : [-(_1265922 = c_Orderings_Obot__class_Obot(_1265920))], (27295 ^ _779300) ^ [] : [-(_1265924 = c_Orderings_Obot__class_Obot(_1265920))]]], (27297 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265920), _1265922), _1265924) = c_Orderings_Obot__class_Obot(_1265920)), _1265922 = c_Orderings_Obot__class_Obot(_1265920), _1265924 = c_Orderings_Obot__class_Obot(_1265920)]]], (27307 ^ _779300) ^ [_1266247, _1266249] : [class_Lattices_Obounded__lattice__bot(_1266247), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266247), _1266249), c_Orderings_Obot__class_Obot(_1266247)) = _1266249)], (27313 ^ _779300) ^ [_1266342, _1266344] : [class_Lattices_Obounded__lattice__bot(_1266342), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266342), c_Orderings_Obot__class_Obot(_1266342)), _1266344) = _1266344)], (27319 ^ _779300) ^ [_1266437] : [class_Lattices_Osemilattice__sup(_1266437), -(c_Finite__Set_Ofun__left__comm__idem(_1266437, _1266437, c_Lattices_Osemilattice__sup__class_Osup(_1266437)))], (27325 ^ _779300) ^ [_1266537, _1266539, _1266541, _1266543] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266537, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1266537, tc_fun(_1266537, tc_HOL_Obool), tc_HOL_Obool), c_member(_1266537)), _1266539)), hAPP(hAPP(c_COMBC(_1266537, tc_fun(_1266537, tc_HOL_Obool), tc_HOL_Obool), c_member(_1266537)), _1266541)), _1266543)), -(hBOOL(hAPP(hAPP(c_member(_1266537), _1266543), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266537, tc_HOL_Obool)), _1266539), _1266541))))], (27331 ^ _779300) ^ [_1266736, _1266738, _1266740, _1266742] : [hBOOL(hAPP(hAPP(c_member(_1266736), _1266742), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266736, tc_HOL_Obool)), _1266738), _1266740))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266736, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1266736, tc_fun(_1266736, tc_HOL_Obool), tc_HOL_Obool), c_member(_1266736)), _1266738)), hAPP(hAPP(c_COMBC(_1266736, tc_fun(_1266736, tc_HOL_Obool), tc_HOL_Obool), c_member(_1266736)), _1266740)), _1266742)))], (27337 ^ _779300) ^ [_1266941, _1266943, _1266945] : [class_Orderings_Olinorder(_1266941), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266941), _1266943)), -(_1266943 = c_Orderings_Obot__class_Obot(tc_fun(_1266941, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266941), _1266945)), -(_1266945 = c_Orderings_Obot__class_Obot(tc_fun(_1266941, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1266941, c_Orderings_Oord__class_Omax(_1266941), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266941, tc_HOL_Obool)), _1266943), _1266945)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1266941), c_Big__Operators_Olattice_OSup__fin(_1266941, c_Orderings_Oord__class_Omax(_1266941), _1266943)), c_Big__Operators_Olattice_OSup__fin(_1266941, c_Orderings_Oord__class_Omax(_1266941), _1266945)))], (27359 ^ _779300) ^ [_1267308, _1267310, _1267312] : [-(hAPP(hAPP(c_Set_Oinsert(_1267308), _1267310), _1267312) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267308, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1267308), _1267310), c_Orderings_Obot__class_Obot(tc_fun(_1267308, tc_HOL_Obool)))), _1267312))], (27361 ^ _779300) ^ [_1267388, _1267390, _1267392, _1267394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267388, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1267388, tc_HOL_Obool)), _1267390), _1267392)), _1267394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267388, tc_HOL_Obool)), _1267390), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267388, tc_HOL_Obool)), _1267392), _1267394))))], (27367 ^ _779300) ^ [_1267549, _1267551, _1267553, _1267555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267549, tc_HOL_Obool)), _1267551), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267549, tc_HOL_Obool)), _1267553), _1267555))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267549, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1267549, tc_HOL_Obool)), _1267551), _1267553)), _1267555)))], (27373 ^ _779300) ^ [_1267716, _1267718, _1267720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1267716, tc_HOL_Obool)), _1267718), _1267720)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267716, tc_HOL_Obool)), _1267718), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1267716, tc_HOL_Obool)), _1267720), _1267718)) = _1267720)], (27379 ^ _779300) ^ [_1267859, _1267861, _1267863, _1267865, _1267867] : [c_Fun_Oinj__on(_1267859, _1267861, _1267863, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267859, tc_HOL_Obool)), _1267865), _1267867)), 27382 ^ _779300 : [(27383 ^ _779300) ^ [] : [hAPP(c_Set_Oimage(_1267859, _1267861, _1267863), _1267865) = hAPP(c_Set_Oimage(_1267859, _1267861, _1267863), _1267867), -(_1267865 = _1267867)], (27389 ^ _779300) ^ [] : [_1267865 = _1267867, -(hAPP(c_Set_Oimage(_1267859, _1267861, _1267863), _1267865) = hAPP(c_Set_Oimage(_1267859, _1267861, _1267863), _1267867))]]], (27395 ^ _779300) ^ [_1268152, _1268154, _1268156] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1268152, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1268152, tc_HOL_Obool)), _1268154), _1268156)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1268152, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1268152, tc_HOL_Obool)), _1268154)), _1268156))], (27397 ^ _779300) ^ [_1268217, _1268219] : [-(c_FunDef_Orp__inv__image(_1268217, _1268219) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool), tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool), tc_fun(tc_fun(_1268219, _1268217), tc_prod(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool), tc_fun(tc_fun(_1268219, _1268217), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool), tc_fun(tc_fun(_1268219, _1268217), tc_prod(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1268219, _1268217), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)), tc_fun(tc_fun(_1268219, _1268217), tc_prod(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool), tc_fun(tc_fun(_1268219, _1268217), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool), tc_fun(tc_fun(_1268219, _1268217), tc_prod(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool))))), tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1268219, _1268217), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)), tc_fun(tc_fun(_1268219, _1268217), tc_prod(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool))), tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1268219, _1268217), tc_fun(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1268219, _1268217), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)), tc_fun(tc_fun(_1268219, _1268217), tc_prod(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)))), tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool)), c_COMBS(tc_fun(_1268219, _1268217), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1268219, _1268217), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)), tc_fun(tc_fun(_1268219, _1268217), tc_fun(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)))), tc_fun(tc_prod(_1268217, _1268217), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool))), tc_fun(_1268219, _1268217)), c_Product__Type_OPair(tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool), tc_fun(tc_prod(_1268219, _1268219), tc_HOL_Obool)))), c_Relation_Oinv__image(_1268217, _1268219))))), c_Relation_Oinv__image(_1268217, _1268219))))], (27399 ^ _779300) ^ [_1268730, _1268732, _1268734, _1268736, _1268738, _1268740, _1268742, _1268744] : [c_Finite__Set_Ofolding__image__simple__idem(_1268730, _1268732, _1268734, _1268736, _1268738, _1268740), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268732), _1268742)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268732), _1268744)), -(hAPP(_1268740, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1268732, tc_HOL_Obool)), _1268742), _1268744)) = hAPP(hAPP(_1268734, hAPP(_1268740, _1268742)), hAPP(_1268740, _1268744)))], (27413 ^ _779300) ^ [_1269023, _1269025, _1269027] : [class_Orderings_Olinorder(_1269023), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269023), _1269025)), hBOOL(hAPP(hAPP(c_member(_1269023), _1269027), _1269025)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269023), _1269027), c_Big__Operators_Olattice_OSup__fin(_1269023, c_Orderings_Oord__class_Omax(_1269023), _1269025)) = c_Big__Operators_Olattice_OSup__fin(_1269023, c_Orderings_Oord__class_Omax(_1269023), _1269025))], (27427 ^ _779300) ^ [_1269270, _1269272] : [class_Orderings_Olinorder(_1269270), -(c_Big__Operators_Olattice_OSup__fin(_1269270, c_Orderings_Oord__class_Omax(_1269270), hAPP(hAPP(c_Set_Oinsert(_1269270), _1269272), c_Orderings_Obot__class_Obot(tc_fun(_1269270, tc_HOL_Obool)))) = _1269272)], (27433 ^ _779300) ^ [_1269383, _1269385, _1269387, _1269389, _1269391] : [c_Finite__Set_Ofolding__one__idem(_1269383, _1269385, _1269387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269383), _1269389)), -(_1269389 = c_Orderings_Obot__class_Obot(tc_fun(_1269383, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269383), _1269391)), -(_1269391 = c_Orderings_Obot__class_Obot(tc_fun(_1269383, tc_HOL_Obool))), -(hAPP(_1269387, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1269383, tc_HOL_Obool)), _1269389), _1269391)) = hAPP(hAPP(_1269385, hAPP(_1269387, _1269389)), hAPP(_1269387, _1269391)))], (27455 ^ _779300) ^ [_1269748, _1269750] : [class_Orderings_Olinorder(_1269748), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269748), _1269750)), -(c_Big__Operators_Olattice_OSup__fin(_1269748, c_Orderings_Oord__class_Omax(_1269748), _1269750) = hAPP(c_Finite__Set_Ofold1(_1269748, c_Orderings_Oord__class_Omax(_1269748)), _1269750))], (27465 ^ _779300) ^ [_1269911, _1269913, _1269915] : [class_Lattices_Oab__semigroup__idem__mult(_1269911), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269911), _1269913)), -(_1269913 = c_Orderings_Obot__class_Obot(tc_fun(_1269911, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269911), _1269915)), -(_1269915 = c_Orderings_Obot__class_Obot(tc_fun(_1269911, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1269911, c_Groups_Otimes__class_Otimes(_1269911)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1269911, tc_HOL_Obool)), _1269913), _1269915)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1269911), hAPP(c_Finite__Set_Ofold1(_1269911, c_Groups_Otimes__class_Otimes(_1269911)), _1269913)), hAPP(c_Finite__Set_Ofold1(_1269911, c_Groups_Otimes__class_Otimes(_1269911)), _1269915)))], (27487 ^ _779300) ^ [_1270290, _1270292, _1270294] : [class_Orderings_Olinorder(_1270290), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270290), _1270292)), -(_1270292 = c_Orderings_Obot__class_Obot(tc_fun(_1270290, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270290), _1270294)), -(_1270294 = c_Orderings_Obot__class_Obot(tc_fun(_1270290, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1270290, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270290, tc_HOL_Obool)), _1270292), _1270294)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1270290), c_Big__Operators_Olinorder__class_OMin(_1270290, _1270292)), c_Big__Operators_Olinorder__class_OMin(_1270290, _1270294)))], (27509 ^ _779300) ^ [_1270639, _1270641, _1270643] : [class_Orderings_Olinorder(_1270639), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270639), _1270641)), -(_1270641 = c_Orderings_Obot__class_Obot(tc_fun(_1270639, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270639), _1270643)), -(_1270643 = c_Orderings_Obot__class_Obot(tc_fun(_1270639, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1270639, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270639, tc_HOL_Obool)), _1270641), _1270643)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1270639), c_Big__Operators_Olinorder__class_OMax(_1270639, _1270641)), c_Big__Operators_Olinorder__class_OMax(_1270639, _1270643)))], (27531 ^ _779300) ^ [_1270988, _1270990, _1270992] : [class_Orderings_Olinorder(_1270988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270988), _1270990)), -(_1270990 = c_Orderings_Obot__class_Obot(tc_fun(_1270988, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270988), _1270992)), -(_1270992 = c_Orderings_Obot__class_Obot(tc_fun(_1270988, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1270988, c_Orderings_Oord__class_Omin(_1270988), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270988, tc_HOL_Obool)), _1270990), _1270992)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1270988), c_Big__Operators_Olattice_OInf__fin(_1270988, c_Orderings_Oord__class_Omin(_1270988), _1270990)), c_Big__Operators_Olattice_OInf__fin(_1270988, c_Orderings_Oord__class_Omin(_1270988), _1270992)))], (27553 ^ _779300) ^ [_1271355, _1271357, _1271359, _1271361] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1271355), _1271357)), -(hAPP(c_Set_Oimage(_1271355, _1271359, _1271361), _1271357) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1271359, tc_HOL_Obool), _1271355, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271359, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1271355, tc_fun(_1271359, tc_HOL_Obool), tc_fun(_1271359, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1271359, tc_fun(tc_fun(_1271359, tc_HOL_Obool), tc_fun(_1271359, tc_HOL_Obool)), _1271355), c_Set_Oinsert(_1271359)), _1271361)), c_Orderings_Obot__class_Obot(tc_fun(_1271359, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1271359, tc_HOL_Obool))), _1271357))], (27559 ^ _779300) ^ [_1271594, _1271596, _1271598] : [class_Orderings_Olinorder(_1271594), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271594), _1271596)), -(_1271596 = c_Orderings_Obot__class_Obot(tc_fun(_1271594, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1271594, c_Orderings_Oord__class_Omax(_1271594), hAPP(hAPP(c_Set_Oinsert(_1271594), _1271598), _1271596)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271594), _1271598), c_Big__Operators_Olattice_OSup__fin(_1271594, c_Orderings_Oord__class_Omax(_1271594), _1271596)))], (27573 ^ _779300) ^ [_1271814, _1271816, _1271818] : [class_Orderings_Olinorder(_1271814), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271814), _1271816)), -(_1271818 = c_Orderings_Obot__class_Obot(tc_fun(_1271814, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271814, tc_HOL_Obool)), _1271818), _1271816)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271814), c_Big__Operators_Olattice_OSup__fin(_1271814, c_Orderings_Oord__class_Omax(_1271814), _1271818)), c_Big__Operators_Olattice_OSup__fin(_1271814, c_Orderings_Oord__class_Omax(_1271814), _1271816)) = c_Big__Operators_Olattice_OSup__fin(_1271814, c_Orderings_Oord__class_Omax(_1271814), _1271816))], (27591 ^ _779300) ^ [_1272146, _1272148, _1272150] : [class_Orderings_Olinorder(_1272146), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272146), _1272148)), hBOOL(hAPP(hAPP(c_member(_1272146), _1272150), _1272148)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1272146), _1272150), c_Big__Operators_Olattice_OSup__fin(_1272146, c_Orderings_Oord__class_Omax(_1272146), _1272148)) = _1272150)], (27605 ^ _779300) ^ [_1272381, _1272383, _1272385] : [class_Orderings_Olinorder(_1272381), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272381), _1272383)), -(hBOOL(hAPP(hAPP(c_member(_1272381), _1272385), _1272383))), -(_1272383 = c_Orderings_Obot__class_Obot(tc_fun(_1272381, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1272381, c_Orderings_Oord__class_Omax(_1272381), hAPP(hAPP(c_Set_Oinsert(_1272381), _1272385), _1272383)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1272381), _1272385), c_Big__Operators_Olattice_OSup__fin(_1272381, c_Orderings_Oord__class_Omax(_1272381), _1272383)))], (27623 ^ _779300) ^ [_1272630, _1272632, _1272634] : [class_Orderings_Olinorder(_1272630), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272630), _1272632)), 27630 ^ _779300 : [(27631 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272630, tc_HOL_Obool)), _1272632), hAPP(hAPP(c_Set_Oinsert(_1272630), _1272634), c_Orderings_Obot__class_Obot(tc_fun(_1272630, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1272630, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1272630, c_Orderings_Oord__class_Omax(_1272630), hAPP(hAPP(c_Set_Oinsert(_1272630), _1272634), _1272632)) = _1272634)], (27637 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272630, tc_HOL_Obool)), _1272632), hAPP(hAPP(c_Set_Oinsert(_1272630), _1272634), c_Orderings_Obot__class_Obot(tc_fun(_1272630, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1272630, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1272630, c_Orderings_Oord__class_Omax(_1272630), hAPP(hAPP(c_Set_Oinsert(_1272630), _1272634), _1272632)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1272630), _1272634), c_Big__Operators_Olattice_OSup__fin(_1272630, c_Orderings_Oord__class_Omax(_1272630), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272630, tc_HOL_Obool)), _1272632), hAPP(hAPP(c_Set_Oinsert(_1272630), _1272634), c_Orderings_Obot__class_Obot(tc_fun(_1272630, tc_HOL_Obool)))))))]]], (27643 ^ _779300) ^ [] : [-(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)))))], (27645 ^ _779300) ^ [_1273163, _1273165, _1273167, _1273169, _1273171, _1273173] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1273163, _1273163)), hAPP(hAPP(c_Product__Type_OPair(_1273163, _1273163), _1273165), _1273167)), hAPP(hAPP(c_Relation_Oinv__image(_1273169, _1273163), _1273171), _1273173))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1273169, _1273169)), hAPP(hAPP(c_Product__Type_OPair(_1273169, _1273169), hAPP(_1273173, _1273165)), hAPP(_1273173, _1273167))), _1273171)))], (27651 ^ _779300) ^ [_1273350, _1273352, _1273354, _1273356, _1273358, _1273360] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1273356, _1273356)), hAPP(hAPP(c_Product__Type_OPair(_1273356, _1273356), hAPP(_1273360, _1273352)), hAPP(_1273360, _1273354))), _1273358)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1273350, _1273350)), hAPP(hAPP(c_Product__Type_OPair(_1273350, _1273350), _1273352), _1273354)), hAPP(hAPP(c_Relation_Oinv__image(_1273356, _1273350), _1273358), _1273360))))], (27657 ^ _779300) ^ [_1273543, _1273545] : [class_Orderings_Olinorder(_1273543), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273543), _1273545)), -(_1273545 = c_Orderings_Obot__class_Obot(tc_fun(_1273543, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1273543), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1273543), 27670 ^ [_1273543, _1273545]), 27671 ^ [_1273543, _1273545])), hAPP(hAPP(c_Set_Oinsert(_1273543), 27670 ^ [_1273543, _1273545]), hAPP(hAPP(c_Set_Oinsert(_1273543), 27671 ^ [_1273543, _1273545]), c_Orderings_Obot__class_Obot(tc_fun(_1273543, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1273543), c_Big__Operators_Olattice_OSup__fin(_1273543, c_Orderings_Oord__class_Omax(_1273543), _1273545)), _1273545)))], (27677 ^ _779300) ^ [_1273993, _1273995, _1273997] : [class_Orderings_Olinorder(_1273993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273993), _1273995), _1273997)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273993, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1273993, _1273995, _1273997)), hAPP(hAPP(c_Set_Oinsert(_1273993), _1273997), c_Orderings_Obot__class_Obot(tc_fun(_1273993, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1273993, _1273995, _1273997))], (27687 ^ _779300) ^ [_1274202, _1274204, _1274206] : [class_Lattices_Olattice(_1274202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274202), _1274204)), hBOOL(hAPP(hAPP(c_member(_1274202), _1274206), _1274204)), 27698 ^ _779300 : [(27699 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1274202, tc_HOL_Obool)), _1274204), hAPP(hAPP(c_Set_Oinsert(_1274202), _1274206), c_Orderings_Obot__class_Obot(tc_fun(_1274202, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1274202, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1274202, _1274204) = _1274206)], (27705 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1274202, tc_HOL_Obool)), _1274204), hAPP(hAPP(c_Set_Oinsert(_1274202), _1274206), c_Orderings_Obot__class_Obot(tc_fun(_1274202, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1274202, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1274202, _1274204) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274202), _1274206), c_Big__Operators_Olattice__class_OSup__fin(_1274202, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1274202, tc_HOL_Obool)), _1274204), hAPP(hAPP(c_Set_Oinsert(_1274202), _1274206), c_Orderings_Obot__class_Obot(tc_fun(_1274202, tc_HOL_Obool)))))))]]], (27711 ^ _779300) ^ [_1274708, _1274710] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1274708, _1274710))))], (27713 ^ _779300) ^ [_1274739, _1274741] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1274739, _1274741))))], (27715 ^ _779300) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (27717 ^ _779300) ^ [_1274788, _1274790] : [c_Nat__Transfer_Onat__set(_1274788), c_Nat__Transfer_Onat__set(_1274790), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1274788), _1274790)))], (27727 ^ _779300) ^ [_1274923, _1274925] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1274923), _1274925) = 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)), _1274923)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1274925))))], (27729 ^ _779300) ^ [_1274969, _1274971] : [class_Lattices_Olattice(_1274969), -(c_Big__Operators_Olattice__class_OSup__fin(_1274969, hAPP(hAPP(c_Set_Oinsert(_1274969), _1274971), c_Orderings_Obot__class_Obot(tc_fun(_1274969, tc_HOL_Obool)))) = _1274971)], (27735 ^ _779300) ^ [_1275076, _1275078] : [c_Nat__Transfer_Onat__set(_1275076), c_Nat__Transfer_Onat__set(_1275078), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1275076), _1275078) = 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), _1275076)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1275078))))], (27745 ^ _779300) ^ [_1275243, _1275245, _1275247] : [class_Orderings_Oorder(_1275243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275243), _1275245), _1275247)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1275243, _1275247, _1275245) = c_Orderings_Obot__class_Obot(tc_fun(_1275243, tc_HOL_Obool)))], (27755 ^ _779300) ^ [_1275406, _1275408, _1275410] : [class_Orderings_Oorder(_1275406), 27758 ^ _779300 : [(27759 ^ _779300) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1275406, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1275406, _1275408, _1275410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275406), _1275408), _1275410))], (27765 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275406), _1275408), _1275410))), -(c_Orderings_Obot__class_Obot(tc_fun(_1275406, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1275406, _1275408, _1275410))]]], (27771 ^ _779300) ^ [_1275625, _1275627, _1275629] : [class_Orderings_Oorder(_1275625), 27774 ^ _779300 : [(27775 ^ _779300) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1275625, _1275627, _1275629) = c_Orderings_Obot__class_Obot(tc_fun(_1275625, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275625), _1275627), _1275629))], (27781 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275625), _1275627), _1275629))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1275625, _1275627, _1275629) = c_Orderings_Obot__class_Obot(tc_fun(_1275625, tc_HOL_Obool)))]]], (27787 ^ _779300) ^ [_1275844, _1275846, _1275848, _1275850] : [class_Orderings_Olinorder(_1275844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275844), _1275846), _1275848)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275844), _1275848), _1275850)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275844, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1275844, _1275846, _1275848)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1275844, _1275848, _1275850)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1275844, _1275846, _1275850))], (27801 ^ _779300) ^ [_1276109, _1276111] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1276109, _1276111)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1276111), _1276109))], (27803 ^ _779300) ^ [_1276174, _1276176, _1276178, _1276180, _1276182, _1276184] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276174, tc_fun(_1276176, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1276174, tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_fun(_1276176, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276176, tc_fun(tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_fun(_1276176, tc_HOL_Obool)), _1276174), c_COMBC(_1276176, tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276176, tc_prod(_1276174, _1276176)), tc_fun(_1276176, tc_fun(tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_HOL_Obool)), _1276174), hAPP(c_COMBB(tc_prod(_1276174, _1276176), tc_fun(tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_HOL_Obool), _1276176), c_member(tc_prod(_1276174, _1276176)))), c_Product__Type_OPair(_1276174, _1276176)))), _1276178)), hAPP(hAPP(c_COMBC(_1276174, tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_fun(_1276176, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276176, tc_fun(tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_fun(_1276176, tc_HOL_Obool)), _1276174), c_COMBC(_1276176, tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276176, tc_prod(_1276174, _1276176)), tc_fun(_1276176, tc_fun(tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_HOL_Obool)), _1276174), hAPP(c_COMBB(tc_prod(_1276174, _1276176), tc_fun(tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool), tc_HOL_Obool), _1276176), c_member(tc_prod(_1276174, _1276176)))), c_Product__Type_OPair(_1276174, _1276176)))), _1276180)), _1276182), _1276184)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1276174, _1276176)), hAPP(hAPP(c_Product__Type_OPair(_1276174, _1276176), _1276182), _1276184)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1276174, _1276176), tc_HOL_Obool)), _1276178), _1276180))))], (27809 ^ _779300) ^ [_1276831, _1276833, _1276835, _1276837, _1276839, _1276841] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1276831, _1276833)), hAPP(hAPP(c_Product__Type_OPair(_1276831, _1276833), _1276839), _1276841)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool)), _1276835), _1276837))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276831, tc_fun(_1276833, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1276831, tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_fun(_1276833, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276833, tc_fun(tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_fun(_1276833, tc_HOL_Obool)), _1276831), c_COMBC(_1276833, tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276833, tc_prod(_1276831, _1276833)), tc_fun(_1276833, tc_fun(tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_HOL_Obool)), _1276831), hAPP(c_COMBB(tc_prod(_1276831, _1276833), tc_fun(tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_HOL_Obool), _1276833), c_member(tc_prod(_1276831, _1276833)))), c_Product__Type_OPair(_1276831, _1276833)))), _1276835)), hAPP(hAPP(c_COMBC(_1276831, tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_fun(_1276833, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276833, tc_fun(tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_fun(_1276833, tc_HOL_Obool)), _1276831), c_COMBC(_1276833, tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276833, tc_prod(_1276831, _1276833)), tc_fun(_1276833, tc_fun(tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_HOL_Obool)), _1276831), hAPP(c_COMBB(tc_prod(_1276831, _1276833), tc_fun(tc_fun(tc_prod(_1276831, _1276833), tc_HOL_Obool), tc_HOL_Obool), _1276833), c_member(tc_prod(_1276831, _1276833)))), c_Product__Type_OPair(_1276831, _1276833)))), _1276837)), _1276839), _1276841)))], (27815 ^ _779300) ^ [_1277494, _1277496, _1277498] : [class_Lattices_Olattice(_1277494), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277494), _1277496)), hBOOL(hAPP(hAPP(c_member(_1277494), _1277498), _1277496)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1277494), _1277498), c_Big__Operators_Olattice__class_OSup__fin(_1277494, _1277496)) = c_Big__Operators_Olattice__class_OSup__fin(_1277494, _1277496))], (27829 ^ _779300) ^ [_1277729, _1277731] : [class_Lattices_Olattice(_1277729), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277729), _1277731)), -(c_Big__Operators_Olattice__class_OSup__fin(_1277729, _1277731) = hAPP(c_Finite__Set_Ofold1(_1277729, c_Lattices_Osemilattice__sup__class_Osup(_1277729)), _1277731))], (27839 ^ _779300) ^ [_1277886, _1277888, _1277890] : [class_Lattices_Olattice(_1277886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277886), _1277888)), -(_1277888 = c_Orderings_Obot__class_Obot(tc_fun(_1277886, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1277886, hAPP(hAPP(c_Set_Oinsert(_1277886), _1277890), _1277888)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1277886), _1277890), c_Big__Operators_Olattice__class_OSup__fin(_1277886, _1277888)))], (27853 ^ _779300) ^ [_1278094, _1278096, _1278098] : [class_Lattices_Olattice(_1278094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278094), _1278096)), -(_1278098 = c_Orderings_Obot__class_Obot(tc_fun(_1278094, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1278094, tc_HOL_Obool)), _1278098), _1278096)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278094), c_Big__Operators_Olattice__class_OSup__fin(_1278094, _1278098)), c_Big__Operators_Olattice__class_OSup__fin(_1278094, _1278096)) = c_Big__Operators_Olattice__class_OSup__fin(_1278094, _1278096))], (27871 ^ _779300) ^ [_1278408, _1278410] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1278408, _1278410)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1278410), _1278408)))], (27873 ^ _779300) ^ [_1278449, _1278451, _1278453] : [class_Lattices_Olattice(_1278449), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278449), _1278451)), -(_1278451 = c_Orderings_Obot__class_Obot(tc_fun(_1278449, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278449), _1278453)), -(_1278453 = c_Orderings_Obot__class_Obot(tc_fun(_1278449, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1278449, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278449, tc_HOL_Obool)), _1278451), _1278453)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278449), c_Big__Operators_Olattice__class_OSup__fin(_1278449, _1278451)), c_Big__Operators_Olattice__class_OSup__fin(_1278449, _1278453)))], (27895 ^ _779300) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (27897 ^ _779300) ^ [_1278816, _1278818, _1278820, _1278822] : [class_Orderings_Olinorder(_1278816), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278816), _1278818), _1278820)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278816), _1278820), _1278822)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278816, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1278816, _1278818, _1278820)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1278816, _1278820, _1278822)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1278816, _1278818, _1278822))], (27911 ^ _779300) ^ [_1279081] : [-(c_Wellfounded_Omeasure(_1279081) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1279081), c_Wellfounded_Oless__than))], (27913 ^ _779300) ^ [_1279112, _1279114, _1279116] : [class_Lattices_Olattice(_1279112), hBOOL(hAPP(c_Finite__Set_Ofinite(_1279112), _1279114)), -(hBOOL(hAPP(hAPP(c_member(_1279112), _1279116), _1279114))), -(_1279114 = c_Orderings_Obot__class_Obot(tc_fun(_1279112, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1279112, hAPP(hAPP(c_Set_Oinsert(_1279112), _1279116), _1279114)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279112), _1279116), c_Big__Operators_Olattice__class_OSup__fin(_1279112, _1279114)))], (27931 ^ _779300) ^ [_1279349, _1279351, _1279353] : [class_Lattices_Olattice(_1279349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1279349), _1279351)), 27938 ^ _779300 : [(27939 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279349, tc_HOL_Obool)), _1279351), hAPP(hAPP(c_Set_Oinsert(_1279349), _1279353), c_Orderings_Obot__class_Obot(tc_fun(_1279349, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1279349, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1279349, hAPP(hAPP(c_Set_Oinsert(_1279349), _1279353), _1279351)) = _1279353)], (27945 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279349, tc_HOL_Obool)), _1279351), hAPP(hAPP(c_Set_Oinsert(_1279349), _1279353), c_Orderings_Obot__class_Obot(tc_fun(_1279349, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1279349, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1279349, hAPP(hAPP(c_Set_Oinsert(_1279349), _1279353), _1279351)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279349), _1279353), c_Big__Operators_Olattice__class_OSup__fin(_1279349, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279349, tc_HOL_Obool)), _1279351), hAPP(hAPP(c_Set_Oinsert(_1279349), _1279353), c_Orderings_Obot__class_Obot(tc_fun(_1279349, tc_HOL_Obool)))))))]]], (27951 ^ _779300) ^ [_1279819, _1279821, _1279823, _1279825, _1279827, _1279829] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1279819, tc_HOL_Obool), tc_fun(_1279819, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1279819, tc_HOL_Obool), tc_fun(_1279819, tc_HOL_Obool)), _1279821), _1279823)), c_Wellfounded_Omax__ext(_1279819, _1279825))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1279819, tc_HOL_Obool), tc_fun(_1279819, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1279819, tc_HOL_Obool), tc_fun(_1279819, tc_HOL_Obool)), _1279827), _1279829)), c_Wellfounded_Omax__ext(_1279819, _1279825))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1279819, tc_HOL_Obool), tc_fun(_1279819, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1279819, tc_HOL_Obool), tc_fun(_1279819, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279819, tc_HOL_Obool)), _1279821), _1279827)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279819, tc_HOL_Obool)), _1279823), _1279829))), c_Wellfounded_Omax__ext(_1279819, _1279825))))], (27961 ^ _779300) ^ [_1280233, _1280235, _1280237, _1280239] : [c_Wellfounded_Omax__extp(_1280233, hAPP(hAPP(c_COMBC(_1280233, tc_fun(tc_prod(_1280233, _1280233), tc_HOL_Obool), tc_fun(_1280233, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1280233, tc_fun(tc_fun(tc_prod(_1280233, _1280233), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1280233, _1280233), tc_HOL_Obool), tc_fun(_1280233, tc_HOL_Obool)), _1280233), c_COMBC(_1280233, tc_fun(tc_prod(_1280233, _1280233), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1280233, tc_prod(_1280233, _1280233)), tc_fun(_1280233, tc_fun(tc_fun(tc_prod(_1280233, _1280233), tc_HOL_Obool), tc_HOL_Obool)), _1280233), hAPP(c_COMBB(tc_prod(_1280233, _1280233), tc_fun(tc_fun(tc_prod(_1280233, _1280233), tc_HOL_Obool), tc_HOL_Obool), _1280233), c_member(tc_prod(_1280233, _1280233)))), c_Product__Type_OPair(_1280233, _1280233)))), _1280235), _1280237, _1280239), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1280233, tc_HOL_Obool), tc_fun(_1280233, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1280233, tc_HOL_Obool), tc_fun(_1280233, tc_HOL_Obool)), _1280237), _1280239)), c_Wellfounded_Omax__ext(_1280233, _1280235))))], (27967 ^ _779300) ^ [_1280618, _1280620, _1280622, _1280624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1280618, tc_HOL_Obool), tc_fun(_1280618, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1280618, tc_HOL_Obool), tc_fun(_1280618, tc_HOL_Obool)), _1280622), _1280624)), c_Wellfounded_Omax__ext(_1280618, _1280620))), -(c_Wellfounded_Omax__extp(_1280618, hAPP(hAPP(c_COMBC(_1280618, tc_fun(tc_prod(_1280618, _1280618), tc_HOL_Obool), tc_fun(_1280618, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1280618, tc_fun(tc_fun(tc_prod(_1280618, _1280618), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1280618, _1280618), tc_HOL_Obool), tc_fun(_1280618, tc_HOL_Obool)), _1280618), c_COMBC(_1280618, tc_fun(tc_prod(_1280618, _1280618), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1280618, tc_prod(_1280618, _1280618)), tc_fun(_1280618, tc_fun(tc_fun(tc_prod(_1280618, _1280618), tc_HOL_Obool), tc_HOL_Obool)), _1280618), hAPP(c_COMBB(tc_prod(_1280618, _1280618), tc_fun(tc_fun(tc_prod(_1280618, _1280618), tc_HOL_Obool), tc_HOL_Obool), _1280618), c_member(tc_prod(_1280618, _1280618)))), c_Product__Type_OPair(_1280618, _1280618)))), _1280620), _1280622, _1280624))], (27973 ^ _779300) ^ [_1281024, _1281026] : [c_Relation_Oirrefl(_1281024, _1281026), 27976 ^ _779300 : [(27977 ^ _779300) ^ [_1281106] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1281024, _1281024)), hAPP(hAPP(c_Product__Type_OPair(_1281024, _1281024), _1281106), _1281106)), _1281026))]]], (27979 ^ _779300) ^ [_1281146, _1281148] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1281146, _1281146)), hAPP(hAPP(c_Product__Type_OPair(_1281146, _1281146), 27980 ^ [_1281146, _1281148]), 27980 ^ [_1281146, _1281148])), _1281148))), -(c_Relation_Oirrefl(_1281146, _1281148))], (27986 ^ _779300) ^ [_1281217, _1281219, _1281221, _1281223] : [-(hAPP(c_Relation_OField(_1281217), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1281217, _1281217)), hAPP(hAPP(c_Product__Type_OPair(_1281217, _1281217), _1281219), _1281221)), _1281223)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281217, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1281217), _1281219), hAPP(hAPP(c_Set_Oinsert(_1281217), _1281221), c_Orderings_Obot__class_Obot(tc_fun(_1281217, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1281217), _1281223)))], (27988 ^ _779300) ^ [_1281308, _1281310] : [class_Lattices_Olattice(_1281308), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281308), _1281310)), -(_1281310 = c_Orderings_Obot__class_Obot(tc_fun(_1281308, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1281308), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281308), 28001 ^ [_1281308, _1281310]), 28002 ^ [_1281308, _1281310])), hAPP(hAPP(c_Set_Oinsert(_1281308), 28001 ^ [_1281308, _1281310]), hAPP(hAPP(c_Set_Oinsert(_1281308), 28002 ^ [_1281308, _1281310]), c_Orderings_Obot__class_Obot(tc_fun(_1281308, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1281308), c_Big__Operators_Olattice__class_OSup__fin(_1281308, _1281310)), _1281310)))], (28008 ^ _779300) ^ [_1281752, _1281754, _1281756] : [class_Orderings_Olinorder(_1281752), hAPP(_1281754, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281752), 28013 ^ [_1281752, _1281754, _1281756]), 28014 ^ [_1281752, _1281754, _1281756])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281752), hAPP(_1281754, 28013 ^ [_1281752, _1281754, _1281756])), hAPP(_1281754, 28014 ^ [_1281752, _1281754, _1281756])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281752), _1281756)), -(_1281756 = c_Orderings_Obot__class_Obot(tc_fun(_1281752, tc_HOL_Obool))), -(hAPP(_1281754, c_Big__Operators_Olattice_OSup__fin(_1281752, c_Orderings_Oord__class_Omax(_1281752), _1281756)) = c_Big__Operators_Olattice_OSup__fin(_1281752, c_Orderings_Oord__class_Omax(_1281752), hAPP(c_Set_Oimage(_1281752, _1281752, _1281754), _1281756)))], (28028 ^ _779300) ^ [_1282167, _1282169, _1282171, _1282173, _1282175, _1282177] : [28029 ^ _779300 : [(28030 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1282167, _1282169), _1282171))], (28032 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1282173, _1282169), _1282171))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282175, tc_fun(_1282177, tc_HOL_Obool))), _1282173), _1282167), _1282169), _1282171)))], (28036 ^ _779300) ^ [_1282350, _1282352, _1282354, _1282356, _1282358, _1282360] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282350, tc_fun(_1282352, tc_HOL_Obool))), _1282354), _1282356), _1282358), _1282360)), -(hBOOL(hAPP(hAPP(_1282354, _1282358), _1282360))), -(hBOOL(hAPP(hAPP(_1282356, _1282358), _1282360)))], (28046 ^ _779300) ^ [_1282508, _1282510, _1282512, _1282514, _1282516, _1282518] : [hBOOL(hAPP(hAPP(_1282508, _1282510), _1282512)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282514, tc_fun(_1282516, tc_HOL_Obool))), _1282518), _1282508), _1282510), _1282512)))], (28052 ^ _779300) ^ [_1282641, _1282643, _1282645, _1282647, _1282649, _1282651] : [hBOOL(hAPP(hAPP(_1282641, _1282643), _1282645)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282647, tc_fun(_1282649, tc_HOL_Obool))), _1282641), _1282651), _1282643), _1282645)))], (28058 ^ _779300) ^ [_1282774] : [-(hAPP(c_Relation_OField(_1282774), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1282774, _1282774), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1282774, tc_HOL_Obool)))], (28060 ^ _779300) ^ [_1282815, _1282817, _1282819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1282815, _1282815), tc_HOL_Obool)), _1282817), _1282819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282815, tc_HOL_Obool)), hAPP(c_Relation_OField(_1282815), _1282817)), hAPP(c_Relation_OField(_1282815), _1282819))))], (28066 ^ _779300) ^ [_1282960, _1282962, _1282964] : [-(hAPP(c_Relation_OField(_1282960), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1282960, _1282960), tc_HOL_Obool)), _1282962), _1282964)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282960, tc_HOL_Obool)), hAPP(c_Relation_OField(_1282960), _1282962)), hAPP(c_Relation_OField(_1282960), _1282964)))], (28068 ^ _779300) ^ [_1283027, _1283029] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1283027, _1283027)), _1283029)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283027), hAPP(c_Relation_OField(_1283027), _1283029))))], (28074 ^ _779300) ^ [_1283136, _1283138, _1283140] : [class_Orderings_Olinorder(_1283136), hAPP(_1283138, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283136), 28079 ^ [_1283136, _1283138, _1283140]), 28080 ^ [_1283136, _1283138, _1283140])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283136), hAPP(_1283138, 28079 ^ [_1283136, _1283138, _1283140])), hAPP(_1283138, 28080 ^ [_1283136, _1283138, _1283140])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283136), _1283140)), -(_1283140 = c_Orderings_Obot__class_Obot(tc_fun(_1283136, tc_HOL_Obool))), -(hAPP(_1283138, c_Big__Operators_Olattice_OInf__fin(_1283136, c_Orderings_Oord__class_Omin(_1283136), _1283140)) = c_Big__Operators_Olattice_OInf__fin(_1283136, c_Orderings_Oord__class_Omin(_1283136), hAPP(c_Set_Oimage(_1283136, _1283136, _1283138), _1283140)))], (28094 ^ _779300) ^ [_1283551, _1283553, _1283555] : [class_Orderings_Olinorder(_1283551), hAPP(_1283553, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1283551), 28099 ^ [_1283551, _1283553, _1283555]), 28100 ^ [_1283551, _1283553, _1283555])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1283551), hAPP(_1283553, 28099 ^ [_1283551, _1283553, _1283555])), hAPP(_1283553, 28100 ^ [_1283551, _1283553, _1283555])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283551), _1283555)), -(_1283555 = c_Orderings_Obot__class_Obot(tc_fun(_1283551, tc_HOL_Obool))), -(hAPP(_1283553, c_Big__Operators_Olinorder__class_OMax(_1283551, _1283555)) = c_Big__Operators_Olinorder__class_OMax(_1283551, hAPP(c_Set_Oimage(_1283551, _1283551, _1283553), _1283555)))], (28114 ^ _779300) ^ [_1283954, _1283956, _1283958] : [class_Orderings_Olinorder(_1283954), hAPP(_1283956, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283954), 28119 ^ [_1283954, _1283956, _1283958]), 28120 ^ [_1283954, _1283956, _1283958])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283954), hAPP(_1283956, 28119 ^ [_1283954, _1283956, _1283958])), hAPP(_1283956, 28120 ^ [_1283954, _1283956, _1283958])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283954), _1283958)), -(_1283958 = c_Orderings_Obot__class_Obot(tc_fun(_1283954, tc_HOL_Obool))), -(hAPP(_1283956, c_Big__Operators_Olinorder__class_OMin(_1283954, _1283958)) = c_Big__Operators_Olinorder__class_OMin(_1283954, hAPP(c_Set_Oimage(_1283954, _1283954, _1283956), _1283958)))], (28134 ^ _779300) ^ [_1284357, _1284359, _1284361] : [class_Lattices_Olattice(_1284357), hAPP(_1284359, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284357), 28139 ^ [_1284357, _1284359, _1284361]), 28140 ^ [_1284357, _1284359, _1284361])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284357), hAPP(_1284359, 28139 ^ [_1284357, _1284359, _1284361])), hAPP(_1284359, 28140 ^ [_1284357, _1284359, _1284361])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284357), _1284361)), -(_1284361 = c_Orderings_Obot__class_Obot(tc_fun(_1284357, tc_HOL_Obool))), -(hAPP(_1284359, c_Big__Operators_Olattice__class_OSup__fin(_1284357, _1284361)) = c_Big__Operators_Olattice__class_OSup__fin(_1284357, hAPP(c_Set_Oimage(_1284357, _1284357, _1284359), _1284361)))], (28154 ^ _779300) ^ [_1284760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284760), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1284760 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 28157 ^ [_1284760]))))], (28161 ^ _779300) ^ [_1284873, _1284875, _1284877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284873)), 28167 ^ _779300 : [(28168 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1284875, 28166 ^ [_1284873, _1284875, _1284877])))], (28170 ^ _779300) ^ [] : [hBOOL(hAPP(_1284875, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28166 ^ [_1284873, _1284875, _1284877]), _1284873)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284877)), 28175 ^ _779300 : [(28176 ^ _779300) ^ [_1285162] : [hBOOL(hAPP(_1284875, _1285162)), -(hBOOL(hAPP(_1284875, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1285162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1284877), _1284873)))))]]], (28182 ^ _779300) ^ [_1285285, _1285287, _1285289, _1285291, _1285293] : [class_Groups_Ocomm__monoid__mult(_1285285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285287), _1285289)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1285287, tc_HOL_Obool)), _1285291), _1285289)), 28196 ^ _779300 : [(28197 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1285287), 28195 ^ [_1285285, _1285287, _1285289, _1285291, _1285293]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285287, tc_HOL_Obool)), _1285289), _1285291))))], (28199 ^ _779300) ^ [] : [hAPP(_1285293, 28195 ^ [_1285285, _1285287, _1285289, _1285291, _1285293]) = c_Groups_Oone__class_Oone(_1285285)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1285287, _1285285), _1285293), _1285289) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1285287, _1285285), _1285293), _1285291))], (28203 ^ _779300) ^ [_1285736, _1285738, _1285740, _1285742, _1285744] : [class_Groups_Ocomm__monoid__mult(_1285736), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285738), _1285740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1285738, tc_HOL_Obool)), _1285742), _1285740)), 28217 ^ _779300 : [(28218 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1285738), 28216 ^ [_1285736, _1285738, _1285740, _1285742, _1285744]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285738, tc_HOL_Obool)), _1285740), _1285742))))], (28220 ^ _779300) ^ [] : [hAPP(_1285744, 28216 ^ [_1285736, _1285738, _1285740, _1285742, _1285744]) = c_Groups_Oone__class_Oone(_1285736)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1285738, _1285736), _1285744), _1285742) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1285738, _1285736), _1285744), _1285740))], (28224 ^ _779300) ^ [_1286187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1286187)), 28228 ^ _779300 : [(28229 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28227 ^ [_1286187])))], (28231 ^ _779300) ^ [] : [-(_1286187 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 28227 ^ [_1286187]))]]], (28233 ^ _779300) ^ [_1286317, _1286319] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1286317), _1286319)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1286317, tc_HOL_Obool)), hAPP(c_Set_OPow(_1286317), _1286319)) = 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(_1286317), _1286319)))], (28239 ^ _779300) ^ [_1286444, _1286446, _1286448, _1286450] : [class_Orderings_Olinorder(_1286444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286444), _1286446), _1286448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286444), _1286448), _1286450)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286444, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1286444, _1286446, _1286448)), c_SetInterval_Oord__class_OatLeastAtMost(_1286444, _1286448, _1286450)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1286444, _1286446, _1286450))], (28253 ^ _779300) ^ [_1286724, _1286726] : [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)), _1286724), 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)), _1286726), 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)), _1286724), _1286726)), c_Int_Ointrel)))], (28259 ^ _779300) ^ [_1286855, _1286857] : [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)), _1286855), _1286857)), 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)), _1286855), 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)), _1286857), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (28265 ^ _779300) ^ [_1286992, _1286994] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1286992, _1286994))))], (28267 ^ _779300) ^ [_1287023, _1287025] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1287023, _1287025))))], (28269 ^ _779300) ^ [_1287054, _1287056, _1287058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287054, tc_HOL_Obool)), _1287056), _1287058)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1287054, tc_HOL_Obool)), _1287056), hAPP(c_Set_OPow(_1287054), _1287058))))], (28275 ^ _779300) ^ [_1287183, _1287185, _1287187, _1287189, _1287191] : [-(hAPP(c_Relation_OImage(_1287183, _1287185, _1287187), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287183, tc_HOL_Obool)), _1287189), _1287191)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287185, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1287183, _1287185, _1287187), _1287189)), hAPP(c_Relation_OImage(_1287183, _1287185, _1287187), _1287191)))], (28277 ^ _779300) ^ [_1287269, _1287271] : [hAPP(c_Set_OPow(_1287269), _1287271) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1287269, tc_HOL_Obool), tc_HOL_Obool))], (28279 ^ _779300) ^ [_1287307, _1287309] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1287307, _1287309)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1287307), hAPP(c_Nat_OSuc, _1287309)))], (28281 ^ _779300) ^ [_1287365, _1287367, _1287369] : [hAPP(c_Set_Oimage(_1287367, tc_fun(_1287367, tc_HOL_Obool), _1287365), _1287369) = hAPP(c_Set_OPow(_1287367), _1287369)], (28283 ^ _779300) ^ [_1287407, _1287409] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1287407, tc_HOL_Obool)), _1287409), hAPP(c_Set_OPow(_1287407), _1287409))))], (28285 ^ _779300) ^ [_1287447, _1287449, _1287451] : [-(hAPP(c_Relation_OImage(_1287447, _1287449, _1287451), c_Orderings_Obot__class_Obot(tc_fun(_1287447, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1287449, tc_HOL_Obool)))], (28287 ^ _779300) ^ [_1287491, _1287493] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1287491, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1287491, tc_HOL_Obool))), hAPP(c_Set_OPow(_1287491), _1287493))))], (28289 ^ _779300) ^ [_1287536] : [-(hAPP(c_Set_OPow(_1287536), c_Orderings_Obot__class_Obot(tc_fun(_1287536, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1287536, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1287536, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1287536, tc_HOL_Obool), tc_HOL_Obool))))], (28291 ^ _779300) ^ [_1287608, _1287610] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1287608, tc_HOL_Obool)), hAPP(c_Set_OPow(_1287608), _1287610))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1287608), _1287610)))], (28297 ^ _779300) ^ [_1287713, _1287715] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1287713), _1287715)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1287713, tc_HOL_Obool)), hAPP(c_Set_OPow(_1287713), _1287715))))], (28303 ^ _779300) ^ [_1287824, _1287826, _1287828] : [-(hAPP(c_Set_OPow(_1287824), hAPP(hAPP(c_Set_Oinsert(_1287824), _1287826), _1287828)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1287824, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1287824), _1287828)), hAPP(c_Set_Oimage(tc_fun(_1287824, tc_HOL_Obool), tc_fun(_1287824, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1287824), _1287826)), hAPP(c_Set_OPow(_1287824), _1287828))))], (28305 ^ _779300) ^ [_1287906, _1287908, _1287910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287906, tc_HOL_Obool)), _1287908), _1287910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1287906, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1287906), _1287908)), hAPP(c_Set_OPow(_1287906), _1287910))))], (28311 ^ _779300) ^ [_1288051, _1288053, _1288055] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1288051, tc_HOL_Obool)), _1288053), hAPP(c_Set_OPow(_1288051), _1288055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288051, tc_HOL_Obool)), _1288053), _1288055)))], (28317 ^ _779300) ^ [_1288198, _1288200, _1288202] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1288198, tc_HOL_Obool)), _1288200), hAPP(c_Set_OPow(_1288198), _1288202))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288198, tc_HOL_Obool)), _1288200), _1288202)))], (28323 ^ _779300) ^ [_1288323, _1288325, _1288327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288323, tc_HOL_Obool)), _1288325), _1288327)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1288323, tc_HOL_Obool)), _1288325), hAPP(c_Set_OPow(_1288323), _1288327))))], (28329 ^ _779300) ^ [_1288454, _1288456, _1288458, _1288460, _1288462] : [hAPP(c_Set_Oimage(_1288454, _1288456, _1288458), _1288460) = _1288462, -(hAPP(c_Set_Oimage(tc_fun(_1288454, tc_HOL_Obool), tc_fun(_1288456, tc_HOL_Obool), c_Set_Oimage(_1288454, _1288456, _1288458)), hAPP(c_Set_OPow(_1288454), _1288460)) = hAPP(c_Set_OPow(_1288456), _1288462))], (28335 ^ _779300) ^ [_1288605, _1288607, _1288609] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1288605, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1288605, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1288605), _1288607)), hAPP(c_Set_OPow(_1288605), _1288609))), hAPP(c_Set_OPow(_1288605), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288605, tc_HOL_Obool)), _1288607), _1288609)))))], (28337 ^ _779300) ^ [_1288685, _1288687, _1288689] : [-(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)), _1288685)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1288687, _1288689)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1288687), _1288685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1288689), _1288685)))], (28339 ^ _779300) ^ [_1288742, _1288744] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1288742, _1288744) = 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), _1288742), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1288744))))], (28341 ^ _779300) ^ [_1288784, _1288786] : [c_Nat__Transfer_Ois__nat(_1288784), c_Nat__Transfer_Ois__nat(_1288786), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1288784, _1288786) = 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, _1288784), hAPP(c_Int_Onat, _1288786))))], (28351 ^ _779300) ^ [_1288943, _1288945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1288943), hAPP(c_Nat_OSuc, _1288945))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1288943, hAPP(c_Nat_OSuc, _1288945)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1288945)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1288943, _1288945)))], (28357 ^ _779300) ^ [_1289076, _1289078, _1289080, _1289082, _1289084, _1289086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1289076, _1289078), tc_HOL_Obool)), _1289080), _1289082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289076, tc_HOL_Obool)), _1289084), _1289086)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289078, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1289076, _1289078, _1289080), _1289084)), hAPP(c_Relation_OImage(_1289076, _1289078, _1289082), _1289086))))], (28367 ^ _779300) ^ [_1289315, _1289317, _1289319, _1289321, _1289323] : [-(hAPP(c_Relation_OImage(_1289315, _1289317, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1289315, _1289317), tc_HOL_Obool)), _1289319), _1289321)), _1289323) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289317, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1289315, _1289317, _1289319), _1289323)), hAPP(c_Relation_OImage(_1289315, _1289317, _1289321), _1289323)))], (28369 ^ _779300) ^ [_1289392, _1289394] : [c_Nat__Transfer_Ois__nat(_1289392), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1289392, _1289394)))], (28375 ^ _779300) ^ [_1289473, _1289475, _1289477] : [class_Orderings_Oorder(_1289473), 28378 ^ _779300 : [(28379 ^ _779300) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1289473, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1289473, _1289475, _1289477), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289473), _1289475), _1289477))], (28385 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289473), _1289475), _1289477))), -(c_Orderings_Obot__class_Obot(tc_fun(_1289473, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1289473, _1289475, _1289477))]]], (28391 ^ _779300) ^ [_1289692, _1289694, _1289696] : [class_Orderings_Oorder(_1289692), 28394 ^ _779300 : [(28395 ^ _779300) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1289692, _1289694, _1289696) = c_Orderings_Obot__class_Obot(tc_fun(_1289692, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289692), _1289694), _1289696))], (28401 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289692), _1289694), _1289696))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1289692, _1289694, _1289696) = c_Orderings_Obot__class_Obot(tc_fun(_1289692, tc_HOL_Obool)))]]], (28407 ^ _779300) ^ [_1289911, _1289913, _1289915] : [class_Orderings_Oorder(_1289911), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289911), _1289913), _1289915)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1289911, _1289915, _1289913) = c_Orderings_Obot__class_Obot(tc_fun(_1289911, tc_HOL_Obool)))], (28417 ^ _779300) ^ [_1290074, _1290076, _1290078, _1290080, _1290082] : [class_Orderings_Oorder(_1290074), 28420 ^ _779300 : [(28421 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290074, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1290074, _1290076, _1290078)), c_SetInterval_Oord__class_OatLeastAtMost(_1290074, _1290080, _1290082))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290074), _1290076), _1290078)), 28428 ^ _779300 : [(28429 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290074), _1290080), _1290076)))], (28431 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290074), _1290078), _1290082)))]]], (28433 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290074, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1290074, _1290076, _1290078)), c_SetInterval_Oord__class_OatLeastAtMost(_1290074, _1290080, _1290082)))), 28434 ^ _779300 : [(28435 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290074), _1290076), _1290078)))], (28437 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290074), _1290080), _1290076)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290074), _1290078), _1290082))]]]]], (28445 ^ _779300) ^ [_1290577, _1290579, _1290581] : [class_Orderings_Oorder(_1290577), _1290579 = _1290581, -(c_SetInterval_Oord__class_OatLeastAtMost(_1290577, _1290579, _1290581) = hAPP(hAPP(c_Set_Oinsert(_1290577), _1290579), c_Orderings_Obot__class_Obot(tc_fun(_1290577, tc_HOL_Obool))))], (28455 ^ _779300) ^ [_1290742, _1290744, _1290746, _1290748] : [class_Orderings_Oorder(_1290742), 28458 ^ _779300 : [(28459 ^ _779300) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1290742, _1290744, _1290746) = hAPP(hAPP(c_Set_Oinsert(_1290742), _1290748), c_Orderings_Obot__class_Obot(tc_fun(_1290742, tc_HOL_Obool))), 28462 ^ _779300 : [(28463 ^ _779300) ^ [] : [-(_1290744 = _1290746)], (28465 ^ _779300) ^ [] : [-(_1290746 = _1290748)]]], (28467 ^ _779300) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1290742, _1290744, _1290746) = hAPP(hAPP(c_Set_Oinsert(_1290742), _1290748), c_Orderings_Obot__class_Obot(tc_fun(_1290742, tc_HOL_Obool)))), _1290744 = _1290746, _1290746 = _1290748]]], (28477 ^ _779300) ^ [_1291086, _1291088] : [class_Orderings_Oorder(_1291086), -(c_SetInterval_Oord__class_OatLeastAtMost(_1291086, _1291088, _1291088) = hAPP(hAPP(c_Set_Oinsert(_1291086), _1291088), c_Orderings_Obot__class_Obot(tc_fun(_1291086, tc_HOL_Obool))))], (28483 ^ _779300) ^ [_1291195, _1291197, _1291199] : [class_Groups_Oordered__ab__group__add(_1291195), -(hAPP(c_Set_Oimage(_1291195, _1291195, c_Groups_Ouminus__class_Ouminus(_1291195)), c_SetInterval_Oord__class_OatLeastAtMost(_1291195, _1291197, _1291199)) = c_SetInterval_Oord__class_OatLeastAtMost(_1291195, hAPP(c_Groups_Ouminus__class_Ouminus(_1291195), _1291199), hAPP(c_Groups_Ouminus__class_Ouminus(_1291195), _1291197)))], (28489 ^ _779300) ^ [_1291326, _1291328, _1291330, _1291332, _1291334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291326, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1291328, _1291326, _1291330), _1291332)), _1291334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1291326, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1291328, tc_HOL_Obool), tc_fun(_1291326, tc_HOL_Obool), c_Set_Oimage(_1291328, _1291326, _1291330)), hAPP(c_Set_OPow(_1291328), _1291332))), hAPP(c_Set_OPow(_1291326), _1291334))))], (28495 ^ _779300) ^ [_1291523, _1291525] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1291523), _1291525) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1291523, _1291525))], (28497 ^ _779300) ^ [_1291559, _1291561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291559)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1291559, _1291561)))], (28503 ^ _779300) ^ [_1291670, _1291672, _1291674, _1291676, _1291678] : [hBOOL(hAPP(hAPP(c_member(_1291670), _1291672), hAPP(c_Relation_OImage(_1291674, _1291670, _1291676), _1291678))), 28507 ^ _779300 : [(28508 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1291674), 28506 ^ [_1291670, _1291672, _1291674, _1291676, _1291678]), _1291678)))], (28510 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1291674, _1291670)), hAPP(hAPP(c_Product__Type_OPair(_1291674, _1291670), 28506 ^ [_1291670, _1291672, _1291674, _1291676, _1291678]), _1291672)), _1291676)))]]], (28512 ^ _779300) ^ [_1291886, _1291888, _1291890, _1291892, _1291894] : [-(hBOOL(hAPP(hAPP(c_member(_1291886), _1291888), hAPP(c_Relation_OImage(_1291890, _1291886, _1291892), _1291894)))), 28513 ^ _779300 : [(28514 ^ _779300) ^ [_1291972] : [hBOOL(hAPP(hAPP(c_member(_1291890), _1291972), _1291894)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1291890, _1291886)), hAPP(hAPP(c_Product__Type_OPair(_1291890, _1291886), _1291972), _1291888)), _1291892))]]], (28522 ^ _779300) ^ [_1292152, _1292154, _1292156, _1292158, _1292160, _1292162] : [hBOOL(hAPP(hAPP(c_member(_1292152), _1292154), _1292156)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1292152, _1292158)), hAPP(hAPP(c_Product__Type_OPair(_1292152, _1292158), _1292154), _1292160)), _1292162)), -(hBOOL(hAPP(hAPP(c_member(_1292158), _1292160), hAPP(c_Relation_OImage(_1292152, _1292158, _1292162), _1292156))))], (28532 ^ _779300) ^ [_1292377, _1292379] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1292377, _1292379)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1292379)), _1292377))], (28534 ^ _779300) ^ [_1292418, _1292420] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1292418), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1292420) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1292418, _1292420))], (28536 ^ _779300) ^ [_1292457, _1292459, _1292461, _1292463, _1292465] : [class_Orderings_Oorder(_1292457), 28539 ^ _779300 : [(28540 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1292457, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1292457, _1292459, _1292461)), c_SetInterval_Oord__class_OatLeastAtMost(_1292457, _1292463, _1292465))), 28543 ^ _779300 : [(28558 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292457), _1292463), _1292465)))], (28544 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292457), _1292459), _1292461)), 28547 ^ _779300 : [(28548 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292457), _1292463), _1292459)))], (28550 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292457), _1292461), _1292465)))], (28552 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292457), _1292463), _1292459))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292457), _1292461), _1292465)))]]]]], (28560 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1292457, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1292457, _1292459, _1292461)), c_SetInterval_Oord__class_OatLeastAtMost(_1292457, _1292463, _1292465)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292457), _1292463), _1292465)), 28563 ^ _779300 : [(28564 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292457), _1292459), _1292461)))], (28566 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292457), _1292463), _1292459)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292457), _1292461), _1292465)), 28573 ^ _779300 : [(28574 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292457), _1292463), _1292459))], (28576 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292457), _1292461), _1292465))]]]]]]], (28582 ^ _779300) ^ [_1293228, _1293230, _1293232, _1293234] : [class_Orderings_Olinorder(_1293228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293228), _1293230), _1293232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293228), _1293232), _1293234)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293228, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1293228, _1293230, _1293232)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1293228, _1293232, _1293234)) = c_SetInterval_Oord__class_OatLeastAtMost(_1293228, _1293230, _1293234))], (28596 ^ _779300) ^ [_1293502, _1293504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293502), _1293504)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1293504, _1293502) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (28602 ^ _779300) ^ [_1293591, _1293593] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293591), _1293593))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1293593, _1293591) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1293593), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1293593), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1293591)))], (28608 ^ _779300) ^ [_1293678, _1293680, _1293682, _1293684, _1293686] : [hBOOL(hAPP(hAPP(c_member(_1293678), _1293680), hAPP(c_Relation_OImage(_1293682, _1293678, _1293684), hAPP(hAPP(c_Set_Oinsert(_1293682), _1293686), c_Orderings_Obot__class_Obot(tc_fun(_1293682, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1293682, _1293678)), hAPP(hAPP(c_Product__Type_OPair(_1293682, _1293678), _1293686), _1293680)), _1293684)))], (28614 ^ _779300) ^ [_1293849, _1293851, _1293853, _1293855, _1293857] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1293853, _1293849)), hAPP(hAPP(c_Product__Type_OPair(_1293853, _1293849), _1293857), _1293851)), _1293855)), -(hBOOL(hAPP(hAPP(c_member(_1293849), _1293851), hAPP(c_Relation_OImage(_1293853, _1293849, _1293855), hAPP(hAPP(c_Set_Oinsert(_1293853), _1293857), c_Orderings_Obot__class_Obot(tc_fun(_1293853, tc_HOL_Obool)))))))], (28620 ^ _779300) ^ [_1294026, _1294028] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1294026, _1294028)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1294028), _1294026)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (28622 ^ _779300) ^ [_1294073, _1294075, _1294077] : [class_Orderings_Olinorder(_1294073), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294073), _1294075), _1294077)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294073, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1294073), _1294075), c_Orderings_Obot__class_Obot(tc_fun(_1294073, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1294073, _1294075, _1294077)) = c_SetInterval_Oord__class_OatLeastAtMost(_1294073, _1294075, _1294077))], (28632 ^ _779300) ^ [_1294282, _1294284, _1294286] : [class_Rings_Oring__1(_1294282), -(hAPP(c_Int_Oring__1__class_Oof__int(_1294282), 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), _1294284), _1294286)), 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(_1294282), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1294282), _1294284)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1294282), _1294286)))], (28638 ^ _779300) ^ [] : [-(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))))))], (28640 ^ _779300) ^ [_1294459, _1294461, _1294463, _1294465] : [-(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), _1294459), _1294461)), 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), _1294463), _1294465)), 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), _1294459), _1294463)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1294461), _1294465))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1294459), _1294465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1294461), _1294463)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28642 ^ _779300) ^ [_1294605, _1294607, _1294609, _1294611] : [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), _1294605), _1294607)), 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), _1294609), _1294611)), 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), _1294605), _1294611)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294609), _1294607))))], (28648 ^ _779300) ^ [_1294798, _1294800, _1294802, _1294804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294798), _1294804)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294802), _1294800))), -(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), _1294798), _1294800)), 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), _1294802), _1294804)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (28654 ^ _779300) ^ [_1294997, _1294999] : [-(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), _1294997), _1294999)), 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), _1294999), _1294997)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28656 ^ _779300) ^ [] : [-(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))))))], (28658 ^ _779300) ^ [_1295079] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1295079) = 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), _1295079), 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))))))], (28660 ^ _779300) ^ [_1295123, _1295125, _1295127, _1295129] : [-(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), _1295123), _1295125)), 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), _1295127), _1295129)), 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), _1295123), _1295127)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1295125), _1295129))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28662 ^ _779300) ^ [_1295224, _1295226] : [-(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), _1295224), _1295226)), 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), _1295224), _1295226))], (28664 ^ _779300) ^ [_1295297, _1295299, _1295301, _1295303] : [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), _1295297), _1295299)), 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), _1295301), _1295303)), 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), _1295297), _1295303)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1295301), _1295299))))], (28670 ^ _779300) ^ [_1295490, _1295492, _1295494, _1295496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1295490), _1295496)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1295494), _1295492))), -(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), _1295490), _1295492)), 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), _1295494), _1295496)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (28676 ^ _779300) ^ [_1295704, _1295706] : [28684 ^ _779300 : [(28685 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 28683 ^ [_1295704, _1295706]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1295704))))], (28687 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1295706, 28683 ^ [_1295704, _1295706])))]], 28677 ^ _779300 : [(28678 ^ _779300) ^ [_1295773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1295773), _1295704)), hBOOL(hAPP(_1295706, _1295773))]]], (28689 ^ _779300) ^ [_1295934, _1295936] : [28697 ^ _779300 : [(28698 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 28696 ^ [_1295934, _1295936]), _1295934)))], (28700 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1295936, 28696 ^ [_1295934, _1295936])))]], 28690 ^ _779300 : [(28691 ^ _779300) ^ [_1296003] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1296003), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1295934))), hBOOL(hAPP(_1295936, _1296003))]]], (28702 ^ _779300) ^ [_1296189, _1296191] : [28704 ^ _779300 : [(28705 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 28703 ^ [_1296189, _1296191]), _1296189)))], (28707 ^ _779300) ^ [] : [hBOOL(hAPP(_1296191, 28703 ^ [_1296189, _1296191]))]], 28708 ^ _779300 : [(28709 ^ _779300) ^ [_1296340] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1296340), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1296189))), -(hBOOL(hAPP(_1296191, _1296340)))]]], (28715 ^ _779300) ^ [_1296443, _1296445] : [28717 ^ _779300 : [(28718 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 28716 ^ [_1296443, _1296445]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1296443))))], (28720 ^ _779300) ^ [] : [hBOOL(hAPP(_1296445, 28716 ^ [_1296443, _1296445]))]], 28721 ^ _779300 : [(28722 ^ _779300) ^ [_1296598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1296598), _1296443)), -(hBOOL(hAPP(_1296445, _1296598)))]]], (28728 ^ _779300) ^ [_1296699, _1296701, _1296703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1296699)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1296701), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1296703)), 28735 ^ _779300 : [(28736 ^ _779300) ^ [_1296907] : [28738 ^ _779300 : [(28739 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28737 ^ [_1296699, _1296701, _1296703, _1296907]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1296699))))], (28742 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28740 ^ [_1296699, _1296701, _1296703, _1296907]), _1296703)))], (28744 ^ _779300) ^ [] : [-(_1296907 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28740 ^ [_1296699, _1296701, _1296703, _1296907]), 28737 ^ [_1296699, _1296701, _1296703, _1296907]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296701), _1296907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296701), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1296907), _1296699))))]]], (28752 ^ _779300) ^ [_1297183, _1297185, _1297187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1297183)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1297185), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1297187)), 28759 ^ _779300 : [(28760 ^ _779300) ^ [_1297391] : [28762 ^ _779300 : [(28763 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28761 ^ [_1297183, _1297185, _1297187, _1297391]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1297183))))], (28766 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28764 ^ [_1297183, _1297185, _1297187, _1297391]), _1297187)))], (28768 ^ _779300) ^ [] : [-(_1297391 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28764 ^ [_1297183, _1297185, _1297187, _1297391]), 28761 ^ [_1297183, _1297185, _1297187, _1297391]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1297391), _1297185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1297391), _1297183)), _1297185)))]]], (28776 ^ _779300) ^ [_1297685, _1297687, _1297689] : [hBOOL(hAPP(c_Predicate_OPowp(_1297685, hAPP(hAPP(c_COMBC(_1297685, tc_fun(_1297685, tc_HOL_Obool), tc_HOL_Obool), c_member(_1297685)), _1297687)), _1297689)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1297685, tc_HOL_Obool)), _1297689), hAPP(c_Set_OPow(_1297685), _1297687))))], (28782 ^ _779300) ^ [_1297830, _1297832, _1297834] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1297830, tc_HOL_Obool)), _1297834), hAPP(c_Set_OPow(_1297830), _1297832))), -(hBOOL(hAPP(c_Predicate_OPowp(_1297830, hAPP(hAPP(c_COMBC(_1297830, tc_fun(_1297830, tc_HOL_Obool), tc_HOL_Obool), c_member(_1297830)), _1297832)), _1297834)))], (28788 ^ _779300) ^ [_1297981, _1297983, _1297985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1297981)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1297983), _1297985)), 28795 ^ _779300 : [(28796 ^ _779300) ^ [_1298171] : [28798 ^ _779300 : [(28799 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28797 ^ [_1297981, _1297983, _1297985, _1298171]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1297981))))], (28802 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28800 ^ [_1297981, _1297983, _1297985, _1298171]), _1297985)))], (28804 ^ _779300) ^ [] : [-(_1298171 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28800 ^ [_1297981, _1297983, _1297985, _1298171]), 28797 ^ [_1297981, _1297983, _1297985, _1298171]))]], -(_1298171 = _1297983), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1298171), _1297981) = _1297983]]], (28812 ^ _779300) ^ [_1298431, _1298433, _1298435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298431)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1298433), _1298435)), 28819 ^ _779300 : [(28820 ^ _779300) ^ [_1298621] : [28822 ^ _779300 : [(28823 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28821 ^ [_1298431, _1298433, _1298435, _1298621]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1298431))))], (28826 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28824 ^ [_1298431, _1298433, _1298435, _1298621]), _1298435)))], (28828 ^ _779300) ^ [] : [-(_1298621 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28824 ^ [_1298431, _1298433, _1298435, _1298621]), 28821 ^ [_1298431, _1298433, _1298435, _1298621]))]], -(_1298621 = _1298433), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1298621), _1298431) = _1298433]]], (28836 ^ _779300) ^ [_1298881, _1298883, _1298885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298881)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1298883), _1298885)), 28843 ^ _779300 : [(28844 ^ _779300) ^ [_1299077] : [28846 ^ _779300 : [(28847 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28845 ^ [_1298881, _1298883, _1298885, _1299077]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1298881))))], (28850 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28848 ^ [_1298881, _1298883, _1298885, _1299077]), _1298885)))], (28852 ^ _779300) ^ [] : [-(_1299077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28848 ^ [_1298881, _1298883, _1298885, _1299077]), 28845 ^ [_1298881, _1298883, _1298885, _1299077]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1298883), _1299077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1298883), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1299077), _1298881))))]]], (28860 ^ _779300) ^ [_1299353, _1299355, _1299357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1299353, tc_HOL_Obool)), _1299355), _1299357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1299353, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1299353, _1299355)), c_Predicate_OPowp(_1299353, _1299357))))], (28866 ^ _779300) ^ [_1299490, _1299492, _1299494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299490)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1299492), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1299494)), 28876 ^ _779300 : [(28877 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28875 ^ [_1299490, _1299492, _1299494]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1299490))))], (28880 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28878 ^ [_1299490, _1299492, _1299494]), _1299494)))], (28882 ^ _779300) ^ [] : [-(_1299492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28878 ^ [_1299490, _1299492, _1299494]), 28875 ^ [_1299490, _1299492, _1299494]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1299492), _1299490) = _1299492)], (28886 ^ _779300) ^ [_1299829, _1299831, _1299833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299829)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1299831), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1299833)), 28896 ^ _779300 : [(28897 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28895 ^ [_1299829, _1299831, _1299833]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1299829))))], (28900 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28898 ^ [_1299829, _1299831, _1299833]), _1299833)))], (28902 ^ _779300) ^ [] : [-(_1299831 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28898 ^ [_1299829, _1299831, _1299833]), 28895 ^ [_1299829, _1299831, _1299833]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1299831), _1299829) = _1299831)], (28906 ^ _779300) ^ [_1300168, _1300170, _1300172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300168)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1300170), _1300172)), 28913 ^ _779300 : [(28914 ^ _779300) ^ [_1300364] : [28916 ^ _779300 : [(28917 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28915 ^ [_1300168, _1300170, _1300172, _1300364]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1300168))))], (28920 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28918 ^ [_1300168, _1300170, _1300172, _1300364]), _1300172)))], (28922 ^ _779300) ^ [] : [-(_1300364 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28918 ^ [_1300168, _1300170, _1300172, _1300364]), 28915 ^ [_1300168, _1300170, _1300172, _1300364]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1300364), _1300170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1300364), _1300168)), _1300170)))]]], (28930 ^ _779300) ^ [_1300640, _1300642, _1300644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300640)), 28933 ^ _779300 : [(28934 ^ _779300) ^ [_1300774] : [28936 ^ _779300 : [(28937 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28935 ^ [_1300640, _1300642, _1300644, _1300774]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1300640))))], (28940 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28938 ^ [_1300640, _1300642, _1300644, _1300774]), _1300642)))], (28942 ^ _779300) ^ [] : [-(_1300774 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28938 ^ [_1300640, _1300642, _1300644, _1300774]), 28935 ^ [_1300640, _1300642, _1300644, _1300774]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1300644), _1300774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1300644), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1300774), _1300640))))]]], (28950 ^ _779300) ^ [_1301048, _1301050, _1301052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301048)), 28953 ^ _779300 : [(28954 ^ _779300) ^ [_1301182] : [28956 ^ _779300 : [(28957 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28955 ^ [_1301048, _1301050, _1301052, _1301182]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1301048))))], (28960 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28958 ^ [_1301048, _1301050, _1301052, _1301182]), _1301050)))], (28962 ^ _779300) ^ [] : [-(_1301182 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28958 ^ [_1301048, _1301050, _1301052, _1301182]), 28955 ^ [_1301048, _1301050, _1301052, _1301182]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1301182), _1301052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1301182), _1301048)), _1301052)))]]], (28972 ^ _779300) ^ [_1301456] : [-(_1301456 = 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), 28969 ^ [_1301456]), 28970 ^ [_1301456])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28974 ^ _779300) ^ [_1301507, _1301509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301507)), 28983 ^ _779300 : [(28984 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1301509, 28979 ^ [_1301507, _1301509])))], (28986 ^ _779300) ^ [] : [hBOOL(hAPP(_1301509, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28979 ^ [_1301507, _1301509]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 28980 ^ [_1301507, _1301509]), _1301507))))]], 28987 ^ _779300 : [(28988 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1301509, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28979 ^ [_1301507, _1301509]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 28980 ^ [_1301507, _1301509]), _1301507)))))], (28990 ^ _779300) ^ [] : [hBOOL(hAPP(_1301509, 28979 ^ [_1301507, _1301509]))]], 28991 ^ _779300 : [(28992 ^ _779300) ^ [] : [28993 ^ _779300 : [(28994 ^ _779300) ^ [_1301939] : [hBOOL(hAPP(_1301509, _1301939))]], 28996 ^ _779300 : [(28997 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28995 ^ [_1301507, _1301509]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1301507))))], (28999 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1301509, 28995 ^ [_1301507, _1301509])))]]], (29001 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1301509, 29008 ^ [_1301507, _1301509]))), 29002 ^ _779300 : [(29003 ^ _779300) ^ [_1302054] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1302054), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1301507))), hBOOL(hAPP(_1301509, _1302054))]]]]], (29012 ^ _779300) ^ [_1302201, _1302203, _1302205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302201)), 29015 ^ _779300 : [(29016 ^ _779300) ^ [_1302335] : [29018 ^ _779300 : [(29019 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29017 ^ [_1302201, _1302203, _1302205, _1302335]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1302201))))], (29022 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29020 ^ [_1302201, _1302203, _1302205, _1302335]), _1302203)))], (29024 ^ _779300) ^ [] : [-(_1302335 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 29020 ^ [_1302201, _1302203, _1302205, _1302335]), 29017 ^ [_1302201, _1302203, _1302205, _1302335]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1302335), _1302205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1302335), _1302201)), _1302205)))]]], (29032 ^ _779300) ^ [_1302609, _1302611, _1302613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302609)), 29035 ^ _779300 : [(29036 ^ _779300) ^ [_1302743] : [29038 ^ _779300 : [(29039 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29037 ^ [_1302609, _1302611, _1302613, _1302743]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1302609))))], (29042 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29040 ^ [_1302609, _1302611, _1302613, _1302743]), _1302611)))], (29044 ^ _779300) ^ [] : [-(_1302743 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 29040 ^ [_1302609, _1302611, _1302613, _1302743]), 29037 ^ [_1302609, _1302611, _1302613, _1302743]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1302613), _1302743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1302613), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1302743), _1302609))))]]], (29052 ^ _779300) ^ [_1303029, _1303031, _1303033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1303029), _1303031)), -(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)), _1303029)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1303033), _1303031)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1303033), _1303029)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1303031), _1303029)))], (29058 ^ _779300) ^ [_1303181, _1303183, _1303185] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1303181), _1303183))), 29061 ^ _779300 : [(29062 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1303185), _1303183)), -(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)), _1303181)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1303185), _1303183)) = 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))))], (29068 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1303185), _1303183))), -(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)), _1303181)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1303185), _1303183)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (29074 ^ _779300) ^ [_1303450] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1303450) = 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), _1303450))))], (29076 ^ _779300) ^ [_1303486, _1303488, _1303490, _1303492, _1303494] : [hBOOL(hAPP(hAPP(c_member(_1303486), _1303488), hAPP(c_Relation_OImage(_1303490, _1303486, _1303492), _1303494))), 29080 ^ _779300 : [(29081 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1303490, _1303486)), hAPP(hAPP(c_Product__Type_OPair(_1303490, _1303486), 29079 ^ [_1303486, _1303488, _1303490, _1303492, _1303494]), _1303488)), _1303492)))], (29083 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1303490), 29079 ^ [_1303486, _1303488, _1303490, _1303492, _1303494]), _1303494)))]]], (29085 ^ _779300) ^ [_1303710, _1303712] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1303710), _1303712))))], (29087 ^ _779300) ^ [_1303743] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1303743))))], (29089 ^ _779300) ^ [_1303771, _1303773, _1303775, _1303777, _1303779] : [class_Orderings_Olinorder(_1303771), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1303771, _1303773), _1303775) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1303771, _1303777), _1303779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303771), _1303773), _1303775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303771), _1303777), _1303779)), -(_1303775 = _1303779)], (29107 ^ _779300) ^ [_1304078, _1304080, _1304082, _1304084, _1304086] : [class_Orderings_Olinorder(_1304078), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304078, _1304080), _1304082) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304078, _1304084), _1304086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304078), _1304080), _1304082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304078), _1304084), _1304086)), -(_1304080 = _1304084)], (29125 ^ _779300) ^ [_1304385, _1304387, _1304389, _1304391, _1304393] : [class_Orderings_Olinorder(_1304385), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304385), _1304387), _1304389)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304385), _1304391), _1304393)), 29136 ^ _779300 : [(29137 ^ _779300) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304385, _1304387), _1304389) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304385, _1304391), _1304393), 29140 ^ _779300 : [(29141 ^ _779300) ^ [] : [-(_1304387 = _1304391)], (29143 ^ _779300) ^ [] : [-(_1304389 = _1304393)]]], (29145 ^ _779300) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304385, _1304387), _1304389) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1304385, _1304391), _1304393)), _1304387 = _1304391, _1304389 = _1304393]]], (29155 ^ _779300) ^ [_1304866, _1304868, _1304870] : [class_Orderings_Olinorder(_1304866), 29158 ^ _779300 : [(29159 ^ _779300) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1304866), _1304868) = hAPP(c_SetInterval_Oord__class_OatMost(_1304866), _1304870), -(_1304868 = _1304870)], (29165 ^ _779300) ^ [] : [_1304868 = _1304870, -(hAPP(c_SetInterval_Oord__class_OatMost(_1304866), _1304868) = hAPP(c_SetInterval_Oord__class_OatMost(_1304866), _1304870))]]], (29171 ^ _779300) ^ [_1305122, _1305124] : [29179 ^ _779300 : [(29180 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29178 ^ [_1305122, _1305124]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1305122))))], (29182 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1305124, 29178 ^ [_1305122, _1305124])))]], 29172 ^ _779300 : [(29173 ^ _779300) ^ [_1305190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1305190), _1305122)), hBOOL(hAPP(_1305124, _1305190))]]], (29184 ^ _779300) ^ [_1305350, _1305352] : [29192 ^ _779300 : [(29193 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29191 ^ [_1305350, _1305352]), _1305350)))], (29195 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1305352, 29191 ^ [_1305350, _1305352])))]], 29185 ^ _779300 : [(29186 ^ _779300) ^ [_1305418] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1305418), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1305350))), hBOOL(hAPP(_1305352, _1305418))]]], (29197 ^ _779300) ^ [_1305602, _1305604] : [29199 ^ _779300 : [(29200 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29198 ^ [_1305602, _1305604]), _1305602)))], (29202 ^ _779300) ^ [] : [hBOOL(hAPP(_1305604, 29198 ^ [_1305602, _1305604]))]], 29203 ^ _779300 : [(29204 ^ _779300) ^ [_1305752] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1305752), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1305602))), -(hBOOL(hAPP(_1305604, _1305752)))]]], (29210 ^ _779300) ^ [_1305853, _1305855] : [29212 ^ _779300 : [(29213 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29211 ^ [_1305853, _1305855]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1305853))))], (29215 ^ _779300) ^ [] : [hBOOL(hAPP(_1305855, 29211 ^ [_1305853, _1305855]))]], 29216 ^ _779300 : [(29217 ^ _779300) ^ [_1306006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1306006), _1305853)), -(hBOOL(hAPP(_1305855, _1306006)))]]], (29223 ^ _779300) ^ [_1306107, _1306109] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1306107), hAPP(c_Nat_OSuc, _1306109)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1306107, _1306109))], (29225 ^ _779300) ^ [_1306145] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1306145), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (29227 ^ _779300) ^ [_1306174, _1306176] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1306174), _1306176)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1306176), _1306174))], (29229 ^ _779300) ^ [_1306214, _1306216] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1306214), _1306216)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1306214)), hAPP(c_Nat_OSuc, _1306216)))], (29231 ^ _779300) ^ [_1306260, _1306262, _1306264] : [class_Orderings_Oorder(_1306260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306260), _1306262), _1306264)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306260, _1306264), _1306262) = c_Orderings_Obot__class_Obot(tc_fun(_1306260, tc_HOL_Obool)))], (29241 ^ _779300) ^ [_1306427, _1306429, _1306431] : [class_Orderings_Oorder(_1306427), 29244 ^ _779300 : [(29245 ^ _779300) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1306427, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306427, _1306429), _1306431), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306427), _1306429), _1306431))], (29251 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306427), _1306429), _1306431))), -(c_Orderings_Obot__class_Obot(tc_fun(_1306427, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306427, _1306429), _1306431))]]], (29257 ^ _779300) ^ [_1306652, _1306654, _1306656] : [class_Orderings_Oorder(_1306652), 29260 ^ _779300 : [(29261 ^ _779300) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306652, _1306654), _1306656) = c_Orderings_Obot__class_Obot(tc_fun(_1306652, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306652), _1306654), _1306656))], (29267 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306652), _1306654), _1306656))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306652, _1306654), _1306656) = c_Orderings_Obot__class_Obot(tc_fun(_1306652, tc_HOL_Obool)))]]], (29273 ^ _779300) ^ [_1306877, _1306879, _1306881, _1306883, _1306885] : [class_Orderings_Olinorder(_1306877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306877, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306877, _1306879), _1306881)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306877, _1306883), _1306885))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306877), _1306881), _1306879))), 29284 ^ _779300 : [(29285 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306877), _1306883), _1306879)))], (29287 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306877), _1306881), _1306885)))]]], (29289 ^ _779300) ^ [_1307158, _1307160, _1307162, _1307164] : [class_Orderings_Olinorder(_1307158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307158), _1307160), _1307162)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307158), _1307162), _1307164)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307158, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1307158, _1307160), _1307162)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1307158, _1307162), _1307164)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1307158, _1307160), _1307164))], (29303 ^ _779300) ^ [_1307435, _1307437, _1307439, _1307441] : [class_Orderings_Olinorder(_1307435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307435), _1307437), _1307439)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307435, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1307435, _1307437), _1307441)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1307435, _1307437), _1307439)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1307435, _1307439), _1307441))], (29313 ^ _779300) ^ [_1307642, _1307644] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1307642)), _1307644) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1307642, _1307644))], (29315 ^ _779300) ^ [_1307680] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1307680) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1307680))], (29317 ^ _779300) ^ [_1307710, _1307712, _1307714] : [-(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)), _1307710)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1307712), _1307714)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1307712), _1307710)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1307714), _1307710)))], (29319 ^ _779300) ^ [_1307771] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1307771)) = hAPP(c_Nat_OSuc, _1307771))], (29321 ^ _779300) ^ [_1307803] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1307803)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1307803)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1307803)))], (29323 ^ _779300) ^ [_1307844, _1307846, _1307848] : [class_Orderings_Oord(_1307844), 29326 ^ _779300 : [(29327 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1307844), _1307846), hAPP(c_SetInterval_Oord__class_OatMost(_1307844), _1307848))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307844), _1307846), _1307848)))], (29333 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307844), _1307846), _1307848)), -(hBOOL(hAPP(hAPP(c_member(_1307844), _1307846), hAPP(c_SetInterval_Oord__class_OatMost(_1307844), _1307848))))]]], (29339 ^ _779300) ^ [_1308112, _1308114, _1308116] : [class_Orderings_Oorder(_1308112), 29342 ^ _779300 : [(29343 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1308112, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1308112), _1308114)), hAPP(c_SetInterval_Oord__class_OatMost(_1308112), _1308116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308112), _1308114), _1308116)))], (29349 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308112), _1308114), _1308116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1308112, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1308112), _1308114)), hAPP(c_SetInterval_Oord__class_OatMost(_1308112), _1308116))))]]], (29355 ^ _779300) ^ [_1308404] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1308404), hAPP(c_Nat_OSuc, _1308404)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1308404), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (29357 ^ _779300) ^ [_1308442, _1308444, _1308446, _1308448] : [class_Orderings_Olinorder(_1308442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308442), _1308444), _1308446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308442), _1308446), _1308448)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308442, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1308442, _1308444), _1308446)), c_SetInterval_Oord__class_OatLeastAtMost(_1308442, _1308446, _1308448)) = c_SetInterval_Oord__class_OatLeastAtMost(_1308442, _1308444, _1308448))], (29371 ^ _779300) ^ [_1308711, _1308713, _1308715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1308711), _1308713)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1308711), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1308713), _1308715)) = 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, _1308711), _1308713)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1308713), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1308713), _1308715))))], (29377 ^ _779300) ^ [_1308872, _1308874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1308872), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1308874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1308874), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1308872))))), -(_1308872 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1308874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1308874), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1308872))))], (29383 ^ _779300) ^ [_1309019, _1309021, _1309023] : [class_Groups_Oordered__ab__group__add(_1309019), -(hAPP(c_Set_Oimage(_1309019, _1309019, c_Groups_Ouminus__class_Ouminus(_1309019)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1309019, _1309021), _1309023)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1309019, hAPP(c_Groups_Ouminus__class_Ouminus(_1309019), _1309023), hAPP(c_Groups_Ouminus__class_Ouminus(_1309019), _1309021)))], (29389 ^ _779300) ^ [_1309154, _1309156, _1309158] : [class_Groups_Oordered__ab__group__add(_1309154), -(hAPP(c_Set_Oimage(_1309154, _1309154, c_Groups_Ouminus__class_Ouminus(_1309154)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1309154, _1309156, _1309158)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1309154, hAPP(c_Groups_Ouminus__class_Ouminus(_1309154), _1309158)), hAPP(c_Groups_Ouminus__class_Ouminus(_1309154), _1309156)))], (29395 ^ _779300) ^ [_1309298, _1309300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1309298), _1309300)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1309298), hAPP(c_Nat_OSuc, _1309300)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1309300), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1309298), _1309300)))], (29401 ^ _779300) ^ [_1309421, _1309423] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1309421), _1309423))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1309421), hAPP(c_Nat_OSuc, _1309423)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (29407 ^ _779300) ^ [] : [-(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))))], (29409 ^ _779300) ^ [_1309491, _1309493, _1309495] : [class_Orderings_Olinorder(_1309491), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309491), _1309493), _1309495)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309491, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1309491), _1309493)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1309491, _1309493, _1309495)) = hAPP(c_SetInterval_Oord__class_OatMost(_1309491), _1309495))], (29419 ^ _779300) ^ [_1309686, _1309688, _1309690, _1309692] : [class_Orderings_Olinorder(_1309686), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309686), _1309688), _1309690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309686), _1309690), _1309692)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309686, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1309686, _1309688, _1309690)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1309686, _1309690), _1309692)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1309686, _1309688, _1309692))], (29433 ^ _779300) ^ [_1309955, _1309957, _1309959] : [class_Orderings_Olinorder(_1309955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309955), _1309957), _1309959)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309955, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1309955, _1309957), _1309959)), hAPP(hAPP(c_Set_Oinsert(_1309955), _1309959), c_Orderings_Obot__class_Obot(tc_fun(_1309955, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1309955, _1309957, _1309959))], (29443 ^ _779300) ^ [_1310168, _1310170, _1310172] : [class_Orderings_Olinorder(_1310168), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310168), _1310170), _1310172)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310168, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1310168), _1310170), c_Orderings_Obot__class_Obot(tc_fun(_1310168, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1310168, _1310170, _1310172)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1310168, _1310170), _1310172))], (29453 ^ _779300) ^ [_1310381, _1310383, _1310385, _1310387] : [class_Orderings_Olinorder(_1310381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310381), _1310383), _1310385)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310381), _1310385), _1310387)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310381, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1310381, _1310383, _1310385)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1310381, _1310385, _1310387)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1310381, _1310383), _1310387))], (29467 ^ _779300) ^ [_1310650, _1310652, _1310654] : [class_Orderings_Olinorder(_1310650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310650), _1310652), _1310654)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310650, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1310650), _1310652)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1310650, _1310652, _1310654)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1310650), _1310654))], (29477 ^ _779300) ^ [_1310845, _1310847, _1310849] : [class_Orderings_Olinorder(_1310845), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310845), _1310847), _1310849)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310845, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1310845), _1310847)), c_SetInterval_Oord__class_OatLeastAtMost(_1310845, _1310847, _1310849)) = hAPP(c_SetInterval_Oord__class_OatMost(_1310845), _1310849))], (29487 ^ _779300) ^ [_1311040, _1311042] : [class_Orderings_Olinorder(_1311040), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311040, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1311040), _1311042)), hAPP(hAPP(c_Set_Oinsert(_1311040), _1311042), c_Orderings_Obot__class_Obot(tc_fun(_1311040, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1311040), _1311042))], (29493 ^ _779300) ^ [_1311183, _1311185, _1311187, _1311189, _1311191] : [class_Groups_Ocomm__monoid__mult(_1311183), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311185), _1311187)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311185), _1311189)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311185, tc_HOL_Obool)), _1311187), _1311189) = c_Orderings_Obot__class_Obot(tc_fun(_1311185, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1311183, _1311185, c_Groups_Otimes__class_Otimes(_1311183)), _1311191), c_Groups_Oone__class_Oone(_1311183)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311185, tc_HOL_Obool)), _1311187), _1311189)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1311183), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1311183, _1311185, c_Groups_Otimes__class_Otimes(_1311183)), _1311191), c_Groups_Oone__class_Oone(_1311183)), _1311187)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1311183, _1311185, c_Groups_Otimes__class_Otimes(_1311183)), _1311191), c_Groups_Oone__class_Oone(_1311183)), _1311189)))], (29511 ^ _779300) ^ [_1311626, _1311628, _1311630, _1311632] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311626, tc_HOL_Obool)), _1311628), _1311630), _1311632)), 29514 ^ _779300 : [(29515 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1311628, _1311632)))], (29517 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1311630, _1311632)))]]], (29519 ^ _779300) ^ [_1311771, _1311773, _1311775, _1311777] : [hBOOL(hAPP(_1311771, _1311773)), hBOOL(hAPP(_1311775, _1311773)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311777, tc_HOL_Obool)), _1311771), _1311775), _1311773)))], (29529 ^ _779300) ^ [_1311942] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1311942))))], (29531 ^ _779300) ^ [_1311970, _1311972] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1311970), _1311972))))], (29533 ^ _779300) ^ [_1312003, _1312005, _1312007, _1312009] : [hBOOL(hAPP(hAPP(c_member(_1312003), _1312005), _1312007)), hBOOL(hAPP(hAPP(c_member(_1312003), _1312005), _1312009)), -(hBOOL(hAPP(hAPP(c_member(_1312003), _1312005), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312003, tc_HOL_Obool)), _1312007), _1312009))))], (29543 ^ _779300) ^ [_1312204, _1312206, _1312208, _1312210] : [hBOOL(hAPP(hAPP(c_member(_1312204), _1312206), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312204, tc_HOL_Obool)), _1312208), _1312210))), 29546 ^ _779300 : [(29547 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1312204), _1312206), _1312208)))], (29549 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1312204), _1312206), _1312210)))]]], (29551 ^ _779300) ^ [_1312379, _1312381, _1312383] : [29552 ^ _779300 : [(29553 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312379), _1312381))], (29555 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1312379), _1312383))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1312379), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312379, tc_HOL_Obool)), _1312381), _1312383))))], (29559 ^ _779300) ^ [_1312542, _1312544, _1312546] : [class_Orderings_Oorder(_1312542), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312542, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1312542), _1312544)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1312542, _1312544), _1312546)) = c_Orderings_Obot__class_Obot(tc_fun(_1312542, tc_HOL_Obool)))], (29565 ^ _779300) ^ [_1312673, _1312675, _1312677] : [-(hAPP(c_Set_OPow(_1312673), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312673, tc_HOL_Obool)), _1312675), _1312677)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1312673, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1312673), _1312675)), hAPP(c_Set_OPow(_1312673), _1312677)))], (29567 ^ _779300) ^ [_1312740, _1312742, _1312744, _1312746, _1312748] : [class_Lattices_Olattice(_1312740), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312742, _1312740)), _1312744), _1312746), _1312748) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1312740), hAPP(_1312744, _1312748)), hAPP(_1312746, _1312748)))], (29573 ^ _779300) ^ [_1312877, _1312879, _1312881, _1312883] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312877, tc_HOL_Obool)), _1312879), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312877, tc_HOL_Obool)), _1312881), _1312883)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312877, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312877, tc_HOL_Obool)), _1312879), _1312881)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312877, tc_HOL_Obool)), _1312879), _1312883)))], (29575 ^ _779300) ^ [_1312961, _1312963, _1312965, _1312967] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312961, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312961, tc_HOL_Obool)), _1312963), _1312965)), _1312967) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312961, tc_HOL_Obool)), _1312963), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312961, tc_HOL_Obool)), _1312965), _1312967)))], (29577 ^ _779300) ^ [_1313034, _1313036, _1313038, _1313040] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313034, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1313034, tc_HOL_Obool)), _1313036), _1313038)), _1313040) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1313034, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313034, tc_HOL_Obool)), _1313036), _1313040)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313034, tc_HOL_Obool)), _1313038), _1313040)))], (29579 ^ _779300) ^ [_1313118, _1313120, _1313122, _1313124] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1313118, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313118, tc_HOL_Obool)), _1313120), _1313122)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313118, tc_HOL_Obool)), _1313124), _1313122)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1313118, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313118, tc_HOL_Obool)), _1313120), _1313122)), _1313124))], (29581 ^ _779300) ^ [_1313202] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1313202) = c_Orderings_Oord__class_Omin(_1313202)), class_Lattices_Osemilattice__inf(_1313202), class_Orderings_Olinorder(_1313202)], (29591 ^ _779300) ^ [_1313331, _1313333] : [class_Lattices_Olattice(_1313331), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313331), _1313333), _1313333) = _1313333)], (29597 ^ _779300) ^ [_1313422, _1313424, _1313426, _1313428, _1313430] : [class_Lattices_Olattice(_1313422), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313424, _1313422)), _1313426), _1313428), _1313430) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313422), hAPP(_1313426, _1313430)), hAPP(_1313428, _1313430)))], (29603 ^ _779300) ^ [_1313559, _1313561, _1313563, _1313565] : [class_Lattices_Osemilattice__inf(_1313559), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313559), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313559), _1313561), _1313563)), _1313565) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313559), _1313561), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313559), _1313563), _1313565)))], (29609 ^ _779300) ^ [_1313702, _1313704, _1313706, _1313708] : [class_Lattices_Olattice(_1313702), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313702), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313702), _1313704), _1313706)), _1313708) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313702), _1313704), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313702), _1313706), _1313708)))], (29615 ^ _779300) ^ [_1313845, _1313847, _1313849, _1313851] : [class_Lattices_Osemilattice__inf(_1313845), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313845), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313845), _1313847), _1313849)), _1313851) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313845), _1313847), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313845), _1313849), _1313851)))], (29621 ^ _779300) ^ [_1313988, _1313990, _1313992, _1313994] : [class_Lattices_Osemilattice__inf(_1313988), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313988), _1313990), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313988), _1313992), _1313994)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313988), _1313992), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313988), _1313990), _1313994)))], (29627 ^ _779300) ^ [_1314131, _1314133, _1314135, _1314137] : [class_Lattices_Olattice(_1314131), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314131), _1314133), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314131), _1314135), _1314137)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314131), _1314135), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314131), _1314133), _1314137)))], (29633 ^ _779300) ^ [_1314274, _1314276, _1314278, _1314280] : [class_Lattices_Osemilattice__inf(_1314274), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314274), _1314276), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314274), _1314278), _1314280)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314274), _1314278), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314274), _1314276), _1314280)))], (29639 ^ _779300) ^ [_1314417, _1314419, _1314421] : [class_Lattices_Osemilattice__inf(_1314417), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314417), _1314419), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314417), _1314419), _1314421)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314417), _1314419), _1314421))], (29645 ^ _779300) ^ [_1314542, _1314544, _1314546] : [class_Lattices_Olattice(_1314542), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314542), _1314544), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314542), _1314544), _1314546)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314542), _1314544), _1314546))], (29651 ^ _779300) ^ [_1314667, _1314669, _1314671] : [class_Lattices_Osemilattice__inf(_1314667), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314667), _1314669), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314667), _1314669), _1314671)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314667), _1314669), _1314671))], (29657 ^ _779300) ^ [_1314792, _1314794, _1314796] : [class_Lattices_Osemilattice__inf(_1314792), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314792), _1314794), _1314796) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314792), _1314796), _1314794))], (29663 ^ _779300) ^ [_1314901, _1314903, _1314905] : [class_Lattices_Olattice(_1314901), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314901), _1314903), _1314905) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314901), _1314905), _1314903))], (29669 ^ _779300) ^ [_1315010, _1315012, _1315014] : [class_Lattices_Osemilattice__inf(_1315010), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1315010), _1315012), _1315014) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1315010), _1315014), _1315012))], (29675 ^ _779300) ^ [_1315119, _1315121] : [class_Lattices_Osemilattice__inf(_1315119), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1315119), _1315121), _1315121) = _1315121)], (29681 ^ _779300) ^ [_1315210, _1315212] : [class_Lattices_Osemilattice__inf(_1315210), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1315210), _1315212), _1315212) = _1315212)], (29687 ^ _779300) ^ [_1315301, _1315303, _1315305, _1315307] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315301, tc_HOL_Obool)), _1315303), _1315305), _1315307)), -(hBOOL(hAPP(_1315305, _1315307)))], (29693 ^ _779300) ^ [_1315412, _1315414, _1315416, _1315418] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315412, tc_HOL_Obool)), _1315414), _1315416), _1315418)), -(hBOOL(hAPP(_1315414, _1315418)))], (29699 ^ _779300) ^ [_1315523, _1315525, _1315527, _1315529] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315523, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315523, tc_HOL_Obool)), _1315525), _1315527)), _1315529) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315523, tc_HOL_Obool)), _1315525), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315523, tc_HOL_Obool)), _1315527), _1315529)))], (29701 ^ _779300) ^ [_1315596, _1315598, _1315600, _1315602] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315596, tc_HOL_Obool)), _1315598), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315596, tc_HOL_Obool)), _1315600), _1315602)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315596, tc_HOL_Obool)), _1315600), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315596, tc_HOL_Obool)), _1315598), _1315602)))], (29703 ^ _779300) ^ [_1315669, _1315671, _1315673] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315669, tc_HOL_Obool)), _1315671), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315669, tc_HOL_Obool)), _1315671), _1315673)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315669, tc_HOL_Obool)), _1315671), _1315673))], (29705 ^ _779300) ^ [_1315729, _1315731, _1315733] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315729, tc_HOL_Obool)), _1315731), _1315733) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315729, tc_HOL_Obool)), _1315733), _1315731))], (29707 ^ _779300) ^ [_1315778, _1315780] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315778, tc_HOL_Obool)), _1315780), _1315780) = _1315780)], (29709 ^ _779300) ^ [_1315814, _1315816, _1315818] : [class_Orderings_Olinorder(_1315814), 29712 ^ _779300 : [(29713 ^ _779300) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1315814), _1315816) = hAPP(c_SetInterval_Oord__class_OlessThan(_1315814), _1315818), -(_1315816 = _1315818)], (29719 ^ _779300) ^ [] : [_1315816 = _1315818, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1315814), _1315816) = hAPP(c_SetInterval_Oord__class_OlessThan(_1315814), _1315818))]]], (29725 ^ _779300) ^ [_1316055, _1316057, _1316059, _1316061] : [class_Lattices_Osemilattice__inf(_1316055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316055), _1316057), _1316059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316055), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316055), _1316057), _1316061)), _1316059)))], (29735 ^ _779300) ^ [_1316234, _1316236, _1316238, _1316240] : [class_Lattices_Osemilattice__inf(_1316234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316234), _1316236), _1316238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316234), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316234), _1316240), _1316236)), _1316238)))], (29745 ^ _779300) ^ [_1316413, _1316415, _1316417, _1316419, _1316421] : [c_Fun_Oinj__on(_1316413, _1316415, _1316417, _1316419), c_Fun_Oinj__on(_1316413, _1316415, _1316417, _1316421), -(c_Fun_Oinj__on(_1316413, _1316415, _1316417, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316413, tc_HOL_Obool)), _1316419), _1316421)))], (29755 ^ _779300) ^ [_1316588, _1316590] : [c_Nat__Transfer_Onat__set(_1316588), c_Nat__Transfer_Onat__set(_1316590), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1316588), _1316590)))], (29765 ^ _779300) ^ [_1316723, _1316725, _1316727, _1316729] : [class_Lattices_Odistrib__lattice(_1316723), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316723), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316723), _1316725), _1316727)), _1316729) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316723), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316723), _1316725), _1316729)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316723), _1316727), _1316729)))], (29771 ^ _779300) ^ [_1316882, _1316884, _1316886, _1316888] : [class_Lattices_Odistrib__lattice(_1316882), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316882), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316882), _1316884), _1316886)), _1316888) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316882), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316882), _1316884), _1316888)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316882), _1316886), _1316888)))], (29777 ^ _779300) ^ [_1317041, _1317043, _1317045, _1317047] : [class_Lattices_Odistrib__lattice(_1317041), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1317041), _1317043), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317041), _1317045), _1317047)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317041), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1317041), _1317043), _1317045)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1317041), _1317043), _1317047)))], (29783 ^ _779300) ^ [_1317200, _1317202, _1317204, _1317206] : [class_Lattices_Odistrib__lattice(_1317200), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317200), _1317202), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1317200), _1317204), _1317206)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1317200), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317200), _1317202), _1317204)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317200), _1317202), _1317206)))], (29789 ^ _779300) ^ [_1317359, _1317361, _1317363] : [class_Lattices_Olattice(_1317359), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1317359), _1317361), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317359), _1317361), _1317363)) = _1317361)], (29795 ^ _779300) ^ [_1317468, _1317470, _1317472] : [class_Lattices_Olattice(_1317468), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317468), _1317470), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1317468), _1317470), _1317472)) = _1317470)], (29801 ^ _779300) ^ [_1317577, _1317579, _1317581, _1317583] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317577, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317577, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317577, tc_HOL_Obool)), _1317579), _1317581)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317577, tc_HOL_Obool)), _1317581), _1317583))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317577, tc_HOL_Obool)), _1317583), _1317579)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317577, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317577, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317577, tc_HOL_Obool)), _1317579), _1317581)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317577, tc_HOL_Obool)), _1317581), _1317583))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317577, tc_HOL_Obool)), _1317583), _1317579)))], (29803 ^ _779300) ^ [_1317716, _1317718, _1317720, _1317722] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317716, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317716, tc_HOL_Obool)), _1317718), _1317720)), _1317722) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317716, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317716, tc_HOL_Obool)), _1317718), _1317722)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317716, tc_HOL_Obool)), _1317720), _1317722)))], (29805 ^ _779300) ^ [_1317800, _1317802, _1317804, _1317806] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317800, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317800, tc_HOL_Obool)), _1317802), _1317804)), _1317806) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317800, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317800, tc_HOL_Obool)), _1317802), _1317806)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317800, tc_HOL_Obool)), _1317804), _1317806)))], (29807 ^ _779300) ^ [_1317884, _1317886, _1317888, _1317890] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317884, tc_HOL_Obool)), _1317886), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317884, tc_HOL_Obool)), _1317888), _1317890)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317884, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317884, tc_HOL_Obool)), _1317886), _1317888)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317884, tc_HOL_Obool)), _1317886), _1317890)))], (29809 ^ _779300) ^ [_1317968, _1317970, _1317972, _1317974] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317968, tc_HOL_Obool)), _1317970), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317968, tc_HOL_Obool)), _1317972), _1317974)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317968, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317968, tc_HOL_Obool)), _1317970), _1317972)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317968, tc_HOL_Obool)), _1317970), _1317974)))], (29811 ^ _779300) ^ [_1318052, _1318054, _1318056, _1318058] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318052, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1318052), _1318054), _1318056)), hAPP(hAPP(c_Set_Oinsert(_1318052), _1318054), _1318058)) = hAPP(hAPP(c_Set_Oinsert(_1318052), _1318054), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318052, tc_HOL_Obool)), _1318056), _1318058)))], (29827 ^ _779300) ^ [_1318459, _1318461, _1318463] : [29829 ^ _779300 : [(29830 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318459), 29828 ^ [_1318459, _1318461, _1318463]), _1318461)))], (29833 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1318459), 29831 ^ [_1318459, _1318461, _1318463]), _1318463)))], (29835 ^ _779300) ^ [] : [-(29828 ^ [_1318459, _1318461, _1318463] = 29831 ^ [_1318459, _1318461, _1318463])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318459, tc_HOL_Obool)), _1318461), _1318463) = c_Orderings_Obot__class_Obot(tc_fun(_1318459, tc_HOL_Obool)))], (29813 ^ _779300) ^ [_1318145, _1318147, _1318149] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318145, tc_HOL_Obool)), _1318147), _1318149) = c_Orderings_Obot__class_Obot(tc_fun(_1318145, tc_HOL_Obool)), 29816 ^ _779300 : [(29817 ^ _779300) ^ [_1318269] : [hBOOL(hAPP(hAPP(c_member(_1318145), _1318269), _1318147)), 29820 ^ _779300 : [(29821 ^ _779300) ^ [_1318359] : [hBOOL(hAPP(hAPP(c_member(_1318145), _1318359), _1318149)), _1318269 = _1318359]]]]], (29839 ^ _779300) ^ [_1318620, _1318622] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318620, tc_HOL_Obool)), _1318622), c_Orderings_Obot__class_Obot(tc_fun(_1318620, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1318620, tc_HOL_Obool)))], (29841 ^ _779300) ^ [_1318666, _1318668] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318666, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1318666, tc_HOL_Obool))), _1318668) = c_Orderings_Obot__class_Obot(tc_fun(_1318666, tc_HOL_Obool)))], (29843 ^ _779300) ^ [_1318712, _1318714] : [class_Lattices_Obounded__lattice__bot(_1318712), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1318712), _1318714), c_Orderings_Obot__class_Obot(_1318712)) = c_Orderings_Obot__class_Obot(_1318712))], (29849 ^ _779300) ^ [_1318811, _1318813] : [class_Lattices_Obounded__lattice__bot(_1318811), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1318811), c_Orderings_Obot__class_Obot(_1318811)), _1318813) = c_Orderings_Obot__class_Obot(_1318811))], (29855 ^ _779300) ^ [_1318910, _1318912, _1318914, _1318916, _1318918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318910, tc_HOL_Obool)), _1318912), _1318914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318910, tc_HOL_Obool)), _1318916), _1318918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318910, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318910, tc_HOL_Obool)), _1318912), _1318916)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318910, tc_HOL_Obool)), _1318914), _1318918))))], (29865 ^ _779300) ^ [_1319155, _1319157, _1319159, _1319161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319155, tc_HOL_Obool)), _1319157), _1319159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319155, tc_HOL_Obool)), _1319157), _1319161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319155, tc_HOL_Obool)), _1319157), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319155, tc_HOL_Obool)), _1319159), _1319161))))], (29875 ^ _779300) ^ [_1319374, _1319376, _1319378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319374, tc_HOL_Obool)), _1319376), _1319378)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319374, tc_HOL_Obool)), _1319378), _1319376) = _1319376)], (29881 ^ _779300) ^ [_1319495, _1319497, _1319499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319495, tc_HOL_Obool)), _1319497), _1319499)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319495, tc_HOL_Obool)), _1319497), _1319499) = _1319497)], (29887 ^ _779300) ^ [_1319616, _1319618, _1319620] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319616, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319616, tc_HOL_Obool)), _1319618), _1319620)), _1319620)))], (29889 ^ _779300) ^ [_1319664, _1319666, _1319668] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319664, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319664, tc_HOL_Obool)), _1319666), _1319668)), _1319666)))], (29891 ^ _779300) ^ [_1319712, _1319714, _1319716] : [class_Lattices_Olattice(_1319712), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319712), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319712), _1319714), _1319716)), _1319714)))], (29897 ^ _779300) ^ [_1319819, _1319821, _1319823] : [class_Lattices_Osemilattice__inf(_1319819), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319819), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319819), _1319821), _1319823)), _1319821)))], (29903 ^ _779300) ^ [_1319926, _1319928, _1319930] : [class_Lattices_Olattice(_1319926), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319926), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319926), _1319928), _1319930)), _1319930)))], (29909 ^ _779300) ^ [_1320033, _1320035, _1320037] : [class_Lattices_Osemilattice__inf(_1320033), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320033), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320033), _1320035), _1320037)), _1320037)))], (29915 ^ _779300) ^ [_1320140, _1320142, _1320144] : [class_Lattices_Osemilattice__inf(_1320140), 29918 ^ _779300 : [(29919 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320140), _1320142), _1320144)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320140), _1320142), _1320144) = _1320142)], (29925 ^ _779300) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320140), _1320142), _1320144) = _1320142, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320140), _1320142), _1320144)))]]], (29931 ^ _779300) ^ [_1320396, _1320398, _1320400, _1320402] : [class_Lattices_Osemilattice__inf(_1320396), 29934 ^ _779300 : [(29935 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320396), _1320398), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320396), _1320400), _1320402))), 29938 ^ _779300 : [(29939 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320396), _1320398), _1320400)))], (29941 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320396), _1320398), _1320402)))]]], (29943 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320396), _1320398), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320396), _1320400), _1320402)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320396), _1320398), _1320400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320396), _1320398), _1320402))]]], (29953 ^ _779300) ^ [_1320776, _1320778, _1320780, _1320782] : [class_Lattices_Osemilattice__inf(_1320776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320776), _1320778), _1320780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320776), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320776), _1320778), _1320782)), _1320780)))], (29963 ^ _779300) ^ [_1320955, _1320957, _1320959, _1320961] : [class_Lattices_Osemilattice__inf(_1320955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320955), _1320957), _1320959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320955), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320955), _1320961), _1320957)), _1320959)))], (29973 ^ _779300) ^ [_1321134, _1321136, _1321138] : [class_Lattices_Osemilattice__inf(_1321134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321134), _1321136), _1321138)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321134), _1321136), _1321138) = _1321136)], (29983 ^ _779300) ^ [_1321295, _1321297, _1321299] : [class_Lattices_Osemilattice__inf(_1321295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321295), _1321297), _1321299)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321295), _1321299), _1321297) = _1321297)], (29993 ^ _779300) ^ [_1321456, _1321458, _1321460, _1321462] : [class_Lattices_Osemilattice__inf(_1321456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321456), _1321458), _1321460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321456), _1321458), _1321462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321456), _1321458), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321456), _1321460), _1321462))))], (30007 ^ _779300) ^ [_1321705, _1321707, _1321709, _1321711] : [class_Lattices_Osemilattice__inf(_1321705), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321705), _1321707), _1321709)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321705), _1321707), _1321711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321705), _1321707), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321705), _1321709), _1321711))))], (30021 ^ _779300) ^ [_1321954, _1321956, _1321958, _1321960, _1321962] : [class_Lattices_Osemilattice__inf(_1321954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321954), _1321956), _1321958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321954), _1321960), _1321962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321954), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321954), _1321956), _1321960)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321954), _1321958), _1321962))))], (30035 ^ _779300) ^ [_1322225, _1322227, _1322229, _1322231] : [class_Lattices_Osemilattice__inf(_1322225), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322225), _1322227), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1322225), _1322229), _1322231))), 30042 ^ _779300 : [(30043 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322225), _1322227), _1322229)))], (30045 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322225), _1322227), _1322231)))]]], (30047 ^ _779300) ^ [_1322469, _1322471, _1322473, _1322475] : [hBOOL(hAPP(hAPP(c_member(_1322469), _1322471), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322469, tc_HOL_Obool)), _1322473), _1322475))), 30050 ^ _779300 : [(30051 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322469), _1322471), _1322473)))], (30053 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322469), _1322471), _1322475)))]]], (30055 ^ _779300) ^ [_1322636, _1322638, _1322640, _1322642] : [-(hBOOL(hAPP(hAPP(c_member(_1322636), _1322638), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322636, tc_HOL_Obool)), _1322640), _1322642)))), hBOOL(hAPP(hAPP(c_member(_1322636), _1322638), _1322640)), hBOOL(hAPP(hAPP(c_member(_1322636), _1322638), _1322642))], (30065 ^ _779300) ^ [_1322839, _1322841, _1322843, _1322845] : [hBOOL(hAPP(hAPP(c_member(_1322839), _1322841), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322839, tc_HOL_Obool)), _1322843), _1322845))), -(hBOOL(hAPP(hAPP(c_member(_1322839), _1322841), _1322843)))], (30071 ^ _779300) ^ [_1322970, _1322972, _1322974, _1322976] : [hBOOL(hAPP(hAPP(c_member(_1322970), _1322972), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322970, tc_HOL_Obool)), _1322974), _1322976))), -(hBOOL(hAPP(hAPP(c_member(_1322970), _1322972), _1322976)))], (30077 ^ _779300) ^ [_1323101, _1323103, _1323105] : [class_Orderings_Oorder(_1323101), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323101, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1323101), _1323103)), c_SetInterval_Oord__class_OatLeastAtMost(_1323101, _1323103, _1323105)) = c_Orderings_Obot__class_Obot(tc_fun(_1323101, tc_HOL_Obool)))], (30083 ^ _779300) ^ [_1323228] : [class_Lattices_Osemilattice__inf(_1323228), -(c_Finite__Set_Ofun__left__comm__idem(_1323228, _1323228, c_Lattices_Osemilattice__inf__class_Oinf(_1323228)))], (30089 ^ _779300) ^ [_1323328, _1323330, _1323332, _1323334] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323328, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1323328, tc_fun(_1323328, tc_HOL_Obool), tc_HOL_Obool), c_member(_1323328)), _1323330)), hAPP(hAPP(c_COMBC(_1323328, tc_fun(_1323328, tc_HOL_Obool), tc_HOL_Obool), c_member(_1323328)), _1323332)), _1323334)), -(hBOOL(hAPP(hAPP(c_member(_1323328), _1323334), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323328, tc_HOL_Obool)), _1323330), _1323332))))], (30095 ^ _779300) ^ [_1323527, _1323529, _1323531, _1323533] : [hBOOL(hAPP(hAPP(c_member(_1323527), _1323533), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323527, tc_HOL_Obool)), _1323529), _1323531))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323527, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1323527, tc_fun(_1323527, tc_HOL_Obool), tc_HOL_Obool), c_member(_1323527)), _1323529)), hAPP(hAPP(c_COMBC(_1323527, tc_fun(_1323527, tc_HOL_Obool), tc_HOL_Obool), c_member(_1323527)), _1323531)), _1323533)))], (30101 ^ _779300) ^ [_1323732] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1323732)) = _1323732)], (30103 ^ _779300) ^ [_1323761, _1323763, _1323765, _1323767] : [class_Lattices_Olattice(_1323761), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323761), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1323761), _1323763), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323761), _1323765), _1323767))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323761), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1323761), _1323763), _1323765)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1323761), _1323763), _1323767)))))], (30109 ^ _779300) ^ [_1323934, _1323936, _1323938, _1323940] : [class_Lattices_Olattice(_1323934), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323934), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1323934), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323934), _1323936), _1323938)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323934), _1323936), _1323940))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323934), _1323936), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1323934), _1323938), _1323940)))))], (30115 ^ _779300) ^ [_1324107, _1324109] : [class_Lattices_Oboolean__algebra(_1324107), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324107), _1324109), hAPP(c_Groups_Ouminus__class_Ouminus(_1324107), _1324109)) = c_Orderings_Obot__class_Obot(_1324107))], (30121 ^ _779300) ^ [_1324212, _1324214] : [class_Lattices_Oboolean__algebra(_1324212), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324212), hAPP(c_Groups_Ouminus__class_Ouminus(_1324212), _1324214)), _1324214) = c_Orderings_Obot__class_Obot(_1324212))], (30127 ^ _779300) ^ [_1324317, _1324319, _1324321] : [class_Lattices_Oboolean__algebra(_1324317), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1324317), _1324319), _1324321) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324317), _1324319), hAPP(c_Groups_Ouminus__class_Ouminus(_1324317), _1324321)))], (30133 ^ _779300) ^ [_1324436, _1324438, _1324440] : [class_Lattices_Oboolean__algebra(_1324436), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1324436), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324436), _1324438), _1324440)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1324436), hAPP(c_Groups_Ouminus__class_Ouminus(_1324436), _1324438)), hAPP(c_Groups_Ouminus__class_Ouminus(_1324436), _1324440)))], (30139 ^ _779300) ^ [_1324575, _1324577, _1324579] : [class_Lattices_Oboolean__algebra(_1324575), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1324575), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1324575), _1324577), _1324579)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324575), hAPP(c_Groups_Ouminus__class_Ouminus(_1324575), _1324577)), hAPP(c_Groups_Ouminus__class_Ouminus(_1324575), _1324579)))], (30145 ^ _779300) ^ [_1324714, _1324716, _1324718, _1324720] : [hBOOL(hAPP(hAPP(c_member(_1324714), _1324716), _1324718)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324714, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1324714), _1324716), _1324720)), _1324718) = hAPP(hAPP(c_Set_Oinsert(_1324714), _1324716), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324714, tc_HOL_Obool)), _1324720), _1324718)))], (30151 ^ _779300) ^ [_1324885, _1324887, _1324889, _1324891] : [hBOOL(hAPP(hAPP(c_member(_1324885), _1324887), _1324889)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324885, tc_HOL_Obool)), _1324889), hAPP(hAPP(c_Set_Oinsert(_1324885), _1324887), _1324891)) = hAPP(hAPP(c_Set_Oinsert(_1324885), _1324887), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324885, tc_HOL_Obool)), _1324889), _1324891)))], (30157 ^ _779300) ^ [_1325052, _1325054, _1325056, _1325058] : [-(hBOOL(hAPP(hAPP(c_member(_1325052), _1325054), _1325056))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325052, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1325052), _1325054), _1325058)), _1325056) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325052, tc_HOL_Obool)), _1325058), _1325056))], (30163 ^ _779300) ^ [_1325125, _1325127, _1325129, _1325131] : [-(hBOOL(hAPP(hAPP(c_member(_1325125), _1325127), _1325129))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325125, tc_HOL_Obool)), _1325129), hAPP(hAPP(c_Set_Oinsert(_1325125), _1325127), _1325131)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325125, tc_HOL_Obool)), _1325129), _1325131))], (30169 ^ _779300) ^ [_1325217, _1325219, _1325221, _1325223] : [hBOOL(hAPP(hAPP(c_member(_1325217), _1325219), _1325221)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325217, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1325217), _1325219), _1325223)), _1325221) = hAPP(hAPP(c_Set_Oinsert(_1325217), _1325219), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325217, tc_HOL_Obool)), _1325223), _1325221)))], (30175 ^ _779300) ^ [_1325382, _1325384, _1325386, _1325388] : [-(hBOOL(hAPP(hAPP(c_member(_1325382), _1325384), _1325386))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325382, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1325382), _1325384), _1325388)), _1325386) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325382, tc_HOL_Obool)), _1325388), _1325386))], (30181 ^ _779300) ^ [_1325476, _1325478, _1325480, _1325482] : [hBOOL(hAPP(hAPP(c_member(_1325476), _1325478), _1325480)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325476, tc_HOL_Obool)), _1325480), hAPP(hAPP(c_Set_Oinsert(_1325476), _1325478), _1325482)) = hAPP(hAPP(c_Set_Oinsert(_1325476), _1325478), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325476, tc_HOL_Obool)), _1325480), _1325482)))], (30187 ^ _779300) ^ [_1325641, _1325643, _1325645, _1325647] : [-(hBOOL(hAPP(hAPP(c_member(_1325641), _1325643), _1325645))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325641, tc_HOL_Obool)), _1325645), hAPP(hAPP(c_Set_Oinsert(_1325641), _1325643), _1325647)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325641, tc_HOL_Obool)), _1325645), _1325647))], (30193 ^ _779300) ^ [_1325720, _1325722, _1325724, _1325726, _1325728] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1325720, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1325722, _1325720, _1325724), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325722, tc_HOL_Obool)), _1325726), _1325728))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325720, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1325722, _1325720, _1325724), _1325726)), hAPP(c_Set_Oimage(_1325722, _1325720, _1325724), _1325728)))))], (30195 ^ _779300) ^ [_1325804, _1325806, _1325808] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325804, tc_HOL_Obool)), _1325806), _1325808) = c_Orderings_Obot__class_Obot(tc_fun(_1325804, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325804, tc_HOL_Obool)), _1325806), _1325808) = _1325806)], (30201 ^ _779300) ^ [_1325937, _1325939, _1325941] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325937, tc_HOL_Obool)), _1325939), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325937, tc_HOL_Obool)), _1325941), _1325939)) = c_Orderings_Obot__class_Obot(tc_fun(_1325937, tc_HOL_Obool)))], (30203 ^ _779300) ^ [_1326012, _1326014, _1326016, _1326018] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326012, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326012, tc_HOL_Obool)), _1326014), _1326016)), _1326018) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326012, tc_HOL_Obool)), _1326014), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326012, tc_HOL_Obool)), _1326016), _1326018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326012, tc_HOL_Obool)), _1326018), _1326014)))], (30209 ^ _779300) ^ [_1326197, _1326199, _1326201, _1326203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326197, tc_HOL_Obool)), _1326203), _1326199)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326197, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326197, tc_HOL_Obool)), _1326199), _1326201)), _1326203) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326197, tc_HOL_Obool)), _1326199), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326197, tc_HOL_Obool)), _1326201), _1326203)))], (30215 ^ _779300) ^ [_1326388, _1326390, _1326392, _1326394] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326388, tc_HOL_Obool)), _1326390), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326388, tc_HOL_Obool)), _1326392), _1326394)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326388, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326388, tc_HOL_Obool)), _1326390), _1326392)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326388, tc_HOL_Obool)), _1326390), _1326394)))], (30217 ^ _779300) ^ [_1326472, _1326474, _1326476, _1326478] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326472, tc_HOL_Obool)), _1326474), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326472, tc_HOL_Obool)), _1326476), _1326478)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326472, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326472, tc_HOL_Obool)), _1326474), _1326476)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326472, tc_HOL_Obool)), _1326474), _1326478)))], (30219 ^ _779300) ^ [_1326556, _1326558, _1326560] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326556, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326556, tc_HOL_Obool)), _1326558), _1326560)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326556, tc_HOL_Obool)), _1326558), _1326560)) = _1326558)], (30221 ^ _779300) ^ [_1326616, _1326618, _1326620, _1326622] : [class_Orderings_Oorder(_1326616), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326616, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1326616, _1326618), _1326620)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1326616, _1326620), _1326622)) = c_Orderings_Obot__class_Obot(tc_fun(_1326616, tc_HOL_Obool)))], (30227 ^ _779300) ^ [_1326751, _1326753] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1326751), _1326753) = 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)), _1326751)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1326753))))], (30229 ^ _779300) ^ [_1326797, _1326799] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326797, tc_HOL_Obool)), _1326799), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326797, tc_HOL_Obool)), _1326799)) = c_Orderings_Obot__class_Obot(tc_fun(_1326797, tc_HOL_Obool)))], (30231 ^ _779300) ^ [_1326846, _1326848] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326846, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326846, tc_HOL_Obool)), _1326848)), _1326848) = c_Orderings_Obot__class_Obot(tc_fun(_1326846, tc_HOL_Obool)))], (30233 ^ _779300) ^ [_1326895, _1326897, _1326899, _1326901, _1326903] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326895, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1326897, _1326895, _1326899), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326897, tc_HOL_Obool)), _1326901), _1326903))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326895, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1326897, _1326895, _1326899), _1326901)), hAPP(c_Relation_OImage(_1326897, _1326895, _1326899), _1326903)))))], (30235 ^ _779300) ^ [_1326979, _1326981, _1326983] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326979, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326979, tc_HOL_Obool)), _1326981), _1326983)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326979, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326979, tc_HOL_Obool)), _1326981)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326979, tc_HOL_Obool)), _1326983)))], (30237 ^ _779300) ^ [_1327052, _1327054, _1327056] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1327052, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327052, tc_HOL_Obool)), _1327054), _1327056)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327052, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1327052, tc_HOL_Obool)), _1327054)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1327052, tc_HOL_Obool)), _1327056)))], (30239 ^ _779300) ^ [_1327125, _1327127, _1327129] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327125, tc_HOL_Obool)), _1327127), _1327129) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327125, tc_HOL_Obool)), _1327127), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1327125, tc_HOL_Obool)), _1327129)))], (30241 ^ _779300) ^ [_1327182, _1327184, _1327186] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327182, tc_HOL_Obool)), _1327184), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1327182, tc_HOL_Obool)), _1327186)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327182, tc_HOL_Obool)), _1327184), _1327186))], (30243 ^ _779300) ^ [_1327239, _1327241, _1327243, _1327245] : [class_Orderings_Oorder(_1327239), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327239, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1327239, _1327241, _1327243)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1327239, _1327243, _1327245)) = c_Orderings_Obot__class_Obot(tc_fun(_1327239, tc_HOL_Obool)))], (30249 ^ _779300) ^ [_1327366] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1327366) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1327366))], (30251 ^ _779300) ^ [] : [-(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)))], (30253 ^ _779300) ^ [_1327413, _1327415] : [c_Nat__Transfer_Onat__set(_1327413), c_Nat__Transfer_Onat__set(_1327415), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1327413), _1327415) = 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), _1327413)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1327415))))], (30263 ^ _779300) ^ [_1327580] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1327580)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1327580), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1327580)))], (30265 ^ _779300) ^ [_1327618] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1327618)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1327618))], (30267 ^ _779300) ^ [_1327650] : [-(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)), _1327650))))], (30269 ^ _779300) ^ [_1327678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327678)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327678) = 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, _1327678))))], (30275 ^ _779300) ^ [_1327781, _1327783, _1327785] : [class_Orderings_Oord(_1327781), 30278 ^ _779300 : [(30279 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1327781), _1327783), hAPP(c_SetInterval_Oord__class_OlessThan(_1327781), _1327785))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327781), _1327783), _1327785)))], (30285 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327781), _1327783), _1327785)), -(hBOOL(hAPP(hAPP(c_member(_1327781), _1327783), hAPP(c_SetInterval_Oord__class_OlessThan(_1327781), _1327785))))]]], (30291 ^ _779300) ^ [_1328049, _1328051, _1328053] : [class_Lattices_Olattice(_1328049), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328049), _1328051)), hBOOL(hAPP(hAPP(c_member(_1328049), _1328053), _1328051)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1328049), _1328053), c_Big__Operators_Olattice__class_OSup__fin(_1328049, _1328051)) = _1328053)], (30305 ^ _779300) ^ [_1328278, _1328280, _1328282] : [class_Orderings_Olinorder(_1328278), 30308 ^ _779300 : [(30309 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328278, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1328278), _1328280)), hAPP(c_SetInterval_Oord__class_OlessThan(_1328278), _1328282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328278), _1328280), _1328282)))], (30315 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328278), _1328280), _1328282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328278, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1328278), _1328280)), hAPP(c_SetInterval_Oord__class_OlessThan(_1328278), _1328282))))]]], (30321 ^ _779300) ^ [_1328570, _1328572, _1328574, _1328576, _1328578, _1328580] : [c_Fun_Oinj__on(_1328570, _1328572, _1328574, _1328576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328570, tc_HOL_Obool)), _1328578), _1328576)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328570, tc_HOL_Obool)), _1328580), _1328576)), -(hAPP(c_Set_Oimage(_1328570, _1328572, _1328574), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328570, tc_HOL_Obool)), _1328578), _1328580)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328572, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1328570, _1328572, _1328574), _1328578)), hAPP(c_Set_Oimage(_1328570, _1328572, _1328574), _1328580)))], (30335 ^ _779300) ^ [_1328923, _1328925, _1328927] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328923, tc_HOL_Obool)), _1328925), _1328927) = c_Orderings_Obot__class_Obot(tc_fun(_1328923, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328923, tc_HOL_Obool)), _1328925), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328923, tc_HOL_Obool)), _1328927))))], (30341 ^ _779300) ^ [_1329066, _1329068, _1329070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329066, tc_HOL_Obool)), _1329068), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1329066, tc_HOL_Obool)), _1329070))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329066, tc_HOL_Obool)), _1329068), _1329070) = c_Orderings_Obot__class_Obot(tc_fun(_1329066, tc_HOL_Obool)))], (30347 ^ _779300) ^ [_1329215, _1329217, _1329219, _1329221] : [class_Orderings_Oorder(_1329215), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329215, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1329215, _1329217), _1329219)), c_SetInterval_Oord__class_OatLeastAtMost(_1329215, _1329219, _1329221)) = c_Orderings_Obot__class_Obot(tc_fun(_1329215, tc_HOL_Obool)))], (30353 ^ _779300) ^ [_1329346, _1329348, _1329350, _1329352, _1329354] : [class_Orderings_Olinorder(_1329346), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329346, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1329346, _1329348, _1329350)), c_SetInterval_Oord__class_OatLeastAtMost(_1329346, _1329352, _1329354)) = c_SetInterval_Oord__class_OatLeastAtMost(_1329346, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1329346), _1329348), _1329352), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1329346), _1329350), _1329354)))], (30359 ^ _779300) ^ [_1329505, _1329507, _1329509, _1329511, _1329513] : [class_Orderings_Olinorder(_1329505), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329505, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1329505, _1329507), _1329509)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1329505, _1329511), _1329513)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1329505, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1329505), _1329507), _1329511)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1329505), _1329509), _1329513)))], (30365 ^ _779300) ^ [_1329676, _1329678, _1329680] : [class_Orderings_Olinorder(_1329676), 30368 ^ _779300 : [(30369 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1329676, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1329676), _1329678)), hAPP(c_SetInterval_Oord__class_OlessThan(_1329676), _1329680))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329676), _1329678), _1329680)))], (30375 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329676), _1329678), _1329680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1329676, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1329676), _1329678)), hAPP(c_SetInterval_Oord__class_OlessThan(_1329676), _1329680))))]]], (30381 ^ _779300) ^ [_1329968, _1329970, _1329972, _1329974] : [class_Orderings_Oorder(_1329968), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329968, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1329968, _1329970, _1329972)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1329968, _1329972, _1329974)) = c_Orderings_Obot__class_Obot(tc_fun(_1329968, tc_HOL_Obool)))], (30387 ^ _779300) ^ [_1330095, _1330097, _1330099, _1330101] : [class_Orderings_Oorder(_1330095), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330095, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1330095, _1330097, _1330099)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1330095, _1330099, _1330101)) = c_Orderings_Obot__class_Obot(tc_fun(_1330095, tc_HOL_Obool)))], (30393 ^ _779300) ^ [_1330222, _1330224, _1330226, _1330228] : [class_Orderings_Oorder(_1330222), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330222, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1330222, _1330224, _1330226)), c_SetInterval_Oord__class_OatLeastAtMost(_1330222, _1330226, _1330228)) = c_Orderings_Obot__class_Obot(tc_fun(_1330222, tc_HOL_Obool)))], (30399 ^ _779300) ^ [_1330349, _1330351, _1330353, _1330355, _1330357] : [class_Orderings_Olinorder(_1330349), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330349, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1330349, _1330351, _1330353)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1330349, _1330355, _1330357)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1330349, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1330349), _1330351), _1330355), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330349), _1330353), _1330357)))], (30405 ^ _779300) ^ [_1330508, _1330510, _1330512, _1330514] : [class_Orderings_Oorder(_1330508), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330508, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1330508, _1330510, _1330512)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1330508, _1330512), _1330514)) = c_Orderings_Obot__class_Obot(tc_fun(_1330508, tc_HOL_Obool)))], (30411 ^ _779300) ^ [_1330639, _1330641, _1330643, _1330645, _1330647] : [class_Orderings_Olinorder(_1330639), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330639, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1330639, _1330641, _1330643)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1330639, _1330645, _1330647)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1330639, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1330639), _1330641), _1330645), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330639), _1330643), _1330647)))], (30417 ^ _779300) ^ [_1330798, _1330800, _1330802, _1330804] : [class_Orderings_Olinorder(_1330798), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330798, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1330798, _1330800, _1330802)), hAPP(c_SetInterval_Oord__class_OatMost(_1330798), _1330804)) = c_SetInterval_Oord__class_OatLeastAtMost(_1330798, _1330800, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330798), _1330802), _1330804)))], (30423 ^ _779300) ^ [_1330941, _1330943, _1330945, _1330947] : [class_Orderings_Olinorder(_1330941), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330941, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1330941), _1330943)), c_SetInterval_Oord__class_OatLeastAtMost(_1330941, _1330945, _1330947)) = c_SetInterval_Oord__class_OatLeastAtMost(_1330941, _1330945, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330941), _1330943), _1330947)))], (30429 ^ _779300) ^ [_1331084, _1331086, _1331088] : [class_Orderings_Oorder(_1331084), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331084, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1331084), _1331086)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1331084, _1331086, _1331088)) = c_Orderings_Obot__class_Obot(tc_fun(_1331084, tc_HOL_Obool)))], (30435 ^ _779300) ^ [_1331211, _1331213, _1331215, _1331217] : [class_Orderings_Oorder(_1331211), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331211, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1331211, _1331213, _1331215)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1331211, _1331215, _1331217)) = c_Orderings_Obot__class_Obot(tc_fun(_1331211, tc_HOL_Obool)))], (30441 ^ _779300) ^ [_1331338, _1331340, _1331342] : [class_Orderings_Oorder(_1331338), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331338, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1331338), _1331340)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1331338, _1331340, _1331342)) = c_Orderings_Obot__class_Obot(tc_fun(_1331338, tc_HOL_Obool)))], (30447 ^ _779300) ^ [_1331465, _1331467, _1331469, _1331471, _1331473, _1331475, _1331477, _1331479] : [c_Finite__Set_Ofolding__image__simple(_1331465, _1331467, _1331469, _1331471, _1331473, _1331475), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331467), _1331477)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331467), _1331479)), -(hAPP(hAPP(_1331469, hAPP(_1331475, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1331467, tc_HOL_Obool)), _1331477), _1331479))), hAPP(_1331475, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331467, tc_HOL_Obool)), _1331477), _1331479))) = hAPP(hAPP(_1331469, hAPP(_1331475, _1331477)), hAPP(_1331475, _1331479)))], (30461 ^ _779300) ^ [_1331798, _1331800] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1331798), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1331800), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1331798, _1331800))], (30463 ^ _779300) ^ [_1331839, _1331841, _1331843] : [class_Lattices_Osemilattice__inf(_1331839), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331839), _1331841)), hBOOL(hAPP(hAPP(c_member(_1331839), _1331843), _1331841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331839), hAPP(c_Finite__Set_Ofold1(_1331839, c_Lattices_Osemilattice__inf__class_Oinf(_1331839)), _1331841)), _1331843)))], (30477 ^ _779300) ^ [_1332076, _1332078] : [-(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)), _1332076)), 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), _1332078), _1332076))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1332076), _1332078))], (30479 ^ _779300) ^ [_1332126, _1332128, _1332130] : [class_Lattices_Osemilattice__inf(_1332126), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332126), _1332128)), -(_1332128 = c_Orderings_Obot__class_Obot(tc_fun(_1332126, tc_HOL_Obool))), 30490 ^ _779300 : [(30501 ^ _779300) ^ [] : [30503 ^ _779300 : [(30504 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1332126), 30502 ^ [_1332126, _1332128, _1332130]), _1332128)))], (30506 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332126), _1332130), 30502 ^ [_1332126, _1332128, _1332130]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332126), _1332130), hAPP(c_Finite__Set_Ofold1(_1332126, c_Lattices_Osemilattice__inf__class_Oinf(_1332126)), _1332128))))], (30491 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332126), _1332130), hAPP(c_Finite__Set_Ofold1(_1332126, c_Lattices_Osemilattice__inf__class_Oinf(_1332126)), _1332128))), 30494 ^ _779300 : [(30495 ^ _779300) ^ [_1332419] : [hBOOL(hAPP(hAPP(c_member(_1332126), _1332419), _1332128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1332126), _1332130), _1332419)))]]]]], (30510 ^ _779300) ^ [_1332704] : [-(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)), _1332704)) = hAPP(c_Int_Onat, _1332704))], (30512 ^ _779300) ^ [_1332736, _1332738] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1332736), _1332738)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1332738), _1332736)))], (30514 ^ _779300) ^ [_1332779, _1332781, _1332783, _1332785, _1332787] : [class_Groups_Ocomm__monoid__mult(_1332779), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332781), _1332783)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332781), _1332785)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332779), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332781, _1332779), _1332787), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332781, tc_HOL_Obool)), _1332783), _1332785))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332781, _1332779), _1332787), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332781, tc_HOL_Obool)), _1332783), _1332785))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332779), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332781, _1332779), _1332787), _1332783)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332781, _1332779), _1332787), _1332785)))], (30528 ^ _779300) ^ [_1333140, _1333142, _1333144, _1333146, _1333148] : [class_Groups_Ocomm__monoid__mult(_1333140), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333142), _1333144)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333142), _1333146)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333140), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333142, _1333140), _1333148), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333142, tc_HOL_Obool)), _1333144), _1333146))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333142, _1333140), _1333148), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333142, tc_HOL_Obool)), _1333144), _1333146))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333140), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333142, _1333140), _1333148), _1333144)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333142, _1333140), _1333148), _1333146)))], (30542 ^ _779300) ^ [_1333501, _1333503, _1333505] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333501), _1333503)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333501), _1333505)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1333501), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333501, tc_HOL_Obool)), _1333503), _1333505))), hAPP(c_Finite__Set_Ocard(_1333501), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333501, tc_HOL_Obool)), _1333503), _1333505))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1333501), _1333503)), hAPP(c_Finite__Set_Ocard(_1333501), _1333505)))], (30552 ^ _779300) ^ [_1333758, _1333760, _1333762] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333758), _1333760)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333758), _1333762)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1333758), _1333760)), hAPP(c_Finite__Set_Ocard(_1333758), _1333762)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1333758), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333758, tc_HOL_Obool)), _1333760), _1333762))), hAPP(c_Finite__Set_Ocard(_1333758), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333758, tc_HOL_Obool)), _1333760), _1333762))))], (30562 ^ _779300) ^ [_1334015, _1334017, _1334019] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1334015), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334015, tc_HOL_Obool)), _1334017), _1334019))), -(hAPP(c_Finite__Set_Ocard(_1334015), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334015, tc_HOL_Obool)), _1334017), _1334019)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1334015), _1334017)), hAPP(c_Finite__Set_Ocard(_1334015), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334015, tc_HOL_Obool)), _1334017), _1334019))))], (30568 ^ _779300) ^ [_1334210, _1334212] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1334210), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1334212) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1334210, _1334212))], (30570 ^ _779300) ^ [_1334251, _1334253, _1334255, _1334257, _1334259, _1334261, _1334263, _1334265] : [c_Finite__Set_Ofolding__image__simple(_1334251, _1334253, _1334255, _1334257, _1334259, _1334261), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334253), _1334263)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334253), _1334265)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334253, tc_HOL_Obool)), _1334263), _1334265) = c_Orderings_Obot__class_Obot(tc_fun(_1334253, tc_HOL_Obool)), -(hAPP(_1334261, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334253, tc_HOL_Obool)), _1334263), _1334265)) = hAPP(hAPP(_1334255, hAPP(_1334261, _1334263)), hAPP(_1334261, _1334265)))], (30588 ^ _779300) ^ [_1334640, _1334642, _1334644, _1334646, _1334648] : [c_Finite__Set_Ofolding__one(_1334640, _1334642, _1334644), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334640), _1334646)), -(_1334646 = c_Orderings_Obot__class_Obot(tc_fun(_1334640, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334640), _1334648)), -(_1334648 = c_Orderings_Obot__class_Obot(tc_fun(_1334640, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334640, tc_HOL_Obool)), _1334646), _1334648) = c_Orderings_Obot__class_Obot(tc_fun(_1334640, tc_HOL_Obool)), -(hAPP(_1334644, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334640, tc_HOL_Obool)), _1334646), _1334648)) = hAPP(hAPP(_1334642, hAPP(_1334644, _1334646)), hAPP(_1334644, _1334648)))], (30614 ^ _779300) ^ [_1335141, _1335143, _1335145, _1335147, _1335149] : [c_Finite__Set_Ofolding__one(_1335141, _1335143, _1335145), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335141), _1335147)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335141), _1335149)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335141, tc_HOL_Obool)), _1335147), _1335149) = c_Orderings_Obot__class_Obot(tc_fun(_1335141, tc_HOL_Obool))), -(hAPP(hAPP(_1335143, hAPP(_1335145, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1335141, tc_HOL_Obool)), _1335147), _1335149))), hAPP(_1335145, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335141, tc_HOL_Obool)), _1335147), _1335149))) = hAPP(hAPP(_1335143, hAPP(_1335145, _1335147)), hAPP(_1335145, _1335149)))], (30632 ^ _779300) ^ [_1335497, _1335499] : [class_Orderings_Oorder(_1335497), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335497, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1335497), _1335499), c_Orderings_Obot__class_Obot(tc_fun(_1335497, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1335497), _1335499)) = hAPP(hAPP(c_Set_Oinsert(_1335497), _1335499), c_Orderings_Obot__class_Obot(tc_fun(_1335497, tc_HOL_Obool))))], (30638 ^ _779300) ^ [_1335656, _1335658, _1335660] : [class_Orderings_Olinorder(_1335656), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335656), _1335658), _1335660)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1335656, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1335656), _1335658)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1335656, _1335658), _1335660)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1335656), _1335660))], (30648 ^ _779300) ^ [_1335855, _1335857, _1335859, _1335861, _1335863] : [class_Groups_Ocomm__monoid__mult(_1335855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335857), _1335859)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335857), _1335861)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335857, tc_HOL_Obool)), _1335859), _1335861) = c_Orderings_Obot__class_Obot(tc_fun(_1335857, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335857, _1335855), _1335863), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1335857, tc_HOL_Obool)), _1335859), _1335861)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335855), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335857, _1335855), _1335863), _1335859)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335857, _1335855), _1335863), _1335861)))], (30666 ^ _779300) ^ [_1336250, _1336252, _1336254, _1336256, _1336258] : [class_Groups_Ocomm__monoid__mult(_1336250), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336252), _1336254)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336252), _1336256)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336252, tc_HOL_Obool)), _1336254), _1336256) = c_Orderings_Obot__class_Obot(tc_fun(_1336252, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336252, _1336250), _1336258), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1336252, tc_HOL_Obool)), _1336254), _1336256)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336250), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336252, _1336250), _1336258), _1336254)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336252, _1336250), _1336258), _1336256)))], (30684 ^ _779300) ^ [_1336645, _1336647, _1336649] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1336645), _1336647)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336645), _1336649)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336645, tc_HOL_Obool)), _1336647), _1336649) = c_Orderings_Obot__class_Obot(tc_fun(_1336645, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1336645), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1336645, tc_HOL_Obool)), _1336647), _1336649)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1336645), _1336647)), hAPP(c_Finite__Set_Ocard(_1336645), _1336649)))], (30698 ^ _779300) ^ [_1336968, _1336970, _1336972, _1336974, _1336976] : [c_Fun_Oinj__on(_1336968, _1336970, _1336972, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1336968, tc_HOL_Obool)), _1336974), _1336976)), 30701 ^ _779300 : [(30702 ^ _779300) ^ [] : [-(c_Fun_Oinj__on(_1336968, _1336970, _1336972, _1336974))], (30704 ^ _779300) ^ [] : [-(c_Fun_Oinj__on(_1336968, _1336970, _1336972, _1336976))], (30706 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336970, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1336968, _1336970, _1336972), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336968, tc_HOL_Obool)), _1336974), _1336976))), hAPP(c_Set_Oimage(_1336968, _1336970, _1336972), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336968, tc_HOL_Obool)), _1336976), _1336974))) = c_Orderings_Obot__class_Obot(tc_fun(_1336970, tc_HOL_Obool)))]]], (30708 ^ _779300) ^ [_1337235, _1337237, _1337239, _1337241, _1337243] : [-(c_Fun_Oinj__on(_1337235, _1337237, _1337239, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337235, tc_HOL_Obool)), _1337241), _1337243))), c_Fun_Oinj__on(_1337235, _1337237, _1337239, _1337241), c_Fun_Oinj__on(_1337235, _1337237, _1337239, _1337243), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337237, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1337235, _1337237, _1337239), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337235, tc_HOL_Obool)), _1337241), _1337243))), hAPP(c_Set_Oimage(_1337235, _1337237, _1337239), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337235, tc_HOL_Obool)), _1337243), _1337241))) = c_Orderings_Obot__class_Obot(tc_fun(_1337237, tc_HOL_Obool))], (30722 ^ _779300) ^ [_1337574, _1337576, _1337578, _1337580, _1337582] : [class_Groups_Ocomm__monoid__mult(_1337574), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337576), _1337578)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337576), _1337580)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337574), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1337574, _1337576, c_Groups_Otimes__class_Otimes(_1337574)), _1337582), c_Groups_Oone__class_Oone(_1337574)), _1337578)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1337574, _1337576, c_Groups_Otimes__class_Otimes(_1337574)), _1337582), c_Groups_Oone__class_Oone(_1337574)), _1337580)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337574), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1337574, _1337576, c_Groups_Otimes__class_Otimes(_1337574)), _1337582), c_Groups_Oone__class_Oone(_1337574)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337576, tc_HOL_Obool)), _1337578), _1337580))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1337574, _1337576, c_Groups_Otimes__class_Otimes(_1337574)), _1337582), c_Groups_Oone__class_Oone(_1337574)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337576, tc_HOL_Obool)), _1337578), _1337580))))], (30736 ^ _779300) ^ [_1337999, _1338001, _1338003] : [class_Groups_Oab__semigroup__mult(_1337999), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337999), _1338001)), -(_1338001 = c_Orderings_Obot__class_Obot(tc_fun(_1337999, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337999), _1338003)), -(_1338003 = c_Orderings_Obot__class_Obot(tc_fun(_1337999, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337999, tc_HOL_Obool)), _1338001), _1338003) = c_Orderings_Obot__class_Obot(tc_fun(_1337999, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1337999, c_Groups_Otimes__class_Otimes(_1337999)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337999, tc_HOL_Obool)), _1338001), _1338003)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337999), hAPP(c_Finite__Set_Ofold1(_1337999, c_Groups_Otimes__class_Otimes(_1337999)), _1338001)), hAPP(c_Finite__Set_Ofold1(_1337999, c_Groups_Otimes__class_Otimes(_1337999)), _1338003)))], (30762 ^ _779300) ^ [_1338506, _1338508, _1338510] : [class_Lattices_Olattice(_1338506), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338506), _1338508)), -(_1338508 = c_Orderings_Obot__class_Obot(tc_fun(_1338506, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338506), _1338510)), -(_1338510 = c_Orderings_Obot__class_Obot(tc_fun(_1338506, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338506, tc_HOL_Obool)), _1338508), _1338510) = c_Orderings_Obot__class_Obot(tc_fun(_1338506, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1338506, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338506, tc_HOL_Obool)), _1338508), _1338510)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1338506), c_Big__Operators_Olattice__class_OSup__fin(_1338506, _1338508)), c_Big__Operators_Olattice__class_OSup__fin(_1338506, _1338510)))], (30788 ^ _779300) ^ [_1338983, _1338985, _1338987] : [class_Lattices_Olattice(_1338983), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338983), _1338985)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338983), _1338987)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338983, tc_HOL_Obool)), _1338985), _1338987) = c_Orderings_Obot__class_Obot(tc_fun(_1338983, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1338983), c_Big__Operators_Olattice__class_OSup__fin(_1338983, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338983, tc_HOL_Obool)), _1338985), _1338987))), c_Big__Operators_Olattice__class_OSup__fin(_1338983, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338983, tc_HOL_Obool)), _1338985), _1338987))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1338983), c_Big__Operators_Olattice__class_OSup__fin(_1338983, _1338985)), c_Big__Operators_Olattice__class_OSup__fin(_1338983, _1338987)))], (30806 ^ _779300) ^ [_1339331, _1339333, _1339335] : [class_Orderings_Olinorder(_1339331), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339331), _1339333)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339331), _1339335)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339331, tc_HOL_Obool)), _1339333), _1339335) = c_Orderings_Obot__class_Obot(tc_fun(_1339331, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1339331), c_Big__Operators_Olinorder__class_OMin(_1339331, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339331, tc_HOL_Obool)), _1339333), _1339335))), c_Big__Operators_Olinorder__class_OMin(_1339331, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339331, tc_HOL_Obool)), _1339333), _1339335))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1339331), c_Big__Operators_Olinorder__class_OMin(_1339331, _1339333)), c_Big__Operators_Olinorder__class_OMin(_1339331, _1339335)))], (30824 ^ _779300) ^ [_1339679, _1339681, _1339683] : [class_Orderings_Olinorder(_1339679), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339679), _1339681)), -(_1339681 = c_Orderings_Obot__class_Obot(tc_fun(_1339679, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339679), _1339683)), -(_1339683 = c_Orderings_Obot__class_Obot(tc_fun(_1339679, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339679, tc_HOL_Obool)), _1339681), _1339683) = c_Orderings_Obot__class_Obot(tc_fun(_1339679, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1339679, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339679, tc_HOL_Obool)), _1339681), _1339683)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1339679), c_Big__Operators_Olinorder__class_OMin(_1339679, _1339681)), c_Big__Operators_Olinorder__class_OMin(_1339679, _1339683)))], (30850 ^ _779300) ^ [_1340156, _1340158, _1340160] : [class_Orderings_Olinorder(_1340156), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340156), _1340158)), -(_1340158 = c_Orderings_Obot__class_Obot(tc_fun(_1340156, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340156), _1340160)), -(_1340160 = c_Orderings_Obot__class_Obot(tc_fun(_1340156, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340156, tc_HOL_Obool)), _1340158), _1340160) = c_Orderings_Obot__class_Obot(tc_fun(_1340156, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1340156, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340156, tc_HOL_Obool)), _1340158), _1340160)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340156), c_Big__Operators_Olinorder__class_OMax(_1340156, _1340158)), c_Big__Operators_Olinorder__class_OMax(_1340156, _1340160)))], (30876 ^ _779300) ^ [_1340633, _1340635, _1340637] : [class_Orderings_Olinorder(_1340633), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340633), _1340635)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340633), _1340637)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340633, tc_HOL_Obool)), _1340635), _1340637) = c_Orderings_Obot__class_Obot(tc_fun(_1340633, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340633), c_Big__Operators_Olinorder__class_OMax(_1340633, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340633, tc_HOL_Obool)), _1340635), _1340637))), c_Big__Operators_Olinorder__class_OMax(_1340633, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340633, tc_HOL_Obool)), _1340635), _1340637))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340633), c_Big__Operators_Olinorder__class_OMax(_1340633, _1340635)), c_Big__Operators_Olinorder__class_OMax(_1340633, _1340637)))], (30894 ^ _779300) ^ [_1340981, _1340983, _1340985] : [class_Orderings_Olinorder(_1340981), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340981), _1340983)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340981), _1340985)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340981, tc_HOL_Obool)), _1340983), _1340985) = c_Orderings_Obot__class_Obot(tc_fun(_1340981, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1340981), c_Big__Operators_Olattice_OInf__fin(_1340981, c_Orderings_Oord__class_Omin(_1340981), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340981, tc_HOL_Obool)), _1340983), _1340985))), c_Big__Operators_Olattice_OInf__fin(_1340981, c_Orderings_Oord__class_Omin(_1340981), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340981, tc_HOL_Obool)), _1340983), _1340985))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1340981), c_Big__Operators_Olattice_OInf__fin(_1340981, c_Orderings_Oord__class_Omin(_1340981), _1340983)), c_Big__Operators_Olattice_OInf__fin(_1340981, c_Orderings_Oord__class_Omin(_1340981), _1340985)))], (30912 ^ _779300) ^ [_1341353, _1341355, _1341357] : [class_Orderings_Olinorder(_1341353), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341353), _1341355)), -(_1341355 = c_Orderings_Obot__class_Obot(tc_fun(_1341353, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341353), _1341357)), -(_1341357 = c_Orderings_Obot__class_Obot(tc_fun(_1341353, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341353, tc_HOL_Obool)), _1341355), _1341357) = c_Orderings_Obot__class_Obot(tc_fun(_1341353, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1341353, c_Orderings_Oord__class_Omin(_1341353), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341353, tc_HOL_Obool)), _1341355), _1341357)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1341353), c_Big__Operators_Olattice_OInf__fin(_1341353, c_Orderings_Oord__class_Omin(_1341353), _1341355)), c_Big__Operators_Olattice_OInf__fin(_1341353, c_Orderings_Oord__class_Omin(_1341353), _1341357)))], (30938 ^ _779300) ^ [_1341848, _1341850, _1341852] : [class_Orderings_Olinorder(_1341848), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341848), _1341850)), -(_1341850 = c_Orderings_Obot__class_Obot(tc_fun(_1341848, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341848), _1341852)), -(_1341852 = c_Orderings_Obot__class_Obot(tc_fun(_1341848, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341848, tc_HOL_Obool)), _1341850), _1341852) = c_Orderings_Obot__class_Obot(tc_fun(_1341848, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1341848, c_Orderings_Oord__class_Omax(_1341848), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341848, tc_HOL_Obool)), _1341850), _1341852)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341848), c_Big__Operators_Olattice_OSup__fin(_1341848, c_Orderings_Oord__class_Omax(_1341848), _1341850)), c_Big__Operators_Olattice_OSup__fin(_1341848, c_Orderings_Oord__class_Omax(_1341848), _1341852)))], (30964 ^ _779300) ^ [_1342343, _1342345, _1342347] : [class_Orderings_Olinorder(_1342343), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342343), _1342345)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342343), _1342347)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342343, tc_HOL_Obool)), _1342345), _1342347) = c_Orderings_Obot__class_Obot(tc_fun(_1342343, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342343), c_Big__Operators_Olattice_OSup__fin(_1342343, c_Orderings_Oord__class_Omax(_1342343), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342343, tc_HOL_Obool)), _1342345), _1342347))), c_Big__Operators_Olattice_OSup__fin(_1342343, c_Orderings_Oord__class_Omax(_1342343), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342343, tc_HOL_Obool)), _1342345), _1342347))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342343), c_Big__Operators_Olattice_OSup__fin(_1342343, c_Orderings_Oord__class_Omax(_1342343), _1342345)), c_Big__Operators_Olattice_OSup__fin(_1342343, c_Orderings_Oord__class_Omax(_1342343), _1342347)))], (30982 ^ _779300) ^ [_1342715] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1342715)) = 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), _1342715))))], (30984 ^ _779300) ^ [_1342753, _1342755, _1342757] : [-(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), _1342753)), 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))), _1342755))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1342757))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1342757)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1342753), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1342753), 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), _1342757), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1342755)))))], (30986 ^ _779300) ^ [_1342840, _1342842, _1342844] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1342840), _1342842)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342840), _1342844)), 30996 ^ _779300 : [(30997 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1342840), 30995 ^ [_1342840, _1342842, _1342844]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342840, tc_HOL_Obool)), _1342842), _1342844))))], (30999 ^ _779300) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1342840), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342840, tc_HOL_Obool)), _1342842), _1342844)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1342840), _1342842)), hAPP(c_Finite__Set_Ocard(_1342840), _1342844)))], (31003 ^ _779300) ^ [_1343184, _1343186, _1343188, _1343190, _1343192] : [class_Fields_Ofield(_1343184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343186), _1343188)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343186), _1343190)), 31017 ^ _779300 : [(31018 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1343186), 31016 ^ [_1343184, _1343186, _1343188, _1343190, _1343192]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343186, tc_HOL_Obool)), _1343188), _1343190))))], (31020 ^ _779300) ^ [] : [-(hAPP(_1343192, 31016 ^ [_1343184, _1343186, _1343188, _1343190, _1343192]) = c_Groups_Ozero__class_Ozero(_1343184))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343186, _1343184), _1343192), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1343186, tc_HOL_Obool)), _1343188), _1343190)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1343184), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343184), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343186, _1343184), _1343192), _1343188)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343186, _1343184), _1343192), _1343190))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343186, _1343184), _1343192), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343186, tc_HOL_Obool)), _1343188), _1343190))))], (31024 ^ _779300) ^ [_1343680, _1343682, _1343684, _1343686, _1343688] : [class_Groups_Ocomm__monoid__mult(_1343680), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343682), _1343684)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343682), _1343686)), 31038 ^ _779300 : [(31039 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1343682), 31037 ^ [_1343680, _1343682, _1343684, _1343686, _1343688]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343682, tc_HOL_Obool)), _1343684), _1343686))))], (31041 ^ _779300) ^ [] : [hAPP(_1343688, 31037 ^ [_1343680, _1343682, _1343684, _1343686, _1343688]) = c_Groups_Oone__class_Oone(_1343680)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1343680, _1343682, c_Groups_Otimes__class_Otimes(_1343680)), _1343688), c_Groups_Oone__class_Oone(_1343680)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1343682, tc_HOL_Obool)), _1343684), _1343686)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343680), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1343680, _1343682, c_Groups_Otimes__class_Otimes(_1343680)), _1343688), c_Groups_Oone__class_Oone(_1343680)), _1343684)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1343680, _1343682, c_Groups_Otimes__class_Otimes(_1343680)), _1343688), c_Groups_Oone__class_Oone(_1343680)), _1343686)))], (31045 ^ _779300) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (31047 ^ _779300) ^ [_1344241, _1344243, _1344245, _1344247] : [class_Groups_Oab__group__add(_1344241), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344243, _1344241), hAPP(hAPP(c_COMBB(_1344241, _1344241, _1344243), c_Groups_Ouminus__class_Ouminus(_1344241)), _1344245)), _1344247) = hAPP(c_Groups_Ouminus__class_Ouminus(_1344241), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344243, _1344241), _1344245), _1344247)))], (31053 ^ _779300) ^ [_1344390, _1344392, _1344394] : [class_Groups_Ocomm__monoid__add(_1344390), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344392, _1344390), hAPP(c_COMBK(_1344390, _1344392), c_Groups_Ozero__class_Ozero(_1344390))), _1344394) = c_Groups_Ozero__class_Ozero(_1344390))], (31059 ^ _779300) ^ [_1344505, _1344507, _1344509, _1344511, _1344513] : [class_Groups_Ocomm__monoid__add(_1344505), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344507, _1344505), hAPP(hAPP(c_COMBS(_1344507, _1344505, _1344505), hAPP(hAPP(c_COMBB(_1344505, tc_fun(_1344505, _1344505), _1344507), c_Groups_Oplus__class_Oplus(_1344505)), _1344509)), _1344511)), _1344513) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344505), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344507, _1344505), _1344509), _1344513)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344507, _1344505), _1344511), _1344513)))], (31065 ^ _779300) ^ [_1344706, _1344708, _1344710, _1344712, _1344714] : [class_Rings_Osemiring__0(_1344706), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1344706), _1344708), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344710, _1344706), _1344712), _1344714)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344710, _1344706), hAPP(hAPP(c_COMBB(_1344706, _1344706, _1344710), hAPP(c_Groups_Otimes__class_Otimes(_1344706), _1344708)), _1344712)), _1344714))], (31071 ^ _779300) ^ [_1344869, _1344871, _1344873, _1344875, _1344877] : [class_Rings_Osemiring__0(_1344869), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1344869), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344871, _1344869), _1344873), _1344875)), _1344877) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344871, _1344869), hAPP(hAPP(c_COMBC(_1344871, _1344869, _1344869), hAPP(hAPP(c_COMBB(_1344869, tc_fun(_1344869, _1344869), _1344871), c_Groups_Otimes__class_Otimes(_1344869)), _1344873)), _1344877)), _1344875))], (31077 ^ _779300) ^ [_1345052, _1345054, _1345056, _1345058, _1345060, _1345062, _1345064] : [class_Rings_Osemiring__0(_1345052), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345052), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345054, _1345052), _1345056), _1345058)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345060, _1345052), _1345062), _1345064)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345054, _1345052), hAPP(hAPP(c_COMBC(_1345054, tc_fun(_1345060, tc_HOL_Obool), _1345052), hAPP(hAPP(c_COMBB(tc_fun(_1345060, _1345052), tc_fun(tc_fun(_1345060, tc_HOL_Obool), _1345052), _1345054), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345060, _1345052)), hAPP(hAPP(c_COMBC(_1345054, tc_fun(_1345060, _1345052), tc_fun(_1345060, _1345052)), hAPP(hAPP(c_COMBB(tc_fun(_1345052, _1345052), tc_fun(tc_fun(_1345060, _1345052), tc_fun(_1345060, _1345052)), _1345054), c_COMBB(_1345052, _1345052, _1345060)), hAPP(hAPP(c_COMBB(_1345052, tc_fun(_1345052, _1345052), _1345054), c_Groups_Otimes__class_Otimes(_1345052)), _1345056))), _1345062))), _1345064)), _1345058))], (31083 ^ _779300) ^ [_1345391, _1345393, _1345395, _1345397, _1345399] : [class_Groups_Oab__group__add(_1345391), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345393, _1345391), hAPP(hAPP(c_COMBS(_1345393, _1345391, _1345391), hAPP(hAPP(c_COMBB(_1345391, tc_fun(_1345391, _1345391), _1345393), c_Groups_Ominus__class_Ominus(_1345391)), _1345395)), _1345397)), _1345399) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1345391), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345393, _1345391), _1345395), _1345399)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345393, _1345391), _1345397), _1345399)))], (31089 ^ _779300) ^ [_1345592, _1345594, _1345596, _1345598, _1345600, _1345602] : [class_Groups_Ocomm__monoid__add(_1345592), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345594, _1345592), hAPP(hAPP(c_COMBC(_1345594, tc_fun(_1345596, tc_HOL_Obool), _1345592), hAPP(hAPP(c_COMBB(tc_fun(_1345596, _1345592), tc_fun(tc_fun(_1345596, tc_HOL_Obool), _1345592), _1345594), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345596, _1345592)), _1345598)), _1345600)), _1345602) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345596, _1345592), hAPP(hAPP(c_COMBC(_1345596, tc_fun(_1345594, tc_HOL_Obool), _1345592), hAPP(hAPP(c_COMBB(tc_fun(_1345594, _1345592), tc_fun(tc_fun(_1345594, tc_HOL_Obool), _1345592), _1345596), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345594, _1345592)), hAPP(c_COMBC(_1345594, _1345596, _1345592), _1345598))), _1345602)), _1345600))], (31095 ^ _779300) ^ [_1345865, _1345867, _1345869, _1345871] : [class_Rings_Osemiring__1(_1345865), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1345865), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345867, tc_Nat_Onat), _1345869), _1345871)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345867, _1345865), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1345865, _1345867), c_Nat_Osemiring__1__class_Oof__nat(_1345865)), _1345869)), _1345871))], (31101 ^ _779300) ^ [_1346014, _1346016, _1346018, _1346020] : [class_Rings_Oring__1(_1346014), -(hAPP(c_Int_Oring__1__class_Oof__int(_1346014), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346016, tc_Int_Oint), _1346018), _1346020)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346016, _1346014), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1346014, _1346016), c_Int_Oring__1__class_Oof__int(_1346014)), _1346018)), _1346020))], (31107 ^ _779300) ^ [_1346163, _1346165, _1346167, _1346169, _1346171] : [class_Fields_Ofield(_1346163), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1346163), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346165, _1346163), _1346167), _1346169)), _1346171) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346165, _1346163), hAPP(hAPP(c_COMBC(_1346165, _1346163, _1346163), hAPP(hAPP(c_COMBB(_1346163, tc_fun(_1346163, _1346163), _1346165), c_Rings_Oinverse__class_Odivide(_1346163)), _1346167)), _1346171)), _1346169))], (31113 ^ _779300) ^ [_1346346, _1346348, _1346350] : [class_Groups_Ocomm__monoid__add(_1346346), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346348, _1346346), _1346350), c_Orderings_Obot__class_Obot(tc_fun(_1346348, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1346346))], (31119 ^ _779300) ^ [_1346455, _1346457, _1346459] : [class_Groups_Ocomm__monoid__add(_1346455), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346457, _1346455), _1346459), c_Orderings_Obot__class_Obot(tc_fun(_1346457, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1346455))], (31125 ^ _779300) ^ [_1346564, _1346566, _1346568, _1346570] : [class_Groups_Ocomm__monoid__add(_1346564), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1346566), _1346568))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346566, _1346564), _1346570), _1346568) = c_Groups_Ozero__class_Ozero(_1346564))], (31135 ^ _779300) ^ [_1346688, _1346690, _1346692, _1346694] : [class_Groups_Ocomm__monoid__add(_1346688), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1346690), _1346692))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346690, _1346688), _1346694), _1346692) = c_Groups_Ozero__class_Ozero(_1346688))], (31145 ^ _779300) ^ [_1346839, _1346841, _1346843, _1346845, _1346847, _1346849] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346839, tc_fun(_1346841, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1346839, tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_fun(_1346841, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346841, tc_fun(tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_fun(_1346841, tc_HOL_Obool)), _1346839), c_COMBC(_1346841, tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346841, tc_prod(_1346839, _1346841)), tc_fun(_1346841, tc_fun(tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_HOL_Obool)), _1346839), hAPP(c_COMBB(tc_prod(_1346839, _1346841), tc_fun(tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_HOL_Obool), _1346841), c_member(tc_prod(_1346839, _1346841)))), c_Product__Type_OPair(_1346839, _1346841)))), _1346843)), hAPP(hAPP(c_COMBC(_1346839, tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_fun(_1346841, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346841, tc_fun(tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_fun(_1346841, tc_HOL_Obool)), _1346839), c_COMBC(_1346841, tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346841, tc_prod(_1346839, _1346841)), tc_fun(_1346841, tc_fun(tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_HOL_Obool)), _1346839), hAPP(c_COMBB(tc_prod(_1346839, _1346841), tc_fun(tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool), tc_HOL_Obool), _1346841), c_member(tc_prod(_1346839, _1346841)))), c_Product__Type_OPair(_1346839, _1346841)))), _1346845)), _1346847), _1346849)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1346839, _1346841)), hAPP(hAPP(c_Product__Type_OPair(_1346839, _1346841), _1346847), _1346849)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1346839, _1346841), tc_HOL_Obool)), _1346843), _1346845))))], (31151 ^ _779300) ^ [_1347496, _1347498, _1347500, _1347502, _1347504, _1347506] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1347496, _1347498)), hAPP(hAPP(c_Product__Type_OPair(_1347496, _1347498), _1347504), _1347506)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool)), _1347500), _1347502))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1347496, tc_fun(_1347498, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1347496, tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_fun(_1347498, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1347498, tc_fun(tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_fun(_1347498, tc_HOL_Obool)), _1347496), c_COMBC(_1347498, tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1347498, tc_prod(_1347496, _1347498)), tc_fun(_1347498, tc_fun(tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_HOL_Obool)), _1347496), hAPP(c_COMBB(tc_prod(_1347496, _1347498), tc_fun(tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_HOL_Obool), _1347498), c_member(tc_prod(_1347496, _1347498)))), c_Product__Type_OPair(_1347496, _1347498)))), _1347500)), hAPP(hAPP(c_COMBC(_1347496, tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_fun(_1347498, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1347498, tc_fun(tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_fun(_1347498, tc_HOL_Obool)), _1347496), c_COMBC(_1347498, tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1347498, tc_prod(_1347496, _1347498)), tc_fun(_1347498, tc_fun(tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_HOL_Obool)), _1347496), hAPP(c_COMBB(tc_prod(_1347496, _1347498), tc_fun(tc_fun(tc_prod(_1347496, _1347498), tc_HOL_Obool), tc_HOL_Obool), _1347498), c_member(tc_prod(_1347496, _1347498)))), c_Product__Type_OPair(_1347496, _1347498)))), _1347502)), _1347504), _1347506)))], (31157 ^ _779300) ^ [_1348159, _1348161, _1348163, _1348165, _1348167] : [class_Groups_Ocomm__monoid__add(_1348159), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348161), _1348163)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348161, _1348159), hAPP(hAPP(c_COMBS(_1348161, _1348159, _1348159), hAPP(hAPP(c_COMBB(_1348159, tc_fun(_1348159, _1348159), _1348161), c_Groups_Oplus__class_Oplus(_1348159)), _1348165)), _1348167)), _1348163) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348159), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348161, _1348159), _1348165), _1348163)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348161, _1348159), _1348167), _1348163)))], (31167 ^ _779300) ^ [_1348426, _1348428, _1348430] : [class_Groups_Ocomm__monoid__add(_1348426), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348426), _1348428), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1348430))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348426), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348426), _1348428), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1348430))), hAPP(_1348428, _1348430)))], (31173 ^ _779300) ^ [_1348579, _1348581, _1348583, _1348585] : [class_Groups_Ocomm__monoid__add(_1348579), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348579), _1348581), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1348583)), hAPP(c_Nat_OSuc, _1348585))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348579), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1348579, tc_Nat_Onat), _1348581), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348583), _1348585)))], (31179 ^ _779300) ^ [_1348750, _1348752, _1348754, _1348756, _1348758] : [class_Groups_Ocomm__monoid__add(_1348750), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348750), _1348752), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1348754), _1348756)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1348758), _1348756))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348750), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1348750, tc_Nat_Onat), _1348752), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1348756))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348754), _1348758)))], (31185 ^ _779300) ^ [_1348941, _1348943, _1348945, _1348947] : [class_Groups_Ocomm__monoid__add(_1348941), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348941), _1348943), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1348945), hAPP(c_Nat_OSuc, _1348947))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348941), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1348941, tc_Nat_Onat), _1348943), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1348945, _1348947)))], (31191 ^ _779300) ^ [_1349104, _1349106, _1349108, _1349110, _1349112] : [class_Groups_Ocomm__monoid__add(_1349104), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349104), _1349106), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1349108), _1349110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1349112), _1349110))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349104), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1349104, tc_Nat_Onat), _1349106), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1349110))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1349108, _1349112)))], (31197 ^ _779300) ^ [_1349287, _1349289, _1349291, _1349293, _1349295] : [class_Groups_Ocomm__monoid__add(_1349287), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1349289), _1349291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1349291), _1349293)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349287), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349287), _1349295), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1349289), _1349291))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349287), _1349295), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1349291), _1349293))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349287), _1349295), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1349289), _1349293)))], (31211 ^ _779300) ^ [_1349610, _1349612, _1349614, _1349616, _1349618] : [class_Groups_Oab__group__add(_1349610), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1349612), _1349614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1349614), _1349616)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1349610), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349610), _1349618), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1349612), _1349616))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349610), _1349618), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1349612), _1349614))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349610), _1349618), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1349614), _1349616)))], (31225 ^ _779300) ^ [_1349933, _1349935, _1349937, _1349939, _1349941] : [class_Groups_Ocomm__monoid__add(_1349933), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349935), _1349937)), 31232 ^ _779300 : [(31233 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1349935), _1349939), _1349937)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349935, _1349933), hAPP(hAPP(c_COMBC(_1349935, _1349933, _1349933), hAPP(hAPP(c_COMBS(_1349935, _1349933, tc_fun(_1349933, _1349933)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1349933, tc_fun(_1349933, _1349933)), _1349935), c_If(_1349933)), hAPP(c_fequal, _1349939))), _1349941)), c_Groups_Ozero__class_Ozero(_1349933))), _1349937) = hAPP(_1349941, _1349939))], (31239 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1349935), _1349939), _1349937))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349935, _1349933), hAPP(hAPP(c_COMBC(_1349935, _1349933, _1349933), hAPP(hAPP(c_COMBS(_1349935, _1349933, tc_fun(_1349933, _1349933)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1349933, tc_fun(_1349933, _1349933)), _1349935), c_If(_1349933)), hAPP(c_fequal, _1349939))), _1349941)), c_Groups_Ozero__class_Ozero(_1349933))), _1349937) = c_Groups_Ozero__class_Ozero(_1349933))]]], (31245 ^ _779300) ^ [_1350443, _1350445, _1350447, _1350449, _1350451] : [class_Groups_Ocomm__monoid__add(_1350443), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350445), _1350447)), 31252 ^ _779300 : [(31253 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1350445), _1350449), _1350447)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350445, _1350443), hAPP(hAPP(c_COMBC(_1350445, _1350443, _1350443), hAPP(hAPP(c_COMBS(_1350445, _1350443, tc_fun(_1350443, _1350443)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1350443, tc_fun(_1350443, _1350443)), _1350445), c_If(_1350443)), hAPP(hAPP(c_COMBC(_1350445, _1350445, tc_HOL_Obool), c_fequal), _1350449))), _1350451)), c_Groups_Ozero__class_Ozero(_1350443))), _1350447) = hAPP(_1350451, _1350449))], (31259 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1350445), _1350449), _1350447))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350445, _1350443), hAPP(hAPP(c_COMBC(_1350445, _1350443, _1350443), hAPP(hAPP(c_COMBS(_1350445, _1350443, tc_fun(_1350443, _1350443)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1350443, tc_fun(_1350443, _1350443)), _1350445), c_If(_1350443)), hAPP(hAPP(c_COMBC(_1350445, _1350445, tc_HOL_Obool), c_fequal), _1350449))), _1350451)), c_Groups_Ozero__class_Ozero(_1350443))), _1350447) = c_Groups_Ozero__class_Ozero(_1350443))]]], (31265 ^ _779300) ^ [_1350981, _1350983, _1350985, _1350987] : [class_Rings_Osemiring__1(_1350981), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350983, _1350981), hAPP(c_COMBK(_1350981, _1350983), _1350985)), _1350987) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350981), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1350981), hAPP(c_Finite__Set_Ocard(_1350983), _1350987))), _1350985))], (31271 ^ _779300) ^ [_1351126, _1351128, _1351130] : [class_Groups_Ocomm__monoid__add(_1351126), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1351126), _1351128), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1351130))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351126), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1351126), _1351128), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1351130))), hAPP(_1351128, hAPP(c_Nat_OSuc, _1351130))))], (31277 ^ _779300) ^ [_1351285, _1351287, _1351289, _1351291, _1351293] : [class_Groups_Ocomm__monoid__add(_1351285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351287), _1351289)), -(hBOOL(hAPP(hAPP(c_member(_1351287), _1351291), _1351289))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351287, _1351285), _1351293), hAPP(hAPP(c_Set_Oinsert(_1351287), _1351291), _1351289)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351285), hAPP(_1351293, _1351291)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351287, _1351285), _1351293), _1351289)))], (31291 ^ _779300) ^ [_1351535, _1351537, _1351539, _1351541, _1351543] : [class_Groups_Ocomm__monoid__add(_1351535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351537), _1351539)), -(hBOOL(hAPP(hAPP(c_member(_1351537), _1351541), _1351539))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351537, _1351535), _1351543), hAPP(hAPP(c_Set_Oinsert(_1351537), _1351541), _1351539)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351535), hAPP(_1351543, _1351541)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351537, _1351535), _1351543), _1351539)))], (31305 ^ _779300) ^ [_1351785, _1351787, _1351789, _1351791, _1351793] : [class_Groups_Ocomm__monoid__add(_1351785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351787), _1351789)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351787), _1351791)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351785), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351787, _1351785), _1351793), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351787, tc_HOL_Obool)), _1351789), _1351791))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351787, _1351785), _1351793), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1351787, tc_HOL_Obool)), _1351789), _1351791))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351785), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351787, _1351785), _1351793), _1351789)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351787, _1351785), _1351793), _1351791)))], (31319 ^ _779300) ^ [_1352146, _1352148, _1352150, _1352152, _1352154] : [class_Groups_Oab__group__add(_1352146), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352148), _1352150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1352148, tc_HOL_Obool)), _1352152), _1352150)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352148, _1352146), _1352154), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352148, tc_HOL_Obool)), _1352150), _1352152)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1352146), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352148, _1352146), _1352154), _1352150)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352148, _1352146), _1352154), _1352152)))], (31333 ^ _779300) ^ [_1352463, _1352465, _1352467, _1352469] : [class_Groups_Ocomm__monoid__add(_1352463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352465), _1352467)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352465, _1352463), _1352469), _1352467) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1352463, _1352465, c_Groups_Oplus__class_Oplus(_1352463)), _1352469), c_Groups_Ozero__class_Ozero(_1352463)), _1352467))], (31343 ^ _779300) ^ [_1352658, _1352660, _1352662, _1352664] : [class_Groups_Ocomm__monoid__add(_1352658), 31346 ^ _779300 : [(31347 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1352660), _1352662)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352660, _1352658), _1352664), _1352662) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1352658, _1352660, c_Groups_Oplus__class_Oplus(_1352658)), _1352664), c_Groups_Ozero__class_Ozero(_1352658)), _1352662))], (31353 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1352660), _1352662))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352660, _1352658), _1352664), _1352662) = c_Groups_Ozero__class_Ozero(_1352658))]]], (31359 ^ _779300) ^ [_1352930, _1352932, _1352934] : [class_Groups_Ocomm__monoid__add(_1352930), hAPP(_1352932, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1352930), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352930), _1352932), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1352934)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352930), _1352932), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1352934)))], (31369 ^ _779300) ^ [_1353119, _1353121, _1353123, _1353125] : [class_Groups_Ocomm__monoid__add(_1353119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1353121), _1353123)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353119), _1353125), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1353121), _1353123)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353119), hAPP(_1353125, _1353121)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353119), _1353125), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1353121)), _1353123))))], (31379 ^ _779300) ^ [_1353352, _1353354, _1353356, _1353358] : [class_Groups_Ocomm__monoid__add(_1353352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1353354), _1353356)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353352), _1353358), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1353354, _1353356)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353352), hAPP(_1353358, _1353354)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353352), _1353358), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1353354), _1353356))))], (31389 ^ _779300) ^ [_1353577, _1353579, _1353581, _1353583, _1353585] : [class_Groups_Ocomm__monoid__add(_1353577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353579), _1353581)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353579, _1353577), _1353583), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1353579, tc_HOL_Obool)), _1353581), _1353585)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353579, _1353577), hAPP(hAPP(c_COMBC(_1353579, _1353577, _1353577), hAPP(hAPP(c_COMBS(_1353579, _1353577, tc_fun(_1353577, _1353577)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1353577, tc_fun(_1353577, _1353577)), _1353579), c_If(_1353577)), hAPP(hAPP(c_COMBC(_1353579, tc_fun(_1353579, tc_HOL_Obool), tc_HOL_Obool), c_member(_1353579)), _1353585))), _1353583)), c_Groups_Ozero__class_Ozero(_1353577))), _1353581))], (31399 ^ _779300) ^ [_1353898, _1353900, _1353902, _1353904, _1353906] : [class_Groups_Ocomm__monoid__add(_1353898), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353900), _1353902)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353900, _1353898), _1353904), hAPP(hAPP(c_Set_Oinsert(_1353900), _1353906), _1353902)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353898), hAPP(_1353904, _1353906)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353900, _1353898), _1353904), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353900, tc_HOL_Obool)), _1353902), hAPP(hAPP(c_Set_Oinsert(_1353900), _1353906), c_Orderings_Obot__class_Obot(tc_fun(_1353900, tc_HOL_Obool)))))))], (31409 ^ _779300) ^ [_1354167, _1354169, _1354171, _1354173, _1354175] : [class_Groups_Ocomm__monoid__add(_1354167), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354169), _1354171)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354169), _1354173)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1354169, tc_HOL_Obool)), _1354171), _1354173) = c_Orderings_Obot__class_Obot(tc_fun(_1354169, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354169, _1354167), _1354175), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1354169, tc_HOL_Obool)), _1354171), _1354173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354167), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354169, _1354167), _1354175), _1354171)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354169, _1354167), _1354175), _1354173)))], (31427 ^ _779300) ^ [_1354562, _1354564, _1354566, _1354568, _1354570] : [class_Groups_Oab__group__add(_1354562), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354564), _1354566)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354564), _1354568)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354564, _1354562), _1354570), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1354564, tc_HOL_Obool)), _1354566), _1354568)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1354562), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354562), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354564, _1354562), _1354570), _1354566)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354564, _1354562), _1354570), _1354568))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354564, _1354562), _1354570), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1354564, tc_HOL_Obool)), _1354566), _1354568))))], (31441 ^ _779300) ^ [_1354923, _1354925, _1354927, _1354929] : [class_Groups_Ocomm__monoid__add(_1354923), 31444 ^ _779300 : [(31445 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1354925), _1354927)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354923), _1354929), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1354927), hAPP(c_Nat_OSuc, _1354925))) = c_Groups_Ozero__class_Ozero(_1354923))], (31451 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1354925), _1354927))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354923), _1354929), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1354927), hAPP(c_Nat_OSuc, _1354925))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354923), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354923), _1354929), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1354927), _1354925))), hAPP(_1354929, _1354925)))]]], (31457 ^ _779300) ^ [_1355253, _1355255, _1355257, _1355259] : [class_Groups_Ocomm__monoid__add(_1355253), 31460 ^ _779300 : [(31461 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1355255)), _1355257)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355253), _1355259), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1355257, hAPP(c_Nat_OSuc, _1355255))) = c_Groups_Ozero__class_Ozero(_1355253))], (31467 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1355255)), _1355257))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355253), _1355259), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1355257, hAPP(c_Nat_OSuc, _1355255))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355253), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355253), _1355259), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1355257, _1355255))), hAPP(_1355259, hAPP(c_Nat_OSuc, _1355255))))]]], (31473 ^ _779300) ^ [_1355589, _1355591, _1355593, _1355595] : [class_Groups_Ocomm__monoid__add(_1355589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1355591), _1355593)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355589), _1355595), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1355591, _1355593)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355589), hAPP(_1355595, _1355591)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355589), _1355595), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1355591, _1355593))))], (31483 ^ _779300) ^ [_1355808, _1355810, _1355812, _1355814, _1355816] : [class_Groups_Ocomm__monoid__add(_1355808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1355810), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1355812), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355808), _1355814), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1355810, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1355812), _1355816))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355808), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355808), _1355814), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1355810, _1355812))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355808), _1355814), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1355812), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1355812), _1355816)))))], (31493 ^ _779300) ^ [_1356099, _1356101, _1356103, _1356105, _1356107] : [class_Groups_Ocomm__monoid__add(_1356099), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356101), _1356103)), hBOOL(hAPP(hAPP(c_member(_1356101), _1356105), _1356103)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356101, _1356099), _1356107), _1356103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356099), hAPP(_1356107, _1356105)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356101, _1356099), _1356107), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356101, tc_HOL_Obool)), _1356103), hAPP(hAPP(c_Set_Oinsert(_1356101), _1356105), c_Orderings_Obot__class_Obot(tc_fun(_1356101, tc_HOL_Obool)))))))], (31507 ^ _779300) ^ [_1356424, _1356426, _1356428, _1356430, _1356432] : [class_Groups_Ocomm__monoid__add(_1356424), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356426), _1356428)), hBOOL(hAPP(hAPP(c_member(_1356426), _1356430), _1356428)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356426, _1356424), _1356432), _1356428) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356424), hAPP(_1356432, _1356430)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356426, _1356424), _1356432), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356426, tc_HOL_Obool)), _1356428), hAPP(hAPP(c_Set_Oinsert(_1356426), _1356430), c_Orderings_Obot__class_Obot(tc_fun(_1356426, tc_HOL_Obool)))))))], (31521 ^ _779300) ^ [_1356749, _1356751, _1356753, _1356755, _1356757] : [class_Groups_Oab__group__add(_1356749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356751), _1356753)), 31528 ^ _779300 : [(31529 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1356751), _1356755), _1356753)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356751, _1356749), _1356757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356751, tc_HOL_Obool)), _1356753), hAPP(hAPP(c_Set_Oinsert(_1356751), _1356755), c_Orderings_Obot__class_Obot(tc_fun(_1356751, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1356749), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356751, _1356749), _1356757), _1356753)), hAPP(_1356757, _1356755)))], (31535 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1356751), _1356755), _1356753))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356751, _1356749), _1356757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356751, tc_HOL_Obool)), _1356753), hAPP(hAPP(c_Set_Oinsert(_1356751), _1356755), c_Orderings_Obot__class_Obot(tc_fun(_1356751, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356751, _1356749), _1356757), _1356753))]]], (31541 ^ _779300) ^ [_1357219, _1357221, _1357223, _1357225, _1357227] : [class_Rings_Oring(_1357219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357221), _1357223)), hBOOL(hAPP(hAPP(c_member(_1357221), _1357225), _1357223)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357221, _1357219), _1357227), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357221, tc_HOL_Obool)), _1357223), hAPP(hAPP(c_Set_Oinsert(_1357221), _1357225), c_Orderings_Obot__class_Obot(tc_fun(_1357221, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357219), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357221, _1357219), _1357227), _1357223)), hAPP(_1357227, _1357225)))], (31555 ^ _779300) ^ [_1357544, _1357546, _1357548, _1357550] : [class_Rings_Ocomm__semiring__1(_1357544), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357544), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357544), c_Groups_Oone__class_Oone(_1357544)), c_Groups_Oone__class_Oone(_1357544))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1357544), hAPP(hAPP(c_COMBB(_1357544, _1357544, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1357544), _1357546)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1357544, _1357544), hAPP(hAPP(c_COMBB(_1357544, tc_fun(_1357544, _1357544), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1357544)), c_Nat_Osemiring__1__class_Oof__nat(_1357544))), _1357548))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1357550))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357544), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1357544), _1357550)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357544), _1357546), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357544), _1357546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357544), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1357544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1357550), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1357548)))))], (31561 ^ _779300) ^ [_1357867, _1357869, _1357871] : [class_Fields_Ofield(_1357867), -(_1357869 = c_Groups_Oone__class_Oone(_1357867)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1357867), hAPP(c_Power_Opower__class_Opower(_1357867), _1357869)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1357871)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357867), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357867), hAPP(hAPP(c_Power_Opower__class_Opower(_1357867), _1357869), _1357871)), c_Groups_Oone__class_Oone(_1357867))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357867), _1357869), c_Groups_Oone__class_Oone(_1357867))))], (31571 ^ _779300) ^ [_1358069, _1358071] : [class_Rings_Ocomm__semiring__1(_1358069), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1358069), c_Groups_Oone__class_Oone(_1358069)), c_Groups_Oone__class_Oone(_1358069))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1358069), c_Nat_Osemiring__1__class_Oof__nat(_1358069)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1358071))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358069), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1358069), _1358071)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1358069), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1358069), _1358071)), c_Groups_Oone__class_Oone(_1358069))))], (31577 ^ _779300) ^ [_1358270, _1358272, _1358274, _1358276] : [class_Groups_Oab__group__add(_1358270), 31580 ^ _779300 : [(31581 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1358272), _1358274)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1358270), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1358270, _1358270), hAPP(hAPP(c_COMBB(_1358270, tc_fun(_1358270, _1358270), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1358270)), _1358276)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1358270, tc_Nat_Onat), _1358276), 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, _1358272, _1358274)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358270), hAPP(_1358276, _1358272)), hAPP(_1358276, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1358274), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (31587 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1358272), _1358274))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1358270), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1358270, _1358270), hAPP(hAPP(c_COMBB(_1358270, tc_fun(_1358270, _1358270), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1358270)), _1358276)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1358270, tc_Nat_Onat), _1358276), 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, _1358272, _1358274)) = c_Groups_Ozero__class_Ozero(_1358270))]]], (31593 ^ _779300) ^ [_1358708, _1358710, _1358712, _1358714, _1358716] : [class_Groups_Oordered__comm__monoid__add(_1358708), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358710), _1358712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1358710, tc_HOL_Obool)), _1358714), _1358712)), 31607 ^ _779300 : [(31608 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358710), 31606 ^ [_1358708, _1358710, _1358712, _1358714, _1358716]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1358710, tc_HOL_Obool)), _1358712), _1358714))))], (31610 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358708), c_Groups_Ozero__class_Ozero(_1358708)), hAPP(_1358716, 31606 ^ [_1358708, _1358710, _1358712, _1358714, _1358716])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358708), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358710, _1358708), _1358716), _1358714)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1358710, _1358708), _1358716), _1358712))))], (31614 ^ _779300) ^ [_1359194, _1359196, _1359198, _1359200, _1359202] : [class_Groups_Ocomm__monoid__mult(_1359194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359196), _1359198)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359196), _1359200)), 31628 ^ _779300 : [(31629 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359196), 31627 ^ [_1359194, _1359196, _1359198, _1359200, _1359202]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1359196, tc_HOL_Obool)), _1359198), _1359200))))], (31631 ^ _779300) ^ [] : [hAPP(_1359202, 31627 ^ [_1359194, _1359196, _1359198, _1359200, _1359202]) = c_Groups_Oone__class_Oone(_1359194)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1359196, _1359194), _1359202), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1359196, tc_HOL_Obool)), _1359198), _1359200)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359194), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1359196, _1359194), _1359202), _1359198)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1359196, _1359194), _1359202), _1359200)))], (31635 ^ _779300) ^ [_1359689, _1359691, _1359693, _1359695, _1359697] : [class_Groups_Ocomm__monoid__mult(_1359689), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359691), _1359693)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359691), _1359695)), 31649 ^ _779300 : [(31650 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359691), 31648 ^ [_1359689, _1359691, _1359693, _1359695, _1359697]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1359691, tc_HOL_Obool)), _1359693), _1359695))))], (31652 ^ _779300) ^ [] : [hAPP(_1359697, 31648 ^ [_1359689, _1359691, _1359693, _1359695, _1359697]) = c_Groups_Oone__class_Oone(_1359689)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1359691, _1359689), _1359697), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1359691, tc_HOL_Obool)), _1359693), _1359695)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359689), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1359691, _1359689), _1359697), _1359693)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1359691, _1359689), _1359697), _1359695)))], (31656 ^ _779300) ^ [_1360184, _1360186, _1360188, _1360190, _1360192] : [class_Groups_Oordered__ab__semigroup__add(_1360184), class_Rings_Osemiring__1(_1360184), 31666 ^ _779300 : [(31667 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1360186), 31665 ^ [_1360184, _1360186, _1360188, _1360190, _1360192]), _1360188)))], (31669 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360184), hAPP(_1360190, 31665 ^ [_1360184, _1360186, _1360188, _1360190, _1360192])), _1360192))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360184), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360186, _1360184), _1360190), _1360188)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360184), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1360184), hAPP(c_Finite__Set_Ocard(_1360186), _1360188))), _1360192))))], (31673 ^ _779300) ^ [_1360574, _1360576, _1360578, _1360580, _1360582, _1360584] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360574, tc_fun(_1360576, tc_HOL_Obool))), _1360578), _1360580), _1360582), _1360584)), 31676 ^ _779300 : [(31677 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1360578, _1360582), _1360584)))], (31679 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1360580, _1360582), _1360584)))]]], (31681 ^ _779300) ^ [_1360747, _1360749, _1360751, _1360753, _1360755, _1360757] : [hBOOL(hAPP(hAPP(_1360747, _1360749), _1360751)), hBOOL(hAPP(hAPP(_1360753, _1360749), _1360751)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360755, tc_fun(_1360757, tc_HOL_Obool))), _1360747), _1360753), _1360749), _1360751)))], (31691 ^ _779300) ^ [_1360950, _1360952, _1360954, _1360956, _1360958, _1360960] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360950, tc_fun(_1360952, tc_HOL_Obool))), _1360954), _1360956), _1360958), _1360960)), -(hBOOL(hAPP(hAPP(_1360956, _1360958), _1360960)))], (31697 ^ _779300) ^ [_1361083, _1361085, _1361087, _1361089, _1361091, _1361093] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361083, tc_fun(_1361085, tc_HOL_Obool))), _1361087), _1361089), _1361091), _1361093)), -(hBOOL(hAPP(hAPP(_1361087, _1361091), _1361093)))], (31703 ^ _779300) ^ [_1361216, _1361218, _1361220] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1361216), _1361218)), 31706 ^ _779300 : [(31717 ^ _779300) ^ [] : [31719 ^ _779300 : [(31720 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1361216), 31718 ^ [_1361216, _1361218, _1361220]), _1361218)))], (31722 ^ _779300) ^ [] : [hAPP(_1361220, 31718 ^ [_1361216, _1361218, _1361220]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361216, tc_Nat_Onat), _1361220), _1361218) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31707 ^ _779300) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361216, tc_Nat_Onat), _1361220), _1361218) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 31710 ^ _779300 : [(31711 ^ _779300) ^ [_1361378] : [hBOOL(hAPP(hAPP(c_member(_1361216), _1361378), _1361218)), -(hAPP(_1361220, _1361378) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (31726 ^ _779300) ^ [_1361636, _1361638] : [-(hAPP(c_Finite__Set_Ocard(_1361636), _1361638) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361636, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1361636), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1361638))], (31728 ^ _779300) ^ [_1361681, _1361683, _1361685] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361681, tc_Nat_Onat), _1361683), _1361685)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361681, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1361681), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1361683)), _1361685))], (31730 ^ _779300) ^ [_1361739, _1361741, _1361743] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1361739), _1361741)), 31733 ^ _779300 : [(31734 ^ _779300) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361739, tc_Nat_Onat), _1361743), _1361741) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31738 ^ _779300 : [(31739 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1361739), 31737 ^ [_1361739, _1361741, _1361743]), _1361741)))], (31741 ^ _779300) ^ [] : [-(hAPP(_1361743, 31737 ^ [_1361739, _1361741, _1361743]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31743 ^ _779300) ^ [_1362059] : [hBOOL(hAPP(hAPP(c_member(_1361739), _1362059), _1361741)), -(31737 ^ [_1361739, _1361741, _1361743] = _1362059), -(hAPP(_1361743, _1362059) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31753 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361739, tc_Nat_Onat), _1361743), _1361741) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 31754 ^ _779300 : [(31755 ^ _779300) ^ [_1362220] : [hBOOL(hAPP(hAPP(c_member(_1361739), _1362220), _1361741)), hAPP(_1361743, _1362220) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31763 ^ _779300 : [(31764 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1361739), 31762 ^ [_1361739, _1361741, _1361743, _1362220]), _1361741)))], (31766 ^ _779300) ^ [] : [_1362220 = 31762 ^ [_1361739, _1361741, _1361743, _1362220]], (31768 ^ _779300) ^ [] : [hAPP(_1361743, 31762 ^ [_1361739, _1361741, _1361743, _1362220]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (31772 ^ _779300) ^ [_1362573, _1362575, _1362577] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362573), _1362575)), 31775 ^ _779300 : [(31776 ^ _779300) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362573, tc_Nat_Onat), _1362577), _1362575) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 31780 ^ _779300 : [(31781 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1362573), 31779 ^ [_1362573, _1362575, _1362577]), _1362575)))], (31783 ^ _779300) ^ [] : [-(hAPP(_1362577, 31779 ^ [_1362573, _1362575, _1362577]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31785 ^ _779300) ^ [_1362893] : [hBOOL(hAPP(hAPP(c_member(_1362573), _1362893), _1362575)), -(31779 ^ [_1362573, _1362575, _1362577] = _1362893), -(hAPP(_1362577, _1362893) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31795 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362573, tc_Nat_Onat), _1362577), _1362575) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 31796 ^ _779300 : [(31797 ^ _779300) ^ [_1363054] : [hBOOL(hAPP(hAPP(c_member(_1362573), _1363054), _1362575)), hAPP(_1362577, _1363054) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 31805 ^ _779300 : [(31806 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1362573), 31804 ^ [_1362573, _1362575, _1362577, _1363054]), _1362575)))], (31808 ^ _779300) ^ [] : [_1363054 = 31804 ^ [_1362573, _1362575, _1362577, _1363054]], (31810 ^ _779300) ^ [] : [hAPP(_1362577, 31804 ^ [_1362573, _1362575, _1362577, _1363054]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (31814 ^ _779300) ^ [_1363407, _1363409] : [hAPP(_1363407, 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), _1363407), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1363409)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1363407), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1363409)))], (31820 ^ _779300) ^ [_1363530, _1363532, _1363534] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363530, tc_Nat_Onat), _1363532), _1363534) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363530, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1363530), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1363532)), _1363534)))], (31822 ^ _779300) ^ [_1363588, _1363590, _1363592, _1363594] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1363588), _1363590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1363588, tc_HOL_Obool)), _1363590), _1363592)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363588, tc_Nat_Onat), _1363594), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363588, tc_HOL_Obool)), _1363592), _1363590)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363588, tc_Nat_Onat), _1363594), _1363592)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363588, tc_Nat_Onat), _1363594), _1363590)))], (31832 ^ _779300) ^ [_1363841, _1363843, _1363845] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363841), _1363843), _1363845) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1363841), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1363841, tc_Int_Oint), _1363843), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1363845))), class_Groups_Ocomm__monoid__add(_1363841), class_Groups_Ocomm__monoid__mult(_1363841)], (31842 ^ _779300) ^ [_1364047, _1364049, _1364051, _1364053] : [hBOOL(hAPP(hAPP(c_member(_1364047), _1364049), _1364051)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364047, tc_Nat_Onat), _1364053), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364047, tc_HOL_Obool)), _1364051), hAPP(hAPP(c_Set_Oinsert(_1364047), _1364049), c_Orderings_Obot__class_Obot(tc_fun(_1364047, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364047, tc_Nat_Onat), _1364053), _1364051)), hAPP(_1364053, _1364049)))], (31848 ^ _779300) ^ [_1364238, _1364240, _1364242, _1364244] : [-(hBOOL(hAPP(hAPP(c_member(_1364238), _1364240), _1364242))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364238, tc_Nat_Onat), _1364244), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364238, tc_HOL_Obool)), _1364242), hAPP(hAPP(c_Set_Oinsert(_1364238), _1364240), c_Orderings_Obot__class_Obot(tc_fun(_1364238, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364238, tc_Nat_Onat), _1364244), _1364242))], (31854 ^ _779300) ^ [_1364329, _1364331, _1364333, _1364335] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1364329), _1364331)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364329), _1364333)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364329, tc_Nat_Onat), _1364335), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364329, tc_HOL_Obool)), _1364331), _1364333)) = 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(_1364329, tc_Nat_Onat), _1364335), _1364331)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364329, tc_Nat_Onat), _1364335), _1364333))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364329, tc_Nat_Onat), _1364335), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364329, tc_HOL_Obool)), _1364331), _1364333))))], (31864 ^ _779300) ^ [_1364622, _1364624, _1364626] : [class_Groups_Ocomm__monoid__add(_1364622), class_Groups_Ocomm__monoid__mult(_1364622), c_Nat__Transfer_Onat__set(_1364624), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1364622), _1364626), _1364624) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1364622), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1364622, tc_Nat_Onat), _1364626), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1364624)))], (31878 ^ _779300) ^ [_1364867, _1364869, _1364871] : [-(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), _1364867)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1364869))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1364871))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1364871), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1364867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1364867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1364871), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1364869)))))], (31880 ^ _779300) ^ [_1364948, _1364950, _1364952] : [31882 ^ _779300 : [(31883 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364948), 31881 ^ [_1364948, _1364950, _1364952]), _1364950)))], (31885 ^ _779300) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1364952, 31881 ^ [_1364948, _1364950, _1364952]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364948, tc_Int_Oint), _1364952), _1364950) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364948, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1364948), c_Int_Onat), _1364952)), _1364950)))], (31889 ^ _779300) ^ [_1365178, _1365180, _1365182, _1365184, _1365186] : [class_Groups_Ocomm__monoid__add(_1365178), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365180), _1365182)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365180), _1365184)), 31903 ^ _779300 : [(31904 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1365180), 31902 ^ [_1365178, _1365180, _1365182, _1365184, _1365186]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365180, tc_HOL_Obool)), _1365182), _1365184))))], (31906 ^ _779300) ^ [] : [hAPP(_1365186, 31902 ^ [_1365178, _1365180, _1365182, _1365184, _1365186]) = c_Groups_Ozero__class_Ozero(_1365178)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365180, _1365178), _1365186), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1365180, tc_HOL_Obool)), _1365182), _1365184)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1365178), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365180, _1365178), _1365186), _1365182)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365180, _1365178), _1365186), _1365184)))], (31910 ^ _779300) ^ [_1365673, _1365675, _1365677, _1365679, _1365681] : [class_Groups_Ocomm__monoid__add(_1365673), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365675), _1365677)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365675), _1365679)), 31924 ^ _779300 : [(31925 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1365675), 31923 ^ [_1365673, _1365675, _1365677, _1365679, _1365681]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365675, tc_HOL_Obool)), _1365677), _1365679))))], (31927 ^ _779300) ^ [] : [hAPP(_1365681, 31923 ^ [_1365673, _1365675, _1365677, _1365679, _1365681]) = c_Groups_Ozero__class_Ozero(_1365673)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365675, _1365673), _1365681), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1365675, tc_HOL_Obool)), _1365677), _1365679)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1365673), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365675, _1365673), _1365681), _1365677)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365675, _1365673), _1365681), _1365679)))], (31931 ^ _779300) ^ [_1366168, _1366170, _1366172, _1366174, _1366176] : [class_Groups_Ocomm__monoid__add(_1366168), class_Groups_Oordered__ab__semigroup__add(_1366168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366170), _1366172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1366170, tc_HOL_Obool)), _1366174), _1366172)), 31949 ^ _779300 : [(31950 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366170), 31948 ^ [_1366168, _1366170, _1366172, _1366174, _1366176]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366170, tc_HOL_Obool)), _1366172), _1366174))))], (31952 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366168), c_Groups_Ozero__class_Ozero(_1366168)), hAPP(_1366176, 31948 ^ [_1366168, _1366170, _1366172, _1366174, _1366176])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366168), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1366170, _1366168), _1366176), _1366174)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1366170, _1366168), _1366176), _1366172))))], (31956 ^ _779300) ^ [_1366712, _1366714, _1366716] : [class_Lattices_Olattice(_1366712), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366712), _1366714)), hBOOL(hAPP(hAPP(c_member(_1366712), _1366716), _1366714)), 31967 ^ _779300 : [(31968 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366712, tc_HOL_Obool)), _1366714), hAPP(hAPP(c_Set_Oinsert(_1366712), _1366716), c_Orderings_Obot__class_Obot(tc_fun(_1366712, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1366712, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1366712, _1366714) = _1366716)], (31974 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366712, tc_HOL_Obool)), _1366714), hAPP(hAPP(c_Set_Oinsert(_1366712), _1366716), c_Orderings_Obot__class_Obot(tc_fun(_1366712, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1366712, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1366712, _1366714) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1366712), _1366716), c_Big__Operators_Olattice__class_OInf__fin(_1366712, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366712, tc_HOL_Obool)), _1366714), hAPP(hAPP(c_Set_Oinsert(_1366712), _1366716), c_Orderings_Obot__class_Obot(tc_fun(_1366712, tc_HOL_Obool)))))))]]], (31980 ^ _779300) ^ [_1367218, _1367220, _1367222, _1367224, _1367226] : [class_Groups_Oordered__ab__group__add(_1367218), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367220), _1367222)), 31990 ^ _779300 : [(31991 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1367220), 31989 ^ [_1367218, _1367220, _1367222, _1367224, _1367226]), _1367222)))], (31993 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367218), c_Groups_Ozero__class_Ozero(_1367218)), hAPP(_1367224, 31989 ^ [_1367218, _1367220, _1367222, _1367224, _1367226])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1367220, _1367218), _1367224), _1367222) = c_Groups_Ozero__class_Ozero(_1367218), hBOOL(hAPP(hAPP(c_member(_1367220), _1367226), _1367222)), -(hAPP(_1367224, _1367226) = c_Groups_Ozero__class_Ozero(_1367218))], (32005 ^ _779300) ^ [_1367716, _1367718, _1367720, _1367722, _1367724, _1367726] : [class_Groups_Oordered__ab__group__add(_1367716), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367718), _1367720)), 32015 ^ _779300 : [(32016 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1367718), 32014 ^ [_1367716, _1367718, _1367720, _1367722, _1367724, _1367726]), _1367720)))], (32018 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367716), c_Groups_Ozero__class_Ozero(_1367716)), hAPP(_1367722, 32014 ^ [_1367716, _1367718, _1367720, _1367722, _1367724, _1367726])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1367718, _1367716), _1367722), _1367720) = _1367724, hBOOL(hAPP(hAPP(c_member(_1367718), _1367726), _1367720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367716), hAPP(_1367722, _1367726)), _1367724)))], (32030 ^ _779300) ^ [_1368236, _1368238, _1368240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1368236, 32031 ^ [_1368236, _1368238, _1368240])), hAPP(_1368238, 32031 ^ [_1368236, _1368238, _1368240]))), -(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), _1368238), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1368240))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1368236), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1368240))) = 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)), _1368238)), _1368236)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1368240)))], (32037 ^ _779300) ^ [_1368469, _1368471] : [class_Lattices_Olattice(_1368469), -(c_Big__Operators_Olattice__class_OInf__fin(_1368469, hAPP(hAPP(c_Set_Oinsert(_1368469), _1368471), c_Orderings_Obot__class_Obot(tc_fun(_1368469, tc_HOL_Obool)))) = _1368471)], (32043 ^ _779300) ^ [_1368576, _1368578, _1368580] : [class_Lattices_Olattice(_1368576), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368576), _1368578)), hBOOL(hAPP(hAPP(c_member(_1368576), _1368580), _1368578)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1368576), _1368580), c_Big__Operators_Olattice__class_OInf__fin(_1368576, _1368578)) = _1368580)], (32057 ^ _779300) ^ [_1368805, _1368807, _1368809] : [class_Lattices_Olattice(_1368805), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368805), _1368807)), hBOOL(hAPP(hAPP(c_member(_1368805), _1368809), _1368807)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1368805), _1368809), c_Big__Operators_Olattice__class_OInf__fin(_1368805, _1368807)) = c_Big__Operators_Olattice__class_OInf__fin(_1368805, _1368807))], (32071 ^ _779300) ^ [_1369040, _1369042] : [class_Lattices_Olattice(_1369040), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369040), _1369042)), -(c_Big__Operators_Olattice__class_OInf__fin(_1369040, _1369042) = hAPP(c_Finite__Set_Ofold1(_1369040, c_Lattices_Osemilattice__inf__class_Oinf(_1369040)), _1369042))], (32081 ^ _779300) ^ [_1369197, _1369199, _1369201] : [class_Lattices_Olattice(_1369197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369197), _1369199)), -(_1369199 = c_Orderings_Obot__class_Obot(tc_fun(_1369197, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1369197, hAPP(hAPP(c_Set_Oinsert(_1369197), _1369201), _1369199)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1369197), _1369201), c_Big__Operators_Olattice__class_OInf__fin(_1369197, _1369199)))], (32095 ^ _779300) ^ [_1369405, _1369407, _1369409] : [class_Lattices_Olattice(_1369405), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369405), _1369407)), -(_1369409 = c_Orderings_Obot__class_Obot(tc_fun(_1369405, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1369405, tc_HOL_Obool)), _1369409), _1369407)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1369405), c_Big__Operators_Olattice__class_OInf__fin(_1369405, _1369409)), c_Big__Operators_Olattice__class_OInf__fin(_1369405, _1369407)) = c_Big__Operators_Olattice__class_OInf__fin(_1369405, _1369407))], (32113 ^ _779300) ^ [_1369719, _1369721, _1369723] : [class_Lattices_Olattice(_1369719), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369719), _1369721)), -(_1369721 = c_Orderings_Obot__class_Obot(tc_fun(_1369719, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369719), _1369723)), -(_1369723 = c_Orderings_Obot__class_Obot(tc_fun(_1369719, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1369719, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1369719, tc_HOL_Obool)), _1369721), _1369723)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1369719), c_Big__Operators_Olattice__class_OInf__fin(_1369719, _1369721)), c_Big__Operators_Olattice__class_OInf__fin(_1369719, _1369723)))], (32135 ^ _779300) ^ [_1370068, _1370070] : [class_Lattices_Olattice(_1370068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370068), _1370070)), -(_1370070 = c_Orderings_Obot__class_Obot(tc_fun(_1370068, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370068), c_Big__Operators_Olattice__class_OInf__fin(_1370068, _1370070)), c_Big__Operators_Olattice__class_OSup__fin(_1370068, _1370070))))], (32149 ^ _779300) ^ [_1370254, _1370256, _1370258] : [class_Lattices_Olattice(_1370254), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370254), _1370256)), -(hBOOL(hAPP(hAPP(c_member(_1370254), _1370258), _1370256))), -(_1370256 = c_Orderings_Obot__class_Obot(tc_fun(_1370254, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1370254, hAPP(hAPP(c_Set_Oinsert(_1370254), _1370258), _1370256)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1370254), _1370258), c_Big__Operators_Olattice__class_OInf__fin(_1370254, _1370256)))], (32167 ^ _779300) ^ [_1370491, _1370493, _1370495] : [class_Lattices_Olattice(_1370491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370491), _1370493)), 32174 ^ _779300 : [(32175 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370491, tc_HOL_Obool)), _1370493), hAPP(hAPP(c_Set_Oinsert(_1370491), _1370495), c_Orderings_Obot__class_Obot(tc_fun(_1370491, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1370491, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1370491, hAPP(hAPP(c_Set_Oinsert(_1370491), _1370495), _1370493)) = _1370495)], (32181 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370491, tc_HOL_Obool)), _1370493), hAPP(hAPP(c_Set_Oinsert(_1370491), _1370495), c_Orderings_Obot__class_Obot(tc_fun(_1370491, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1370491, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1370491, hAPP(hAPP(c_Set_Oinsert(_1370491), _1370495), _1370493)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1370491), _1370495), c_Big__Operators_Olattice__class_OInf__fin(_1370491, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370491, tc_HOL_Obool)), _1370493), hAPP(hAPP(c_Set_Oinsert(_1370491), _1370495), c_Orderings_Obot__class_Obot(tc_fun(_1370491, tc_HOL_Obool)))))))]]], (32187 ^ _779300) ^ [_1370961, _1370963, _1370965] : [class_Lattices_Olattice(_1370961), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370961), _1370963)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370961), _1370965)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370961, tc_HOL_Obool)), _1370963), _1370965) = c_Orderings_Obot__class_Obot(tc_fun(_1370961, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1370961), c_Big__Operators_Olattice__class_OInf__fin(_1370961, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1370961, tc_HOL_Obool)), _1370963), _1370965))), c_Big__Operators_Olattice__class_OInf__fin(_1370961, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370961, tc_HOL_Obool)), _1370963), _1370965))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1370961), c_Big__Operators_Olattice__class_OInf__fin(_1370961, _1370963)), c_Big__Operators_Olattice__class_OInf__fin(_1370961, _1370965)))], (32205 ^ _779300) ^ [_1371309, _1371311, _1371313] : [class_Lattices_Olattice(_1371309), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371309), _1371311)), -(_1371311 = c_Orderings_Obot__class_Obot(tc_fun(_1371309, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371309), _1371313)), -(_1371313 = c_Orderings_Obot__class_Obot(tc_fun(_1371309, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371309, tc_HOL_Obool)), _1371311), _1371313) = c_Orderings_Obot__class_Obot(tc_fun(_1371309, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1371309, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1371309, tc_HOL_Obool)), _1371311), _1371313)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371309), c_Big__Operators_Olattice__class_OInf__fin(_1371309, _1371311)), c_Big__Operators_Olattice__class_OInf__fin(_1371309, _1371313)))], (32231 ^ _779300) ^ [_1371786, _1371788] : [class_Lattices_Olattice(_1371786), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371786), _1371788)), -(_1371788 = c_Orderings_Obot__class_Obot(tc_fun(_1371786, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1371786), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371786), 32244 ^ [_1371786, _1371788]), 32245 ^ [_1371786, _1371788])), hAPP(hAPP(c_Set_Oinsert(_1371786), 32244 ^ [_1371786, _1371788]), hAPP(hAPP(c_Set_Oinsert(_1371786), 32245 ^ [_1371786, _1371788]), c_Orderings_Obot__class_Obot(tc_fun(_1371786, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1371786), c_Big__Operators_Olattice__class_OInf__fin(_1371786, _1371788)), _1371788)))], (32251 ^ _779300) ^ [_1372230, _1372232, _1372234] : [class_Lattices_Olattice(_1372230), hAPP(_1372232, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1372230), 32256 ^ [_1372230, _1372232, _1372234]), 32257 ^ [_1372230, _1372232, _1372234])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1372230), hAPP(_1372232, 32256 ^ [_1372230, _1372232, _1372234])), hAPP(_1372232, 32257 ^ [_1372230, _1372232, _1372234])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372230), _1372234)), -(_1372234 = c_Orderings_Obot__class_Obot(tc_fun(_1372230, tc_HOL_Obool))), -(hAPP(_1372232, c_Big__Operators_Olattice__class_OInf__fin(_1372230, _1372234)) = c_Big__Operators_Olattice__class_OInf__fin(_1372230, hAPP(c_Set_Oimage(_1372230, _1372230, _1372232), _1372234)))], (32271 ^ _779300) ^ [_1372633, _1372635, _1372637, _1372639, _1372641] : [class_Groups_Ocomm__monoid__add(_1372633), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372635), _1372637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1372635, tc_HOL_Obool)), _1372639), _1372637)), 32285 ^ _779300 : [(32286 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372635), 32284 ^ [_1372633, _1372635, _1372637, _1372639, _1372641]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1372635, tc_HOL_Obool)), _1372637), _1372639))))], (32288 ^ _779300) ^ [] : [hAPP(_1372641, 32284 ^ [_1372633, _1372635, _1372637, _1372639, _1372641]) = c_Groups_Ozero__class_Ozero(_1372633)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372635, _1372633), _1372641), _1372639) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372635, _1372633), _1372641), _1372637))], (32292 ^ _779300) ^ [_1373084, _1373086, _1373088, _1373090, _1373092] : [class_Groups_Ocomm__monoid__add(_1373084), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373086), _1373088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373086, tc_HOL_Obool)), _1373090), _1373088)), 32306 ^ _779300 : [(32307 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373086), 32305 ^ [_1373084, _1373086, _1373088, _1373090, _1373092]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373086, tc_HOL_Obool)), _1373088), _1373090))))], (32309 ^ _779300) ^ [] : [hAPP(_1373092, 32305 ^ [_1373084, _1373086, _1373088, _1373090, _1373092]) = c_Groups_Ozero__class_Ozero(_1373084)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1373086, _1373084), _1373092), _1373088) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1373086, _1373084), _1373092), _1373090))], (32313 ^ _779300) ^ [_1373535, _1373537, _1373539, _1373541, _1373543] : [class_Groups_Ocomm__monoid__add(_1373535), class_Groups_Oordered__cancel__ab__semigroup__add(_1373535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373537), _1373539)), -(_1373539 = c_Orderings_Obot__class_Obot(tc_fun(_1373537, tc_HOL_Obool))), 32331 ^ _779300 : [(32332 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373537), 32330 ^ [_1373535, _1373537, _1373539, _1373541, _1373543]), _1373539)))], (32334 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373535), hAPP(_1373541, 32330 ^ [_1373535, _1373537, _1373539, _1373541, _1373543])), hAPP(_1373543, 32330 ^ [_1373535, _1373537, _1373539, _1373541, _1373543])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373535), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1373537, _1373535), _1373541), _1373539)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1373537, _1373535), _1373543), _1373539))))], (32338 ^ _779300) ^ [_1374066, _1374068] : [class_Orderings_Oorder(_1374066), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1374066, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1374066), _1374068)), hAPP(c_SetInterval_Oord__class_OatLeast(_1374066), _1374068)) = hAPP(hAPP(c_Set_Oinsert(_1374066), _1374068), c_Orderings_Obot__class_Obot(tc_fun(_1374066, tc_HOL_Obool))))], (32344 ^ _779300) ^ [_1374209, _1374211, _1374213] : [class_Fields_Olinordered__field__inverse__zero(_1374209), 32350 ^ _779300 : [(32351 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1374209), c_Groups_Ozero__class_Ozero(_1374209)), 32349 ^ [_1374209, _1374211, _1374213])))], (32353 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1374209), 32349 ^ [_1374209, _1374211, _1374213]), c_Groups_Oone__class_Oone(_1374209))))], (32355 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374209), 32349 ^ [_1374209, _1374211, _1374213]), _1374211)), _1374213))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374209), _1374211), _1374213)))], (32359 ^ _779300) ^ [_1374558, _1374560, _1374562, _1374564, _1374566] : [class_Groups_Ocomm__monoid__add(_1374558), class_Groups_Ocomm__monoid__mult(_1374558), _1374560 = _1374562, c_Nat__Transfer_Onat__set(_1374562), 32377 ^ _779300 : [(32378 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32376 ^ [_1374558, _1374560, _1374562, _1374564, _1374566])))], (32380 ^ _779300) ^ [] : [hAPP(_1374564, 32376 ^ [_1374558, _1374560, _1374562, _1374564, _1374566]) = hAPP(_1374566, 32376 ^ [_1374558, _1374560, _1374562, _1374564, _1374566])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1374558), _1374564), _1374560) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1374558), _1374566), _1374562))], (32384 ^ _779300) ^ [_1375021, _1375023, _1375025] : [class_Orderings_Olinorder(_1375021), 32387 ^ _779300 : [(32388 ^ _779300) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1375021), _1375023) = hAPP(c_SetInterval_Oord__class_OatLeast(_1375021), _1375025), -(_1375023 = _1375025)], (32394 ^ _779300) ^ [] : [_1375023 = _1375025, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1375021), _1375023) = hAPP(c_SetInterval_Oord__class_OatLeast(_1375021), _1375025))]]], (32400 ^ _779300) ^ [_1375262, _1375264, _1375266] : [class_Orderings_Oord(_1375262), 32403 ^ _779300 : [(32404 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1375262), _1375264), hAPP(c_SetInterval_Oord__class_OatLeast(_1375262), _1375266))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375262), _1375266), _1375264)))], (32410 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375262), _1375266), _1375264)), -(hBOOL(hAPP(hAPP(c_member(_1375262), _1375264), hAPP(c_SetInterval_Oord__class_OatLeast(_1375262), _1375266))))]]], (32416 ^ _779300) ^ [_1375530, _1375532, _1375534] : [class_Orderings_Oorder(_1375530), 32419 ^ _779300 : [(32420 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375530, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375530), _1375532)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375530), _1375534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375530), _1375534), _1375532)))], (32426 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375530), _1375534), _1375532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375530, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375530), _1375532)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375530), _1375534))))]]], (32432 ^ _779300) ^ [_1375822, _1375824] : [class_Orderings_Olinorder(_1375822), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1375822, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375822), _1375824)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1375822), _1375824))], (32438 ^ _779300) ^ [_1375933, _1375935] : [class_Orderings_Olinorder(_1375933), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1375933, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1375933), _1375935)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1375933), _1375935))], (32444 ^ _779300) ^ [_1376044, _1376046, _1376048] : [class_Orderings_Olinorder(_1376044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376044), _1376046), _1376048)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1376044, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1376044, _1376046), _1376048)), hAPP(c_SetInterval_Oord__class_OatLeast(_1376044), _1376048)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1376044), _1376046))], (32454 ^ _779300) ^ [_1376243, _1376245, _1376247] : [class_Orderings_Oorder(_1376243), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376243, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1376243, _1376245), _1376247)), hAPP(c_SetInterval_Oord__class_OatLeast(_1376243), _1376247)) = c_Orderings_Obot__class_Obot(tc_fun(_1376243, tc_HOL_Obool)))], (32460 ^ _779300) ^ [_1376374, _1376376, _1376378, _1376380] : [class_Orderings_Olinorder(_1376374), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376374, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1376374, _1376376, _1376378)), hAPP(c_SetInterval_Oord__class_OatLeast(_1376374), _1376380)) = c_SetInterval_Oord__class_OatLeastAtMost(_1376374, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376374), _1376376), _1376380), _1376378))], (32466 ^ _779300) ^ [_1376517, _1376519, _1376521, _1376523] : [class_Orderings_Olinorder(_1376517), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376517, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1376517), _1376519)), c_SetInterval_Oord__class_OatLeastAtMost(_1376517, _1376521, _1376523)) = c_SetInterval_Oord__class_OatLeastAtMost(_1376517, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376517), _1376519), _1376521), _1376523))], (32472 ^ _779300) ^ [_1376660, _1376662, _1376664] : [class_Orderings_Oorder(_1376660), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376660, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1376660, _1376662, _1376664)), hAPP(c_SetInterval_Oord__class_OatLeast(_1376660), _1376664)) = c_Orderings_Obot__class_Obot(tc_fun(_1376660, tc_HOL_Obool)))], (32478 ^ _779300) ^ [_1376787, _1376789] : [class_Groups_Oordered__ab__group__add(_1376787), -(hAPP(c_Set_Oimage(_1376787, _1376787, c_Groups_Ouminus__class_Ouminus(_1376787)), hAPP(c_SetInterval_Oord__class_OatLeast(_1376787), _1376789)) = hAPP(c_SetInterval_Oord__class_OatMost(_1376787), hAPP(c_Groups_Ouminus__class_Ouminus(_1376787), _1376789)))], (32484 ^ _779300) ^ [_1376910, _1376912] : [class_Groups_Oordered__ab__group__add(_1376910), -(hAPP(c_Set_Oimage(_1376910, _1376910, c_Groups_Ouminus__class_Ouminus(_1376910)), hAPP(c_SetInterval_Oord__class_OatMost(_1376910), _1376912)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1376910), hAPP(c_Groups_Ouminus__class_Ouminus(_1376910), _1376912)))], (32490 ^ _779300) ^ [_1377033] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1377033)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1377033)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1377033), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (32492 ^ _779300) ^ [_1377077, _1377079, _1377081] : [class_Orderings_Olinorder(_1377077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377077), _1377079), _1377081)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377077, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1377077, _1377079, _1377081)), hAPP(c_SetInterval_Oord__class_OatLeast(_1377077), _1377081)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1377077), _1377079))], (32502 ^ _779300) ^ [_1377272, _1377274, _1377276] : [class_Orderings_Olinorder(_1377272), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377272), _1377274), _1377276)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377272, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1377272, _1377274, _1377276)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1377272), _1377276)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1377272), _1377274))], (32512 ^ _779300) ^ [_1377467, _1377469] : [class_Orderings_Olinorder(_1377467), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377467, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1377467), _1377469), c_Orderings_Obot__class_Obot(tc_fun(_1377467, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1377467), _1377469)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1377467), _1377469))], (32518 ^ _779300) ^ [_1377610, _1377612] : [class_Groups_Osgn__if(_1377610), 32521 ^ _779300 : [(32522 ^ _779300) ^ [] : [_1377612 = c_Groups_Ozero__class_Ozero(_1377610), -(c_Groups_Osgn__class_Osgn(_1377610, _1377612) = c_Groups_Ozero__class_Ozero(_1377610))], (32528 ^ _779300) ^ [] : [-(_1377612 = c_Groups_Ozero__class_Ozero(_1377610)), 32531 ^ _779300 : [(32532 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377610), c_Groups_Ozero__class_Ozero(_1377610)), _1377612)), -(c_Groups_Osgn__class_Osgn(_1377610, _1377612) = c_Groups_Oone__class_Oone(_1377610))], (32538 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377610), c_Groups_Ozero__class_Ozero(_1377610)), _1377612))), -(c_Groups_Osgn__class_Osgn(_1377610, _1377612) = hAPP(c_Groups_Ouminus__class_Ouminus(_1377610), c_Groups_Oone__class_Oone(_1377610)))]]]]], (32544 ^ _779300) ^ [_1378007, _1378009, _1378011] : [class_Orderings_Olinorder(_1378007), 32547 ^ _779300 : [(32548 ^ _779300) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1378007), _1378009) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1378007), _1378011), -(_1378009 = _1378011)], (32554 ^ _779300) ^ [] : [_1378009 = _1378011, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1378007), _1378009) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1378007), _1378011))]]], (32560 ^ _779300) ^ [_1378248, _1378250] : [class_Rings_Olinordered__idom(_1378248), -(c_Groups_Osgn__class_Osgn(_1378248, c_Groups_Osgn__class_Osgn(_1378248, _1378250)) = c_Groups_Osgn__class_Osgn(_1378248, _1378250))], (32566 ^ _779300) ^ [_1378341] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1378341)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1378341))], (32568 ^ _779300) ^ [_1378373, _1378375] : [class_Rings_Olinordered__idom(_1378373), 32571 ^ _779300 : [(32572 ^ _779300) ^ [] : [c_Groups_Osgn__class_Osgn(_1378373, _1378375) = c_Groups_Ozero__class_Ozero(_1378373), -(_1378375 = c_Groups_Ozero__class_Ozero(_1378373))], (32578 ^ _779300) ^ [] : [_1378375 = c_Groups_Ozero__class_Ozero(_1378373), -(c_Groups_Osgn__class_Osgn(_1378373, _1378375) = c_Groups_Ozero__class_Ozero(_1378373))]]], (32584 ^ _779300) ^ [_1378599] : [class_Groups_Osgn__if(_1378599), -(c_Groups_Osgn__class_Osgn(_1378599, c_Groups_Ozero__class_Ozero(_1378599)) = c_Groups_Ozero__class_Ozero(_1378599))], (32590 ^ _779300) ^ [_1378686, _1378688, _1378690] : [class_Rings_Olinordered__idom(_1378686), -(c_Groups_Osgn__class_Osgn(_1378686, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1378686), _1378688), _1378690)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1378686), c_Groups_Osgn__class_Osgn(_1378686, _1378688)), c_Groups_Osgn__class_Osgn(_1378686, _1378690)))], (32596 ^ _779300) ^ [_1378813, _1378815] : [class_Rings_Olinordered__idom(_1378813), 32599 ^ _779300 : [(32600 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378813), c_Groups_Osgn__class_Osgn(_1378813, _1378815)), c_Groups_Ozero__class_Ozero(_1378813))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378813), _1378815), c_Groups_Ozero__class_Ozero(_1378813))))], (32606 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378813), _1378815), c_Groups_Ozero__class_Ozero(_1378813))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378813), c_Groups_Osgn__class_Osgn(_1378813, _1378815)), c_Groups_Ozero__class_Ozero(_1378813))))]]], (32612 ^ _779300) ^ [_1379081, _1379083] : [class_Rings_Olinordered__idom(_1379081), 32615 ^ _779300 : [(32616 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379081), c_Groups_Ozero__class_Ozero(_1379081)), c_Groups_Osgn__class_Osgn(_1379081, _1379083))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379081), c_Groups_Ozero__class_Ozero(_1379081)), _1379083)))], (32622 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379081), c_Groups_Ozero__class_Ozero(_1379081)), _1379083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379081), c_Groups_Ozero__class_Ozero(_1379081)), c_Groups_Osgn__class_Osgn(_1379081, _1379083))))]]], (32628 ^ _779300) ^ [_1379349, _1379351, _1379353] : [class_Orderings_Oord(_1379349), 32631 ^ _779300 : [(32632 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1379349), _1379351), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379349), _1379353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379349), _1379353), _1379351)))], (32638 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379349), _1379353), _1379351)), -(hBOOL(hAPP(hAPP(c_member(_1379349), _1379351), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379349), _1379353))))]]], (32644 ^ _779300) ^ [_1379617, _1379619, _1379621] : [class_Orderings_Olinorder(_1379617), 32647 ^ _779300 : [(32648 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379617, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379617), _1379619)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379617), _1379621))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1379617), _1379621), _1379619)))], (32654 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1379617), _1379621), _1379619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379617, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379617), _1379619)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379617), _1379621))))]]], (32660 ^ _779300) ^ [_1379909, _1379911] : [class_Orderings_Olinorder(_1379909), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1379909, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379909), _1379911)) = hAPP(c_SetInterval_Oord__class_OatMost(_1379909), _1379911))], (32666 ^ _779300) ^ [_1380020, _1380022] : [class_Orderings_Olinorder(_1380020), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1380020, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1380020), _1380022)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1380020), _1380022))], (32672 ^ _779300) ^ [_1380131, _1380133] : [class_Rings_Olinordered__idom(_1380131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380131), c_Groups_Ozero__class_Ozero(_1380131)), _1380133)), -(c_Groups_Osgn__class_Osgn(_1380131, _1380133) = c_Groups_Oone__class_Oone(_1380131))], (32682 ^ _779300) ^ [_1380286, _1380288] : [class_Rings_Olinordered__idom(_1380286), 32685 ^ _779300 : [(32686 ^ _779300) ^ [] : [c_Groups_Osgn__class_Osgn(_1380286, _1380288) = c_Groups_Oone__class_Oone(_1380286), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380286), c_Groups_Ozero__class_Ozero(_1380286)), _1380288)))], (32692 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380286), c_Groups_Ozero__class_Ozero(_1380286)), _1380288)), -(c_Groups_Osgn__class_Osgn(_1380286, _1380288) = c_Groups_Oone__class_Oone(_1380286))]]], (32698 ^ _779300) ^ [_1380533, _1380535, _1380537] : [class_Orderings_Oorder(_1380533), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380533, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1380533, _1380535, _1380537)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1380533), _1380537)) = c_Orderings_Obot__class_Obot(tc_fun(_1380533, tc_HOL_Obool)))], (32704 ^ _779300) ^ [_1380660, _1380662, _1380664] : [class_Orderings_Olinorder(_1380660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1380660), _1380662), _1380664)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1380660, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1380660, _1380662, _1380664)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1380660), _1380664)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1380660), _1380662))], (32714 ^ _779300) ^ [_1380855, _1380857] : [class_Groups_Oordered__ab__group__add(_1380855), -(hAPP(c_Set_Oimage(_1380855, _1380855, c_Groups_Ouminus__class_Ouminus(_1380855)), hAPP(c_SetInterval_Oord__class_OlessThan(_1380855), _1380857)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1380855), hAPP(c_Groups_Ouminus__class_Ouminus(_1380855), _1380857)))], (32720 ^ _779300) ^ [_1380978, _1380980] : [class_Groups_Oordered__ab__group__add(_1380978), -(hAPP(c_Set_Oimage(_1380978, _1380978, c_Groups_Ouminus__class_Ouminus(_1380978)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1380978), _1380980)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1380978), hAPP(c_Groups_Ouminus__class_Ouminus(_1380978), _1380980)))], (32726 ^ _779300) ^ [_1381101, _1381103, _1381105] : [class_Orderings_Oorder(_1381101), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1381101, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1381101, _1381103, _1381105)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1381101), _1381105)) = c_Orderings_Obot__class_Obot(tc_fun(_1381101, tc_HOL_Obool)))], (32732 ^ _779300) ^ [_1381228] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1381228)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1381228)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1381228)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (32734 ^ _779300) ^ [_1381281] : [_1381281 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1381281) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32740 ^ _779300) ^ [_1381357] : [-(_1381357 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32743 ^ _779300 : [(32744 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1381357)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1381357) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (32750 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1381357))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1381357) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (32756 ^ _779300) ^ [_1381549, _1381551] : [class_Rings_Olinordered__idom(_1381549), 32759 ^ _779300 : [(32760 ^ _779300) ^ [] : [c_Groups_Osgn__class_Osgn(_1381549, _1381551) = hAPP(c_Groups_Ouminus__class_Ouminus(_1381549), c_Groups_Oone__class_Oone(_1381549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381549), _1381551), c_Groups_Ozero__class_Ozero(_1381549))))], (32766 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381549), _1381551), c_Groups_Ozero__class_Ozero(_1381549))), -(c_Groups_Osgn__class_Osgn(_1381549, _1381551) = hAPP(c_Groups_Ouminus__class_Ouminus(_1381549), c_Groups_Oone__class_Oone(_1381549)))]]], (32772 ^ _779300) ^ [_1381811, _1381813] : [class_Rings_Olinordered__idom(_1381811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381811), _1381813), c_Groups_Ozero__class_Ozero(_1381811))), -(c_Groups_Osgn__class_Osgn(_1381811, _1381813) = hAPP(c_Groups_Ouminus__class_Ouminus(_1381811), c_Groups_Oone__class_Oone(_1381811)))], (32782 ^ _779300) ^ [_1381976, _1381978, _1381980, _1381982, _1381984, _1381986] : [c_Equiv__Relations_Oequiv(_1381976, _1381978, _1381980), hBOOL(hAPP(hAPP(c_member(_1381976), _1381982), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1381976, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1381976, _1381976, _1381980), hAPP(hAPP(c_Set_Oinsert(_1381976), _1381984), c_Orderings_Obot__class_Obot(tc_fun(_1381976, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1381976, _1381976, _1381980), hAPP(hAPP(c_Set_Oinsert(_1381976), _1381986), c_Orderings_Obot__class_Obot(tc_fun(_1381976, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1381976, _1381976)), hAPP(hAPP(c_Product__Type_OPair(_1381976, _1381976), _1381984), _1381986)), _1381980)))], (32792 ^ _779300) ^ [_1382277, _1382279, _1382281, _1382283, _1382285] : [c_Equiv__Relations_Oequiv(_1382277, _1382279, _1382281), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382277, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1382277, _1382277, _1382281), hAPP(hAPP(c_Set_Oinsert(_1382277), _1382283), c_Orderings_Obot__class_Obot(tc_fun(_1382277, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1382277, _1382277, _1382281), hAPP(hAPP(c_Set_Oinsert(_1382277), _1382285), c_Orderings_Obot__class_Obot(tc_fun(_1382277, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1382277), _1382283), _1382279)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1382277, _1382277)), hAPP(hAPP(c_Product__Type_OPair(_1382277, _1382277), _1382285), _1382283)), _1382281)))], (32806 ^ _779300) ^ [_1382630, _1382632, _1382634, _1382636] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1382630, _1382632, _1382634, c_Code__Numeral_OSuc__code__numeral(_1382636)) = hAPP(_1382634, _1382636))], (32808 ^ _779300) ^ [_1382669, _1382671, _1382673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1382669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1382671), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1382673), 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), _1382673), _1382671))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1382669)))))], (32814 ^ _779300) ^ [_1382816, _1382818, _1382820, _1382822] : [class_Groups_Oordered__ab__group__add__abs(_1382816), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382816), hAPP(c_Groups_Oabs__class_Oabs(_1382816), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382818, _1382816), _1382820), _1382822))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382818, _1382816), hAPP(hAPP(c_COMBB(_1382816, _1382816, _1382818), c_Groups_Oabs__class_Oabs(_1382816)), _1382820)), _1382822))))], (32820 ^ _779300) ^ [_1382979, _1382981, _1382983, _1382985] : [class_Groups_Oordered__ab__group__add__abs(_1382979), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382979), c_Groups_Ozero__class_Ozero(_1382979)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382981, _1382979), hAPP(hAPP(c_COMBB(_1382979, _1382979, _1382981), c_Groups_Oabs__class_Oabs(_1382979)), _1382983)), _1382985))))], (32826 ^ _779300) ^ [_1383118, _1383120, _1383122] : [class_Groups_Oordered__ab__group__add__abs(_1383118), -(hAPP(c_Groups_Oabs__class_Oabs(_1383118), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1383118), _1383120), _1383122)) = hAPP(c_Groups_Oabs__class_Oabs(_1383118), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1383118), _1383122), _1383120)))], (32832 ^ _779300) ^ [_1383247, _1383249, _1383251, _1383253] : [class_Groups_Oordered__ab__group__add__abs(_1383247), -(hAPP(c_Groups_Oabs__class_Oabs(_1383247), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1383249, _1383247), hAPP(hAPP(c_COMBB(_1383247, _1383247, _1383249), c_Groups_Oabs__class_Oabs(_1383247)), _1383251)), _1383253)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1383249, _1383247), hAPP(hAPP(c_COMBB(_1383247, _1383247, _1383249), c_Groups_Oabs__class_Oabs(_1383247)), _1383251)), _1383253))], (32838 ^ _779300) ^ [_1383420, _1383422, _1383424, _1383426] : [class_Fields_Olinordered__field(_1383420), -(hAPP(c_Groups_Oabs__class_Oabs(_1383420), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1383422, _1383420), _1383424), _1383426)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1383422, _1383420), hAPP(hAPP(c_COMBB(_1383420, _1383420, _1383422), c_Groups_Oabs__class_Oabs(_1383420)), _1383424)), _1383426))], (32844 ^ _779300) ^ [_1383569, _1383571, _1383573] : [class_Fields_Olinordered__field__inverse__zero(_1383569), -(hAPP(c_Groups_Oabs__class_Oabs(_1383569), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383569), _1383571), _1383573)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383569), hAPP(c_Groups_Oabs__class_Oabs(_1383569), _1383571)), hAPP(c_Groups_Oabs__class_Oabs(_1383569), _1383573)))], (32850 ^ _779300) ^ [_1383708] : [class_Rings_Olinordered__idom(_1383708), -(hAPP(c_Groups_Oabs__class_Oabs(_1383708), c_Groups_Oone__class_Oone(_1383708)) = c_Groups_Oone__class_Oone(_1383708))], (32856 ^ _779300) ^ [_1383799, _1383801] : [class_Groups_Oordered__ab__group__add__abs(_1383799), -(hAPP(c_Groups_Oabs__class_Oabs(_1383799), hAPP(c_Groups_Ouminus__class_Ouminus(_1383799), _1383801)) = hAPP(c_Groups_Oabs__class_Oabs(_1383799), _1383801))], (32862 ^ _779300) ^ [_1383904] : [class_Groups_Oordered__ab__group__add__abs(_1383904), -(hAPP(c_Groups_Oabs__class_Oabs(_1383904), c_Groups_Ozero__class_Ozero(_1383904)) = c_Groups_Ozero__class_Ozero(_1383904))], (32868 ^ _779300) ^ [_1383995, _1383997] : [class_Groups_Oordered__ab__group__add__abs(_1383995), 32871 ^ _779300 : [(32872 ^ _779300) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1383995), _1383997) = c_Groups_Ozero__class_Ozero(_1383995), -(_1383997 = c_Groups_Ozero__class_Ozero(_1383995))], (32878 ^ _779300) ^ [] : [_1383997 = c_Groups_Ozero__class_Ozero(_1383995), -(hAPP(c_Groups_Oabs__class_Oabs(_1383995), _1383997) = c_Groups_Ozero__class_Ozero(_1383995))]]], (32884 ^ _779300) ^ [_1384227, _1384229] : [class_Groups_Oordered__ab__group__add__abs(_1384227), -(hAPP(c_Groups_Oabs__class_Oabs(_1384227), hAPP(c_Groups_Oabs__class_Oabs(_1384227), _1384229)) = hAPP(c_Groups_Oabs__class_Oabs(_1384227), _1384229))], (32890 ^ _779300) ^ [_1384332, _1384334, _1384336] : [class_Rings_Olinordered__idom(_1384332), -(hAPP(c_Groups_Oabs__class_Oabs(_1384332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384332), _1384334), _1384336)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384332), hAPP(c_Groups_Oabs__class_Oabs(_1384332), _1384334)), hAPP(c_Groups_Oabs__class_Oabs(_1384332), _1384336)))], (32896 ^ _779300) ^ [_1384471, _1384473] : [class_Rings_Olinordered__idom(_1384471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384471), hAPP(c_Groups_Oabs__class_Oabs(_1384471), _1384473)), hAPP(c_Groups_Oabs__class_Oabs(_1384471), _1384473)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384471), _1384473), _1384473))], (32902 ^ _779300) ^ [_1384598, _1384600, _1384602] : [class_Groups_Oordered__ab__group__add__abs(_1384598), -(hAPP(c_Groups_Oabs__class_Oabs(_1384598), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384598), hAPP(c_Groups_Oabs__class_Oabs(_1384598), _1384600)), hAPP(c_Groups_Oabs__class_Oabs(_1384598), _1384602))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384598), hAPP(c_Groups_Oabs__class_Oabs(_1384598), _1384600)), hAPP(c_Groups_Oabs__class_Oabs(_1384598), _1384602)))], (32908 ^ _779300) ^ [_1384757, _1384759, _1384761] : [class_Rings_Olinordered__idom(_1384757), -(hAPP(c_Groups_Oabs__class_Oabs(_1384757), hAPP(hAPP(c_Power_Opower__class_Opower(_1384757), _1384759), _1384761)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1384757), hAPP(c_Groups_Oabs__class_Oabs(_1384757), _1384759)), _1384761))], (32914 ^ _779300) ^ [_1384886, _1384888] : [class_Rings_Olinordered__idom(_1384886), -(hAPP(c_Groups_Oabs__class_Oabs(_1384886), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1384886), _1384888)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1384886), _1384888))], (32920 ^ _779300) ^ [_1384991] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1384991)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1384991))], (32922 ^ _779300) ^ [_1385023, _1385025] : [class_Groups_Oordered__ab__group__add__abs(_1385023), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385023), _1385025), hAPP(c_Groups_Oabs__class_Oabs(_1385023), _1385025))))], (32928 ^ _779300) ^ [_1385122, _1385124, _1385126] : [class_Groups_Oordered__ab__group__add__abs(_1385122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385122), hAPP(c_Groups_Oabs__class_Oabs(_1385122), _1385124)), _1385126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385122), _1385124), _1385126)))], (32938 ^ _779300) ^ [_1385291, _1385293] : [class_Groups_Oordered__ab__group__add__abs(_1385291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385291), c_Groups_Ozero__class_Ozero(_1385291)), _1385293)), -(hAPP(c_Groups_Oabs__class_Oabs(_1385291), _1385293) = _1385293)], (32948 ^ _779300) ^ [_1385446, _1385448] : [class_Groups_Oordered__ab__group__add__abs(_1385446), 32951 ^ _779300 : [(32952 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385446), hAPP(c_Groups_Oabs__class_Oabs(_1385446), _1385448)), c_Groups_Ozero__class_Ozero(_1385446))), -(_1385448 = c_Groups_Ozero__class_Ozero(_1385446))], (32958 ^ _779300) ^ [] : [_1385448 = c_Groups_Ozero__class_Ozero(_1385446), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385446), hAPP(c_Groups_Oabs__class_Oabs(_1385446), _1385448)), c_Groups_Ozero__class_Ozero(_1385446))))]]], (32964 ^ _779300) ^ [_1385699, _1385701] : [class_Groups_Oordered__ab__group__add__abs(_1385699), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385699), c_Groups_Ozero__class_Ozero(_1385699)), hAPP(c_Groups_Oabs__class_Oabs(_1385699), _1385701))))], (32970 ^ _779300) ^ [_1385802, _1385804] : [class_Groups_Oordered__ab__group__add__abs(_1385802), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385802), hAPP(c_Groups_Oabs__class_Oabs(_1385802), _1385804)), c_Groups_Ozero__class_Ozero(_1385802)))], (32976 ^ _779300) ^ [_1385906, _1385908] : [class_Groups_Oordered__ab__group__add__abs(_1385906), 32979 ^ _779300 : [(32980 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385906), c_Groups_Ozero__class_Ozero(_1385906)), hAPP(c_Groups_Oabs__class_Oabs(_1385906), _1385908))), _1385908 = c_Groups_Ozero__class_Ozero(_1385906)], (32986 ^ _779300) ^ [] : [-(_1385908 = c_Groups_Ozero__class_Ozero(_1385906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385906), c_Groups_Ozero__class_Ozero(_1385906)), hAPP(c_Groups_Oabs__class_Oabs(_1385906), _1385908))))]]], (32992 ^ _779300) ^ [_1386121, _1386123] : [class_Groups_Oordered__ab__group__add__abs(_1386121), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386121), c_Groups_Ozero__class_Ozero(_1386121)), _1386123)), -(hAPP(c_Groups_Oabs__class_Oabs(_1386121), _1386123) = _1386123)], (33002 ^ _779300) ^ [_1386276, _1386278, _1386280] : [class_Groups_Oordered__ab__group__add__abs(_1386276), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386276), hAPP(c_Groups_Oabs__class_Oabs(_1386276), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386276), _1386278), _1386280))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386276), hAPP(c_Groups_Oabs__class_Oabs(_1386276), _1386278)), hAPP(c_Groups_Oabs__class_Oabs(_1386276), _1386280)))))], (33008 ^ _779300) ^ [_1386429, _1386431, _1386433, _1386435, _1386437] : [class_Rings_Olinordered__idom(_1386429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386429), hAPP(c_Groups_Oabs__class_Oabs(_1386429), _1386431)), _1386433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386429), hAPP(c_Groups_Oabs__class_Oabs(_1386429), _1386435)), _1386437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386429), hAPP(c_Groups_Oabs__class_Oabs(_1386429), _1386431)), hAPP(c_Groups_Oabs__class_Oabs(_1386429), _1386435))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386429), _1386433), _1386437))))], (33022 ^ _779300) ^ [_1386740, _1386742, _1386744] : [class_Groups_Oordered__ab__group__add__abs(_1386740), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386740), hAPP(c_Groups_Oabs__class_Oabs(_1386740), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1386740), hAPP(c_Groups_Oabs__class_Oabs(_1386740), _1386742)), hAPP(c_Groups_Oabs__class_Oabs(_1386740), _1386744)))), hAPP(c_Groups_Oabs__class_Oabs(_1386740), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1386740), _1386742), _1386744)))))], (33028 ^ _779300) ^ [_1386903, _1386905, _1386907] : [class_Groups_Oordered__ab__group__add__abs(_1386903), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386903), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1386903), hAPP(c_Groups_Oabs__class_Oabs(_1386903), _1386905)), hAPP(c_Groups_Oabs__class_Oabs(_1386903), _1386907))), hAPP(c_Groups_Oabs__class_Oabs(_1386903), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1386903), _1386905), _1386907)))))], (33034 ^ _779300) ^ [_1387056, _1387058, _1387060] : [class_Groups_Oordered__ab__group__add__abs(_1387056), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387056), hAPP(c_Groups_Oabs__class_Oabs(_1387056), _1387058)), hAPP(c_Groups_Oabs__class_Oabs(_1387056), _1387060))), hAPP(c_Groups_Oabs__class_Oabs(_1387056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387056), _1387060), _1387058)))))], (33040 ^ _779300) ^ [_1387209, _1387211, _1387213] : [class_Groups_Oordered__ab__group__add__abs(_1387209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387209), hAPP(c_Groups_Oabs__class_Oabs(_1387209), _1387211)), _1387213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387209), hAPP(c_Groups_Ouminus__class_Ouminus(_1387209), _1387211)), _1387213)))], (33050 ^ _779300) ^ [_1387388, _1387390, _1387392] : [class_Groups_Oordered__ab__group__add__abs(_1387388), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387388), _1387390), _1387392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387388), hAPP(c_Groups_Ouminus__class_Ouminus(_1387388), _1387390)), _1387392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387388), hAPP(c_Groups_Oabs__class_Oabs(_1387388), _1387390)), _1387392)))], (33064 ^ _779300) ^ [_1387635, _1387637, _1387639] : [class_Groups_Oordered__ab__group__add__abs(_1387635), 33067 ^ _779300 : [(33068 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387635), hAPP(c_Groups_Oabs__class_Oabs(_1387635), _1387637)), _1387639)), 33071 ^ _779300 : [(33072 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387635), _1387637), _1387639)))], (33074 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387635), hAPP(c_Groups_Ouminus__class_Ouminus(_1387635), _1387637)), _1387639)))]]], (33076 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387635), hAPP(c_Groups_Oabs__class_Oabs(_1387635), _1387637)), _1387639))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387635), _1387637), _1387639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387635), hAPP(c_Groups_Ouminus__class_Ouminus(_1387635), _1387637)), _1387639))]]], (33086 ^ _779300) ^ [_1388013, _1388015] : [class_Groups_Oordered__ab__group__add__abs(_1388013), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388013), hAPP(c_Groups_Ouminus__class_Ouminus(_1388013), _1388015)), hAPP(c_Groups_Oabs__class_Oabs(_1388013), _1388015))))], (33092 ^ _779300) ^ [_1388122, _1388124, _1388126] : [class_Rings_Olinordered__idom(_1388122), 33095 ^ _779300 : [(33096 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388122), hAPP(c_Groups_Oabs__class_Oabs(_1388122), _1388124)), _1388126)), 33099 ^ _779300 : [(33100 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388122), _1388124), _1388126)))], (33102 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388122), hAPP(c_Groups_Ouminus__class_Ouminus(_1388122), _1388124)), _1388126)))]]], (33104 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388122), hAPP(c_Groups_Oabs__class_Oabs(_1388122), _1388124)), _1388126))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388122), _1388124), _1388126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388122), hAPP(c_Groups_Ouminus__class_Ouminus(_1388122), _1388124)), _1388126))]]], (33114 ^ _779300) ^ [_1388500, _1388502, _1388504] : [class_Fields_Olinordered__field(_1388500), -(_1388502 = c_Groups_Ozero__class_Ozero(_1388500)), -(hAPP(c_Groups_Oabs__class_Oabs(_1388500), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388500), _1388504), _1388502)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388500), hAPP(c_Groups_Oabs__class_Oabs(_1388500), _1388504)), hAPP(c_Groups_Oabs__class_Oabs(_1388500), _1388502)))], (33124 ^ _779300) ^ [_1388658, _1388660, _1388662] : [class_Rings_Olinordered__idom(_1388658), -(hAPP(c_Groups_Oabs__class_Oabs(_1388658), hAPP(hAPP(c_Power_Opower__class_Opower(_1388658), hAPP(c_Groups_Ouminus__class_Ouminus(_1388658), _1388660)), _1388662)) = hAPP(c_Groups_Oabs__class_Oabs(_1388658), hAPP(hAPP(c_Power_Opower__class_Opower(_1388658), _1388660), _1388662)))], (33130 ^ _779300) ^ [_1388797, _1388799] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1388797), _1388799)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1388797) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (33136 ^ _779300) ^ [_1388898, _1388900] : [class_Rings_Olinordered__idom(_1388898), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388898), c_Groups_Osgn__class_Osgn(_1388898, _1388900)), hAPP(c_Groups_Oabs__class_Oabs(_1388898), _1388900)) = _1388900)], (33142 ^ _779300) ^ [_1389005, _1389007] : [class_Rings_Olinordered__idom(_1389005), -(hAPP(c_Groups_Oabs__class_Oabs(_1389005), _1389007) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389005), _1389007), c_Groups_Osgn__class_Osgn(_1389005, _1389007)))], (33148 ^ _779300) ^ [_1389112, _1389114, _1389116] : [class_Rings_Olinordered__idom(_1389112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389112), c_Groups_Ozero__class_Ozero(_1389112)), _1389114)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389112), hAPP(c_Groups_Oabs__class_Oabs(_1389112), _1389116)), _1389114) = hAPP(c_Groups_Oabs__class_Oabs(_1389112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389112), _1389116), _1389114)))], (33158 ^ _779300) ^ [_1389313, _1389315, _1389317] : [class_Rings_Oordered__ring__abs(_1389313), -(hAPP(c_Groups_Oabs__class_Oabs(_1389313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389313), _1389315), _1389317)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389313), hAPP(c_Groups_Oabs__class_Oabs(_1389313), _1389315)), hAPP(c_Groups_Oabs__class_Oabs(_1389313), _1389317))), 33165 ^ _779300 : [(33166 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389313), c_Groups_Ozero__class_Ozero(_1389313)), _1389315))], (33168 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389313), _1389315), c_Groups_Ozero__class_Ozero(_1389313)))]], 33169 ^ _779300 : [(33170 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389313), c_Groups_Ozero__class_Ozero(_1389313)), _1389317))], (33172 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389313), _1389317), c_Groups_Ozero__class_Ozero(_1389313)))]]], (33176 ^ _779300) ^ [_1389708, _1389710, _1389712] : [class_Groups_Oordered__ab__group__add__abs(_1389708), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389708), hAPP(c_Groups_Oabs__class_Oabs(_1389708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1389708), _1389710), _1389712))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389708), hAPP(c_Groups_Oabs__class_Oabs(_1389708), _1389710)), hAPP(c_Groups_Oabs__class_Oabs(_1389708), _1389712)))))], (33182 ^ _779300) ^ [_1389861, _1389863, _1389865, _1389867, _1389869] : [class_Groups_Oordered__ab__group__add__abs(_1389861), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389861), hAPP(c_Groups_Oabs__class_Oabs(_1389861), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1389861), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389861), _1389863), _1389865)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389861), _1389867), _1389869)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389861), hAPP(c_Groups_Oabs__class_Oabs(_1389861), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1389861), _1389863), _1389867))), hAPP(c_Groups_Oabs__class_Oabs(_1389861), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1389861), _1389865), _1389869))))))], (33188 ^ _779300) ^ [_1390082, _1390084] : [class_Groups_Oordered__ab__group__add__abs(_1390082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390082), _1390084), c_Groups_Ozero__class_Ozero(_1390082))), -(hAPP(c_Groups_Oabs__class_Oabs(_1390082), _1390084) = hAPP(c_Groups_Ouminus__class_Ouminus(_1390082), _1390084))], (33198 ^ _779300) ^ [_1390247, _1390249] : [class_Groups_Oordered__ab__group__add__abs(_1390247), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390247), hAPP(c_Groups_Ouminus__class_Ouminus(_1390247), hAPP(c_Groups_Oabs__class_Oabs(_1390247), _1390249))), c_Groups_Ozero__class_Ozero(_1390247))))], (33204 ^ _779300) ^ [_1390360, _1390362] : [class_Groups_Oordered__ab__group__add__abs(_1390360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390360), _1390362), c_Groups_Ozero__class_Ozero(_1390360))), -(hAPP(c_Groups_Oabs__class_Oabs(_1390360), _1390362) = hAPP(c_Groups_Ouminus__class_Ouminus(_1390360), _1390362))], (33214 ^ _779300) ^ [_1390525, _1390527] : [class_Groups_Oabs__if(_1390525), 33217 ^ _779300 : [(33218 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390525), _1390527), c_Groups_Ozero__class_Ozero(_1390525))), -(hAPP(c_Groups_Oabs__class_Oabs(_1390525), _1390527) = hAPP(c_Groups_Ouminus__class_Ouminus(_1390525), _1390527))], (33224 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390525), _1390527), c_Groups_Ozero__class_Ozero(_1390525)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1390525), _1390527) = _1390527)]]], (33230 ^ _779300) ^ [_1390765, _1390767, _1390769] : [class_Rings_Olinordered__idom(_1390765), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390765), c_Groups_Ozero__class_Ozero(_1390765)), hAPP(hAPP(c_Power_Opower__class_Opower(_1390765), hAPP(c_Groups_Oabs__class_Oabs(_1390765), _1390767)), _1390769))))], (33236 ^ _779300) ^ [_1390886, _1390888, _1390890] : [class_Fields_Olinordered__field__inverse__zero(_1390886), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390886), c_Groups_Ozero__class_Ozero(_1390886)), _1390888)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1390886), hAPP(c_Groups_Oabs__class_Oabs(_1390886), _1390890)), _1390888) = hAPP(c_Groups_Oabs__class_Oabs(_1390886), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1390886), _1390890), _1390888)))], (33246 ^ _779300) ^ [_1391087] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1391087), hAPP(c_Int_Onumber__class_Onumber__of(_1391087), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1391087)), class_Int_Onumber__ring(_1391087), class_Rings_Olinordered__idom(_1391087)], (33256 ^ _779300) ^ [_1391244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1391244)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1391244 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33262 ^ _779300) ^ [_1391331] : [_1391331 = 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), _1391331)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (33268 ^ _779300) ^ [_1391430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1391430), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1391430) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1391430))], (33274 ^ _779300) ^ [_1391521] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1391521), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1391521) = _1391521)], (33280 ^ _779300) ^ [_1391565, _1391567] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1391565), _1391567))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1391565))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1391567))))], (33282 ^ _779300) ^ [_1391620, _1391622] : [-(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), _1391620)), _1391622))))], (33284 ^ _779300) ^ [_1391656, _1391658, _1391660, _1391662] : [c_Equiv__Relations_Oequiv(_1391656, _1391658, _1391660), hBOOL(hAPP(hAPP(c_member(_1391656), _1391662), _1391658)), -(hBOOL(hAPP(hAPP(c_member(_1391656), _1391662), hAPP(c_Relation_OImage(_1391656, _1391656, _1391660), hAPP(hAPP(c_Set_Oinsert(_1391656), _1391662), c_Orderings_Obot__class_Obot(tc_fun(_1391656, tc_HOL_Obool)))))))], (33294 ^ _779300) ^ [_1391863, _1391865] : [class_Int_Onumber__ring(_1391863), class_Rings_Olinordered__idom(_1391863), 33301 ^ _779300 : [(33302 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391863), hAPP(c_Int_Onumber__class_Onumber__of(_1391863), _1391865)), c_Groups_Ozero__class_Ozero(_1391863))), -(hAPP(c_Groups_Oabs__class_Oabs(_1391863), hAPP(c_Int_Onumber__class_Onumber__of(_1391863), _1391865)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1391863), hAPP(c_Int_Onumber__class_Onumber__of(_1391863), _1391865)))], (33308 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391863), hAPP(c_Int_Onumber__class_Onumber__of(_1391863), _1391865)), c_Groups_Ozero__class_Ozero(_1391863)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1391863), hAPP(c_Int_Onumber__class_Onumber__of(_1391863), _1391865)) = hAPP(c_Int_Onumber__class_Onumber__of(_1391863), _1391865))]]], (33314 ^ _779300) ^ [_1392215, _1392217] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1392215), hAPP(hAPP(c_Power_Opower__class_Opower(_1392215), hAPP(c_Int_Onumber__class_Onumber__of(_1392215), c_Int_OMin)), _1392217)) = c_Groups_Oone__class_Oone(_1392215)), class_Int_Onumber__ring(_1392215), class_Rings_Olinordered__idom(_1392215)], (33334 ^ _779300) ^ [_1392544, _1392546] : [33335 ^ _779300 : [(33336 ^ _779300) ^ [] : [-(_1392544 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33338 ^ _779300) ^ [] : [_1392546 = 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), _1392544)), _1392546))))], (33324 ^ _779300) ^ [_1392395, _1392397] : [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), _1392395)), _1392397))), _1392395 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1392397 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33342 ^ _779300) ^ [_1392680, _1392682, _1392684, _1392686, _1392688] : [c_Equiv__Relations_Oequiv(_1392680, _1392682, _1392684), hBOOL(hAPP(hAPP(c_member(tc_prod(_1392680, _1392680)), hAPP(hAPP(c_Product__Type_OPair(_1392680, _1392680), _1392686), _1392688)), _1392684)), -(hAPP(c_Relation_OImage(_1392680, _1392680, _1392684), hAPP(hAPP(c_Set_Oinsert(_1392680), _1392686), c_Orderings_Obot__class_Obot(tc_fun(_1392680, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1392680, _1392680, _1392684), hAPP(hAPP(c_Set_Oinsert(_1392680), _1392688), c_Orderings_Obot__class_Obot(tc_fun(_1392680, tc_HOL_Obool)))))], (33352 ^ _779300) ^ [_1392941, _1392943] : [class_Rings_Olinordered__idom(_1392941), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1392941), hAPP(c_Groups_Oabs__class_Oabs(_1392941), _1392943)), 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(_1392941), _1392943), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (33358 ^ _779300) ^ [_1393058, _1393060] : [class_Rings_Olinordered__idom(_1393058), -(hAPP(c_Groups_Oabs__class_Oabs(_1393058), hAPP(hAPP(c_Power_Opower__class_Opower(_1393058), _1393060), 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(_1393058), _1393060), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (33364 ^ _779300) ^ [_1393175, _1393177, _1393179, _1393181, _1393183] : [c_Equiv__Relations_Oequiv(_1393175, _1393177, _1393179), 33367 ^ _779300 : [(33368 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1393175, _1393175)), hAPP(hAPP(c_Product__Type_OPair(_1393175, _1393175), _1393181), _1393183)), _1393179)), 33371 ^ _779300 : [(33372 ^ _779300) ^ [] : [-(hAPP(c_Relation_OImage(_1393175, _1393175, _1393179), hAPP(hAPP(c_Set_Oinsert(_1393175), _1393181), c_Orderings_Obot__class_Obot(tc_fun(_1393175, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1393175, _1393175, _1393179), hAPP(hAPP(c_Set_Oinsert(_1393175), _1393183), c_Orderings_Obot__class_Obot(tc_fun(_1393175, tc_HOL_Obool)))))], (33374 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1393175), _1393181), _1393177)))], (33376 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1393175), _1393183), _1393177)))]]], (33378 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1393175, _1393175)), hAPP(hAPP(c_Product__Type_OPair(_1393175, _1393175), _1393181), _1393183)), _1393179))), hAPP(c_Relation_OImage(_1393175, _1393175, _1393179), hAPP(hAPP(c_Set_Oinsert(_1393175), _1393181), c_Orderings_Obot__class_Obot(tc_fun(_1393175, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1393175, _1393175, _1393179), hAPP(hAPP(c_Set_Oinsert(_1393175), _1393183), c_Orderings_Obot__class_Obot(tc_fun(_1393175, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1393175), _1393181), _1393177)), hBOOL(hAPP(hAPP(c_member(_1393175), _1393183), _1393177))]]], (33392 ^ _779300) ^ [_1393775, _1393777, _1393779, _1393781, _1393783] : [hAPP(c_Relation_OImage(_1393775, _1393775, _1393777), hAPP(hAPP(c_Set_Oinsert(_1393775), _1393779), c_Orderings_Obot__class_Obot(tc_fun(_1393775, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1393775, _1393775, _1393777), hAPP(hAPP(c_Set_Oinsert(_1393775), _1393781), c_Orderings_Obot__class_Obot(tc_fun(_1393775, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1393775, _1393783, _1393777), hBOOL(hAPP(hAPP(c_member(_1393775), _1393781), _1393783)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1393775, _1393775)), hAPP(hAPP(c_Product__Type_OPair(_1393775, _1393775), _1393779), _1393781)), _1393777)))], (33406 ^ _779300) ^ [_1394108, _1394110, _1394112, _1394114, _1394116] : [c_Equiv__Relations_Oequiv(_1394108, _1394110, _1394112), hBOOL(hAPP(hAPP(c_member(_1394108), _1394114), _1394110)), hBOOL(hAPP(hAPP(c_member(_1394108), _1394116), _1394110)), 33417 ^ _779300 : [(33418 ^ _779300) ^ [] : [hAPP(c_Relation_OImage(_1394108, _1394108, _1394112), hAPP(hAPP(c_Set_Oinsert(_1394108), _1394114), c_Orderings_Obot__class_Obot(tc_fun(_1394108, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1394108, _1394108, _1394112), hAPP(hAPP(c_Set_Oinsert(_1394108), _1394116), c_Orderings_Obot__class_Obot(tc_fun(_1394108, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1394108, _1394108)), hAPP(hAPP(c_Product__Type_OPair(_1394108, _1394108), _1394114), _1394116)), _1394112)))], (33424 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1394108, _1394108)), hAPP(hAPP(c_Product__Type_OPair(_1394108, _1394108), _1394114), _1394116)), _1394112)), -(hAPP(c_Relation_OImage(_1394108, _1394108, _1394112), hAPP(hAPP(c_Set_Oinsert(_1394108), _1394114), c_Orderings_Obot__class_Obot(tc_fun(_1394108, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1394108, _1394108, _1394112), hAPP(hAPP(c_Set_Oinsert(_1394108), _1394116), c_Orderings_Obot__class_Obot(tc_fun(_1394108, tc_HOL_Obool)))))]]], (33430 ^ _779300) ^ [_1394656, _1394658, _1394660, _1394662, _1394664] : [c_Equiv__Relations_Oequiv(_1394656, _1394658, _1394660), hBOOL(hAPP(hAPP(c_member(tc_prod(_1394656, _1394656)), hAPP(hAPP(c_Product__Type_OPair(_1394656, _1394656), _1394662), _1394664)), _1394660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1394656, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1394656, _1394656, _1394660), hAPP(hAPP(c_Set_Oinsert(_1394656), _1394662), c_Orderings_Obot__class_Obot(tc_fun(_1394656, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1394656, _1394656, _1394660), hAPP(hAPP(c_Set_Oinsert(_1394656), _1394664), c_Orderings_Obot__class_Obot(tc_fun(_1394656, tc_HOL_Obool)))))))], (33440 ^ _779300) ^ [_1394937, _1394939, _1394941] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1394937, _1394939, _1394941, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1394939)], (33442 ^ _779300) ^ [_1394969, _1394971, _1394973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1394969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1394971), 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), _1394971), _1394973))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1394969))), _1394973)))], (33448 ^ _779300) ^ [_1395125, _1395127] : [_1395125 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1395125, _1395127) = 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)))], (33454 ^ _779300) ^ [_1395203, _1395205] : [-(_1395203 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 33457 ^ _779300 : [(33458 ^ _779300) ^ [] : [_1395205 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1395203, _1395205) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395203))], (33464 ^ _779300) ^ [] : [-(_1395205 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1395203, _1395205) = 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, _1395205))), 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)), _1395205)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395203))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395205), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395203), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1395203, _1395205)), 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), _1395205))))), c_Divides_Opdivmod(_1395203, _1395205)))))]]], (33470 ^ _779300) ^ [_1395563, _1395565] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1395563), _1395565) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nitpick_Onat__gcd(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1395563)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1395565)))))], (33472 ^ _779300) ^ [_1395621, _1395623] : [_1395621 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1395621, _1395623) = 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)))], (33478 ^ _779300) ^ [_1395699, _1395701] : [-(_1395699 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 33481 ^ _779300 : [(33482 ^ _779300) ^ [] : [_1395701 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1395699, _1395701) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395699))], (33488 ^ _779300) ^ [] : [-(_1395701 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1395699, _1395701) = 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, _1395701))), 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, _1395699)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1395701))), c_Divides_Opdivmod(_1395699, _1395701)), 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), _1395701))))), c_Divides_Opdivmod(_1395699, _1395701)))))]]], (33494 ^ _779300) ^ [_1396020, _1396022] : [_1396020 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1396022, _1396020) = 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), _1396022)))], (33500 ^ _779300) ^ [_1396109, _1396111] : [-(_1396109 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1396111, _1396109) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1396111), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1396109)))], (33506 ^ _779300) ^ [_1396159, _1396161, _1396163, _1396165, _1396167, _1396169] : [-(hAPP(c_Product__Type_Oapsnd(_1396159, _1396161, _1396163, _1396165), hAPP(hAPP(c_Product__Type_OPair(_1396163, _1396159), _1396167), _1396169)) = hAPP(hAPP(c_Product__Type_OPair(_1396163, _1396161), _1396167), hAPP(_1396165, _1396169)))], (33508 ^ _779300) ^ [_1396221, _1396223, _1396225, _1396227, _1396229] : [-(hAPP(c_Product__Type_Ofst(_1396221, _1396223), hAPP(c_Product__Type_Oapsnd(_1396225, _1396223, _1396221, _1396227), _1396229)) = hAPP(c_Product__Type_Ofst(_1396221, _1396225), _1396229))], (33510 ^ _779300) ^ [_1396272, _1396274, _1396276, _1396278, _1396280] : [-(hAPP(c_Product__Type_Osnd(_1396272, _1396274), hAPP(c_Product__Type_Oapsnd(_1396276, _1396274, _1396272, _1396278), _1396280)) = hAPP(_1396278, hAPP(c_Product__Type_Osnd(_1396272, _1396276), _1396280)))], (33512 ^ _779300) ^ [_1396353, _1396355, _1396357, _1396359, _1396361, _1396363] : [hAPP(c_Product__Type_Oapsnd(_1396353, _1396355, _1396357, _1396359), _1396361) = hAPP(c_Product__Type_Oapsnd(_1396353, _1396355, _1396357, _1396363), _1396361), -(hAPP(_1396359, hAPP(c_Product__Type_Osnd(_1396357, _1396353), _1396361)) = hAPP(_1396363, hAPP(c_Product__Type_Osnd(_1396357, _1396353), _1396361)))], (33518 ^ _779300) ^ [_1396502, _1396504, _1396506, _1396508, _1396510, _1396512] : [hAPP(_1396508, hAPP(c_Product__Type_Osnd(_1396506, _1396502), _1396510)) = hAPP(_1396512, hAPP(c_Product__Type_Osnd(_1396506, _1396502), _1396510)), -(hAPP(c_Product__Type_Oapsnd(_1396502, _1396504, _1396506, _1396508), _1396510) = hAPP(c_Product__Type_Oapsnd(_1396502, _1396504, _1396506, _1396512), _1396510))], (33524 ^ _779300) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (33526 ^ _779300) ^ [_1396684, _1396686] : [_1396684 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1396686, _1396684) = _1396686)], (33532 ^ _779300) ^ [_1396761, _1396763] : [-(_1396761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1396763, _1396761) = c_Nitpick_Onat__gcd(_1396761, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1396763, _1396761)))], (33538 ^ _779300) ^ [_1396809, _1396811] : [-(c_Divides_Opdivmod(_1396809, _1396811) = 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), _1396809)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1396811))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1396809), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1396811))))], (33540 ^ _779300) ^ [_1396865, _1396867] : [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), _1396865), _1396867))), 33543 ^ _779300 : [(33544 ^ _779300) ^ [] : [_1396867 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1396865, _1396867) = _1396865)], (33550 ^ _779300) ^ [] : [-(_1396867 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1396865, _1396867) = c_Nitpick_Onat__gcd(_1396867, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1396865, _1396867)))]]], (33556 ^ _779300) ^ [_1397083, _1397085] : [-(c_Nitpick_Onat__lcm(_1397083, _1397085) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1397083), _1397085)), c_Nitpick_Onat__gcd(_1397083, _1397085)))], (33558 ^ _779300) ^ [_1397126, _1397128, _1397130] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1397126), _1397128)), c_Fun_Oinj__on(_1397126, tc_fun(tc_fun(_1397126, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1397126, tc_fun(tc_prod(_1397126, _1397126), tc_HOL_Obool), tc_fun(tc_fun(_1397126, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1397126, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1397126, _1397126), tc_HOL_Obool), tc_fun(tc_fun(_1397126, tc_HOL_Obool), tc_HOL_Obool)), _1397126), c_Equiv__Relations_Oquotient(_1397126)), hAPP(hAPP(c_COMBC(_1397126, tc_fun(_1397126, tc_HOL_Obool), tc_fun(_1397126, tc_HOL_Obool)), c_Set_Oinsert(_1397126)), c_Orderings_Obot__class_Obot(tc_fun(_1397126, tc_HOL_Obool))))), _1397130), _1397128), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1397126, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397126), _1397128), _1397130)) = hAPP(c_Finite__Set_Ocard(_1397126), _1397128))], (33568 ^ _779300) ^ [_1397475, _1397477, _1397479, _1397481, _1397483] : [c_Equiv__Relations_Oequiv(_1397475, _1397477, _1397479), hBOOL(hAPP(hAPP(c_member(_1397475), _1397481), _1397477)), hBOOL(hAPP(hAPP(c_member(_1397475), _1397483), _1397477)), 33579 ^ _779300 : [(33580 ^ _779300) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397475), hAPP(hAPP(c_Set_Oinsert(_1397475), _1397481), c_Orderings_Obot__class_Obot(tc_fun(_1397475, tc_HOL_Obool)))), _1397479) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397475), hAPP(hAPP(c_Set_Oinsert(_1397475), _1397483), c_Orderings_Obot__class_Obot(tc_fun(_1397475, tc_HOL_Obool)))), _1397479), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1397475, _1397475)), hAPP(hAPP(c_Product__Type_OPair(_1397475, _1397475), _1397481), _1397483)), _1397479)))], (33586 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1397475, _1397475)), hAPP(hAPP(c_Product__Type_OPair(_1397475, _1397475), _1397481), _1397483)), _1397479)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397475), hAPP(hAPP(c_Set_Oinsert(_1397475), _1397481), c_Orderings_Obot__class_Obot(tc_fun(_1397475, tc_HOL_Obool)))), _1397479) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397475), hAPP(hAPP(c_Set_Oinsert(_1397475), _1397483), c_Orderings_Obot__class_Obot(tc_fun(_1397475, tc_HOL_Obool)))), _1397479))]]], (33592 ^ _779300) ^ [_1398029, _1398031] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398029), c_Orderings_Obot__class_Obot(tc_fun(_1398029, tc_HOL_Obool))), _1398031) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1398029, tc_HOL_Obool), tc_HOL_Obool)))], (33594 ^ _779300) ^ [_1398093, _1398095, _1398097] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1398093, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398093), _1398095), _1398097), -(_1398095 = c_Orderings_Obot__class_Obot(tc_fun(_1398093, tc_HOL_Obool)))], (33600 ^ _779300) ^ [_1398210, _1398212, _1398214] : [_1398212 = c_Orderings_Obot__class_Obot(tc_fun(_1398210, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1398210, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398210), _1398212), _1398214))], (33606 ^ _779300) ^ [_1398351, _1398353, _1398355] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398351), _1398353), _1398355) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1398351, tc_HOL_Obool), tc_HOL_Obool)), -(_1398353 = c_Orderings_Obot__class_Obot(tc_fun(_1398351, tc_HOL_Obool)))], (33612 ^ _779300) ^ [_1398468, _1398470, _1398472] : [_1398470 = c_Orderings_Obot__class_Obot(tc_fun(_1398468, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398468), _1398470), _1398472) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1398468, tc_HOL_Obool), tc_HOL_Obool)))], (33618 ^ _779300) ^ [_1398591, _1398593, _1398595, _1398597, _1398599] : [c_Equiv__Relations_Oequiv(_1398591, _1398593, _1398595), hBOOL(hAPP(hAPP(c_member(tc_fun(_1398591, tc_HOL_Obool)), _1398597), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398591), _1398593), _1398595))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1398591, tc_HOL_Obool)), _1398599), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398591), _1398593), _1398595))), -(_1398597 = _1398599), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398591, tc_HOL_Obool)), _1398597), _1398599) = c_Orderings_Obot__class_Obot(tc_fun(_1398591, tc_HOL_Obool)))], (33636 ^ _779300) ^ [_1398909, _1398911, _1398913, _1398915] : [c_Fun_Oinj__on(_1398909, tc_fun(tc_fun(_1398909, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1398909, tc_fun(tc_prod(_1398909, _1398909), tc_HOL_Obool), tc_fun(tc_fun(_1398909, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1398909, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1398909, _1398909), tc_HOL_Obool), tc_fun(tc_fun(_1398909, tc_HOL_Obool), tc_HOL_Obool)), _1398909), c_Equiv__Relations_Oquotient(_1398909)), hAPP(hAPP(c_COMBC(_1398909, tc_fun(_1398909, tc_HOL_Obool), tc_fun(_1398909, tc_HOL_Obool)), c_Set_Oinsert(_1398909)), c_Orderings_Obot__class_Obot(tc_fun(_1398909, tc_HOL_Obool))))), _1398911), _1398913), hBOOL(hAPP(hAPP(c_member(_1398909), _1398915), _1398913)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398909), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398909, tc_HOL_Obool)), _1398913), hAPP(hAPP(c_Set_Oinsert(_1398909), _1398915), c_Orderings_Obot__class_Obot(tc_fun(_1398909, tc_HOL_Obool))))), _1398911) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1398909, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398909), _1398913), _1398911)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398909), hAPP(hAPP(c_Set_Oinsert(_1398909), _1398915), c_Orderings_Obot__class_Obot(tc_fun(_1398909, tc_HOL_Obool)))), _1398911)))], (33646 ^ _779300) ^ [_1399376, _1399378, _1399380, _1399382] : [hBOOL(hAPP(hAPP(c_member(_1399376), _1399378), _1399380)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1399376, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1399376, _1399376, _1399382), hAPP(hAPP(c_Set_Oinsert(_1399376), _1399378), c_Orderings_Obot__class_Obot(tc_fun(_1399376, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399376), _1399380), _1399382))))], (33652 ^ _779300) ^ [_1399547, _1399549, _1399551, _1399553, _1399555, _1399557, _1399559] : [c_Equiv__Relations_Oequiv(_1399547, _1399549, _1399551), hBOOL(hAPP(hAPP(c_member(tc_fun(_1399547, tc_HOL_Obool)), _1399553), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399547), _1399549), _1399551))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1399547, tc_HOL_Obool)), _1399555), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399547), _1399549), _1399551))), hBOOL(hAPP(hAPP(c_member(_1399547), _1399557), _1399553)), hBOOL(hAPP(hAPP(c_member(_1399547), _1399559), _1399555)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1399547, _1399547)), hAPP(hAPP(c_Product__Type_OPair(_1399547, _1399547), _1399557), _1399559)), _1399551)), -(_1399553 = _1399555)], (33678 ^ _779300) ^ [_1400084, _1400086, _1400088, _1400090, _1400092, _1400094, _1400096] : [c_Equiv__Relations_Oequiv(_1400084, _1400086, _1400088), hBOOL(hAPP(hAPP(c_member(tc_fun(_1400084, tc_HOL_Obool)), _1400090), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400084), _1400086), _1400088))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1400084, tc_HOL_Obool)), _1400092), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400084), _1400086), _1400088))), hBOOL(hAPP(hAPP(c_member(_1400084), _1400094), _1400090)), hBOOL(hAPP(hAPP(c_member(_1400084), _1400096), _1400092)), 33697 ^ _779300 : [(33698 ^ _779300) ^ [] : [_1400090 = _1400092, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1400084, _1400084)), hAPP(hAPP(c_Product__Type_OPair(_1400084, _1400084), _1400094), _1400096)), _1400088)))], (33704 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1400084, _1400084)), hAPP(hAPP(c_Product__Type_OPair(_1400084, _1400084), _1400094), _1400096)), _1400088)), -(_1400090 = _1400092)]]], (33710 ^ _779300) ^ [_1400728, _1400730, _1400732] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400728), hAPP(hAPP(c_Set_Oinsert(_1400728), _1400730), c_Orderings_Obot__class_Obot(tc_fun(_1400728, tc_HOL_Obool)))), _1400732) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1400728, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1400728, _1400728, _1400732), hAPP(hAPP(c_Set_Oinsert(_1400728), _1400730), c_Orderings_Obot__class_Obot(tc_fun(_1400728, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1400728, tc_HOL_Obool), tc_HOL_Obool))))], (33712 ^ _779300) ^ [_1400815, _1400817] : [-(c_Nitpick_Oint__lcm(_1400815, _1400817) = 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), _1400815)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1400817)))))], (33714 ^ _779300) ^ [_1400861, _1400863, _1400865] : [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), _1400861), _1400863))), -(hBOOL(hAPP(hAPP(_1400865, _1400861), _1400863))), 33721 ^ _779300 : [(33722 ^ _779300) ^ [] : [-(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), 33719 ^ [_1400861, _1400863, _1400865]), 33720 ^ [_1400861, _1400863, _1400865]))))], (33730 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1400865, 33719 ^ [_1400861, _1400863, _1400865]), 33720 ^ [_1400861, _1400863, _1400865]))], (33724 ^ _779300) ^ [] : [-(33720 ^ [_1400861, _1400863, _1400865] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1400865, 33720 ^ [_1400861, _1400863, _1400865]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 33719 ^ [_1400861, _1400863, _1400865], 33720 ^ [_1400861, _1400863, _1400865]))))]]], (33734 ^ _779300) ^ [_1401283, _1401285, _1401287, _1401289] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1401283, tc_HOL_Obool)), _1401285), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401283), _1401287), _1401289))), 33738 ^ _779300 : [(33739 ^ _779300) ^ [] : [-(_1401285 = hAPP(c_Relation_OImage(_1401283, _1401283, _1401289), hAPP(hAPP(c_Set_Oinsert(_1401283), 33737 ^ [_1401283, _1401285, _1401287, _1401289]), c_Orderings_Obot__class_Obot(tc_fun(_1401283, tc_HOL_Obool)))))], (33741 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401283), 33737 ^ [_1401283, _1401285, _1401287, _1401289]), _1401287)))]]], (33743 ^ _779300) ^ [_1401511, _1401513, _1401515] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401511), _1401513), _1401515) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401511, tc_fun(tc_fun(_1401511, tc_HOL_Obool), tc_HOL_Obool)), _1401513), hAPP(hAPP(c_COMBC(_1401511, tc_fun(tc_fun(_1401511, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1401511, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401511, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1401511, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1401511, tc_HOL_Obool), tc_HOL_Obool)), _1401511), c_Set_Oinsert(tc_fun(_1401511, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1401511, tc_HOL_Obool), tc_fun(_1401511, tc_HOL_Obool), _1401511), c_Relation_OImage(_1401511, _1401511, _1401515)), hAPP(hAPP(c_COMBC(_1401511, tc_fun(_1401511, tc_HOL_Obool), tc_fun(_1401511, tc_HOL_Obool)), c_Set_Oinsert(_1401511)), c_Orderings_Obot__class_Obot(tc_fun(_1401511, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1401511, tc_HOL_Obool), tc_HOL_Obool)))))], (33745 ^ _779300) ^ [_1401667, _1401669, _1401671, _1401673, _1401675, _1401677] : [hBOOL(hAPP(hAPP(c_member(_1401667), _1401669), _1401671)), hBOOL(hAPP(hAPP(_1401673, _1401669), _1401675)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401667, tc_fun(_1401677, tc_HOL_Obool)), _1401671), _1401673), _1401675)))], (33755 ^ _779300) ^ [_1401864, _1401866, _1401868, _1401870] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1401864), _1401866)), 33758 ^ _779300 : [(33769 ^ _779300) ^ [] : [33771 ^ _779300 : [(33772 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401864), 33770 ^ [_1401864, _1401866, _1401868, _1401870]), _1401866)))], (33774 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1401868), hAPP(_1401870, 33770 ^ [_1401864, _1401866, _1401868, _1401870])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1401868), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401864, tc_fun(_1401868, tc_HOL_Obool)), _1401866), _1401870))))], (33759 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1401868), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401864, tc_fun(_1401868, tc_HOL_Obool)), _1401866), _1401870))), 33762 ^ _779300 : [(33763 ^ _779300) ^ [_1402048] : [hBOOL(hAPP(hAPP(c_member(_1401864), _1402048), _1401866)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1401868), hAPP(_1401870, _1402048))))]]]]], (33778 ^ _779300) ^ [_1402363, _1402365, _1402367, _1402369, _1402371] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402363, tc_fun(_1402365, tc_HOL_Obool)), _1402367), _1402369), _1402371)), 33782 ^ _779300 : [(33783 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1402363), 33781 ^ [_1402363, _1402365, _1402367, _1402369, _1402371]), _1402367)))], (33785 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1402369, 33781 ^ [_1402363, _1402365, _1402367, _1402369, _1402371]), _1402371)))]]], (33787 ^ _779300) ^ [_1402551, _1402553, _1402555, _1402557, _1402559] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402551, tc_fun(_1402553, tc_HOL_Obool)), _1402555), _1402557), _1402559))), 33788 ^ _779300 : [(33789 ^ _779300) ^ [_1402623] : [hBOOL(hAPP(hAPP(c_member(_1402551), _1402623), _1402555)), hBOOL(hAPP(hAPP(_1402557, _1402623), _1402559))]]], (33797 ^ _779300) ^ [_1402775, _1402777, _1402779, _1402781, _1402783, _1402785] : [-(hAPP(c_Relation_OImage(_1402775, _1402777, _1402779), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402781, tc_fun(_1402775, tc_HOL_Obool)), _1402783), _1402785)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402781, tc_fun(_1402777, tc_HOL_Obool)), _1402783), hAPP(hAPP(c_COMBB(tc_fun(_1402775, tc_HOL_Obool), tc_fun(_1402777, tc_HOL_Obool), _1402781), c_Relation_OImage(_1402775, _1402777, _1402779)), _1402785)))], (33799 ^ _779300) ^ [_1402859, _1402861, _1402863, _1402865] : [-(hAPP(c_Relation_OImage(_1402859, _1402861, _1402863), _1402865) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402859, tc_fun(_1402861, tc_HOL_Obool)), _1402865), hAPP(hAPP(c_COMBB(tc_fun(_1402859, tc_HOL_Obool), tc_fun(_1402861, tc_HOL_Obool), _1402859), c_Relation_OImage(_1402859, _1402861, _1402863)), hAPP(hAPP(c_COMBC(_1402859, tc_fun(_1402859, tc_HOL_Obool), tc_fun(_1402859, tc_HOL_Obool)), c_Set_Oinsert(_1402859)), c_Orderings_Obot__class_Obot(tc_fun(_1402859, tc_HOL_Obool))))))], (33801 ^ _779300) ^ [_1402950, _1402952, _1402954, _1402956, _1402958, _1402960] : [hBOOL(hAPP(hAPP(c_member(_1402950), _1402952), _1402954)), hBOOL(hAPP(hAPP(c_member(_1402956), _1402958), hAPP(_1402960, _1402952))), -(hBOOL(hAPP(hAPP(c_member(_1402956), _1402958), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402950, tc_fun(_1402956, tc_HOL_Obool)), _1402954), _1402960))))], (33811 ^ _779300) ^ [_1403167, _1403169, _1403171, _1403173] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1403167, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403169, tc_fun(tc_fun(_1403167, tc_HOL_Obool), tc_HOL_Obool)), _1403171), hAPP(hAPP(c_COMBB(tc_fun(_1403167, tc_HOL_Obool), tc_fun(tc_fun(_1403167, tc_HOL_Obool), tc_HOL_Obool), _1403169), c_Set_OPow(_1403167)), _1403173))), hAPP(c_Set_OPow(_1403167), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403169, tc_fun(_1403167, tc_HOL_Obool)), _1403171), _1403173)))))], (33813 ^ _779300) ^ [_1403262, _1403264, _1403266, _1403268] : [-(hAPP(c_Set_Oimage(_1403262, _1403264, _1403266), _1403268) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403262, tc_fun(_1403264, tc_HOL_Obool)), _1403268), hAPP(hAPP(c_COMBC(_1403262, tc_fun(_1403264, tc_HOL_Obool), tc_fun(_1403264, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1403264, tc_fun(tc_fun(_1403264, tc_HOL_Obool), tc_fun(_1403264, tc_HOL_Obool)), _1403262), c_Set_Oinsert(_1403264)), _1403266)), c_Orderings_Obot__class_Obot(tc_fun(_1403264, tc_HOL_Obool)))))], (33815 ^ _779300) ^ [_1403352, _1403354, _1403356, _1403358, _1403360, _1403362, _1403364, _1403366, _1403368, _1403370] : [c_Equiv__Relations_Oequiv(_1403352, _1403354, _1403356), c_Equiv__Relations_Oequiv(_1403358, _1403360, _1403362), c_Equiv__Relations_Ocongruent2(_1403352, _1403358, tc_fun(_1403364, tc_HOL_Obool), _1403356, _1403362, _1403366), hBOOL(hAPP(hAPP(c_member(_1403352), _1403368), _1403354)), hBOOL(hAPP(hAPP(c_member(_1403358), _1403370), _1403360)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403352, tc_fun(_1403364, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403352, _1403352, _1403356), hAPP(hAPP(c_Set_Oinsert(_1403352), _1403368), c_Orderings_Obot__class_Obot(tc_fun(_1403352, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1403358, tc_fun(_1403364, tc_HOL_Obool)), tc_fun(_1403364, tc_HOL_Obool), _1403352), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403358, tc_fun(_1403364, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403358, _1403358, _1403362), hAPP(hAPP(c_Set_Oinsert(_1403358), _1403370), c_Orderings_Obot__class_Obot(tc_fun(_1403358, tc_HOL_Obool)))))), _1403366)) = hAPP(hAPP(_1403366, _1403368), _1403370))], (33854 ^ _779300) ^ [_1404395, _1404397, _1404399, _1404401, _1404403] : [33856 ^ _779300 : [(33857 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404397), 33855 ^ [_1404395, _1404397, _1404399, _1404401, _1404403]), _1404399)))], (33860 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404395), 33858 ^ [_1404395, _1404397, _1404399, _1404401, _1404403]), hAPP(_1404401, 33855 ^ [_1404395, _1404397, _1404399, _1404401, _1404403]))))], (33862 ^ _779300) ^ [] : [hBOOL(hAPP(_1404403, 33858 ^ [_1404395, _1404397, _1404399, _1404401, _1404403]))]], 33863 ^ _779300 : [(33864 ^ _779300) ^ [_1404705] : [hBOOL(hAPP(hAPP(c_member(_1404395), _1404705), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404397, tc_fun(_1404395, tc_HOL_Obool)), _1404399), _1404401))), -(hBOOL(hAPP(_1404403, _1404705)))]]], (33837 ^ _779300) ^ [_1403959, _1403961, _1403963, _1403965, _1403967] : [33839 ^ _779300 : [(33840 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403959), 33838 ^ [_1403959, _1403961, _1403963, _1403965, _1403967]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403961, tc_fun(_1403959, tc_HOL_Obool)), _1403963), _1403965))))], (33842 ^ _779300) ^ [] : [hBOOL(hAPP(_1403967, 33838 ^ [_1403959, _1403961, _1403963, _1403965, _1403967]))]], 33843 ^ _779300 : [(33844 ^ _779300) ^ [_1404181] : [hBOOL(hAPP(hAPP(c_member(_1403961), _1404181), _1403963)), 33847 ^ _779300 : [(33848 ^ _779300) ^ [_1404278] : [hBOOL(hAPP(hAPP(c_member(_1403959), _1404278), hAPP(_1403965, _1404181))), -(hBOOL(hAPP(_1403967, _1404278)))]]]]], (33870 ^ _779300) ^ [_1404840, _1404842, _1404844, _1404846] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1404840, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1404842)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1404840, tc_HOL_Obool), tc_Nat_Onat), _1404844), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1404846))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1404840, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1404846, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1404842), _1404846))), _1404844))], (33872 ^ _779300) ^ [_1404922, _1404924, _1404926, _1404928, _1404930, _1404932] : [class_Complete__Lattice_Ocomplete__lattice(_1404922), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404924, _1404922), _1404926), hAPP(hAPP(c_COMBB(tc_fun(_1404928, _1404922), _1404922, _1404924), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404928, _1404922), _1404930)), _1404932)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404928, _1404922), _1404930), hAPP(hAPP(c_COMBB(tc_fun(_1404924, _1404922), _1404922, _1404928), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404924, _1404922), _1404926)), hAPP(c_COMBC(_1404924, _1404928, _1404922), _1404932))))], (33878 ^ _779300) ^ [_1405131, _1405133, _1405135, _1405137, _1405139, _1405141] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405131, tc_fun(_1405133, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405135, tc_fun(_1405131, tc_HOL_Obool)), _1405137), _1405139)), _1405141) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405135, tc_fun(_1405133, tc_HOL_Obool)), _1405137), hAPP(hAPP(c_COMBC(_1405135, tc_fun(_1405131, tc_fun(_1405133, tc_HOL_Obool)), tc_fun(_1405133, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405131, tc_HOL_Obool), tc_fun(tc_fun(_1405131, tc_fun(_1405133, tc_HOL_Obool)), tc_fun(_1405133, tc_HOL_Obool)), _1405135), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405131, tc_fun(_1405133, tc_HOL_Obool))), _1405139)), _1405141)))], (33880 ^ _779300) ^ [_1405250, _1405252, _1405254, _1405256, _1405258, _1405260] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405250, tc_fun(_1405252, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405254, tc_fun(_1405250, tc_HOL_Obool)), _1405256), _1405258)), _1405260) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405254, tc_fun(_1405252, tc_HOL_Obool)), _1405256), hAPP(hAPP(c_COMBC(_1405254, tc_fun(_1405250, tc_fun(_1405252, tc_HOL_Obool)), tc_fun(_1405252, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405250, tc_HOL_Obool), tc_fun(tc_fun(_1405250, tc_fun(_1405252, tc_HOL_Obool)), tc_fun(_1405252, tc_HOL_Obool)), _1405254), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405250, tc_fun(_1405252, tc_HOL_Obool))), _1405258)), _1405260)))], (33882 ^ _779300) ^ [_1405369, _1405371, _1405373, _1405375, _1405377, _1405379] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405369, tc_fun(_1405371, tc_HOL_Obool)), _1405373), hAPP(hAPP(c_COMBC(_1405369, tc_fun(_1405375, tc_fun(_1405371, tc_HOL_Obool)), tc_fun(_1405371, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405375, tc_HOL_Obool), tc_fun(tc_fun(_1405375, tc_fun(_1405371, tc_HOL_Obool)), tc_fun(_1405371, tc_HOL_Obool)), _1405369), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405375, tc_fun(_1405371, tc_HOL_Obool))), _1405377)), _1405379)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405375, tc_fun(_1405371, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405369, tc_fun(_1405375, tc_HOL_Obool)), _1405373), _1405377)), _1405379))], (33884 ^ _779300) ^ [_1405488, _1405490, _1405492, _1405494, _1405496, _1405498, _1405500, _1405502, _1405504, _1405506] : [c_Equiv__Relations_Ocongruent2(_1405488, _1405490, _1405492, _1405494, _1405496, _1405498), hBOOL(hAPP(hAPP(c_member(tc_prod(_1405488, _1405488)), hAPP(hAPP(c_Product__Type_OPair(_1405488, _1405488), _1405500), _1405502)), _1405494)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1405490, _1405490)), hAPP(hAPP(c_Product__Type_OPair(_1405490, _1405490), _1405504), _1405506)), _1405496)), -(hAPP(hAPP(_1405498, _1405500), _1405504) = hAPP(hAPP(_1405498, _1405502), _1405506))], (33898 ^ _779300) ^ [_1405825, _1405827, _1405829] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1405825, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1405827)), _1405829) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405825, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1405825, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1405827)), _1405829)), hAPP(_1405829, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (33900 ^ _779300) ^ [_1405897, _1405899, _1405901, _1405903, _1405905] : [class_Complete__Lattice_Ocomplete__lattice(_1405897), 33903 ^ _779300 : [(33914 ^ _779300) ^ [] : [33916 ^ _779300 : [(33917 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405899), 33915 ^ [_1405897, _1405899, _1405901, _1405903, _1405905]), _1405901)))], (33919 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405897), hAPP(_1405903, 33915 ^ [_1405897, _1405899, _1405901, _1405903, _1405905])), _1405905))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405897), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405899, _1405897), _1405901), _1405903)), _1405905)))], (33904 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405897), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405899, _1405897), _1405901), _1405903)), _1405905)), 33907 ^ _779300 : [(33908 ^ _779300) ^ [_1406078] : [hBOOL(hAPP(hAPP(c_member(_1405899), _1406078), _1405901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405897), hAPP(_1405903, _1406078)), _1405905)))]]]]], (33923 ^ _779300) ^ [_1406391, _1406393, _1406395, _1406397, _1406399] : [class_Complete__Lattice_Ocomplete__lattice(_1406391), class_Orderings_Olinorder(_1406391), 33930 ^ _779300 : [(33931 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406391), _1406393), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406395, _1406391), _1406397), _1406399))), 33935 ^ _779300 : [(33936 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406395), 33934 ^ [_1406391, _1406393, _1406395, _1406397, _1406399]), _1406397)))], (33938 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406391), _1406393), hAPP(_1406399, 33934 ^ [_1406391, _1406393, _1406395, _1406397, _1406399]))))]]], (33940 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406391), _1406393), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406395, _1406391), _1406397), _1406399)))), 33941 ^ _779300 : [(33942 ^ _779300) ^ [_1406739] : [hBOOL(hAPP(hAPP(c_member(_1406395), _1406739), _1406397)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406391), _1406393), hAPP(_1406399, _1406739)))]]]]], (33950 ^ _779300) ^ [_1406933, _1406935, _1406937, _1406939, _1406941] : [hBOOL(hAPP(hAPP(c_member(_1406933), _1406935), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406937, tc_fun(_1406933, tc_HOL_Obool)), _1406939), _1406941))), 33954 ^ _779300 : [(33955 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406937), 33953 ^ [_1406933, _1406935, _1406937, _1406939, _1406941]), _1406939)))], (33957 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406933), _1406935), hAPP(_1406941, 33953 ^ [_1406933, _1406935, _1406937, _1406939, _1406941]))))]]], (33959 ^ _779300) ^ [_1407141, _1407143, _1407145, _1407147, _1407149] : [-(hBOOL(hAPP(hAPP(c_member(_1407141), _1407143), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407145, tc_fun(_1407141, tc_HOL_Obool)), _1407147), _1407149)))), 33960 ^ _779300 : [(33961 ^ _779300) ^ [_1407223] : [hBOOL(hAPP(hAPP(c_member(_1407145), _1407223), _1407147)), hBOOL(hAPP(hAPP(c_member(_1407141), _1407143), hAPP(_1407149, _1407223)))]]], (33969 ^ _779300) ^ [_1407390, _1407392, _1407394, _1407396] : [class_Complete__Lattice_Ocomplete__lattice(_1407390), -(_1407392 = c_Orderings_Obot__class_Obot(tc_fun(_1407394, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407394, _1407390), _1407392), hAPP(c_COMBK(_1407390, _1407394), _1407396)) = _1407396)], (33989 ^ _779300) ^ [_1407774, _1407776, _1407778, _1407780] : [33991 ^ _779300 : [(33992 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1407776), 33990 ^ [_1407774, _1407776, _1407778, _1407780]), _1407778)))], (33994 ^ _779300) ^ [] : [hAPP(_1407780, 33990 ^ [_1407774, _1407776, _1407778, _1407780]) = c_Orderings_Obot__class_Obot(tc_fun(_1407774, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1407774, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407776, tc_fun(_1407774, tc_HOL_Obool)), _1407778), _1407780))], (33979 ^ _779300) ^ [_1407545, _1407547, _1407549, _1407551] : [c_Orderings_Obot__class_Obot(tc_fun(_1407545, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407547, tc_fun(_1407545, tc_HOL_Obool)), _1407549), _1407551), 33982 ^ _779300 : [(33983 ^ _779300) ^ [_1407661] : [hBOOL(hAPP(hAPP(c_member(_1407547), _1407661), _1407549)), -(hAPP(_1407551, _1407661) = c_Orderings_Obot__class_Obot(tc_fun(_1407545, tc_HOL_Obool)))]]], (33998 ^ _779300) ^ [_1408004, _1408006, _1408008] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408004, tc_fun(_1408006, tc_HOL_Obool)), _1408008), hAPP(c_COMBK(tc_fun(_1408006, tc_HOL_Obool), _1408004), c_Orderings_Obot__class_Obot(tc_fun(_1408006, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1408006, tc_HOL_Obool)))], (34000 ^ _779300) ^ [_1408077, _1408079, _1408081, _1408083] : [_1408077 = c_Orderings_Obot__class_Obot(tc_fun(_1408079, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408079, tc_fun(_1408081, tc_HOL_Obool)), _1408077), hAPP(c_COMBK(tc_fun(_1408081, tc_HOL_Obool), _1408079), _1408083)) = c_Orderings_Obot__class_Obot(tc_fun(_1408081, tc_HOL_Obool)))], (34006 ^ _779300) ^ [_1408214, _1408216, _1408218, _1408220] : [-(_1408214 = c_Orderings_Obot__class_Obot(tc_fun(_1408216, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408216, tc_fun(_1408218, tc_HOL_Obool)), _1408214), hAPP(c_COMBK(tc_fun(_1408218, tc_HOL_Obool), _1408216), _1408220)) = _1408220)], (34022 ^ _779300) ^ [_1408532, _1408534, _1408536, _1408538] : [34024 ^ _779300 : [(34025 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1408532), 34023 ^ [_1408532, _1408534, _1408536, _1408538]), _1408536)))], (34027 ^ _779300) ^ [] : [hAPP(_1408538, 34023 ^ [_1408532, _1408534, _1408536, _1408538]) = c_Orderings_Obot__class_Obot(tc_fun(_1408534, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408532, tc_fun(_1408534, tc_HOL_Obool)), _1408536), _1408538) = c_Orderings_Obot__class_Obot(tc_fun(_1408534, tc_HOL_Obool)))], (34012 ^ _779300) ^ [_1408303, _1408305, _1408307, _1408309] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408303, tc_fun(_1408305, tc_HOL_Obool)), _1408307), _1408309) = c_Orderings_Obot__class_Obot(tc_fun(_1408305, tc_HOL_Obool)), 34015 ^ _779300 : [(34016 ^ _779300) ^ [_1408419] : [hBOOL(hAPP(hAPP(c_member(_1408303), _1408419), _1408307)), -(hAPP(_1408309, _1408419) = c_Orderings_Obot__class_Obot(tc_fun(_1408305, tc_HOL_Obool)))]]], (34041 ^ _779300) ^ [_1409044, _1409046, _1409048, _1409050, _1409052] : [34043 ^ _779300 : [(34044 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409046), 34042 ^ [_1409044, _1409046, _1409048, _1409050, _1409052]), _1409048)))], (34046 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1409044, tc_HOL_Obool)), hAPP(_1409050, 34042 ^ [_1409044, _1409046, _1409048, _1409050, _1409052])), _1409052))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1409044, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409046, tc_fun(_1409044, tc_HOL_Obool)), _1409048), _1409050)), _1409052)))], (34031 ^ _779300) ^ [_1408786, _1408788, _1408790, _1408792, _1408794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408786, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408788, tc_fun(_1408786, tc_HOL_Obool)), _1408790), _1408792)), _1408794)), 34034 ^ _779300 : [(34035 ^ _779300) ^ [_1408919] : [hBOOL(hAPP(hAPP(c_member(_1408788), _1408919), _1408790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408786, tc_HOL_Obool)), hAPP(_1408792, _1408919)), _1408794)))]]], (34050 ^ _779300) ^ [_1409307, _1409309, _1409311, _1409313, _1409315, _1409317] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409307, tc_fun(_1409309, tc_HOL_Obool)), _1409311), hAPP(hAPP(c_COMBB(_1409313, tc_fun(_1409309, tc_HOL_Obool), _1409307), _1409315), _1409317)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409313, tc_fun(_1409309, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1409307, _1409313, _1409317), _1409311)), _1409315))], (34052 ^ _779300) ^ [_1409384, _1409386, _1409388, _1409390, _1409392, _1409394] : [-(hAPP(c_Set_Oimage(_1409384, _1409386, _1409388), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409390, tc_fun(_1409384, tc_HOL_Obool)), _1409392), _1409394)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409390, tc_fun(_1409386, tc_HOL_Obool)), _1409392), hAPP(hAPP(c_COMBB(tc_fun(_1409384, tc_HOL_Obool), tc_fun(_1409386, tc_HOL_Obool), _1409390), c_Set_Oimage(_1409384, _1409386, _1409388)), _1409394)))], (34054 ^ _779300) ^ [_1409468, _1409470, _1409472, _1409474, _1409476, _1409478] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409468, tc_fun(_1409470, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1409472, _1409468, _1409474), _1409476)), _1409478) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409472, tc_fun(_1409470, tc_HOL_Obool)), _1409476), hAPP(hAPP(c_COMBB(_1409468, tc_fun(_1409470, tc_HOL_Obool), _1409472), _1409478), _1409474)))], (34056 ^ _779300) ^ [_1409545, _1409547, _1409549, _1409551, _1409553] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409545, tc_fun(_1409547, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409545, tc_HOL_Obool)), _1409549), _1409551)), _1409553) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409547, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409545, tc_fun(_1409547, tc_HOL_Obool)), _1409549), _1409553)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409545, tc_fun(_1409547, tc_HOL_Obool)), _1409551), _1409553)))], (34058 ^ _779300) ^ [_1409634, _1409636, _1409638, _1409640, _1409642] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409634, tc_fun(_1409636, tc_HOL_Obool)), _1409638), hAPP(hAPP(c_COMBS(_1409634, tc_fun(_1409636, tc_HOL_Obool), tc_fun(_1409636, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409636, tc_HOL_Obool), tc_fun(tc_fun(_1409636, tc_HOL_Obool), tc_fun(_1409636, tc_HOL_Obool)), _1409634), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409636, tc_HOL_Obool))), _1409640)), _1409642)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409636, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409634, tc_fun(_1409636, tc_HOL_Obool)), _1409638), _1409640)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409634, tc_fun(_1409636, tc_HOL_Obool)), _1409638), _1409642)))], (34060 ^ _779300) ^ [_1409755, _1409757, _1409759, _1409761, _1409763] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409755, tc_fun(_1409757, tc_HOL_Obool)), _1409759), hAPP(hAPP(c_COMBB(tc_fun(_1409757, tc_HOL_Obool), tc_fun(_1409757, tc_HOL_Obool), _1409755), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409757, tc_HOL_Obool)), _1409761)), _1409763)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409757, tc_HOL_Obool)), _1409761), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409755, tc_fun(_1409757, tc_HOL_Obool)), _1409759), _1409763)))], (34062 ^ _779300) ^ [_1409845, _1409847, _1409849, _1409851, _1409853] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409845, tc_fun(_1409847, tc_HOL_Obool)), _1409849), hAPP(hAPP(c_COMBC(_1409845, tc_fun(_1409847, tc_HOL_Obool), tc_fun(_1409847, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409847, tc_HOL_Obool), tc_fun(tc_fun(_1409847, tc_HOL_Obool), tc_fun(_1409847, tc_HOL_Obool)), _1409845), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409847, tc_HOL_Obool))), _1409851)), _1409853)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409847, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409845, tc_fun(_1409847, tc_HOL_Obool)), _1409849), _1409851)), _1409853))], (34064 ^ _779300) ^ [_1409954, _1409956, _1409958, _1409960, _1409962] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409954, tc_HOL_Obool)), _1409956), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409958, tc_fun(_1409954, tc_HOL_Obool)), _1409960), _1409962)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409958, tc_fun(_1409954, tc_HOL_Obool)), _1409960), hAPP(hAPP(c_COMBB(tc_fun(_1409954, tc_HOL_Obool), tc_fun(_1409954, tc_HOL_Obool), _1409958), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409954, tc_HOL_Obool)), _1409956)), _1409962)))], (34066 ^ _779300) ^ [_1410044, _1410046, _1410048, _1410050, _1410052] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410044, tc_HOL_Obool)), _1410046), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410048, tc_fun(_1410044, tc_HOL_Obool)), _1410050), _1410052)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410048, tc_fun(_1410044, tc_HOL_Obool)), _1410050), hAPP(hAPP(c_COMBB(tc_fun(_1410044, tc_HOL_Obool), tc_fun(_1410044, tc_HOL_Obool), _1410048), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410044, tc_HOL_Obool)), _1410046)), _1410052)))], (34068 ^ _779300) ^ [_1410134, _1410136, _1410138, _1410140, _1410142] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410134, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410136, tc_fun(_1410134, tc_HOL_Obool)), _1410138), _1410140)), _1410142) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410136, tc_fun(_1410134, tc_HOL_Obool)), _1410138), hAPP(hAPP(c_COMBC(_1410136, tc_fun(_1410134, tc_HOL_Obool), tc_fun(_1410134, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410134, tc_HOL_Obool), tc_fun(tc_fun(_1410134, tc_HOL_Obool), tc_fun(_1410134, tc_HOL_Obool)), _1410136), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410134, tc_HOL_Obool))), _1410140)), _1410142)))], (34070 ^ _779300) ^ [_1410243, _1410245, _1410247, _1410249, _1410251, _1410253, _1410255] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410243, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410245, tc_fun(_1410243, tc_HOL_Obool)), _1410247), _1410249)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410251, tc_fun(_1410243, tc_HOL_Obool)), _1410253), _1410255)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410245, tc_fun(_1410243, tc_HOL_Obool)), _1410247), hAPP(hAPP(c_COMBB(tc_fun(_1410251, tc_fun(_1410243, tc_HOL_Obool)), tc_fun(_1410243, tc_HOL_Obool), _1410245), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410251, tc_fun(_1410243, tc_HOL_Obool)), _1410253)), hAPP(hAPP(c_COMBC(_1410245, tc_fun(_1410251, tc_fun(_1410243, tc_HOL_Obool)), tc_fun(_1410251, tc_fun(_1410243, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1410243, tc_HOL_Obool), tc_fun(_1410243, tc_HOL_Obool)), tc_fun(tc_fun(_1410251, tc_fun(_1410243, tc_HOL_Obool)), tc_fun(_1410251, tc_fun(_1410243, tc_HOL_Obool))), _1410245), c_COMBB(tc_fun(_1410243, tc_HOL_Obool), tc_fun(_1410243, tc_HOL_Obool), _1410251)), hAPP(hAPP(c_COMBB(tc_fun(_1410243, tc_HOL_Obool), tc_fun(tc_fun(_1410243, tc_HOL_Obool), tc_fun(_1410243, tc_HOL_Obool)), _1410245), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410243, tc_HOL_Obool))), _1410249))), _1410255))))], (34072 ^ _779300) ^ [_1410446, _1410448, _1410450, _1410452, _1410454, _1410456] : [class_Complete__Lattice_Ocomplete__lattice(_1410446), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410448, tc_fun(_1410450, _1410446)), _1410452), _1410454), _1410456) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410448, _1410446), _1410452), hAPP(hAPP(c_COMBC(_1410448, _1410450, _1410446), _1410454), _1410456)))], (34078 ^ _779300) ^ [_1410597, _1410599, _1410601, _1410603, _1410605] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410597, tc_fun(_1410599, tc_HOL_Obool)), _1410601), hAPP(hAPP(c_COMBC(_1410597, tc_fun(_1410599, tc_HOL_Obool), tc_fun(_1410599, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410599, tc_HOL_Obool), tc_fun(tc_fun(_1410599, tc_HOL_Obool), tc_fun(_1410599, tc_HOL_Obool)), _1410597), c_Groups_Ominus__class_Ominus(tc_fun(_1410599, tc_HOL_Obool))), _1410603)), _1410605)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410599, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410597, tc_fun(_1410599, tc_HOL_Obool)), _1410601), _1410603)), _1410605))], (34080 ^ _779300) ^ [_1410706, _1410708, _1410710, _1410712, _1410714] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410706, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410708, tc_fun(_1410706, tc_HOL_Obool)), _1410710), _1410712)), _1410714) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410708, tc_fun(_1410706, tc_HOL_Obool)), _1410710), hAPP(hAPP(c_COMBC(_1410708, tc_fun(_1410706, tc_HOL_Obool), tc_fun(_1410706, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410706, tc_HOL_Obool), tc_fun(tc_fun(_1410706, tc_HOL_Obool), tc_fun(_1410706, tc_HOL_Obool)), _1410708), c_Groups_Ominus__class_Ominus(tc_fun(_1410706, tc_HOL_Obool))), _1410712)), _1410714)))], (34082 ^ _779300) ^ [_1410815, _1410817, _1410819, _1410821, _1410823] : [class_Complete__Lattice_Ocomplete__lattice(_1410815), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410817, tc_HOL_Obool)), _1410819), _1410821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410815), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410817, _1410815), _1410819), _1410823)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410817, _1410815), _1410821), _1410823))))], (34092 ^ _779300) ^ [_1411024, _1411026, _1411028, _1411030, _1411032] : [class_Complete__Lattice_Ocomplete__lattice(_1411024), hBOOL(hAPP(hAPP(c_member(_1411026), _1411028), _1411030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411024), hAPP(_1411032, _1411028)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411026, _1411024), _1411030), _1411032))))], (34102 ^ _779300) ^ [_1411215, _1411217, _1411219, _1411221, _1411223, _1411225] : [hBOOL(hAPP(hAPP(c_member(_1411215), _1411217), _1411219)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411215, tc_fun(_1411221, tc_HOL_Obool)), _1411219), hAPP(hAPP(c_COMBB(tc_fun(_1411221, tc_HOL_Obool), tc_fun(_1411221, tc_HOL_Obool), _1411215), hAPP(c_Set_Oinsert(_1411221), _1411223)), _1411225)) = hAPP(hAPP(c_Set_Oinsert(_1411221), _1411223), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411215, tc_fun(_1411221, tc_HOL_Obool)), _1411219), _1411225)))], (34108 ^ _779300) ^ [_1411420, _1411422, _1411424, _1411426, _1411428] : [hBOOL(hAPP(hAPP(c_member(_1411420), _1411422), _1411424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1411426, tc_HOL_Obool)), hAPP(_1411428, _1411422)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411420, tc_fun(_1411426, tc_HOL_Obool)), _1411424), _1411428))))], (34114 ^ _779300) ^ [_1411567, _1411569, _1411571, _1411573, _1411575] : [hBOOL(hAPP(hAPP(c_member(_1411567), _1411569), _1411571)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411573, tc_HOL_Obool)), hAPP(_1411575, _1411569)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411567, tc_fun(_1411573, tc_HOL_Obool)), _1411571), _1411575)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411567, tc_fun(_1411573, tc_HOL_Obool)), _1411571), _1411575))], (34120 ^ _779300) ^ [_1411758, _1411760, _1411762, _1411764, _1411766] : [_1411758 = c_Orderings_Obot__class_Obot(tc_fun(_1411760, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1411762), _1411764), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411760, tc_fun(_1411762, tc_HOL_Obool)), _1411758), _1411766)) = hAPP(hAPP(c_Set_Oinsert(_1411762), _1411764), c_Orderings_Obot__class_Obot(tc_fun(_1411762, tc_HOL_Obool))))], (34126 ^ _779300) ^ [_1411911, _1411913, _1411915, _1411917, _1411919] : [-(_1411911 = c_Orderings_Obot__class_Obot(tc_fun(_1411913, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1411915), _1411917), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411913, tc_fun(_1411915, tc_HOL_Obool)), _1411911), _1411919)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411913, tc_fun(_1411915, tc_HOL_Obool)), _1411911), hAPP(hAPP(c_COMBB(tc_fun(_1411915, tc_HOL_Obool), tc_fun(_1411915, tc_HOL_Obool), _1411913), hAPP(c_Set_Oinsert(_1411915), _1411917)), _1411919)))], (34132 ^ _779300) ^ [_1412013, _1412015] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412013, tc_fun(_1412013, tc_HOL_Obool)), _1412015), hAPP(hAPP(c_COMBC(_1412013, tc_fun(_1412013, tc_HOL_Obool), tc_fun(_1412013, tc_HOL_Obool)), c_Set_Oinsert(_1412013)), c_Orderings_Obot__class_Obot(tc_fun(_1412013, tc_HOL_Obool)))) = _1412015)], (34134 ^ _779300) ^ [_1412091, _1412093, _1412095, _1412097, _1412099] : [_1412091 = c_Orderings_Obot__class_Obot(tc_fun(_1412093, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412093, tc_fun(_1412095, tc_HOL_Obool)), _1412091), hAPP(hAPP(c_COMBB(tc_fun(_1412095, tc_HOL_Obool), tc_fun(_1412095, tc_HOL_Obool), _1412093), hAPP(c_Set_Oinsert(_1412095), _1412097)), _1412099)) = c_Orderings_Obot__class_Obot(tc_fun(_1412095, tc_HOL_Obool)))], (34140 ^ _779300) ^ [_1412254, _1412256, _1412258, _1412260, _1412262] : [-(_1412254 = c_Orderings_Obot__class_Obot(tc_fun(_1412256, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412256, tc_fun(_1412258, tc_HOL_Obool)), _1412254), hAPP(hAPP(c_COMBB(tc_fun(_1412258, tc_HOL_Obool), tc_fun(_1412258, tc_HOL_Obool), _1412256), hAPP(c_Set_Oinsert(_1412258), _1412260)), _1412262)) = hAPP(hAPP(c_Set_Oinsert(_1412258), _1412260), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412256, tc_fun(_1412258, tc_HOL_Obool)), _1412254), _1412262)))], (34146 ^ _779300) ^ [_1412374, _1412376, _1412378, _1412380, _1412382] : [_1412374 = c_Orderings_Obot__class_Obot(tc_fun(_1412376, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412378, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412376, tc_fun(_1412378, tc_HOL_Obool)), _1412374), _1412380)), _1412382) = _1412382)], (34152 ^ _779300) ^ [_1412507, _1412509, _1412511, _1412513, _1412515] : [-(_1412507 = c_Orderings_Obot__class_Obot(tc_fun(_1412509, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412511, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412509, tc_fun(_1412511, tc_HOL_Obool)), _1412507), _1412513)), _1412515) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412509, tc_fun(_1412511, tc_HOL_Obool)), _1412507), hAPP(hAPP(c_COMBC(_1412509, tc_fun(_1412511, tc_HOL_Obool), tc_fun(_1412511, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412511, tc_HOL_Obool), tc_fun(tc_fun(_1412511, tc_HOL_Obool), tc_fun(_1412511, tc_HOL_Obool)), _1412509), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412511, tc_HOL_Obool))), _1412513)), _1412515)))], (34158 ^ _779300) ^ [_1412652, _1412654, _1412656, _1412658, _1412660] : [_1412652 = c_Orderings_Obot__class_Obot(tc_fun(_1412654, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412656, tc_HOL_Obool)), _1412658), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412654, tc_fun(_1412656, tc_HOL_Obool)), _1412652), _1412660)) = _1412658)], (34164 ^ _779300) ^ [_1412785, _1412787, _1412789, _1412791, _1412793] : [-(_1412785 = c_Orderings_Obot__class_Obot(tc_fun(_1412787, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412789, tc_HOL_Obool)), _1412791), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412787, tc_fun(_1412789, tc_HOL_Obool)), _1412785), _1412793)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412787, tc_fun(_1412789, tc_HOL_Obool)), _1412785), hAPP(hAPP(c_COMBB(tc_fun(_1412789, tc_HOL_Obool), tc_fun(_1412789, tc_HOL_Obool), _1412787), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412789, tc_HOL_Obool)), _1412791)), _1412793)))], (34170 ^ _779300) ^ [_1412911, _1412913, _1412915, _1412917, _1412919] : [_1412911 = c_Orderings_Obot__class_Obot(tc_fun(_1412913, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412913, tc_fun(_1412915, tc_HOL_Obool)), _1412911), hAPP(hAPP(c_COMBC(_1412913, tc_fun(_1412915, tc_HOL_Obool), tc_fun(_1412915, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412915, tc_HOL_Obool), tc_fun(tc_fun(_1412915, tc_HOL_Obool), tc_fun(_1412915, tc_HOL_Obool)), _1412913), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412915, tc_HOL_Obool))), _1412917)), _1412919)) = c_Orderings_Obot__class_Obot(tc_fun(_1412915, tc_HOL_Obool)))], (34176 ^ _779300) ^ [_1413118, _1413120, _1413122, _1413124, _1413126] : [-(_1413118 = c_Orderings_Obot__class_Obot(tc_fun(_1413120, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413120, tc_fun(_1413122, tc_HOL_Obool)), _1413118), hAPP(hAPP(c_COMBC(_1413120, tc_fun(_1413122, tc_HOL_Obool), tc_fun(_1413122, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1413122, tc_HOL_Obool), tc_fun(tc_fun(_1413122, tc_HOL_Obool), tc_fun(_1413122, tc_HOL_Obool)), _1413120), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413122, tc_HOL_Obool))), _1413124)), _1413126)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413122, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413120, tc_fun(_1413122, tc_HOL_Obool)), _1413118), _1413124)), _1413126))], (34182 ^ _779300) ^ [_1413263, _1413265, _1413267, _1413269, _1413271] : [_1413263 = c_Orderings_Obot__class_Obot(tc_fun(_1413265, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413265, tc_fun(_1413267, tc_HOL_Obool)), _1413263), hAPP(hAPP(c_COMBB(tc_fun(_1413267, tc_HOL_Obool), tc_fun(_1413267, tc_HOL_Obool), _1413265), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413267, tc_HOL_Obool)), _1413269)), _1413271)) = c_Orderings_Obot__class_Obot(tc_fun(_1413267, tc_HOL_Obool)))], (34188 ^ _779300) ^ [_1413432, _1413434, _1413436, _1413438, _1413440] : [-(_1413432 = c_Orderings_Obot__class_Obot(tc_fun(_1413434, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413434, tc_fun(_1413436, tc_HOL_Obool)), _1413432), hAPP(hAPP(c_COMBB(tc_fun(_1413436, tc_HOL_Obool), tc_fun(_1413436, tc_HOL_Obool), _1413434), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413436, tc_HOL_Obool)), _1413438)), _1413440)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413436, tc_HOL_Obool)), _1413438), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413434, tc_fun(_1413436, tc_HOL_Obool)), _1413432), _1413440)))], (34194 ^ _779300) ^ [_1413540, _1413542, _1413544, _1413546, _1413548] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413540, tc_fun(_1413542, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1413540), _1413544), _1413546)), _1413548) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413542, tc_HOL_Obool)), hAPP(_1413548, _1413544)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413540, tc_fun(_1413542, tc_HOL_Obool)), _1413546), _1413548)))], (34196 ^ _779300) ^ [_1413617, _1413619, _1413621, _1413623, _1413625, _1413627, _1413629, _1413631, _1413633] : [c_Equiv__Relations_Oequiv(_1413617, _1413619, _1413621), c_Equiv__Relations_Oequiv(_1413623, _1413625, _1413627), c_Equiv__Relations_Ocongruent2(_1413617, _1413623, tc_fun(_1413629, tc_HOL_Obool), _1413621, _1413627, _1413631), hBOOL(hAPP(hAPP(c_member(_1413623), _1413633), _1413625)), -(c_Equiv__Relations_Ocongruent(_1413617, tc_fun(_1413629, tc_HOL_Obool), _1413621, hAPP(hAPP(c_COMBB(tc_fun(_1413623, tc_fun(_1413629, tc_HOL_Obool)), tc_fun(_1413629, tc_HOL_Obool), _1413617), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413623, tc_fun(_1413629, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1413623, _1413623, _1413627), hAPP(hAPP(c_Set_Oinsert(_1413623), _1413633), c_Orderings_Obot__class_Obot(tc_fun(_1413623, tc_HOL_Obool)))))), _1413631)))], (34214 ^ _779300) ^ [_1414044] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1414044) = 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, _1414044)), 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))))))))], (34216 ^ _779300) ^ [_1414082, _1414084, _1414086, _1414088, _1414090, _1414092] : [c_Equiv__Relations_Oequiv(_1414082, _1414084, _1414086), c_Equiv__Relations_Ocongruent(_1414082, tc_fun(_1414088, tc_HOL_Obool), _1414086, _1414090), hBOOL(hAPP(hAPP(c_member(_1414082), _1414092), _1414084)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414082, tc_fun(_1414088, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1414082, _1414082, _1414086), hAPP(hAPP(c_Set_Oinsert(_1414082), _1414092), c_Orderings_Obot__class_Obot(tc_fun(_1414082, tc_HOL_Obool))))), _1414090) = hAPP(_1414090, _1414092))], (34230 ^ _779300) ^ [_1414383, _1414385, _1414387, _1414389, _1414391, _1414393, _1414395, _1414397] : [hBOOL(hAPP(hAPP(c_member(_1414383), _1414385), _1414387)), hBOOL(hAPP(hAPP(hAPP(_1414389, _1414385), _1414391), _1414393)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414383, tc_fun(_1414395, tc_fun(_1414397, tc_HOL_Obool))), _1414387), _1414389), _1414391), _1414393)))], (34240 ^ _779300) ^ [_1414621, _1414623] : [hAPP(c_Int_ORep__Integ, _1414621) = hAPP(c_Int_ORep__Integ, _1414623), -(_1414621 = _1414623)], (34246 ^ _779300) ^ [_1414706, _1414708] : [_1414706 = _1414708, -(hAPP(c_Int_ORep__Integ, _1414706) = hAPP(c_Int_ORep__Integ, _1414708))], (34252 ^ _779300) ^ [_1414797] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1414797)) = _1414797)], (34254 ^ _779300) ^ [_1414826, _1414828, _1414830, _1414832, _1414834, _1414836] : [c_Equiv__Relations_Ocongruent(_1414826, _1414828, _1414830, _1414832), hBOOL(hAPP(hAPP(c_member(tc_prod(_1414826, _1414826)), hAPP(hAPP(c_Product__Type_OPair(_1414826, _1414826), _1414834), _1414836)), _1414830)), -(hAPP(_1414832, _1414834) = hAPP(_1414832, _1414836))], (34264 ^ _779300) ^ [_1415025] : [-(hAPP(c_Int_Onat, _1415025) = 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, _1415025)), 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)))))))], (34266 ^ _779300) ^ [_1415063, _1415065, _1415067, _1415069, _1415071, _1415073, _1415075, _1415077] : [c_Equiv__Relations_Oequiv(_1415063, _1415065, _1415067), c_Equiv__Relations_Ocongruent2(_1415063, _1415069, _1415071, _1415067, _1415073, _1415075), hBOOL(hAPP(hAPP(c_member(_1415063), _1415077), _1415065)), -(c_Equiv__Relations_Ocongruent(_1415069, _1415071, _1415073, hAPP(_1415075, _1415077)))], (34280 ^ _779300) ^ [_1415314, _1415316, _1415318, _1415320, _1415322, _1415324, _1415326] : [c_Equiv__Relations_Oequiv(_1415314, _1415316, _1415318), c_Equiv__Relations_Ocongruent(_1415314, tc_fun(_1415320, tc_HOL_Obool), _1415318, _1415322), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415314, tc_fun(_1415320, tc_HOL_Obool)), _1415324), _1415322) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415314, tc_fun(_1415320, tc_HOL_Obool)), _1415326), _1415322), hBOOL(hAPP(hAPP(c_member(tc_fun(_1415314, tc_HOL_Obool)), _1415324), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1415314), _1415316), _1415318))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1415314, tc_HOL_Obool)), _1415326), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1415314), _1415316), _1415318))), 34302 ^ _779300 : [(34303 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415314), 34301 ^ [_1415314, _1415316, _1415318, _1415320, _1415322, _1415324, _1415326]), _1415316)))], (34306 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415314), 34304 ^ [_1415314, _1415316, _1415318, _1415320, _1415322, _1415324, _1415326]), _1415316)))], (34308 ^ _779300) ^ [] : [-(hAPP(_1415322, 34301 ^ [_1415314, _1415316, _1415318, _1415320, _1415322, _1415324, _1415326]) = hAPP(_1415322, 34304 ^ [_1415314, _1415316, _1415318, _1415320, _1415322, _1415324, _1415326]))], (34310 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1415314, _1415314)), hAPP(hAPP(c_Product__Type_OPair(_1415314, _1415314), 34301 ^ [_1415314, _1415316, _1415318, _1415320, _1415322, _1415324, _1415326]), 34304 ^ [_1415314, _1415316, _1415318, _1415320, _1415322, _1415324, _1415326])), _1415318))]], -(_1415324 = _1415326)], (34314 ^ _779300) ^ [_1416284, _1416286, _1416288, _1416290, _1416292, _1416294, _1416296, _1416298, _1416300, _1416302, _1416304] : [c_Equiv__Relations_Oequiv(_1416284, _1416286, _1416288), c_Equiv__Relations_Oequiv(_1416290, _1416292, _1416294), c_Equiv__Relations_Ocongruent2(_1416284, _1416290, tc_fun(_1416296, tc_HOL_Obool), _1416288, _1416294, _1416298), hBOOL(hAPP(hAPP(c_member(tc_fun(_1416284, tc_HOL_Obool)), _1416300), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1416284), _1416286), _1416288))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1416290, tc_HOL_Obool)), _1416302), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1416290), _1416292), _1416294))), 34336 ^ _779300 : [(34337 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416284), 34335 ^ [_1416284, _1416286, _1416288, _1416290, _1416292, _1416294, _1416296, _1416298, _1416300, _1416302, _1416304]), _1416286)))], (34340 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416290), 34338 ^ [_1416284, _1416286, _1416288, _1416290, _1416292, _1416294, _1416296, _1416298, _1416300, _1416302, _1416304]), _1416292)))], (34342 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1416296, tc_HOL_Obool)), hAPP(hAPP(_1416298, 34335 ^ [_1416284, _1416286, _1416288, _1416290, _1416292, _1416294, _1416296, _1416298, _1416300, _1416302, _1416304]), 34338 ^ [_1416284, _1416286, _1416288, _1416290, _1416292, _1416294, _1416296, _1416298, _1416300, _1416302, _1416304])), _1416304))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1416296, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416284, tc_fun(_1416296, tc_HOL_Obool)), _1416300), hAPP(hAPP(c_COMBB(tc_fun(_1416290, tc_fun(_1416296, tc_HOL_Obool)), tc_fun(_1416296, tc_HOL_Obool), _1416284), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416290, tc_fun(_1416296, tc_HOL_Obool)), _1416302)), _1416298))), _1416304)))], (34346 ^ _779300) ^ [_1417286, _1417288, _1417290, _1417292, _1417294, _1417296, _1417298] : [c_Equiv__Relations_Oequiv(_1417286, _1417288, _1417290), c_Equiv__Relations_Ocongruent(_1417286, tc_fun(_1417292, tc_HOL_Obool), _1417290, _1417294), hBOOL(hAPP(hAPP(c_member(tc_fun(_1417286, tc_HOL_Obool)), _1417296), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1417286), _1417288), _1417290))), 34360 ^ _779300 : [(34361 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417286), 34359 ^ [_1417286, _1417288, _1417290, _1417292, _1417294, _1417296, _1417298]), _1417288)))], (34363 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1417292, tc_HOL_Obool)), hAPP(_1417294, 34359 ^ [_1417286, _1417288, _1417290, _1417292, _1417294, _1417296, _1417298])), _1417298))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1417292, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417286, tc_fun(_1417292, tc_HOL_Obool)), _1417296), _1417294)), _1417298)))], (34367 ^ _779300) ^ [_1417827, _1417829, _1417831, _1417833, _1417835, _1417837, _1417839] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417827, tc_fun(_1417829, tc_fun(_1417831, tc_HOL_Obool))), _1417833), _1417835), _1417837), _1417839)), 34371 ^ _779300 : [(34372 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417827), 34370 ^ [_1417827, _1417829, _1417831, _1417833, _1417835, _1417837, _1417839]), _1417833)))], (34374 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1417835, 34370 ^ [_1417827, _1417829, _1417831, _1417833, _1417835, _1417837, _1417839]), _1417837), _1417839)))]]], (34376 ^ _779300) ^ [_1418045, _1418047, _1418049, _1418051, _1418053, _1418055, _1418057] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418045, tc_fun(_1418047, tc_fun(_1418049, tc_HOL_Obool))), _1418051), _1418053), _1418055), _1418057))), 34377 ^ _779300 : [(34378 ^ _779300) ^ [_1418130] : [hBOOL(hAPP(hAPP(c_member(_1418045), _1418130), _1418051)), hBOOL(hAPP(hAPP(hAPP(_1418053, _1418130), _1418055), _1418057))]]], (34386 ^ _779300) ^ [_1418298, _1418300] : [-(c_Relation_OId__on(_1418298, _1418300) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418298, tc_fun(tc_prod(_1418298, _1418298), tc_HOL_Obool)), _1418300), hAPP(hAPP(c_COMBC(_1418298, tc_fun(tc_prod(_1418298, _1418298), tc_HOL_Obool), tc_fun(tc_prod(_1418298, _1418298), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1418298, _1418298), tc_fun(tc_fun(tc_prod(_1418298, _1418298), tc_HOL_Obool), tc_fun(tc_prod(_1418298, _1418298), tc_HOL_Obool)), _1418298), c_Set_Oinsert(tc_prod(_1418298, _1418298))), hAPP(hAPP(c_COMBS(_1418298, _1418298, tc_prod(_1418298, _1418298)), c_Product__Type_OPair(_1418298, _1418298)), c_COMBI(_1418298)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1418298, _1418298), tc_HOL_Obool)))))], (34388 ^ _779300) ^ [_1418422, _1418424, _1418426, _1418428, _1418430, _1418432, _1418434] : [-(hAPP(c_Product__Type_Oapsnd(_1418422, _1418424, _1418426, _1418428), hAPP(c_Product__Type_Oapfst(_1418430, _1418426, _1418422, _1418432), _1418434)) = hAPP(hAPP(c_Product__Type_OPair(_1418426, _1418424), hAPP(_1418432, hAPP(c_Product__Type_Ofst(_1418430, _1418422), _1418434))), hAPP(_1418428, hAPP(c_Product__Type_Osnd(_1418430, _1418422), _1418434))))], (34390 ^ _779300) ^ [_1418500, _1418502, _1418504, _1418506, _1418508, _1418510, _1418512] : [-(hAPP(c_Product__Type_Oapfst(_1418500, _1418502, _1418504, _1418506), hAPP(c_Product__Type_Oapsnd(_1418508, _1418504, _1418500, _1418510), _1418512)) = hAPP(hAPP(c_Product__Type_OPair(_1418502, _1418504), hAPP(_1418506, hAPP(c_Product__Type_Ofst(_1418500, _1418508), _1418512))), hAPP(_1418510, hAPP(c_Product__Type_Osnd(_1418500, _1418508), _1418512))))], (34392 ^ _779300) ^ [_1418578, _1418580, _1418582, _1418584, _1418586, _1418588] : [-(hAPP(c_Product__Type_Oapfst(_1418578, _1418580, _1418582, _1418584), hAPP(hAPP(c_Product__Type_OPair(_1418578, _1418582), _1418586), _1418588)) = hAPP(hAPP(c_Product__Type_OPair(_1418580, _1418582), hAPP(_1418584, _1418586)), _1418588))], (34394 ^ _779300) ^ [_1418640, _1418642, _1418644, _1418646, _1418648] : [-(hAPP(c_Product__Type_Ofst(_1418640, _1418642), hAPP(c_Product__Type_Oapfst(_1418644, _1418640, _1418642, _1418646), _1418648)) = hAPP(_1418646, hAPP(c_Product__Type_Ofst(_1418644, _1418642), _1418648)))], (34396 ^ _779300) ^ [_1418721, _1418723, _1418725, _1418727, _1418729, _1418731] : [hAPP(c_Product__Type_Oapfst(_1418721, _1418723, _1418725, _1418727), _1418729) = hAPP(c_Product__Type_Oapfst(_1418721, _1418723, _1418725, _1418731), _1418729), -(hAPP(_1418727, hAPP(c_Product__Type_Ofst(_1418721, _1418725), _1418729)) = hAPP(_1418731, hAPP(c_Product__Type_Ofst(_1418721, _1418725), _1418729)))], (34402 ^ _779300) ^ [_1418870, _1418872, _1418874, _1418876, _1418878, _1418880] : [hAPP(_1418876, hAPP(c_Product__Type_Ofst(_1418870, _1418874), _1418878)) = hAPP(_1418880, hAPP(c_Product__Type_Ofst(_1418870, _1418874), _1418878)), -(hAPP(c_Product__Type_Oapfst(_1418870, _1418872, _1418874, _1418876), _1418878) = hAPP(c_Product__Type_Oapfst(_1418870, _1418872, _1418874, _1418880), _1418878))], (34408 ^ _779300) ^ [_1419025, _1419027, _1419029, _1419031, _1419033] : [-(hAPP(c_Product__Type_Osnd(_1419025, _1419027), hAPP(c_Product__Type_Oapfst(_1419029, _1419025, _1419027, _1419031), _1419033)) = hAPP(c_Product__Type_Osnd(_1419029, _1419027), _1419033))], (34410 ^ _779300) ^ [_1419076, _1419078, _1419080, _1419082, _1419084, _1419086, _1419088] : [-(hAPP(c_Product__Type_Oapsnd(_1419076, _1419078, _1419080, _1419082), hAPP(c_Product__Type_Oapfst(_1419084, _1419080, _1419076, _1419086), _1419088)) = hAPP(c_Product__Type_Oapfst(_1419084, _1419080, _1419078, _1419086), hAPP(c_Product__Type_Oapsnd(_1419076, _1419078, _1419084, _1419082), _1419088)))], (34412 ^ _779300) ^ [_1419143, _1419145] : [-(c_Relation_OId__on(_1419143, _1419145) = hAPP(c_Product__Type_Oprod_Oprod__case(_1419143, _1419143, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1419143, tc_HOL_Obool, tc_fun(_1419143, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419143, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1419143, tc_HOL_Obool)), _1419143), c_COMBC(_1419143, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419143, tc_HOL_Obool), tc_fun(_1419143, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1419143), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1419143), c_fconj)), c_fequal))), _1419145)))], (34414 ^ _779300) ^ [_1419237] : [-(c_Relation_OId__on(_1419237, c_Orderings_Obot__class_Obot(tc_fun(_1419237, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1419237, _1419237), tc_HOL_Obool)))], (34416 ^ _779300) ^ [_1419276, _1419278, _1419280] : [-(hAPP(c_Relation_OImage(_1419276, _1419276, c_Relation_OId__on(_1419276, _1419278)), _1419280) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1419276, tc_HOL_Obool)), _1419278), _1419280))], (34418 ^ _779300) ^ [_1419345, _1419347, _1419349, _1419351] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1419345, _1419345)), hAPP(hAPP(c_Product__Type_OPair(_1419345, _1419345), _1419347), _1419349)), c_Relation_OId__on(_1419345, _1419351))), 34421 ^ _779300 : [(34422 ^ _779300) ^ [] : [-(_1419347 = _1419349)], (34424 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1419345), _1419347), _1419351)))]]], (34426 ^ _779300) ^ [_1419506, _1419508, _1419510, _1419512] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1419506, _1419506)), hAPP(hAPP(c_Product__Type_OPair(_1419506, _1419506), _1419508), _1419510)), c_Relation_OId__on(_1419506, _1419512)))), _1419508 = _1419510, hBOOL(hAPP(hAPP(c_member(_1419506), _1419508), _1419512))], (34436 ^ _779300) ^ [_1419703, _1419705, _1419707, _1419709] : [_1419703 = _1419705, hBOOL(hAPP(hAPP(c_member(_1419707), _1419703), _1419709)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1419707, _1419707)), hAPP(hAPP(c_Product__Type_OPair(_1419707, _1419707), _1419703), _1419705)), c_Relation_OId__on(_1419707, _1419709))))], (34446 ^ _779300) ^ [_1419898, _1419900, _1419902] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1419898, _1419898)), _1419900), c_Relation_OId__on(_1419898, _1419902))), 34450 ^ _779300 : [(34451 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1419898), 34449 ^ [_1419898, _1419900, _1419902]), _1419902)))], (34453 ^ _779300) ^ [] : [-(_1419900 = hAPP(hAPP(c_Product__Type_OPair(_1419898, _1419898), 34449 ^ [_1419898, _1419900, _1419902]), 34449 ^ [_1419898, _1419900, _1419902]))]]], (34455 ^ _779300) ^ [_1420097, _1420099, _1420101] : [class_Lattices_Oboolean__algebra(_1420097), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1420097), _1420099), _1420101) = c_Orderings_Obot__class_Obot(_1420097), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1420097), _1420099), _1420101) = c_Orderings_Otop__class_Otop(_1420097), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1420097), _1420099) = _1420101)], (34469 ^ _779300) ^ [_1420332, _1420334, _1420336, _1420338, _1420340] : [class_Groups_Ocomm__monoid__add(_1420332), class_Groups_Ocomm__monoid__mult(_1420332), _1420334 = _1420336, c_Nat__Transfer_Onat__set(_1420336), 34487 ^ _779300 : [(34488 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34486 ^ [_1420332, _1420334, _1420336, _1420338, _1420340])))], (34490 ^ _779300) ^ [] : [hAPP(_1420338, 34486 ^ [_1420332, _1420334, _1420336, _1420338, _1420340]) = hAPP(_1420340, 34486 ^ [_1420332, _1420334, _1420336, _1420338, _1420340])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1420332), _1420338), _1420334) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1420332), _1420340), _1420336))], (34494 ^ _779300) ^ [_1420795, _1420797] : [-(hBOOL(hAPP(hAPP(c_member(_1420795), _1420797), c_Orderings_Otop__class_Otop(tc_fun(_1420795, tc_HOL_Obool)))))], (34496 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (34498 ^ _779300) ^ [_1420856] : [-(hAPP(c_Set_OPow(_1420856), c_Orderings_Otop__class_Otop(tc_fun(_1420856, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1420856, tc_HOL_Obool), tc_HOL_Obool)))], (34500 ^ _779300) ^ [] : [-(hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit), c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34502 ^ _779300) ^ [_1420915, _1420917] : [-(c_Sum__Type_OPlus(_1420915, _1420917, c_Orderings_Otop__class_Otop(tc_fun(_1420915, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1420917, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1420915, _1420917), tc_HOL_Obool)))], (34504 ^ _779300) ^ [_1420963, _1420965, _1420967] : [class_Orderings_Otop(_1420963), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1420965, _1420963)), _1420967) = c_Orderings_Otop__class_Otop(_1420963))], (34510 ^ _779300) ^ [_1421060, _1421062] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421060, tc_HOL_Obool)), _1421062), c_Orderings_Otop__class_Otop(tc_fun(_1421060, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1421060, tc_HOL_Obool)))], (34512 ^ _779300) ^ [_1421106, _1421108] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421106, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1421106, tc_HOL_Obool))), _1421108) = c_Orderings_Otop__class_Otop(tc_fun(_1421106, tc_HOL_Obool)))], (34514 ^ _779300) ^ [_1421161] : [c_Orderings_Otop__class_Otop(tc_fun(_1421161, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1421161, tc_HOL_Obool))], (34516 ^ _779300) ^ [_1421194, _1421196] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1421194, tc_HOL_Obool)), _1421196), c_Orderings_Otop__class_Otop(tc_fun(_1421194, tc_HOL_Obool)))))], (34518 ^ _779300) ^ [_1421234, _1421236] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1421234, _1421236)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1421234, _1421236), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1421236), c_Orderings_Otop__class_Otop(tc_fun(_1421236, tc_HOL_Obool)))))], (34524 ^ _779300) ^ [_1421359, _1421361] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1421359), c_Orderings_Otop__class_Otop(tc_fun(_1421359, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421361), c_Orderings_Otop__class_Otop(tc_fun(_1421361, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1421359, _1421361)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1421359, _1421361), tc_HOL_Obool)))))], (34534 ^ _779300) ^ [_1421566] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1421566)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1421566), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1421566), c_Orderings_Otop__class_Otop(tc_fun(_1421566, tc_HOL_Obool)))))], (34540 ^ _779300) ^ [_1421681] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1421681), c_Orderings_Otop__class_Otop(tc_fun(_1421681, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1421681)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1421681), tc_HOL_Obool)))))], (34546 ^ _779300) ^ [_1421802] : [class_Finite__Set_Ofinite(_1421802), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1421802), c_Orderings_Otop__class_Otop(tc_fun(_1421802, tc_HOL_Obool)))))], (34552 ^ _779300) ^ [_1421908, _1421910] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1421908, _1421910)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1421908, _1421910), tc_HOL_Obool)))), 34555 ^ _779300 : [(34556 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1421908), c_Orderings_Otop__class_Otop(tc_fun(_1421908, tc_HOL_Obool)))))], (34558 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1421910), c_Orderings_Otop__class_Otop(tc_fun(_1421910, tc_HOL_Obool)))))]]], (34560 ^ _779300) ^ [_1422073, _1422075] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1422073, _1422075)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1422073, _1422075), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422073), c_Orderings_Otop__class_Otop(tc_fun(_1422073, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422075), c_Orderings_Otop__class_Otop(tc_fun(_1422075, tc_HOL_Obool))))], (34570 ^ _779300) ^ [_1422270, _1422272] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422270, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1422270, tc_HOL_Obool))), _1422272) = _1422272)], (34572 ^ _779300) ^ [_1422311, _1422313] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422311, tc_HOL_Obool)), _1422313), c_Orderings_Otop__class_Otop(tc_fun(_1422311, tc_HOL_Obool))) = _1422313)], (34574 ^ _779300) ^ [_1422352, _1422354, _1422356, _1422358, _1422360] : [-(hAPP(c_Set_Oimage(_1422352, _1422354, hAPP(hAPP(c_COMBB(_1422356, _1422354, _1422352), _1422358), _1422360)), c_Orderings_Otop__class_Otop(tc_fun(_1422352, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1422356, _1422354, _1422358), hAPP(c_Set_Oimage(_1422352, _1422356, _1422360), c_Orderings_Otop__class_Otop(tc_fun(_1422352, tc_HOL_Obool)))))], (34576 ^ _779300) ^ [] : [-(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))], (34578 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (34580 ^ _779300) ^ [] : [-(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))))], (34582 ^ _779300) ^ [_1422484, _1422486, _1422488, _1422490, _1422492] : [c_Fun_Oinj__on(_1422484, _1422486, _1422488, c_Orderings_Otop__class_Otop(tc_fun(_1422484, tc_HOL_Obool))), 34585 ^ _779300 : [(34586 ^ _779300) ^ [] : [hAPP(_1422488, _1422490) = hAPP(_1422488, _1422492), -(_1422490 = _1422492)], (34592 ^ _779300) ^ [] : [_1422490 = _1422492, -(hAPP(_1422488, _1422490) = hAPP(_1422488, _1422492))]]], (34598 ^ _779300) ^ [_1422741, _1422743, _1422745, _1422747, _1422749] : [c_Fun_Oinj__on(_1422741, _1422743, _1422745, c_Orderings_Otop__class_Otop(tc_fun(_1422741, tc_HOL_Obool))), hAPP(_1422745, _1422747) = hAPP(_1422745, _1422749), -(_1422747 = _1422749)], (34608 ^ _779300) ^ [_1422908, _1422910] : [class_Orderings_Otop(_1422908), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422908), _1422910), c_Orderings_Otop__class_Otop(_1422908))))], (34614 ^ _779300) ^ [_1423001, _1423003] : [class_Lattices_Obounded__lattice__top(_1423001), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1423001), _1423003), c_Orderings_Otop__class_Otop(_1423001)) = c_Orderings_Otop__class_Otop(_1423001))], (34620 ^ _779300) ^ [_1423100, _1423102] : [class_Lattices_Obounded__lattice__top(_1423100), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1423100), c_Orderings_Otop__class_Otop(_1423100)), _1423102) = c_Orderings_Otop__class_Otop(_1423100))], (34626 ^ _779300) ^ [_1423199, _1423201, _1423203] : [class_Lattices_Obounded__lattice__top(_1423199), 34629 ^ _779300 : [(34630 ^ _779300) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423199), _1423201), _1423203) = c_Orderings_Otop__class_Otop(_1423199), 34633 ^ _779300 : [(34634 ^ _779300) ^ [] : [-(_1423201 = c_Orderings_Otop__class_Otop(_1423199))], (34636 ^ _779300) ^ [] : [-(_1423203 = c_Orderings_Otop__class_Otop(_1423199))]]], (34638 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423199), _1423201), _1423203) = c_Orderings_Otop__class_Otop(_1423199)), _1423201 = c_Orderings_Otop__class_Otop(_1423199), _1423203 = c_Orderings_Otop__class_Otop(_1423199)]]], (34648 ^ _779300) ^ [_1423526, _1423528] : [class_Lattices_Obounded__lattice__top(_1423526), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423526), _1423528), c_Orderings_Otop__class_Otop(_1423526)) = _1423528)], (34654 ^ _779300) ^ [_1423621, _1423623] : [class_Lattices_Obounded__lattice__top(_1423621), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423621), c_Orderings_Otop__class_Otop(_1423621)), _1423623) = _1423623)], (34660 ^ _779300) ^ [] : [-(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)))], (34662 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34664 ^ _779300) ^ [_1423752, _1423754, _1423756, _1423758] : [-(hBOOL(hAPP(hAPP(c_member(_1423752), hAPP(_1423754, _1423756)), hAPP(c_Set_Oimage(_1423758, _1423752, _1423754), c_Orderings_Otop__class_Otop(tc_fun(_1423758, tc_HOL_Obool))))))], (34666 ^ _779300) ^ [_1423803, _1423805, _1423807, _1423809, _1423811] : [_1423803 = hAPP(_1423805, _1423807), -(hBOOL(hAPP(hAPP(c_member(_1423809), _1423803), hAPP(c_Set_Oimage(_1423811, _1423809, _1423805), c_Orderings_Otop__class_Otop(tc_fun(_1423811, tc_HOL_Obool))))))], (34672 ^ _779300) ^ [] : [-(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)))], (34674 ^ _779300) ^ [_1423948, _1423950] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1423948, tc_HOL_Obool)), _1423950), c_Orderings_Otop__class_Otop(tc_fun(_1423948, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1423948, tc_HOL_Obool)))], (34676 ^ _779300) ^ [_1423994, _1423996] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1423994), c_Orderings_Otop__class_Otop(tc_fun(_1423994, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1423994), _1423996) = hAPP(c_Finite__Set_Ocard(_1423994), c_Orderings_Otop__class_Otop(tc_fun(_1423994, tc_HOL_Obool))), -(_1423996 = c_Orderings_Otop__class_Otop(tc_fun(_1423994, tc_HOL_Obool)))], (34686 ^ _779300) ^ [_1424181, _1424183, _1424185, _1424187, _1424189] : [c_Fun_Oinj__on(_1424181, _1424183, _1424185, c_Orderings_Otop__class_Otop(tc_fun(_1424181, tc_HOL_Obool))), 34689 ^ _779300 : [(34690 ^ _779300) ^ [] : [hAPP(c_Set_Oimage(_1424181, _1424183, _1424185), _1424187) = hAPP(c_Set_Oimage(_1424181, _1424183, _1424185), _1424189), -(_1424187 = _1424189)], (34696 ^ _779300) ^ [] : [_1424187 = _1424189, -(hAPP(c_Set_Oimage(_1424181, _1424183, _1424185), _1424187) = hAPP(c_Set_Oimage(_1424181, _1424183, _1424185), _1424189))]]], (34702 ^ _779300) ^ [_1424462] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1424462, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1424462, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1424462, tc_HOL_Obool)))], (34704 ^ _779300) ^ [_1424503] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1424503, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1424503, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1424503, tc_HOL_Obool)))], (34706 ^ _779300) ^ [_1424544, _1424546] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1424544), _1424546)), 34709 ^ _779300 : [(34710 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1424544), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1424544, tc_HOL_Obool)), _1424546))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1424544), c_Orderings_Otop__class_Otop(tc_fun(_1424544, tc_HOL_Obool)))))], (34716 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1424544), c_Orderings_Otop__class_Otop(tc_fun(_1424544, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1424544), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1424544, tc_HOL_Obool)), _1424546))))]]], (34722 ^ _779300) ^ [_1424822, _1424824] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424822, tc_HOL_Obool)), _1424824), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1424822, tc_HOL_Obool)), _1424824)) = c_Orderings_Otop__class_Otop(tc_fun(_1424822, tc_HOL_Obool)))], (34724 ^ _779300) ^ [_1424871, _1424873] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424871, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1424871, tc_HOL_Obool)), _1424873)), _1424873) = c_Orderings_Otop__class_Otop(tc_fun(_1424871, tc_HOL_Obool)))], (34726 ^ _779300) ^ [_1424920, _1424922] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1424920, tc_HOL_Obool)), _1424922) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1424920, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1424920, tc_HOL_Obool))), _1424922))], (34728 ^ _779300) ^ [_1424990, _1424992, _1424994, _1424996] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1424990, tc_fun(_1424992, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1424990, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1424992, tc_HOL_Obool), tc_fun(_1424992, tc_HOL_Obool), _1424990), hAPP(c_COMBC(_1424992, tc_fun(_1424992, tc_HOL_Obool), tc_HOL_Obool), c_member(_1424992))), _1424994)), _1424996)), -(hBOOL(hAPP(hAPP(c_member(_1424992), _1424996), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1424990, tc_fun(_1424992, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1424990, tc_HOL_Obool))), _1424994))))], (34734 ^ _779300) ^ [_1425209, _1425211, _1425213, _1425215] : [hBOOL(hAPP(hAPP(c_member(_1425211), _1425215), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425209, tc_fun(_1425211, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1425209, tc_HOL_Obool))), _1425213))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425209, tc_fun(_1425211, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1425209, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1425211, tc_HOL_Obool), tc_fun(_1425211, tc_HOL_Obool), _1425209), hAPP(c_COMBC(_1425211, tc_fun(_1425211, tc_HOL_Obool), tc_HOL_Obool), c_member(_1425211))), _1425213)), _1425215)))], (34740 ^ _779300) ^ [_1425434, _1425436, _1425438, _1425440, _1425442] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1425434), hAPP(c_Set_Oimage(_1425436, _1425434, _1425438), c_Orderings_Otop__class_Otop(tc_fun(_1425436, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1425440), hAPP(c_Set_Oimage(_1425436, _1425440, hAPP(hAPP(c_COMBB(_1425434, _1425440, _1425436), _1425442), _1425438)), c_Orderings_Otop__class_Otop(tc_fun(_1425436, tc_HOL_Obool))))))], (34746 ^ _779300) ^ [_1425601, _1425603, _1425605, _1425607] : [c_Fun_Oinj__on(_1425601, _1425603, _1425605, c_Orderings_Otop__class_Otop(tc_fun(_1425601, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1425601, _1425603, c_Orderings_Otop__class_Otop(tc_fun(_1425601, tc_HOL_Obool)), _1425605), hAPP(_1425605, _1425607)) = _1425607)], (34752 ^ _779300) ^ [_1425728, _1425730] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1425728, _1425730)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1425728, _1425730), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1425730), c_Orderings_Otop__class_Otop(tc_fun(_1425730, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1425728), c_Orderings_Otop__class_Otop(tc_fun(_1425728, tc_HOL_Obool)))))], (34762 ^ _779300) ^ [_1425888] : [class_Nat_Osemiring__char__0(_1425888), -(c_Fun_Oinj__on(tc_Nat_Onat, _1425888, c_Nat_Osemiring__1__class_Oof__nat(_1425888), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (34768 ^ _779300) ^ [] : [-(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)))], (34770 ^ _779300) ^ [_1425987, _1425989, _1425991, _1425993] : [c_Fun_Oinj__on(_1425987, _1425989, _1425991, c_Orderings_Otop__class_Otop(tc_fun(_1425987, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1425987, tc_fun(_1425993, _1425989), hAPP(hAPP(c_COMBB(_1425989, tc_fun(_1425993, _1425989), _1425987), c_COMBK(_1425989, _1425993)), _1425991), c_Orderings_Otop__class_Otop(tc_fun(_1425987, tc_HOL_Obool))))], (34776 ^ _779300) ^ [_1426134] : [class_Lattices_Oboolean__algebra(_1426134), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1426134), c_Orderings_Obot__class_Obot(_1426134)) = c_Orderings_Otop__class_Otop(_1426134))], (34782 ^ _779300) ^ [_1426225] : [class_Lattices_Oboolean__algebra(_1426225), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1426225), c_Orderings_Otop__class_Otop(_1426225)) = c_Orderings_Obot__class_Obot(_1426225))], (34788 ^ _779300) ^ [_1426316, _1426318] : [class_Lattices_Oboolean__algebra(_1426316), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1426316), _1426318), hAPP(c_Groups_Ouminus__class_Ouminus(_1426316), _1426318)) = c_Orderings_Otop__class_Otop(_1426316))], (34794 ^ _779300) ^ [_1426421, _1426423] : [class_Lattices_Oboolean__algebra(_1426421), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1426421), hAPP(c_Groups_Ouminus__class_Ouminus(_1426421), _1426423)), _1426423) = c_Orderings_Otop__class_Otop(_1426421))], (34800 ^ _779300) ^ [_1426526, _1426528, _1426530, _1426532, _1426534] : [c_Fun_Oinj__on(_1426526, _1426528, _1426530, c_Orderings_Otop__class_Otop(tc_fun(_1426526, tc_HOL_Obool))), 34803 ^ _779300 : [(34804 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1426528), hAPP(_1426530, _1426532)), hAPP(c_Set_Oimage(_1426526, _1426528, _1426530), _1426534))), -(hBOOL(hAPP(hAPP(c_member(_1426526), _1426532), _1426534)))], (34810 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1426526), _1426532), _1426534)), -(hBOOL(hAPP(hAPP(c_member(_1426528), hAPP(_1426530, _1426532)), hAPP(c_Set_Oimage(_1426526, _1426528, _1426530), _1426534))))]]], (34816 ^ _779300) ^ [_1426837, _1426839, _1426841, _1426843] : [c_Fun_Oinj__on(_1426837, _1426839, _1426841, c_Orderings_Otop__class_Otop(tc_fun(_1426837, tc_HOL_Obool))), 34819 ^ _779300 : [(34820 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1426839), _1426843), hAPP(c_Set_Oimage(_1426837, _1426839, _1426841), c_Orderings_Otop__class_Otop(tc_fun(_1426837, tc_HOL_Obool))))), 34824 ^ _779300 : [(34825 ^ _779300) ^ [] : [-(_1426843 = hAPP(_1426841, 34823 ^ [_1426837, _1426839, _1426841, _1426843]))], (34827 ^ _779300) ^ [_1427102] : [_1426843 = hAPP(_1426841, _1427102), -(_1427102 = 34823 ^ [_1426837, _1426839, _1426841, _1426843])]]], (34833 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1426839), _1426843), hAPP(c_Set_Oimage(_1426837, _1426839, _1426841), c_Orderings_Otop__class_Otop(tc_fun(_1426837, tc_HOL_Obool)))))), 34834 ^ _779300 : [(34835 ^ _779300) ^ [_1427240] : [_1426843 = hAPP(_1426841, _1427240), 34839 ^ _779300 : [(34840 ^ _779300) ^ [] : [-(_1426843 = hAPP(_1426841, 34838 ^ [_1426837, _1426839, _1426841, _1426843, _1427240]))], (34842 ^ _779300) ^ [] : [34838 ^ [_1426837, _1426839, _1426841, _1426843, _1427240] = _1427240]]]]]]], (34846 ^ _779300) ^ [_1427468, _1427470] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1427468), c_Orderings_Otop__class_Otop(tc_fun(_1427468, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1427468, _1427468, _1427470), c_Orderings_Otop__class_Otop(tc_fun(_1427468, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1427468, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1427468, _1427468, _1427470, c_Orderings_Otop__class_Otop(tc_fun(_1427468, tc_HOL_Obool))))], (34856 ^ _779300) ^ [_1427663, _1427665] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1427663), c_Orderings_Otop__class_Otop(tc_fun(_1427663, tc_HOL_Obool)))), c_Fun_Oinj__on(_1427663, _1427663, _1427665, c_Orderings_Otop__class_Otop(tc_fun(_1427663, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1427663, _1427663, _1427665), c_Orderings_Otop__class_Otop(tc_fun(_1427663, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1427663, tc_HOL_Obool)))], (34866 ^ _779300) ^ [_1427858, _1427860, _1427862, _1427864, _1427866] : [c_Fun_Oinj__on(_1427858, _1427860, _1427862, c_Orderings_Otop__class_Otop(tc_fun(_1427858, tc_HOL_Obool))), 34869 ^ _779300 : [(34870 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427860, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1427858, _1427860, _1427862), _1427864)), hAPP(c_Set_Oimage(_1427858, _1427860, _1427862), _1427866))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427858, tc_HOL_Obool)), _1427864), _1427866)))], (34876 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427858, tc_HOL_Obool)), _1427864), _1427866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427860, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1427858, _1427860, _1427862), _1427864)), hAPP(c_Set_Oimage(_1427858, _1427860, _1427862), _1427866))))]]], (34882 ^ _779300) ^ [_1428199, _1428201, _1428203, _1428205, _1428207] : [c_Fun_Oinj__on(_1428199, _1428201, _1428203, c_Orderings_Otop__class_Otop(tc_fun(_1428199, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1428199, _1428201, _1428203), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428199, tc_HOL_Obool)), _1428205), _1428207)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428201, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1428199, _1428201, _1428203), _1428205)), hAPP(c_Set_Oimage(_1428199, _1428201, _1428203), _1428207)))], (34888 ^ _779300) ^ [_1428382, _1428384, _1428386, _1428388, _1428390] : [c_Fun_Oinj__on(_1428382, _1428384, _1428386, c_Orderings_Otop__class_Otop(tc_fun(_1428382, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1428382, _1428384, _1428386), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1428382, tc_HOL_Obool)), _1428388), _1428390)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1428384, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1428382, _1428384, _1428386), _1428388)), hAPP(c_Set_Oimage(_1428382, _1428384, _1428386), _1428390)))], (34894 ^ _779300) ^ [_1428565, _1428567, _1428569, _1428571] : [hAPP(c_Set_Oimage(_1428565, _1428567, _1428569), c_Orderings_Otop__class_Otop(tc_fun(_1428565, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1428567, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428567, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1428567, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1428565, _1428567, _1428569), _1428571))), hAPP(c_Set_Oimage(_1428565, _1428567, _1428569), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1428565, tc_HOL_Obool)), _1428571)))))], (34900 ^ _779300) ^ [_1428760, _1428762] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1428760, 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(_1428760, tc_HOL_Obool)), tc_fun(_1428760, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1428760, tc_HOL_Obool)), tc_fun(_1428760, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1428760, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1428762)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1428760, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1428762))], (34902 ^ _779300) ^ [_1428856] : [-(c_Fun_Oinj__on(_1428856, tc_fun(_1428856, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1428856, tc_fun(_1428856, tc_HOL_Obool), tc_fun(_1428856, tc_HOL_Obool)), c_Set_Oinsert(_1428856)), c_Orderings_Obot__class_Obot(tc_fun(_1428856, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1428856, tc_HOL_Obool))))], (34904 ^ _779300) ^ [_1428912] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1428912), c_Orderings_Otop__class_Otop(tc_fun(_1428912, 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(_1428912), c_Orderings_Otop__class_Otop(tc_fun(_1428912, tc_HOL_Obool))))))], (34910 ^ _779300) ^ [] : [-(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))))], (34912 ^ _779300) ^ [_1429047, _1429049, _1429051, _1429053] : [c_Fun_Oinj__on(_1429047, _1429049, _1429051, c_Orderings_Otop__class_Otop(tc_fun(_1429047, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429049, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1429047, _1429049, _1429051), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1429047, tc_HOL_Obool)), _1429053))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1429049, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1429047, _1429049, _1429051), _1429053)))))], (34918 ^ _779300) ^ [] : [-(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))))], (34920 ^ _779300) ^ [_1429267, _1429269, _1429271, _1429273, _1429275, _1429277] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1429267, tc_fun(_1429269, tc_fun(_1429271, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1429267, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1429269, _1429271), tc_HOL_Obool), tc_fun(_1429269, tc_fun(_1429271, tc_HOL_Obool)), _1429267), hAPP(c_COMBC(_1429269, tc_fun(tc_prod(_1429269, _1429271), tc_HOL_Obool), tc_fun(_1429271, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429271, tc_fun(tc_fun(tc_prod(_1429269, _1429271), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1429269, _1429271), tc_HOL_Obool), tc_fun(_1429271, tc_HOL_Obool)), _1429269), c_COMBC(_1429271, tc_fun(tc_prod(_1429269, _1429271), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429271, tc_prod(_1429269, _1429271)), tc_fun(_1429271, tc_fun(tc_fun(tc_prod(_1429269, _1429271), tc_HOL_Obool), tc_HOL_Obool)), _1429269), hAPP(c_COMBB(tc_prod(_1429269, _1429271), tc_fun(tc_fun(tc_prod(_1429269, _1429271), tc_HOL_Obool), tc_HOL_Obool), _1429271), c_member(tc_prod(_1429269, _1429271)))), c_Product__Type_OPair(_1429269, _1429271))))), _1429273)), _1429275), _1429277)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1429269, _1429271)), hAPP(hAPP(c_Product__Type_OPair(_1429269, _1429271), _1429275), _1429277)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1429267, tc_fun(tc_prod(_1429269, _1429271), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1429267, tc_HOL_Obool))), _1429273))))], (34926 ^ _779300) ^ [_1429750, _1429752, _1429754, _1429756, _1429758, _1429760] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1429752, _1429754)), hAPP(hAPP(c_Product__Type_OPair(_1429752, _1429754), _1429758), _1429760)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1429750, tc_fun(tc_prod(_1429752, _1429754), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1429750, tc_HOL_Obool))), _1429756))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1429750, tc_fun(_1429752, tc_fun(_1429754, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1429750, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1429752, _1429754), tc_HOL_Obool), tc_fun(_1429752, tc_fun(_1429754, tc_HOL_Obool)), _1429750), hAPP(c_COMBC(_1429752, tc_fun(tc_prod(_1429752, _1429754), tc_HOL_Obool), tc_fun(_1429754, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429754, tc_fun(tc_fun(tc_prod(_1429752, _1429754), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1429752, _1429754), tc_HOL_Obool), tc_fun(_1429754, tc_HOL_Obool)), _1429752), c_COMBC(_1429754, tc_fun(tc_prod(_1429752, _1429754), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429754, tc_prod(_1429752, _1429754)), tc_fun(_1429754, tc_fun(tc_fun(tc_prod(_1429752, _1429754), tc_HOL_Obool), tc_HOL_Obool)), _1429752), hAPP(c_COMBB(tc_prod(_1429752, _1429754), tc_fun(tc_fun(tc_prod(_1429752, _1429754), tc_HOL_Obool), tc_HOL_Obool), _1429754), c_member(tc_prod(_1429752, _1429754)))), c_Product__Type_OPair(_1429752, _1429754))))), _1429756)), _1429758), _1429760)))], (34932 ^ _779300) ^ [_1430239, _1430241, _1430243, _1430245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430239, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430239, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34933 ^ [_1430239, _1430241, _1430243, _1430245])), _1430241)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430239, 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), 34933 ^ [_1430239, _1430241, _1430243, _1430245]), _1430243))), _1430245))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430239, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430239, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1430241)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430239, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1430245))))], (34939 ^ _779300) ^ [_1430569, _1430571, _1430573, _1430575] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430569, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34940 ^ [_1430569, _1430571, _1430573, _1430575])), _1430571) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430569, 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), 34940 ^ [_1430569, _1430571, _1430573, _1430575]), _1430573))), _1430575), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430569, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1430571) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430569, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1430575))], (34946 ^ _779300) ^ [_1430849, _1430851, _1430853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430849, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430849, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34947 ^ [_1430849, _1430851, _1430853])), _1430851)), _1430853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430849, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430849, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1430851)), _1430853)))], (34953 ^ _779300) ^ [_1431075, _1431077] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1431075, tc_HOL_Obool)), _1431077)))], (34955 ^ _779300) ^ [] : [-(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))], (34957 ^ _779300) ^ [_1431125, _1431127] : [-(hBOOL(hAPP(hAPP(c_member(_1431125), _1431127), c_Orderings_Otop__class_Otop(tc_fun(_1431125, tc_HOL_Obool)))))], (34959 ^ _779300) ^ [_1431177, _1431179] : [c_Equiv__Relations_Oequiv(_1431177, c_Orderings_Otop__class_Otop(tc_fun(_1431177, tc_HOL_Obool)), _1431179), -(c_Equiv__Relations_Oequivp(_1431177, hAPP(hAPP(c_COMBC(_1431177, tc_fun(tc_prod(_1431177, _1431177), tc_HOL_Obool), tc_fun(_1431177, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1431177, tc_fun(tc_fun(tc_prod(_1431177, _1431177), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1431177, _1431177), tc_HOL_Obool), tc_fun(_1431177, tc_HOL_Obool)), _1431177), c_COMBC(_1431177, tc_fun(tc_prod(_1431177, _1431177), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1431177, tc_prod(_1431177, _1431177)), tc_fun(_1431177, tc_fun(tc_fun(tc_prod(_1431177, _1431177), tc_HOL_Obool), tc_HOL_Obool)), _1431177), hAPP(c_COMBB(tc_prod(_1431177, _1431177), tc_fun(tc_fun(tc_prod(_1431177, _1431177), tc_HOL_Obool), tc_HOL_Obool), _1431177), c_member(tc_prod(_1431177, _1431177)))), c_Product__Type_OPair(_1431177, _1431177)))), _1431179)))], (34965 ^ _779300) ^ [_1431498, _1431500] : [c_Equiv__Relations_Oequivp(_1431498, hAPP(hAPP(c_COMBC(_1431498, tc_fun(tc_prod(_1431498, _1431498), tc_HOL_Obool), tc_fun(_1431498, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1431498, tc_fun(tc_fun(tc_prod(_1431498, _1431498), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1431498, _1431498), tc_HOL_Obool), tc_fun(_1431498, tc_HOL_Obool)), _1431498), c_COMBC(_1431498, tc_fun(tc_prod(_1431498, _1431498), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1431498, tc_prod(_1431498, _1431498)), tc_fun(_1431498, tc_fun(tc_fun(tc_prod(_1431498, _1431498), tc_HOL_Obool), tc_HOL_Obool)), _1431498), hAPP(c_COMBB(tc_prod(_1431498, _1431498), tc_fun(tc_fun(tc_prod(_1431498, _1431498), tc_HOL_Obool), tc_HOL_Obool), _1431498), c_member(tc_prod(_1431498, _1431498)))), c_Product__Type_OPair(_1431498, _1431498)))), _1431500)), -(c_Equiv__Relations_Oequiv(_1431498, c_Orderings_Otop__class_Otop(tc_fun(_1431498, tc_HOL_Obool)), _1431500))], (34971 ^ _779300) ^ [_1431825, _1431827, _1431829, _1431831, _1431833] : [c_Equiv__Relations_Oequivp(_1431825, _1431827), hBOOL(hAPP(hAPP(_1431827, _1431829), _1431831)), hBOOL(hAPP(hAPP(_1431827, _1431831), _1431833)), -(hBOOL(hAPP(hAPP(_1431827, _1431829), _1431833)))], (34985 ^ _779300) ^ [_1432054, _1432056, _1432058, _1432060] : [c_Equiv__Relations_Oequivp(_1432054, _1432056), hBOOL(hAPP(hAPP(_1432056, _1432058), _1432060)), -(hBOOL(hAPP(hAPP(_1432056, _1432060), _1432058)))], (34995 ^ _779300) ^ [_1432211, _1432213, _1432215] : [c_Equiv__Relations_Oequivp(_1432211, _1432213), -(hBOOL(hAPP(hAPP(_1432213, _1432215), _1432215)))], (35017 ^ _779300) ^ [_1432613, _1432615] : [-(c_Equiv__Relations_Oequivp(_1432613, _1432615)), 35022 ^ _779300 : [(35023 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1432615, 35018 ^ [_1432613, _1432615]), 35019 ^ [_1432613, _1432615])))], (35025 ^ _779300) ^ [] : [hAPP(_1432615, 35018 ^ [_1432613, _1432615]) = hAPP(_1432615, 35019 ^ [_1432613, _1432615])]], 35026 ^ _779300 : [(35027 ^ _779300) ^ [] : [-(hAPP(_1432615, 35018 ^ [_1432613, _1432615]) = hAPP(_1432615, 35019 ^ [_1432613, _1432615]))], (35029 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1432615, 35018 ^ [_1432613, _1432615]), 35019 ^ [_1432613, _1432615]))]]], (35001 ^ _779300) ^ [_1432315, _1432317] : [c_Equiv__Relations_Oequivp(_1432315, _1432317), 35004 ^ _779300 : [(35005 ^ _779300) ^ [_1432409, _1432411] : [hBOOL(hAPP(hAPP(_1432317, _1432411), _1432409)), -(hAPP(_1432317, _1432411) = hAPP(_1432317, _1432409))], (35011 ^ _779300) ^ [_1432508, _1432510] : [hAPP(_1432317, _1432510) = hAPP(_1432317, _1432508), -(hBOOL(hAPP(hAPP(_1432317, _1432510), _1432508)))]]], (35033 ^ _779300) ^ [_1432942] : [-(c_Equiv__Relations_Oequivp(_1432942, c_fequal))], (35035 ^ _779300) ^ [_1432965] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1432965)), c_Int_OInteg)))], (35037 ^ _779300) ^ [] : [-(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))], (35039 ^ _779300) ^ [_1433014, _1433016, _1433018, _1433020] : [c_Fun_Oinj__on(_1433014, _1433016, _1433018, c_Orderings_Otop__class_Otop(tc_fun(_1433014, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1433014, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1433014, _1433016, _1433018), hAPP(hAPP(c_Set_Oinsert(_1433016), _1433020), c_Orderings_Obot__class_Obot(tc_fun(_1433016, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1433014), c_HOL_OThe(_1433014, hAPP(hAPP(c_COMBC(_1433014, _1433016, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1433016, tc_fun(_1433016, tc_HOL_Obool), _1433014), c_fequal), _1433018)), _1433020))), c_Orderings_Obot__class_Obot(tc_fun(_1433014, tc_HOL_Obool))))))], (35045 ^ _779300) ^ [_1433265, _1433267, _1433269] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1433265, hAPP(hAPP(c_COMBC(_1433265, tc_fun(tc_prod(_1433265, _1433265), tc_HOL_Obool), tc_fun(_1433265, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1433265, tc_fun(tc_fun(tc_prod(_1433265, _1433265), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1433265, _1433265), tc_HOL_Obool), tc_fun(_1433265, tc_HOL_Obool)), _1433265), c_COMBC(_1433265, tc_fun(tc_prod(_1433265, _1433265), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1433265, tc_prod(_1433265, _1433265)), tc_fun(_1433265, tc_fun(tc_fun(tc_prod(_1433265, _1433265), tc_HOL_Obool), tc_HOL_Obool)), _1433265), hAPP(c_COMBB(tc_prod(_1433265, _1433265), tc_fun(tc_fun(tc_prod(_1433265, _1433265), tc_HOL_Obool), tc_HOL_Obool), _1433265), c_member(tc_prod(_1433265, _1433265)))), c_Product__Type_OPair(_1433265, _1433265)))), _1433267)), _1433269)), -(hBOOL(hAPP(hAPP(c_member(_1433265), _1433269), c_Wellfounded_Oacc(_1433265, _1433267))))], (35051 ^ _779300) ^ [_1433606, _1433608, _1433610] : [hBOOL(hAPP(hAPP(c_member(_1433606), _1433610), c_Wellfounded_Oacc(_1433606, _1433608))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1433606, hAPP(hAPP(c_COMBC(_1433606, tc_fun(tc_prod(_1433606, _1433606), tc_HOL_Obool), tc_fun(_1433606, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1433606, tc_fun(tc_fun(tc_prod(_1433606, _1433606), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1433606, _1433606), tc_HOL_Obool), tc_fun(_1433606, tc_HOL_Obool)), _1433606), c_COMBC(_1433606, tc_fun(tc_prod(_1433606, _1433606), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1433606, tc_prod(_1433606, _1433606)), tc_fun(_1433606, tc_fun(tc_fun(tc_prod(_1433606, _1433606), tc_HOL_Obool), tc_HOL_Obool)), _1433606), hAPP(c_COMBB(tc_prod(_1433606, _1433606), tc_fun(tc_fun(tc_prod(_1433606, _1433606), tc_HOL_Obool), tc_HOL_Obool), _1433606), c_member(tc_prod(_1433606, _1433606)))), c_Product__Type_OPair(_1433606, _1433606)))), _1433608)), _1433610)))], (35057 ^ _779300) ^ [_1433953, _1433955, _1433957, _1433959, _1433961, _1433963] : [hAPP(_1433953, _1433955) = _1433957, hBOOL(hAPP(hAPP(c_member(_1433959), _1433957), _1433961)), -(hBOOL(hAPP(hAPP(c_member(_1433963), _1433955), hAPP(c_Set_Ovimage(_1433963, _1433959, _1433953), _1433961))))], (35067 ^ _779300) ^ [_1434146, _1434148, _1434150, _1434152, _1434154] : [-(hAPP(c_Set_Ovimage(_1434146, _1434148, _1434150), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434148, tc_HOL_Obool)), _1434152), _1434154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434146, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1434146, _1434148, _1434150), _1434152)), hAPP(c_Set_Ovimage(_1434146, _1434148, _1434150), _1434154)))], (35069 ^ _779300) ^ [_1434220, _1434222, _1434224, _1434226, _1434228] : [hBOOL(hAPP(hAPP(c_member(_1434220), hAPP(_1434222, _1434224)), _1434226)), -(hBOOL(hAPP(hAPP(c_member(_1434228), _1434224), hAPP(c_Set_Ovimage(_1434228, _1434220, _1434222), _1434226))))], (35075 ^ _779300) ^ [_1434351, _1434353, _1434355, _1434357, _1434359] : [hBOOL(hAPP(hAPP(c_member(_1434351), _1434353), hAPP(c_Set_Ovimage(_1434351, _1434355, _1434357), _1434359))), -(hBOOL(hAPP(hAPP(c_member(_1434355), hAPP(_1434357, _1434353)), _1434359)))], (35081 ^ _779300) ^ [_1434506, _1434508, _1434510, _1434512, _1434514] : [hBOOL(hAPP(hAPP(c_member(_1434506), _1434508), hAPP(c_Set_Ovimage(_1434506, _1434510, _1434512), _1434514))), -(hBOOL(hAPP(hAPP(c_member(_1434510), hAPP(_1434512, _1434508)), _1434514)))], (35087 ^ _779300) ^ [_1434633, _1434635, _1434637, _1434639, _1434641] : [hBOOL(hAPP(hAPP(c_member(_1434637), hAPP(_1434639, _1434635)), _1434641)), -(hBOOL(hAPP(hAPP(c_member(_1434633), _1434635), hAPP(c_Set_Ovimage(_1434633, _1434637, _1434639), _1434641))))], (35093 ^ _779300) ^ [_1434766, _1434768, _1434770, _1434772, _1434774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434766, tc_HOL_Obool)), _1434768), _1434770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434772, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1434772, _1434766, _1434774), _1434768)), hAPP(c_Set_Ovimage(_1434772, _1434766, _1434774), _1434770))))], (35099 ^ _779300) ^ [_1434917, _1434919, _1434921] : [-(hAPP(c_Set_Ovimage(_1434917, _1434919, _1434921), c_Orderings_Obot__class_Obot(tc_fun(_1434919, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1434917, tc_HOL_Obool)))], (35101 ^ _779300) ^ [_1434961, _1434963, _1434965, _1434967, _1434969] : [-(hAPP(c_Set_Ovimage(_1434961, _1434963, _1434965), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1434963, tc_HOL_Obool)), _1434967), _1434969)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1434961, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1434961, _1434963, _1434965), _1434967)), hAPP(c_Set_Ovimage(_1434961, _1434963, _1434965), _1434969)))], (35103 ^ _779300) ^ [_1435059, _1435061, _1435063, _1435065, _1435067] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1435059, _1435061, _1435063), _1435065), _1435067)), -(hBOOL(hAPP(_1435065, hAPP(_1435063, _1435067))))], (35109 ^ _779300) ^ [_1435166, _1435168, _1435170, _1435172, _1435174] : [hBOOL(hAPP(_1435172, hAPP(_1435170, _1435174))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1435166, _1435168, _1435170), _1435172), _1435174)))], (35115 ^ _779300) ^ [_1435279, _1435281] : [-(hAPP(c_Set_Ovimage(_1435279, _1435279, c_COMBI(_1435279)), _1435281) = _1435281)], (35117 ^ _779300) ^ [_1435313, _1435315, _1435317, _1435319] : [-(hAPP(c_Set_Ovimage(_1435313, _1435315, _1435317), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1435315, tc_HOL_Obool)), _1435319)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1435313, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1435313, _1435315, _1435317), _1435319)))], (35119 ^ _779300) ^ [_1435372, _1435374, _1435376, _1435378, _1435380] : [-(hAPP(c_Set_Ovimage(_1435372, _1435374, _1435376), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1435374, tc_HOL_Obool)), _1435378), _1435380)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1435372, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1435372, _1435374, _1435376), _1435378)), hAPP(c_Set_Ovimage(_1435372, _1435374, _1435376), _1435380)))], (35121 ^ _779300) ^ [_1435446, _1435448, _1435450, _1435452, _1435454, _1435456] : [-(hAPP(c_Set_Ovimage(_1435446, _1435448, _1435450), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1435452, tc_fun(_1435448, tc_HOL_Obool)), _1435454), _1435456)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1435452, tc_fun(_1435446, tc_HOL_Obool)), _1435454), hAPP(hAPP(c_COMBB(tc_fun(_1435448, tc_HOL_Obool), tc_fun(_1435446, tc_HOL_Obool), _1435452), c_Set_Ovimage(_1435446, _1435448, _1435450)), _1435456)))], (35123 ^ _779300) ^ [_1435530, _1435532, _1435534] : [-(hAPP(c_Set_Ovimage(_1435530, _1435532, _1435534), c_Orderings_Otop__class_Otop(tc_fun(_1435532, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1435530, tc_HOL_Obool)))], (35125 ^ _779300) ^ [_1435574, _1435576, _1435578, _1435580] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1435574, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1435576, _1435574, _1435578), hAPP(c_Set_Ovimage(_1435576, _1435574, _1435578), _1435580))), _1435580)))], (35127 ^ _779300) ^ [_1435627, _1435629, _1435631, _1435633] : [hAPP(c_Set_Oimage(_1435627, _1435629, _1435631), c_Orderings_Otop__class_Otop(tc_fun(_1435627, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1435629, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1435627, _1435629, _1435631), hAPP(c_Set_Ovimage(_1435627, _1435629, _1435631), _1435633)) = _1435633)], (35133 ^ _779300) ^ [_1435770, _1435772, _1435774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1435770, _1435770), tc_HOL_Obool)), _1435772), _1435774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1435770, tc_HOL_Obool)), c_Wellfounded_Oacc(_1435770, _1435774)), c_Wellfounded_Oacc(_1435770, _1435772))))], (35139 ^ _779300) ^ [_1435931, _1435933, _1435935, _1435937, _1435939] : [hBOOL(hAPP(hAPP(c_member(_1435931), _1435933), hAPP(c_Set_Ovimage(_1435931, _1435935, _1435937), hAPP(hAPP(c_Set_Oinsert(_1435935), _1435939), c_Orderings_Obot__class_Obot(tc_fun(_1435935, tc_HOL_Obool)))))), -(hAPP(_1435937, _1435933) = _1435939)], (35145 ^ _779300) ^ [_1436070, _1436072, _1436074, _1436076, _1436078] : [hAPP(_1436076, _1436072) = _1436078, -(hBOOL(hAPP(hAPP(c_member(_1436070), _1436072), hAPP(c_Set_Ovimage(_1436070, _1436074, _1436076), hAPP(hAPP(c_Set_Oinsert(_1436074), _1436078), c_Orderings_Obot__class_Obot(tc_fun(_1436074, tc_HOL_Obool)))))))], (35151 ^ _779300) ^ [_1436215, _1436217, _1436219, _1436221, _1436223] : [-(hAPP(c_Set_Ovimage(_1436215, _1436217, _1436219), hAPP(hAPP(c_Set_Oinsert(_1436217), _1436221), _1436223)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1436215, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1436215, _1436217, _1436219), hAPP(hAPP(c_Set_Oinsert(_1436217), _1436221), c_Orderings_Obot__class_Obot(tc_fun(_1436217, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1436215, _1436217, _1436219), _1436223)))], (35153 ^ _779300) ^ [_1436299, _1436301, _1436303, _1436305] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1436299), hAPP(c_Set_Ovimage(_1436299, _1436301, _1436303), _1436305))), hAPP(c_Set_Oimage(_1436299, _1436301, _1436303), c_Orderings_Otop__class_Otop(tc_fun(_1436299, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1436301, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1436301), _1436305)))], (35163 ^ _779300) ^ [_1436500, _1436502, _1436504, _1436506, _1436508] : [hAPP(c_Set_Oimage(_1436500, _1436502, _1436504), c_Orderings_Otop__class_Otop(tc_fun(_1436500, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1436502, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1436500, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1436500, _1436502, _1436504), _1436506)), _1436508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1436502, tc_HOL_Obool)), _1436506), hAPP(c_Set_Oimage(_1436500, _1436502, _1436504), _1436508))))], (35173 ^ _779300) ^ [_1436743, _1436745, _1436747, _1436749] : [-(hAPP(c_Set_Oimage(_1436743, _1436745, _1436747), hAPP(c_Set_Ovimage(_1436743, _1436745, _1436747), _1436749)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436745, tc_HOL_Obool)), _1436749), hAPP(c_Set_Oimage(_1436743, _1436745, _1436747), c_Orderings_Otop__class_Otop(tc_fun(_1436743, tc_HOL_Obool)))))], (35175 ^ _779300) ^ [_1436809, _1436811, _1436813, _1436815] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1436809), _1436811)), c_Fun_Oinj__on(_1436813, _1436809, _1436815, c_Orderings_Otop__class_Otop(tc_fun(_1436813, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1436813), hAPP(c_Set_Ovimage(_1436813, _1436809, _1436815), _1436811))))], (35185 ^ _779300) ^ [_1436990, _1436992, _1436994, _1436996] : [c_Fun_Oinj__on(_1436990, _1436992, _1436994, c_Orderings_Otop__class_Otop(tc_fun(_1436990, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1436990, _1436992, _1436994), hAPP(c_Set_Oimage(_1436990, _1436992, _1436994), _1436996)) = _1436996)], (35191 ^ _779300) ^ [_1437128, _1437130, _1437132, _1437134] : [hBOOL(hAPP(hAPP(c_member(_1437128), _1437130), _1437132)), -(hAPP(c_Set_Ovimage(_1437134, _1437128, hAPP(c_COMBK(_1437128, _1437134), _1437130)), _1437132) = c_Orderings_Otop__class_Otop(tc_fun(_1437134, tc_HOL_Obool)))], (35197 ^ _779300) ^ [_1437253, _1437255, _1437257, _1437259] : [-(hBOOL(hAPP(hAPP(c_member(_1437253), _1437255), _1437257))), -(hAPP(c_Set_Ovimage(_1437259, _1437253, hAPP(c_COMBK(_1437253, _1437259), _1437255)), _1437257) = c_Orderings_Obot__class_Obot(tc_fun(_1437259, tc_HOL_Obool)))], (35203 ^ _779300) ^ [_1437320, _1437322, _1437324, _1437326] : [-(hAPP(c_Set_Ovimage(_1437320, _1437322, _1437324), _1437326) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1437322, tc_fun(_1437320, tc_HOL_Obool)), _1437326), hAPP(hAPP(c_COMBB(tc_fun(_1437322, tc_HOL_Obool), tc_fun(_1437320, tc_HOL_Obool), _1437322), c_Set_Ovimage(_1437320, _1437322, _1437324)), hAPP(hAPP(c_COMBC(_1437322, tc_fun(_1437322, tc_HOL_Obool), tc_fun(_1437322, tc_HOL_Obool)), c_Set_Oinsert(_1437322)), c_Orderings_Obot__class_Obot(tc_fun(_1437322, tc_HOL_Obool))))))], (35215 ^ _779300) ^ [_1437682, _1437684, _1437686] : [35217 ^ _779300 : [(35218 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1437682, _1437682)), hAPP(hAPP(c_Product__Type_OPair(_1437682, _1437682), 35216 ^ [_1437682, _1437684, _1437686]), _1437684)), _1437686)))], (35220 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1437682), 35216 ^ [_1437682, _1437684, _1437686]), c_Wellfounded_Oacc(_1437682, _1437686)))]], -(hBOOL(hAPP(hAPP(c_member(_1437682), _1437684), c_Wellfounded_Oacc(_1437682, _1437686))))], (35205 ^ _779300) ^ [_1437429, _1437431, _1437433] : [hBOOL(hAPP(hAPP(c_member(_1437429), _1437431), c_Wellfounded_Oacc(_1437429, _1437433))), 35208 ^ _779300 : [(35209 ^ _779300) ^ [_1437543] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1437429, _1437429)), hAPP(hAPP(c_Product__Type_OPair(_1437429, _1437429), _1437543), _1437431)), _1437433)), -(hBOOL(hAPP(hAPP(c_member(_1437429), _1437543), c_Wellfounded_Oacc(_1437429, _1437433))))]]], (35224 ^ _779300) ^ [_1437922, _1437924, _1437926, _1437928] : [hBOOL(hAPP(hAPP(c_member(_1437922), _1437924), c_Wellfounded_Oacc(_1437922, _1437926))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1437922, _1437922)), hAPP(hAPP(c_Product__Type_OPair(_1437922, _1437922), _1437928), _1437924)), _1437926)), -(hBOOL(hAPP(hAPP(c_member(_1437922), _1437928), c_Wellfounded_Oacc(_1437922, _1437926))))], (35234 ^ _779300) ^ [_1438137, _1438139, _1438141, _1438143, _1438145] : [c_Fun_Oinj__on(_1438137, _1438139, _1438141, c_Orderings_Otop__class_Otop(tc_fun(_1438137, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438139, tc_HOL_Obool)), _1438143), hAPP(c_Set_Oimage(_1438137, _1438139, _1438141), _1438145))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438137, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1438137, _1438139, _1438141), _1438143)), _1438145)))], (35244 ^ _779300) ^ [_1438381, _1438383, _1438385, _1438387, _1438389, _1438391] : [hBOOL(hAPP(hAPP(c_member(_1438381), _1438383), _1438385)), 35247 ^ _779300 : [(35248 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1438381), _1438387), _1438385)), -(hAPP(c_Set_Ovimage(_1438389, _1438381, hAPP(hAPP(c_COMBC(_1438389, _1438381, _1438381), hAPP(hAPP(c_COMBC(_1438389, _1438381, tc_fun(_1438381, _1438381)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1438381, tc_fun(_1438381, _1438381)), _1438389), c_If(_1438381)), hAPP(hAPP(c_COMBC(_1438389, tc_fun(_1438389, tc_HOL_Obool), tc_HOL_Obool), c_member(_1438389)), _1438391))), _1438383)), _1438387)), _1438385) = c_Orderings_Otop__class_Otop(tc_fun(_1438389, tc_HOL_Obool)))], (35254 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438381), _1438387), _1438385))), -(hAPP(c_Set_Ovimage(_1438389, _1438381, hAPP(hAPP(c_COMBC(_1438389, _1438381, _1438381), hAPP(hAPP(c_COMBC(_1438389, _1438381, tc_fun(_1438381, _1438381)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1438381, tc_fun(_1438381, _1438381)), _1438389), c_If(_1438381)), hAPP(hAPP(c_COMBC(_1438389, tc_fun(_1438389, tc_HOL_Obool), tc_HOL_Obool), c_member(_1438389)), _1438391))), _1438383)), _1438387)), _1438385) = _1438391)]]], (35260 ^ _779300) ^ [_1438872, _1438874, _1438876, _1438878, _1438880, _1438882] : [-(hBOOL(hAPP(hAPP(c_member(_1438872), _1438874), _1438876))), 35263 ^ _779300 : [(35264 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1438872), _1438878), _1438876)), -(hAPP(c_Set_Ovimage(_1438880, _1438872, hAPP(hAPP(c_COMBC(_1438880, _1438872, _1438872), hAPP(hAPP(c_COMBC(_1438880, _1438872, tc_fun(_1438872, _1438872)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1438872, tc_fun(_1438872, _1438872)), _1438880), c_If(_1438872)), hAPP(hAPP(c_COMBC(_1438880, tc_fun(_1438880, tc_HOL_Obool), tc_HOL_Obool), c_member(_1438880)), _1438882))), _1438874)), _1438878)), _1438876) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1438880, tc_HOL_Obool)), _1438882))], (35270 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438872), _1438878), _1438876))), -(hAPP(c_Set_Ovimage(_1438880, _1438872, hAPP(hAPP(c_COMBC(_1438880, _1438872, _1438872), hAPP(hAPP(c_COMBC(_1438880, _1438872, tc_fun(_1438872, _1438872)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1438872, tc_fun(_1438872, _1438872)), _1438880), c_If(_1438872)), hAPP(hAPP(c_COMBC(_1438880, tc_fun(_1438880, tc_HOL_Obool), tc_HOL_Obool), c_member(_1438880)), _1438882))), _1438874)), _1438878)), _1438876) = c_Orderings_Obot__class_Obot(tc_fun(_1438880, tc_HOL_Obool)))]]], (35276 ^ _779300) ^ [_1439377, _1439379, _1439381, _1439383, _1439385] : [c_Typedef_Otype__definition(_1439377, _1439379, _1439381, _1439383, _1439385), -(hAPP(c_Set_Oimage(_1439377, _1439379, _1439381), c_Orderings_Otop__class_Otop(tc_fun(_1439377, tc_HOL_Obool))) = _1439385)], (35282 ^ _779300) ^ [_1439490, _1439492, _1439494, _1439496, _1439498] : [c_Typedef_Otype__definition(_1439490, _1439492, _1439494, _1439496, _1439498), -(hAPP(c_Set_Oimage(_1439492, _1439490, _1439496), _1439498) = c_Orderings_Otop__class_Otop(tc_fun(_1439490, tc_HOL_Obool)))], (35288 ^ _779300) ^ [_1439603, _1439605, _1439607, _1439609, _1439611, _1439613, _1439615] : [c_Typedef_Otype__definition(_1439603, _1439605, _1439607, _1439609, _1439611), hBOOL(hAPP(hAPP(c_member(_1439605), _1439613), _1439611)), hBOOL(hAPP(hAPP(c_member(_1439605), _1439615), _1439611)), 35299 ^ _779300 : [(35300 ^ _779300) ^ [] : [hAPP(_1439609, _1439613) = hAPP(_1439609, _1439615), -(_1439613 = _1439615)], (35306 ^ _779300) ^ [] : [_1439613 = _1439615, -(hAPP(_1439609, _1439613) = hAPP(_1439609, _1439615))]]], (35312 ^ _779300) ^ [_1440016, _1440018, _1440020, _1440022, _1440024, _1440026] : [c_Typedef_Otype__definition(_1440016, _1440018, _1440020, _1440022, _1440024), -(hAPP(_1440022, hAPP(_1440020, _1440026)) = _1440026)], (35318 ^ _779300) ^ [_1440119, _1440121, _1440123, _1440125, _1440127, _1440129, _1440131] : [c_Typedef_Otype__definition(_1440119, _1440121, _1440123, _1440125, _1440127), 35321 ^ _779300 : [(35322 ^ _779300) ^ [] : [hAPP(_1440123, _1440129) = hAPP(_1440123, _1440131), -(_1440129 = _1440131)], (35328 ^ _779300) ^ [] : [_1440129 = _1440131, -(hAPP(_1440123, _1440129) = hAPP(_1440123, _1440131))]]], (35334 ^ _779300) ^ [_1440380, _1440382, _1440384, _1440386, _1440388, _1440390] : [c_Typedef_Otype__definition(_1440380, _1440382, _1440384, _1440386, _1440388), -(hBOOL(hAPP(hAPP(c_member(_1440382), hAPP(_1440384, _1440390)), _1440388)))], (35340 ^ _779300) ^ [_1440491, _1440493, _1440495, _1440497, _1440499, _1440501] : [c_Typedef_Otype__definition(_1440491, _1440493, _1440495, _1440497, _1440499), hBOOL(hAPP(hAPP(c_member(_1440493), _1440501), _1440499)), -(hAPP(_1440495, hAPP(_1440497, _1440501)) = _1440501)], (35350 ^ _779300) ^ [_1440689, _1440691, _1440693, _1440695] : [c_Wellfounded_Omax__extp(_1440689, _1440691, _1440693, _1440695), 35353 ^ _779300 : [(35354 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1440689), _1440693)))], (35356 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1440689), _1440695)))], (35358 ^ _779300) ^ [] : [_1440695 = c_Orderings_Obot__class_Obot(tc_fun(_1440689, tc_HOL_Obool))], (35360 ^ _779300) ^ [_1440905] : [hBOOL(hAPP(hAPP(c_member(_1440689), _1440905), _1440693)), 35364 ^ _779300 : [(35365 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1440689), 35363 ^ [_1440689, _1440691, _1440693, _1440695, _1440905]), _1440695)))], (35367 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1440691, _1440905), 35363 ^ [_1440689, _1440691, _1440693, _1440695, _1440905])))]]]]], (35369 ^ _779300) ^ [_1441089, _1441091, _1441093, _1441095] : [-(c_Wellfounded_Omax__extp(_1441089, _1441091, _1441093, _1441095)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441089), _1441093)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441089), _1441095)), -(_1441095 = c_Orderings_Obot__class_Obot(tc_fun(_1441089, tc_HOL_Obool))), 35383 ^ _779300 : [(35384 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1441089), 35382 ^ [_1441089, _1441091, _1441093, _1441095]), _1441093)))], (35386 ^ _779300) ^ [_1441434] : [hBOOL(hAPP(hAPP(c_member(_1441089), _1441434), _1441095)), hBOOL(hAPP(hAPP(_1441091, 35382 ^ [_1441089, _1441091, _1441093, _1441095]), _1441434))]]], (35394 ^ _779300) ^ [_1441602, _1441604, _1441606, _1441608] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1441602), _1441604)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441602), _1441606)), -(_1441606 = c_Orderings_Obot__class_Obot(tc_fun(_1441602, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1441602, tc_HOL_Obool), tc_fun(_1441602, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1441602, tc_HOL_Obool), tc_fun(_1441602, tc_HOL_Obool)), _1441604), _1441606)), c_Wellfounded_Omax__ext(_1441602, _1441608)))), 35408 ^ _779300 : [(35409 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1441602), 35407 ^ [_1441602, _1441604, _1441606, _1441608]), _1441604)))], (35411 ^ _779300) ^ [_1442007] : [hBOOL(hAPP(hAPP(c_member(_1441602), _1442007), _1441606)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1441602, _1441602)), hAPP(hAPP(c_Product__Type_OPair(_1441602, _1441602), 35407 ^ [_1441602, _1441604, _1441606, _1441608]), _1442007)), _1441608))]]], (35419 ^ _779300) ^ [_1442233] : [-(c_Nitpick_Ozero__frac(_1442233) = c_Nitpick_OAbs__Frac(_1442233, 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))))], (35421 ^ _779300) ^ [_1442261] : [-(c_Nitpick_Oone__frac(_1442261) = c_Nitpick_OAbs__Frac(_1442261, 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))))], (35423 ^ _779300) ^ [_1442289, _1442291] : [-(c_Nitpick_Onumber__of__frac(_1442289, _1442291) = c_Nitpick_OAbs__Frac(_1442289, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1442291), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35425 ^ _779300) ^ [_1442326, _1442328, _1442330] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1442326), _1442328), _1442330) = c_Nitpick_OAbs__Frac(_1442326, c_Nitpick_Onorm__frac(_1442328, _1442330)))], (35427 ^ _779300) ^ [_1442367, _1442369, _1442371, _1442373, _1442375, _1442377] : [-(hAPP(c_Set_Oimage(_1442367, tc_prod(_1442369, _1442371), hAPP(hAPP(c_COMBS(_1442367, _1442371, tc_prod(_1442369, _1442371)), hAPP(hAPP(c_COMBB(_1442369, tc_fun(_1442371, tc_prod(_1442369, _1442371)), _1442367), c_Product__Type_OPair(_1442369, _1442371)), _1442373)), _1442375)), _1442377) = hAPP(hAPP(c_Product__Type_OSigma(_1442369, _1442371), hAPP(c_Set_Oimage(_1442367, _1442369, _1442373), _1442377)), hAPP(hAPP(c_COMBB(tc_fun(_1442367, tc_HOL_Obool), tc_fun(_1442371, tc_HOL_Obool), _1442369), c_Set_Oimage(_1442367, _1442371, _1442375)), hAPP(hAPP(c_COMBC(_1442369, tc_fun(_1442367, tc_HOL_Obool), tc_fun(_1442367, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442367, tc_HOL_Obool), tc_fun(tc_fun(_1442367, tc_HOL_Obool), tc_fun(_1442367, tc_HOL_Obool)), _1442369), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442367, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1442369, tc_HOL_Obool), tc_fun(_1442367, tc_HOL_Obool), _1442369), c_Set_Ovimage(_1442367, _1442369, _1442373)), hAPP(hAPP(c_COMBC(_1442369, tc_fun(_1442369, tc_HOL_Obool), tc_fun(_1442369, tc_HOL_Obool)), c_Set_Oinsert(_1442369)), c_Orderings_Obot__class_Obot(tc_fun(_1442369, tc_HOL_Obool)))))), _1442377))))], (35429 ^ _779300) ^ [_1442564, _1442566, _1442568] : [35431 ^ _779300 : [(35432 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 35430 ^ [_1442564, _1442566, _1442568]), _1442564)))], (35434 ^ _779300) ^ [] : [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(_1442566, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 35430 ^ [_1442564, _1442566, _1442568]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1442566, 35430 ^ [_1442564, _1442566, _1442568])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1442566, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1442568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1442568), hAPP(_1442566, _1442564))), 35444 ^ _779300 : [(35445 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35443 ^ [_1442564, _1442566, _1442568]), _1442564)))], (35447 ^ _779300) ^ [] : [-(hAPP(_1442566, 35443 ^ [_1442564, _1442566, _1442568]) = _1442568)]]], (35449 ^ _779300) ^ [_1443014, _1443016, _1443018] : [35451 ^ _779300 : [(35452 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 35450 ^ [_1443014, _1443016, _1443018]), _1443014)))], (35454 ^ _779300) ^ [] : [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(_1443016, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 35450 ^ [_1443014, _1443016, _1443018]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1443016, 35450 ^ [_1443014, _1443016, _1443018])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1443016, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1443018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1443018), hAPP(_1443016, _1443014))), 35464 ^ _779300 : [(35465 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35463 ^ [_1443014, _1443016, _1443018]), _1443014)))], (35467 ^ _779300) ^ [] : [-(hAPP(_1443016, 35463 ^ [_1443014, _1443016, _1443018]) = _1443018)]]], (35469 ^ _779300) ^ [_1443464, _1443466, _1443468, _1443470, _1443472, _1443474] : [hBOOL(hAPP(hAPP(c_member(_1443464), _1443466), _1443468)), hBOOL(hAPP(hAPP(c_member(_1443470), _1443472), hAPP(_1443474, _1443466))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1443464, _1443470)), hAPP(hAPP(c_Product__Type_OPair(_1443464, _1443470), _1443466), _1443472)), hAPP(hAPP(c_Product__Type_OSigma(_1443464, _1443470), _1443468), _1443474))))], (35479 ^ _779300) ^ [_1443699, _1443701, _1443703, _1443705, _1443707] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1443699, _1443701), _1443703), hAPP(hAPP(c_COMBS(_1443699, tc_fun(_1443701, tc_HOL_Obool), tc_fun(_1443701, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1443701, tc_HOL_Obool), tc_fun(tc_fun(_1443701, tc_HOL_Obool), tc_fun(_1443701, tc_HOL_Obool)), _1443699), c_Groups_Ominus__class_Ominus(tc_fun(_1443701, tc_HOL_Obool))), _1443705)), _1443707)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1443699, _1443701), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1443699, _1443701), _1443703), _1443705)), hAPP(hAPP(c_Product__Type_OSigma(_1443699, _1443701), _1443703), _1443707)))], (35481 ^ _779300) ^ [_1443814, _1443816, _1443818, _1443820, _1443822] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1443814, _1443816), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443814, tc_HOL_Obool)), _1443818), _1443820)), hAPP(c_COMBK(tc_fun(_1443816, tc_HOL_Obool), _1443814), _1443822)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1443814, _1443816), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1443814, _1443816), _1443818), hAPP(c_COMBK(tc_fun(_1443816, tc_HOL_Obool), _1443814), _1443822))), hAPP(hAPP(c_Product__Type_OSigma(_1443814, _1443816), _1443820), hAPP(c_COMBK(tc_fun(_1443816, tc_HOL_Obool), _1443814), _1443822))))], (35483 ^ _779300) ^ [_1443924, _1443926, _1443928, _1443930, _1443932] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1443924, _1443926), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443924, tc_HOL_Obool)), _1443928), _1443930)), _1443932) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1443924, _1443926), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1443924, _1443926), _1443928), _1443932)), hAPP(hAPP(c_Product__Type_OSigma(_1443924, _1443926), _1443930), _1443932)))], (35485 ^ _779300) ^ [_1444007, _1444009, _1444011, _1444013, _1444015, _1444017] : [hBOOL(hAPP(hAPP(c_member(_1444007), _1444009), _1444011)), 35488 ^ _779300 : [(35489 ^ _779300) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1444013, _1444007), _1444015), hAPP(c_COMBK(tc_fun(_1444007, tc_HOL_Obool), _1444013), _1444011)) = hAPP(hAPP(c_Product__Type_OSigma(_1444013, _1444007), _1444017), hAPP(c_COMBK(tc_fun(_1444007, tc_HOL_Obool), _1444013), _1444011)), -(_1444015 = _1444017)], (35495 ^ _779300) ^ [] : [_1444015 = _1444017, -(hAPP(hAPP(c_Product__Type_OSigma(_1444013, _1444007), _1444015), hAPP(c_COMBK(tc_fun(_1444007, tc_HOL_Obool), _1444013), _1444011)) = hAPP(hAPP(c_Product__Type_OSigma(_1444013, _1444007), _1444017), hAPP(c_COMBK(tc_fun(_1444007, tc_HOL_Obool), _1444013), _1444011)))]]], (35501 ^ _779300) ^ [_1444360, _1444362, _1444364] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1444360, _1444362), c_Orderings_Obot__class_Obot(tc_fun(_1444360, tc_HOL_Obool))), _1444364) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1444360, _1444362), tc_HOL_Obool)))], (35503 ^ _779300) ^ [_1444409, _1444411, _1444413, _1444415] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1444409, _1444411)), hAPP(hAPP(c_Product__Type_OSigma(_1444409, _1444411), _1444413), hAPP(c_COMBK(tc_fun(_1444411, tc_HOL_Obool), _1444409), _1444415))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1444409), _1444413)), hAPP(c_Finite__Set_Ocard(_1444411), _1444415)))], (35505 ^ _779300) ^ [_1444480, _1444482, _1444484, _1444486, _1444488, _1444490] : [class_Groups_Ocomm__monoid__add(_1444480), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444482, _1444480), hAPP(hAPP(c_COMBC(_1444482, tc_fun(_1444484, tc_HOL_Obool), _1444480), hAPP(hAPP(c_COMBB(tc_fun(_1444484, _1444480), tc_fun(tc_fun(_1444484, tc_HOL_Obool), _1444480), _1444482), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444484, _1444480)), _1444486)), _1444488)), _1444490) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1444482, _1444484), _1444480), hAPP(c_Product__Type_Oprod_Oprod__case(_1444482, _1444484, _1444480), _1444486)), hAPP(hAPP(c_Product__Type_OSigma(_1444482, _1444484), _1444490), hAPP(c_COMBK(tc_fun(_1444484, tc_HOL_Obool), _1444482), _1444488))))], (35511 ^ _779300) ^ [_1444725, _1444727, _1444729] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1444725, _1444727), _1444729), hAPP(c_COMBK(tc_fun(_1444727, tc_HOL_Obool), _1444725), c_Orderings_Obot__class_Obot(tc_fun(_1444727, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1444725, _1444727), tc_HOL_Obool)))], (35523 ^ _779300) ^ [_1444966, _1444968, _1444970, _1444972] : [35524 ^ _779300 : [(35525 ^ _779300) ^ [] : [_1444970 = c_Orderings_Obot__class_Obot(tc_fun(_1444966, tc_HOL_Obool))], (35527 ^ _779300) ^ [] : [_1444972 = c_Orderings_Obot__class_Obot(tc_fun(_1444968, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1444966, _1444968), _1444970), hAPP(c_COMBK(tc_fun(_1444968, tc_HOL_Obool), _1444966), _1444972)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1444966, _1444968), tc_HOL_Obool)))], (35513 ^ _779300) ^ [_1444804, _1444806, _1444808, _1444810] : [hAPP(hAPP(c_Product__Type_OSigma(_1444804, _1444806), _1444808), hAPP(c_COMBK(tc_fun(_1444806, tc_HOL_Obool), _1444804), _1444810)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1444804, _1444806), tc_HOL_Obool)), -(_1444808 = c_Orderings_Obot__class_Obot(tc_fun(_1444804, tc_HOL_Obool))), -(_1444810 = c_Orderings_Obot__class_Obot(tc_fun(_1444806, tc_HOL_Obool)))], (35531 ^ _779300) ^ [_1445159, _1445161, _1445163] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1445159, _1445161), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1445159, _1445161), _1445163), hAPP(c_COMBK(tc_fun(_1445161, tc_HOL_Obool), _1445159), c_Orderings_Otop__class_Otop(tc_fun(_1445161, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1445159, _1445161), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1445159, tc_HOL_Obool)), _1445163)), hAPP(c_COMBK(tc_fun(_1445161, tc_HOL_Obool), _1445159), c_Orderings_Otop__class_Otop(tc_fun(_1445161, tc_HOL_Obool)))))], (35533 ^ _779300) ^ [_1445251, _1445253, _1445255] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1445251, _1445253), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1445251, _1445253), c_Orderings_Otop__class_Otop(tc_fun(_1445251, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1445253, tc_HOL_Obool), _1445251), _1445255))) = hAPP(hAPP(c_Product__Type_OSigma(_1445251, _1445253), c_Orderings_Otop__class_Otop(tc_fun(_1445251, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1445253, tc_HOL_Obool), _1445251), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1445253, tc_HOL_Obool)), _1445255))))], (35535 ^ _779300) ^ [_1445343, _1445345, _1445347, _1445349, _1445351, _1445353] : [class_Groups_Ocomm__monoid__mult(_1445343), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1445345, _1445343), hAPP(hAPP(c_COMBC(_1445345, tc_fun(_1445347, tc_HOL_Obool), _1445343), hAPP(hAPP(c_COMBB(tc_fun(_1445347, _1445343), tc_fun(tc_fun(_1445347, tc_HOL_Obool), _1445343), _1445345), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1445347, _1445343)), _1445349)), _1445351)), _1445353) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1445345, _1445347), _1445343), hAPP(c_Product__Type_Oprod_Oprod__case(_1445345, _1445347, _1445343), _1445349)), hAPP(hAPP(c_Product__Type_OSigma(_1445345, _1445347), _1445353), hAPP(c_COMBK(tc_fun(_1445347, tc_HOL_Obool), _1445345), _1445351))))], (35541 ^ _779300) ^ [_1445588, _1445590, _1445592, _1445594, _1445596] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1445588, _1445590), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445588, tc_HOL_Obool)), _1445592), _1445594)), _1445596) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1445588, _1445590), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1445588, _1445590), _1445592), _1445596)), hAPP(hAPP(c_Product__Type_OSigma(_1445588, _1445590), _1445594), _1445596)))], (35543 ^ _779300) ^ [_1445671, _1445673, _1445675, _1445677, _1445679] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1445671, _1445673), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445671, tc_HOL_Obool)), _1445675), _1445677)), hAPP(c_COMBK(tc_fun(_1445673, tc_HOL_Obool), _1445671), _1445679)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1445671, _1445673), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1445671, _1445673), _1445675), hAPP(c_COMBK(tc_fun(_1445673, tc_HOL_Obool), _1445671), _1445679))), hAPP(hAPP(c_Product__Type_OSigma(_1445671, _1445673), _1445677), hAPP(c_COMBK(tc_fun(_1445673, tc_HOL_Obool), _1445671), _1445679))))], (35545 ^ _779300) ^ [_1445781, _1445783, _1445785, _1445787, _1445789] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1445781, _1445783), _1445785), hAPP(hAPP(c_COMBS(_1445781, tc_fun(_1445783, tc_HOL_Obool), tc_fun(_1445783, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445783, tc_HOL_Obool), tc_fun(tc_fun(_1445783, tc_HOL_Obool), tc_fun(_1445783, tc_HOL_Obool)), _1445781), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445783, tc_HOL_Obool))), _1445787)), _1445789)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1445781, _1445783), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1445781, _1445783), _1445785), _1445787)), hAPP(hAPP(c_Product__Type_OSigma(_1445781, _1445783), _1445785), _1445789)))], (35547 ^ _779300) ^ [_1445896, _1445898, _1445900, _1445902] : [-(hAPP(c_Set_Oimage(tc_prod(_1445896, _1445898), tc_prod(_1445898, _1445896), hAPP(c_Product__Type_Oprod_Oprod__case(_1445896, _1445898, tc_prod(_1445898, _1445896)), hAPP(c_COMBC(_1445898, _1445896, tc_prod(_1445898, _1445896)), c_Product__Type_OPair(_1445898, _1445896)))), hAPP(hAPP(c_Product__Type_OSigma(_1445896, _1445898), _1445900), hAPP(c_COMBK(tc_fun(_1445898, tc_HOL_Obool), _1445896), _1445902))) = hAPP(hAPP(c_Product__Type_OSigma(_1445898, _1445896), _1445902), hAPP(c_COMBK(tc_fun(_1445896, tc_HOL_Obool), _1445898), _1445900)))], (35549 ^ _779300) ^ [_1445997, _1445999, _1446001, _1446003] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1445997), _1445999)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446001), _1446003)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1445997, _1446001)), hAPP(hAPP(c_Product__Type_OSigma(_1445997, _1446001), _1445999), hAPP(c_COMBK(tc_fun(_1446001, tc_HOL_Obool), _1445997), _1446003)))))], (35559 ^ _779300) ^ [_1446200, _1446202, _1446204] : [c_Equiv__Relations_Oequiv(_1446200, _1446202, _1446204), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1446200, _1446200), tc_HOL_Obool)), _1446204), hAPP(hAPP(c_Product__Type_OSigma(_1446200, _1446200), _1446202), hAPP(c_COMBK(tc_fun(_1446200, tc_HOL_Obool), _1446200), _1446202)))))], (35565 ^ _779300) ^ [_1446343, _1446345, _1446347, _1446349, _1446351] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1446343, _1446345), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446343, tc_HOL_Obool)), _1446347), _1446349)), _1446351) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1446343, _1446345), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1446343, _1446345), _1446347), _1446351)), hAPP(hAPP(c_Product__Type_OSigma(_1446343, _1446345), _1446349), _1446351)))], (35567 ^ _779300) ^ [_1446426, _1446428, _1446430, _1446432, _1446434] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1446426, _1446428), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446426, tc_HOL_Obool)), _1446430), _1446432)), hAPP(c_COMBK(tc_fun(_1446428, tc_HOL_Obool), _1446426), _1446434)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1446426, _1446428), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1446426, _1446428), _1446430), hAPP(c_COMBK(tc_fun(_1446428, tc_HOL_Obool), _1446426), _1446434))), hAPP(hAPP(c_Product__Type_OSigma(_1446426, _1446428), _1446432), hAPP(c_COMBK(tc_fun(_1446428, tc_HOL_Obool), _1446426), _1446434))))], (35569 ^ _779300) ^ [_1446536, _1446538, _1446540, _1446542, _1446544] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1446536, _1446538), _1446540), hAPP(hAPP(c_COMBS(_1446536, tc_fun(_1446538, tc_HOL_Obool), tc_fun(_1446538, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446538, tc_HOL_Obool), tc_fun(tc_fun(_1446538, tc_HOL_Obool), tc_fun(_1446538, tc_HOL_Obool)), _1446536), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446538, tc_HOL_Obool))), _1446542)), _1446544)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1446536, _1446538), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1446536, _1446538), _1446540), _1446542)), hAPP(hAPP(c_Product__Type_OSigma(_1446536, _1446538), _1446540), _1446544)))], (35571 ^ _779300) ^ [_1446651, _1446653] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1446651, _1446651), tc_HOL_Obool)), c_Relation_OId__on(_1446651, _1446653)), hAPP(hAPP(c_Product__Type_OSigma(_1446651, _1446651), _1446653), hAPP(c_COMBK(tc_fun(_1446651, tc_HOL_Obool), _1446651), _1446653)))))], (35573 ^ _779300) ^ [_1446710, _1446712] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1446710, _1446712), c_Orderings_Otop__class_Otop(tc_fun(_1446710, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1446712, tc_HOL_Obool), _1446710), c_Orderings_Otop__class_Otop(tc_fun(_1446712, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1446710, _1446712), tc_HOL_Obool)))], (35575 ^ _779300) ^ [_1446798, _1446800, _1446802, _1446804, _1446806, _1446808] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1446798, _1446800)), hAPP(hAPP(c_Product__Type_OPair(_1446798, _1446800), _1446802), _1446804)), hAPP(hAPP(c_Product__Type_OSigma(_1446798, _1446800), _1446806), _1446808))), 35578 ^ _779300 : [(35579 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1446798), _1446802), _1446806)))], (35581 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1446800), _1446804), hAPP(_1446808, _1446802))))]]], (35583 ^ _779300) ^ [_1446995, _1446997, _1446999, _1447001, _1447003, _1447005] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446995, _1446997)), hAPP(hAPP(c_Product__Type_OPair(_1446995, _1446997), _1446999), _1447001)), hAPP(hAPP(c_Product__Type_OSigma(_1446995, _1446997), _1447003), _1447005)))), hBOOL(hAPP(hAPP(c_member(_1446995), _1446999), _1447003)), hBOOL(hAPP(hAPP(c_member(_1446997), _1447001), hAPP(_1447005, _1446999)))], (35593 ^ _779300) ^ [_1447232, _1447234, _1447236, _1447238, _1447240, _1447242] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1447232, _1447234)), hAPP(hAPP(c_Product__Type_OPair(_1447232, _1447234), _1447236), _1447238)), hAPP(hAPP(c_Product__Type_OSigma(_1447232, _1447234), _1447240), _1447242))), -(hBOOL(hAPP(hAPP(c_member(_1447232), _1447236), _1447240)))], (35599 ^ _779300) ^ [_1447387, _1447389, _1447391, _1447393, _1447395, _1447397] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1447387, _1447389)), hAPP(hAPP(c_Product__Type_OPair(_1447387, _1447389), _1447391), _1447393)), hAPP(hAPP(c_Product__Type_OSigma(_1447387, _1447389), _1447395), _1447397))), -(hBOOL(hAPP(hAPP(c_member(_1447389), _1447393), hAPP(_1447397, _1447391))))], (35605 ^ _779300) ^ [_1447548, _1447550, _1447552, _1447554, _1447556, _1447558] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1447548, _1447550)), hAPP(hAPP(c_Product__Type_OPair(_1447548, _1447550), _1447552), _1447554)), hAPP(hAPP(c_Product__Type_OSigma(_1447548, _1447550), _1447556), _1447558))), 35608 ^ _779300 : [(35609 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1447548), _1447552), _1447556)))], (35611 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1447550), _1447554), hAPP(_1447558, _1447552))))]]], (35613 ^ _779300) ^ [_1447753, _1447755, _1447757, _1447759] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1447753, _1447755)), hAPP(hAPP(c_Product__Type_OSigma(_1447753, _1447755), hAPP(hAPP(c_Set_Oinsert(_1447753), _1447757), c_Orderings_Obot__class_Obot(tc_fun(_1447753, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1447755, tc_HOL_Obool), _1447753), _1447759))) = hAPP(c_Finite__Set_Ocard(_1447755), _1447759))], (35615 ^ _779300) ^ [_1447826, _1447828, _1447830, _1447832, _1447834, _1447836] : [hBOOL(hAPP(hAPP(c_member(_1447826), _1447828), _1447830)), 35618 ^ _779300 : [(35619 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1447832, _1447826), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1447832, _1447826), _1447834), hAPP(c_COMBK(tc_fun(_1447826, tc_HOL_Obool), _1447832), _1447830))), hAPP(hAPP(c_Product__Type_OSigma(_1447832, _1447826), _1447836), hAPP(c_COMBK(tc_fun(_1447826, tc_HOL_Obool), _1447832), _1447830)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447832, tc_HOL_Obool)), _1447834), _1447836)))], (35625 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447832, tc_HOL_Obool)), _1447834), _1447836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1447832, _1447826), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1447832, _1447826), _1447834), hAPP(c_COMBK(tc_fun(_1447826, tc_HOL_Obool), _1447832), _1447830))), hAPP(hAPP(c_Product__Type_OSigma(_1447832, _1447826), _1447836), hAPP(c_COMBK(tc_fun(_1447826, tc_HOL_Obool), _1447832), _1447830)))))]]], (35631 ^ _779300) ^ [_1448248, _1448250, _1448252, _1448254, _1448256, _1448258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1448248, _1448250), tc_HOL_Obool)), _1448252), hAPP(hAPP(c_Product__Type_OSigma(_1448248, _1448250), _1448254), hAPP(c_COMBK(tc_fun(_1448250, tc_HOL_Obool), _1448248), _1448256)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1448250, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1448248, _1448250, _1448252), _1448258)), _1448256)))], (35637 ^ _779300) ^ [_1448429, _1448431, _1448433, _1448435] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1448429, _1448431)), hAPP(hAPP(c_Product__Type_OSigma(_1448429, _1448431), _1448433), hAPP(c_COMBK(tc_fun(_1448431, tc_HOL_Obool), _1448429), _1448435)))), -(_1448433 = c_Orderings_Obot__class_Obot(tc_fun(_1448429, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1448431), _1448435)))], (35647 ^ _779300) ^ [_1448593, _1448595, _1448597, _1448599] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1448593, _1448595)), hAPP(hAPP(c_Product__Type_OSigma(_1448593, _1448595), _1448597), hAPP(c_COMBK(tc_fun(_1448595, tc_HOL_Obool), _1448593), _1448599)))), -(_1448599 = c_Orderings_Obot__class_Obot(tc_fun(_1448595, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1448593), _1448597)))], (35657 ^ _779300) ^ [_1448772, _1448774, _1448776, _1448778] : [_1448772 = c_Orderings_Obot__class_Obot(tc_fun(_1448774, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1448776, _1448774), _1448776, c_Product__Type_Ofst(_1448776, _1448774)), hAPP(hAPP(c_Product__Type_OSigma(_1448776, _1448774), _1448778), hAPP(c_COMBK(tc_fun(_1448774, tc_HOL_Obool), _1448776), _1448772))) = c_Orderings_Obot__class_Obot(tc_fun(_1448776, tc_HOL_Obool)))], (35663 ^ _779300) ^ [_1448929, _1448931, _1448933, _1448935] : [-(_1448929 = c_Orderings_Obot__class_Obot(tc_fun(_1448931, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1448933, _1448931), _1448933, c_Product__Type_Ofst(_1448933, _1448931)), hAPP(hAPP(c_Product__Type_OSigma(_1448933, _1448931), _1448935), hAPP(c_COMBK(tc_fun(_1448931, tc_HOL_Obool), _1448933), _1448929))) = _1448935)], (35669 ^ _779300) ^ [_1449022, _1449024, _1449026, _1449028] : [_1449022 = c_Orderings_Obot__class_Obot(tc_fun(_1449024, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1449024, _1449026), _1449026, c_Product__Type_Osnd(_1449024, _1449026)), hAPP(hAPP(c_Product__Type_OSigma(_1449024, _1449026), _1449022), hAPP(c_COMBK(tc_fun(_1449026, tc_HOL_Obool), _1449024), _1449028))) = c_Orderings_Obot__class_Obot(tc_fun(_1449026, tc_HOL_Obool)))], (35675 ^ _779300) ^ [_1449179, _1449181, _1449183, _1449185] : [-(_1449179 = c_Orderings_Obot__class_Obot(tc_fun(_1449181, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1449181, _1449183), _1449183, c_Product__Type_Osnd(_1449181, _1449183)), hAPP(hAPP(c_Product__Type_OSigma(_1449181, _1449183), _1449179), hAPP(c_COMBK(tc_fun(_1449183, tc_HOL_Obool), _1449181), _1449185))) = _1449185)], (35681 ^ _779300) ^ [_1449257, _1449259, _1449261, _1449263, _1449265, _1449267] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1449257, _1449259), hAPP(hAPP(c_Set_Oinsert(_1449257), _1449261), _1449263)), hAPP(c_COMBK(tc_fun(_1449259, tc_HOL_Obool), _1449257), hAPP(hAPP(c_Set_Oinsert(_1449259), _1449265), _1449267))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1449257, _1449259)), hAPP(hAPP(c_Product__Type_OPair(_1449257, _1449259), _1449261), _1449265)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1449257, _1449259), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1449257, _1449259), _1449263), hAPP(c_COMBK(tc_fun(_1449259, tc_HOL_Obool), _1449257), hAPP(hAPP(c_Set_Oinsert(_1449259), _1449265), _1449267)))), hAPP(hAPP(c_Product__Type_OSigma(_1449257, _1449259), hAPP(hAPP(c_Set_Oinsert(_1449257), _1449261), _1449263)), hAPP(c_COMBK(tc_fun(_1449259, tc_HOL_Obool), _1449257), _1449267)))))], (35683 ^ _779300) ^ [_1449410, _1449412, _1449414, _1449416] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1449410), _1449412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1449410, _1449410), tc_HOL_Obool)), _1449414), hAPP(hAPP(c_Product__Type_OSigma(_1449410, _1449410), _1449412), hAPP(c_COMBK(tc_fun(_1449410, tc_HOL_Obool), _1449410), _1449412)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449410, tc_HOL_Obool)), _1449416), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449410), _1449412), _1449414))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1449410), _1449416)))], (35697 ^ _779300) ^ [_1449717, _1449719, _1449721, _1449723, _1449725, _1449727, _1449729, _1449731] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1449717, _1449719), tc_fun(tc_prod(_1449721, _1449723), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1449717, _1449719), _1449725), hAPP(c_COMBK(tc_fun(_1449719, tc_HOL_Obool), _1449717), _1449727))), hAPP(c_Product__Type_Oprod_Oprod__case(_1449717, _1449719, tc_fun(tc_prod(_1449721, _1449723), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1449717, tc_fun(_1449719, tc_fun(_1449721, tc_fun(_1449723, tc_HOL_Obool))), tc_fun(_1449719, tc_fun(tc_prod(_1449721, _1449723), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449721, tc_fun(_1449723, tc_HOL_Obool)), tc_fun(tc_prod(_1449721, _1449723), tc_HOL_Obool)), tc_fun(tc_fun(_1449719, tc_fun(_1449721, tc_fun(_1449723, tc_HOL_Obool))), tc_fun(_1449719, tc_fun(tc_prod(_1449721, _1449723), tc_HOL_Obool))), _1449717), c_COMBB(tc_fun(_1449721, tc_fun(_1449723, tc_HOL_Obool)), tc_fun(tc_prod(_1449721, _1449723), tc_HOL_Obool), _1449719)), hAPP(hAPP(c_COMBB(tc_fun(_1449721, tc_HOL_Obool), tc_fun(tc_fun(_1449721, tc_fun(_1449723, tc_HOL_Obool)), tc_fun(tc_prod(_1449721, _1449723), tc_HOL_Obool)), _1449717), c_Product__Type_OSigma(_1449721, _1449723)), _1449729))), hAPP(hAPP(c_COMBB(tc_fun(_1449723, tc_HOL_Obool), tc_fun(_1449721, tc_fun(_1449723, tc_HOL_Obool)), _1449719), c_COMBK(tc_fun(_1449723, tc_HOL_Obool), _1449721)), _1449731)))) = hAPP(hAPP(c_Product__Type_OSigma(_1449721, _1449723), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449717, tc_fun(_1449721, tc_HOL_Obool)), _1449725), _1449729)), hAPP(c_COMBK(tc_fun(_1449723, tc_HOL_Obool), _1449721), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449719, tc_fun(_1449723, tc_HOL_Obool)), _1449727), _1449731))))], (35699 ^ _779300) ^ [_1449991, _1449993, _1449995, _1449997] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1449991, _1449993), _1449995), _1449997) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449991, tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool)), _1449995), hAPP(hAPP(c_COMBS(_1449991, tc_fun(_1449993, tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool)), tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449993, tc_HOL_Obool), tc_fun(tc_fun(_1449993, tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool)), tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool)), _1449991), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449993, tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool))), _1449997)), hAPP(hAPP(c_COMBC(_1449991, tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool), tc_fun(_1449993, tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1449993, tc_fun(tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool), tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool), tc_fun(_1449993, tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool))), _1449991), c_COMBC(_1449993, tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool), tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1449993, tc_prod(_1449991, _1449993)), tc_fun(_1449993, tc_fun(tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool), tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool))), _1449991), hAPP(c_COMBB(tc_prod(_1449991, _1449993), tc_fun(tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool), tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool)), _1449993), c_Set_Oinsert(tc_prod(_1449991, _1449993)))), c_Product__Type_OPair(_1449991, _1449993)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1449991, _1449993), tc_HOL_Obool))))))], (35701 ^ _779300) ^ [_1450271, _1450273, _1450275] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450271), _1450273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1450271, _1450271), tc_HOL_Obool)), _1450275), hAPP(hAPP(c_Product__Type_OSigma(_1450271, _1450271), _1450273), hAPP(c_COMBK(tc_fun(_1450271, tc_HOL_Obool), _1450271), _1450273)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1450271, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1450271), _1450273), _1450275))))], (35712 ^ _779300) ^ [_1450502, _1450504, _1450506, _1450508] : [-(c_Fun_Oinj__on(_1450502, tc_prod(_1450504, _1450502), 35710 ^ [_1450502, _1450504, _1450506, _1450508], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1450504, tc_fun(_1450502, tc_HOL_Obool)), _1450506), _1450508)))], (35714 ^ _779300) ^ [_1450556, _1450558, _1450560, _1450562] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1450558, _1450556), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1450556, tc_prod(_1450558, _1450556), 35710 ^ [_1450556, _1450558, _1450560, _1450562]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1450558, tc_fun(_1450556, tc_HOL_Obool)), _1450560), _1450562))), hAPP(hAPP(c_Product__Type_OSigma(_1450558, _1450556), _1450560), _1450562))))], (35716 ^ _779300) ^ [_1450642, _1450644, _1450646, _1450648, _1450650, _1450652] : [class_Groups_Ocomm__monoid__mult(_1450642), hBOOL(hAPP(c_Finite__Set_Ofinite(_1450644), _1450646)), 35726 ^ _779300 : [(35727 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450644), 35725 ^ [_1450642, _1450644, _1450646, _1450648, _1450650, _1450652]), _1450646)))], (35729 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450648), hAPP(_1450650, 35725 ^ [_1450642, _1450644, _1450646, _1450648, _1450650, _1450652])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1450642, _1450644, c_Groups_Otimes__class_Otimes(_1450642)), hAPP(hAPP(c_COMBS(_1450644, tc_fun(_1450648, tc_HOL_Obool), _1450642), hAPP(hAPP(c_COMBC(_1450644, _1450642, tc_fun(tc_fun(_1450648, tc_HOL_Obool), _1450642)), hAPP(hAPP(c_COMBB(tc_fun(_1450648, _1450642), tc_fun(_1450642, tc_fun(tc_fun(_1450648, tc_HOL_Obool), _1450642)), _1450644), c_Finite__Set_Ofold__image(_1450642, _1450648, c_Groups_Otimes__class_Otimes(_1450642))), _1450652)), c_Groups_Oone__class_Oone(_1450642))), _1450650)), c_Groups_Oone__class_Oone(_1450642)), _1450646) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1450642, tc_prod(_1450644, _1450648), c_Groups_Otimes__class_Otimes(_1450642)), hAPP(c_Product__Type_Oprod_Oprod__case(_1450644, _1450648, _1450642), _1450652)), c_Groups_Oone__class_Oone(_1450642)), hAPP(hAPP(c_Product__Type_OSigma(_1450644, _1450648), _1450646), _1450650)))], (35733 ^ _779300) ^ [_1451199, _1451201, _1451203, _1451205] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1451199), _1451201)), 35739 ^ _779300 : [(35740 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451199), 35738 ^ [_1451199, _1451201, _1451203, _1451205]), _1451201)))], (35742 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1451203), hAPP(_1451205, 35738 ^ [_1451199, _1451201, _1451203, _1451205])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1451199, _1451203)), hAPP(hAPP(c_Product__Type_OSigma(_1451199, _1451203), _1451201), _1451205))))], (35746 ^ _779300) ^ [_1451486, _1451488, _1451490, _1451492, _1451494, _1451496] : [class_Groups_Ocomm__monoid__mult(_1451486), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451488), _1451490)), 35756 ^ _779300 : [(35757 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451488), 35755 ^ [_1451486, _1451488, _1451490, _1451492, _1451494, _1451496]), _1451490)))], (35759 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1451492), hAPP(_1451494, 35755 ^ [_1451486, _1451488, _1451490, _1451492, _1451494, _1451496])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1451488, _1451486), hAPP(hAPP(c_COMBS(_1451488, tc_fun(_1451492, tc_HOL_Obool), _1451486), hAPP(hAPP(c_COMBB(tc_fun(_1451492, _1451486), tc_fun(tc_fun(_1451492, tc_HOL_Obool), _1451486), _1451488), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1451492, _1451486)), _1451496)), _1451494)), _1451490) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1451488, _1451492), _1451486), hAPP(c_Product__Type_Oprod_Oprod__case(_1451488, _1451492, _1451486), _1451496)), hAPP(hAPP(c_Product__Type_OSigma(_1451488, _1451492), _1451490), _1451494)))], (35763 ^ _779300) ^ [_1451963, _1451965, _1451967, _1451969, _1451971, _1451973] : [class_Groups_Ocomm__monoid__add(_1451963), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451965), _1451967)), 35773 ^ _779300 : [(35774 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451965), 35772 ^ [_1451963, _1451965, _1451967, _1451969, _1451971, _1451973]), _1451967)))], (35776 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1451969), hAPP(_1451971, 35772 ^ [_1451963, _1451965, _1451967, _1451969, _1451971, _1451973])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1451965, _1451963), hAPP(hAPP(c_COMBS(_1451965, tc_fun(_1451969, tc_HOL_Obool), _1451963), hAPP(hAPP(c_COMBB(tc_fun(_1451969, _1451963), tc_fun(tc_fun(_1451969, tc_HOL_Obool), _1451963), _1451965), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1451969, _1451963)), _1451973)), _1451971)), _1451967) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1451965, _1451969), _1451963), hAPP(c_Product__Type_Oprod_Oprod__case(_1451965, _1451969, _1451963), _1451973)), hAPP(hAPP(c_Product__Type_OSigma(_1451965, _1451969), _1451967), _1451971)))], (35780 ^ _779300) ^ [_1452440, _1452442, _1452444, _1452446] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1452440), _1452442)), 35786 ^ _779300 : [(35787 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1452440), 35785 ^ [_1452440, _1452442, _1452444, _1452446]), _1452442)))], (35789 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1452444), hAPP(_1452446, 35785 ^ [_1452440, _1452442, _1452444, _1452446])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1452440, _1452444)), hAPP(hAPP(c_Product__Type_OSigma(_1452440, _1452444), _1452442), _1452446)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1452440, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1452444, tc_HOL_Obool), tc_Nat_Onat, _1452440), c_Finite__Set_Ocard(_1452444)), _1452446)), _1452442))], (35793 ^ _779300) ^ [_1452777, _1452779, _1452781, _1452783, _1452785] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1452777, _1452779)), _1452781), hAPP(hAPP(c_Product__Type_OSigma(_1452777, _1452779), _1452783), _1452785))), 35797 ^ _779300 : [(35798 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1452777), 35796 ^ [_1452777, _1452779, _1452781, _1452783, _1452785]), _1452783)))], (35801 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1452779), 35799 ^ [_1452777, _1452779, _1452781, _1452783, _1452785]), hAPP(_1452785, 35796 ^ [_1452777, _1452779, _1452781, _1452783, _1452785]))))], (35803 ^ _779300) ^ [] : [-(_1452781 = hAPP(hAPP(c_Product__Type_OPair(_1452777, _1452779), 35796 ^ [_1452777, _1452779, _1452781, _1452783, _1452785]), 35799 ^ [_1452777, _1452779, _1452781, _1452783, _1452785]))]]], (35805 ^ _779300) ^ [_1453079, _1453081, _1453083, _1453085, _1453087, _1453089] : [hAPP(c_Set_Oimage(_1453079, _1453081, _1453083), c_Orderings_Otop__class_Otop(tc_fun(_1453079, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1453081, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1453085, _1453087, _1453089), c_Orderings_Otop__class_Otop(tc_fun(_1453085, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1453087, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1453079, _1453085), tc_prod(_1453081, _1453087), c_Product__Type_Omap__pair(_1453079, _1453081, _1453085, _1453087, _1453083, _1453089)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1453079, _1453085), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1453081, _1453087), tc_HOL_Obool)))], (35815 ^ _779300) ^ [_1453364, _1453366, _1453368, _1453370, _1453372, _1453374, _1453376, _1453378] : [c_Fun_Oinj__on(_1453364, _1453366, _1453368, _1453370), c_Fun_Oinj__on(_1453372, _1453374, _1453376, _1453378), -(c_Fun_Oinj__on(tc_prod(_1453364, _1453372), tc_prod(_1453366, _1453374), c_Product__Type_Omap__pair(_1453364, _1453366, _1453372, _1453374, _1453368, _1453376), hAPP(hAPP(c_Product__Type_OSigma(_1453364, _1453372), _1453370), hAPP(c_COMBK(tc_fun(_1453372, tc_HOL_Obool), _1453364), _1453378))))], (35825 ^ _779300) ^ [_1453591, _1453593, _1453595, _1453597, _1453599, _1453601, _1453603, _1453605, _1453607] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1453591, _1453593)), hAPP(hAPP(c_Product__Type_OPair(_1453591, _1453593), _1453595), _1453597)), _1453599)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1453601, _1453603)), hAPP(hAPP(c_Product__Type_OPair(_1453601, _1453603), hAPP(_1453605, _1453595)), hAPP(_1453607, _1453597))), hAPP(c_Set_Oimage(tc_prod(_1453591, _1453593), tc_prod(_1453601, _1453603), c_Product__Type_Omap__pair(_1453591, _1453601, _1453593, _1453603, _1453605, _1453607)), _1453599))))], (35831 ^ _779300) ^ [_1453810, _1453812, _1453814, _1453816, _1453818, _1453820, _1453822] : [-(hAPP(c_Product__Type_Ofst(_1453810, _1453812), hAPP(c_Product__Type_Omap__pair(_1453814, _1453810, _1453816, _1453812, _1453818, _1453820), _1453822)) = hAPP(_1453818, hAPP(c_Product__Type_Ofst(_1453814, _1453816), _1453822)))], (35833 ^ _779300) ^ [_1453870, _1453872, _1453874, _1453876, _1453878, _1453880, _1453882, _1453884] : [-(hAPP(c_Product__Type_Omap__pair(_1453870, _1453872, _1453874, _1453876, _1453878, _1453880), hAPP(hAPP(c_Product__Type_OPair(_1453870, _1453874), _1453882), _1453884)) = hAPP(hAPP(c_Product__Type_OPair(_1453872, _1453876), hAPP(_1453878, _1453882)), hAPP(_1453880, _1453884)))], (35835 ^ _779300) ^ [_1453941, _1453943, _1453945] : [-(hAPP(c_Product__Type_Omap__pair(_1453941, _1453941, _1453943, _1453943, c_COMBI(_1453941), c_COMBI(_1453943)), _1453945) = _1453945)], (35837 ^ _779300) ^ [_1453982, _1453984, _1453986, _1453988, _1453990, _1453992, _1453994] : [-(hAPP(c_Product__Type_Osnd(_1453982, _1453984), hAPP(c_Product__Type_Omap__pair(_1453986, _1453982, _1453988, _1453984, _1453990, _1453992), _1453994)) = hAPP(_1453992, hAPP(c_Product__Type_Osnd(_1453986, _1453988), _1453994)))], (35839 ^ _779300) ^ [_1454042, _1454044, _1454046, _1454048, _1454050, _1454052] : [-(c_Product__Type_Omap__pair(_1454042, _1454044, _1454046, _1454048, _1454050, _1454052) = hAPP(c_Product__Type_Oprod_Oprod__case(_1454042, _1454046, tc_prod(_1454044, _1454048)), hAPP(hAPP(c_COMBC(_1454042, tc_fun(_1454046, _1454048), tc_fun(_1454046, tc_prod(_1454044, _1454048))), hAPP(hAPP(c_COMBB(tc_fun(_1454048, tc_prod(_1454044, _1454048)), tc_fun(tc_fun(_1454046, _1454048), tc_fun(_1454046, tc_prod(_1454044, _1454048))), _1454042), c_COMBB(_1454048, tc_prod(_1454044, _1454048), _1454046)), hAPP(hAPP(c_COMBB(_1454044, tc_fun(_1454048, tc_prod(_1454044, _1454048)), _1454042), c_Product__Type_OPair(_1454044, _1454048)), _1454050))), _1454052)))], (35841 ^ _779300) ^ [_1454165, _1454167, _1454169, _1454171, _1454173, _1454175, _1454177, _1454179, _1454181, _1454183] : [hAPP(c_Set_Oimage(_1454165, _1454167, _1454169), _1454171) = _1454173, hAPP(c_Set_Oimage(_1454175, _1454177, _1454179), _1454181) = _1454183, -(hAPP(c_Set_Oimage(tc_prod(_1454165, _1454175), tc_prod(_1454167, _1454177), c_Product__Type_Omap__pair(_1454165, _1454167, _1454175, _1454177, _1454169, _1454179)), hAPP(hAPP(c_Product__Type_OSigma(_1454165, _1454175), _1454171), hAPP(c_COMBK(tc_fun(_1454175, tc_HOL_Obool), _1454165), _1454181))) = hAPP(hAPP(c_Product__Type_OSigma(_1454167, _1454177), _1454173), hAPP(c_COMBK(tc_fun(_1454177, tc_HOL_Obool), _1454167), _1454183)))], (35851 ^ _779300) ^ [_1454466, _1454468, _1454470, _1454472, _1454474, _1454476, _1454478, _1454480] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1454466, _1454468)), _1454470), hAPP(c_Set_Oimage(tc_prod(_1454472, _1454474), tc_prod(_1454466, _1454468), c_Product__Type_Omap__pair(_1454472, _1454466, _1454474, _1454468, _1454476, _1454478)), _1454480))), 35856 ^ _779300 : [(35857 ^ _779300) ^ [] : [-(_1454470 = hAPP(hAPP(c_Product__Type_OPair(_1454466, _1454468), hAPP(_1454476, 35854 ^ [_1454466, _1454468, _1454470, _1454472, _1454474, _1454476, _1454478, _1454480])), hAPP(_1454478, 35855 ^ [_1454466, _1454468, _1454470, _1454472, _1454474, _1454476, _1454478, _1454480])))], (35859 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1454472, _1454474)), hAPP(hAPP(c_Product__Type_OPair(_1454472, _1454474), 35854 ^ [_1454466, _1454468, _1454470, _1454472, _1454474, _1454476, _1454478, _1454480]), 35855 ^ [_1454466, _1454468, _1454470, _1454472, _1454474, _1454476, _1454478, _1454480])), _1454480)))]]], (35861 ^ _779300) ^ [_1454817, _1454819, _1454821] : [c_Relation_Orefl__on(_1454817, _1454819, _1454821), 35864 ^ _779300 : [(35865 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1454817, _1454817), tc_HOL_Obool)), _1454821), hAPP(hAPP(c_Product__Type_OSigma(_1454817, _1454817), _1454819), hAPP(c_COMBK(tc_fun(_1454817, tc_HOL_Obool), _1454817), _1454819)))))], (35867 ^ _779300) ^ [_1454999] : [hBOOL(hAPP(hAPP(c_member(_1454817), _1454999), _1454819)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1454817, _1454817)), hAPP(hAPP(c_Product__Type_OPair(_1454817, _1454817), _1454999), _1454999)), _1454821)))]]], (35873 ^ _779300) ^ [_1455134, _1455136, _1455138] : [-(c_Relation_Orefl__on(_1455134, _1455136, _1455138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1455134, _1455134), tc_HOL_Obool)), _1455138), hAPP(hAPP(c_Product__Type_OSigma(_1455134, _1455134), _1455136), hAPP(c_COMBK(tc_fun(_1455134, tc_HOL_Obool), _1455134), _1455136)))), 35879 ^ _779300 : [(35880 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1455134), 35878 ^ [_1455134, _1455136, _1455138]), _1455136)))], (35882 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1455134, _1455134)), hAPP(hAPP(c_Product__Type_OPair(_1455134, _1455134), 35878 ^ [_1455134, _1455136, _1455138]), 35878 ^ [_1455134, _1455136, _1455138])), _1455138))]]], (35886 ^ _779300) ^ [_1455483, _1455485, _1455487] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1455483), _1455485)), 35892 ^ _779300 : [(35893 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1455483), 35891 ^ [_1455483, _1455485, _1455487]), _1455485)))], (35895 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1455487, 35891 ^ [_1455483, _1455485, _1455487])))]], -(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(_1455483, tc_Nat_Onat), _1455487), _1455485))))], (35899 ^ _779300) ^ [_1455744, _1455746] : [-(c_Relation_Orefl__on(_1455744, _1455746, c_Relation_OId__on(_1455744, _1455746)))], (35901 ^ _779300) ^ [_1455773] : [-(c_Relation_Orefl__on(_1455773, c_Orderings_Obot__class_Obot(tc_fun(_1455773, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1455773, _1455773), tc_HOL_Obool))))], (35903 ^ _779300) ^ [_1455810, _1455812, _1455814, _1455816, _1455818] : [c_Relation_Orefl__on(_1455810, _1455812, _1455814), c_Relation_Orefl__on(_1455810, _1455816, _1455818), -(c_Relation_Orefl__on(_1455810, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1455810, tc_HOL_Obool)), _1455812), _1455816), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1455810, _1455810), tc_HOL_Obool)), _1455814), _1455818)))], (35913 ^ _779300) ^ [_1456007, _1456009, _1456011, _1456013, _1456015] : [c_Relation_Orefl__on(_1456007, _1456009, _1456011), c_Relation_Orefl__on(_1456007, _1456013, _1456015), -(c_Relation_Orefl__on(_1456007, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456007, tc_HOL_Obool)), _1456009), _1456013), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1456007, _1456007), tc_HOL_Obool)), _1456011), _1456015)))], (35923 ^ _779300) ^ [_1456204, _1456206, _1456208, _1456210] : [c_Relation_Orefl__on(_1456204, _1456206, _1456208), hBOOL(hAPP(hAPP(c_member(_1456204), _1456210), _1456206)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1456204, _1456204)), hAPP(hAPP(c_Product__Type_OPair(_1456204, _1456204), _1456210), _1456210)), _1456208)))], (35933 ^ _779300) ^ [_1456395, _1456397, _1456399, _1456401, _1456403] : [c_Relation_Orefl__on(_1456395, _1456397, _1456399), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456395, _1456395)), hAPP(hAPP(c_Product__Type_OPair(_1456395, _1456395), _1456401), _1456403)), _1456399)), -(hBOOL(hAPP(hAPP(c_member(_1456395), _1456401), _1456397)))], (35943 ^ _779300) ^ [_1456590, _1456592, _1456594, _1456596, _1456598] : [c_Relation_Orefl__on(_1456590, _1456592, _1456594), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456590, _1456590)), hAPP(hAPP(c_Product__Type_OPair(_1456590, _1456590), _1456596), _1456598)), _1456594)), -(hBOOL(hAPP(hAPP(c_member(_1456590), _1456598), _1456592)))], (35953 ^ _779300) ^ [_1456785, _1456787, _1456789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1456785, _1456785), tc_HOL_Obool)), _1456787), hAPP(hAPP(c_Product__Type_OSigma(_1456785, _1456785), _1456789), hAPP(c_COMBK(tc_fun(_1456785, tc_HOL_Obool), _1456785), _1456789)))), 35959 ^ _779300 : [(35960 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456785), 35958 ^ [_1456785, _1456787, _1456789]), _1456789)))], (35962 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1456785, _1456785)), hAPP(hAPP(c_Product__Type_OPair(_1456785, _1456785), 35958 ^ [_1456785, _1456787, _1456789]), 35958 ^ [_1456785, _1456787, _1456789])), _1456787))]], -(c_Relation_Orefl__on(_1456785, _1456789, _1456787))], (35966 ^ _779300) ^ [_1457132] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1457132), c_Int_OInteg)), -(_1457132 = hAPP(c_Int_ORep__Integ, 35969 ^ [_1457132]))], (35973 ^ _779300) ^ [_1457237, _1457239] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1457237), c_Int_OInteg)), hBOOL(hAPP(_1457239, hAPP(c_Int_ORep__Integ, 35978 ^ [_1457237, _1457239]))), -(hBOOL(hAPP(_1457239, _1457237)))], (35984 ^ _779300) ^ [_1457419, _1457421, _1457423, _1457425, _1457427, _1457429, _1457431, _1457433] : [c_Finite__Set_Ofolding__image__simple(_1457419, _1457421, _1457423, _1457425, _1457427, _1457429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457421), _1457431)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457421), _1457433)), 35998 ^ _779300 : [(35999 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457421), 35997 ^ [_1457419, _1457421, _1457423, _1457425, _1457427, _1457429, _1457431, _1457433]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1457421, tc_HOL_Obool)), _1457431), _1457433))))], (36001 ^ _779300) ^ [] : [hAPP(_1457427, 35997 ^ [_1457419, _1457421, _1457423, _1457425, _1457427, _1457429, _1457431, _1457433]) = _1457425]], -(hAPP(_1457429, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1457421, tc_HOL_Obool)), _1457431), _1457433)) = hAPP(hAPP(_1457423, hAPP(_1457429, _1457431)), hAPP(_1457429, _1457433)))], (36005 ^ _779300) ^ [_1457916, _1457918] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457916))), -(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)), _1457916))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1457918)))) = 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)), _1457916))), 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, _1457918))))))], (36011 ^ _779300) ^ [_1457999, _1458001] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457999)), 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)), _1457999))), 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, _1458001))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36017 ^ _779300) ^ [_1458129, _1458131, _1458133] : [hBOOL(hAPP(_1458129, _1458131)), -(hBOOL(hAPP(hAPP(c_member(_1458133), _1458131), hAPP(c_Set_OCollect(_1458133), _1458129))))], (36023 ^ _779300) ^ [_1458236, _1458238, _1458240] : [36024 ^ _779300 : [(36025 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1458236), hAPP(c_Set_OCollect(_1458236), _1458238)))], (36027 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1458236), hAPP(c_Set_OCollect(_1458236), _1458240)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1458236), hAPP(c_Set_OCollect(_1458236), hAPP(hAPP(c_COMBS(_1458236, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1458236), c_fconj), _1458238)), _1458240)))))], (36031 ^ _779300) ^ [_1458447] : [-(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)), _1458447)))))], (36033 ^ _779300) ^ [_1458478] : [-(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)), _1458478)))))], (36035 ^ _779300) ^ [_1458509, _1458511, _1458513, _1458515] : [-(hAPP(c_Set_OCollect(tc_prod(_1458509, _1458511)), hAPP(c_Product__Type_Oprod_Oprod__case(_1458509, _1458511, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1458509, tc_fun(_1458511, tc_HOL_Obool), tc_fun(_1458511, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1458511, tc_HOL_Obool), tc_fun(_1458511, tc_HOL_Obool)), _1458509), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1458511)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1458509), c_fconj), _1458513))), _1458515))) = hAPP(hAPP(c_Product__Type_OSigma(_1458509, _1458511), hAPP(c_Set_OCollect(_1458509), _1458513)), hAPP(c_COMBK(tc_fun(_1458511, tc_HOL_Obool), _1458509), hAPP(c_Set_OCollect(_1458511), _1458515))))], (36037 ^ _779300) ^ [_1458630, _1458632, _1458634, _1458636] : [-(hAPP(c_Set_OCollect(tc_prod(_1458630, _1458632)), hAPP(c_Product__Type_Oprod_Oprod__case(_1458630, _1458632, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1458630, tc_fun(_1458632, tc_HOL_Obool), tc_fun(_1458632, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1458632, tc_HOL_Obool), tc_fun(_1458632, tc_HOL_Obool)), _1458630), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1458632)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1458630), c_fconj), _1458634))), _1458636))) = hAPP(hAPP(c_Product__Type_OSigma(_1458630, _1458632), hAPP(c_Set_OCollect(_1458630), _1458634)), hAPP(hAPP(c_COMBB(tc_fun(_1458632, tc_HOL_Obool), tc_fun(_1458632, tc_HOL_Obool), _1458630), c_Set_OCollect(_1458632)), _1458636)))], (36039 ^ _779300) ^ [_1458755, _1458757] : [-(hAPP(c_Set_OCollect(_1458755), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1458755), c_fNot), _1458757)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1458755, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1458755), _1458757)))], (36041 ^ _779300) ^ [_1458808, _1458810, _1458812] : [-(hAPP(c_Set_OCollect(_1458808), hAPP(hAPP(c_COMBS(_1458808, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1458808), c_fconj), _1458810)), _1458812)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458808, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1458808), _1458810)), hAPP(c_Set_OCollect(_1458808), _1458812)))], (36043 ^ _779300) ^ [_1458896, _1458898] : [hAPP(c_Set_OCollect(_1458896), _1458898) = c_Orderings_Obot__class_Obot(tc_fun(_1458896, tc_HOL_Obool)), 36046 ^ _779300 : [(36047 ^ _779300) ^ [_1458981] : [hBOOL(hAPP(_1458898, _1458981))]]], (36049 ^ _779300) ^ [_1459004, _1459006] : [-(hBOOL(hAPP(_1459006, 36050 ^ [_1459004, _1459006]))), -(hAPP(c_Set_OCollect(_1459004), _1459006) = c_Orderings_Obot__class_Obot(tc_fun(_1459004, tc_HOL_Obool)))], (36056 ^ _779300) ^ [_1459076, _1459078] : [c_Orderings_Obot__class_Obot(tc_fun(_1459076, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1459076), _1459078), 36059 ^ _779300 : [(36060 ^ _779300) ^ [_1459161] : [hBOOL(hAPP(_1459078, _1459161))]]], (36062 ^ _779300) ^ [_1459184, _1459186] : [-(hBOOL(hAPP(_1459186, 36063 ^ [_1459184, _1459186]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1459184, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1459184), _1459186))], (36069 ^ _779300) ^ [_1459241, _1459243] : [-(hAPP(c_Set_OCollect(_1459241), _1459243) = _1459243)], (36071 ^ _779300) ^ [_1459271, _1459273, _1459275] : [-(hAPP(c_Set_OCollect(_1459271), hAPP(hAPP(c_COMBS(_1459271, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1459271), c_fdisj), _1459273)), _1459275)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459271, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1459271), _1459273)), hAPP(c_Set_OCollect(_1459271), _1459275)))], (36073 ^ _779300) ^ [_1459344, _1459346, _1459348] : [-(hAPP(hAPP(c_Set_Oinsert(_1459344), _1459346), hAPP(c_Set_OCollect(_1459344), _1459348)) = hAPP(c_Set_OCollect(_1459344), hAPP(hAPP(c_COMBS(_1459344, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1459344), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1459344), c_fNot), hAPP(hAPP(c_COMBC(_1459344, _1459344, tc_HOL_Obool), c_fequal), _1459346)))), _1459348)))], (36075 ^ _779300) ^ [_1459429] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1459429, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1459429), hAPP(c_COMBK(tc_HOL_Obool, _1459429), c_fFalse)))], (36077 ^ _779300) ^ [_1459486, _1459488, _1459490] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1459486), hAPP(c_Set_OCollect(_1459486), hAPP(hAPP(c_COMBS(_1459486, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1459486), c_fdisj), _1459488)), _1459490)))), 36080 ^ _779300 : [(36081 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1459486), hAPP(c_Set_OCollect(_1459486), _1459488))))], (36083 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1459486), hAPP(c_Set_OCollect(_1459486), _1459490))))]]], (36085 ^ _779300) ^ [_1459681, _1459683, _1459685] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1459681), hAPP(c_Set_OCollect(_1459681), hAPP(hAPP(c_COMBS(_1459681, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1459681), c_fdisj), _1459683)), _1459685))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459681), hAPP(c_Set_OCollect(_1459681), _1459683))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459681), hAPP(c_Set_OCollect(_1459681), _1459685)))], (36095 ^ _779300) ^ [_1459910] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1459910, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1459910), hAPP(c_COMBK(tc_HOL_Obool, _1459910), c_fTrue)))], (36097 ^ _779300) ^ [_1459949, _1459951, _1459953, _1459955] : [-(hAPP(c_Set_Ovimage(_1459949, _1459951, _1459953), hAPP(c_Set_OCollect(_1459951), _1459955)) = hAPP(c_Set_OCollect(_1459949), hAPP(hAPP(c_COMBB(_1459951, tc_HOL_Obool, _1459949), _1459955), _1459953)))], (36099 ^ _779300) ^ [_1460005, _1460007] : [-(hAPP(c_Set_OCollect(_1460005), hAPP(hAPP(c_COMBC(_1460005, tc_fun(_1460005, tc_HOL_Obool), tc_HOL_Obool), c_member(_1460005)), _1460007)) = _1460007)], (36101 ^ _779300) ^ [_1460068, _1460070, _1460072] : [hBOOL(hAPP(hAPP(c_member(_1460068), _1460070), hAPP(c_Set_OCollect(_1460068), _1460072))), -(hBOOL(hAPP(_1460072, _1460070)))], (36107 ^ _779300) ^ [_1460171, _1460173, _1460175] : [hBOOL(hAPP(_1460175, _1460173)), -(hBOOL(hAPP(hAPP(c_member(_1460171), _1460173), hAPP(c_Set_OCollect(_1460171), _1460175))))], (36113 ^ _779300) ^ [_1460280, _1460282, _1460284] : [hBOOL(hAPP(hAPP(c_member(_1460280), _1460282), hAPP(c_Set_OCollect(_1460280), _1460284))), -(hBOOL(hAPP(_1460284, _1460282)))], (36119 ^ _779300) ^ [_1460387, _1460389, _1460391] : [hBOOL(hAPP(hAPP(c_member(_1460387), _1460389), hAPP(c_Set_OCollect(_1460387), _1460391))), -(hBOOL(hAPP(_1460391, _1460389)))], (36125 ^ _779300) ^ [_1460494, _1460496, _1460498] : [-(hAPP(hAPP(c_Set_Oinsert(_1460494), _1460496), _1460498) = hAPP(c_Set_OCollect(_1460494), hAPP(hAPP(c_COMBS(_1460494, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1460494), c_fdisj), hAPP(hAPP(c_COMBC(_1460494, _1460494, tc_HOL_Obool), c_fequal), _1460496))), hAPP(hAPP(c_COMBC(_1460494, tc_fun(_1460494, tc_HOL_Obool), tc_HOL_Obool), c_member(_1460494)), _1460498))))], (36127 ^ _779300) ^ [_1460579, _1460581, _1460583] : [-(hAPP(hAPP(c_Set_Oinsert(_1460579), _1460581), _1460583) = hAPP(c_Set_OCollect(_1460579), hAPP(hAPP(c_COMBS(_1460579, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1460579), c_fdisj), hAPP(hAPP(c_COMBC(_1460579, _1460579, tc_HOL_Obool), c_fequal), _1460581))), hAPP(hAPP(c_COMBC(_1460579, tc_fun(_1460579, tc_HOL_Obool), tc_HOL_Obool), c_member(_1460579)), _1460583))))], (36129 ^ _779300) ^ [_1460664, _1460666, _1460668] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460664, tc_HOL_Obool)), _1460666), _1460668) = hAPP(c_Set_OCollect(_1460664), hAPP(hAPP(c_COMBS(_1460664, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1460664), c_fdisj), hAPP(hAPP(c_COMBC(_1460664, tc_fun(_1460664, tc_HOL_Obool), tc_HOL_Obool), c_member(_1460664)), _1460666))), hAPP(hAPP(c_COMBC(_1460664, tc_fun(_1460664, tc_HOL_Obool), tc_HOL_Obool), c_member(_1460664)), _1460668))))], (36131 ^ _779300) ^ [_1460778, _1460780, _1460782, _1460784] : [hBOOL(hAPP(hAPP(c_member(_1460778), _1460780), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460778, tc_HOL_Obool)), _1460782), hAPP(c_Set_OCollect(_1460778), _1460784)))), 36134 ^ _779300 : [(36135 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1460778), _1460780), _1460782)))], (36137 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1460784, _1460780)))]]], (36139 ^ _779300) ^ [_1460945, _1460947, _1460949, _1460951] : [-(hBOOL(hAPP(hAPP(c_member(_1460945), _1460947), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460945, tc_HOL_Obool)), _1460949), hAPP(c_Set_OCollect(_1460945), _1460951))))), hBOOL(hAPP(hAPP(c_member(_1460945), _1460947), _1460949)), hBOOL(hAPP(_1460951, _1460947))], (36149 ^ _779300) ^ [_1461148, _1461150, _1461152] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461148, tc_HOL_Obool)), _1461150), _1461152) = hAPP(c_Set_OCollect(_1461148), hAPP(hAPP(c_COMBS(_1461148, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461148), c_fconj), hAPP(hAPP(c_COMBC(_1461148, tc_fun(_1461148, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461148)), _1461150))), hAPP(hAPP(c_COMBC(_1461148, tc_fun(_1461148, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461148)), _1461152))))], (36151 ^ _779300) ^ [_1461241, _1461243] : [-(hAPP(c_Set_OCollect(_1461241), hAPP(c_fequal, _1461243)) = hAPP(hAPP(c_Set_Oinsert(_1461241), _1461243), c_Orderings_Obot__class_Obot(tc_fun(_1461241, tc_HOL_Obool))))], (36153 ^ _779300) ^ [_1461287, _1461289] : [-(hAPP(c_Set_OCollect(_1461287), hAPP(hAPP(c_COMBC(_1461287, _1461287, tc_HOL_Obool), c_fequal), _1461289)) = hAPP(hAPP(c_Set_Oinsert(_1461287), _1461289), c_Orderings_Obot__class_Obot(tc_fun(_1461287, tc_HOL_Obool))))], (36155 ^ _779300) ^ [_1461352, _1461354, _1461356] : [hBOOL(hAPP(_1461352, _1461354)), -(hAPP(c_Set_OCollect(_1461356), hAPP(hAPP(c_COMBS(_1461356, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461356), c_fconj), hAPP(c_fequal, _1461354))), _1461352)) = hAPP(hAPP(c_Set_Oinsert(_1461356), _1461354), c_Orderings_Obot__class_Obot(tc_fun(_1461356, tc_HOL_Obool))))], (36161 ^ _779300) ^ [_1461511, _1461513, _1461515] : [-(hBOOL(hAPP(_1461511, _1461513))), -(hAPP(c_Set_OCollect(_1461515), hAPP(hAPP(c_COMBS(_1461515, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461515), c_fconj), hAPP(c_fequal, _1461513))), _1461511)) = c_Orderings_Obot__class_Obot(tc_fun(_1461515, tc_HOL_Obool)))], (36167 ^ _779300) ^ [_1461598, _1461600, _1461602] : [hBOOL(hAPP(_1461598, _1461600)), -(hAPP(c_Set_OCollect(_1461602), hAPP(hAPP(c_COMBS(_1461602, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461602), c_fconj), hAPP(hAPP(c_COMBC(_1461602, _1461602, tc_HOL_Obool), c_fequal), _1461600))), _1461598)) = hAPP(hAPP(c_Set_Oinsert(_1461602), _1461600), c_Orderings_Obot__class_Obot(tc_fun(_1461602, tc_HOL_Obool))))], (36173 ^ _779300) ^ [_1461771, _1461773, _1461775] : [-(hBOOL(hAPP(_1461771, _1461773))), -(hAPP(c_Set_OCollect(_1461775), hAPP(hAPP(c_COMBS(_1461775, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461775), c_fconj), hAPP(hAPP(c_COMBC(_1461775, _1461775, tc_HOL_Obool), c_fequal), _1461773))), _1461771)) = c_Orderings_Obot__class_Obot(tc_fun(_1461775, tc_HOL_Obool)))], (36179 ^ _779300) ^ [_1461853, _1461855, _1461857] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461853, tc_HOL_Obool)), _1461855), _1461857) = hAPP(c_Set_OCollect(_1461853), hAPP(hAPP(c_COMBS(_1461853, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461853), c_fconj), hAPP(hAPP(c_COMBC(_1461853, tc_fun(_1461853, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461853)), _1461855))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1461853), c_fNot), hAPP(hAPP(c_COMBC(_1461853, tc_fun(_1461853, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461853)), _1461857)))))], (36181 ^ _779300) ^ [_1461956, _1461958] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1461956), hAPP(c_Set_OCollect(_1461956), _1461958))), 36184 ^ _779300 : [(36185 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1461956), hAPP(c_Set_OCollect(_1461956), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1461956), c_fNot), _1461958)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1461956), c_Orderings_Otop__class_Otop(tc_fun(_1461956, tc_HOL_Obool)))))], (36191 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1461956), c_Orderings_Otop__class_Otop(tc_fun(_1461956, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1461956), hAPP(c_Set_OCollect(_1461956), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1461956), c_fNot), _1461958)))))]]], (36197 ^ _779300) ^ [_1462265, _1462267, _1462269] : [-(hAPP(hAPP(c_Set_Oinsert(_1462265), _1462267), _1462269) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1462265, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1462265), hAPP(hAPP(c_COMBC(_1462265, _1462265, tc_HOL_Obool), c_fequal), _1462267))), _1462269))], (36199 ^ _779300) ^ [_1462326, _1462328] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1462326, tc_HOL_Obool)), _1462328) = hAPP(c_Set_OCollect(_1462326), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1462326), c_fNot), hAPP(hAPP(c_COMBC(_1462326, tc_fun(_1462326, tc_HOL_Obool), tc_HOL_Obool), c_member(_1462326)), _1462328))))], (36201 ^ _779300) ^ [_1462389, _1462391, _1462393, _1462395] : [-(hAPP(c_Set_Ovimage(_1462389, _1462391, _1462393), _1462395) = hAPP(c_Set_OCollect(_1462389), hAPP(hAPP(c_COMBC(_1462389, tc_fun(_1462391, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1462391, tc_fun(tc_fun(_1462391, tc_HOL_Obool), tc_HOL_Obool), _1462389), c_member(_1462391)), _1462393)), _1462395)))], (36203 ^ _779300) ^ [_1462461, _1462463, _1462465] : [-(hAPP(c_Set_OCollect(_1462461), hAPP(hAPP(c_COMBS(_1462461, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1462461), c_fimplies), _1462463)), _1462465)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1462461, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1462461, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1462461), _1462463))), hAPP(c_Set_OCollect(_1462461), _1462465)))], (36205 ^ _779300) ^ [_1462542, _1462544] : [-(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), _1462542)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1462544))))))], (36207 ^ _779300) ^ [_1462584, _1462586, _1462588, _1462590, _1462592, _1462594, _1462596] : [class_Groups_Ocomm__monoid__add(_1462584), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462586), _1462588)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462590), _1462592)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462586, _1462584), hAPP(hAPP(c_COMBS(_1462586, tc_fun(_1462590, tc_HOL_Obool), _1462584), hAPP(hAPP(c_COMBB(tc_fun(_1462590, _1462584), tc_fun(tc_fun(_1462590, tc_HOL_Obool), _1462584), _1462586), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462590, _1462584)), _1462594)), hAPP(hAPP(c_COMBB(tc_fun(_1462590, tc_HOL_Obool), tc_fun(_1462590, tc_HOL_Obool), _1462586), c_Set_OCollect(_1462590)), hAPP(hAPP(c_COMBB(tc_fun(_1462590, tc_HOL_Obool), tc_fun(_1462590, tc_HOL_Obool), _1462586), hAPP(c_COMBS(_1462590, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1462590), c_fconj), hAPP(hAPP(c_COMBC(_1462590, tc_fun(_1462590, tc_HOL_Obool), tc_HOL_Obool), c_member(_1462590)), _1462592)))), _1462596)))), _1462588) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462590, _1462584), hAPP(hAPP(c_COMBS(_1462590, tc_fun(_1462586, tc_HOL_Obool), _1462584), hAPP(hAPP(c_COMBB(tc_fun(_1462586, _1462584), tc_fun(tc_fun(_1462586, tc_HOL_Obool), _1462584), _1462590), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462586, _1462584)), hAPP(c_COMBC(_1462586, _1462590, _1462584), _1462594))), hAPP(hAPP(c_COMBB(tc_fun(_1462586, tc_HOL_Obool), tc_fun(_1462586, tc_HOL_Obool), _1462590), c_Set_OCollect(_1462586)), hAPP(hAPP(c_COMBB(tc_fun(_1462586, tc_HOL_Obool), tc_fun(_1462586, tc_HOL_Obool), _1462590), hAPP(c_COMBS(_1462586, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1462586), c_fconj), hAPP(hAPP(c_COMBC(_1462586, tc_fun(_1462586, tc_HOL_Obool), tc_HOL_Obool), c_member(_1462586)), _1462588)))), hAPP(c_COMBC(_1462586, _1462590, tc_HOL_Obool), _1462596))))), _1462592))], (36221 ^ _779300) ^ [_1463277, _1463279, _1463281, _1463283, _1463285, _1463287] : [-(hAPP(c_Set_Oimage(_1463277, _1463279, hAPP(hAPP(c_COMBS(_1463277, _1463279, _1463279), hAPP(hAPP(c_COMBS(_1463277, _1463279, tc_fun(_1463279, _1463279)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1463279, tc_fun(_1463279, _1463279)), _1463277), c_If(_1463279)), _1463281)), _1463283)), _1463285)), _1463287) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463279, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1463277, _1463279, _1463283), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463277, tc_HOL_Obool)), _1463287), hAPP(c_Set_OCollect(_1463277), _1463281)))), hAPP(c_Set_Oimage(_1463277, _1463279, _1463285), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463277, tc_HOL_Obool)), _1463287), hAPP(c_Set_OCollect(_1463277), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1463277), c_fNot), _1463281))))))], (36223 ^ _779300) ^ [_1463425, _1463427, _1463429, _1463431] : [_1463425 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1463427, _1463429), 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)), _1463431))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1463427), _1463425)))], (36229 ^ _779300) ^ [_1463540, _1463542, _1463544, _1463546, _1463548] : [class_Groups_Ocomm__monoid__add(_1463540), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463542), _1463544)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463542, _1463540), _1463546), hAPP(c_Set_OCollect(_1463542), hAPP(hAPP(c_COMBS(_1463542, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1463542), c_fconj), hAPP(hAPP(c_COMBC(_1463542, tc_fun(_1463542, tc_HOL_Obool), tc_HOL_Obool), c_member(_1463542)), _1463544))), hAPP(hAPP(c_COMBC(_1463542, tc_fun(_1463542, tc_HOL_Obool), tc_HOL_Obool), c_member(_1463542)), _1463548)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463542, _1463540), hAPP(hAPP(c_COMBC(_1463542, _1463540, _1463540), hAPP(hAPP(c_COMBS(_1463542, _1463540, tc_fun(_1463540, _1463540)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1463540, tc_fun(_1463540, _1463540)), _1463542), c_If(_1463540)), hAPP(hAPP(c_COMBC(_1463542, tc_fun(_1463542, tc_HOL_Obool), tc_HOL_Obool), c_member(_1463542)), _1463548))), _1463546)), c_Groups_Ozero__class_Ozero(_1463540))), _1463544))], (36239 ^ _779300) ^ [_1463949, _1463951, _1463953, _1463955, _1463957, _1463959] : [class_Groups_Ocomm__monoid__add(_1463949), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463951), _1463953)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463951, _1463949), _1463955), _1463953) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463957, _1463949), hAPP(hAPP(c_COMBB(tc_fun(_1463951, tc_HOL_Obool), _1463949, _1463957), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463951, _1463949), _1463955)), hAPP(hAPP(c_COMBB(tc_fun(_1463951, tc_HOL_Obool), tc_fun(_1463951, tc_HOL_Obool), _1463957), c_Set_OCollect(_1463951)), hAPP(hAPP(c_COMBB(tc_fun(_1463951, tc_HOL_Obool), tc_fun(_1463951, tc_HOL_Obool), _1463957), hAPP(c_COMBS(_1463951, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1463951), c_fconj), hAPP(hAPP(c_COMBC(_1463951, tc_fun(_1463951, tc_HOL_Obool), tc_HOL_Obool), c_member(_1463951)), _1463953)))), hAPP(c_COMBC(_1463951, _1463957, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1463957, tc_fun(_1463957, tc_HOL_Obool), _1463951), c_fequal), _1463959)))))), hAPP(c_Set_Oimage(_1463951, _1463957, _1463959), _1463953)))], (36249 ^ _779300) ^ [_1464360, _1464362, _1464364, _1464366] : [-(hAPP(c_Relation_OImage(_1464360, _1464362, _1464364), hAPP(hAPP(c_Set_Oinsert(_1464360), _1464366), c_Orderings_Obot__class_Obot(tc_fun(_1464360, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1464362), hAPP(hAPP(c_COMBC(_1464362, tc_fun(tc_prod(_1464360, _1464362), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1464360, _1464362), tc_fun(tc_fun(tc_prod(_1464360, _1464362), tc_HOL_Obool), tc_HOL_Obool), _1464362), c_member(tc_prod(_1464360, _1464362))), hAPP(c_Product__Type_OPair(_1464360, _1464362), _1464366))), _1464364)))], (36251 ^ _779300) ^ [_1464463, _1464465, _1464467, _1464469, _1464471, _1464473] : [class_Groups_Ocomm__monoid__add(_1464463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464465), _1464467)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464465, _1464463), hAPP(hAPP(c_COMBS(_1464465, _1464463, _1464463), hAPP(hAPP(c_COMBS(_1464465, _1464463, tc_fun(_1464463, _1464463)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1464463, tc_fun(_1464463, _1464463)), _1464465), c_If(_1464463)), _1464469)), _1464471)), _1464473)), _1464467) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1464463), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464465, _1464463), _1464471), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464465, tc_HOL_Obool)), _1464467), hAPP(c_Set_OCollect(_1464465), _1464469)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464465, _1464463), _1464473), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464465, tc_HOL_Obool)), _1464467), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464465, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1464465), _1464469))))))], (36261 ^ _779300) ^ [_1464846, _1464848] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1464846)), -(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)), _1464846))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1464848))))) = 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)), _1464846))), 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, _1464848))))))], (36267 ^ _779300) ^ [_1465023, _1465025, _1465027, _1465029, _1465031, _1465033] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465023), _1465025)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465027), _1465029)), 36277 ^ _779300 : [(36278 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1465027), 36276 ^ [_1465023, _1465025, _1465027, _1465029, _1465031, _1465033]), _1465029)))], (36280 ^ _779300) ^ [] : [hAPP(c_Finite__Set_Ocard(_1465023), hAPP(c_Set_OCollect(_1465023), hAPP(hAPP(c_COMBS(_1465023, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1465023), c_fconj), hAPP(hAPP(c_COMBC(_1465023, tc_fun(_1465023, tc_HOL_Obool), tc_HOL_Obool), c_member(_1465023)), _1465025))), hAPP(hAPP(c_COMBC(_1465023, _1465027, tc_HOL_Obool), _1465031), 36276 ^ [_1465023, _1465025, _1465027, _1465029, _1465031, _1465033])))) = _1465033]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465023, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1465027, tc_HOL_Obool), tc_Nat_Onat, _1465023), c_Finite__Set_Ocard(_1465027)), hAPP(hAPP(c_COMBB(tc_fun(_1465027, tc_HOL_Obool), tc_fun(_1465027, tc_HOL_Obool), _1465023), c_Set_OCollect(_1465027)), hAPP(hAPP(c_COMBB(tc_fun(_1465027, tc_HOL_Obool), tc_fun(_1465027, tc_HOL_Obool), _1465023), hAPP(c_COMBS(_1465027, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1465027), c_fconj), hAPP(hAPP(c_COMBC(_1465027, tc_fun(_1465027, tc_HOL_Obool), tc_HOL_Obool), c_member(_1465027)), _1465029)))), _1465031)))), _1465025) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1465033), hAPP(c_Finite__Set_Ocard(_1465027), _1465029)))], (36284 ^ _779300) ^ [_1465713, _1465715, _1465717] : [class_Orderings_Olinorder(_1465713), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465713), _1465715)), -(_1465715 = c_Orderings_Obot__class_Obot(tc_fun(_1465713, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1465713), _1465717), c_Big__Operators_Olattice_OInf__fin(_1465713, c_Orderings_Oord__class_Omin(_1465713), _1465715)) = c_Big__Operators_Olattice_OInf__fin(_1465713, c_Orderings_Oord__class_Omin(_1465713), hAPP(c_Set_OCollect(_1465713), hAPP(hAPP(c_COMBB(tc_fun(_1465713, tc_HOL_Obool), tc_HOL_Obool, _1465713), c_HOL_OEx(_1465713)), hAPP(hAPP(c_COMBC(_1465713, tc_fun(_1465713, tc_HOL_Obool), tc_fun(_1465713, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1465713, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1465713, tc_HOL_Obool), tc_fun(_1465713, tc_HOL_Obool)), _1465713), c_COMBS(_1465713, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1465713, tc_HOL_Obool), tc_fun(_1465713, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1465713), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1465713), c_fconj)), hAPP(hAPP(c_COMBC(_1465713, tc_fun(_1465713, _1465713), tc_fun(_1465713, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1465713, tc_HOL_Obool), tc_fun(tc_fun(_1465713, _1465713), tc_fun(_1465713, tc_HOL_Obool)), _1465713), c_COMBB(_1465713, tc_HOL_Obool, _1465713)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1465713), _1465717))))), hAPP(hAPP(c_COMBC(_1465713, tc_fun(_1465713, tc_HOL_Obool), tc_HOL_Obool), c_member(_1465713)), _1465715))))))], (36298 ^ _779300) ^ [_1466211, _1466213, _1466215] : [class_Orderings_Olinorder(_1466211), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466211), _1466213)), -(_1466213 = c_Orderings_Obot__class_Obot(tc_fun(_1466211, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466211), _1466215)), -(_1466215 = c_Orderings_Obot__class_Obot(tc_fun(_1466211, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1466211), c_Big__Operators_Olattice_OInf__fin(_1466211, c_Orderings_Oord__class_Omin(_1466211), _1466213)), c_Big__Operators_Olattice_OInf__fin(_1466211, c_Orderings_Oord__class_Omin(_1466211), _1466215)) = c_Big__Operators_Olattice_OInf__fin(_1466211, c_Orderings_Oord__class_Omin(_1466211), hAPP(c_Set_OCollect(_1466211), hAPP(hAPP(c_COMBB(tc_fun(_1466211, tc_HOL_Obool), tc_HOL_Obool, _1466211), c_HOL_OEx(_1466211)), hAPP(hAPP(c_COMBB(tc_fun(_1466211, tc_fun(_1466211, tc_HOL_Obool)), tc_fun(_1466211, tc_HOL_Obool), _1466211), hAPP(c_COMBB(tc_fun(_1466211, tc_HOL_Obool), tc_HOL_Obool, _1466211), c_HOL_OEx(_1466211))), hAPP(hAPP(c_COMBC(_1466211, tc_fun(_1466211, tc_fun(_1466211, tc_HOL_Obool)), tc_fun(_1466211, tc_fun(_1466211, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1466211, tc_fun(tc_fun(_1466211, tc_HOL_Obool), tc_fun(_1466211, tc_HOL_Obool))), tc_fun(tc_fun(_1466211, tc_fun(_1466211, tc_HOL_Obool)), tc_fun(_1466211, tc_fun(_1466211, tc_HOL_Obool))), _1466211), c_COMBS(_1466211, tc_fun(_1466211, tc_HOL_Obool), tc_fun(_1466211, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1466211, tc_fun(_1466211, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1466211, tc_fun(tc_fun(_1466211, tc_HOL_Obool), tc_fun(_1466211, tc_HOL_Obool))), _1466211), hAPP(c_COMBB(tc_fun(_1466211, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1466211, tc_HOL_Obool), tc_fun(_1466211, tc_HOL_Obool)), _1466211), c_COMBS(_1466211, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1466211, tc_fun(_1466211, tc_HOL_Obool)), tc_fun(_1466211, tc_fun(_1466211, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1466211), hAPP(c_COMBB(tc_fun(_1466211, tc_HOL_Obool), tc_fun(_1466211, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1466211), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1466211), c_fconj))), hAPP(hAPP(c_COMBC(_1466211, tc_fun(_1466211, tc_fun(_1466211, _1466211)), tc_fun(_1466211, tc_fun(_1466211, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1466211, _1466211), tc_fun(_1466211, tc_HOL_Obool)), tc_fun(tc_fun(_1466211, tc_fun(_1466211, _1466211)), tc_fun(_1466211, tc_fun(_1466211, tc_HOL_Obool))), _1466211), c_COMBB(tc_fun(_1466211, _1466211), tc_fun(_1466211, tc_HOL_Obool), _1466211)), hAPP(hAPP(c_COMBB(tc_fun(_1466211, tc_HOL_Obool), tc_fun(tc_fun(_1466211, _1466211), tc_fun(_1466211, tc_HOL_Obool)), _1466211), c_COMBB(_1466211, tc_HOL_Obool, _1466211)), c_fequal))), c_Orderings_Oord__class_Omax(_1466211)))))), hAPP(hAPP(c_COMBC(_1466211, tc_fun(_1466211, tc_HOL_Obool), tc_fun(_1466211, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1466211, tc_HOL_Obool), tc_fun(_1466211, tc_HOL_Obool)), _1466211), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1466211)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1466211), c_fconj), hAPP(hAPP(c_COMBC(_1466211, tc_fun(_1466211, tc_HOL_Obool), tc_HOL_Obool), c_member(_1466211)), _1466213)))), hAPP(hAPP(c_COMBC(_1466211, tc_fun(_1466211, tc_HOL_Obool), tc_HOL_Obool), c_member(_1466211)), _1466215))))))))], (36320 ^ _779300) ^ [_1467328, _1467330] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467328), _1467330)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1467328, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1467328, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1467328, tc_HOL_Obool), tc_fun(_1467328, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1467328, tc_HOL_Obool))), _1467330)))))], (36326 ^ _779300) ^ [_1467485, _1467487] : [-(hAPP(c_Set_OPow(_1467485), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1467485, tc_HOL_Obool)), _1467487)) = hAPP(c_Set_OCollect(tc_fun(_1467485, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1467485, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1467485, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1467485, tc_HOL_Obool), tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1467485, tc_HOL_Obool)), c_COMBS(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1467485, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1467485, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1467485, tc_HOL_Obool), tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_fun(_1467485, tc_HOL_Obool)), tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_fun(_1467485, tc_HOL_Obool)), tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1467485, tc_HOL_Obool)), c_COMBB(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1467485, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1467485, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1467485, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1467485, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1467485, tc_HOL_Obool)), _1467487)), c_Set_OPow(_1467485))))))], (36328 ^ _779300) ^ [_1467765, _1467767] : [-(hAPP(c_Set_OPow(_1467765), _1467767) = hAPP(c_Set_OCollect(tc_fun(_1467765, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1467765, tc_HOL_Obool), tc_fun(_1467765, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1467765, tc_HOL_Obool))), _1467767)))], (36330 ^ _779300) ^ [_1467824, _1467826, _1467828, _1467830] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467824), hAPP(c_Set_OCollect(_1467824), _1467826))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1467828), hAPP(c_Set_OCollect(_1467828), hAPP(hAPP(c_COMBB(tc_fun(_1467824, tc_HOL_Obool), tc_HOL_Obool, _1467828), c_HOL_OEx(_1467824)), hAPP(hAPP(c_COMBC(_1467828, tc_fun(_1467824, tc_HOL_Obool), tc_fun(_1467824, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467824, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1467824, tc_HOL_Obool), tc_fun(_1467824, tc_HOL_Obool)), _1467828), c_COMBS(_1467824, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467824, tc_HOL_Obool), tc_fun(_1467824, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1467828), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1467824), c_fconj)), hAPP(hAPP(c_COMBC(_1467828, tc_fun(_1467824, _1467828), tc_fun(_1467824, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467828, tc_HOL_Obool), tc_fun(tc_fun(_1467824, _1467828), tc_fun(_1467824, tc_HOL_Obool)), _1467828), c_COMBB(_1467828, tc_HOL_Obool, _1467824)), c_fequal)), _1467830)))), _1467826))))))], (36336 ^ _779300) ^ [_1468185, _1468187, _1468189, _1468191] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468185), hAPP(c_Set_OCollect(_1468185), _1468187))), 36339 ^ _779300 : [(36350 ^ _779300) ^ [] : [36352 ^ _779300 : [(36353 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1468187, 36351 ^ [_1468185, _1468187, _1468189, _1468191])))], (36355 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468189), hAPP(c_Set_OCollect(_1468189), hAPP(hAPP(c_COMBC(_1468189, _1468185, tc_HOL_Obool), _1468191), 36351 ^ [_1468185, _1468187, _1468189, _1468191]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1468189), hAPP(c_Set_OCollect(_1468189), hAPP(hAPP(c_COMBB(tc_fun(_1468185, tc_HOL_Obool), tc_HOL_Obool, _1468189), c_HOL_OEx(_1468185)), hAPP(hAPP(c_COMBB(tc_fun(_1468185, tc_HOL_Obool), tc_fun(_1468185, tc_HOL_Obool), _1468189), hAPP(c_COMBS(_1468185, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1468185), c_fconj), _1468187))), _1468191))))))], (36340 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468189), hAPP(c_Set_OCollect(_1468189), hAPP(hAPP(c_COMBB(tc_fun(_1468185, tc_HOL_Obool), tc_HOL_Obool, _1468189), c_HOL_OEx(_1468185)), hAPP(hAPP(c_COMBB(tc_fun(_1468185, tc_HOL_Obool), tc_fun(_1468185, tc_HOL_Obool), _1468189), hAPP(c_COMBS(_1468185, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1468185), c_fconj), _1468187))), _1468191))))), 36343 ^ _779300 : [(36344 ^ _779300) ^ [_1468468] : [hBOOL(hAPP(_1468187, _1468468)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1468189), hAPP(c_Set_OCollect(_1468189), hAPP(hAPP(c_COMBC(_1468189, _1468185, tc_HOL_Obool), _1468191), _1468468)))))]]]]], (36359 ^ _779300) ^ [_1468833, _1468835] : [-(c_Fun_Oinj__on(tc_fun(_1468833, _1468835), tc_fun(tc_prod(_1468833, _1468835), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1468833, _1468835), tc_HOL_Obool), tc_fun(tc_prod(_1468833, _1468835), tc_HOL_Obool), tc_fun(_1468833, _1468835)), c_Set_OCollect(tc_prod(_1468833, _1468835))), hAPP(hAPP(c_COMBB(tc_fun(_1468833, tc_fun(_1468835, tc_HOL_Obool)), tc_fun(tc_prod(_1468833, _1468835), tc_HOL_Obool), tc_fun(_1468833, _1468835)), c_Product__Type_Oprod_Oprod__case(_1468833, _1468835, tc_HOL_Obool)), hAPP(c_COMBB(_1468835, tc_fun(_1468835, tc_HOL_Obool), _1468833), hAPP(c_COMBC(_1468835, _1468835, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1468833, _1468835), tc_HOL_Obool))))], (36361 ^ _779300) ^ [_1468953] : [-(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)))), _1468953))))], (36363 ^ _779300) ^ [_1468981] : [-(c_Wellfounded_Ofinite__psubset(_1468981) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1468981, tc_HOL_Obool), tc_fun(_1468981, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1468981, tc_HOL_Obool), tc_fun(_1468981, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1468981, tc_HOL_Obool), tc_fun(tc_fun(_1468981, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1468981, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1468981, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1468981, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1468981, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1468981, tc_HOL_Obool)), c_COMBS(tc_fun(_1468981, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1468981, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1468981, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1468981, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1468981, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1468981, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1468981)))))], (36365 ^ _779300) ^ [_1469141, _1469143, _1469145, _1469147] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1469141, _1469143), _1469145), _1469147) = hAPP(c_Set_OCollect(tc_prod(_1469143, _1469143)), hAPP(c_Product__Type_Oprod_Oprod__case(_1469143, _1469143, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1469143, tc_fun(tc_prod(_1469141, _1469141), tc_HOL_Obool), tc_fun(_1469143, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469143, tc_fun(tc_fun(tc_prod(_1469141, _1469141), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469141, _1469141), tc_HOL_Obool), tc_fun(_1469143, tc_HOL_Obool)), _1469143), c_COMBC(_1469143, tc_fun(tc_prod(_1469141, _1469141), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469143, tc_prod(_1469141, _1469141)), tc_fun(_1469143, tc_fun(tc_fun(tc_prod(_1469141, _1469141), tc_HOL_Obool), tc_HOL_Obool)), _1469143), hAPP(c_COMBB(tc_prod(_1469141, _1469141), tc_fun(tc_fun(tc_prod(_1469141, _1469141), tc_HOL_Obool), tc_HOL_Obool), _1469143), c_member(tc_prod(_1469141, _1469141)))), hAPP(hAPP(c_COMBC(_1469143, tc_fun(_1469143, _1469141), tc_fun(_1469143, tc_prod(_1469141, _1469141))), hAPP(hAPP(c_COMBB(tc_fun(_1469141, tc_prod(_1469141, _1469141)), tc_fun(tc_fun(_1469143, _1469141), tc_fun(_1469143, tc_prod(_1469141, _1469141))), _1469143), c_COMBB(_1469141, tc_prod(_1469141, _1469141), _1469143)), hAPP(hAPP(c_COMBB(_1469141, tc_fun(_1469141, tc_prod(_1469141, _1469141)), _1469143), c_Product__Type_OPair(_1469141, _1469141)), _1469147))), _1469147)))), _1469145))))], (36367 ^ _779300) ^ [_1469382] : [-(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)))), _1469382)) = 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), _1469382), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (36369 ^ _779300) ^ [_1469423] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1469423) = 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), _1469423), c_Int_Onat)))))], (36371 ^ _779300) ^ [_1469464, _1469466, _1469468] : [class_Groups_Olinordered__ab__semigroup__add(_1469464), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469464), _1469466)), -(_1469466 = c_Orderings_Obot__class_Obot(tc_fun(_1469464, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469464), _1469468), c_Big__Operators_Olinorder__class_OMin(_1469464, _1469466)) = c_Big__Operators_Olinorder__class_OMin(_1469464, hAPP(c_Set_OCollect(_1469464), hAPP(hAPP(c_COMBB(tc_fun(_1469464, tc_HOL_Obool), tc_HOL_Obool, _1469464), c_HOL_OEx(_1469464)), hAPP(hAPP(c_COMBC(_1469464, tc_fun(_1469464, tc_HOL_Obool), tc_fun(_1469464, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469464, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1469464, tc_HOL_Obool), tc_fun(_1469464, tc_HOL_Obool)), _1469464), c_COMBS(_1469464, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469464, tc_HOL_Obool), tc_fun(_1469464, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1469464), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1469464), c_fconj)), hAPP(hAPP(c_COMBC(_1469464, tc_fun(_1469464, _1469464), tc_fun(_1469464, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469464, tc_HOL_Obool), tc_fun(tc_fun(_1469464, _1469464), tc_fun(_1469464, tc_HOL_Obool)), _1469464), c_COMBB(_1469464, tc_HOL_Obool, _1469464)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1469464), _1469468))))), hAPP(hAPP(c_COMBC(_1469464, tc_fun(_1469464, tc_HOL_Obool), tc_HOL_Obool), c_member(_1469464)), _1469466))))))], (36385 ^ _779300) ^ [_1469950, _1469952, _1469954] : [class_Groups_Olinordered__ab__semigroup__add(_1469950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469950), _1469952)), -(_1469952 = c_Orderings_Obot__class_Obot(tc_fun(_1469950, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469950), _1469954), c_Big__Operators_Olinorder__class_OMax(_1469950, _1469952)) = c_Big__Operators_Olinorder__class_OMax(_1469950, hAPP(c_Set_OCollect(_1469950), hAPP(hAPP(c_COMBB(tc_fun(_1469950, tc_HOL_Obool), tc_HOL_Obool, _1469950), c_HOL_OEx(_1469950)), hAPP(hAPP(c_COMBC(_1469950, tc_fun(_1469950, tc_HOL_Obool), tc_fun(_1469950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469950, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1469950, tc_HOL_Obool), tc_fun(_1469950, tc_HOL_Obool)), _1469950), c_COMBS(_1469950, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469950, tc_HOL_Obool), tc_fun(_1469950, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1469950), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1469950), c_fconj)), hAPP(hAPP(c_COMBC(_1469950, tc_fun(_1469950, _1469950), tc_fun(_1469950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469950, tc_HOL_Obool), tc_fun(tc_fun(_1469950, _1469950), tc_fun(_1469950, tc_HOL_Obool)), _1469950), c_COMBB(_1469950, tc_HOL_Obool, _1469950)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1469950), _1469954))))), hAPP(hAPP(c_COMBC(_1469950, tc_fun(_1469950, tc_HOL_Obool), tc_HOL_Obool), c_member(_1469950)), _1469952))))))], (36399 ^ _779300) ^ [_1470436, _1470438, _1470440] : [class_Lattices_Odistrib__lattice(_1470436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470436), _1470438)), -(_1470438 = c_Orderings_Obot__class_Obot(tc_fun(_1470436, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470436), _1470440)), -(_1470440 = c_Orderings_Obot__class_Obot(tc_fun(_1470436, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1470436), c_Big__Operators_Olattice__class_OInf__fin(_1470436, _1470438)), c_Big__Operators_Olattice__class_OInf__fin(_1470436, _1470440)) = c_Big__Operators_Olattice__class_OInf__fin(_1470436, hAPP(c_Set_OCollect(_1470436), hAPP(hAPP(c_COMBB(tc_fun(_1470436, tc_HOL_Obool), tc_HOL_Obool, _1470436), c_HOL_OEx(_1470436)), hAPP(hAPP(c_COMBB(tc_fun(_1470436, tc_fun(_1470436, tc_HOL_Obool)), tc_fun(_1470436, tc_HOL_Obool), _1470436), hAPP(c_COMBB(tc_fun(_1470436, tc_HOL_Obool), tc_HOL_Obool, _1470436), c_HOL_OEx(_1470436))), hAPP(hAPP(c_COMBC(_1470436, tc_fun(_1470436, tc_fun(_1470436, tc_HOL_Obool)), tc_fun(_1470436, tc_fun(_1470436, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1470436, tc_fun(tc_fun(_1470436, tc_HOL_Obool), tc_fun(_1470436, tc_HOL_Obool))), tc_fun(tc_fun(_1470436, tc_fun(_1470436, tc_HOL_Obool)), tc_fun(_1470436, tc_fun(_1470436, tc_HOL_Obool))), _1470436), c_COMBS(_1470436, tc_fun(_1470436, tc_HOL_Obool), tc_fun(_1470436, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1470436, tc_fun(_1470436, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1470436, tc_fun(tc_fun(_1470436, tc_HOL_Obool), tc_fun(_1470436, tc_HOL_Obool))), _1470436), hAPP(c_COMBB(tc_fun(_1470436, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1470436, tc_HOL_Obool), tc_fun(_1470436, tc_HOL_Obool)), _1470436), c_COMBS(_1470436, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1470436, tc_fun(_1470436, tc_HOL_Obool)), tc_fun(_1470436, tc_fun(_1470436, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1470436), hAPP(c_COMBB(tc_fun(_1470436, tc_HOL_Obool), tc_fun(_1470436, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1470436), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1470436), c_fconj))), hAPP(hAPP(c_COMBC(_1470436, tc_fun(_1470436, tc_fun(_1470436, _1470436)), tc_fun(_1470436, tc_fun(_1470436, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1470436, _1470436), tc_fun(_1470436, tc_HOL_Obool)), tc_fun(tc_fun(_1470436, tc_fun(_1470436, _1470436)), tc_fun(_1470436, tc_fun(_1470436, tc_HOL_Obool))), _1470436), c_COMBB(tc_fun(_1470436, _1470436), tc_fun(_1470436, tc_HOL_Obool), _1470436)), hAPP(hAPP(c_COMBB(tc_fun(_1470436, tc_HOL_Obool), tc_fun(tc_fun(_1470436, _1470436), tc_fun(_1470436, tc_HOL_Obool)), _1470436), c_COMBB(_1470436, tc_HOL_Obool, _1470436)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1470436)))))), hAPP(hAPP(c_COMBC(_1470436, tc_fun(_1470436, tc_HOL_Obool), tc_fun(_1470436, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1470436, tc_HOL_Obool), tc_fun(_1470436, tc_HOL_Obool)), _1470436), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1470436)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1470436), c_fconj), hAPP(hAPP(c_COMBC(_1470436, tc_fun(_1470436, tc_HOL_Obool), tc_HOL_Obool), c_member(_1470436)), _1470438)))), hAPP(hAPP(c_COMBC(_1470436, tc_fun(_1470436, tc_HOL_Obool), tc_HOL_Obool), c_member(_1470436)), _1470440))))))))], (36421 ^ _779300) ^ [_1471535, _1471537, _1471539] : [class_Lattices_Odistrib__lattice(_1471535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471535), _1471537)), -(_1471537 = c_Orderings_Obot__class_Obot(tc_fun(_1471535, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1471535), _1471539), c_Big__Operators_Olattice__class_OInf__fin(_1471535, _1471537)) = c_Big__Operators_Olattice__class_OInf__fin(_1471535, hAPP(c_Set_OCollect(_1471535), hAPP(hAPP(c_COMBB(tc_fun(_1471535, tc_HOL_Obool), tc_HOL_Obool, _1471535), c_HOL_OEx(_1471535)), hAPP(hAPP(c_COMBC(_1471535, tc_fun(_1471535, tc_HOL_Obool), tc_fun(_1471535, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471535, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1471535, tc_HOL_Obool), tc_fun(_1471535, tc_HOL_Obool)), _1471535), c_COMBS(_1471535, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471535, tc_HOL_Obool), tc_fun(_1471535, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1471535), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1471535), c_fconj)), hAPP(hAPP(c_COMBC(_1471535, tc_fun(_1471535, _1471535), tc_fun(_1471535, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471535, tc_HOL_Obool), tc_fun(tc_fun(_1471535, _1471535), tc_fun(_1471535, tc_HOL_Obool)), _1471535), c_COMBB(_1471535, tc_HOL_Obool, _1471535)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1471535), _1471539))))), hAPP(hAPP(c_COMBC(_1471535, tc_fun(_1471535, tc_HOL_Obool), tc_HOL_Obool), c_member(_1471535)), _1471537))))))], (36435 ^ _779300) ^ [_1472021, _1472023, _1472025] : [class_Lattices_Odistrib__lattice(_1472021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472021), _1472023)), -(_1472023 = c_Orderings_Obot__class_Obot(tc_fun(_1472021, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1472021), _1472025), c_Big__Operators_Olattice__class_OSup__fin(_1472021, _1472023)) = c_Big__Operators_Olattice__class_OSup__fin(_1472021, hAPP(c_Set_OCollect(_1472021), hAPP(hAPP(c_COMBB(tc_fun(_1472021, tc_HOL_Obool), tc_HOL_Obool, _1472021), c_HOL_OEx(_1472021)), hAPP(hAPP(c_COMBC(_1472021, tc_fun(_1472021, tc_HOL_Obool), tc_fun(_1472021, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472021, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1472021, tc_HOL_Obool), tc_fun(_1472021, tc_HOL_Obool)), _1472021), c_COMBS(_1472021, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472021, tc_HOL_Obool), tc_fun(_1472021, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1472021), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1472021), c_fconj)), hAPP(hAPP(c_COMBC(_1472021, tc_fun(_1472021, _1472021), tc_fun(_1472021, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472021, tc_HOL_Obool), tc_fun(tc_fun(_1472021, _1472021), tc_fun(_1472021, tc_HOL_Obool)), _1472021), c_COMBB(_1472021, tc_HOL_Obool, _1472021)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1472021), _1472025))))), hAPP(hAPP(c_COMBC(_1472021, tc_fun(_1472021, tc_HOL_Obool), tc_HOL_Obool), c_member(_1472021)), _1472023))))))], (36449 ^ _779300) ^ [_1472507, _1472509, _1472511] : [class_Lattices_Odistrib__lattice(_1472507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472507), _1472509)), -(_1472509 = c_Orderings_Obot__class_Obot(tc_fun(_1472507, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472507), _1472511)), -(_1472511 = c_Orderings_Obot__class_Obot(tc_fun(_1472507, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1472507), c_Big__Operators_Olattice__class_OSup__fin(_1472507, _1472509)), c_Big__Operators_Olattice__class_OSup__fin(_1472507, _1472511)) = c_Big__Operators_Olattice__class_OSup__fin(_1472507, hAPP(c_Set_OCollect(_1472507), hAPP(hAPP(c_COMBB(tc_fun(_1472507, tc_HOL_Obool), tc_HOL_Obool, _1472507), c_HOL_OEx(_1472507)), hAPP(hAPP(c_COMBB(tc_fun(_1472507, tc_fun(_1472507, tc_HOL_Obool)), tc_fun(_1472507, tc_HOL_Obool), _1472507), hAPP(c_COMBB(tc_fun(_1472507, tc_HOL_Obool), tc_HOL_Obool, _1472507), c_HOL_OEx(_1472507))), hAPP(hAPP(c_COMBC(_1472507, tc_fun(_1472507, tc_fun(_1472507, tc_HOL_Obool)), tc_fun(_1472507, tc_fun(_1472507, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1472507, tc_fun(tc_fun(_1472507, tc_HOL_Obool), tc_fun(_1472507, tc_HOL_Obool))), tc_fun(tc_fun(_1472507, tc_fun(_1472507, tc_HOL_Obool)), tc_fun(_1472507, tc_fun(_1472507, tc_HOL_Obool))), _1472507), c_COMBS(_1472507, tc_fun(_1472507, tc_HOL_Obool), tc_fun(_1472507, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1472507, tc_fun(_1472507, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1472507, tc_fun(tc_fun(_1472507, tc_HOL_Obool), tc_fun(_1472507, tc_HOL_Obool))), _1472507), hAPP(c_COMBB(tc_fun(_1472507, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1472507, tc_HOL_Obool), tc_fun(_1472507, tc_HOL_Obool)), _1472507), c_COMBS(_1472507, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1472507, tc_fun(_1472507, tc_HOL_Obool)), tc_fun(_1472507, tc_fun(_1472507, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1472507), hAPP(c_COMBB(tc_fun(_1472507, tc_HOL_Obool), tc_fun(_1472507, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1472507), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1472507), c_fconj))), hAPP(hAPP(c_COMBC(_1472507, tc_fun(_1472507, tc_fun(_1472507, _1472507)), tc_fun(_1472507, tc_fun(_1472507, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1472507, _1472507), tc_fun(_1472507, tc_HOL_Obool)), tc_fun(tc_fun(_1472507, tc_fun(_1472507, _1472507)), tc_fun(_1472507, tc_fun(_1472507, tc_HOL_Obool))), _1472507), c_COMBB(tc_fun(_1472507, _1472507), tc_fun(_1472507, tc_HOL_Obool), _1472507)), hAPP(hAPP(c_COMBB(tc_fun(_1472507, tc_HOL_Obool), tc_fun(tc_fun(_1472507, _1472507), tc_fun(_1472507, tc_HOL_Obool)), _1472507), c_COMBB(_1472507, tc_HOL_Obool, _1472507)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1472507)))))), hAPP(hAPP(c_COMBC(_1472507, tc_fun(_1472507, tc_HOL_Obool), tc_fun(_1472507, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1472507, tc_HOL_Obool), tc_fun(_1472507, tc_HOL_Obool)), _1472507), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1472507)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1472507), c_fconj), hAPP(hAPP(c_COMBC(_1472507, tc_fun(_1472507, tc_HOL_Obool), tc_HOL_Obool), c_member(_1472507)), _1472509)))), hAPP(hAPP(c_COMBC(_1472507, tc_fun(_1472507, tc_HOL_Obool), tc_HOL_Obool), c_member(_1472507)), _1472511))))))))], (36471 ^ _779300) ^ [_1473606, _1473608, _1473610] : [class_Orderings_Olinorder(_1473606), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473606), _1473608)), -(_1473608 = c_Orderings_Obot__class_Obot(tc_fun(_1473606, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473606), _1473610)), -(_1473610 = c_Orderings_Obot__class_Obot(tc_fun(_1473606, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1473606), c_Big__Operators_Olattice_OSup__fin(_1473606, c_Orderings_Oord__class_Omax(_1473606), _1473608)), c_Big__Operators_Olattice_OSup__fin(_1473606, c_Orderings_Oord__class_Omax(_1473606), _1473610)) = c_Big__Operators_Olattice_OSup__fin(_1473606, c_Orderings_Oord__class_Omax(_1473606), hAPP(c_Set_OCollect(_1473606), hAPP(hAPP(c_COMBB(tc_fun(_1473606, tc_HOL_Obool), tc_HOL_Obool, _1473606), c_HOL_OEx(_1473606)), hAPP(hAPP(c_COMBB(tc_fun(_1473606, tc_fun(_1473606, tc_HOL_Obool)), tc_fun(_1473606, tc_HOL_Obool), _1473606), hAPP(c_COMBB(tc_fun(_1473606, tc_HOL_Obool), tc_HOL_Obool, _1473606), c_HOL_OEx(_1473606))), hAPP(hAPP(c_COMBC(_1473606, tc_fun(_1473606, tc_fun(_1473606, tc_HOL_Obool)), tc_fun(_1473606, tc_fun(_1473606, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1473606, tc_fun(tc_fun(_1473606, tc_HOL_Obool), tc_fun(_1473606, tc_HOL_Obool))), tc_fun(tc_fun(_1473606, tc_fun(_1473606, tc_HOL_Obool)), tc_fun(_1473606, tc_fun(_1473606, tc_HOL_Obool))), _1473606), c_COMBS(_1473606, tc_fun(_1473606, tc_HOL_Obool), tc_fun(_1473606, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1473606, tc_fun(_1473606, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1473606, tc_fun(tc_fun(_1473606, tc_HOL_Obool), tc_fun(_1473606, tc_HOL_Obool))), _1473606), hAPP(c_COMBB(tc_fun(_1473606, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1473606, tc_HOL_Obool), tc_fun(_1473606, tc_HOL_Obool)), _1473606), c_COMBS(_1473606, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1473606, tc_fun(_1473606, tc_HOL_Obool)), tc_fun(_1473606, tc_fun(_1473606, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1473606), hAPP(c_COMBB(tc_fun(_1473606, tc_HOL_Obool), tc_fun(_1473606, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1473606), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1473606), c_fconj))), hAPP(hAPP(c_COMBC(_1473606, tc_fun(_1473606, tc_fun(_1473606, _1473606)), tc_fun(_1473606, tc_fun(_1473606, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1473606, _1473606), tc_fun(_1473606, tc_HOL_Obool)), tc_fun(tc_fun(_1473606, tc_fun(_1473606, _1473606)), tc_fun(_1473606, tc_fun(_1473606, tc_HOL_Obool))), _1473606), c_COMBB(tc_fun(_1473606, _1473606), tc_fun(_1473606, tc_HOL_Obool), _1473606)), hAPP(hAPP(c_COMBB(tc_fun(_1473606, tc_HOL_Obool), tc_fun(tc_fun(_1473606, _1473606), tc_fun(_1473606, tc_HOL_Obool)), _1473606), c_COMBB(_1473606, tc_HOL_Obool, _1473606)), c_fequal))), c_Orderings_Oord__class_Omin(_1473606)))))), hAPP(hAPP(c_COMBC(_1473606, tc_fun(_1473606, tc_HOL_Obool), tc_fun(_1473606, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1473606, tc_HOL_Obool), tc_fun(_1473606, tc_HOL_Obool)), _1473606), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1473606)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1473606), c_fconj), hAPP(hAPP(c_COMBC(_1473606, tc_fun(_1473606, tc_HOL_Obool), tc_HOL_Obool), c_member(_1473606)), _1473608)))), hAPP(hAPP(c_COMBC(_1473606, tc_fun(_1473606, tc_HOL_Obool), tc_HOL_Obool), c_member(_1473606)), _1473610))))))))], (36493 ^ _779300) ^ [_1474723, _1474725, _1474727] : [class_Orderings_Olinorder(_1474723), hBOOL(hAPP(c_Finite__Set_Ofinite(_1474723), _1474725)), -(_1474725 = c_Orderings_Obot__class_Obot(tc_fun(_1474723, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1474723), _1474727), c_Big__Operators_Olattice_OSup__fin(_1474723, c_Orderings_Oord__class_Omax(_1474723), _1474725)) = c_Big__Operators_Olattice_OSup__fin(_1474723, c_Orderings_Oord__class_Omax(_1474723), hAPP(c_Set_OCollect(_1474723), hAPP(hAPP(c_COMBB(tc_fun(_1474723, tc_HOL_Obool), tc_HOL_Obool, _1474723), c_HOL_OEx(_1474723)), hAPP(hAPP(c_COMBC(_1474723, tc_fun(_1474723, tc_HOL_Obool), tc_fun(_1474723, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1474723, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1474723, tc_HOL_Obool), tc_fun(_1474723, tc_HOL_Obool)), _1474723), c_COMBS(_1474723, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1474723, tc_HOL_Obool), tc_fun(_1474723, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1474723), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1474723), c_fconj)), hAPP(hAPP(c_COMBC(_1474723, tc_fun(_1474723, _1474723), tc_fun(_1474723, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1474723, tc_HOL_Obool), tc_fun(tc_fun(_1474723, _1474723), tc_fun(_1474723, tc_HOL_Obool)), _1474723), c_COMBB(_1474723, tc_HOL_Obool, _1474723)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1474723), _1474727))))), hAPP(hAPP(c_COMBC(_1474723, tc_fun(_1474723, tc_HOL_Obool), tc_HOL_Obool), c_member(_1474723)), _1474725))))))], (36507 ^ _779300) ^ [_1475221, _1475223, _1475225, _1475227] : [-(c_Nitpick_Oprod(_1475221, _1475223, _1475225, _1475227) = hAPP(c_Set_OCollect(tc_prod(_1475221, _1475223)), hAPP(c_Product__Type_Oprod_Oprod__case(_1475221, _1475223, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1475221, tc_fun(_1475223, tc_HOL_Obool), tc_fun(_1475223, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1475223, tc_HOL_Obool), tc_fun(_1475223, tc_HOL_Obool)), _1475221), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1475223)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1475221), c_fconj), hAPP(hAPP(c_COMBC(_1475221, tc_fun(_1475221, tc_HOL_Obool), tc_HOL_Obool), c_member(_1475221)), _1475225)))), hAPP(hAPP(c_COMBC(_1475223, tc_fun(_1475223, tc_HOL_Obool), tc_HOL_Obool), c_member(_1475223)), _1475227)))))], (36509 ^ _779300) ^ [_1475349] : [-(c_Int_Oint__ge__less__than2(_1475349) = 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), _1475349)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (36511 ^ _779300) ^ [_1475395] : [-(c_Int_Oint__ge__less__than(_1475395) = 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), _1475395)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (36513 ^ _779300) ^ [_1475456, _1475458] : [c_Predicate_Oreflp(_1475456, _1475458), -(c_Relation_Orefl__on(_1475456, c_Orderings_Otop__class_Otop(tc_fun(_1475456, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1475456, _1475456)), hAPP(c_Product__Type_Oprod_Oprod__case(_1475456, _1475456, tc_HOL_Obool), _1475458))))], (36519 ^ _779300) ^ [_1475571, _1475573] : [c_Relation_Orefl__on(_1475571, c_Orderings_Otop__class_Otop(tc_fun(_1475571, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1475571, _1475571)), hAPP(c_Product__Type_Oprod_Oprod__case(_1475571, _1475571, tc_HOL_Obool), _1475573))), -(c_Predicate_Oreflp(_1475571, _1475573))], (36525 ^ _779300) ^ [_1475692, _1475694, _1475696, _1475698, _1475700, _1475702, _1475704] : [class_Rings_Osemiring__0(_1475692), c_Fun_Oinj__on(tc_prod(_1475694, _1475696), _1475692, hAPP(c_Product__Type_Oprod_Oprod__case(_1475694, _1475696, _1475692), hAPP(hAPP(c_COMBC(_1475694, tc_fun(_1475696, _1475692), tc_fun(_1475696, _1475692)), hAPP(hAPP(c_COMBB(tc_fun(_1475692, _1475692), tc_fun(tc_fun(_1475696, _1475692), tc_fun(_1475696, _1475692)), _1475694), c_COMBB(_1475692, _1475692, _1475696)), hAPP(hAPP(c_COMBB(_1475692, tc_fun(_1475692, _1475692), _1475694), c_Groups_Otimes__class_Otimes(_1475692)), _1475698))), _1475700)), hAPP(hAPP(c_Product__Type_OSigma(_1475694, _1475696), _1475702), hAPP(c_COMBK(tc_fun(_1475696, tc_HOL_Obool), _1475694), _1475704))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1475692), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475694, _1475692), _1475698), _1475702)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475696, _1475692), _1475700), _1475704)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475692, _1475692), c_Fun_Oid(_1475692)), hAPP(c_Set_OCollect(_1475692), hAPP(hAPP(c_COMBB(tc_fun(_1475694, tc_HOL_Obool), tc_HOL_Obool, _1475692), c_HOL_OEx(_1475694)), hAPP(hAPP(c_COMBB(tc_fun(_1475694, tc_fun(_1475696, tc_HOL_Obool)), tc_fun(_1475694, tc_HOL_Obool), _1475692), hAPP(c_COMBB(tc_fun(_1475696, tc_HOL_Obool), tc_HOL_Obool, _1475694), c_HOL_OEx(_1475696))), hAPP(hAPP(c_COMBC(_1475692, tc_fun(_1475694, tc_fun(_1475696, tc_HOL_Obool)), tc_fun(_1475694, tc_fun(_1475696, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1475694, tc_fun(tc_fun(_1475696, tc_HOL_Obool), tc_fun(_1475696, tc_HOL_Obool))), tc_fun(tc_fun(_1475694, tc_fun(_1475696, tc_HOL_Obool)), tc_fun(_1475694, tc_fun(_1475696, tc_HOL_Obool))), _1475692), c_COMBS(_1475694, tc_fun(_1475696, tc_HOL_Obool), tc_fun(_1475696, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1475694, tc_fun(_1475696, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1475694, tc_fun(tc_fun(_1475696, tc_HOL_Obool), tc_fun(_1475696, tc_HOL_Obool))), _1475692), hAPP(c_COMBB(tc_fun(_1475696, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1475696, tc_HOL_Obool), tc_fun(_1475696, tc_HOL_Obool)), _1475694), c_COMBS(_1475696, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1475694, tc_fun(_1475696, tc_HOL_Obool)), tc_fun(_1475694, tc_fun(_1475696, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1475692), hAPP(c_COMBB(tc_fun(_1475696, tc_HOL_Obool), tc_fun(_1475696, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1475694), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1475696), c_fconj))), hAPP(hAPP(c_COMBC(_1475692, tc_fun(_1475694, tc_fun(_1475696, _1475692)), tc_fun(_1475694, tc_fun(_1475696, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1475696, _1475692), tc_fun(_1475696, tc_HOL_Obool)), tc_fun(tc_fun(_1475694, tc_fun(_1475696, _1475692)), tc_fun(_1475694, tc_fun(_1475696, tc_HOL_Obool))), _1475692), c_COMBB(tc_fun(_1475696, _1475692), tc_fun(_1475696, tc_HOL_Obool), _1475694)), hAPP(hAPP(c_COMBB(tc_fun(_1475692, tc_HOL_Obool), tc_fun(tc_fun(_1475696, _1475692), tc_fun(_1475696, tc_HOL_Obool)), _1475692), c_COMBB(_1475692, tc_HOL_Obool, _1475696)), c_fequal))), hAPP(hAPP(c_COMBC(_1475694, tc_fun(_1475696, _1475692), tc_fun(_1475696, _1475692)), hAPP(hAPP(c_COMBB(tc_fun(_1475692, _1475692), tc_fun(tc_fun(_1475696, _1475692), tc_fun(_1475696, _1475692)), _1475694), c_COMBB(_1475692, _1475692, _1475696)), hAPP(hAPP(c_COMBB(_1475692, tc_fun(_1475692, _1475692), _1475694), c_Groups_Otimes__class_Otimes(_1475692)), _1475698))), _1475700)))))), hAPP(hAPP(c_COMBC(_1475694, tc_fun(_1475696, tc_HOL_Obool), tc_fun(_1475696, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1475696, tc_HOL_Obool), tc_fun(_1475696, tc_HOL_Obool)), _1475694), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1475696)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1475694), c_fconj), hAPP(hAPP(c_COMBC(_1475694, tc_fun(_1475694, tc_HOL_Obool), tc_HOL_Obool), c_member(_1475694)), _1475702)))), hAPP(hAPP(c_COMBC(_1475696, tc_fun(_1475696, tc_HOL_Obool), tc_HOL_Obool), c_member(_1475696)), _1475704))))))))], (36535 ^ _779300) ^ [_1476969, _1476971, _1476973, _1476975, _1476977, _1476979] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1476969), _1476971)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476973), _1476975)), 36545 ^ _779300 : [(36546 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476973), 36544 ^ [_1476969, _1476971, _1476973, _1476975, _1476977, _1476979]), _1476975)))], (36548 ^ _779300) ^ [] : [hAPP(c_Finite__Set_Ocard(_1476969), hAPP(c_Set_OCollect(_1476969), hAPP(hAPP(c_COMBS(_1476969, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1476969), c_fconj), hAPP(hAPP(c_COMBC(_1476969, tc_fun(_1476969, tc_HOL_Obool), tc_HOL_Obool), c_member(_1476969)), _1476971))), hAPP(hAPP(c_COMBC(_1476969, _1476973, tc_HOL_Obool), _1476977), 36544 ^ [_1476969, _1476971, _1476973, _1476975, _1476977, _1476979])))) = hAPP(_1476979, 36544 ^ [_1476969, _1476971, _1476973, _1476975, _1476977, _1476979])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476969, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1476973, tc_HOL_Obool), tc_Nat_Onat, _1476969), c_Finite__Set_Ocard(_1476973)), hAPP(hAPP(c_COMBB(tc_fun(_1476973, tc_HOL_Obool), tc_fun(_1476973, tc_HOL_Obool), _1476969), c_Set_OCollect(_1476973)), hAPP(hAPP(c_COMBB(tc_fun(_1476973, tc_HOL_Obool), tc_fun(_1476973, tc_HOL_Obool), _1476969), hAPP(c_COMBS(_1476973, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1476973), c_fconj), hAPP(hAPP(c_COMBC(_1476973, tc_fun(_1476973, tc_HOL_Obool), tc_HOL_Obool), c_member(_1476973)), _1476975)))), _1476977)))), _1476971) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476973, tc_Nat_Onat), _1476979), _1476975))], (36552 ^ _779300) ^ [_1477679, _1477681] : [-(c_Fun_Oinj__on(_1477679, _1477679, c_Fun_Oid(_1477679), _1477681))], (36554 ^ _779300) ^ [_1477708, _1477710] : [-(hAPP(c_Set_Ovimage(_1477708, _1477708, c_Fun_Oid(_1477708)), _1477710) = _1477710)], (36556 ^ _779300) ^ [_1477742, _1477744] : [-(c_Product__Type_Oapfst(_1477742, _1477742, _1477744, c_Fun_Oid(_1477742)) = c_Fun_Oid(tc_prod(_1477742, _1477744)))], (36558 ^ _779300) ^ [_1477779, _1477781] : [-(hAPP(c_Fun_Oid(_1477779), _1477781) = _1477781)], (36560 ^ _779300) ^ [_1477809, _1477811] : [-(hAPP(c_Fun_Oid(_1477809), _1477811) = _1477811)], (36562 ^ _779300) ^ [_1477839, _1477841, _1477843] : [c_Predicate_Oreflp(_1477839, _1477841), -(hBOOL(hAPP(hAPP(_1477841, _1477843), _1477843)))], (36568 ^ _779300) ^ [_1477928, _1477930] : [-(c_Product__Type_Oapsnd(_1477928, _1477928, _1477930, c_Fun_Oid(_1477928)) = c_Fun_Oid(tc_prod(_1477930, _1477928)))], (36570 ^ _779300) ^ [_1477965, _1477967] : [-(c_Product__Type_Omap__pair(_1477965, _1477965, _1477967, _1477967, c_Fun_Oid(_1477965), c_Fun_Oid(_1477967)) = c_Fun_Oid(tc_prod(_1477965, _1477967)))], (36572 ^ _779300) ^ [_1478006, _1478008] : [-(c_Product__Type_Omap__pair(_1478006, _1478006, _1478008, _1478008, c_COMBI(_1478006), c_COMBI(_1478008)) = c_Fun_Oid(tc_prod(_1478006, _1478008)))], (36574 ^ _779300) ^ [_1478047, _1478049] : [-(hAPP(c_Set_Oimage(_1478047, _1478047, c_Fun_Oid(_1478047)), _1478049) = _1478049)], (36576 ^ _779300) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (36578 ^ _779300) ^ [_1478099] : [-(hAPP(c_Set_Oimage(_1478099, _1478099, c_Fun_Oid(_1478099)), c_Orderings_Otop__class_Otop(tc_fun(_1478099, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1478099, tc_HOL_Obool)))], (36580 ^ _779300) ^ [_1478141, _1478143, _1478145, _1478147] : [-(c_Product__Type_Oapfst(_1478141, _1478143, _1478145, _1478147) = c_Product__Type_Omap__pair(_1478141, _1478143, _1478145, _1478145, _1478147, c_Fun_Oid(_1478145)))], (36582 ^ _779300) ^ [_1478184, _1478186, _1478188, _1478190] : [-(c_Product__Type_Oapsnd(_1478184, _1478186, _1478188, _1478190) = c_Product__Type_Omap__pair(_1478188, _1478188, _1478184, _1478186, c_Fun_Oid(_1478188), _1478190))], (36584 ^ _779300) ^ [_1478227, _1478229] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1478227, _1478229, tc_prod(_1478227, _1478229)), c_Product__Type_OPair(_1478227, _1478229)) = c_Fun_Oid(tc_prod(_1478227, _1478229)))], (36586 ^ _779300) ^ [_1478270, _1478272, _1478274, _1478276] : [class_Groups_Ocomm__monoid__add(_1478270), c_Fun_Oinj__on(_1478272, _1478270, _1478274, _1478276), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478272, _1478270), _1478274), _1478276) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478270, _1478270), c_Fun_Oid(_1478270)), hAPP(c_Set_Oimage(_1478272, _1478270, _1478274), _1478276)))], (36596 ^ _779300) ^ [_1478463, _1478465, _1478467, _1478469] : [class_Groups_Ocomm__monoid__mult(_1478463), c_Fun_Oinj__on(_1478465, _1478463, _1478467, _1478469), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1478465, _1478463), _1478467), _1478469) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1478463, _1478463), c_Fun_Oid(_1478463)), hAPP(c_Set_Oimage(_1478465, _1478463, _1478467), _1478469)))], (36606 ^ _779300) ^ [_1478671, _1478673] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1478671), _1478673)), -(_1478673 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1478671, 36610 ^ [_1478671, _1478673]), 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)), 36609 ^ [_1478671, _1478673]))))], (36614 ^ _779300) ^ [_1478802, _1478804] : [36615 ^ _779300 : [(36616 ^ _779300) ^ [_1478866, _1478868] : [_1478804 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1478802, _1478866), 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)), _1478868)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1478802), _1478804)))], (36620 ^ _779300) ^ [_1478938, _1478940, _1478942, _1478944, _1478946] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1478938, _1478940, _1478942), _1478944), _1478946) = hAPP(c_Set_OCollect(tc_prod(_1478938, _1478942)), hAPP(c_Product__Type_Oprod_Oprod__case(_1478938, _1478942, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1478942, tc_fun(_1478940, tc_HOL_Obool)), tc_fun(_1478942, tc_HOL_Obool), _1478938), hAPP(c_COMBB(tc_fun(_1478940, tc_HOL_Obool), tc_HOL_Obool, _1478942), c_HOL_OEx(_1478940))), hAPP(hAPP(c_COMBC(_1478938, tc_fun(_1478942, tc_fun(_1478940, tc_HOL_Obool)), tc_fun(_1478942, tc_fun(_1478940, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1478940, tc_HOL_Obool), tc_fun(_1478940, tc_HOL_Obool)), tc_fun(tc_fun(_1478942, tc_fun(_1478940, tc_HOL_Obool)), tc_fun(_1478942, tc_fun(_1478940, tc_HOL_Obool))), _1478938), c_COMBB(tc_fun(_1478940, tc_HOL_Obool), tc_fun(_1478940, tc_HOL_Obool), _1478942)), hAPP(hAPP(c_COMBB(tc_fun(_1478940, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1478940, tc_HOL_Obool), tc_fun(_1478940, tc_HOL_Obool)), _1478938), c_COMBS(_1478940, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478940, tc_HOL_Obool), tc_fun(_1478940, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1478938), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1478940), c_fconj)), hAPP(hAPP(c_COMBC(_1478938, tc_fun(tc_prod(_1478938, _1478940), tc_HOL_Obool), tc_fun(_1478940, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478940, tc_fun(tc_fun(tc_prod(_1478938, _1478940), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1478938, _1478940), tc_HOL_Obool), tc_fun(_1478940, tc_HOL_Obool)), _1478938), c_COMBC(_1478940, tc_fun(tc_prod(_1478938, _1478940), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478940, tc_prod(_1478938, _1478940)), tc_fun(_1478940, tc_fun(tc_fun(tc_prod(_1478938, _1478940), tc_HOL_Obool), tc_HOL_Obool)), _1478938), hAPP(c_COMBB(tc_prod(_1478938, _1478940), tc_fun(tc_fun(tc_prod(_1478938, _1478940), tc_HOL_Obool), tc_HOL_Obool), _1478940), c_member(tc_prod(_1478938, _1478940)))), c_Product__Type_OPair(_1478938, _1478940)))), _1478944))))), hAPP(hAPP(c_COMBC(_1478942, tc_fun(tc_prod(_1478940, _1478942), tc_HOL_Obool), tc_fun(_1478940, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478940, tc_fun(tc_fun(tc_prod(_1478940, _1478942), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1478940, _1478942), tc_HOL_Obool), tc_fun(_1478940, tc_HOL_Obool)), _1478942), c_COMBC(_1478940, tc_fun(tc_prod(_1478940, _1478942), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478940, tc_prod(_1478940, _1478942)), tc_fun(_1478940, tc_fun(tc_fun(tc_prod(_1478940, _1478942), tc_HOL_Obool), tc_HOL_Obool)), _1478942), hAPP(c_COMBB(tc_prod(_1478940, _1478942), tc_fun(tc_fun(tc_prod(_1478940, _1478942), tc_HOL_Obool), tc_HOL_Obool), _1478940), c_member(tc_prod(_1478940, _1478942)))), hAPP(c_COMBC(_1478940, _1478942, tc_prod(_1478940, _1478942)), c_Product__Type_OPair(_1478940, _1478942))))), _1478946))))))], (36622 ^ _779300) ^ [_1479386, _1479388, _1479390] : [-(hAPP(c_Relation_ORange(_1479386, _1479388), hAPP(c_Set_OCollect(tc_prod(_1479386, _1479388)), hAPP(c_Product__Type_Oprod_Oprod__case(_1479386, _1479388, tc_HOL_Obool), _1479390))) = hAPP(c_Set_OCollect(_1479388), hAPP(hAPP(c_COMBB(tc_fun(_1479386, tc_HOL_Obool), tc_HOL_Obool, _1479388), c_HOL_OEx(_1479386)), hAPP(c_COMBC(_1479386, _1479388, tc_HOL_Obool), _1479390))))], (36624 ^ _779300) ^ [_1479461, _1479463, _1479465, _1479467, _1479469, _1479471, _1479473, _1479475] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1479461, _1479463)), hAPP(hAPP(c_Product__Type_OPair(_1479461, _1479463), _1479465), _1479467)), _1479469)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1479463, _1479471)), hAPP(hAPP(c_Product__Type_OPair(_1479463, _1479471), _1479467), _1479473)), _1479475)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1479461, _1479471)), hAPP(hAPP(c_Product__Type_OPair(_1479461, _1479471), _1479465), _1479473)), hAPP(hAPP(c_Relation_Orel__comp(_1479461, _1479463, _1479471), _1479469), _1479475))))], (36634 ^ _779300) ^ [_1479748, _1479750, _1479752, _1479754, _1479756] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1479748, _1479750)), hAPP(hAPP(c_Product__Type_OPair(_1479748, _1479750), _1479752), _1479754)), _1479756)), -(hBOOL(hAPP(hAPP(c_member(_1479750), _1479754), hAPP(c_Relation_ORange(_1479748, _1479750), _1479756))))], (36640 ^ _779300) ^ [_1479895, _1479897, _1479899, _1479901, _1479903, _1479905, _1479907] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1479895, _1479897, _1479899), _1479901), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479903, tc_fun(tc_prod(_1479897, _1479899), tc_HOL_Obool)), _1479905), _1479907)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479903, tc_fun(tc_prod(_1479895, _1479899), tc_HOL_Obool)), _1479905), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1479897, _1479899), tc_HOL_Obool), tc_fun(tc_prod(_1479895, _1479899), tc_HOL_Obool), _1479903), hAPP(c_Relation_Orel__comp(_1479895, _1479897, _1479899), _1479901)), _1479907)))], (36642 ^ _779300) ^ [_1479999, _1480001, _1480003, _1480005, _1480007, _1480009, _1480011] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1479999, _1480001, _1480003), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480005, tc_fun(tc_prod(_1479999, _1480001), tc_HOL_Obool)), _1480007), _1480009)), _1480011) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480005, tc_fun(tc_prod(_1479999, _1480003), tc_HOL_Obool)), _1480007), hAPP(hAPP(c_COMBC(_1480005, tc_fun(tc_prod(_1480001, _1480003), tc_HOL_Obool), tc_fun(tc_prod(_1479999, _1480003), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1479999, _1480001), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1480001, _1480003), tc_HOL_Obool), tc_fun(tc_prod(_1479999, _1480003), tc_HOL_Obool)), _1480005), c_Relation_Orel__comp(_1479999, _1480001, _1480003)), _1480009)), _1480011)))], (36644 ^ _779300) ^ [_1480131, _1480133, _1480135, _1480137, _1480139, _1480141, _1480143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1480131, _1480133), tc_HOL_Obool)), _1480135), _1480137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1480133, _1480139), tc_HOL_Obool)), _1480141), _1480143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1480131, _1480139), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1480131, _1480133, _1480139), _1480135), _1480141)), hAPP(hAPP(c_Relation_Orel__comp(_1480131, _1480133, _1480139), _1480137), _1480143))))], (36654 ^ _779300) ^ [_1480398, _1480400, _1480402, _1480404] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1480398, _1480400, _1480402), _1480404), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480400, _1480402), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480398, _1480402), tc_HOL_Obool)))], (36656 ^ _779300) ^ [_1480453, _1480455, _1480457, _1480459] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1480453, _1480455, _1480457), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480453, _1480455), tc_HOL_Obool))), _1480459) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480453, _1480457), tc_HOL_Obool)))], (36658 ^ _779300) ^ [_1480508, _1480510, _1480512, _1480514, _1480516, _1480518] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1480508, _1480510, _1480512), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1480508, _1480510), tc_HOL_Obool)), _1480514), _1480516)), _1480518) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1480508, _1480512), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1480508, _1480510, _1480512), _1480514), _1480518)), hAPP(hAPP(c_Relation_Orel__comp(_1480508, _1480510, _1480512), _1480516), _1480518)))], (36660 ^ _779300) ^ [_1480599, _1480601, _1480603, _1480605, _1480607, _1480609] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1480599, _1480601, _1480603), _1480605), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1480601, _1480603), tc_HOL_Obool)), _1480607), _1480609)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1480599, _1480603), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1480599, _1480601, _1480603), _1480605), _1480607)), hAPP(hAPP(c_Relation_Orel__comp(_1480599, _1480601, _1480603), _1480605), _1480609)))], (36662 ^ _779300) ^ [_1480690, _1480692, _1480694, _1480696, _1480698, _1480700, _1480702] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1480690, _1480692, _1480694), hAPP(hAPP(c_Relation_Orel__comp(_1480690, _1480696, _1480692), _1480698), _1480700)), _1480702) = hAPP(hAPP(c_Relation_Orel__comp(_1480690, _1480696, _1480694), _1480698), hAPP(hAPP(c_Relation_Orel__comp(_1480696, _1480692, _1480694), _1480700), _1480702)))], (36664 ^ _779300) ^ [_1480765, _1480767] : [-(hAPP(c_Relation_ORange(_1480765, _1480765), c_Relation_OId__on(_1480765, _1480767)) = _1480767)], (36666 ^ _779300) ^ [_1480799, _1480801, _1480803, _1480805] : [hAPP(hAPP(c_Relation_Orel__comp(_1480799, _1480799, _1480799), _1480801), _1480803) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480799, _1480799), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1480799, _1480799, _1480799), _1480805), _1480803) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480799, _1480799), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1480799, _1480799, _1480799), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1480799, _1480799), tc_HOL_Obool)), _1480801), _1480805)), _1480803) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480799, _1480799), tc_HOL_Obool)))], (36676 ^ _779300) ^ [_1481072, _1481074, _1481076, _1481078] : [hAPP(hAPP(c_Relation_Orel__comp(_1481072, _1481072, _1481072), _1481074), _1481076) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1481072, _1481072), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1481072, _1481072, _1481072), _1481074), _1481078) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1481072, _1481072), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1481072, _1481072, _1481072), _1481074), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1481072, _1481072), tc_HOL_Obool)), _1481076), _1481078)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1481072, _1481072), tc_HOL_Obool)))], (36686 ^ _779300) ^ [_1481363, _1481365, _1481367] : [hAPP(c_Relation_ORange(_1481363, _1481365), _1481367) = c_Orderings_Obot__class_Obot(tc_fun(_1481365, tc_HOL_Obool)), -(_1481367 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1481363, _1481365), tc_HOL_Obool)))], (36692 ^ _779300) ^ [_1481476, _1481478, _1481480] : [_1481480 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1481476, _1481478), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1481476, _1481478), _1481480) = c_Orderings_Obot__class_Obot(tc_fun(_1481478, tc_HOL_Obool)))], (36698 ^ _779300) ^ [_1481595, _1481597] : [-(hAPP(c_Relation_ORange(_1481595, _1481597), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1481595, _1481597), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1481597, tc_HOL_Obool)))], (36700 ^ _779300) ^ [_1481639, _1481641, _1481643, _1481645, _1481647, _1481649, _1481651, _1481653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1481639, _1481641), tc_HOL_Obool)), _1481643), hAPP(hAPP(c_Product__Type_OSigma(_1481639, _1481641), _1481645), hAPP(c_COMBK(tc_fun(_1481641, tc_HOL_Obool), _1481639), _1481647)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1481641, _1481649), tc_HOL_Obool)), _1481651), hAPP(hAPP(c_Product__Type_OSigma(_1481641, _1481649), _1481647), hAPP(c_COMBK(tc_fun(_1481649, tc_HOL_Obool), _1481641), _1481653)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1481639, _1481649), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1481639, _1481641, _1481649), _1481643), _1481651)), hAPP(hAPP(c_Product__Type_OSigma(_1481639, _1481649), _1481645), hAPP(c_COMBK(tc_fun(_1481649, tc_HOL_Obool), _1481639), _1481653)))))], (36710 ^ _779300) ^ [_1481998, _1482000, _1482002, _1482004] : [-(hAPP(c_Relation_ORange(_1481998, _1482000), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1481998, _1482000), tc_HOL_Obool)), _1482002), _1482004)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482000, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1481998, _1482000), _1482002)), hAPP(c_Relation_ORange(_1481998, _1482000), _1482004)))], (36712 ^ _779300) ^ [_1482070, _1482072, _1482074] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1482070, _1482072)), _1482074)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1482072), hAPP(c_Relation_ORange(_1482070, _1482072), _1482074))))], (36718 ^ _779300) ^ [_1482183, _1482185, _1482187] : [-(hAPP(c_Set_Oimage(tc_prod(_1482183, _1482185), _1482185, c_Product__Type_Osnd(_1482183, _1482185)), _1482187) = hAPP(c_Relation_ORange(_1482183, _1482185), _1482187))], (36720 ^ _779300) ^ [_1482250, _1482252, _1482254, _1482256] : [hBOOL(hAPP(hAPP(c_member(_1482250), _1482252), hAPP(c_Relation_ORange(_1482254, _1482250), _1482256))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1482254, _1482250)), hAPP(hAPP(c_Product__Type_OPair(_1482254, _1482250), 36723 ^ [_1482250, _1482252, _1482254, _1482256]), _1482252)), _1482256)))], (36727 ^ _779300) ^ [_1482407, _1482409, _1482411, _1482413] : [36728 ^ _779300 : [(36729 ^ _779300) ^ [_1482482] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1482411, _1482407)), hAPP(hAPP(c_Product__Type_OPair(_1482411, _1482407), _1482482), _1482409)), _1482413))]], -(hBOOL(hAPP(hAPP(c_member(_1482407), _1482409), hAPP(c_Relation_ORange(_1482411, _1482407), _1482413))))], (36733 ^ _779300) ^ [_1482567, _1482569, _1482571, _1482573, _1482575] : [-(hAPP(c_Relation_ORange(_1482567, _1482569), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1482567, _1482569)), hAPP(hAPP(c_Product__Type_OPair(_1482567, _1482569), _1482571), _1482573)), _1482575)) = hAPP(hAPP(c_Set_Oinsert(_1482569), _1482573), hAPP(c_Relation_ORange(_1482567, _1482569), _1482575)))], (36735 ^ _779300) ^ [_1482638, _1482640, _1482642, _1482644] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1482638, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1482640, _1482638), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1482640, _1482638), tc_HOL_Obool)), _1482642), _1482644))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482638, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1482640, _1482638), _1482642)), hAPP(c_Relation_ORange(_1482640, _1482638), _1482644)))))], (36737 ^ _779300) ^ [_1482720, _1482722, _1482724, _1482726] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1482720, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1482720, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1482722, _1482720), _1482724)), hAPP(c_Relation_ORange(_1482722, _1482720), _1482726))), hAPP(c_Relation_ORange(_1482722, _1482720), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1482722, _1482720), tc_HOL_Obool)), _1482724), _1482726)))))], (36739 ^ _779300) ^ [_1482802, _1482804, _1482806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1482802, _1482802), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1482802, _1482802, _1482802), _1482804), _1482806)), _1482804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1482802, tc_HOL_Obool), tc_fun(_1482802, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1482802, tc_HOL_Obool), tc_fun(_1482802, tc_HOL_Obool), tc_fun(_1482802, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1482802, _1482804)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1482802, tc_HOL_Obool), tc_fun(_1482802, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1482802, _1482806)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1482802, tc_HOL_Obool), tc_fun(_1482802, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1482802, tc_HOL_Obool), tc_fun(_1482802, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1482802, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1482802, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1482802, tc_HOL_Obool), tc_fun(_1482802, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1482802, _1482804))))], (36745 ^ _779300) ^ [_1483173, _1483175, _1483177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1483173, _1483173), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1483173, _1483173, _1483173), _1483175), _1483177)), _1483175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1483173, tc_HOL_Obool), tc_fun(_1483173, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1483173, tc_HOL_Obool), tc_fun(_1483173, tc_HOL_Obool), tc_fun(_1483173, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1483173, _1483175)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1483173, tc_HOL_Obool), tc_fun(_1483173, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1483173, _1483177)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1483173, tc_HOL_Obool), tc_fun(_1483173, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1483173, tc_HOL_Obool), tc_fun(_1483173, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1483173, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1483173, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1483173, tc_HOL_Obool), tc_fun(_1483173, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1483173, _1483175))))], (36751 ^ _779300) ^ [_1483565, _1483567, _1483569, _1483571] : [hBOOL(hAPP(c_Predicate_ORangeP(_1483565, _1483567, hAPP(hAPP(c_COMBC(_1483565, tc_fun(tc_prod(_1483565, _1483567), tc_HOL_Obool), tc_fun(_1483567, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483567, tc_fun(tc_fun(tc_prod(_1483565, _1483567), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1483565, _1483567), tc_HOL_Obool), tc_fun(_1483567, tc_HOL_Obool)), _1483565), c_COMBC(_1483567, tc_fun(tc_prod(_1483565, _1483567), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483567, tc_prod(_1483565, _1483567)), tc_fun(_1483567, tc_fun(tc_fun(tc_prod(_1483565, _1483567), tc_HOL_Obool), tc_HOL_Obool)), _1483565), hAPP(c_COMBB(tc_prod(_1483565, _1483567), tc_fun(tc_fun(tc_prod(_1483565, _1483567), tc_HOL_Obool), tc_HOL_Obool), _1483567), c_member(tc_prod(_1483565, _1483567)))), c_Product__Type_OPair(_1483565, _1483567)))), _1483569)), _1483571)), -(hBOOL(hAPP(hAPP(c_member(_1483567), _1483571), hAPP(c_Relation_ORange(_1483565, _1483567), _1483569))))], (36757 ^ _779300) ^ [_1483916, _1483918, _1483920, _1483922] : [hBOOL(hAPP(hAPP(c_member(_1483918), _1483922), hAPP(c_Relation_ORange(_1483916, _1483918), _1483920))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1483916, _1483918, hAPP(hAPP(c_COMBC(_1483916, tc_fun(tc_prod(_1483916, _1483918), tc_HOL_Obool), tc_fun(_1483918, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483918, tc_fun(tc_fun(tc_prod(_1483916, _1483918), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1483916, _1483918), tc_HOL_Obool), tc_fun(_1483918, tc_HOL_Obool)), _1483916), c_COMBC(_1483918, tc_fun(tc_prod(_1483916, _1483918), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483918, tc_prod(_1483916, _1483918)), tc_fun(_1483918, tc_fun(tc_fun(tc_prod(_1483916, _1483918), tc_HOL_Obool), tc_HOL_Obool)), _1483916), hAPP(c_COMBB(tc_prod(_1483916, _1483918), tc_fun(tc_fun(tc_prod(_1483916, _1483918), tc_HOL_Obool), tc_HOL_Obool), _1483918), c_member(tc_prod(_1483916, _1483918)))), c_Product__Type_OPair(_1483916, _1483918)))), _1483920)), _1483922)))], (36763 ^ _779300) ^ [_1484273, _1484275, _1484277, _1484279] : [hBOOL(hAPP(hAPP(c_member(_1484273), _1484275), hAPP(c_Relation_ORange(_1484277, _1484273), _1484279))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1484277, _1484273)), hAPP(hAPP(c_Product__Type_OPair(_1484277, _1484273), 36766 ^ [_1484273, _1484275, _1484277, _1484279]), _1484275)), _1484279)))], (36770 ^ _779300) ^ [_1484468, _1484470, _1484472, _1484474, _1484476, _1484478, _1484480] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1484468, _1484470, _1484472, hAPP(hAPP(c_COMBC(_1484468, tc_fun(tc_prod(_1484468, _1484470), tc_HOL_Obool), tc_fun(_1484470, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484470, tc_fun(tc_fun(tc_prod(_1484468, _1484470), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484468, _1484470), tc_HOL_Obool), tc_fun(_1484470, tc_HOL_Obool)), _1484468), c_COMBC(_1484470, tc_fun(tc_prod(_1484468, _1484470), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484470, tc_prod(_1484468, _1484470)), tc_fun(_1484470, tc_fun(tc_fun(tc_prod(_1484468, _1484470), tc_HOL_Obool), tc_HOL_Obool)), _1484468), hAPP(c_COMBB(tc_prod(_1484468, _1484470), tc_fun(tc_fun(tc_prod(_1484468, _1484470), tc_HOL_Obool), tc_HOL_Obool), _1484470), c_member(tc_prod(_1484468, _1484470)))), c_Product__Type_OPair(_1484468, _1484470)))), _1484474), hAPP(hAPP(c_COMBC(_1484470, tc_fun(tc_prod(_1484470, _1484472), tc_HOL_Obool), tc_fun(_1484472, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484472, tc_fun(tc_fun(tc_prod(_1484470, _1484472), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484470, _1484472), tc_HOL_Obool), tc_fun(_1484472, tc_HOL_Obool)), _1484470), c_COMBC(_1484472, tc_fun(tc_prod(_1484470, _1484472), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484472, tc_prod(_1484470, _1484472)), tc_fun(_1484472, tc_fun(tc_fun(tc_prod(_1484470, _1484472), tc_HOL_Obool), tc_HOL_Obool)), _1484470), hAPP(c_COMBB(tc_prod(_1484470, _1484472), tc_fun(tc_fun(tc_prod(_1484470, _1484472), tc_HOL_Obool), tc_HOL_Obool), _1484472), c_member(tc_prod(_1484470, _1484472)))), c_Product__Type_OPair(_1484470, _1484472)))), _1484476)), _1484478), _1484480)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1484468, _1484472)), hAPP(hAPP(c_Product__Type_OPair(_1484468, _1484472), _1484478), _1484480)), hAPP(hAPP(c_Relation_Orel__comp(_1484468, _1484470, _1484472), _1484474), _1484476))))], (36776 ^ _779300) ^ [_1485103, _1485105, _1485107, _1485109, _1485111, _1485113, _1485115] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1485103, _1485107)), hAPP(hAPP(c_Product__Type_OPair(_1485103, _1485107), _1485113), _1485115)), hAPP(hAPP(c_Relation_Orel__comp(_1485103, _1485105, _1485107), _1485109), _1485111))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1485103, _1485105, _1485107, hAPP(hAPP(c_COMBC(_1485103, tc_fun(tc_prod(_1485103, _1485105), tc_HOL_Obool), tc_fun(_1485105, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485105, tc_fun(tc_fun(tc_prod(_1485103, _1485105), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1485103, _1485105), tc_HOL_Obool), tc_fun(_1485105, tc_HOL_Obool)), _1485103), c_COMBC(_1485105, tc_fun(tc_prod(_1485103, _1485105), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485105, tc_prod(_1485103, _1485105)), tc_fun(_1485105, tc_fun(tc_fun(tc_prod(_1485103, _1485105), tc_HOL_Obool), tc_HOL_Obool)), _1485103), hAPP(c_COMBB(tc_prod(_1485103, _1485105), tc_fun(tc_fun(tc_prod(_1485103, _1485105), tc_HOL_Obool), tc_HOL_Obool), _1485105), c_member(tc_prod(_1485103, _1485105)))), c_Product__Type_OPair(_1485103, _1485105)))), _1485109), hAPP(hAPP(c_COMBC(_1485105, tc_fun(tc_prod(_1485105, _1485107), tc_HOL_Obool), tc_fun(_1485107, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485107, tc_fun(tc_fun(tc_prod(_1485105, _1485107), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1485105, _1485107), tc_HOL_Obool), tc_fun(_1485107, tc_HOL_Obool)), _1485105), c_COMBC(_1485107, tc_fun(tc_prod(_1485105, _1485107), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485107, tc_prod(_1485105, _1485107)), tc_fun(_1485107, tc_fun(tc_fun(tc_prod(_1485105, _1485107), tc_HOL_Obool), tc_HOL_Obool)), _1485105), hAPP(c_COMBB(tc_prod(_1485105, _1485107), tc_fun(tc_fun(tc_prod(_1485105, _1485107), tc_HOL_Obool), tc_HOL_Obool), _1485107), c_member(tc_prod(_1485105, _1485107)))), c_Product__Type_OPair(_1485105, _1485107)))), _1485111)), _1485113), _1485115)))], (36782 ^ _779300) ^ [_1485744, _1485746, _1485748, _1485750, _1485752, _1485754, _1485756, _1485758] : [hBOOL(hAPP(hAPP(_1485744, _1485746), _1485748)), hBOOL(hAPP(hAPP(_1485750, _1485748), _1485752)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1485754, _1485756, _1485758, _1485744, _1485750), _1485746), _1485752)))], (36792 ^ _779300) ^ [_1485939, _1485941, _1485943, _1485945, _1485947] : [hBOOL(hAPP(hAPP(_1485939, _1485941), _1485943)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1485945, _1485947, _1485939), _1485943)))], (36798 ^ _779300) ^ [_1486074, _1486076, _1486078, _1486080, _1486082, _1486084, _1486086] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1486074, _1486076, _1486078, _1486080, _1486082), _1486084), _1486086)), 36802 ^ _779300 : [(36803 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1486080, _1486084), 36801 ^ [_1486074, _1486076, _1486078, _1486080, _1486082, _1486084, _1486086])))], (36805 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1486082, 36801 ^ [_1486074, _1486076, _1486078, _1486080, _1486082, _1486084, _1486086]), _1486086)))]]], (36807 ^ _779300) ^ [_1486264, _1486266, _1486268, _1486270, _1486272, _1486274, _1486276] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1486264, _1486266, _1486268, _1486270, _1486272), _1486274), _1486276))), 36808 ^ _779300 : [(36809 ^ _779300) ^ [_1486335] : [hBOOL(hAPP(hAPP(_1486270, _1486274), _1486335)), hBOOL(hAPP(hAPP(_1486272, _1486335), _1486276))]]], (36817 ^ _779300) ^ [_1486505, _1486507, _1486509, _1486511] : [hBOOL(hAPP(c_Predicate_ORangeP(_1486505, _1486507, _1486509), _1486511)), -(hBOOL(hAPP(hAPP(_1486509, 36820 ^ [_1486505, _1486507, _1486509, _1486511]), _1486511)))], (36824 ^ _779300) ^ [_1486620, _1486622, _1486624, _1486626] : [36825 ^ _779300 : [(36826 ^ _779300) ^ [_1486674] : [hBOOL(hAPP(hAPP(_1486624, _1486674), _1486626))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1486620, _1486622, _1486624), _1486626)))], (36830 ^ _779300) ^ [_1486738, _1486740, _1486742] : [c_Wellfounded_Owf(_1486738, _1486740), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1486738, _1486738), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1486738, _1486738, _1486738), _1486740), _1486742)), _1486740)), -(c_FunDef_Oreduction__pair(_1486738, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1486738, _1486738), tc_HOL_Obool), tc_fun(tc_prod(_1486738, _1486738), tc_HOL_Obool)), _1486740), _1486742)))], (36840 ^ _779300) ^ [_1486959, _1486961, _1486963] : [-(hAPP(c_Relation_ODomain(_1486959, _1486961), hAPP(c_Set_OCollect(tc_prod(_1486959, _1486961)), hAPP(c_Product__Type_Oprod_Oprod__case(_1486959, _1486961, tc_HOL_Obool), _1486963))) = hAPP(c_Set_OCollect(_1486959), hAPP(hAPP(c_COMBB(tc_fun(_1486961, tc_HOL_Obool), tc_HOL_Obool, _1486959), c_HOL_OEx(_1486961)), _1486963)))], (36842 ^ _779300) ^ [_1487026, _1487028, _1487030, _1487032] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1487026), _1487028))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487030), hAPP(c_Set_Oimage(_1487026, _1487030, _1487032), _1487028))), 36850 ^ _779300 : [(36851 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487026), 36849 ^ [_1487026, _1487028, _1487030, _1487032]), _1487028)))], (36853 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1487026), hAPP(c_Set_OCollect(_1487026), hAPP(hAPP(c_COMBS(_1487026, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1487026), c_fconj), hAPP(hAPP(c_COMBC(_1487026, tc_fun(_1487026, tc_HOL_Obool), tc_HOL_Obool), c_member(_1487026)), _1487028))), hAPP(hAPP(c_COMBC(_1487026, _1487030, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1487030, tc_fun(_1487030, tc_HOL_Obool), _1487026), c_fequal), _1487032)), hAPP(_1487032, 36849 ^ [_1487026, _1487028, _1487030, _1487032]))))))]]], (36855 ^ _779300) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (36857 ^ _779300) ^ [_1487509] : [-(c_Wellfounded_Owf(_1487509, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1487509, _1487509), tc_HOL_Obool))))], (36859 ^ _779300) ^ [_1487540, _1487542, _1487544, _1487546] : [c_Wellfounded_Owf(_1487540, _1487542), -(c_Wellfounded_Owf(_1487544, hAPP(hAPP(c_Relation_Oinv__image(_1487540, _1487544), _1487542), _1487546)))], (36865 ^ _779300) ^ [_1487639, _1487641, _1487643, _1487645] : [c_Wellfounded_Owf(_1487639, _1487641), c_Wellfounded_Owf(_1487643, _1487645), -(c_Wellfounded_Owf(tc_prod(_1487639, _1487643), c_Wellfounded_Olex__prod(_1487639, _1487643, _1487641, _1487645)))], (36875 ^ _779300) ^ [_1487792, _1487794] : [-(c_Wellfounded_Owf(_1487792, hAPP(c_Wellfounded_Omeasure(_1487792), _1487794)))], (36877 ^ _779300) ^ [_1487822, _1487824, _1487826, _1487828, _1487830] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1487822, _1487824)), hAPP(hAPP(c_Product__Type_OPair(_1487822, _1487824), _1487826), _1487828)), _1487830)), -(hBOOL(hAPP(hAPP(c_member(_1487822), _1487826), hAPP(c_Relation_ODomain(_1487822, _1487824), _1487830))))], (36883 ^ _779300) ^ [_1487984, _1487986] : [c_Wellfounded_Owf(_1487984, _1487986), -(c_Wellfounded_Owf(_1487984, hAPP(hAPP(c_Relation_Orel__comp(_1487984, _1487984, _1487984), _1487986), _1487986)))], (36889 ^ _779300) ^ [_1488077, _1488079] : [c_Wellfounded_Owf(_1488077, hAPP(hAPP(c_Relation_Orel__comp(_1488077, _1488077, _1488077), _1488079), _1488079)), -(c_Wellfounded_Owf(_1488077, _1488079))], (36895 ^ _779300) ^ [_1488176, _1488178] : [c_Wellfounded_Owf(_1488176, _1488178), -(c_Wellfounded_Owf(tc_fun(_1488176, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1488176, _1488178)))], (36901 ^ _779300) ^ [_1488265, _1488267, _1488269] : [c_Wellfounded_Owf(_1488265, _1488267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1488265, _1488265), tc_HOL_Obool)), _1488269), _1488267)), -(c_Wellfounded_Owf(_1488265, _1488269))], (36911 ^ _779300) ^ [_1488424] : [-(c_Wellfounded_Owf(tc_fun(_1488424, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1488424)))], (36913 ^ _779300) ^ [_1488452, _1488454, _1488456] : [c_Wellfounded_Owf(_1488452, _1488454), -(c_Wellfounded_Owf(_1488452, c_Wellfounded_Omlex__prod(_1488452, _1488456, _1488454)))], (36919 ^ _779300) ^ [_1488539, _1488541, _1488543] : [c_Wellfounded_Owf(_1488539, _1488541), -(c_Wellfounded_Owf(_1488539, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1488539, _1488539), tc_HOL_Obool)), _1488543), _1488541)))], (36925 ^ _779300) ^ [_1488646, _1488648, _1488650] : [c_Wellfounded_Owf(_1488646, _1488648), -(c_Wellfounded_Owf(_1488646, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1488646, _1488646), tc_HOL_Obool)), _1488648), _1488650)))], (36931 ^ _779300) ^ [_1488753, _1488755] : [c_Wellfounded_Owf(_1488753, _1488755), -(c_Wellfounded_Owf(tc_fun(_1488753, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1488753, _1488755)))], (36937 ^ _779300) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (36939 ^ _779300) ^ [_1488860, _1488862] : [-(hAPP(c_Relation_ODomain(_1488860, _1488860), c_Relation_OId__on(_1488860, _1488862)) = _1488862)], (36941 ^ _779300) ^ [] : [-(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)))))], (36943 ^ _779300) ^ [_1488912, _1488914, _1488916] : [c_Wellfounded_Owf(_1488912, _1488914), hBOOL(hAPP(hAPP(c_member(tc_prod(_1488912, _1488912)), hAPP(hAPP(c_Product__Type_OPair(_1488912, _1488912), _1488916), _1488916)), _1488914))], (36949 ^ _779300) ^ [_1489030, _1489032, _1489034, _1489036] : [c_Wellfounded_Owf(_1489030, _1489032), hBOOL(hAPP(hAPP(c_member(tc_prod(_1489030, _1489030)), hAPP(hAPP(c_Product__Type_OPair(_1489030, _1489030), _1489034), _1489036)), _1489032)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1489030, _1489030)), hAPP(hAPP(c_Product__Type_OPair(_1489030, _1489030), _1489036), _1489034)), _1489032))], (36959 ^ _779300) ^ [_1489244, _1489246, _1489248, _1489250] : [c_Wellfounded_Owf(_1489244, _1489246), hBOOL(hAPP(hAPP(c_member(tc_prod(_1489244, _1489244)), hAPP(hAPP(c_Product__Type_OPair(_1489244, _1489244), _1489248), _1489250)), _1489246)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1489244, _1489244)), hAPP(hAPP(c_Product__Type_OPair(_1489244, _1489244), _1489250), _1489248)), _1489246))], (36969 ^ _779300) ^ [_1489458, _1489460, _1489462] : [c_Wellfounded_Owf(_1489458, _1489460), hBOOL(hAPP(hAPP(c_member(tc_prod(_1489458, _1489458)), hAPP(hAPP(c_Product__Type_OPair(_1489458, _1489458), _1489462), _1489462)), _1489460))], (36975 ^ _779300) ^ [_1489576] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1489576)))], (36977 ^ _779300) ^ [_1489601] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1489601)))], (36979 ^ _779300) ^ [_1489626, _1489628, _1489630] : [c_Wellfounded_Owf(_1489626, _1489628), c_Wellfounded_Owf(_1489626, _1489630), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1489626, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1489626, _1489626), _1489628)), hAPP(c_Relation_ORange(_1489626, _1489626), _1489630)) = c_Orderings_Obot__class_Obot(tc_fun(_1489626, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1489626, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1489626, _1489626), tc_HOL_Obool)), _1489628), _1489630)))], (36993 ^ _779300) ^ [_1489912, _1489914] : [c_Wellfounded_Owf(_1489912, _1489914), 36996 ^ _779300 : [(36997 ^ _779300) ^ [_1489981] : [-(hBOOL(hAPP(hAPP(c_member(_1489912), _1489981), c_Wellfounded_Oacc(_1489912, _1489914))))]]], (36999 ^ _779300) ^ [_1490014, _1490016] : [hBOOL(hAPP(hAPP(c_member(_1490014), 37000 ^ [_1490014, _1490016]), c_Wellfounded_Oacc(_1490014, _1490016))), -(c_Wellfounded_Owf(_1490014, _1490016))], (37006 ^ _779300) ^ [_1490147, _1490149, _1490151] : [c_Wellfounded_Owf(_1490147, _1490149), -(hBOOL(hAPP(hAPP(c_member(_1490147), _1490151), c_Wellfounded_Oacc(_1490147, _1490149))))], (37012 ^ _779300) ^ [_1490246, _1490248] : [hAPP(hAPP(c_Relation_Orel__comp(_1490246, _1490246, _1490246), _1490248), _1490248) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490246, _1490246), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1490246, _1490248))], (37018 ^ _779300) ^ [_1490377, _1490379, _1490381] : [c_Wellfounded_Owf(_1490377, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1490377, _1490377), tc_HOL_Obool)), _1490379), _1490381)), -(c_Wellfounded_Owf(_1490377, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1490377, _1490377), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1490377, _1490377), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1490377, _1490377, _1490377), _1490379), _1490379)), hAPP(hAPP(c_Relation_Orel__comp(_1490377, _1490377, _1490377), _1490381), _1490379))), _1490381)))], (37024 ^ _779300) ^ [_1490576, _1490578, _1490580] : [c_Wellfounded_Owf(_1490576, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1490576, _1490576), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1490576, _1490576), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1490576, _1490576, _1490576), _1490578), _1490578)), hAPP(hAPP(c_Relation_Orel__comp(_1490576, _1490576, _1490576), _1490580), _1490578))), _1490580)), -(c_Wellfounded_Owf(_1490576, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1490576, _1490576), tc_HOL_Obool)), _1490578), _1490580)))], (37030 ^ _779300) ^ [_1490799, _1490801, _1490803] : [hAPP(c_Relation_ODomain(_1490799, _1490801), _1490803) = c_Orderings_Obot__class_Obot(tc_fun(_1490799, tc_HOL_Obool)), -(_1490803 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490799, _1490801), tc_HOL_Obool)))], (37036 ^ _779300) ^ [_1490912, _1490914, _1490916] : [_1490916 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490912, _1490914), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1490912, _1490914), _1490916) = c_Orderings_Obot__class_Obot(tc_fun(_1490912, tc_HOL_Obool)))], (37042 ^ _779300) ^ [_1491031, _1491033] : [-(hAPP(c_Relation_ODomain(_1491031, _1491033), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1491031, _1491033), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1491031, tc_HOL_Obool)))], (37044 ^ _779300) ^ [_1491075, _1491077, _1491079, _1491081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1491075, _1491077), tc_HOL_Obool)), _1491079), _1491081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491075, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1491075, _1491077), _1491079)), hAPP(c_Relation_ODomain(_1491075, _1491077), _1491081))))], (37050 ^ _779300) ^ [_1491226, _1491228, _1491230, _1491232] : [-(hAPP(c_Relation_ODomain(_1491226, _1491228), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491226, _1491228), tc_HOL_Obool)), _1491230), _1491232)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491226, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1491226, _1491228), _1491230)), hAPP(c_Relation_ODomain(_1491226, _1491228), _1491232)))], (37052 ^ _779300) ^ [_1491298, _1491300, _1491302] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1491298, _1491300)), _1491302)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1491298), hAPP(c_Relation_ODomain(_1491298, _1491300), _1491302))))], (37058 ^ _779300) ^ [_1491411, _1491413, _1491415] : [-(hAPP(c_Set_Oimage(tc_prod(_1491411, _1491413), _1491411, c_Product__Type_Ofst(_1491411, _1491413)), _1491415) = hAPP(c_Relation_ODomain(_1491411, _1491413), _1491415))], (37060 ^ _779300) ^ [_1491472, _1491474] : [c_Wellfounded_Owf(_1491472, _1491474), 37064 ^ _779300 : [(37065 ^ _779300) ^ [_1491608] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1491472, _1491472)), hAPP(hAPP(c_Product__Type_OPair(_1491472, _1491472), hAPP(_1491608, hAPP(c_Nat_OSuc, 37063 ^ [_1491472, _1491474, _1491608]))), hAPP(_1491608, 37063 ^ [_1491472, _1491474, _1491608]))), _1491474))]]], (37067 ^ _779300) ^ [_1491675, _1491677] : [37069 ^ _779300 : [(37070 ^ _779300) ^ [_1491700] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491675, _1491675)), hAPP(hAPP(c_Product__Type_OPair(_1491675, _1491675), hAPP(37068 ^ [_1491675, _1491677], hAPP(c_Nat_OSuc, _1491700))), hAPP(37068 ^ [_1491675, _1491677], _1491700))), _1491677)))]], -(c_Wellfounded_Owf(_1491675, _1491677))], (37074 ^ _779300) ^ [_1491776, _1491778, _1491780] : [c_Wellfounded_Owf(_1491776, _1491778), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491776, tc_HOL_Obool)), _1491780), hAPP(c_Relation_OImage(_1491776, _1491776, _1491778), _1491780))), -(_1491780 = c_Orderings_Obot__class_Obot(tc_fun(_1491776, tc_HOL_Obool)))], (37084 ^ _779300) ^ [_1491953, _1491955, _1491957] : [c_Wellfounded_Owf(_1491953, _1491955), c_Wellfounded_Owf(_1491953, _1491957), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1491953, _1491953), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1491953, _1491953, _1491953), _1491955), _1491957)), _1491955)), -(c_Wellfounded_Owf(_1491953, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491953, _1491953), tc_HOL_Obool)), _1491955), _1491957)))], (37098 ^ _779300) ^ [_1492235, _1492237, _1492239, _1492241] : [hBOOL(hAPP(hAPP(c_member(_1492235), _1492237), hAPP(c_Relation_ODomain(_1492235, _1492239), _1492241))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492235, _1492239)), hAPP(hAPP(c_Product__Type_OPair(_1492235, _1492239), _1492237), 37101 ^ [_1492235, _1492237, _1492239, _1492241])), _1492241)))], (37105 ^ _779300) ^ [_1492392, _1492394, _1492396, _1492398] : [37106 ^ _779300 : [(37107 ^ _779300) ^ [_1492467] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492392, _1492396)), hAPP(hAPP(c_Product__Type_OPair(_1492392, _1492396), _1492394), _1492467)), _1492398))]], -(hBOOL(hAPP(hAPP(c_member(_1492392), _1492394), hAPP(c_Relation_ODomain(_1492392, _1492396), _1492398))))], (37111 ^ _779300) ^ [_1492552] : [class_Orderings_Owellorder(_1492552), -(c_Wellfounded_Owf(_1492552, hAPP(c_Set_OCollect(tc_prod(_1492552, _1492552)), hAPP(c_Product__Type_Oprod_Oprod__case(_1492552, _1492552, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1492552)))))], (37117 ^ _779300) ^ [_1492659, _1492661, _1492663, _1492665, _1492667] : [-(hAPP(c_Relation_ODomain(_1492659, _1492661), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1492659, _1492661)), hAPP(hAPP(c_Product__Type_OPair(_1492659, _1492661), _1492663), _1492665)), _1492667)) = hAPP(hAPP(c_Set_Oinsert(_1492659), _1492663), hAPP(c_Relation_ODomain(_1492659, _1492661), _1492667)))], (37119 ^ _779300) ^ [_1492745, _1492747] : [c_FunDef_Oreduction__pair(_1492745, _1492747), 37122 ^ _779300 : [(37123 ^ _779300) ^ [] : [-(c_Wellfounded_Owf(_1492745, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1492745, _1492745), tc_HOL_Obool), tc_fun(tc_prod(_1492745, _1492745), tc_HOL_Obool)), _1492747)))], (37125 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1492745, _1492745), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1492745, _1492745, _1492745), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1492745, _1492745), tc_HOL_Obool), tc_fun(tc_prod(_1492745, _1492745), tc_HOL_Obool)), _1492747)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1492745, _1492745), tc_HOL_Obool), tc_fun(tc_prod(_1492745, _1492745), tc_HOL_Obool)), _1492747))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1492745, _1492745), tc_HOL_Obool), tc_fun(tc_prod(_1492745, _1492745), tc_HOL_Obool)), _1492747))))]]], (37127 ^ _779300) ^ [_1493034, _1493036] : [-(c_FunDef_Oreduction__pair(_1493034, _1493036)), c_Wellfounded_Owf(_1493034, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1493034, _1493034), tc_HOL_Obool), tc_fun(tc_prod(_1493034, _1493034), tc_HOL_Obool)), _1493036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1493034, _1493034), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1493034, _1493034, _1493034), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1493034, _1493034), tc_HOL_Obool), tc_fun(tc_prod(_1493034, _1493034), tc_HOL_Obool)), _1493036)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1493034, _1493034), tc_HOL_Obool), tc_fun(tc_prod(_1493034, _1493034), tc_HOL_Obool)), _1493036))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1493034, _1493034), tc_HOL_Obool), tc_fun(tc_prod(_1493034, _1493034), tc_HOL_Obool)), _1493036)))], (37137 ^ _779300) ^ [_1493355, _1493357, _1493359, _1493361] : [c_FunDef_Oreduction__pair(_1493355, _1493357), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1493355, _1493355), tc_HOL_Obool)), _1493359), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1493355, _1493355), tc_HOL_Obool), tc_fun(tc_prod(_1493355, _1493355), tc_HOL_Obool)), _1493357))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1493355, _1493355), tc_HOL_Obool)), _1493361), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1493355, _1493355), tc_HOL_Obool), tc_fun(tc_prod(_1493355, _1493355), tc_HOL_Obool)), _1493357))), c_Wellfounded_Owf(_1493355, _1493361), -(c_Wellfounded_Owf(_1493355, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1493355, _1493355), tc_HOL_Obool)), _1493359), _1493361)))], (37155 ^ _779300) ^ [_1493756, _1493758, _1493760, _1493762] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493756, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1493756, _1493758), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1493756, _1493758), tc_HOL_Obool)), _1493760), _1493762))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493756, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1493756, _1493758), _1493760)), hAPP(c_Relation_ODomain(_1493756, _1493758), _1493762)))))], (37157 ^ _779300) ^ [_1493838, _1493840, _1493842, _1493844] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493838, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493838, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1493838, _1493840), _1493842)), hAPP(c_Relation_ODomain(_1493838, _1493840), _1493844))), hAPP(c_Relation_ODomain(_1493838, _1493840), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1493838, _1493840), tc_HOL_Obool)), _1493842), _1493844)))))], (37159 ^ _779300) ^ [_1493920, _1493922] : [-(hAPP(c_Relation_OField(_1493920), _1493922) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1493920, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1493920, _1493920), _1493922)), hAPP(c_Relation_ORange(_1493920, _1493920), _1493922)))], (37161 ^ _779300) ^ [_1493973, _1493975, _1493977, _1493979] : [c_Wellfounded_Owf(_1493973, _1493975), c_Fun_Oinj__on(_1493973, _1493977, _1493979, c_Orderings_Otop__class_Otop(tc_fun(_1493973, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1493977, hAPP(c_Set_Oimage(tc_prod(_1493973, _1493973), tc_prod(_1493977, _1493977), c_Product__Type_Omap__pair(_1493973, _1493977, _1493973, _1493977, _1493979, _1493979)), _1493975)))], (37171 ^ _779300) ^ [_1494185, _1494187, _1494189, _1494191] : [hBOOL(hAPP(c_Predicate_ODomainP(_1494185, _1494187, hAPP(hAPP(c_COMBC(_1494185, tc_fun(tc_prod(_1494185, _1494187), tc_HOL_Obool), tc_fun(_1494187, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494187, tc_fun(tc_fun(tc_prod(_1494185, _1494187), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1494185, _1494187), tc_HOL_Obool), tc_fun(_1494187, tc_HOL_Obool)), _1494185), c_COMBC(_1494187, tc_fun(tc_prod(_1494185, _1494187), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494187, tc_prod(_1494185, _1494187)), tc_fun(_1494187, tc_fun(tc_fun(tc_prod(_1494185, _1494187), tc_HOL_Obool), tc_HOL_Obool)), _1494185), hAPP(c_COMBB(tc_prod(_1494185, _1494187), tc_fun(tc_fun(tc_prod(_1494185, _1494187), tc_HOL_Obool), tc_HOL_Obool), _1494187), c_member(tc_prod(_1494185, _1494187)))), c_Product__Type_OPair(_1494185, _1494187)))), _1494189)), _1494191)), -(hBOOL(hAPP(hAPP(c_member(_1494185), _1494191), hAPP(c_Relation_ODomain(_1494185, _1494187), _1494189))))], (37177 ^ _779300) ^ [_1494536, _1494538, _1494540, _1494542] : [hBOOL(hAPP(hAPP(c_member(_1494536), _1494542), hAPP(c_Relation_ODomain(_1494536, _1494538), _1494540))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1494536, _1494538, hAPP(hAPP(c_COMBC(_1494536, tc_fun(tc_prod(_1494536, _1494538), tc_HOL_Obool), tc_fun(_1494538, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494538, tc_fun(tc_fun(tc_prod(_1494536, _1494538), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1494536, _1494538), tc_HOL_Obool), tc_fun(_1494538, tc_HOL_Obool)), _1494536), c_COMBC(_1494538, tc_fun(tc_prod(_1494536, _1494538), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494538, tc_prod(_1494536, _1494538)), tc_fun(_1494538, tc_fun(tc_fun(tc_prod(_1494536, _1494538), tc_HOL_Obool), tc_HOL_Obool)), _1494536), hAPP(c_COMBB(tc_prod(_1494536, _1494538), tc_fun(tc_fun(tc_prod(_1494536, _1494538), tc_HOL_Obool), tc_HOL_Obool), _1494538), c_member(tc_prod(_1494536, _1494538)))), c_Product__Type_OPair(_1494536, _1494538)))), _1494540)), _1494542)))], (37183 ^ _779300) ^ [_1494893, _1494895] : [c_Wellfounded_Owf(_1494893, _1494895), -(c_Wellfounded_Owf(tc_List_Olist(_1494893), c_List_Olenlex(_1494893, _1494895)))], (37189 ^ _779300) ^ [_1494980, _1494982, _1494984, _1494986] : [hBOOL(hAPP(hAPP(c_member(_1494980), _1494982), hAPP(c_Relation_ODomain(_1494980, _1494984), _1494986))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494980, _1494984)), hAPP(hAPP(c_Product__Type_OPair(_1494980, _1494984), _1494982), 37192 ^ [_1494980, _1494982, _1494984, _1494986])), _1494986)))], (37196 ^ _779300) ^ [_1495145, _1495147, _1495149, _1495151, _1495153] : [hBOOL(hAPP(hAPP(_1495145, _1495147), _1495149)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1495151, _1495153, _1495145), _1495147)))], (37202 ^ _779300) ^ [_1495271, _1495273, _1495275, _1495277] : [hBOOL(hAPP(c_Predicate_ODomainP(_1495271, _1495273, _1495275), _1495277)), -(hBOOL(hAPP(hAPP(_1495275, _1495277), 37205 ^ [_1495271, _1495273, _1495275, _1495277])))], (37209 ^ _779300) ^ [_1495386, _1495388, _1495390, _1495392] : [37210 ^ _779300 : [(37211 ^ _779300) ^ [_1495440] : [hBOOL(hAPP(hAPP(_1495390, _1495392), _1495440))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1495386, _1495388, _1495390), _1495392)))], (37215 ^ _779300) ^ [] : [-(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))))], (37217 ^ _779300) ^ [_1495522, _1495524] : [c_Wellfounded_Owf(_1495522, _1495524), -(c_Wellfounded_Owf(tc_List_Olist(_1495522), c_List_Olex(_1495522, _1495524)))], (37223 ^ _779300) ^ [_1495609, _1495611, _1495613] : [c_Wellfounded_Owf(_1495609, _1495611), -(c_Wellfounded_Owf(tc_List_Olist(_1495609), hAPP(c_List_Olexn(_1495609, _1495611), _1495613)))], (37229 ^ _779300) ^ [_1495704, _1495706] : [-(c_List_Olex(_1495704, _1495706) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1495704), tc_List_Olist(_1495704)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1495704, _1495706)))], (37231 ^ _779300) ^ [_1495754, _1495756] : [-(hAPP(c_List_Olexn(_1495754, _1495756), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1495754), tc_List_Olist(_1495754)), tc_HOL_Obool)))], (37233 ^ _779300) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (37235 ^ _779300) ^ [_1495815, _1495817, _1495819, _1495821] : [37237 ^ _779300 : [(37238 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1495815, 37236 ^ [_1495815, _1495817, _1495819, _1495821])))], (37240 ^ _779300) ^ [] : [c_Wellfounded_Owf(_1495817, hAPP(_1495819, 37236 ^ [_1495815, _1495817, _1495819, _1495821]))]], -(c_Wellfounded_Owf(tc_prod(_1495821, _1495817), c_Recdef_Osame__fst(_1495821, _1495817, _1495815, _1495819)))], (37244 ^ _779300) ^ [_1496000, _1496002, _1496004, _1496006] : [37246 ^ _779300 : [(37247 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1496000, 37245 ^ [_1496000, _1496002, _1496004, _1496006])))], (37249 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1496002, hAPP(_1496004, 37245 ^ [_1496000, _1496002, _1496004, _1496006]))), hAPP(_1496002, 37245 ^ [_1496000, _1496002, _1496004, _1496006])))]], -(c_Wellfounded_Owf(_1496006, hAPP(c_Set_OCollect(tc_prod(_1496006, _1496006)), hAPP(c_Product__Type_Oprod_Oprod__case(_1496006, _1496006, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1496006, tc_HOL_Obool), tc_fun(_1496006, tc_HOL_Obool), _1496006), hAPP(c_COMBS(_1496006, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1496006), c_fconj), _1496000))), hAPP(hAPP(c_COMBC(_1496006, tc_fun(_1496006, _1496006), tc_fun(_1496006, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1496006, tc_HOL_Obool), tc_fun(tc_fun(_1496006, _1496006), tc_fun(_1496006, tc_HOL_Obool)), _1496006), c_COMBB(_1496006, tc_HOL_Obool, _1496006)), c_fequal)), _1496004))))))], (37253 ^ _779300) ^ [_1496408, _1496410] : [c_Wellfounded_OwfP(_1496408, _1496410), -(c_Wellfounded_Owf(_1496408, hAPP(c_Set_OCollect(tc_prod(_1496408, _1496408)), hAPP(c_Product__Type_Oprod_Oprod__case(_1496408, _1496408, tc_HOL_Obool), _1496410))))], (37259 ^ _779300) ^ [_1496511, _1496513] : [c_Wellfounded_Owf(_1496511, hAPP(c_Set_OCollect(tc_prod(_1496511, _1496511)), hAPP(c_Product__Type_Oprod_Oprod__case(_1496511, _1496511, tc_HOL_Obool), _1496513))), -(c_Wellfounded_OwfP(_1496511, _1496513))], (37265 ^ _779300) ^ [_1496620] : [-(c_Wellfounded_OwfP(_1496620, hAPP(c_COMBK(tc_fun(_1496620, tc_HOL_Obool), _1496620), hAPP(c_COMBK(tc_HOL_Obool, _1496620), c_fFalse))))], (37267 ^ _779300) ^ [_1496673, _1496675] : [c_Wellfounded_OwfP(_1496673, _1496675), 37270 ^ _779300 : [(37271 ^ _779300) ^ [_1496737] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1496673, _1496675), _1496737)))]]], (37273 ^ _779300) ^ [_1496765, _1496767] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1496765, _1496767), 37274 ^ [_1496765, _1496767])), -(c_Wellfounded_OwfP(_1496765, _1496767))], (37280 ^ _779300) ^ [_1496883, _1496885, _1496887] : [c_Wellfounded_OwfP(_1496883, _1496885), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1496883, _1496885), _1496887)))], (37286 ^ _779300) ^ [_1496972, _1496974, _1496976] : [c_Wellfounded_OwfP(_1496972, _1496974), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496972, tc_fun(_1496972, tc_HOL_Obool))), _1496976), _1496974)), -(c_Wellfounded_OwfP(_1496972, _1496976))], (37296 ^ _779300) ^ [_1497131, _1497133] : [c_Wellfounded_Owf(_1497131, _1497133), -(c_Wellfounded_OwfP(_1497131, c_FunDef_Oin__rel(_1497131, _1497131, _1497133)))], (37302 ^ _779300) ^ [_1497231, _1497233] : [c_Wellfounded_OwfP(_1497231, hAPP(hAPP(c_COMBC(_1497231, tc_fun(tc_prod(_1497231, _1497231), tc_HOL_Obool), tc_fun(_1497231, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497231, tc_fun(tc_fun(tc_prod(_1497231, _1497231), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1497231, _1497231), tc_HOL_Obool), tc_fun(_1497231, tc_HOL_Obool)), _1497231), c_COMBC(_1497231, tc_fun(tc_prod(_1497231, _1497231), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497231, tc_prod(_1497231, _1497231)), tc_fun(_1497231, tc_fun(tc_fun(tc_prod(_1497231, _1497231), tc_HOL_Obool), tc_HOL_Obool)), _1497231), hAPP(c_COMBB(tc_prod(_1497231, _1497231), tc_fun(tc_fun(tc_prod(_1497231, _1497231), tc_HOL_Obool), tc_HOL_Obool), _1497231), c_member(tc_prod(_1497231, _1497231)))), c_Product__Type_OPair(_1497231, _1497231)))), _1497233)), -(c_Wellfounded_Owf(_1497231, _1497233))], (37308 ^ _779300) ^ [_1497540, _1497542] : [c_Wellfounded_Owf(_1497540, _1497542), -(c_Wellfounded_OwfP(_1497540, hAPP(hAPP(c_COMBC(_1497540, tc_fun(tc_prod(_1497540, _1497540), tc_HOL_Obool), tc_fun(_1497540, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497540, tc_fun(tc_fun(tc_prod(_1497540, _1497540), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1497540, _1497540), tc_HOL_Obool), tc_fun(_1497540, tc_HOL_Obool)), _1497540), c_COMBC(_1497540, tc_fun(tc_prod(_1497540, _1497540), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497540, tc_prod(_1497540, _1497540)), tc_fun(_1497540, tc_fun(tc_fun(tc_prod(_1497540, _1497540), tc_HOL_Obool), tc_HOL_Obool)), _1497540), hAPP(c_COMBB(tc_prod(_1497540, _1497540), tc_fun(tc_fun(tc_prod(_1497540, _1497540), tc_HOL_Obool), tc_HOL_Obool), _1497540), c_member(tc_prod(_1497540, _1497540)))), c_Product__Type_OPair(_1497540, _1497540)))), _1497542)))], (37314 ^ _779300) ^ [_1497855, _1497857] : [c_Wellfounded_OwfP(_1497855, _1497857), -(c_Wellfounded_Oacyclic(_1497855, hAPP(c_Set_OCollect(tc_prod(_1497855, _1497855)), hAPP(c_Product__Type_Oprod_Oprod__case(_1497855, _1497855, tc_HOL_Obool), _1497857))))], (37336 ^ _779300) ^ [_1498599, _1498601, _1498603] : [-(c_Relation_Orefl__on(_1498599, _1498601, _1498603)), 37340 ^ _779300 : [(37341 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1498599, _1498599)), 37339 ^ [_1498599, _1498601, _1498603]), _1498603)))], (37343 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1498599, _1498599, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1498599, tc_fun(_1498599, tc_HOL_Obool), tc_fun(_1498599, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1498599, tc_HOL_Obool), tc_fun(_1498599, tc_HOL_Obool)), _1498599), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1498599)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1498599), c_fconj), hAPP(hAPP(c_COMBC(_1498599, tc_fun(_1498599, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498599)), _1498601)))), hAPP(hAPP(c_COMBC(_1498599, tc_fun(_1498599, tc_HOL_Obool), tc_HOL_Obool), c_member(_1498599)), _1498601))), 37339 ^ [_1498599, _1498601, _1498603]))]], 37345 ^ _779300 : [(37346 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1498599), 37344 ^ [_1498599, _1498601, _1498603]), _1498601)))], (37348 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1498599, _1498599)), hAPP(hAPP(c_Product__Type_OPair(_1498599, _1498599), 37344 ^ [_1498599, _1498601, _1498603]), 37344 ^ [_1498599, _1498601, _1498603])), _1498603))]]], (37320 ^ _779300) ^ [_1497980, _1497982, _1497984] : [c_Relation_Orefl__on(_1497980, _1497982, _1497984), 37323 ^ _779300 : [(37324 ^ _779300) ^ [_1498191] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1497980, _1497980)), _1498191), _1497984)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1497980, _1497980, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1497980, tc_fun(_1497980, tc_HOL_Obool), tc_fun(_1497980, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1497980, tc_HOL_Obool), tc_fun(_1497980, tc_HOL_Obool)), _1497980), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1497980)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497980), c_fconj), hAPP(hAPP(c_COMBC(_1497980, tc_fun(_1497980, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497980)), _1497982)))), hAPP(hAPP(c_COMBC(_1497980, tc_fun(_1497980, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497980)), _1497982))), _1498191)))], (37330 ^ _779300) ^ [_1498464] : [hBOOL(hAPP(hAPP(c_member(_1497980), _1498464), _1497982)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1497980, _1497980)), hAPP(hAPP(c_Product__Type_OPair(_1497980, _1497980), _1498464), _1498464)), _1497984)))]]], (37352 ^ _779300) ^ [_1499240, _1499242] : [37354 ^ _779300 : [(37355 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 37353 ^ [_1499240, _1499242]), c_Int_OInteg)))], (37357 ^ _779300) ^ [] : [hBOOL(hAPP(_1499240, hAPP(c_Int_OAbs__Integ, 37353 ^ [_1499240, _1499242])))]], -(hBOOL(hAPP(_1499240, _1499242)))], (37361 ^ _779300) ^ [_1499409, _1499411, _1499413] : [hBOOL(hAPP(hAPP(c_member(_1499411), _1499409), c_Orderings_Obot__class_Obot(tc_fun(_1499411, tc_HOL_Obool)))), -(hBOOL(hAPP(_1499413, _1499409)))], (37367 ^ _779300) ^ [_1499516, _1499518] : [c_Wellfounded_Owf(_1499516, _1499518), -(c_Wellfounded_Oacyclic(_1499516, _1499518))], (37373 ^ _779300) ^ [_1499593, _1499595, _1499597] : [c_Wellfounded_Oacyclic(_1499593, _1499595), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1499593, _1499593), tc_HOL_Obool)), _1499597), _1499595)), -(c_Wellfounded_Oacyclic(_1499593, _1499597))], (37393 ^ _779300) ^ [_1499953, _1499955, _1499957] : [37395 ^ _779300 : [(37396 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1499953), 37394 ^ [_1499953, _1499955, _1499957]), _1499957)))], (37398 ^ _779300) ^ [] : [hBOOL(hAPP(_1499955, 37394 ^ [_1499953, _1499955, _1499957]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1499953, _1499955), _1499957)))], (37383 ^ _779300) ^ [_1499770, _1499772, _1499774] : [hBOOL(hAPP(c_Predicate_OPowp(_1499770, _1499772), _1499774)), 37386 ^ _779300 : [(37387 ^ _779300) ^ [_1499854] : [hBOOL(hAPP(hAPP(c_member(_1499770), _1499854), _1499774)), -(hBOOL(hAPP(_1499772, _1499854)))]]], (37412 ^ _779300) ^ [_1500530, _1500532, _1500534, _1500536] : [37414 ^ _779300 : [(37415 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1500530, _1500530)), 37413 ^ [_1500530, _1500532, _1500534, _1500536]), _1500534)))], (37417 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500530, _1500530, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1500530, tc_fun(_1500530, _1500532), tc_fun(_1500530, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500532, tc_HOL_Obool), tc_fun(tc_fun(_1500530, _1500532), tc_fun(_1500530, tc_HOL_Obool)), _1500530), c_COMBB(_1500532, tc_HOL_Obool, _1500530)), hAPP(hAPP(c_COMBB(_1500532, tc_fun(_1500532, tc_HOL_Obool), _1500530), c_fequal), _1500536))), _1500536)), 37413 ^ [_1500530, _1500532, _1500534, _1500536]))]], -(c_Equiv__Relations_Ocongruent(_1500530, _1500532, _1500534, _1500536))], (37402 ^ _779300) ^ [_1500154, _1500156, _1500158, _1500160] : [c_Equiv__Relations_Ocongruent(_1500154, _1500156, _1500158, _1500160), 37405 ^ _779300 : [(37406 ^ _779300) ^ [_1500299] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1500154, _1500154)), _1500299), _1500158)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500154, _1500154, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1500154, tc_fun(_1500154, _1500156), tc_fun(_1500154, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500156, tc_HOL_Obool), tc_fun(tc_fun(_1500154, _1500156), tc_fun(_1500154, tc_HOL_Obool)), _1500154), c_COMBB(_1500156, tc_HOL_Obool, _1500154)), hAPP(hAPP(c_COMBB(_1500156, tc_fun(_1500156, tc_HOL_Obool), _1500154), c_fequal), _1500160))), _1500160)), _1500299)))]]], (37421 ^ _779300) ^ [_1500905, _1500907] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1500905, _1500905)), _1500907)), 37424 ^ _779300 : [(37425 ^ _779300) ^ [] : [c_Wellfounded_Owf(_1500905, _1500907), -(c_Wellfounded_Oacyclic(_1500905, _1500907))], (37431 ^ _779300) ^ [] : [c_Wellfounded_Oacyclic(_1500905, _1500907), -(c_Wellfounded_Owf(_1500905, _1500907))]]], (37437 ^ _779300) ^ [_1501126, _1501128] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1501126, _1501126)), _1501128)), c_Wellfounded_Oacyclic(_1501126, _1501128), -(c_Wellfounded_Owf(_1501126, _1501128))], (37447 ^ _779300) ^ [_1501284, _1501286] : [c_Nitpick_Owf_H(_1501284, _1501286), 37450 ^ _779300 : [(37451 ^ _779300) ^ [] : [-(c_Wellfounded_Oacyclic(_1501284, _1501286))], (37453 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1501284, _1501284)), _1501286))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (37459 ^ _779300) ^ [_1501404, _1501406] : [-(c_Nitpick_Owf_H(_1501404, _1501406)), c_Wellfounded_Oacyclic(_1501404, _1501406), 37464 ^ _779300 : [(37465 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1501404, _1501404)), _1501406))], (37467 ^ _779300) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (37472 ^ _779300) ^ [_1501579] : [-(_1501579 = hAPP(c_Int_OAbs__Integ, 37470 ^ [_1501579]))], (37474 ^ _779300) ^ [_1501607] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 37470 ^ [_1501607]), c_Int_OInteg)))], (37476 ^ _779300) ^ [_1501642, _1501644, _1501646, _1501648] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501642), _1501644)), 37482 ^ _779300 : [(37483 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501642), 37481 ^ [_1501642, _1501644, _1501646, _1501648]), _1501644)))], (37485 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501646), hAPP(_1501648, 37481 ^ [_1501642, _1501644, _1501646, _1501648])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1501646), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501642, tc_fun(_1501646, tc_HOL_Obool)), _1501644), _1501648))))], (37489 ^ _779300) ^ [_1501929, _1501931, _1501933] : [c_Wellfounded_OwfP(_1501929, hAPP(_1501931, 37490 ^ [_1501929, _1501931, _1501933])), 37497 ^ _779300 : [(37498 ^ _779300) ^ [] : [hAPP(_1501931, 37495 ^ [_1501929, _1501931, _1501933]) = hAPP(_1501931, 37496 ^ [_1501929, _1501931, _1501933])], (37500 ^ _779300) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501929, tc_HOL_Obool)), c_Predicate_ODomainP(_1501929, _1501929, hAPP(_1501931, 37495 ^ [_1501929, _1501931, _1501933]))), c_Predicate_ORangeP(_1501929, _1501929, hAPP(_1501931, 37496 ^ [_1501929, _1501931, _1501933]))) = c_Orderings_Obot__class_Obot(tc_fun(_1501929, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1501929, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501933, tc_fun(_1501929, tc_fun(_1501929, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1501933, tc_HOL_Obool))), _1501931)))], (37504 ^ _779300) ^ [_1502369, _1502371, _1502373, _1502375, _1502377, _1502379] : [hBOOL(hAPP(hAPP(c_member(_1502369), _1502371), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1502373, _1502375, tc_fun(_1502369, tc_HOL_Obool)), _1502377), _1502379))), 37509 ^ _779300 : [(37510 ^ _779300) ^ [] : [-(_1502379 = hAPP(hAPP(c_Product__Type_OPair(_1502373, _1502375), 37507 ^ [_1502369, _1502371, _1502373, _1502375, _1502377, _1502379]), 37508 ^ [_1502369, _1502371, _1502373, _1502375, _1502377, _1502379]))], (37512 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502369), _1502371), hAPP(hAPP(_1502377, 37507 ^ [_1502369, _1502371, _1502373, _1502375, _1502377, _1502379]), 37508 ^ [_1502369, _1502371, _1502373, _1502375, _1502377, _1502379]))))]]], (37514 ^ _779300) ^ [_1502638, _1502640, _1502642, _1502644, _1502646, _1502648] : [37517 ^ _779300 : [(37518 ^ _779300) ^ [] : [-(_1502638 = hAPP(hAPP(c_Product__Type_OPair(_1502640, _1502642), 37515 ^ [_1502638, _1502640, _1502642, _1502644, _1502646, _1502648]), 37516 ^ [_1502638, _1502640, _1502642, _1502644, _1502646, _1502648]))], (37520 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1502644), _1502646), hAPP(hAPP(_1502648, 37515 ^ [_1502638, _1502640, _1502642, _1502644, _1502646, _1502648]), 37516 ^ [_1502638, _1502640, _1502642, _1502644, _1502646, _1502648])))]], -(hBOOL(hAPP(hAPP(c_member(_1502644), _1502646), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1502640, _1502642, tc_fun(_1502644, tc_HOL_Obool)), _1502648), _1502638))))], (37524 ^ _779300) ^ [_1502963, _1502965, _1502967, _1502969, _1502971, _1502973] : [-(hAPP(c_Set_Ovimage(_1502963, tc_prod(_1502965, _1502967), _1502969), hAPP(hAPP(c_Product__Type_OSigma(_1502965, _1502967), _1502971), hAPP(c_COMBK(tc_fun(_1502967, tc_HOL_Obool), _1502965), _1502973))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1502963, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1502963, _1502965, hAPP(c_Fun_Ocomp(tc_prod(_1502965, _1502967), _1502965, _1502963, c_Product__Type_Ofst(_1502965, _1502967)), _1502969)), _1502971)), hAPP(c_Set_Ovimage(_1502963, _1502967, hAPP(c_Fun_Ocomp(tc_prod(_1502965, _1502967), _1502967, _1502963, c_Product__Type_Osnd(_1502965, _1502967)), _1502969)), _1502973)))], (37526 ^ _779300) ^ [_1503077, _1503079, _1503081, _1503083] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503077, tc_Nat_Onat), _1503079), _1503081) = hAPP(c_Nat_OSuc, _1503083), 37530 ^ _779300 : [(37531 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503077), 37529 ^ [_1503077, _1503079, _1503081, _1503083]), _1503081)))], (37533 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1503079, 37529 ^ [_1503077, _1503079, _1503081, _1503083]))))]]], (37535 ^ _779300) ^ [_1503259, _1503261, _1503263] : [-(c_Hilbert__Choice_OEps(tc_prod(_1503259, _1503261), hAPP(c_Product__Type_Oprod_Oprod__case(_1503259, _1503261, tc_HOL_Obool), _1503263)) = c_Hilbert__Choice_OEps(tc_prod(_1503259, _1503261), hAPP(hAPP(c_COMBS(tc_prod(_1503259, _1503261), _1503261, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1503259, tc_fun(_1503261, tc_HOL_Obool), tc_prod(_1503259, _1503261)), _1503263), c_Product__Type_Ofst(_1503259, _1503261))), c_Product__Type_Osnd(_1503259, _1503261))))], (37537 ^ _779300) ^ [_1503340, _1503342, _1503344, _1503346, _1503348] : [hAPP(c_Set_Oimage(_1503340, _1503342, _1503344), c_Orderings_Otop__class_Otop(tc_fun(_1503340, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1503342, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1503342, _1503346, _1503348), c_Orderings_Otop__class_Otop(tc_fun(_1503342, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1503346, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1503340, _1503346, hAPP(c_Fun_Ocomp(_1503342, _1503346, _1503340, _1503348), _1503344)), c_Orderings_Otop__class_Otop(tc_fun(_1503340, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1503346, tc_HOL_Obool)))], (37547 ^ _779300) ^ [_1503599, _1503601, _1503603] : [-(hAPP(c_Fun_Ocomp(_1503599, _1503601, _1503599, _1503603), c_Fun_Oid(_1503599)) = _1503603)], (37549 ^ _779300) ^ [_1503636, _1503638, _1503640] : [-(hAPP(c_Fun_Ocomp(_1503636, _1503636, _1503638, c_Fun_Oid(_1503636)), _1503640) = _1503640)], (37551 ^ _779300) ^ [_1503673, _1503675, _1503677, _1503679, _1503681, _1503683, _1503685] : [hAPP(c_Fun_Ocomp(_1503673, _1503675, _1503677, _1503679), _1503681) = hAPP(c_Fun_Ocomp(_1503675, _1503675, _1503677, c_Fun_Oid(_1503675)), _1503683), -(hAPP(_1503679, hAPP(_1503681, _1503685)) = hAPP(_1503683, _1503685))], (37557 ^ _779300) ^ [_1503814, _1503816, _1503818] : [37558 ^ _779300 : [(37559 ^ _779300) ^ [_1503868] : [hBOOL(hAPP(_1503814, _1503868))]], _1503816 = c_Hilbert__Choice_OEps(_1503818, _1503814), -(hBOOL(hAPP(_1503814, _1503816)))], (37567 ^ _779300) ^ [_1503974, _1503976, _1503978, _1503980, _1503982, _1503984] : [-(hAPP(c_Set_Ovimage(_1503974, _1503976, hAPP(c_Fun_Ocomp(_1503978, _1503976, _1503974, _1503980), _1503982)), _1503984) = hAPP(c_Set_Ovimage(_1503974, _1503978, _1503982), hAPP(c_Set_Ovimage(_1503978, _1503976, _1503980), _1503984)))], (37569 ^ _779300) ^ [_1504036, _1504038, _1504040, _1504042, _1504044, _1504046, _1504048] : [-(hAPP(c_Product__Type_Oapfst(_1504036, _1504038, _1504040, _1504042), hAPP(c_Product__Type_Oapfst(_1504044, _1504036, _1504040, _1504046), _1504048)) = hAPP(c_Product__Type_Oapfst(_1504044, _1504038, _1504040, hAPP(c_Fun_Ocomp(_1504036, _1504038, _1504044, _1504042), _1504046)), _1504048))], (37571 ^ _779300) ^ [_1504103, _1504105, _1504107, _1504109] : [c_Finite__Set_Ofun__left__comm__idem(_1504103, _1504105, _1504107), -(hAPP(c_Fun_Ocomp(_1504105, _1504105, _1504105, hAPP(_1504107, _1504109)), hAPP(_1504107, _1504109)) = hAPP(_1504107, _1504109))], (37577 ^ _779300) ^ [_1504220, _1504222, _1504224, _1504226, _1504228, _1504230] : [-(hAPP(hAPP(c_Fun_Ocomp(_1504220, _1504222, _1504224, _1504226), _1504228), _1504230) = hAPP(_1504226, hAPP(_1504228, _1504230)))], (37579 ^ _779300) ^ [_1504270, _1504272] : [-(c_Hilbert__Choice_OEps(_1504270, hAPP(c_fequal, _1504272)) = _1504272)], (37581 ^ _779300) ^ [_1504301, _1504303] : [-(c_Hilbert__Choice_OEps(_1504301, hAPP(hAPP(c_COMBC(_1504301, _1504301, tc_HOL_Obool), c_fequal), _1504303)) = _1504303)], (37583 ^ _779300) ^ [_1504354, _1504356] : [hBOOL(hAPP(_1504354, c_Hilbert__Choice_OEps(_1504356, _1504354))), -(hBOOL(hAPP(_1504354, 37586 ^ [_1504354, _1504356])))], (37590 ^ _779300) ^ [_1504453, _1504455] : [37591 ^ _779300 : [(37592 ^ _779300) ^ [_1504499] : [hBOOL(hAPP(_1504453, _1504499))]], -(hBOOL(hAPP(_1504453, c_Hilbert__Choice_OEps(_1504455, _1504453))))], (37596 ^ _779300) ^ [_1504559, _1504561] : [37597 ^ _779300 : [(37598 ^ _779300) ^ [_1504605] : [hBOOL(hAPP(_1504559, _1504605))]], -(hBOOL(hAPP(_1504559, c_Hilbert__Choice_OEps(_1504561, _1504559))))], (37602 ^ _779300) ^ [_1504663, _1504665, _1504667, _1504669, _1504671, _1504673, _1504675, _1504677] : [hAPP(c_Fun_Ocomp(_1504663, _1504665, _1504667, _1504669), _1504671) = hAPP(c_Fun_Ocomp(_1504673, _1504665, _1504667, _1504675), _1504677), 37605 ^ _779300 : [(37606 ^ _779300) ^ [_1504778] : [-(hAPP(_1504669, hAPP(_1504671, _1504778)) = hAPP(_1504675, hAPP(_1504677, _1504778)))]]], (37608 ^ _779300) ^ [_1504817, _1504819, _1504821, _1504823, _1504825, _1504827, _1504829, _1504831, _1504833] : [hAPP(c_Fun_Ocomp(_1504817, _1504819, _1504821, _1504823), _1504825) = hAPP(c_Fun_Ocomp(_1504827, _1504819, _1504821, _1504829), _1504831), -(hAPP(_1504823, hAPP(_1504825, _1504833)) = hAPP(_1504829, hAPP(_1504831, _1504833)))], (37614 ^ _779300) ^ [_1504964, _1504966, _1504968, _1504970, _1504972, _1504974] : [-(hAPP(hAPP(c_Fun_Ocomp(_1504964, _1504966, _1504968, _1504970), _1504972), _1504974) = hAPP(_1504970, hAPP(_1504972, _1504974)))], (37616 ^ _779300) ^ [_1505014, _1505016, _1505018, _1505020, _1505022, _1505024, _1505026] : [-(hAPP(c_Fun_Ocomp(_1505014, _1505016, _1505018, _1505020), hAPP(c_Fun_Ocomp(_1505022, _1505014, _1505018, _1505024), _1505026)) = hAPP(c_Fun_Ocomp(_1505022, _1505016, _1505018, hAPP(c_Fun_Ocomp(_1505014, _1505016, _1505022, _1505020), _1505024)), _1505026))], (37618 ^ _779300) ^ [_1505081, _1505083, _1505085] : [hBOOL(hAPP(_1505081, _1505083)), -(hBOOL(hAPP(_1505081, c_Hilbert__Choice_OEps(_1505085, _1505081))))], (37624 ^ _779300) ^ [_1505174, _1505176] : [37625 ^ _779300 : [(37626 ^ _779300) ^ [_1505220] : [hBOOL(hAPP(_1505174, _1505220))]], -(hBOOL(hAPP(_1505174, c_Hilbert__Choice_OEps(_1505176, _1505174))))], (37630 ^ _779300) ^ [_1505278, _1505280, _1505282, _1505284, _1505286, _1505288, _1505290, _1505292, _1505294, _1505296, _1505298] : [hAPP(_1505278, hAPP(_1505280, _1505282)) = hAPP(_1505284, hAPP(_1505286, _1505288)), -(hAPP(hAPP(c_Fun_Ocomp(_1505290, _1505292, _1505294, _1505278), _1505280), _1505282) = hAPP(hAPP(c_Fun_Ocomp(_1505296, _1505292, _1505298, _1505284), _1505286), _1505288))], (37636 ^ _779300) ^ [_1505441, _1505443, _1505445, _1505447, _1505449, _1505451, _1505453] : [-(hAPP(c_Fun_Ocomp(_1505441, _1505443, _1505445, _1505447), c_Fun_Ofun__upd(_1505445, _1505441, _1505449, _1505451, _1505453)) = c_Fun_Ofun__upd(_1505445, _1505443, hAPP(c_Fun_Ocomp(_1505441, _1505443, _1505445, _1505447), _1505449), _1505451, hAPP(_1505447, _1505453)))], (37638 ^ _779300) ^ [_1505507, _1505509, _1505511, _1505513, _1505515, _1505517, _1505519] : [-(hAPP(c_Product__Type_Oapsnd(_1505507, _1505509, _1505511, _1505513), hAPP(c_Product__Type_Oapsnd(_1505515, _1505507, _1505511, _1505517), _1505519)) = hAPP(c_Product__Type_Oapsnd(_1505515, _1505509, _1505511, hAPP(c_Fun_Ocomp(_1505507, _1505509, _1505515, _1505513), _1505517)), _1505519))], (37640 ^ _779300) ^ [_1505574, _1505576, _1505578, _1505580, _1505582, _1505584, _1505586] : [hAPP(c_Fun_Ocomp(_1505574, _1505576, _1505578, _1505580), _1505582) = _1505584, -(hAPP(_1505580, hAPP(_1505582, _1505586)) = hAPP(_1505584, _1505586))], (37646 ^ _779300) ^ [_1505695, _1505697, _1505699, _1505701, _1505703, _1505705] : [-(hAPP(hAPP(c_Fun_Ocomp(_1505695, _1505697, _1505699, hAPP(c_COMBK(_1505697, _1505695), _1505701)), _1505703), _1505705) = _1505701)], (37648 ^ _779300) ^ [_1505745, _1505747, _1505749, _1505751, _1505753, _1505755, _1505757, _1505759, _1505761, _1505763] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1505745, _1505747), tc_prod(_1505749, _1505751), tc_prod(_1505753, _1505755), c_Product__Type_Omap__pair(_1505745, _1505749, _1505747, _1505751, _1505757, _1505759)), c_Product__Type_Omap__pair(_1505753, _1505745, _1505755, _1505747, _1505761, _1505763)) = c_Product__Type_Omap__pair(_1505753, _1505749, _1505755, _1505751, hAPP(c_Fun_Ocomp(_1505745, _1505749, _1505753, _1505757), _1505761), hAPP(c_Fun_Ocomp(_1505747, _1505751, _1505755, _1505759), _1505763)))], (37650 ^ _779300) ^ [_1505840, _1505842, _1505844, _1505846, _1505848, _1505850, _1505852, _1505854, _1505856, _1505858] : [-(c_Product__Type_Omap__pair(_1505840, _1505842, _1505844, _1505846, hAPP(c_Fun_Ocomp(_1505848, _1505842, _1505840, _1505850), _1505852), hAPP(c_Fun_Ocomp(_1505854, _1505846, _1505844, _1505856), _1505858)) = hAPP(c_Fun_Ocomp(tc_prod(_1505848, _1505854), tc_prod(_1505842, _1505846), tc_prod(_1505840, _1505844), c_Product__Type_Omap__pair(_1505848, _1505842, _1505854, _1505846, _1505850, _1505856)), c_Product__Type_Omap__pair(_1505840, _1505848, _1505844, _1505854, _1505852, _1505858)))], (37652 ^ _779300) ^ [_1505935, _1505937, _1505939, _1505941, _1505943, _1505945, _1505947, _1505949, _1505951, _1505953, _1505955] : [-(hAPP(c_Product__Type_Omap__pair(_1505935, _1505937, _1505939, _1505941, _1505943, _1505945), hAPP(c_Product__Type_Omap__pair(_1505947, _1505935, _1505949, _1505939, _1505951, _1505953), _1505955)) = hAPP(c_Product__Type_Omap__pair(_1505947, _1505937, _1505949, _1505941, hAPP(c_Fun_Ocomp(_1505935, _1505937, _1505947, _1505943), _1505951), hAPP(c_Fun_Ocomp(_1505939, _1505941, _1505949, _1505945), _1505953)), _1505955))], (37654 ^ _779300) ^ [_1506024, _1506026, _1506028, _1506030, _1506032, _1506034] : [-(hAPP(c_Set_Oimage(_1506024, _1506026, hAPP(c_Fun_Ocomp(_1506028, _1506026, _1506024, _1506030), _1506032)), _1506034) = hAPP(c_Set_Oimage(_1506028, _1506026, _1506030), hAPP(c_Set_Oimage(_1506024, _1506028, _1506032), _1506034)))], (37656 ^ _779300) ^ [_1506086, _1506088, _1506090, _1506092, _1506094, _1506096] : [c_Fun_Oinj__on(_1506086, _1506088, hAPP(c_Fun_Ocomp(_1506090, _1506088, _1506086, _1506092), _1506094), _1506096), -(c_Fun_Oinj__on(_1506086, _1506090, _1506094, _1506096))], (37662 ^ _779300) ^ [_1506195, _1506197, _1506199, _1506201, _1506203, _1506205] : [c_Fun_Oinj__on(_1506195, _1506197, _1506199, _1506201), 37665 ^ _779300 : [(37666 ^ _779300) ^ [] : [c_Fun_Oinj__on(_1506197, _1506203, _1506205, hAPP(c_Set_Oimage(_1506195, _1506197, _1506199), _1506201)), -(c_Fun_Oinj__on(_1506195, _1506203, hAPP(c_Fun_Ocomp(_1506197, _1506203, _1506195, _1506205), _1506199), _1506201))], (37672 ^ _779300) ^ [] : [c_Fun_Oinj__on(_1506195, _1506203, hAPP(c_Fun_Ocomp(_1506197, _1506203, _1506195, _1506205), _1506199), _1506201), -(c_Fun_Oinj__on(_1506197, _1506203, _1506205, hAPP(c_Set_Oimage(_1506195, _1506197, _1506199), _1506201)))]]], (37678 ^ _779300) ^ [_1506487, _1506489, _1506491, _1506493, _1506495, _1506497] : [c_Fun_Oinj__on(_1506487, _1506489, _1506491, _1506493), c_Fun_Oinj__on(_1506489, _1506495, _1506497, hAPP(c_Set_Oimage(_1506487, _1506489, _1506491), _1506493)), -(c_Fun_Oinj__on(_1506487, _1506495, hAPP(c_Fun_Ocomp(_1506489, _1506495, _1506487, _1506497), _1506491), _1506493))], (37688 ^ _779300) ^ [_1506674, _1506676, _1506678, _1506680, _1506682, _1506684] : [c_Fun_Oinj__on(_1506674, _1506676, hAPP(c_Fun_Ocomp(_1506678, _1506676, _1506674, _1506680), _1506682), _1506684), -(c_Fun_Oinj__on(_1506678, _1506676, _1506680, hAPP(c_Set_Oimage(_1506674, _1506678, _1506682), _1506684)))], (37694 ^ _779300) ^ [_1506797, _1506799, _1506801, _1506803, _1506805] : [c_Fun_Oinj__on(_1506797, _1506799, _1506801, c_Orderings_Otop__class_Otop(tc_fun(_1506797, tc_HOL_Obool))), c_Fun_Oinj__on(_1506803, _1506797, _1506805, c_Orderings_Otop__class_Otop(tc_fun(_1506803, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1506803, _1506799, hAPP(c_Fun_Ocomp(_1506797, _1506799, _1506803, _1506801), _1506805), c_Orderings_Otop__class_Otop(tc_fun(_1506803, tc_HOL_Obool))))], (37704 ^ _779300) ^ [_1506996, _1506998, _1507000, _1507002, _1507004, _1507006] : [class_Groups_Ocomm__monoid__add(_1506996), c_Fun_Oinj__on(_1506998, _1507000, _1507002, _1507004), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1507000, _1506996), _1507006), hAPP(c_Set_Oimage(_1506998, _1507000, _1507002), _1507004)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1506998, _1506996), hAPP(c_Fun_Ocomp(_1507000, _1506996, _1506998, _1507006), _1507002)), _1507004))], (37714 ^ _779300) ^ [_1507209, _1507211, _1507213, _1507215, _1507217, _1507219, _1507221, _1507223] : [class_Groups_Ocomm__monoid__mult(_1507209), c_Fun_Oinj__on(_1507211, _1507213, _1507215, _1507217), _1507219 = hAPP(c_Set_Oimage(_1507211, _1507213, _1507215), _1507217), _1507221 = hAPP(c_Fun_Ocomp(_1507213, _1507209, _1507211, _1507223), _1507215), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1507213, _1507209), _1507223), _1507219) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1507211, _1507209), _1507221), _1507217))], (37732 ^ _779300) ^ [_1507558, _1507560, _1507562, _1507564, _1507566, _1507568] : [class_Groups_Ocomm__monoid__mult(_1507558), c_Fun_Oinj__on(_1507560, _1507562, _1507564, _1507566), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1507562, _1507558), _1507568), hAPP(c_Set_Oimage(_1507560, _1507562, _1507564), _1507566)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1507560, _1507558), hAPP(c_Fun_Ocomp(_1507562, _1507558, _1507560, _1507568), _1507564)), _1507566))], (37742 ^ _779300) ^ [_1507771, _1507773, _1507775] : [-(c_Hilbert__Choice_OEps(tc_prod(_1507771, _1507773), _1507775) = c_Hilbert__Choice_OEps(tc_prod(_1507771, _1507773), hAPP(c_Product__Type_Oprod_Oprod__case(_1507771, _1507773, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1507773, tc_prod(_1507771, _1507773)), tc_fun(_1507773, tc_HOL_Obool), _1507771), hAPP(c_COMBB(tc_prod(_1507771, _1507773), tc_HOL_Obool, _1507773), _1507775)), c_Product__Type_OPair(_1507771, _1507773)))))], (37744 ^ _779300) ^ [_1507849, _1507851, _1507853, _1507855] : [-(c_Hilbert__Choice_OEps(tc_prod(_1507849, _1507851), hAPP(c_Product__Type_Oprod_Oprod__case(_1507849, _1507851, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1507849, tc_fun(_1507851, tc_HOL_Obool), tc_fun(_1507851, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1507851, tc_HOL_Obool), tc_fun(_1507851, tc_HOL_Obool)), _1507849), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1507851)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507849), c_fconj), hAPP(c_fequal, _1507853)))), hAPP(c_fequal, _1507855)))) = hAPP(hAPP(c_Product__Type_OPair(_1507849, _1507851), _1507853), _1507855))], (37746 ^ _779300) ^ [_1507955, _1507957, _1507959, _1507961, _1507963] : [class_Groups_Ocomm__monoid__add(_1507955), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507957), _1507959)), c_Fun_Oinj__on(_1507957, _1507957, _1507961, _1507959), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1507957, _1507955), _1507963), hAPP(c_Set_Oimage(_1507957, _1507957, _1507961), _1507959)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1507957, _1507955), hAPP(c_Fun_Ocomp(_1507957, _1507955, _1507957, _1507963), _1507961)), _1507959))], (37760 ^ _779300) ^ [_1508230, _1508232, _1508234, _1508236, _1508238] : [class_Groups_Ocomm__monoid__mult(_1508230), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508232), _1508234)), c_Fun_Oinj__on(_1508232, _1508232, _1508236, _1508234), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1508232, _1508230), _1508238), hAPP(c_Set_Oimage(_1508232, _1508232, _1508236), _1508234)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1508232, _1508230), hAPP(c_Fun_Ocomp(_1508232, _1508230, _1508232, _1508238), _1508236)), _1508234))], (37774 ^ _779300) ^ [_1508505, _1508507, _1508509, _1508511, _1508513, _1508515, _1508517] : [c_Fun_Oinj__on(_1508505, _1508507, _1508509, hAPP(c_Set_Oimage(_1508511, _1508505, _1508513), _1508515)), c_Fun_Oinj__on(_1508511, _1508505, _1508513, _1508515), hBOOL(hAPP(hAPP(c_member(_1508507), _1508517), hAPP(c_Set_Oimage(_1508505, _1508507, _1508509), hAPP(c_Set_Oimage(_1508511, _1508505, _1508513), _1508515)))), -(hAPP(c_Fun_Othe__inv__into(_1508511, _1508507, _1508515, hAPP(c_Fun_Ocomp(_1508505, _1508507, _1508511, _1508509), _1508513)), _1508517) = hAPP(hAPP(c_Fun_Ocomp(_1508505, _1508511, _1508507, c_Fun_Othe__inv__into(_1508511, _1508505, _1508515, _1508513)), c_Fun_Othe__inv__into(_1508505, _1508507, hAPP(c_Set_Oimage(_1508511, _1508505, _1508513), _1508515), _1508509)), _1508517))], (37788 ^ _779300) ^ [_1508868, _1508870, _1508872, _1508874, _1508876, _1508878, _1508880, _1508882] : [c_Finite__Set_Ofolding__image(_1508868, _1508870, _1508872, _1508874, _1508876), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508870), _1508878)), c_Fun_Oinj__on(_1508870, _1508870, _1508880, _1508878), -(hAPP(hAPP(_1508876, _1508882), hAPP(c_Set_Oimage(_1508870, _1508870, _1508880), _1508878)) = hAPP(hAPP(_1508876, hAPP(c_Fun_Ocomp(_1508870, _1508868, _1508870, _1508882), _1508880)), _1508878))], (37802 ^ _779300) ^ [_1509157, _1509159, _1509161, _1509163, _1509165, _1509167, _1509169] : [class_Groups_Oab__semigroup__mult(_1509157), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509159), _1509161)), c_Fun_Oinj__on(_1509159, _1509163, _1509165, _1509161), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1509157, _1509163, c_Groups_Otimes__class_Otimes(_1509157)), _1509167), _1509169), hAPP(c_Set_Oimage(_1509159, _1509163, _1509165), _1509161)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1509157, _1509159, c_Groups_Otimes__class_Otimes(_1509157)), hAPP(c_Fun_Ocomp(_1509163, _1509157, _1509159, _1509167), _1509165)), _1509169), _1509161))], (37816 ^ _779300) ^ [_1509468, _1509470, _1509472, _1509474, _1509476, _1509478] : [c_Finite__Set_Ofolding(_1509468, _1509470, _1509472, _1509474), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509468), _1509476)), hBOOL(hAPP(hAPP(c_member(_1509468), _1509478), _1509476)), -(hAPP(_1509474, _1509476) = hAPP(c_Fun_Ocomp(_1509470, _1509470, _1509470, hAPP(_1509474, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1509468, tc_HOL_Obool)), _1509476), hAPP(hAPP(c_Set_Oinsert(_1509468), _1509478), c_Orderings_Obot__class_Obot(tc_fun(_1509468, tc_HOL_Obool)))))), hAPP(_1509472, _1509478)))], (37830 ^ _779300) ^ [_1509781, _1509783, _1509785, _1509787, _1509789, _1509791] : [c_Finite__Set_Ofolding(_1509781, _1509783, _1509785, _1509787), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509781), _1509789)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509781), _1509791)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509781, tc_HOL_Obool)), _1509789), _1509791) = c_Orderings_Obot__class_Obot(tc_fun(_1509781, tc_HOL_Obool)), -(hAPP(_1509787, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1509781, tc_HOL_Obool)), _1509789), _1509791)) = hAPP(c_Fun_Ocomp(_1509783, _1509783, _1509783, hAPP(_1509787, _1509789)), hAPP(_1509787, _1509791)))], (37848 ^ _779300) ^ [_1510154, _1510156, _1510158, _1510160, _1510162, _1510164] : [c_Finite__Set_Ofolding(_1510154, _1510156, _1510158, _1510160), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510154), _1510162)), -(hAPP(_1510160, hAPP(hAPP(c_Set_Oinsert(_1510154), _1510164), _1510162)) = hAPP(c_Fun_Ocomp(_1510156, _1510156, _1510156, hAPP(_1510160, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1510154, tc_HOL_Obool)), _1510162), hAPP(hAPP(c_Set_Oinsert(_1510154), _1510164), c_Orderings_Obot__class_Obot(tc_fun(_1510154, tc_HOL_Obool)))))), hAPP(_1510158, _1510164)))], (37858 ^ _779300) ^ [_1510409, _1510411, _1510413, _1510415, _1510417, _1510419, _1510421, _1510423] : [c_Finite__Set_Ofolding(_1510409, _1510411, _1510413, _1510415), -(hAPP(c_Fun_Ocomp(_1510411, _1510411, _1510417, hAPP(_1510413, _1510419)), hAPP(c_Fun_Ocomp(_1510411, _1510411, _1510417, hAPP(_1510413, _1510421)), _1510423)) = hAPP(c_Fun_Ocomp(_1510411, _1510411, _1510417, hAPP(_1510413, _1510421)), hAPP(c_Fun_Ocomp(_1510411, _1510411, _1510417, hAPP(_1510413, _1510419)), _1510423)))], (37864 ^ _779300) ^ [_1510590, _1510592, _1510594, _1510596, _1510598, _1510600] : [c_Finite__Set_Ofolding(_1510590, _1510592, _1510594, _1510596), -(hAPP(c_Fun_Ocomp(_1510592, _1510592, _1510592, hAPP(_1510594, _1510598)), hAPP(_1510594, _1510600)) = hAPP(c_Fun_Ocomp(_1510592, _1510592, _1510592, hAPP(_1510594, _1510600)), hAPP(_1510594, _1510598)))], (37870 ^ _779300) ^ [_1510735, _1510737, _1510739, _1510741, _1510743, _1510745, _1510747, _1510749, _1510751, _1510753, _1510755] : [c_Finite__Set_Ofolding(_1510735, _1510737, _1510739, _1510741), -(hAPP(c_Fun_Ocomp(_1510743, _1510745, _1510747, _1510749), hAPP(c_Fun_Ocomp(_1510751, _1510743, _1510747, _1510753), _1510755)) = hAPP(c_Fun_Ocomp(_1510751, _1510745, _1510747, hAPP(c_Fun_Ocomp(_1510743, _1510745, _1510751, _1510749), _1510753)), _1510755))], (37876 ^ _779300) ^ [_1510898, _1510900, _1510902, _1510904, _1510906, _1510908] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510898, tc_fun(_1510900, tc_HOL_Obool)), _1510902), hAPP(c_Fun_Ocomp(_1510904, tc_fun(_1510900, tc_HOL_Obool), _1510898, _1510906), _1510908)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510904, tc_fun(_1510900, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1510898, _1510904, _1510908), _1510902)), _1510906))], (37878 ^ _779300) ^ [_1510973, _1510975, _1510977, _1510979, _1510981, _1510983] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1510973, _1510975), _1510973, tc_prod(_1510977, _1510979), c_Product__Type_Ofst(_1510973, _1510975)), c_Product__Type_Omap__pair(_1510977, _1510973, _1510979, _1510975, _1510981, _1510983)) = hAPP(c_Fun_Ocomp(_1510977, _1510973, tc_prod(_1510977, _1510979), _1510981), c_Product__Type_Ofst(_1510977, _1510979)))], (37880 ^ _779300) ^ [_1511044, _1511046, _1511048, _1511050, _1511052, _1511054] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1511044, _1511046), _1511046, tc_prod(_1511048, _1511050), c_Product__Type_Osnd(_1511044, _1511046)), c_Product__Type_Omap__pair(_1511048, _1511044, _1511050, _1511046, _1511052, _1511054)) = hAPP(c_Fun_Ocomp(_1511050, _1511046, tc_prod(_1511048, _1511050), _1511054), c_Product__Type_Osnd(_1511048, _1511050)))], (37882 ^ _779300) ^ [_1511115, _1511117, _1511119, _1511121, _1511123, _1511125, _1511127] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1511115, _1511117, _1511119), hAPP(c_Fun_Ocomp(_1511121, tc_fun(_1511117, _1511119), _1511115, _1511123), _1511125)), _1511127) = hAPP(hAPP(_1511123, hAPP(_1511125, hAPP(c_Product__Type_Ofst(_1511115, _1511117), _1511127))), hAPP(c_Product__Type_Osnd(_1511115, _1511117), _1511127)))], (37884 ^ _779300) ^ [_1511192, _1511194, _1511196, _1511198, _1511200, _1511202, _1511204, _1511206] : [c_Finite__Set_Ofolding(_1511192, _1511194, _1511196, _1511198), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511192), _1511200)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511192), _1511202)), -(hAPP(c_Fun_Ocomp(_1511194, _1511194, _1511204, hAPP(_1511198, _1511202)), hAPP(c_Fun_Ocomp(_1511194, _1511194, _1511204, hAPP(_1511198, _1511200)), _1511206)) = hAPP(c_Fun_Ocomp(_1511194, _1511194, _1511204, hAPP(_1511198, _1511200)), hAPP(c_Fun_Ocomp(_1511194, _1511194, _1511204, hAPP(_1511198, _1511202)), _1511206)))], (37898 ^ _779300) ^ [_1511517, _1511519, _1511521, _1511523, _1511525, _1511527] : [c_Finite__Set_Ofolding(_1511517, _1511519, _1511521, _1511523), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511517), _1511525)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511517), _1511527)), -(hAPP(c_Fun_Ocomp(_1511519, _1511519, _1511519, hAPP(_1511523, _1511527)), hAPP(_1511523, _1511525)) = hAPP(c_Fun_Ocomp(_1511519, _1511519, _1511519, hAPP(_1511523, _1511525)), hAPP(_1511523, _1511527)))], (37912 ^ _779300) ^ [_1511798, _1511800, _1511802, _1511804, _1511806, _1511808, _1511810, _1511812] : [c_Finite__Set_Ofolding(_1511798, _1511800, _1511802, _1511804), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511798), _1511806)), -(hAPP(c_Fun_Ocomp(_1511800, _1511800, _1511808, hAPP(_1511802, _1511810)), hAPP(c_Fun_Ocomp(_1511800, _1511800, _1511808, hAPP(_1511804, _1511806)), _1511812)) = hAPP(c_Fun_Ocomp(_1511800, _1511800, _1511808, hAPP(_1511804, _1511806)), hAPP(c_Fun_Ocomp(_1511800, _1511800, _1511808, hAPP(_1511802, _1511810)), _1511812)))], (37922 ^ _779300) ^ [_1512051, _1512053, _1512055, _1512057, _1512059, _1512061] : [c_Finite__Set_Ofolding(_1512051, _1512053, _1512055, _1512057), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512051), _1512059)), -(hAPP(c_Fun_Ocomp(_1512053, _1512053, _1512053, hAPP(_1512055, _1512061)), hAPP(_1512057, _1512059)) = hAPP(c_Fun_Ocomp(_1512053, _1512053, _1512053, hAPP(_1512057, _1512059)), hAPP(_1512055, _1512061)))], (37932 ^ _779300) ^ [_1512264, _1512266, _1512268, _1512270] : [c_Finite__Set_Ofolding(_1512264, _1512266, _1512268, _1512270), -(hAPP(_1512270, c_Orderings_Obot__class_Obot(tc_fun(_1512264, tc_HOL_Obool))) = c_Fun_Oid(_1512266))], (37938 ^ _779300) ^ [_1512369, _1512371, _1512373, _1512375, _1512377, _1512379] : [c_Finite__Set_Ofolding(_1512369, _1512371, _1512373, _1512375), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512369), _1512377)), -(hBOOL(hAPP(hAPP(c_member(_1512369), _1512379), _1512377))), -(hAPP(_1512375, hAPP(hAPP(c_Set_Oinsert(_1512369), _1512379), _1512377)) = hAPP(c_Fun_Ocomp(_1512371, _1512371, _1512371, hAPP(_1512375, _1512377)), hAPP(_1512373, _1512379)))], (37952 ^ _779300) ^ [_1512605, _1512607, _1512609, _1512611, _1512613, _1512615] : [c_Finite__Set_Ofolding(_1512605, _1512607, _1512609, _1512611), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512605), _1512613)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512605), _1512615)), -(hAPP(c_Fun_Ocomp(_1512607, _1512607, _1512607, hAPP(_1512611, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1512605, tc_HOL_Obool)), _1512613), _1512615))), hAPP(_1512611, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1512605, tc_HOL_Obool)), _1512613), _1512615))) = hAPP(c_Fun_Ocomp(_1512607, _1512607, _1512607, hAPP(_1512611, _1512613)), hAPP(_1512611, _1512615)))], (37966 ^ _779300) ^ [_1512930, _1512932, _1512934, _1512936, _1512938, _1512940] : [class_Groups_Ocomm__monoid__add(_1512930), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512932), _1512934)), 37976 ^ _779300 : [(37977 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512932), 37975 ^ [_1512930, _1512932, _1512934, _1512936, _1512938, _1512940]), _1512934)))], (37980 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512932), 37978 ^ [_1512930, _1512932, _1512934, _1512936, _1512938, _1512940]), _1512934)))], (37982 ^ _779300) ^ [] : [37975 ^ [_1512930, _1512932, _1512934, _1512936, _1512938, _1512940] = 37978 ^ [_1512930, _1512932, _1512934, _1512936, _1512938, _1512940]], (37984 ^ _779300) ^ [] : [-(hAPP(_1512936, 37975 ^ [_1512930, _1512932, _1512934, _1512936, _1512938, _1512940]) = hAPP(_1512936, 37978 ^ [_1512930, _1512932, _1512934, _1512936, _1512938, _1512940]))], (37986 ^ _779300) ^ [] : [hAPP(_1512938, hAPP(_1512936, 37975 ^ [_1512930, _1512932, _1512934, _1512936, _1512938, _1512940])) = c_Groups_Ozero__class_Ozero(_1512930)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512940, _1512930), _1512938), hAPP(c_Set_Oimage(_1512932, _1512940, _1512936), _1512934)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512932, _1512930), hAPP(c_Fun_Ocomp(_1512940, _1512930, _1512932, _1512938), _1512936)), _1512934))], (37990 ^ _779300) ^ [_1513667, _1513669, _1513671, _1513673, _1513675, _1513677] : [c_Finite__Set_Ofolding__idem(_1513667, _1513669, _1513671, _1513673), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513667), _1513675)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513667), _1513677)), -(hAPP(_1513673, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1513667, tc_HOL_Obool)), _1513675), _1513677)) = hAPP(c_Fun_Ocomp(_1513669, _1513669, _1513669, hAPP(_1513673, _1513675)), hAPP(_1513673, _1513677)))], (38004 ^ _779300) ^ [_1513948, _1513950, _1513952, _1513954, _1513956, _1513958] : [c_Finite__Set_Ofolding__idem(_1513948, _1513950, _1513952, _1513954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513948), _1513956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1513948, tc_HOL_Obool)), _1513958), _1513956)), -(hAPP(c_Fun_Ocomp(_1513950, _1513950, _1513950, hAPP(_1513954, _1513956)), hAPP(_1513954, _1513958)) = hAPP(_1513954, _1513956))], (38018 ^ _779300) ^ [_1514219, _1514221, _1514223, _1514225, _1514227, _1514229, _1514231] : [c_Finite__Set_Ofolding__idem(_1514219, _1514221, _1514223, _1514225), -(hAPP(c_Fun_Ocomp(_1514221, _1514221, _1514227, hAPP(_1514223, _1514229)), hAPP(c_Fun_Ocomp(_1514221, _1514221, _1514227, hAPP(_1514223, _1514229)), _1514231)) = hAPP(c_Fun_Ocomp(_1514221, _1514221, _1514227, hAPP(_1514223, _1514229)), _1514231))], (38024 ^ _779300) ^ [_1514376, _1514378, _1514380, _1514382, _1514384] : [c_Finite__Set_Ofolding__idem(_1514376, _1514378, _1514380, _1514382), -(hAPP(c_Fun_Ocomp(_1514378, _1514378, _1514378, hAPP(_1514380, _1514384)), hAPP(_1514380, _1514384)) = hAPP(_1514380, _1514384))], (38030 ^ _779300) ^ [_1514497, _1514499, _1514501, _1514503, _1514505, _1514507] : [c_Finite__Set_Ofolding__idem(_1514497, _1514499, _1514501, _1514503), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514497), _1514505)), hBOOL(hAPP(hAPP(c_member(_1514497), _1514507), _1514505)), -(hAPP(c_Fun_Ocomp(_1514499, _1514499, _1514499, hAPP(_1514503, _1514505)), hAPP(_1514501, _1514507)) = hAPP(_1514503, _1514505))], (38044 ^ _779300) ^ [_1514762, _1514764, _1514766, _1514768, _1514770, _1514772] : [c_Finite__Set_Ofolding__idem(_1514762, _1514764, _1514766, _1514768), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514762), _1514770)), -(hAPP(_1514768, hAPP(hAPP(c_Set_Oinsert(_1514762), _1514772), _1514770)) = hAPP(c_Fun_Ocomp(_1514764, _1514764, _1514764, hAPP(_1514768, _1514770)), hAPP(_1514766, _1514772)))], (38054 ^ _779300) ^ [_1514969, _1514971, _1514973, _1514975, _1514977, _1514979, _1514981, _1514983] : [class_Groups_Ocomm__monoid__mult(_1514969), c_Fun_Oinj__on(_1514971, _1514973, _1514975, _1514977), _1514979 = hAPP(c_Set_Oimage(_1514971, _1514973, _1514975), _1514977), 38068 ^ _779300 : [(38069 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514971), 38067 ^ [_1514969, _1514971, _1514973, _1514975, _1514977, _1514979, _1514981, _1514983]), _1514977)))], (38071 ^ _779300) ^ [] : [hAPP(_1514981, 38067 ^ [_1514969, _1514971, _1514973, _1514975, _1514977, _1514979, _1514981, _1514983]) = hAPP(hAPP(c_Fun_Ocomp(_1514973, _1514969, _1514971, _1514983), _1514975), 38067 ^ [_1514969, _1514971, _1514973, _1514975, _1514977, _1514979, _1514981, _1514983])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514973, _1514969), _1514983), _1514979) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514971, _1514969), _1514981), _1514977))], (38075 ^ _779300) ^ [_1515477, _1515479, _1515481] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1515477, _1515479) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1515481, _1515479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1515481), _1515477)), -(_1515477 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1515481), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1515479), 38082 ^ [_1515477, _1515479, _1515481])))], (38086 ^ _779300) ^ [_1515674, _1515676] : [38088 ^ _779300 : [(38089 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515674, tc_HOL_Obool)), 38087 ^ [_1515674, _1515676]), hAPP(c_Relation_OImage(_1515674, _1515674, _1515676), 38087 ^ [_1515674, _1515676]))))], (38091 ^ _779300) ^ [] : [38087 ^ [_1515674, _1515676] = c_Orderings_Obot__class_Obot(tc_fun(_1515674, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1515674, _1515676))], (38095 ^ _779300) ^ [_1515871, _1515873, _1515875, _1515877, _1515879, _1515881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515871, tc_HOL_Obool)), _1515873), _1515875)), 38101 ^ _779300 : [(38102 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515871), 38100 ^ [_1515871, _1515873, _1515875, _1515877, _1515879, _1515881]), _1515873)))], (38104 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515877, tc_HOL_Obool)), hAPP(_1515879, 38100 ^ [_1515871, _1515873, _1515875, _1515877, _1515879, _1515881])), hAPP(_1515881, 38100 ^ [_1515871, _1515873, _1515875, _1515877, _1515879, _1515881])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1515871, _1515877), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1515871, _1515877), _1515873), _1515879)), hAPP(hAPP(c_Product__Type_OSigma(_1515871, _1515877), _1515875), _1515881))))], (38108 ^ _779300) ^ [_1516261, _1516263, _1516265] : [-(hBOOL(hAPP(hAPP(c_member(_1516261), _1516263), c_Wellfounded_Oacc(_1516261, _1516265)))), 38112 ^ _779300 : [(38113 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516261, _1516261)), hAPP(hAPP(c_Product__Type_OPair(_1516261, _1516261), 38111 ^ [_1516261, _1516263, _1516265]), _1516263)), _1516265)))], (38115 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1516261), 38111 ^ [_1516261, _1516263, _1516265]), c_Wellfounded_Oacc(_1516261, _1516265)))]]], (38117 ^ _779300) ^ [_1516488, _1516490, _1516492] : [38119 ^ _779300 : [(38120 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516488, _1516488)), hAPP(hAPP(c_Product__Type_OPair(_1516488, _1516488), 38118 ^ [_1516488, _1516490, _1516492]), _1516490)), _1516492)))], (38122 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1516488), 38118 ^ [_1516488, _1516490, _1516492]), c_Wellfounded_Oacc(_1516488, _1516492)))]], -(hBOOL(hAPP(hAPP(c_member(_1516488), _1516490), c_Wellfounded_Oacc(_1516488, _1516492))))], (38126 ^ _779300) ^ [_1516747, _1516749, _1516751, _1516753] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1516747, tc_HOL_Obool), tc_fun(_1516747, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1516747, tc_HOL_Obool), tc_fun(_1516747, tc_HOL_Obool)), _1516749), _1516751)), c_Wellfounded_Omax__ext(_1516747, _1516753))), 38129 ^ _779300 : [(38130 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1516747), _1516749)))], (38132 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1516747), _1516751)))], (38134 ^ _779300) ^ [] : [_1516751 = c_Orderings_Obot__class_Obot(tc_fun(_1516747, tc_HOL_Obool))], (38136 ^ _779300) ^ [_1517041] : [hBOOL(hAPP(hAPP(c_member(_1516747), _1517041), _1516749)), 38140 ^ _779300 : [(38141 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1516747), 38139 ^ [_1516747, _1516749, _1516751, _1516753, _1517041]), _1516751)))], (38143 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516747, _1516747)), hAPP(hAPP(c_Product__Type_OPair(_1516747, _1516747), _1517041), 38139 ^ [_1516747, _1516749, _1516751, _1516753, _1517041])), _1516753)))]]]]], (38145 ^ _779300) ^ [_1517253, _1517255, _1517257, _1517259] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1517253, tc_HOL_Obool), tc_fun(_1517253, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1517253, tc_HOL_Obool), tc_fun(_1517253, tc_HOL_Obool)), _1517255), _1517257)), c_Wellfounded_Omax__ext(_1517253, _1517259)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517253), _1517255)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517253), _1517257)), -(_1517257 = c_Orderings_Obot__class_Obot(tc_fun(_1517253, tc_HOL_Obool))), 38159 ^ _779300 : [(38160 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1517253), 38158 ^ [_1517253, _1517255, _1517257, _1517259]), _1517255)))], (38162 ^ _779300) ^ [_1517658] : [hBOOL(hAPP(hAPP(c_member(_1517253), _1517658), _1517257)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1517253, _1517253)), hAPP(hAPP(c_Product__Type_OPair(_1517253, _1517253), 38158 ^ [_1517253, _1517255, _1517257, _1517259]), _1517658)), _1517259))]]], (38170 ^ _779300) ^ [_1517886, _1517888, _1517890] : [38172 ^ _779300 : [(38173 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 38171 ^ [_1517886, _1517888, _1517890]), _1517886)))], (38175 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1517888, 38171 ^ [_1517886, _1517888, _1517890])))], (38177 ^ _779300) ^ [] : [hBOOL(hAPP(_1517888, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 38171 ^ [_1517886, _1517888, _1517890]), _1517886)))]], hBOOL(hAPP(_1517888, _1517890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1517890), _1517886)), -(hBOOL(hAPP(_1517888, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38189 ^ _779300) ^ [_1518248, _1518250, _1518252, _1518254, _1518256, _1518258] : [class_Groups_Oab__semigroup__mult(_1518248), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518250), _1518252)), 38199 ^ _779300 : [(38200 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1518250), 38198 ^ [_1518248, _1518250, _1518252, _1518254, _1518256, _1518258]), _1518252)))], (38202 ^ _779300) ^ [] : [hAPP(_1518254, 38198 ^ [_1518248, _1518250, _1518252, _1518254, _1518256, _1518258]) = hAPP(_1518256, 38198 ^ [_1518248, _1518250, _1518252, _1518254, _1518256, _1518258])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1518248, _1518250, c_Groups_Otimes__class_Otimes(_1518248)), _1518254), _1518258), _1518252) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1518248, _1518250, c_Groups_Otimes__class_Otimes(_1518248)), _1518256), _1518258), _1518252))], (38206 ^ _779300) ^ [_1518653, _1518655, _1518657] : [class_Orderings_Olinorder(_1518653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518653), _1518655)), 38216 ^ _779300 : [(38217 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1518653), 38215 ^ [_1518653, _1518655, _1518657]), _1518655)))], (38219 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1518653), 38215 ^ [_1518653, _1518655, _1518657]), _1518657))]], hBOOL(hAPP(hAPP(c_member(_1518653), _1518657), _1518655)), -(c_Big__Operators_Olinorder__class_OMax(_1518653, _1518655) = _1518657)], (38227 ^ _779300) ^ [_1519025, _1519027, _1519029] : [class_Orderings_Olinorder(_1519025), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519025), _1519027)), 38237 ^ _779300 : [(38238 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519025), 38236 ^ [_1519025, _1519027, _1519029]), _1519027)))], (38240 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1519025), _1519029), 38236 ^ [_1519025, _1519027, _1519029]))]], hBOOL(hAPP(hAPP(c_member(_1519025), _1519029), _1519027)), -(c_Big__Operators_Olinorder__class_OMin(_1519025, _1519027) = _1519029)], (38248 ^ _779300) ^ [_1519397, _1519399, _1519401] : [c_Wellfounded_Owf(_1519397, _1519399), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519397, _1519397)), hAPP(hAPP(c_Product__Type_OPair(_1519397, _1519397), hAPP(_1519401, hAPP(c_Nat_OSuc, 38251 ^ [_1519397, _1519399, _1519401]))), hAPP(_1519401, 38251 ^ [_1519397, _1519399, _1519401]))), _1519399))], (38255 ^ _779300) ^ [_1519598, _1519600, _1519602, _1519604, _1519606, _1519608, _1519610, _1519612] : [class_Groups_Ocomm__monoid__add(_1519598), c_Fun_Oinj__on(_1519600, _1519602, _1519604, _1519606), _1519608 = hAPP(c_Set_Oimage(_1519600, _1519602, _1519604), _1519606), 38269 ^ _779300 : [(38270 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519600), 38268 ^ [_1519598, _1519600, _1519602, _1519604, _1519606, _1519608, _1519610, _1519612]), _1519606)))], (38272 ^ _779300) ^ [] : [hAPP(_1519610, 38268 ^ [_1519598, _1519600, _1519602, _1519604, _1519606, _1519608, _1519610, _1519612]) = hAPP(_1519612, hAPP(_1519604, 38268 ^ [_1519598, _1519600, _1519602, _1519604, _1519606, _1519608, _1519610, _1519612]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1519602, _1519598), _1519612), _1519608) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1519600, _1519598), _1519610), _1519606))], (38276 ^ _779300) ^ [_1520090, _1520092, _1520094, _1520096, _1520098, _1520100, _1520102] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1520090, _1520092, _1520094, _1520096), _1520098), _1520100), _1520102) = hAPP(hAPP(_1520100, hAPP(c_Product__Type_Ofst(_1520092, _1520094), hAPP(_1520098, _1520102))), hAPP(c_Product__Type_Osnd(_1520092, _1520094), hAPP(_1520098, _1520102))))], (38278 ^ _779300) ^ [_1520163, _1520165, _1520167, _1520169, _1520171, _1520173, _1520175, _1520177] : [class_Groups_Ocomm__monoid__add(_1520163), class_Orderings_Oord(_1520165), _1520167 = _1520169, _1520171 = _1520173, 38296 ^ _779300 : [(38297 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1520165), _1520169), 38295 ^ [_1520163, _1520165, _1520167, _1520169, _1520171, _1520173, _1520175, _1520177])))], (38299 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1520165), 38295 ^ [_1520163, _1520165, _1520167, _1520169, _1520171, _1520173, _1520175, _1520177]), _1520173)))], (38301 ^ _779300) ^ [] : [hAPP(_1520175, 38295 ^ [_1520163, _1520165, _1520167, _1520169, _1520171, _1520173, _1520175, _1520177]) = hAPP(_1520177, 38295 ^ [_1520163, _1520165, _1520167, _1520169, _1520171, _1520173, _1520175, _1520177])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1520165, _1520163), _1520175), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1520165, _1520167), _1520171)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1520165, _1520163), _1520177), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1520165, _1520169), _1520173)))], (38305 ^ _779300) ^ [_1520792, _1520794, _1520796, _1520798, _1520800] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1520792, _1520794, _1520792, _1520796), hAPP(c_Product__Type_OPair(_1520794, _1520792), _1520798)), _1520800) = hAPP(_1520800, _1520798))], (38307 ^ _779300) ^ [_1520843, _1520845, _1520847, _1520849] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1520843, _1520845, _1520847, tc_prod(_1520845, _1520847)), _1520849), c_Product__Type_OPair(_1520845, _1520847)) = _1520849)], (38309 ^ _779300) ^ [_1520889, _1520891, _1520893, _1520895, _1520897, _1520899, _1520901, _1520903, _1520905] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1520889, _1520891, _1520893, _1520895), hAPP(hAPP(c_Product__Type_Oscomp(_1520889, _1520897, _1520899, tc_prod(_1520891, _1520893)), _1520901), _1520903)), _1520905) = hAPP(hAPP(c_Product__Type_Oscomp(_1520889, _1520897, _1520899, _1520895), _1520901), hAPP(hAPP(c_COMBC(_1520897, tc_fun(_1520891, tc_fun(_1520893, _1520895)), tc_fun(_1520899, _1520895)), hAPP(hAPP(c_COMBB(tc_fun(_1520899, tc_prod(_1520891, _1520893)), tc_fun(tc_fun(_1520891, tc_fun(_1520893, _1520895)), tc_fun(_1520899, _1520895)), _1520897), c_Product__Type_Oscomp(_1520899, _1520891, _1520893, _1520895)), _1520903)), _1520905)))], (38311 ^ _779300) ^ [_1521016, _1521018, _1521020, _1521022, _1521024, _1521026, _1521028] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1521016, _1521018, _1521020, _1521022), _1521024), _1521026), _1521028) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1521018, _1521020, _1521022), _1521026), hAPP(_1521024, _1521028)))], (38313 ^ _779300) ^ [_1521078, _1521080, _1521082, _1521084, _1521086, _1521088, _1521090] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1521078, _1521080, _1521082, _1521084), _1521086), _1521088), _1521090) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1521080, _1521082, _1521084), _1521088), hAPP(_1521086, _1521090)))], (38315 ^ _779300) ^ [_1521158, _1521160, _1521162, _1521164, _1521166] : [_1521158 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1521160, _1521162, _1521158, _1521164), _1521166) = hAPP(c_Product__Type_OPair(_1521160, _1521162), _1521166))], (38321 ^ _779300) ^ [_1521263, _1521265, _1521267, _1521269, _1521271] : [-(_1521263 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1521265, _1521267, _1521263, _1521269), _1521271) = hAPP(hAPP(c_Product__Type_Oscomp(_1521267, _1521265, _1521267, tc_prod(_1521265, _1521267)), hAPP(_1521269, _1521271)), c_Random_Oiterate(_1521265, _1521267, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1521263), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1521269)))], (38327 ^ _779300) ^ [_1521358, _1521360] : [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), _1521358), _1521360)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521358), _1521360)))], (38333 ^ _779300) ^ [_1521463, _1521465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521463), _1521465)), -(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), _1521463), _1521465)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (38339 ^ _779300) ^ [_1521574, _1521576, _1521578, _1521580] : [38341 ^ _779300 : [(38342 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1521574), 38340 ^ [_1521574, _1521576, _1521578, _1521580])))], (38344 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 38340 ^ [_1521574, _1521576, _1521578, _1521580]), _1521576)))], (38346 ^ _779300) ^ [] : [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(_1521578, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 38340 ^ [_1521574, _1521576, _1521578, _1521580]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1521578, 38340 ^ [_1521574, _1521576, _1521578, _1521580])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521574), _1521576)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1521578, _1521574)), _1521580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1521580), hAPP(_1521578, _1521576))), 38360 ^ _779300 : [(38361 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1521574), 38359 ^ [_1521574, _1521576, _1521578, _1521580])))], (38363 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 38359 ^ [_1521574, _1521576, _1521578, _1521580]), _1521576)))], (38365 ^ _779300) ^ [] : [-(hAPP(_1521578, 38359 ^ [_1521574, _1521576, _1521578, _1521580]) = _1521580)]]], (38367 ^ _779300) ^ [_1522200, _1522202] : [c_Wellfounded_Owf(_1522200, _1522202), -(c_Wellfounded_Owf(_1522200, c_Transitive__Closure_Otrancl(_1522200, _1522202)))], (38373 ^ _779300) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (38375 ^ _779300) ^ [_1522316, _1522318] : [c_Wellfounded_Oacyclic(_1522316, _1522318), 38378 ^ _779300 : [(38379 ^ _779300) ^ [_1522401] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522316, _1522316)), hAPP(hAPP(c_Product__Type_OPair(_1522316, _1522316), _1522401), _1522401)), c_Transitive__Closure_Otrancl(_1522316, _1522318)))]]], (38381 ^ _779300) ^ [_1522444, _1522446] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1522444, _1522444)), hAPP(hAPP(c_Product__Type_OPair(_1522444, _1522444), 38382 ^ [_1522444, _1522446]), 38382 ^ [_1522444, _1522446])), c_Transitive__Closure_Otrancl(_1522444, _1522446)))), -(c_Wellfounded_Oacyclic(_1522444, _1522446))], (38388 ^ _779300) ^ [_1522518, _1522520, _1522522, _1522524] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522518, _1522518)), hAPP(hAPP(c_Product__Type_OPair(_1522518, _1522518), _1522520), _1522522)), _1522524)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1522518, _1522518)), hAPP(hAPP(c_Product__Type_OPair(_1522518, _1522518), _1522520), _1522522)), c_Transitive__Closure_Otrancl(_1522518, _1522524))))], (38394 ^ _779300) ^ [_1522681, _1522683] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522681, _1522681), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1522681, _1522683)), hAPP(hAPP(c_Product__Type_OSigma(_1522681, _1522681), hAPP(c_Relation_OField(_1522681), _1522683)), hAPP(c_COMBK(tc_fun(_1522681, tc_HOL_Obool), _1522681), hAPP(c_Relation_OField(_1522681), _1522683))))))], (38396 ^ _779300) ^ [_1522750, _1522752, _1522754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522750, _1522750), tc_HOL_Obool)), _1522752), _1522754)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522750, _1522750), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1522750, _1522750, _1522750), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1522750, _1522750), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1522750, _1522752)), _1522754)), _1522752)), _1522754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522750, _1522750), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1522750, _1522752)), _1522754)))], (38406 ^ _779300) ^ [_1523021, _1523023, _1523025] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523021, _1523021)), _1523023), _1523025)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523021, _1523021)), _1523023), c_Transitive__Closure_Otrancl(_1523021, _1523025))))], (38412 ^ _779300) ^ [_1523146] : [-(c_Transitive__Closure_Otrancl(_1523146, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523146, _1523146), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523146, _1523146), tc_HOL_Obool)))], (38414 ^ _779300) ^ [_1523188, _1523190] : [-(hAPP(c_Relation_ODomain(_1523188, _1523188), c_Transitive__Closure_Otrancl(_1523188, _1523190)) = hAPP(c_Relation_ODomain(_1523188, _1523188), _1523190))], (38416 ^ _779300) ^ [_1523228, _1523230] : [-(hAPP(c_Relation_ORange(_1523228, _1523228), c_Transitive__Closure_Otrancl(_1523228, _1523230)) = hAPP(c_Relation_ORange(_1523228, _1523228), _1523230))], (38418 ^ _779300) ^ [_1523283, _1523285] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523283, _1523283)), c_Transitive__Closure_Otrancl(_1523283, _1523285))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523283, _1523283)), _1523285)))], (38424 ^ _779300) ^ [_1523390, _1523392] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523390, _1523390)), _1523392)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523390, _1523390)), c_Transitive__Closure_Otrancl(_1523390, _1523392))))], (38430 ^ _779300) ^ [_1523503, _1523505, _1523507, _1523509, _1523511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523503, _1523503)), hAPP(hAPP(c_Product__Type_OPair(_1523503, _1523503), _1523505), _1523507)), _1523509)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1523503, _1523503)), hAPP(hAPP(c_Product__Type_OPair(_1523503, _1523503), _1523507), _1523511)), _1523509)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523503, _1523503)), hAPP(hAPP(c_Product__Type_OPair(_1523503, _1523503), _1523505), _1523511)), c_Transitive__Closure_Otrancl(_1523503, _1523509))))], (38440 ^ _779300) ^ [_1523764, _1523766, _1523768, _1523770, _1523772] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523764, _1523764)), hAPP(hAPP(c_Product__Type_OPair(_1523764, _1523764), _1523766), _1523768)), _1523770)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1523764, _1523764)), hAPP(hAPP(c_Product__Type_OPair(_1523764, _1523764), _1523768), _1523772)), c_Transitive__Closure_Otrancl(_1523764, _1523770))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523764, _1523764)), hAPP(hAPP(c_Product__Type_OPair(_1523764, _1523764), _1523766), _1523772)), c_Transitive__Closure_Otrancl(_1523764, _1523770))))], (38450 ^ _779300) ^ [_1524031, _1524033, _1524035, _1524037, _1524039] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524031, _1524031)), hAPP(hAPP(c_Product__Type_OPair(_1524031, _1524031), _1524033), _1524035)), c_Transitive__Closure_Otrancl(_1524031, _1524037))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1524031, _1524031)), hAPP(hAPP(c_Product__Type_OPair(_1524031, _1524031), _1524035), _1524039)), _1524037)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524031, _1524031)), hAPP(hAPP(c_Product__Type_OPair(_1524031, _1524031), _1524033), _1524039)), c_Transitive__Closure_Otrancl(_1524031, _1524037))))], (38460 ^ _779300) ^ [_1524298, _1524300, _1524302, _1524304, _1524306] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524298, _1524298)), hAPP(hAPP(c_Product__Type_OPair(_1524298, _1524298), _1524300), _1524302)), c_Transitive__Closure_Otrancl(_1524298, _1524304))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1524298, _1524298)), hAPP(hAPP(c_Product__Type_OPair(_1524298, _1524298), _1524302), _1524306)), c_Transitive__Closure_Otrancl(_1524298, _1524304))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524298, _1524298)), hAPP(hAPP(c_Product__Type_OPair(_1524298, _1524298), _1524300), _1524306)), c_Transitive__Closure_Otrancl(_1524298, _1524304))))], (38470 ^ _779300) ^ [_1524571, _1524573, _1524575, _1524577] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524571, _1524571)), _1524573), c_Transitive__Closure_Otrancl(_1524571, _1524575))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524571, _1524571), tc_HOL_Obool)), _1524575), _1524577)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524571, _1524571)), _1524573), c_Transitive__Closure_Otrancl(_1524571, _1524577))))], (38480 ^ _779300) ^ [_1524786, _1524788] : [-(c_Transitive__Closure_Otrancl(_1524786, _1524788) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1524786, _1524786), tc_HOL_Obool)), _1524788), hAPP(hAPP(c_Relation_Orel__comp(_1524786, _1524786, _1524786), c_Transitive__Closure_Otrancl(_1524786, _1524788)), _1524788)))], (38482 ^ _779300) ^ [_1524841, _1524843, _1524845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524841, _1524841), tc_HOL_Obool)), _1524843), hAPP(hAPP(c_Product__Type_OSigma(_1524841, _1524841), _1524845), hAPP(c_COMBK(tc_fun(_1524841, tc_HOL_Obool), _1524841), _1524845)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524841, _1524841), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1524841, _1524843)), hAPP(hAPP(c_Product__Type_OSigma(_1524841, _1524841), _1524845), hAPP(c_COMBK(tc_fun(_1524841, tc_HOL_Obool), _1524841), _1524845)))))], (38488 ^ _779300) ^ [_1525059, _1525061] : [38489 ^ _779300 : [(38490 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1525059), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (38492 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1525061), _1525059))]], -(c_Random_Olog(_1525059, _1525061) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (38496 ^ _779300) ^ [_1525194, _1525196] : [-(c_Random_Olog(_1525194, _1525196) = 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(_1525194, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1525196), _1525194)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1525194), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1525196), _1525194)))], (38506 ^ _779300) ^ [_1525276, _1525278, _1525280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1525276), _1525278)), -(c_Random_Ominus__shift(_1525280, _1525276, _1525278) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1525280), _1525276)), _1525278))], (38512 ^ _779300) ^ [_1525391, _1525393, _1525395] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1525391), _1525393))), -(c_Random_Ominus__shift(_1525395, _1525391, _1525393) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1525391), _1525393))], (38518 ^ _779300) ^ [_1525455, _1525457] : [_1525455 = _1525457, -(c_Random_Oinc__shift(_1525455, _1525457) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (38524 ^ _779300) ^ [_1525532, _1525534] : [-(_1525532 = _1525534), -(c_Random_Oinc__shift(_1525532, _1525534) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1525534), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (38530 ^ _779300) ^ [_1525579, _1525581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1525579)), -(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(_1525579), _1525581))), _1525579)))], (38536 ^ _779300) ^ [_1525686, _1525688, _1525690, _1525692] : [-(c_Transitive__Closure_Otrancl(_1525686, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1525686, _1525686)), hAPP(hAPP(c_Product__Type_OPair(_1525686, _1525686), _1525688), _1525690)), _1525692)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1525686, _1525686), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1525686, _1525692)), hAPP(c_Set_OCollect(tc_prod(_1525686, _1525686)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525686, _1525686, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1525686, tc_fun(_1525686, tc_HOL_Obool), tc_fun(_1525686, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1525686, tc_HOL_Obool), tc_fun(_1525686, tc_HOL_Obool)), _1525686), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1525686)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525686), c_fconj), hAPP(hAPP(c_COMBC(_1525686, tc_fun(tc_prod(_1525686, _1525686), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1525686, _1525686), tc_fun(tc_fun(tc_prod(_1525686, _1525686), tc_HOL_Obool), tc_HOL_Obool), _1525686), c_member(tc_prod(_1525686, _1525686))), hAPP(hAPP(c_COMBC(_1525686, _1525686, tc_prod(_1525686, _1525686)), c_Product__Type_OPair(_1525686, _1525686)), _1525688))), c_Transitive__Closure_Ortrancl(_1525686, _1525692))))), hAPP(hAPP(c_COMBC(_1525686, tc_fun(tc_prod(_1525686, _1525686), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1525686, _1525686), tc_fun(tc_fun(tc_prod(_1525686, _1525686), tc_HOL_Obool), tc_HOL_Obool), _1525686), c_member(tc_prod(_1525686, _1525686))), hAPP(c_Product__Type_OPair(_1525686, _1525686), _1525690))), c_Transitive__Closure_Ortrancl(_1525686, _1525692)))))))], (38538 ^ _779300) ^ [_1525954, _1525956, _1525958, _1525960] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525954, tc_fun(_1525954, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1525954, tc_fun(tc_prod(_1525954, _1525954), tc_HOL_Obool), tc_fun(_1525954, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525954, tc_fun(tc_fun(tc_prod(_1525954, _1525954), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525954, _1525954), tc_HOL_Obool), tc_fun(_1525954, tc_HOL_Obool)), _1525954), c_COMBC(_1525954, tc_fun(tc_prod(_1525954, _1525954), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525954, tc_prod(_1525954, _1525954)), tc_fun(_1525954, tc_fun(tc_fun(tc_prod(_1525954, _1525954), tc_HOL_Obool), tc_HOL_Obool)), _1525954), hAPP(c_COMBB(tc_prod(_1525954, _1525954), tc_fun(tc_fun(tc_prod(_1525954, _1525954), tc_HOL_Obool), tc_HOL_Obool), _1525954), c_member(tc_prod(_1525954, _1525954)))), c_Product__Type_OPair(_1525954, _1525954)))), _1525956)), c_fequal), _1525958), _1525960)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1525954, _1525954)), hAPP(hAPP(c_Product__Type_OPair(_1525954, _1525954), _1525958), _1525960)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1525954, _1525954), tc_HOL_Obool)), _1525956), c_Relation_OId(_1525954)))))], (38544 ^ _779300) ^ [_1526375, _1526377, _1526379, _1526381] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526375, _1526375)), hAPP(hAPP(c_Product__Type_OPair(_1526375, _1526375), _1526379), _1526381)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1526375, _1526375), tc_HOL_Obool)), _1526377), c_Relation_OId(_1526375)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1526375, tc_fun(_1526375, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1526375, tc_fun(tc_prod(_1526375, _1526375), tc_HOL_Obool), tc_fun(_1526375, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526375, tc_fun(tc_fun(tc_prod(_1526375, _1526375), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526375, _1526375), tc_HOL_Obool), tc_fun(_1526375, tc_HOL_Obool)), _1526375), c_COMBC(_1526375, tc_fun(tc_prod(_1526375, _1526375), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526375, tc_prod(_1526375, _1526375)), tc_fun(_1526375, tc_fun(tc_fun(tc_prod(_1526375, _1526375), tc_HOL_Obool), tc_HOL_Obool)), _1526375), hAPP(c_COMBB(tc_prod(_1526375, _1526375), tc_fun(tc_fun(tc_prod(_1526375, _1526375), tc_HOL_Obool), tc_HOL_Obool), _1526375), c_member(tc_prod(_1526375, _1526375)))), c_Product__Type_OPair(_1526375, _1526375)))), _1526377)), c_fequal), _1526379), _1526381)))], (38550 ^ _779300) ^ [_1526802, _1526804, _1526806] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526802, _1526802)), _1526804), _1526806)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526802, _1526802)), _1526804), c_Transitive__Closure_Ortrancl(_1526802, _1526806))))], (38556 ^ _779300) ^ [_1526927, _1526929, _1526931] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526927, _1526927)), hAPP(hAPP(c_Product__Type_OPair(_1526927, _1526927), _1526929), _1526929)), c_Transitive__Closure_Ortrancl(_1526927, _1526931))))], (38558 ^ _779300) ^ [_1526976, _1526978] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526976, _1526976)), hAPP(hAPP(c_Product__Type_OPair(_1526976, _1526976), _1526978), _1526978)), c_Relation_OId(_1526976))))], (38560 ^ _779300) ^ [_1527022, _1527024, _1527026, _1527028] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527022, _1527022)), hAPP(hAPP(c_Product__Type_OPair(_1527022, _1527022), _1527024), _1527026)), c_Transitive__Closure_Otrancl(_1527022, _1527028))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1527022, _1527022)), hAPP(hAPP(c_Product__Type_OPair(_1527022, _1527022), _1527024), _1527026)), c_Transitive__Closure_Ortrancl(_1527022, _1527028))))], (38566 ^ _779300) ^ [_1527191, _1527193, _1527195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527191, _1527191), tc_HOL_Obool)), c_Relation_OId(_1527191)), _1527193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527191, _1527191), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1527191, _1527191, _1527191), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1527191, _1527191), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1527191, _1527195)), _1527193)), _1527195)), _1527193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527191, _1527191), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1527191, _1527195)), _1527193)))], (38576 ^ _779300) ^ [_1527466, _1527468, _1527470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1527466, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1527466, _1527466, _1527468), _1527470)), _1527470)), -(hAPP(c_Relation_OImage(_1527466, _1527466, c_Transitive__Closure_Ortrancl(_1527466, _1527468)), _1527470) = _1527470)], (38582 ^ _779300) ^ [_1527599, _1527601, _1527603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527599, _1527599), tc_HOL_Obool)), _1527601), _1527603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527599, _1527599), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1527599, _1527601)), c_Transitive__Closure_Ortrancl(_1527599, _1527603))))], (38588 ^ _779300) ^ [_1527742, _1527744, _1527746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527742, _1527742), tc_HOL_Obool)), _1527744), _1527746)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527742, _1527742), tc_HOL_Obool)), _1527746), c_Transitive__Closure_Ortrancl(_1527742, _1527744))), -(c_Transitive__Closure_Ortrancl(_1527742, _1527746) = c_Transitive__Closure_Ortrancl(_1527742, _1527744))], (38598 ^ _779300) ^ [_1527945, _1527947, _1527949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527945, _1527945), tc_HOL_Obool)), _1527947), c_Transitive__Closure_Ortrancl(_1527945, _1527949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527945, _1527945), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1527945, _1527947)), c_Transitive__Closure_Ortrancl(_1527945, _1527949))))], (38604 ^ _779300) ^ [_1528094, _1528096, _1528098] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1528094, _1528094, _1528096), c_Relation_OId(_1528094)), _1528098) = _1528098)], (38606 ^ _779300) ^ [_1528133, _1528135, _1528137] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1528133, _1528135, _1528135), _1528137), c_Relation_OId(_1528135)) = _1528137)], (38608 ^ _779300) ^ [_1528172, _1528174] : [-(hAPP(c_Relation_OImage(_1528172, _1528172, c_Relation_OId(_1528172)), _1528174) = _1528174)], (38610 ^ _779300) ^ [_1528206, _1528208, _1528210, _1528212, _1528214] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528206, _1528206)), hAPP(hAPP(c_Product__Type_OPair(_1528206, _1528206), _1528208), _1528210)), c_Transitive__Closure_Ortrancl(_1528206, _1528212))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528206, _1528206)), hAPP(hAPP(c_Product__Type_OPair(_1528206, _1528206), _1528210), _1528214)), c_Transitive__Closure_Ortrancl(_1528206, _1528212))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528206, _1528206)), hAPP(hAPP(c_Product__Type_OPair(_1528206, _1528206), _1528208), _1528214)), c_Transitive__Closure_Ortrancl(_1528206, _1528212))))], (38620 ^ _779300) ^ [_1528479, _1528481, _1528483, _1528485, _1528487] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528479, _1528479)), hAPP(hAPP(c_Product__Type_OPair(_1528479, _1528479), _1528481), _1528483)), c_Transitive__Closure_Ortrancl(_1528479, _1528485))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528479, _1528479)), hAPP(hAPP(c_Product__Type_OPair(_1528479, _1528479), _1528483), _1528487)), _1528485)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528479, _1528479)), hAPP(hAPP(c_Product__Type_OPair(_1528479, _1528479), _1528481), _1528487)), c_Transitive__Closure_Ortrancl(_1528479, _1528485))))], (38630 ^ _779300) ^ [_1528746, _1528748, _1528750, _1528752, _1528754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528746, _1528746)), hAPP(hAPP(c_Product__Type_OPair(_1528746, _1528746), _1528748), _1528750)), _1528752)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528746, _1528746)), hAPP(hAPP(c_Product__Type_OPair(_1528746, _1528746), _1528750), _1528754)), c_Transitive__Closure_Ortrancl(_1528746, _1528752))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528746, _1528746)), hAPP(hAPP(c_Product__Type_OPair(_1528746, _1528746), _1528748), _1528754)), c_Transitive__Closure_Ortrancl(_1528746, _1528752))))], (38640 ^ _779300) ^ [_1529013, _1529015] : [-(c_Transitive__Closure_Ortrancl(_1529013, c_Transitive__Closure_Ortrancl(_1529013, _1529015)) = c_Transitive__Closure_Ortrancl(_1529013, _1529015))], (38642 ^ _779300) ^ [_1529047, _1529049] : [-(c_Transitive__Closure_Ortrancl(_1529047, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1529047, _1529047), tc_HOL_Obool)), _1529049), c_Relation_OId(_1529047))) = c_Transitive__Closure_Ortrancl(_1529047, _1529049))], (38644 ^ _779300) ^ [_1529094, _1529096] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529094, _1529094), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1529094, _1529096)), c_Relation_OId(_1529094)) = c_Transitive__Closure_Ortrancl(_1529094, _1529096))], (38646 ^ _779300) ^ [_1529141, _1529143, _1529145] : [-(c_Transitive__Closure_Ortrancl(_1529141, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529141, _1529141), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1529141, _1529143)), c_Transitive__Closure_Ortrancl(_1529141, _1529145))) = c_Transitive__Closure_Ortrancl(_1529141, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529141, _1529141), tc_HOL_Obool)), _1529143), _1529145)))], (38648 ^ _779300) ^ [_1529208, _1529210] : [-(c_Transitive__Closure_Ortrancl(_1529208, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529208, _1529208), tc_HOL_Obool)), _1529210), c_Relation_OId(_1529208))) = c_Transitive__Closure_Ortrancl(_1529208, _1529210))], (38650 ^ _779300) ^ [_1529255, _1529257] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1529255, _1529255, _1529255), _1529257), c_Transitive__Closure_Ortrancl(_1529255, _1529257)) = hAPP(hAPP(c_Relation_Orel__comp(_1529255, _1529255, _1529255), c_Transitive__Closure_Ortrancl(_1529255, _1529257)), _1529257))], (38652 ^ _779300) ^ [_1529306, _1529308] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1529306, _1529306, _1529306), c_Transitive__Closure_Ortrancl(_1529306, _1529308)), c_Transitive__Closure_Ortrancl(_1529306, _1529308)) = c_Transitive__Closure_Ortrancl(_1529306, _1529308))], (38654 ^ _779300) ^ [_1529350, _1529352] : [-(c_Transitive__Closure_Ortrancl(_1529350, _1529352) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529350, _1529350), tc_HOL_Obool)), c_Relation_OId(_1529350)), hAPP(hAPP(c_Relation_Orel__comp(_1529350, _1529350, _1529350), c_Transitive__Closure_Ortrancl(_1529350, _1529352)), _1529352)))], (38656 ^ _779300) ^ [_1529407] : [-(c_Transitive__Closure_Ortrancl(_1529407, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529407, _1529407), tc_HOL_Obool))) = c_Relation_OId(_1529407))], (38658 ^ _779300) ^ [_1529443, _1529445] : [-(c_Transitive__Closure_Otrancl(_1529443, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529443, _1529443), tc_HOL_Obool)), _1529445), c_Relation_OId(_1529443))) = c_Transitive__Closure_Ortrancl(_1529443, _1529445))], (38660 ^ _779300) ^ [_1529490, _1529492] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529490, _1529490), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1529490, _1529492)), c_Relation_OId(_1529490)) = c_Transitive__Closure_Ortrancl(_1529490, _1529492))], (38662 ^ _779300) ^ [_1529537, _1529539] : [-(c_Transitive__Closure_Ortrancl(_1529537, c_Transitive__Closure_Otrancl(_1529537, _1529539)) = c_Transitive__Closure_Ortrancl(_1529537, _1529539))], (38664 ^ _779300) ^ [_1529571, _1529573] : [-(c_Transitive__Closure_Otrancl(_1529571, c_Transitive__Closure_Ortrancl(_1529571, _1529573)) = c_Transitive__Closure_Ortrancl(_1529571, _1529573))], (38666 ^ _779300) ^ [_1529605, _1529607, _1529609, _1529611] : [38667 ^ _779300 : [(38668 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529605, _1529605)), _1529607), c_Transitive__Closure_Ortrancl(_1529605, _1529609)))], (38670 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529605, _1529605)), _1529607), c_Transitive__Closure_Ortrancl(_1529605, _1529611)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1529605, _1529605)), _1529607), c_Transitive__Closure_Ortrancl(_1529605, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529605, _1529605), tc_HOL_Obool)), _1529609), _1529611)))))], (38674 ^ _779300) ^ [_1529830, _1529832] : [-(hAPP(c_Relation_ODomain(_1529830, _1529830), c_Transitive__Closure_Ortrancl(_1529830, _1529832)) = c_Orderings_Otop__class_Otop(tc_fun(_1529830, tc_HOL_Obool)))], (38676 ^ _779300) ^ [_1529869, _1529871] : [-(hAPP(c_Relation_ORange(_1529869, _1529869), c_Transitive__Closure_Ortrancl(_1529869, _1529871)) = c_Orderings_Otop__class_Otop(tc_fun(_1529869, tc_HOL_Obool)))], (38678 ^ _779300) ^ [_1529908, _1529910] : [-(c_Relation_Orefl__on(_1529908, c_Orderings_Otop__class_Otop(tc_fun(_1529908, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1529908, _1529910)))], (38680 ^ _779300) ^ [_1529942, _1529944] : [-(c_Transitive__Closure_Otrancl(_1529942, _1529944) = hAPP(hAPP(c_Relation_Orel__comp(_1529942, _1529942, _1529942), _1529944), c_Transitive__Closure_Ortrancl(_1529942, _1529944)))], (38682 ^ _779300) ^ [_1529983, _1529985] : [-(c_Transitive__Closure_Otrancl(_1529983, _1529985) = hAPP(hAPP(c_Relation_Orel__comp(_1529983, _1529983, _1529983), c_Transitive__Closure_Ortrancl(_1529983, _1529985)), _1529985))], (38684 ^ _779300) ^ [_1530024, _1530026, _1530028] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530024, _1530024), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530024, _1530024), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1530024, _1530026)), c_Transitive__Closure_Ortrancl(_1530024, _1530028))), c_Transitive__Closure_Ortrancl(_1530024, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530024, _1530024), tc_HOL_Obool)), _1530026), _1530028)))))], (38686 ^ _779300) ^ [_1530119, _1530121, _1530123] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530119, _1530119)), hAPP(hAPP(c_Product__Type_OPair(_1530119, _1530119), _1530121), _1530123)), c_Relation_OId(_1530119))), -(_1530121 = _1530123)], (38692 ^ _779300) ^ [_1530236, _1530238, _1530240] : [_1530238 = _1530240, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530236, _1530236)), hAPP(hAPP(c_Product__Type_OPair(_1530236, _1530236), _1530238), _1530240)), c_Relation_OId(_1530236))))], (38698 ^ _779300) ^ [_1530359, _1530361, _1530363, _1530365, _1530367] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530359, _1530359)), hAPP(hAPP(c_Product__Type_OPair(_1530359, _1530359), _1530361), _1530363)), c_Transitive__Closure_Ortrancl(_1530359, _1530365))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1530359, _1530359)), hAPP(hAPP(c_Product__Type_OPair(_1530359, _1530359), _1530363), _1530367)), c_Transitive__Closure_Otrancl(_1530359, _1530365))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530359, _1530359)), hAPP(hAPP(c_Product__Type_OPair(_1530359, _1530359), _1530361), _1530367)), c_Transitive__Closure_Otrancl(_1530359, _1530365))))], (38708 ^ _779300) ^ [_1530632, _1530634, _1530636, _1530638, _1530640] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530632, _1530632)), hAPP(hAPP(c_Product__Type_OPair(_1530632, _1530632), _1530634), _1530636)), c_Transitive__Closure_Otrancl(_1530632, _1530638))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1530632, _1530632)), hAPP(hAPP(c_Product__Type_OPair(_1530632, _1530632), _1530636), _1530640)), c_Transitive__Closure_Ortrancl(_1530632, _1530638))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530632, _1530632)), hAPP(hAPP(c_Product__Type_OPair(_1530632, _1530632), _1530634), _1530640)), c_Transitive__Closure_Otrancl(_1530632, _1530638))))], (38718 ^ _779300) ^ [_1530905, _1530907, _1530909, _1530911, _1530913] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530905, _1530905)), hAPP(hAPP(c_Product__Type_OPair(_1530905, _1530905), _1530907), _1530909)), c_Transitive__Closure_Ortrancl(_1530905, _1530911))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1530905, _1530905)), hAPP(hAPP(c_Product__Type_OPair(_1530905, _1530905), _1530909), _1530913)), _1530911)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530905, _1530905)), hAPP(hAPP(c_Product__Type_OPair(_1530905, _1530905), _1530907), _1530913)), c_Transitive__Closure_Otrancl(_1530905, _1530911))))], (38728 ^ _779300) ^ [_1531172, _1531174, _1531176, _1531178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531172, _1531172)), hAPP(hAPP(c_Product__Type_OPair(_1531172, _1531172), _1531174), _1531176)), c_Transitive__Closure_Ortrancl(_1531172, _1531178))), -(_1531174 = _1531176), 38735 ^ _779300 : [(38736 ^ _779300) ^ [] : [_1531174 = _1531176], (38738 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531172, _1531172)), hAPP(hAPP(c_Product__Type_OPair(_1531172, _1531172), _1531174), _1531176)), c_Transitive__Closure_Otrancl(_1531172, _1531178))))]]], (38740 ^ _779300) ^ [_1531434, _1531436, _1531438, _1531440, _1531442] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531434, _1531434)), hAPP(hAPP(c_Product__Type_OPair(_1531434, _1531434), _1531436), _1531438)), _1531440)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1531434, _1531434)), hAPP(hAPP(c_Product__Type_OPair(_1531434, _1531434), _1531438), _1531442)), c_Transitive__Closure_Ortrancl(_1531434, _1531440))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531434, _1531434)), hAPP(hAPP(c_Product__Type_OPair(_1531434, _1531434), _1531436), _1531442)), c_Transitive__Closure_Otrancl(_1531434, _1531440))))], (38750 ^ _779300) ^ [_1531722, _1531724, _1531726, _1531728] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531722, _1531722)), hAPP(hAPP(c_Product__Type_OPair(_1531722, _1531722), _1531724), _1531726)), c_Transitive__Closure_Ortrancl(_1531722, _1531728))), -(_1531724 = _1531726), 38757 ^ _779300 : [(38758 ^ _779300) ^ [] : [_1531724 = _1531726], (38760 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531722, _1531722)), hAPP(hAPP(c_Product__Type_OPair(_1531722, _1531722), _1531724), _1531726)), c_Transitive__Closure_Otrancl(_1531722, _1531728))))]]], (38762 ^ _779300) ^ [_1531980, _1531982, _1531984, _1531986] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531980, _1531980)), hAPP(hAPP(c_Product__Type_OPair(_1531980, _1531980), _1531982), _1531984)), c_Transitive__Closure_Ortrancl(_1531980, _1531986)))), 38763 ^ _779300 : [(38764 ^ _779300) ^ [] : [_1531982 = _1531984], (38766 ^ _779300) ^ [] : [-(_1531982 = _1531984), hBOOL(hAPP(hAPP(c_member(tc_prod(_1531980, _1531980)), hAPP(hAPP(c_Product__Type_OPair(_1531980, _1531980), _1531982), _1531984)), c_Transitive__Closure_Otrancl(_1531980, _1531986)))]]], (38774 ^ _779300) ^ [_1532246] : [-(hAPP(c_Relation_ODomain(_1532246, _1532246), c_Relation_OId(_1532246)) = c_Orderings_Otop__class_Otop(tc_fun(_1532246, tc_HOL_Obool)))], (38776 ^ _779300) ^ [_1532282] : [-(hAPP(c_Relation_ORange(_1532282, _1532282), c_Relation_OId(_1532282)) = c_Orderings_Otop__class_Otop(tc_fun(_1532282, tc_HOL_Obool)))], (38778 ^ _779300) ^ [_1532318] : [-(c_Relation_Orefl__on(_1532318, c_Orderings_Otop__class_Otop(tc_fun(_1532318, tc_HOL_Obool)), c_Relation_OId(_1532318)))], (38780 ^ _779300) ^ [] : [-(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))))], (38782 ^ _779300) ^ [_1532366, _1532368, _1532370, _1532372] : [-(hBOOL(hAPP(hAPP(c_member(_1532366), _1532368), hAPP(c_Relation_ODomain(_1532366, _1532366), _1532370)))), 38785 ^ _779300 : [(38786 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532366, _1532366)), hAPP(hAPP(c_Product__Type_OPair(_1532366, _1532366), _1532368), _1532372)), c_Transitive__Closure_Ortrancl(_1532366, _1532370))), -(_1532368 = _1532372)], (38792 ^ _779300) ^ [] : [_1532368 = _1532372, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532366, _1532366)), hAPP(hAPP(c_Product__Type_OPair(_1532366, _1532366), _1532368), _1532372)), c_Transitive__Closure_Ortrancl(_1532366, _1532370))))]]], (38798 ^ _779300) ^ [_1532662, _1532664, _1532666, _1532668] : [hBOOL(hAPP(hAPP(c_member(_1532662), _1532664), c_Wellfounded_Oacc(_1532662, _1532666))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1532662, _1532662)), hAPP(hAPP(c_Product__Type_OPair(_1532662, _1532662), _1532668), _1532664)), c_Transitive__Closure_Ortrancl(_1532662, _1532666))), -(hBOOL(hAPP(hAPP(c_member(_1532662), _1532668), c_Wellfounded_Oacc(_1532662, _1532666))))], (38808 ^ _779300) ^ [_1532883, _1532885, _1532887, _1532889] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532883, _1532883)), hAPP(hAPP(c_Product__Type_OPair(_1532883, _1532883), _1532885), _1532887)), c_Transitive__Closure_Ortrancl(_1532883, _1532889))), hBOOL(hAPP(hAPP(c_member(_1532883), _1532887), c_Wellfounded_Oacc(_1532883, _1532889))), -(hBOOL(hAPP(hAPP(c_member(_1532883), _1532885), c_Wellfounded_Oacc(_1532883, _1532889))))], (38818 ^ _779300) ^ [_1533125, _1533127, _1533129, _1533131] : [c_Wellfounded_Owf(_1533125, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1533125, _1533125)), hAPP(hAPP(c_Product__Type_OPair(_1533125, _1533125), _1533127), _1533129)), _1533131)), 38821 ^ _779300 : [(38822 ^ _779300) ^ [] : [-(c_Wellfounded_Owf(_1533125, _1533131))], (38824 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1533125, _1533125)), hAPP(hAPP(c_Product__Type_OPair(_1533125, _1533125), _1533129), _1533127)), c_Transitive__Closure_Ortrancl(_1533125, _1533131)))]]], (38826 ^ _779300) ^ [_1533320, _1533322, _1533324, _1533326] : [-(c_Wellfounded_Owf(_1533320, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1533320, _1533320)), hAPP(hAPP(c_Product__Type_OPair(_1533320, _1533320), _1533322), _1533324)), _1533326))), c_Wellfounded_Owf(_1533320, _1533326), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1533320, _1533320)), hAPP(hAPP(c_Product__Type_OPair(_1533320, _1533320), _1533324), _1533322)), c_Transitive__Closure_Ortrancl(_1533320, _1533326))))], (38836 ^ _779300) ^ [_1533567, _1533569, _1533571, _1533573] : [c_Wellfounded_Oacyclic(_1533567, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1533567, _1533567)), hAPP(hAPP(c_Product__Type_OPair(_1533567, _1533567), _1533569), _1533571)), _1533573)), 38839 ^ _779300 : [(38840 ^ _779300) ^ [] : [-(c_Wellfounded_Oacyclic(_1533567, _1533573))], (38842 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1533567, _1533567)), hAPP(hAPP(c_Product__Type_OPair(_1533567, _1533567), _1533571), _1533569)), c_Transitive__Closure_Ortrancl(_1533567, _1533573)))]]], (38844 ^ _779300) ^ [_1533762, _1533764, _1533766, _1533768] : [-(c_Wellfounded_Oacyclic(_1533762, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1533762, _1533762)), hAPP(hAPP(c_Product__Type_OPair(_1533762, _1533762), _1533764), _1533766)), _1533768))), c_Wellfounded_Oacyclic(_1533762, _1533768), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1533762, _1533762)), hAPP(hAPP(c_Product__Type_OPair(_1533762, _1533762), _1533766), _1533764)), c_Transitive__Closure_Ortrancl(_1533762, _1533768))))], (38854 ^ _779300) ^ [_1533988, _1533990] : [-(c_Relation_Orefl__on(_1533988, c_Orderings_Otop__class_Otop(tc_fun(_1533988, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1533988, _1533988), tc_HOL_Obool)), _1533990), c_Relation_OId(_1533988))))], (38856 ^ _779300) ^ [_1534035] : [-(c_Relation_OId(_1534035) = hAPP(c_Set_OCollect(tc_prod(_1534035, _1534035)), hAPP(hAPP(c_COMBB(tc_fun(_1534035, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1534035, _1534035)), c_HOL_OEx(_1534035)), hAPP(hAPP(c_COMBC(tc_prod(_1534035, _1534035), tc_fun(_1534035, tc_prod(_1534035, _1534035)), tc_fun(_1534035, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1534035, _1534035), tc_HOL_Obool), tc_fun(tc_fun(_1534035, tc_prod(_1534035, _1534035)), tc_fun(_1534035, tc_HOL_Obool)), tc_prod(_1534035, _1534035)), c_COMBB(tc_prod(_1534035, _1534035), tc_HOL_Obool, _1534035)), c_fequal)), hAPP(hAPP(c_COMBS(_1534035, _1534035, tc_prod(_1534035, _1534035)), c_Product__Type_OPair(_1534035, _1534035)), c_COMBI(_1534035))))))], (38858 ^ _779300) ^ [_1534164, _1534166] : [-(c_Relation_Oirrefl(_1534164, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1534164, _1534164), tc_HOL_Obool)), _1534166), c_Relation_OId(_1534164))))], (38860 ^ _779300) ^ [_1534220, _1534222] : [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), _1534220), _1534222)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1534220), _1534222)))], (38866 ^ _779300) ^ [_1534325, _1534327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1534325), _1534327)), -(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), _1534325), _1534327)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (38872 ^ _779300) ^ [_1534436, _1534438, _1534440, _1534442, _1534444] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1534436, _1534436)), hAPP(hAPP(c_Product__Type_OPair(_1534436, _1534436), _1534438), _1534440)), c_Transitive__Closure_Ortrancl(_1534436, _1534442))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534436, _1534436), tc_HOL_Obool)), _1534442), hAPP(hAPP(c_Product__Type_OSigma(_1534436, _1534436), _1534444), hAPP(c_COMBK(tc_fun(_1534436, tc_HOL_Obool), _1534436), _1534444)))), -(_1534438 = _1534440), -(hBOOL(hAPP(hAPP(c_member(_1534436), _1534438), _1534444)))], (38886 ^ _779300) ^ [_1534710, _1534712, _1534714] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1534710, _1534710), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1534710, _1534710), _1534712)), c_Transitive__Closure_Ortrancl(_1534710, _1534712)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1534710, _1534710), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1534710, _1534710)), hAPP(hAPP(c_Product__Type_OPair(_1534710, _1534710), _1534714), _1534714)), c_Transitive__Closure_Otrancl(_1534710, _1534712)))], (38892 ^ _779300) ^ [_1534896, _1534898, _1534900, _1534902, _1534904] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1534896, _1534896)), hAPP(hAPP(c_Product__Type_OPair(_1534896, _1534896), hAPP(_1534898, hAPP(c_Nat_OSuc, 38893 ^ [_1534896, _1534898, _1534900, _1534902, _1534904]))), hAPP(_1534898, 38893 ^ [_1534896, _1534898, _1534900, _1534902, _1534904]))), c_Transitive__Closure_Ortrancl(_1534896, _1534900))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534896, _1534896)), hAPP(hAPP(c_Product__Type_OPair(_1534896, _1534896), hAPP(_1534898, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1534902), _1534904))), hAPP(_1534898, _1534902))), c_Transitive__Closure_Ortrancl(_1534896, _1534900))))], (38899 ^ _779300) ^ [_1535207, _1535209, _1535211] : [c_Relation_Ototal__on(_1535207, _1535209, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1535207, _1535207), tc_HOL_Obool)), _1535211), c_Relation_OId(_1535207))), -(c_Relation_Ototal__on(_1535207, _1535209, _1535211))], (38905 ^ _779300) ^ [_1535318, _1535320, _1535322] : [c_Relation_Ototal__on(_1535318, _1535320, _1535322), -(c_Relation_Ototal__on(_1535318, _1535320, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1535318, _1535318), tc_HOL_Obool)), _1535322), c_Relation_OId(_1535318))))], (38911 ^ _779300) ^ [_1535435] : [-(hAPP(c_Relation_Oconverse(_1535435, _1535435), c_Relation_OId(_1535435)) = c_Relation_OId(_1535435))], (38913 ^ _779300) ^ [_1535468, _1535470] : [-(c_Transitive__Closure_Ortrancl(_1535468, hAPP(c_Relation_Oconverse(_1535468, _1535468), _1535470)) = hAPP(c_Relation_Oconverse(_1535468, _1535468), c_Transitive__Closure_Ortrancl(_1535468, _1535470)))], (38915 ^ _779300) ^ [_1535511, _1535513] : [-(c_Transitive__Closure_Otrancl(_1535511, hAPP(c_Relation_Oconverse(_1535511, _1535511), _1535513)) = hAPP(c_Relation_Oconverse(_1535511, _1535511), c_Transitive__Closure_Otrancl(_1535511, _1535513)))], (38917 ^ _779300) ^ [_1535569, _1535571] : [c_Wellfounded_Oacyclic(_1535569, hAPP(c_Relation_Oconverse(_1535569, _1535569), _1535571)), -(c_Wellfounded_Oacyclic(_1535569, _1535571))], (38923 ^ _779300) ^ [_1535654, _1535656] : [c_Wellfounded_Oacyclic(_1535654, _1535656), -(c_Wellfounded_Oacyclic(_1535654, hAPP(c_Relation_Oconverse(_1535654, _1535654), _1535656)))], (38929 ^ _779300) ^ [_1535763, _1535765, _1535767] : [c_Relation_Orefl__on(_1535763, _1535765, hAPP(c_Relation_Oconverse(_1535763, _1535763), _1535767)), -(c_Relation_Orefl__on(_1535763, _1535765, _1535767))], (38935 ^ _779300) ^ [_1535854, _1535856, _1535858] : [c_Relation_Orefl__on(_1535854, _1535856, _1535858), -(c_Relation_Orefl__on(_1535854, _1535856, hAPP(c_Relation_Oconverse(_1535854, _1535854), _1535858)))], (38941 ^ _779300) ^ [_1535969, _1535971, _1535973] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1535969, _1535971)), hAPP(c_Relation_Oconverse(_1535971, _1535969), _1535973))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1535971, _1535969)), _1535973)))], (38947 ^ _779300) ^ [_1536084, _1536086, _1536088] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1536086, _1536084)), _1536088)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1536084, _1536086)), hAPP(c_Relation_Oconverse(_1536086, _1536084), _1536088))))], (38953 ^ _779300) ^ [_1536205, _1536207] : [-(hAPP(c_Relation_Oconverse(_1536205, _1536205), c_Relation_OId__on(_1536205, _1536207)) = c_Relation_OId__on(_1536205, _1536207))], (38955 ^ _779300) ^ [_1536242, _1536244] : [-(hAPP(c_Relation_OField(_1536242), hAPP(c_Relation_Oconverse(_1536242, _1536242), _1536244)) = hAPP(c_Relation_OField(_1536242), _1536244))], (38957 ^ _779300) ^ [_1536301, _1536303, _1536305] : [c_Relation_Ototal__on(_1536301, _1536303, hAPP(c_Relation_Oconverse(_1536301, _1536301), _1536305)), -(c_Relation_Ototal__on(_1536301, _1536303, _1536305))], (38963 ^ _779300) ^ [_1536392, _1536394, _1536396] : [c_Relation_Ototal__on(_1536392, _1536394, _1536396), -(c_Relation_Ototal__on(_1536392, _1536394, hAPP(c_Relation_Oconverse(_1536392, _1536392), _1536396)))], (38969 ^ _779300) ^ [_1536489, _1536491, _1536493] : [-(hAPP(c_Relation_Oconverse(_1536489, _1536491), hAPP(c_Relation_Oconverse(_1536491, _1536489), _1536493)) = _1536493)], (38971 ^ _779300) ^ [_1536528, _1536530, _1536532, _1536534] : [-(hAPP(c_Relation_Oconverse(_1536528, _1536528), hAPP(hAPP(c_Relation_Oinv__image(_1536530, _1536528), _1536532), _1536534)) = hAPP(hAPP(c_Relation_Oinv__image(_1536530, _1536528), hAPP(c_Relation_Oconverse(_1536530, _1536530), _1536532)), _1536534))], (38973 ^ _779300) ^ [_1536587, _1536589, _1536591, _1536593] : [-(hAPP(c_Relation_Oconverse(_1536587, _1536589), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1536587, _1536589), tc_HOL_Obool)), _1536591), _1536593)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1536589, _1536587), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1536587, _1536589), _1536591)), hAPP(c_Relation_Oconverse(_1536587, _1536589), _1536593)))], (38975 ^ _779300) ^ [_1536662, _1536664, _1536666, _1536668] : [-(hAPP(c_Relation_Oconverse(_1536662, _1536664), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1536662, _1536664), tc_HOL_Obool)), _1536666), _1536668)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1536664, _1536662), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1536662, _1536664), _1536666)), hAPP(c_Relation_Oconverse(_1536662, _1536664), _1536668)))], (38977 ^ _779300) ^ [_1536737, _1536739, _1536741, _1536743, _1536745] : [-(hAPP(c_Relation_Oconverse(_1536737, _1536739), hAPP(hAPP(c_Relation_Orel__comp(_1536737, _1536741, _1536739), _1536743), _1536745)) = hAPP(hAPP(c_Relation_Orel__comp(_1536739, _1536741, _1536737), hAPP(c_Relation_Oconverse(_1536741, _1536739), _1536745)), hAPP(c_Relation_Oconverse(_1536737, _1536741), _1536743)))], (38979 ^ _779300) ^ [_1536806, _1536808, _1536810, _1536812, _1536814] : [-(hAPP(c_Relation_Oconverse(_1536806, _1536808), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536810, tc_fun(tc_prod(_1536806, _1536808), tc_HOL_Obool)), _1536812), _1536814)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536810, tc_fun(tc_prod(_1536808, _1536806), tc_HOL_Obool)), _1536812), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1536806, _1536808), tc_HOL_Obool), tc_fun(tc_prod(_1536808, _1536806), tc_HOL_Obool), _1536810), c_Relation_Oconverse(_1536806, _1536808)), _1536814)))], (38981 ^ _779300) ^ [_1536922, _1536924, _1536926, _1536928, _1536930] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536922, _1536924)), hAPP(hAPP(c_Product__Type_OPair(_1536922, _1536924), _1536926), _1536928)), hAPP(c_Relation_Oconverse(_1536924, _1536922), _1536930))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1536924, _1536922)), hAPP(hAPP(c_Product__Type_OPair(_1536924, _1536922), _1536928), _1536926)), _1536930)))], (38987 ^ _779300) ^ [_1537089, _1537091, _1537093, _1537095, _1537097] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537091, _1537089)), hAPP(hAPP(c_Product__Type_OPair(_1537091, _1537089), _1537095), _1537093)), _1537097)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1537089, _1537091)), hAPP(hAPP(c_Product__Type_OPair(_1537089, _1537091), _1537093), _1537095)), hAPP(c_Relation_Oconverse(_1537091, _1537089), _1537097))))], (38993 ^ _779300) ^ [_1537262, _1537264, _1537266, _1537268, _1537270] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537262, _1537264)), hAPP(hAPP(c_Product__Type_OPair(_1537262, _1537264), _1537266), _1537268)), _1537270)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1537264, _1537262)), hAPP(hAPP(c_Product__Type_OPair(_1537264, _1537262), _1537268), _1537266)), hAPP(c_Relation_Oconverse(_1537262, _1537264), _1537270))))], (38999 ^ _779300) ^ [_1537433, _1537435, _1537437, _1537439, _1537441] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537433, _1537435)), hAPP(hAPP(c_Product__Type_OPair(_1537433, _1537435), _1537437), _1537439)), hAPP(c_Relation_Oconverse(_1537435, _1537433), _1537441))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1537435, _1537433)), hAPP(hAPP(c_Product__Type_OPair(_1537435, _1537433), _1537439), _1537437)), _1537441)))], (39005 ^ _779300) ^ [_1537604, _1537606] : [c_Wellfounded_Owf(_1537604, hAPP(c_Relation_Oconverse(_1537604, _1537604), _1537606)), -(c_Wellfounded_Owf(_1537604, hAPP(c_Relation_Oconverse(_1537604, _1537604), c_Transitive__Closure_Otrancl(_1537604, _1537606))))], (39011 ^ _779300) ^ [_1537711, _1537713, _1537715] : [c_Equiv__Relations_Oequiv(_1537711, _1537713, _1537715), -(hAPP(hAPP(c_Relation_Orel__comp(_1537711, _1537711, _1537711), hAPP(c_Relation_Oconverse(_1537711, _1537711), _1537715)), _1537715) = _1537715)], (39017 ^ _779300) ^ [_1537824, _1537826, _1537828] : [-(hAPP(c_Relation_ORange(_1537824, _1537826), hAPP(c_Relation_Oconverse(_1537826, _1537824), _1537828)) = hAPP(c_Relation_ODomain(_1537826, _1537824), _1537828))], (39019 ^ _779300) ^ [_1537869, _1537871, _1537873] : [-(hAPP(c_Relation_ODomain(_1537869, _1537871), hAPP(c_Relation_Oconverse(_1537871, _1537869), _1537873)) = hAPP(c_Relation_ORange(_1537871, _1537869), _1537873))], (39021 ^ _779300) ^ [_1537914, _1537916, _1537918] : [-(hAPP(c_Relation_ORange(_1537914, _1537916), _1537918) = hAPP(c_Relation_ODomain(_1537916, _1537914), hAPP(c_Relation_Oconverse(_1537914, _1537916), _1537918)))], (39023 ^ _779300) ^ [_1537959, _1537961] : [-(c_Relation_Ototal__on(_1537959, c_Orderings_Obot__class_Obot(tc_fun(_1537959, tc_HOL_Obool)), _1537961))], (39025 ^ _779300) ^ [_1537990, _1537992, _1537994, _1537996] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537990, _1537990)), hAPP(hAPP(c_Product__Type_OPair(_1537990, _1537990), _1537992), _1537994)), c_Transitive__Closure_Ortrancl(_1537990, _1537996))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1537990, _1537990)), hAPP(hAPP(c_Product__Type_OPair(_1537990, _1537990), _1537994), _1537992)), c_Transitive__Closure_Ortrancl(_1537990, hAPP(c_Relation_Oconverse(_1537990, _1537990), _1537996)))))], (39031 ^ _779300) ^ [_1538171, _1538173, _1538175, _1538177] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1538171, _1538171)), hAPP(hAPP(c_Product__Type_OPair(_1538171, _1538171), _1538173), _1538175)), c_Transitive__Closure_Ortrancl(_1538171, hAPP(c_Relation_Oconverse(_1538171, _1538171), _1538177)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1538171, _1538171)), hAPP(hAPP(c_Product__Type_OPair(_1538171, _1538171), _1538175), _1538173)), c_Transitive__Closure_Ortrancl(_1538171, _1538177))))], (39037 ^ _779300) ^ [_1538352, _1538354, _1538356, _1538358] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1538352, _1538352)), hAPP(hAPP(c_Product__Type_OPair(_1538352, _1538352), _1538354), _1538356)), c_Transitive__Closure_Otrancl(_1538352, hAPP(c_Relation_Oconverse(_1538352, _1538352), _1538358)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1538352, _1538352)), hAPP(hAPP(c_Product__Type_OPair(_1538352, _1538352), _1538354), _1538356)), hAPP(c_Relation_Oconverse(_1538352, _1538352), c_Transitive__Closure_Otrancl(_1538352, _1538358)))))], (39043 ^ _779300) ^ [_1538545, _1538547, _1538549, _1538551] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1538545, _1538545)), hAPP(hAPP(c_Product__Type_OPair(_1538545, _1538545), _1538547), _1538549)), hAPP(c_Relation_Oconverse(_1538545, _1538545), c_Transitive__Closure_Otrancl(_1538545, _1538551)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1538545, _1538545)), hAPP(hAPP(c_Product__Type_OPair(_1538545, _1538545), _1538547), _1538549)), c_Transitive__Closure_Otrancl(_1538545, hAPP(c_Relation_Oconverse(_1538545, _1538545), _1538551)))))], (39049 ^ _779300) ^ [_1538762, _1538764, _1538766, _1538768, _1538770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538762, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1538764, _1538762, _1538766), _1538768)), _1538770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538764, tc_HOL_Obool)), _1538768), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1538764, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1538762, _1538764, hAPP(c_Relation_Oconverse(_1538764, _1538762), _1538766)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1538762, tc_HOL_Obool)), _1538770))))))], (39055 ^ _779300) ^ [_1538953, _1538955, _1538957, _1538959, _1538961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538955, tc_HOL_Obool)), _1538959), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1538955, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1538953, _1538955, hAPP(c_Relation_Oconverse(_1538955, _1538953), _1538957)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1538953, tc_HOL_Obool)), _1538961))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538953, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1538955, _1538953, _1538957), _1538959)), _1538961)))], (39061 ^ _779300) ^ [_1539150, _1539152, _1539154] : [c_Relation_Orefl__on(_1539150, _1539152, _1539154), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1539150, _1539150), tc_HOL_Obool)), _1539154), hAPP(hAPP(c_Relation_Orel__comp(_1539150, _1539150, _1539150), hAPP(c_Relation_Oconverse(_1539150, _1539150), _1539154)), _1539154))))], (39067 ^ _779300) ^ [_1539289, _1539291, _1539293] : [hAPP(hAPP(c_Relation_Orel__comp(_1539289, _1539289, _1539289), hAPP(c_Relation_Oconverse(_1539289, _1539289), _1539291)), _1539291) = _1539291, hAPP(c_Relation_ODomain(_1539289, _1539289), _1539291) = _1539293, -(c_Equiv__Relations_Oequiv(_1539289, _1539293, _1539291))], (39077 ^ _779300) ^ [_1539468, _1539470] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539468, _1539468)), _1539470)), c_Wellfounded_Oacyclic(_1539468, _1539470), -(c_Wellfounded_Owf(_1539468, hAPP(c_Relation_Oconverse(_1539468, _1539468), _1539470)))], (39109 ^ _779300) ^ [_1540130, _1540132, _1540134] : [39111 ^ _779300 : [(39112 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540130), 39110 ^ [_1540130, _1540132, _1540134]), _1540132)))], (39115 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540130), 39113 ^ [_1540130, _1540132, _1540134]), _1540132)))], (39117 ^ _779300) ^ [] : [39110 ^ [_1540130, _1540132, _1540134] = 39113 ^ [_1540130, _1540132, _1540134]], (39119 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540130, _1540130)), hAPP(hAPP(c_Product__Type_OPair(_1540130, _1540130), 39110 ^ [_1540130, _1540132, _1540134]), 39113 ^ [_1540130, _1540132, _1540134])), _1540134))], (39121 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540130, _1540130)), hAPP(hAPP(c_Product__Type_OPair(_1540130, _1540130), 39113 ^ [_1540130, _1540132, _1540134]), 39110 ^ [_1540130, _1540132, _1540134])), _1540134))]], -(c_Relation_Ototal__on(_1540130, _1540132, _1540134))], (39087 ^ _779300) ^ [_1539641, _1539643, _1539645] : [c_Relation_Ototal__on(_1539641, _1539643, _1539645), 39090 ^ _779300 : [(39091 ^ _779300) ^ [_1539785] : [hBOOL(hAPP(hAPP(c_member(_1539641), _1539785), _1539643)), 39094 ^ _779300 : [(39095 ^ _779300) ^ [_1539925] : [hBOOL(hAPP(hAPP(c_member(_1539641), _1539925), _1539643)), -(_1539785 = _1539925), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539641, _1539641)), hAPP(hAPP(c_Product__Type_OPair(_1539641, _1539641), _1539785), _1539925)), _1539645))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539641, _1539641)), hAPP(hAPP(c_Product__Type_OPair(_1539641, _1539641), _1539925), _1539785)), _1539645)))]]]]], (39125 ^ _779300) ^ [_1540712, _1540714, _1540716] : [-(hAPP(c_Relation_Oconverse(_1540712, _1540714), _1540716) = hAPP(c_Set_OCollect(tc_prod(_1540714, _1540712)), hAPP(c_Product__Type_Oprod_Oprod__case(_1540714, _1540712, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1540714, tc_fun(tc_prod(_1540712, _1540714), tc_HOL_Obool), tc_fun(_1540712, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540712, tc_fun(tc_fun(tc_prod(_1540712, _1540714), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1540712, _1540714), tc_HOL_Obool), tc_fun(_1540712, tc_HOL_Obool)), _1540714), c_COMBC(_1540712, tc_fun(tc_prod(_1540712, _1540714), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540712, tc_prod(_1540712, _1540714)), tc_fun(_1540712, tc_fun(tc_fun(tc_prod(_1540712, _1540714), tc_HOL_Obool), tc_HOL_Obool)), _1540714), hAPP(c_COMBB(tc_prod(_1540712, _1540714), tc_fun(tc_fun(tc_prod(_1540712, _1540714), tc_HOL_Obool), tc_HOL_Obool), _1540712), c_member(tc_prod(_1540712, _1540714)))), hAPP(c_COMBC(_1540712, _1540714, tc_prod(_1540712, _1540714)), c_Product__Type_OPair(_1540712, _1540714))))), _1540716))))], (39127 ^ _779300) ^ [_1540888, _1540890, _1540892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540888, _1540888)), _1540890), c_Transitive__Closure_Ortrancl(_1540888, _1540892))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540888, _1540888)), _1540890), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1540888, _1540888), 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(_1540888, _1540888), tc_HOL_Obool), tc_fun(tc_prod(_1540888, _1540888), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1540888, _1540888), tc_HOL_Obool)), _1540892)))))], (39133 ^ _779300) ^ [_1541095, _1541097] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1541095, _1541095)), hAPP(hAPP(c_Product__Type_OPair(_1541095, _1541095), 39134 ^ [_1541095, _1541097]), 39134 ^ [_1541095, _1541097])), c_Transitive__Closure_Otrancl(_1541095, _1541097)))), -(c_Wellfounded_Oacyclic(_1541095, _1541097))], (39140 ^ _779300) ^ [_1541167, _1541169, _1541171, _1541173, _1541175] : [c_Relation_Osingle__valued(_1541167, _1541169, hAPP(c_Relation_Oconverse(_1541169, _1541167), _1541171)), -(hAPP(c_Relation_OImage(_1541169, _1541167, _1541171), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1541169, tc_HOL_Obool)), _1541173), _1541175)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1541167, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1541169, _1541167, _1541171), _1541173)), hAPP(c_Relation_OImage(_1541169, _1541167, _1541171), _1541175)))], (39146 ^ _779300) ^ [_1541350, _1541352, _1541354, _1541356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541350, _1541352), tc_HOL_Obool)), _1541354), _1541356)), c_Relation_Osingle__valued(_1541350, _1541352, _1541356), -(c_Relation_Osingle__valued(_1541350, _1541352, _1541354))], (39156 ^ _779300) ^ [_1541517, _1541519, _1541521, _1541523] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1541517, _1541519), tc_fun(_1541517, _1541519)), _1541521), c_Fun_Ocomp(_1541519, _1541519, _1541517, _1541523)) = c_Fun_Ocomp(_1541519, _1541519, _1541517, hAPP(hAPP(c_Nat_Ocompow(_1541519, _1541519), _1541521), _1541523)))], (39158 ^ _779300) ^ [_1541580, _1541582, _1541584] : [c_Wellfounded_Owf(_1541580, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541580, _1541580), tc_HOL_Obool), _1541582), _1541584)), -(c_Wellfounded_Owf(_1541580, _1541584))], (39164 ^ _779300) ^ [_1541683, _1541685, _1541687, _1541689] : [-(hAPP(hAPP(c_Nat_Ocompow(_1541683, _1541683), _1541685), hAPP(hAPP(c_Nat_Ocompow(_1541683, _1541683), _1541687), _1541689)) = hAPP(hAPP(c_Nat_Ocompow(_1541683, _1541683), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1541687), _1541685)), _1541689))], (39166 ^ _779300) ^ [_1541745, _1541747, _1541749, _1541751] : [-(hAPP(_1541745, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1541747, _1541747), _1541749), _1541745), _1541751)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1541747, _1541747), _1541749), _1541745), hAPP(_1541745, _1541751)))], (39168 ^ _779300) ^ [_1541804, _1541806] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541804, _1541804), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1541806) = _1541806)], (39170 ^ _779300) ^ [_1541841, _1541843, _1541845] : [c_Relation_Osingle__valued(_1541841, _1541841, _1541843), -(c_Relation_Osingle__valued(_1541841, _1541841, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541841, _1541841), tc_HOL_Obool), _1541845), _1541843)))], (39176 ^ _779300) ^ [_1541948, _1541950, _1541952] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1541948, _1541948, _1541948), _1541950), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541948, _1541948), tc_HOL_Obool), _1541952), _1541950)) = hAPP(hAPP(c_Relation_Orel__comp(_1541948, _1541948, _1541948), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541948, _1541948), tc_HOL_Obool), _1541952), _1541950)), _1541950))], (39178 ^ _779300) ^ [_1542019, _1542021, _1542023, _1542025, _1542027] : [c_Relation_Osingle__valued(_1542019, _1542021, _1542023), c_Relation_Osingle__valued(_1542021, _1542025, _1542027), -(c_Relation_Osingle__valued(_1542019, _1542025, hAPP(hAPP(c_Relation_Orel__comp(_1542019, _1542021, _1542025), _1542023), _1542027)))], (39188 ^ _779300) ^ [_1542186] : [-(c_Relation_Osingle__valued(_1542186, _1542186, c_Relation_OId(_1542186)))], (39190 ^ _779300) ^ [_1542212, _1542214, _1542216, _1542218] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542212, _1542212)), _1542214), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542212, _1542212), tc_HOL_Obool), _1542216), _1542218))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542212, _1542212)), _1542214), c_Transitive__Closure_Ortrancl(_1542212, _1542218))))], (39196 ^ _779300) ^ [_1542381, _1542383, _1542385] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542381, _1542381)), _1542383), c_Transitive__Closure_Ortrancl(_1542381, _1542385))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542381, _1542381)), _1542383), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542381, _1542381), tc_HOL_Obool), 39199 ^ [_1542381, _1542383, _1542385]), _1542385))))], (39203 ^ _779300) ^ [_1542540, _1542542, _1542544] : [39204 ^ _779300 : [(39205 ^ _779300) ^ [_1542616] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542540, _1542540)), _1542542), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542540, _1542540), tc_HOL_Obool), _1542616), _1542544)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542540, _1542540)), _1542542), c_Transitive__Closure_Ortrancl(_1542540, _1542544))))], (39209 ^ _779300) ^ [_1542704, _1542706] : [-(c_Relation_Osingle__valued(_1542704, _1542704, c_Relation_OId__on(_1542704, _1542706)))], (39211 ^ _779300) ^ [_1542733, _1542735, _1542737] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542733, _1542733), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1542735)), _1542737) = hAPP(hAPP(c_Relation_Orel__comp(_1542733, _1542733, _1542733), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542733, _1542733), tc_HOL_Obool), _1542735), _1542737)), _1542737))], (39213 ^ _779300) ^ [_1542797, _1542799, _1542801, _1542803] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542797, _1542797), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1542799), _1542801)), _1542803) = hAPP(hAPP(c_Relation_Orel__comp(_1542797, _1542797, _1542797), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542797, _1542797), tc_HOL_Obool), _1542799), _1542803)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542797, _1542797), tc_HOL_Obool), _1542801), _1542803)))], (39215 ^ _779300) ^ [_1542878, _1542880] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542878, _1542878), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1542880) = c_Relation_OId(_1542878))], (39217 ^ _779300) ^ [_1542917, _1542919, _1542921] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542917, _1542917)), hAPP(hAPP(c_Product__Type_OPair(_1542917, _1542917), _1542919), _1542919)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542917, _1542917), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1542921))))], (39219 ^ _779300) ^ [_1542975, _1542977, _1542979, _1542981] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542975, _1542975)), hAPP(hAPP(c_Product__Type_OPair(_1542975, _1542975), _1542977), _1542979)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542975, _1542975), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1542981))), -(_1542977 = _1542979)], (39225 ^ _779300) ^ [_1543118, _1543120, _1543122, _1543124, _1543126, _1543128] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1543118, _1543118)), hAPP(hAPP(c_Product__Type_OPair(_1543118, _1543118), _1543120), _1543122)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1543118, _1543118), tc_HOL_Obool), _1543124), _1543126))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543118, _1543118)), hAPP(hAPP(c_Product__Type_OPair(_1543118, _1543118), _1543122), _1543128)), _1543126)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1543118, _1543118)), hAPP(hAPP(c_Product__Type_OPair(_1543118, _1543118), _1543120), _1543128)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1543118, _1543118), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1543124)), _1543126))))], (39235 ^ _779300) ^ [_1543431, _1543433, _1543435, _1543437, _1543439, _1543441] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1543431, _1543431)), hAPP(hAPP(c_Product__Type_OPair(_1543431, _1543431), _1543433), _1543435)), _1543437)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543431, _1543431)), hAPP(hAPP(c_Product__Type_OPair(_1543431, _1543431), _1543435), _1543439)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1543431, _1543431), tc_HOL_Obool), _1543441), _1543437))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1543431, _1543431)), hAPP(hAPP(c_Product__Type_OPair(_1543431, _1543431), _1543433), _1543439)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1543431, _1543431), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1543441)), _1543437))))], (39245 ^ _779300) ^ [_1543744, _1543746, _1543748] : [-(hAPP(hAPP(c_Nat_Ocompow(_1543744, _1543744), hAPP(c_Nat_OSuc, _1543746)), _1543748) = hAPP(c_Fun_Ocomp(_1543744, _1543744, _1543744, _1543748), hAPP(hAPP(c_Nat_Ocompow(_1543744, _1543744), _1543746), _1543748)))], (39247 ^ _779300) ^ [_1543800, _1543802, _1543804, _1543806] : [-(hAPP(hAPP(c_Nat_Ocompow(_1543800, _1543800), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1543802), _1543804)), _1543806) = hAPP(c_Fun_Ocomp(_1543800, _1543800, _1543800, hAPP(hAPP(c_Nat_Ocompow(_1543800, _1543800), _1543802), _1543806)), hAPP(hAPP(c_Nat_Ocompow(_1543800, _1543800), _1543804), _1543806)))], (39249 ^ _779300) ^ [_1543870, _1543872, _1543874, _1543876, _1543878, _1543880] : [c_Relation_Osingle__valued(_1543870, _1543872, _1543874), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543870, _1543872)), hAPP(hAPP(c_Product__Type_OPair(_1543870, _1543872), _1543876), _1543878)), _1543874)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543870, _1543872)), hAPP(hAPP(c_Product__Type_OPair(_1543870, _1543872), _1543876), _1543880)), _1543874)), -(_1543878 = _1543880)], (39277 ^ _779300) ^ [_1544545, _1544547, _1544549] : [39280 ^ _779300 : [(39281 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544545, _1544547)), hAPP(hAPP(c_Product__Type_OPair(_1544545, _1544547), 39278 ^ [_1544545, _1544547, _1544549]), 39279 ^ [_1544545, _1544547, _1544549])), _1544549)))], (39284 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544545, _1544547)), hAPP(hAPP(c_Product__Type_OPair(_1544545, _1544547), 39278 ^ [_1544545, _1544547, _1544549]), 39282 ^ [_1544545, _1544547, _1544549])), _1544549)))], (39286 ^ _779300) ^ [] : [39279 ^ [_1544545, _1544547, _1544549] = 39282 ^ [_1544545, _1544547, _1544549]]], -(c_Relation_Osingle__valued(_1544545, _1544547, _1544549))], (39263 ^ _779300) ^ [_1544171, _1544173, _1544175] : [c_Relation_Osingle__valued(_1544171, _1544173, _1544175), 39266 ^ _779300 : [(39267 ^ _779300) ^ [_1544292, _1544294] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544171, _1544173)), hAPP(hAPP(c_Product__Type_OPair(_1544171, _1544173), _1544294), _1544292)), _1544175)), 39270 ^ _779300 : [(39271 ^ _779300) ^ [_1544418] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544171, _1544173)), hAPP(hAPP(c_Product__Type_OPair(_1544171, _1544173), _1544294), _1544418)), _1544175)), -(_1544292 = _1544418)]]]]], (39290 ^ _779300) ^ [_1544915, _1544917] : [-(hAPP(hAPP(c_Nat_Ocompow(_1544915, _1544915), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1544917) = c_Fun_Oid(_1544915))], (39292 ^ _779300) ^ [_1544969, _1544971, _1544973] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544969, _1544969)), _1544971), c_Transitive__Closure_Otrancl(_1544969, _1544973))), 39296 ^ _779300 : [(39297 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 39295 ^ [_1544969, _1544971, _1544973])))], (39299 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544969, _1544969)), _1544971), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1544969, _1544969), tc_HOL_Obool), 39295 ^ [_1544969, _1544971, _1544973]), _1544973))))]]], (39301 ^ _779300) ^ [_1545167, _1545169, _1545171] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545167, _1545167)), _1545169), c_Transitive__Closure_Otrancl(_1545167, _1545171)))), 39302 ^ _779300 : [(39303 ^ _779300) ^ [_1545246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1545246)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1545167, _1545167)), _1545169), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1545167, _1545167), tc_HOL_Obool), _1545246), _1545171)))]]], (39311 ^ _779300) ^ [_1545417, _1545419] : [-(c_Transitive__Closure_Ortrancl(_1545417, _1545419) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1545417, _1545417), 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(_1545417, _1545417), tc_HOL_Obool), tc_fun(tc_prod(_1545417, _1545417), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1545417, _1545417), tc_HOL_Obool)), _1545419)))], (39313 ^ _779300) ^ [_1545488, _1545490, _1545492, _1545494, _1545496] : [c_Relation_Osingle__valued(_1545488, _1545488, _1545490), hBOOL(hAPP(hAPP(c_member(tc_prod(_1545488, _1545488)), hAPP(hAPP(c_Product__Type_OPair(_1545488, _1545488), _1545492), _1545494)), c_Transitive__Closure_Ortrancl(_1545488, _1545490))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1545488, _1545488)), hAPP(hAPP(c_Product__Type_OPair(_1545488, _1545488), _1545492), _1545496)), c_Transitive__Closure_Ortrancl(_1545488, _1545490))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545488, _1545488)), hAPP(hAPP(c_Product__Type_OPair(_1545488, _1545488), _1545494), _1545496)), c_Transitive__Closure_Ortrancl(_1545488, _1545490)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545488, _1545488)), hAPP(hAPP(c_Product__Type_OPair(_1545488, _1545488), _1545496), _1545494)), c_Transitive__Closure_Ortrancl(_1545488, _1545490))))], (39331 ^ _779300) ^ [_1545878] : [-(c_Nat_Ofunpow(_1545878) = c_Nat_Ocompow(_1545878, _1545878))], (39333 ^ _779300) ^ [_1545906, _1545908, _1545910, _1545912, _1545914] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545906, _1545906)), hAPP(hAPP(c_Product__Type_OPair(_1545906, _1545906), _1545908), _1545910)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1545906, _1545906), tc_HOL_Obool), _1545912), _1545914))), 39338 ^ _779300 : [(39339 ^ _779300) ^ [] : [-(_1545912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39341 ^ _779300) ^ [] : [-(_1545908 = _1545910)]], 39344 ^ _779300 : [(39345 ^ _779300) ^ [] : [-(_1545912 = hAPP(c_Nat_OSuc, 39343 ^ [_1545906, _1545908, _1545910, _1545912, _1545914]))], (39347 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545906, _1545906)), hAPP(hAPP(c_Product__Type_OPair(_1545906, _1545906), _1545908), 39342 ^ [_1545906, _1545908, _1545910, _1545912, _1545914])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1545906, _1545906), tc_HOL_Obool), 39343 ^ [_1545906, _1545908, _1545910, _1545912, _1545914]), _1545914))))], (39349 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545906, _1545906)), hAPP(hAPP(c_Product__Type_OPair(_1545906, _1545906), 39342 ^ [_1545906, _1545908, _1545910, _1545912, _1545914]), _1545910)), _1545914)))]]], (39351 ^ _779300) ^ [_1546348, _1546350, _1546352, _1546354, _1546356] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546348, _1546348)), hAPP(hAPP(c_Product__Type_OPair(_1546348, _1546348), _1546350), _1546352)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1546348, _1546348), tc_HOL_Obool), _1546354), _1546356))), 39356 ^ _779300 : [(39357 ^ _779300) ^ [] : [-(_1546354 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39359 ^ _779300) ^ [] : [-(_1546350 = _1546352)]], 39362 ^ _779300 : [(39363 ^ _779300) ^ [] : [-(_1546354 = hAPP(c_Nat_OSuc, 39361 ^ [_1546348, _1546350, _1546352, _1546354, _1546356]))], (39365 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546348, _1546348)), hAPP(hAPP(c_Product__Type_OPair(_1546348, _1546348), _1546350), 39360 ^ [_1546348, _1546350, _1546352, _1546354, _1546356])), _1546356)))], (39367 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546348, _1546348)), hAPP(hAPP(c_Product__Type_OPair(_1546348, _1546348), 39360 ^ [_1546348, _1546350, _1546352, _1546354, _1546356]), _1546352)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1546348, _1546348), tc_HOL_Obool), 39361 ^ [_1546348, _1546350, _1546352, _1546354, _1546356]), _1546356))))]]], (39369 ^ _779300) ^ [_1546790, _1546792, _1546794, _1546796, _1546798] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546790, _1546790)), hAPP(hAPP(c_Product__Type_OPair(_1546790, _1546790), _1546792), _1546794)), c_Transitive__Closure_Ortrancl(_1546790, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1546790, _1546790), tc_HOL_Obool)), _1546796), _1546798)))), 39375 ^ _779300 : [(39376 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546790, _1546790)), hAPP(hAPP(c_Product__Type_OPair(_1546790, _1546790), _1546792), 39374 ^ [_1546790, _1546792, _1546794, _1546796, _1546798])), c_Transitive__Closure_Ortrancl(_1546790, _1546796))))], (39379 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546790, _1546790)), hAPP(hAPP(c_Product__Type_OPair(_1546790, _1546790), 39374 ^ [_1546790, _1546792, _1546794, _1546796, _1546798]), 39377 ^ [_1546790, _1546792, _1546794, _1546796, _1546798])), _1546798)))], (39381 ^ _779300) ^ [] : [39374 ^ [_1546790, _1546792, _1546794, _1546796, _1546798] = 39377 ^ [_1546790, _1546792, _1546794, _1546796, _1546798]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546790, _1546790)), hAPP(hAPP(c_Product__Type_OPair(_1546790, _1546790), _1546792), _1546794)), c_Transitive__Closure_Ortrancl(_1546790, _1546796))))], (39385 ^ _779300) ^ [_1547349, _1547351, _1547353, _1547355, _1547357] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547349, _1547349)), hAPP(hAPP(c_Product__Type_OPair(_1547349, _1547349), _1547351), _1547353)), c_Transitive__Closure_Ortrancl(_1547349, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1547349, _1547349), tc_HOL_Obool)), _1547355), _1547357)))), 39391 ^ _779300 : [(39392 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547349, _1547349)), hAPP(hAPP(c_Product__Type_OPair(_1547349, _1547349), 39390 ^ [_1547349, _1547351, _1547353, _1547355, _1547357]), _1547353)), c_Transitive__Closure_Ortrancl(_1547349, _1547355))))], (39395 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547349, _1547349)), hAPP(hAPP(c_Product__Type_OPair(_1547349, _1547349), 39393 ^ [_1547349, _1547351, _1547353, _1547355, _1547357]), 39390 ^ [_1547349, _1547351, _1547353, _1547355, _1547357])), _1547357)))], (39397 ^ _779300) ^ [] : [39393 ^ [_1547349, _1547351, _1547353, _1547355, _1547357] = 39390 ^ [_1547349, _1547351, _1547353, _1547355, _1547357]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547349, _1547349)), hAPP(hAPP(c_Product__Type_OPair(_1547349, _1547349), _1547351), _1547353)), c_Transitive__Closure_Ortrancl(_1547349, _1547355))))], (39401 ^ _779300) ^ [_1547908, _1547910, _1547912, _1547914, _1547916] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547908, _1547908)), hAPP(hAPP(c_Product__Type_OPair(_1547908, _1547908), _1547910), _1547912)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1547908, _1547908), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1547914)), _1547916))), 39405 ^ _779300 : [(39406 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547908, _1547908)), hAPP(hAPP(c_Product__Type_OPair(_1547908, _1547908), _1547910), 39404 ^ [_1547908, _1547910, _1547912, _1547914, _1547916])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1547908, _1547908), tc_HOL_Obool), _1547914), _1547916))))], (39408 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547908, _1547908)), hAPP(hAPP(c_Product__Type_OPair(_1547908, _1547908), 39404 ^ [_1547908, _1547910, _1547912, _1547914, _1547916]), _1547912)), _1547916)))]]], (39410 ^ _779300) ^ [_1548220, _1548222, _1548224, _1548226, _1548228] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548220, _1548220)), hAPP(hAPP(c_Product__Type_OPair(_1548220, _1548220), _1548222), _1548224)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1548220, _1548220), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1548226)), _1548228))), 39414 ^ _779300 : [(39415 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548220, _1548220)), hAPP(hAPP(c_Product__Type_OPair(_1548220, _1548220), _1548222), 39413 ^ [_1548220, _1548222, _1548224, _1548226, _1548228])), _1548228)))], (39417 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548220, _1548220)), hAPP(hAPP(c_Product__Type_OPair(_1548220, _1548220), 39413 ^ [_1548220, _1548222, _1548224, _1548226, _1548228]), _1548224)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1548220, _1548220), tc_HOL_Obool), _1548226), _1548228))))]]], (39419 ^ _779300) ^ [_1548528, _1548530, _1548532, _1548534, _1548536] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548528, _1548528)), hAPP(hAPP(c_Product__Type_OPair(_1548528, _1548528), _1548530), _1548532)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1548528, _1548528), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1548534)), _1548536))), 39423 ^ _779300 : [(39424 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548528, _1548528)), hAPP(hAPP(c_Product__Type_OPair(_1548528, _1548528), _1548530), 39422 ^ [_1548528, _1548530, _1548532, _1548534, _1548536])), _1548536)))], (39426 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548528, _1548528)), hAPP(hAPP(c_Product__Type_OPair(_1548528, _1548528), 39422 ^ [_1548528, _1548530, _1548532, _1548534, _1548536]), _1548532)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1548528, _1548528), tc_HOL_Obool), _1548534), _1548536))))]]], (39428 ^ _779300) ^ [_1548840, _1548842, _1548844, _1548846] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548840, _1548840)), hAPP(hAPP(c_Product__Type_OPair(_1548840, _1548840), _1548842), _1548844)), c_Transitive__Closure_Otrancl(_1548840, _1548846))), 39432 ^ _779300 : [(39433 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548840, _1548840)), hAPP(hAPP(c_Product__Type_OPair(_1548840, _1548840), _1548842), 39431 ^ [_1548840, _1548842, _1548844, _1548846])), _1548846)))], (39435 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548840, _1548840)), hAPP(hAPP(c_Product__Type_OPair(_1548840, _1548840), 39431 ^ [_1548840, _1548842, _1548844, _1548846]), _1548844)), c_Transitive__Closure_Ortrancl(_1548840, _1548846))))]]], (39437 ^ _779300) ^ [_1549100, _1549102, _1549104, _1549106] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549100, _1549100)), hAPP(hAPP(c_Product__Type_OPair(_1549100, _1549100), _1549102), _1549104)), c_Transitive__Closure_Otrancl(_1549100, _1549106))), 39441 ^ _779300 : [(39442 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549100, _1549100)), hAPP(hAPP(c_Product__Type_OPair(_1549100, _1549100), _1549102), 39440 ^ [_1549100, _1549102, _1549104, _1549106])), c_Transitive__Closure_Ortrancl(_1549100, _1549106))))], (39444 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549100, _1549100)), hAPP(hAPP(c_Product__Type_OPair(_1549100, _1549100), 39440 ^ [_1549100, _1549102, _1549104, _1549106]), _1549104)), _1549106)))]]], (39446 ^ _779300) ^ [_1549360, _1549362] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549360, _1549360)), _1549362), c_Relation_OId(_1549360))), -(_1549362 = hAPP(hAPP(c_Product__Type_OPair(_1549360, _1549360), 39449 ^ [_1549360, _1549362]), 39449 ^ [_1549360, _1549362]))], (39453 ^ _779300) ^ [_1549502, _1549504, _1549506] : [class_Orderings_Olinorder(_1549502), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549502), _1549504)), -(hBOOL(hAPP(hAPP(c_member(_1549502), _1549506), _1549504))), -(c_Big__Operators_Olattice_OSup__fin(_1549502, c_Orderings_Oord__class_Omax(_1549502), hAPP(hAPP(c_Set_Oinsert(_1549502), _1549506), _1549504)) = hAPP(hAPP(c_Finite__Set_Ofold(_1549502, _1549502, c_Orderings_Oord__class_Omax(_1549502)), _1549506), _1549504))], (39467 ^ _779300) ^ [_1549722, _1549724, _1549726, _1549728] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1549722, _1549724, _1549726), _1549728), c_Orderings_Obot__class_Obot(tc_fun(_1549722, tc_HOL_Obool))) = _1549728)], (39469 ^ _779300) ^ [_1549766, _1549768, _1549770, _1549772] : [-(hAPP(c_Finite__Set_Ofold__image(_1549766, _1549768, _1549770), _1549772) = c_Finite__Set_Ofold(_1549768, _1549766, hAPP(hAPP(c_COMBB(_1549766, tc_fun(_1549766, _1549766), _1549768), _1549770), _1549772)))], (39471 ^ _779300) ^ [_1549819, _1549821, _1549823, _1549825, _1549827, _1549829] : [c_Finite__Set_Ofolding(_1549819, _1549821, _1549823, _1549825), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549819), _1549827)), -(hAPP(hAPP(_1549825, _1549827), _1549829) = hAPP(hAPP(c_Finite__Set_Ofold(_1549819, _1549821, _1549823), _1549829), _1549827))], (39481 ^ _779300) ^ [_1550008, _1550010, _1550012, _1550014, _1550016] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1550008, _1550010, _1550012), _1550014), _1550016) = c_HOL_OThe(_1550010, c_Finite__Set_Ofold__graph(_1550008, _1550010, _1550012, _1550014, _1550016)))], (39483 ^ _779300) ^ [_1550058, _1550060, _1550062] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1550058), _1550060)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1550058, tc_HOL_Obool)), _1550060), _1550062) = hAPP(hAPP(c_Finite__Set_Ofold(_1550058, tc_fun(_1550058, tc_HOL_Obool), c_Set_Oinsert(_1550058)), _1550062), _1550060))], (39489 ^ _779300) ^ [_1550197, _1550199, _1550201, _1550203] : [class_Lattices_Osemilattice__sup(_1550197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550197), _1550199)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1550197, _1550197, c_Lattices_Osemilattice__sup__class_Osup(_1550197)), _1550201), hAPP(hAPP(c_Set_Oinsert(_1550197), _1550203), _1550199)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1550197), _1550203), hAPP(hAPP(c_Finite__Set_Ofold(_1550197, _1550197, c_Lattices_Osemilattice__sup__class_Osup(_1550197)), _1550201), _1550199)))], (39499 ^ _779300) ^ [_1550420, _1550422, _1550424, _1550426] : [class_Lattices_Osemilattice__inf(_1550420), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550420), _1550422)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1550420, _1550420, c_Lattices_Osemilattice__inf__class_Oinf(_1550420)), _1550424), hAPP(hAPP(c_Set_Oinsert(_1550420), _1550426), _1550422)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1550420), _1550426), hAPP(hAPP(c_Finite__Set_Ofold(_1550420, _1550420, c_Lattices_Osemilattice__inf__class_Oinf(_1550420)), _1550424), _1550422)))], (39509 ^ _779300) ^ [_1550643, _1550645, _1550647, _1550649] : [class_Orderings_Olinorder(_1550643), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550643), _1550645)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1550643, _1550643, c_Orderings_Oord__class_Omin(_1550643)), _1550647), hAPP(hAPP(c_Set_Oinsert(_1550643), _1550649), _1550645)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1550643), _1550649), hAPP(hAPP(c_Finite__Set_Ofold(_1550643, _1550643, c_Orderings_Oord__class_Omin(_1550643)), _1550647), _1550645)))], (39519 ^ _779300) ^ [_1550866, _1550868, _1550870, _1550872] : [class_Orderings_Olinorder(_1550866), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550866), _1550868)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1550866, _1550866, c_Orderings_Oord__class_Omax(_1550866)), _1550870), hAPP(hAPP(c_Set_Oinsert(_1550866), _1550872), _1550868)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1550866), _1550872), hAPP(hAPP(c_Finite__Set_Ofold(_1550866, _1550866, c_Orderings_Oord__class_Omax(_1550866)), _1550870), _1550868)))], (39529 ^ _779300) ^ [_1551089, _1551091, _1551093, _1551095, _1551097, _1551099] : [c_Finite__Set_Ofun__left__comm__idem(_1551089, _1551091, _1551093), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551089), _1551095)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1551089, _1551091, _1551093), _1551097), hAPP(hAPP(c_Set_Oinsert(_1551089), _1551099), _1551095)) = hAPP(hAPP(_1551093, _1551099), hAPP(hAPP(c_Finite__Set_Ofold(_1551089, _1551091, _1551093), _1551097), _1551095)))], (39539 ^ _779300) ^ [_1551312, _1551314, _1551316, _1551318, _1551320, _1551322] : [c_Finite__Set_Ofun__left__comm__idem(_1551312, _1551314, _1551316), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551312), _1551318)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1551312, _1551314, _1551316), _1551320), hAPP(hAPP(c_Set_Oinsert(_1551312), _1551322), _1551318)) = hAPP(hAPP(c_Finite__Set_Ofold(_1551312, _1551314, _1551316), hAPP(hAPP(_1551316, _1551322), _1551320)), _1551318))], (39549 ^ _779300) ^ [_1551535, _1551537, _1551539, _1551541, _1551543] : [class_Complete__Lattice_Ocomplete__lattice(_1551535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551537), _1551539)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1551535), _1551541), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1551537, _1551535), _1551539), _1551543)) = hAPP(hAPP(c_Finite__Set_Ofold(_1551537, _1551535, hAPP(hAPP(c_COMBB(_1551535, tc_fun(_1551535, _1551535), _1551537), c_Lattices_Osemilattice__sup__class_Osup(_1551535)), _1551543)), _1551541), _1551539))], (39559 ^ _779300) ^ [_1551766, _1551768, _1551770, _1551772, _1551774] : [c_Finite__Set_Ofolding__one__idem(_1551766, _1551768, _1551770), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551766), _1551772)), -(hAPP(_1551770, hAPP(hAPP(c_Set_Oinsert(_1551766), _1551774), _1551772)) = hAPP(hAPP(c_Finite__Set_Ofold(_1551766, _1551766, _1551768), _1551774), _1551772))], (39569 ^ _779300) ^ [_1551959, _1551961, _1551963, _1551965] : [class_Lattices_Osemilattice__sup(_1551959), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551959), _1551961)), hBOOL(hAPP(hAPP(c_member(_1551959), _1551963), _1551961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1551959), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1551959), _1551963), _1551965)), hAPP(hAPP(c_Finite__Set_Ofold(_1551959, _1551959, c_Lattices_Osemilattice__sup__class_Osup(_1551959)), _1551965), _1551961))))], (39583 ^ _779300) ^ [_1552226, _1552228, _1552230, _1552232] : [class_Lattices_Osemilattice__inf(_1552226), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552226), _1552228)), hBOOL(hAPP(hAPP(c_member(_1552226), _1552230), _1552228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552226), hAPP(hAPP(c_Finite__Set_Ofold(_1552226, _1552226, c_Lattices_Osemilattice__inf__class_Oinf(_1552226)), _1552232), _1552228)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1552226), _1552230), _1552232))))], (39597 ^ _779300) ^ [_1552493, _1552495, _1552497, _1552499] : [class_Orderings_Olinorder(_1552493), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552493), _1552495)), hBOOL(hAPP(hAPP(c_member(_1552493), _1552497), _1552495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552493), hAPP(hAPP(c_Finite__Set_Ofold(_1552493, _1552493, c_Orderings_Oord__class_Omin(_1552493)), _1552499), _1552495)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1552493), _1552497), _1552499))))], (39611 ^ _779300) ^ [_1552760, _1552762, _1552764, _1552766] : [class_Orderings_Olinorder(_1552760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552760), _1552762)), hBOOL(hAPP(hAPP(c_member(_1552760), _1552764), _1552762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552760), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1552760), _1552764), _1552766)), hAPP(hAPP(c_Finite__Set_Ofold(_1552760, _1552760, c_Orderings_Oord__class_Omax(_1552760)), _1552766), _1552762))))], (39625 ^ _779300) ^ [_1553027, _1553029, _1553031] : [class_Lattices_Oab__semigroup__idem__mult(_1553027), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553027), _1553029)), -(hAPP(c_Finite__Set_Ofold1(_1553027, c_Groups_Otimes__class_Otimes(_1553027)), hAPP(hAPP(c_Set_Oinsert(_1553027), _1553031), _1553029)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553027, _1553027, c_Groups_Otimes__class_Otimes(_1553027)), _1553031), _1553029))], (39635 ^ _779300) ^ [_1553222, _1553224, _1553226] : [class_Lattices_Olattice(_1553222), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553222), _1553224)), -(c_Big__Operators_Olattice__class_OSup__fin(_1553222, hAPP(hAPP(c_Set_Oinsert(_1553222), _1553226), _1553224)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553222, _1553222, c_Lattices_Osemilattice__sup__class_Osup(_1553222)), _1553226), _1553224))], (39645 ^ _779300) ^ [_1553407, _1553409, _1553411] : [class_Lattices_Olattice(_1553407), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553407), _1553409)), -(c_Big__Operators_Olattice__class_OInf__fin(_1553407, hAPP(hAPP(c_Set_Oinsert(_1553407), _1553411), _1553409)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553407, _1553407, c_Lattices_Osemilattice__inf__class_Oinf(_1553407)), _1553411), _1553409))], (39655 ^ _779300) ^ [_1553592, _1553594, _1553596] : [class_Orderings_Olinorder(_1553592), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553592), _1553594)), -(c_Big__Operators_Olinorder__class_OMin(_1553592, hAPP(hAPP(c_Set_Oinsert(_1553592), _1553596), _1553594)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553592, _1553592, c_Orderings_Oord__class_Omin(_1553592)), _1553596), _1553594))], (39665 ^ _779300) ^ [_1553777, _1553779, _1553781] : [class_Orderings_Olinorder(_1553777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553777), _1553779)), -(c_Big__Operators_Olinorder__class_OMax(_1553777, hAPP(hAPP(c_Set_Oinsert(_1553777), _1553781), _1553779)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553777, _1553777, c_Orderings_Oord__class_Omax(_1553777)), _1553781), _1553779))], (39675 ^ _779300) ^ [_1553962, _1553964, _1553966] : [class_Orderings_Olinorder(_1553962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553962), _1553964)), -(c_Big__Operators_Olattice_OInf__fin(_1553962, c_Orderings_Oord__class_Omin(_1553962), hAPP(hAPP(c_Set_Oinsert(_1553962), _1553966), _1553964)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553962, _1553962, c_Orderings_Oord__class_Omin(_1553962)), _1553966), _1553964))], (39685 ^ _779300) ^ [_1554153, _1554155, _1554157] : [class_Orderings_Olinorder(_1554153), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554153), _1554155)), -(c_Big__Operators_Olattice_OSup__fin(_1554153, c_Orderings_Oord__class_Omax(_1554153), hAPP(hAPP(c_Set_Oinsert(_1554153), _1554157), _1554155)) = hAPP(hAPP(c_Finite__Set_Ofold(_1554153, _1554153, c_Orderings_Oord__class_Omax(_1554153)), _1554157), _1554155))], (39695 ^ _779300) ^ [_1554344, _1554346, _1554348] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1554344), _1554346)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1554344, tc_HOL_Obool)), _1554348), _1554346) = hAPP(hAPP(c_Finite__Set_Ofold(_1554344, tc_fun(_1554344, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1554344, tc_HOL_Obool), tc_fun(tc_fun(_1554344, tc_HOL_Obool), tc_fun(_1554344, tc_HOL_Obool)), _1554344), hAPP(c_COMBC(tc_fun(_1554344, tc_HOL_Obool), tc_fun(_1554344, tc_HOL_Obool), tc_fun(_1554344, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1554344, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1554344, tc_fun(_1554344, tc_HOL_Obool), tc_fun(_1554344, tc_HOL_Obool)), c_Set_Oinsert(_1554344)), c_Orderings_Obot__class_Obot(tc_fun(_1554344, tc_HOL_Obool))))), _1554348), _1554346))], (39701 ^ _779300) ^ [_1554611, _1554613, _1554615, _1554617, _1554619] : [c_Finite__Set_Ofolding__one(_1554611, _1554613, _1554615), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554611), _1554617)), -(hBOOL(hAPP(hAPP(c_member(_1554611), _1554619), _1554617))), -(hAPP(_1554615, hAPP(hAPP(c_Set_Oinsert(_1554611), _1554619), _1554617)) = hAPP(hAPP(c_Finite__Set_Ofold(_1554611, _1554611, _1554613), _1554619), _1554617))], (39715 ^ _779300) ^ [_1554833, _1554835, _1554837, _1554839] : [class_Complete__Lattice_Ocomplete__lattice(_1554833), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554835), _1554837)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1554835, _1554833), _1554837), _1554839) = hAPP(hAPP(c_Finite__Set_Ofold(_1554835, _1554833, hAPP(hAPP(c_COMBB(_1554833, tc_fun(_1554833, _1554833), _1554835), c_Lattices_Osemilattice__sup__class_Osup(_1554833)), _1554839)), c_Orderings_Obot__class_Obot(_1554833)), _1554837))], (39725 ^ _779300) ^ [_1555048, _1555050, _1555052] : [class_Groups_Oab__semigroup__mult(_1555048), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555048), _1555050)), -(hBOOL(hAPP(hAPP(c_member(_1555048), _1555052), _1555050))), -(hAPP(c_Finite__Set_Ofold1(_1555048, c_Groups_Otimes__class_Otimes(_1555048)), hAPP(hAPP(c_Set_Oinsert(_1555048), _1555052), _1555050)) = hAPP(hAPP(c_Finite__Set_Ofold(_1555048, _1555048, c_Groups_Otimes__class_Otimes(_1555048)), _1555052), _1555050))], (39739 ^ _779300) ^ [_1555272, _1555274, _1555276] : [class_Lattices_Olattice(_1555272), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555272), _1555274)), -(hBOOL(hAPP(hAPP(c_member(_1555272), _1555276), _1555274))), -(c_Big__Operators_Olattice__class_OSup__fin(_1555272, hAPP(hAPP(c_Set_Oinsert(_1555272), _1555276), _1555274)) = hAPP(hAPP(c_Finite__Set_Ofold(_1555272, _1555272, c_Lattices_Osemilattice__sup__class_Osup(_1555272)), _1555276), _1555274))], (39753 ^ _779300) ^ [_1555486, _1555488, _1555490] : [class_Lattices_Olattice(_1555486), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555486), _1555488)), -(hBOOL(hAPP(hAPP(c_member(_1555486), _1555490), _1555488))), -(c_Big__Operators_Olattice__class_OInf__fin(_1555486, hAPP(hAPP(c_Set_Oinsert(_1555486), _1555490), _1555488)) = hAPP(hAPP(c_Finite__Set_Ofold(_1555486, _1555486, c_Lattices_Osemilattice__inf__class_Oinf(_1555486)), _1555490), _1555488))], (39767 ^ _779300) ^ [_1555700, _1555702, _1555704] : [class_Orderings_Olinorder(_1555700), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555700), _1555702)), -(hBOOL(hAPP(hAPP(c_member(_1555700), _1555704), _1555702))), -(c_Big__Operators_Olinorder__class_OMin(_1555700, hAPP(hAPP(c_Set_Oinsert(_1555700), _1555704), _1555702)) = hAPP(hAPP(c_Finite__Set_Ofold(_1555700, _1555700, c_Orderings_Oord__class_Omin(_1555700)), _1555704), _1555702))], (39781 ^ _779300) ^ [_1555914, _1555916, _1555918] : [class_Orderings_Olinorder(_1555914), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555914), _1555916)), -(hBOOL(hAPP(hAPP(c_member(_1555914), _1555918), _1555916))), -(c_Big__Operators_Olinorder__class_OMax(_1555914, hAPP(hAPP(c_Set_Oinsert(_1555914), _1555918), _1555916)) = hAPP(hAPP(c_Finite__Set_Ofold(_1555914, _1555914, c_Orderings_Oord__class_Omax(_1555914)), _1555918), _1555916))], (39795 ^ _779300) ^ [_1556128, _1556130, _1556132] : [class_Orderings_Olinorder(_1556128), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556128), _1556130)), -(hBOOL(hAPP(hAPP(c_member(_1556128), _1556132), _1556130))), -(c_Big__Operators_Olattice_OInf__fin(_1556128, c_Orderings_Oord__class_Omin(_1556128), hAPP(hAPP(c_Set_Oinsert(_1556128), _1556132), _1556130)) = hAPP(hAPP(c_Finite__Set_Ofold(_1556128, _1556128, c_Orderings_Oord__class_Omin(_1556128)), _1556132), _1556130))], (39809 ^ _779300) ^ [_1556348, _1556350, _1556352, _1556354, _1556356, _1556358] : [c_Finite__Set_Ofun__left__comm(_1556348, _1556350, _1556352), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556348), _1556354)), hBOOL(hAPP(hAPP(c_member(_1556348), _1556356), _1556354)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1556348, _1556350, _1556352), _1556358), _1556354) = hAPP(hAPP(_1556352, _1556356), hAPP(hAPP(c_Finite__Set_Ofold(_1556348, _1556350, _1556352), _1556358), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1556348, tc_HOL_Obool)), _1556354), hAPP(hAPP(c_Set_Oinsert(_1556348), _1556356), c_Orderings_Obot__class_Obot(tc_fun(_1556348, tc_HOL_Obool)))))))], (39823 ^ _779300) ^ [_1556677, _1556679, _1556681, _1556683, _1556685, _1556687] : [c_Finite__Set_Ofun__left__comm(_1556677, _1556679, _1556681), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556677), _1556683)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1556677, _1556679, _1556681), _1556685), hAPP(hAPP(c_Set_Oinsert(_1556677), _1556687), _1556683)) = hAPP(hAPP(_1556681, _1556687), hAPP(hAPP(c_Finite__Set_Ofold(_1556677, _1556679, _1556681), _1556685), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1556677, tc_HOL_Obool)), _1556683), hAPP(hAPP(c_Set_Oinsert(_1556677), _1556687), c_Orderings_Obot__class_Obot(tc_fun(_1556677, tc_HOL_Obool)))))))], (39833 ^ _779300) ^ [_1556948, _1556950, _1556952, _1556954] : [class_Complete__Lattice_Ocomplete__lattice(_1556948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556950), _1556952)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1556950, _1556948), _1556952), _1556954) = hAPP(hAPP(c_Finite__Set_Ofold(_1556950, _1556948, hAPP(hAPP(c_COMBB(_1556948, tc_fun(_1556948, _1556948), _1556950), c_Lattices_Osemilattice__inf__class_Oinf(_1556948)), _1556954)), c_Orderings_Otop__class_Otop(_1556948)), _1556952))], (39843 ^ _779300) ^ [_1557163, _1557165, _1557167, _1557169, _1557171, _1557173] : [hBOOL(hAPP(hAPP(c_member(_1557163), _1557165), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1557167, tc_fun(_1557163, tc_HOL_Obool)), _1557169), _1557171))), hBOOL(hAPP(hAPP(c_member(_1557167), _1557173), _1557169)), -(hBOOL(hAPP(hAPP(c_member(_1557163), _1557165), hAPP(_1557171, _1557173))))], (39853 ^ _779300) ^ [_1557380, _1557382, _1557384, _1557386, _1557388, _1557390] : [hBOOL(hAPP(hAPP(c_member(_1557380), _1557382), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1557384, tc_fun(_1557380, tc_HOL_Obool)), _1557386), _1557388))), -(hBOOL(hAPP(hAPP(c_member(_1557380), _1557382), hAPP(_1557388, _1557390)))), hBOOL(hAPP(hAPP(c_member(_1557384), _1557390), _1557386))], (39863 ^ _779300) ^ [_1557601, _1557603, _1557605, _1557607, _1557609, _1557611] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1557601, tc_fun(_1557603, tc_HOL_Obool)), _1557605), _1557607), _1557609)), hBOOL(hAPP(hAPP(c_member(_1557601), _1557611), _1557605)), -(hBOOL(hAPP(hAPP(_1557607, _1557611), _1557609)))], (39873 ^ _779300) ^ [_1557798, _1557800, _1557802, _1557804, _1557806, _1557808] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1557798, tc_fun(_1557800, tc_HOL_Obool)), _1557802), _1557804), _1557806)), -(hBOOL(hAPP(hAPP(_1557804, _1557808), _1557806))), hBOOL(hAPP(hAPP(c_member(_1557798), _1557808), _1557802))], (39883 ^ _779300) ^ [_1557999, _1558001, _1558003, _1558005, _1558007, _1558009, _1558011, _1558013] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1557999, tc_fun(_1558001, tc_fun(_1558003, tc_HOL_Obool))), _1558005), _1558007), _1558009), _1558011)), hBOOL(hAPP(hAPP(c_member(_1557999), _1558013), _1558005)), -(hBOOL(hAPP(hAPP(hAPP(_1558007, _1558013), _1558009), _1558011)))], (39893 ^ _779300) ^ [_1558222, _1558224, _1558226, _1558228, _1558230, _1558232, _1558234, _1558236] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558222, tc_fun(_1558224, tc_fun(_1558226, tc_HOL_Obool))), _1558228), _1558230), _1558232), _1558234)), -(hBOOL(hAPP(hAPP(hAPP(_1558230, _1558236), _1558232), _1558234))), hBOOL(hAPP(hAPP(c_member(_1558222), _1558236), _1558228))], (39903 ^ _779300) ^ [_1558449, _1558451, _1558453, _1558455] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1558453), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558449, tc_fun(_1558453, tc_HOL_Obool)), _1558451), _1558455)))), 39904 ^ _779300 : [(39905 ^ _779300) ^ [_1558523] : [hBOOL(hAPP(hAPP(c_member(_1558449), _1558523), _1558451)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558453), hAPP(_1558455, _1558523)))]]], (39913 ^ _779300) ^ [_1558692, _1558694, _1558696, _1558698] : [_1558692 = c_Orderings_Obot__class_Obot(tc_fun(_1558694, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558694, tc_fun(_1558696, tc_HOL_Obool)), _1558692), hAPP(c_COMBK(tc_fun(_1558696, tc_HOL_Obool), _1558694), _1558698)) = c_Orderings_Otop__class_Otop(tc_fun(_1558696, tc_HOL_Obool)))], (39919 ^ _779300) ^ [_1558829, _1558831, _1558833, _1558835] : [-(_1558829 = c_Orderings_Obot__class_Obot(tc_fun(_1558831, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558831, tc_fun(_1558833, tc_HOL_Obool)), _1558829), hAPP(c_COMBK(tc_fun(_1558833, tc_HOL_Obool), _1558831), _1558835)) = _1558835)], (39925 ^ _779300) ^ [_1558897, _1558899, _1558901] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558897, tc_fun(_1558899, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1558897, tc_HOL_Obool))), _1558901) = c_Orderings_Otop__class_Otop(tc_fun(_1558899, tc_HOL_Obool)))], (39927 ^ _779300) ^ [_1558946, _1558948, _1558950, _1558952, _1558954, _1558956] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558946, tc_fun(_1558948, tc_HOL_Obool)), _1558950), hAPP(hAPP(c_COMBC(_1558946, tc_fun(_1558952, tc_fun(_1558948, tc_HOL_Obool)), tc_fun(_1558948, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558952, tc_HOL_Obool), tc_fun(tc_fun(_1558952, tc_fun(_1558948, tc_HOL_Obool)), tc_fun(_1558948, tc_HOL_Obool)), _1558946), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558952, tc_fun(_1558948, tc_HOL_Obool))), _1558954)), _1558956)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558952, tc_fun(_1558948, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1558946, tc_fun(_1558952, tc_HOL_Obool)), _1558950), _1558954)), _1558956))], (39929 ^ _779300) ^ [_1559065, _1559067, _1559069, _1559071, _1559073, _1559075] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559065, tc_fun(_1559067, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1559069, tc_fun(_1559065, tc_HOL_Obool)), _1559071), _1559073)), _1559075) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559069, tc_fun(_1559067, tc_HOL_Obool)), _1559071), hAPP(hAPP(c_COMBC(_1559069, tc_fun(_1559065, tc_fun(_1559067, tc_HOL_Obool)), tc_fun(_1559067, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559065, tc_HOL_Obool), tc_fun(tc_fun(_1559065, tc_fun(_1559067, tc_HOL_Obool)), tc_fun(_1559067, tc_HOL_Obool)), _1559069), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559065, tc_fun(_1559067, tc_HOL_Obool))), _1559073)), _1559075)))], (39931 ^ _779300) ^ [_1559184, _1559186, _1559188, _1559190, _1559192] : [class_Complete__Lattice_Ocomplete__lattice(_1559184), 39934 ^ _779300 : [(39945 ^ _779300) ^ [] : [39947 ^ _779300 : [(39948 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559188), 39946 ^ [_1559184, _1559186, _1559188, _1559190, _1559192]), _1559190)))], (39950 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1559184), _1559186), hAPP(_1559192, 39946 ^ [_1559184, _1559186, _1559188, _1559190, _1559192])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1559184), _1559186), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559188, _1559184), _1559190), _1559192))))], (39935 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1559184), _1559186), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559188, _1559184), _1559190), _1559192))), 39938 ^ _779300 : [(39939 ^ _779300) ^ [_1559365] : [hBOOL(hAPP(hAPP(c_member(_1559188), _1559365), _1559190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1559184), _1559186), hAPP(_1559192, _1559365))))]]]]], (39954 ^ _779300) ^ [_1559678, _1559680, _1559682, _1559684, _1559686] : [class_Complete__Lattice_Ocomplete__lattice(_1559678), class_Orderings_Olinorder(_1559678), 39961 ^ _779300 : [(39962 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1559678), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559680, _1559678), _1559682), _1559684)), _1559686)), 39966 ^ _779300 : [(39967 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559680), 39965 ^ [_1559678, _1559680, _1559682, _1559684, _1559686]), _1559682)))], (39969 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1559678), hAPP(_1559684, 39965 ^ [_1559678, _1559680, _1559682, _1559684, _1559686])), _1559686)))]]], (39971 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1559678), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559680, _1559678), _1559682), _1559684)), _1559686))), 39972 ^ _779300 : [(39973 ^ _779300) ^ [_1560026] : [hBOOL(hAPP(hAPP(c_member(_1559680), _1560026), _1559682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1559678), hAPP(_1559684, _1560026)), _1559686))]]]]], (39981 ^ _779300) ^ [_1560196, _1560198, _1560200, _1560202, _1560204, _1560206] : [hBOOL(hAPP(hAPP(c_member(_1560196), _1560198), _1560200)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1560196, tc_fun(_1560202, tc_HOL_Obool)), _1560200), hAPP(hAPP(c_COMBB(tc_fun(_1560202, tc_HOL_Obool), tc_fun(_1560202, tc_HOL_Obool), _1560196), hAPP(c_Set_Oinsert(_1560202), _1560204)), _1560206)) = hAPP(hAPP(c_Set_Oinsert(_1560202), _1560204), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1560196, tc_fun(_1560202, tc_HOL_Obool)), _1560200), _1560206)))], (39997 ^ _779300) ^ [_1560668, _1560670, _1560672, _1560674, _1560676] : [39999 ^ _779300 : [(40000 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560672), 39998 ^ [_1560668, _1560670, _1560672, _1560674, _1560676]), _1560674)))], (40002 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1560668), _1560670), hAPP(_1560676, 39998 ^ [_1560668, _1560670, _1560672, _1560674, _1560676])))]], -(hBOOL(hAPP(hAPP(c_member(_1560668), _1560670), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1560672, tc_fun(_1560668, tc_HOL_Obool)), _1560674), _1560676))))], (39987 ^ _779300) ^ [_1560425, _1560427, _1560429, _1560431, _1560433] : [hBOOL(hAPP(hAPP(c_member(_1560425), _1560427), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1560429, tc_fun(_1560425, tc_HOL_Obool)), _1560431), _1560433))), 39990 ^ _779300 : [(39991 ^ _779300) ^ [_1560549] : [hBOOL(hAPP(hAPP(c_member(_1560429), _1560549), _1560431)), -(hBOOL(hAPP(hAPP(c_member(_1560425), _1560427), hAPP(_1560433, _1560549))))]]], (40006 ^ _779300) ^ [_1560943, _1560945, _1560947, _1560949, _1560951, _1560953] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1560943, tc_fun(_1560945, tc_fun(_1560947, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1560943, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1560945, _1560947), tc_HOL_Obool), tc_fun(_1560945, tc_fun(_1560947, tc_HOL_Obool)), _1560943), hAPP(c_COMBC(_1560945, tc_fun(tc_prod(_1560945, _1560947), tc_HOL_Obool), tc_fun(_1560947, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560947, tc_fun(tc_fun(tc_prod(_1560945, _1560947), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1560945, _1560947), tc_HOL_Obool), tc_fun(_1560947, tc_HOL_Obool)), _1560945), c_COMBC(_1560947, tc_fun(tc_prod(_1560945, _1560947), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560947, tc_prod(_1560945, _1560947)), tc_fun(_1560947, tc_fun(tc_fun(tc_prod(_1560945, _1560947), tc_HOL_Obool), tc_HOL_Obool)), _1560945), hAPP(c_COMBB(tc_prod(_1560945, _1560947), tc_fun(tc_fun(tc_prod(_1560945, _1560947), tc_HOL_Obool), tc_HOL_Obool), _1560947), c_member(tc_prod(_1560945, _1560947)))), c_Product__Type_OPair(_1560945, _1560947))))), _1560949)), _1560951), _1560953)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560945, _1560947)), hAPP(hAPP(c_Product__Type_OPair(_1560945, _1560947), _1560951), _1560953)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1560943, tc_fun(tc_prod(_1560945, _1560947), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1560943, tc_HOL_Obool))), _1560949))))], (40012 ^ _779300) ^ [_1561426, _1561428, _1561430, _1561432, _1561434, _1561436] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561428, _1561430)), hAPP(hAPP(c_Product__Type_OPair(_1561428, _1561430), _1561434), _1561436)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1561426, tc_fun(tc_prod(_1561428, _1561430), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1561426, tc_HOL_Obool))), _1561432))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1561426, tc_fun(_1561428, tc_fun(_1561430, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1561426, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1561428, _1561430), tc_HOL_Obool), tc_fun(_1561428, tc_fun(_1561430, tc_HOL_Obool)), _1561426), hAPP(c_COMBC(_1561428, tc_fun(tc_prod(_1561428, _1561430), tc_HOL_Obool), tc_fun(_1561430, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1561430, tc_fun(tc_fun(tc_prod(_1561428, _1561430), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1561428, _1561430), tc_HOL_Obool), tc_fun(_1561430, tc_HOL_Obool)), _1561428), c_COMBC(_1561430, tc_fun(tc_prod(_1561428, _1561430), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1561430, tc_prod(_1561428, _1561430)), tc_fun(_1561430, tc_fun(tc_fun(tc_prod(_1561428, _1561430), tc_HOL_Obool), tc_HOL_Obool)), _1561428), hAPP(c_COMBB(tc_prod(_1561428, _1561430), tc_fun(tc_fun(tc_prod(_1561428, _1561430), tc_HOL_Obool), tc_HOL_Obool), _1561430), c_member(tc_prod(_1561428, _1561430)))), c_Product__Type_OPair(_1561428, _1561430))))), _1561432)), _1561434), _1561436)))], (40028 ^ _779300) ^ [_1562165, _1562167, _1562169, _1562171] : [40030 ^ _779300 : [(40031 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562167), 40029 ^ [_1562165, _1562167, _1562169, _1562171]), _1562169)))], (40033 ^ _779300) ^ [] : [hAPP(_1562171, 40029 ^ [_1562165, _1562167, _1562169, _1562171]) = c_Orderings_Otop__class_Otop(tc_fun(_1562165, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1562165, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1562167, tc_fun(_1562165, tc_HOL_Obool)), _1562169), _1562171))], (40018 ^ _779300) ^ [_1561936, _1561938, _1561940, _1561942] : [c_Orderings_Otop__class_Otop(tc_fun(_1561936, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1561938, tc_fun(_1561936, tc_HOL_Obool)), _1561940), _1561942), 40021 ^ _779300 : [(40022 ^ _779300) ^ [_1562052] : [hBOOL(hAPP(hAPP(c_member(_1561938), _1562052), _1561940)), -(hAPP(_1561942, _1562052) = c_Orderings_Otop__class_Otop(tc_fun(_1561936, tc_HOL_Obool)))]]], (40047 ^ _779300) ^ [_1562645, _1562647, _1562649, _1562651] : [40049 ^ _779300 : [(40050 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562645), 40048 ^ [_1562645, _1562647, _1562649, _1562651]), _1562649)))], (40052 ^ _779300) ^ [] : [hAPP(_1562651, 40048 ^ [_1562645, _1562647, _1562649, _1562651]) = c_Orderings_Otop__class_Otop(tc_fun(_1562647, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1562645, tc_fun(_1562647, tc_HOL_Obool)), _1562649), _1562651) = c_Orderings_Otop__class_Otop(tc_fun(_1562647, tc_HOL_Obool)))], (40037 ^ _779300) ^ [_1562416, _1562418, _1562420, _1562422] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1562416, tc_fun(_1562418, tc_HOL_Obool)), _1562420), _1562422) = c_Orderings_Otop__class_Otop(tc_fun(_1562418, tc_HOL_Obool)), 40040 ^ _779300 : [(40041 ^ _779300) ^ [_1562532] : [hBOOL(hAPP(hAPP(c_member(_1562416), _1562532), _1562420)), -(hAPP(_1562422, _1562532) = c_Orderings_Otop__class_Otop(tc_fun(_1562418, tc_HOL_Obool)))]]], (40056 ^ _779300) ^ [_1562875, _1562877, _1562879, _1562881, _1562883] : [c_Finite__Set_Ofun__left__comm(_1562875, _1562877, _1562879), -(c_Finite__Set_Ofun__left__comm(_1562881, _1562877, hAPP(hAPP(c_COMBB(_1562875, tc_fun(_1562877, _1562877), _1562881), _1562879), _1562883)))], (40062 ^ _779300) ^ [_1562988, _1562990, _1562992, _1562994, _1562996, _1562998] : [c_Finite__Set_Ofun__left__comm(_1562988, _1562990, _1562992), -(hAPP(hAPP(_1562992, _1562994), hAPP(hAPP(_1562992, _1562996), _1562998)) = hAPP(hAPP(_1562992, _1562996), hAPP(hAPP(_1562992, _1562994), _1562998)))], (40068 ^ _779300) ^ [_1563123, _1563125, _1563127, _1563129, _1563131] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563123, tc_fun(_1563125, tc_HOL_Obool)), _1563127), hAPP(hAPP(c_COMBS(_1563123, tc_fun(_1563125, tc_HOL_Obool), tc_fun(_1563125, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1563125, tc_HOL_Obool), tc_fun(tc_fun(_1563125, tc_HOL_Obool), tc_fun(_1563125, tc_HOL_Obool)), _1563123), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1563125, tc_HOL_Obool))), _1563129)), _1563131)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1563125, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563123, tc_fun(_1563125, tc_HOL_Obool)), _1563127), _1563129)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563123, tc_fun(_1563125, tc_HOL_Obool)), _1563127), _1563131)))], (40070 ^ _779300) ^ [_1563244, _1563246, _1563248, _1563250, _1563252, _1563254] : [class_Complete__Lattice_Ocomplete__lattice(_1563244), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563246, _1563244), _1563248), hAPP(hAPP(c_COMBB(tc_fun(_1563250, _1563244), _1563244, _1563246), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563250, _1563244), _1563252)), _1563254)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563250, _1563244), _1563252), hAPP(hAPP(c_COMBB(tc_fun(_1563246, _1563244), _1563244, _1563250), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563246, _1563244), _1563248)), hAPP(c_COMBC(_1563246, _1563250, _1563244), _1563254))))], (40076 ^ _779300) ^ [_1563453, _1563455, _1563457, _1563459, _1563461, _1563463] : [class_Complete__Lattice_Ocomplete__lattice(_1563453), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563455, tc_fun(_1563457, _1563453)), _1563459), _1563461), _1563463) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563455, _1563453), _1563459), hAPP(hAPP(c_COMBC(_1563455, _1563457, _1563453), _1563461), _1563463)))], (40082 ^ _779300) ^ [_1563604, _1563606, _1563608, _1563610] : [-(hAPP(c_Set_OPow(_1563604), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563606, tc_fun(_1563604, tc_HOL_Obool)), _1563608), _1563610)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563606, tc_fun(tc_fun(_1563604, tc_HOL_Obool), tc_HOL_Obool)), _1563608), hAPP(hAPP(c_COMBB(tc_fun(_1563604, tc_HOL_Obool), tc_fun(tc_fun(_1563604, tc_HOL_Obool), tc_HOL_Obool), _1563606), c_Set_OPow(_1563604)), _1563610)))], (40084 ^ _779300) ^ [_1563686] : [class_Groups_Oab__semigroup__mult(_1563686), -(c_Finite__Set_Ofun__left__comm(_1563686, _1563686, c_Groups_Otimes__class_Otimes(_1563686)))], (40090 ^ _779300) ^ [_1563765, _1563767, _1563769, _1563771, _1563773, _1563775] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563765, tc_fun(_1563767, tc_HOL_Obool)), _1563769), hAPP(hAPP(c_COMBB(_1563771, tc_fun(_1563767, tc_HOL_Obool), _1563765), _1563773), _1563775)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563771, tc_fun(_1563767, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1563765, _1563771, _1563775), _1563769)), _1563773))], (40092 ^ _779300) ^ [_1563842, _1563844, _1563846, _1563848, _1563850, _1563852] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563842, tc_fun(_1563844, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1563846, _1563842, _1563848), _1563850)), _1563852) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563846, tc_fun(_1563844, tc_HOL_Obool)), _1563850), hAPP(hAPP(c_COMBB(_1563842, tc_fun(_1563844, tc_HOL_Obool), _1563846), _1563852), _1563848)))], (40094 ^ _779300) ^ [_1563919, _1563921, _1563923, _1563925, _1563927] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563919, tc_fun(_1563921, tc_HOL_Obool)), _1563923), hAPP(hAPP(c_COMBB(tc_fun(_1563921, tc_HOL_Obool), tc_fun(_1563921, tc_HOL_Obool), _1563919), hAPP(c_Set_Oinsert(_1563921), _1563925)), _1563927)) = hAPP(hAPP(c_Set_Oinsert(_1563921), _1563925), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563919, tc_fun(_1563921, tc_HOL_Obool)), _1563923), _1563927)))], (40096 ^ _779300) ^ [_1564003, _1564005, _1564007, _1564009, _1564011] : [-(hAPP(hAPP(c_Set_Oinsert(_1564003), _1564005), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564007, tc_fun(_1564003, tc_HOL_Obool)), _1564009), _1564011)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564007, tc_fun(_1564003, tc_HOL_Obool)), _1564009), hAPP(hAPP(c_COMBB(tc_fun(_1564003, tc_HOL_Obool), tc_fun(_1564003, tc_HOL_Obool), _1564007), hAPP(c_Set_Oinsert(_1564003), _1564005)), _1564011)))], (40098 ^ _779300) ^ [_1564087] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564087, tc_HOL_Obool) = c_Set_OBall(_1564087))], (40100 ^ _779300) ^ [_1564115, _1564117, _1564119, _1564121, _1564123, _1564125] : [-(hAPP(c_Set_Ovimage(_1564115, _1564117, _1564119), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564121, tc_fun(_1564117, tc_HOL_Obool)), _1564123), _1564125)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564121, tc_fun(_1564115, tc_HOL_Obool)), _1564123), hAPP(hAPP(c_COMBB(tc_fun(_1564117, tc_HOL_Obool), tc_fun(_1564115, tc_HOL_Obool), _1564121), c_Set_Ovimage(_1564115, _1564117, _1564119)), _1564125)))], (40102 ^ _779300) ^ [_1564199, _1564201, _1564203, _1564205, _1564207] : [c_Finite__Set_Ofun__left__comm(_1564199, _1564201, _1564203), -(hAPP(c_Fun_Ocomp(_1564201, _1564201, _1564201, hAPP(_1564203, _1564205)), hAPP(_1564203, _1564207)) = hAPP(c_Fun_Ocomp(_1564201, _1564201, _1564201, hAPP(_1564203, _1564207)), hAPP(_1564203, _1564205)))], (40118 ^ _779300) ^ [_1564622, _1564624, _1564626, _1564628, _1564630] : [40120 ^ _779300 : [(40121 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1564626), 40119 ^ [_1564622, _1564624, _1564626, _1564628, _1564630]), _1564628)))], (40123 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564622, tc_HOL_Obool)), _1564624), hAPP(_1564630, 40119 ^ [_1564622, _1564624, _1564626, _1564628, _1564630])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564622, tc_HOL_Obool)), _1564624), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564626, tc_fun(_1564622, tc_HOL_Obool)), _1564628), _1564630))))], (40108 ^ _779300) ^ [_1564364, _1564366, _1564368, _1564370, _1564372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564364, tc_HOL_Obool)), _1564366), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564368, tc_fun(_1564364, tc_HOL_Obool)), _1564370), _1564372))), 40111 ^ _779300 : [(40112 ^ _779300) ^ [_1564497] : [hBOOL(hAPP(hAPP(c_member(_1564368), _1564497), _1564370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564364, tc_HOL_Obool)), _1564366), hAPP(_1564372, _1564497))))]]], (40127 ^ _779300) ^ [_1564885, _1564887, _1564889, _1564891, _1564893, _1564895, _1564897] : [c_Finite__Set_Ofun__left__comm(_1564885, _1564887, _1564889), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1564885, _1564887, _1564889, _1564891, _1564893), _1564895)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1564885, _1564887, _1564889, _1564891, _1564893), _1564897)), -(_1564897 = _1564895)], (40141 ^ _779300) ^ [_1565130, _1565132, _1565134, _1565136, _1565138] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565130, tc_fun(_1565132, tc_HOL_Obool)), _1565134), hAPP(hAPP(c_COMBB(tc_fun(_1565132, tc_HOL_Obool), tc_fun(_1565132, tc_HOL_Obool), _1565130), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565132, tc_HOL_Obool)), _1565136)), _1565138)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565132, tc_HOL_Obool)), _1565136), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565130, tc_fun(_1565132, tc_HOL_Obool)), _1565134), _1565138)))], (40143 ^ _779300) ^ [_1565220, _1565222, _1565224, _1565226, _1565228] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565220, tc_fun(_1565222, tc_HOL_Obool)), _1565224), hAPP(hAPP(c_COMBC(_1565220, tc_fun(_1565222, tc_HOL_Obool), tc_fun(_1565222, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565222, tc_HOL_Obool), tc_fun(tc_fun(_1565222, tc_HOL_Obool), tc_fun(_1565222, tc_HOL_Obool)), _1565220), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565222, tc_HOL_Obool))), _1565226)), _1565228)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565222, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565220, tc_fun(_1565222, tc_HOL_Obool)), _1565224), _1565226)), _1565228))], (40145 ^ _779300) ^ [_1565329, _1565331, _1565333, _1565335, _1565337] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565329, tc_HOL_Obool)), _1565331), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565333, tc_fun(_1565329, tc_HOL_Obool)), _1565335), _1565337)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565333, tc_fun(_1565329, tc_HOL_Obool)), _1565335), hAPP(hAPP(c_COMBB(tc_fun(_1565329, tc_HOL_Obool), tc_fun(_1565329, tc_HOL_Obool), _1565333), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565329, tc_HOL_Obool)), _1565331)), _1565337)))], (40147 ^ _779300) ^ [_1565419, _1565421, _1565423, _1565425, _1565427] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565419, tc_HOL_Obool)), _1565421), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565423, tc_fun(_1565419, tc_HOL_Obool)), _1565425), _1565427)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565423, tc_fun(_1565419, tc_HOL_Obool)), _1565425), hAPP(hAPP(c_COMBB(tc_fun(_1565419, tc_HOL_Obool), tc_fun(_1565419, tc_HOL_Obool), _1565423), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565419, tc_HOL_Obool)), _1565421)), _1565427)))], (40149 ^ _779300) ^ [_1565509, _1565511, _1565513, _1565515, _1565517] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565509, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565511, tc_fun(_1565509, tc_HOL_Obool)), _1565513), _1565515)), _1565517) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565511, tc_fun(_1565509, tc_HOL_Obool)), _1565513), hAPP(hAPP(c_COMBC(_1565511, tc_fun(_1565509, tc_HOL_Obool), tc_fun(_1565509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565509, tc_HOL_Obool), tc_fun(tc_fun(_1565509, tc_HOL_Obool), tc_fun(_1565509, tc_HOL_Obool)), _1565511), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565509, tc_HOL_Obool))), _1565515)), _1565517)))], (40151 ^ _779300) ^ [_1565618, _1565620, _1565622, _1565624, _1565626, _1565628, _1565630] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565618, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565620, tc_fun(_1565618, tc_HOL_Obool)), _1565622), _1565624)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565626, tc_fun(_1565618, tc_HOL_Obool)), _1565628), _1565630)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565620, tc_fun(_1565618, tc_HOL_Obool)), _1565622), hAPP(hAPP(c_COMBB(tc_fun(_1565626, tc_fun(_1565618, tc_HOL_Obool)), tc_fun(_1565618, tc_HOL_Obool), _1565620), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565626, tc_fun(_1565618, tc_HOL_Obool)), _1565628)), hAPP(hAPP(c_COMBC(_1565620, tc_fun(_1565626, tc_fun(_1565618, tc_HOL_Obool)), tc_fun(_1565626, tc_fun(_1565618, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1565618, tc_HOL_Obool), tc_fun(_1565618, tc_HOL_Obool)), tc_fun(tc_fun(_1565626, tc_fun(_1565618, tc_HOL_Obool)), tc_fun(_1565626, tc_fun(_1565618, tc_HOL_Obool))), _1565620), c_COMBB(tc_fun(_1565618, tc_HOL_Obool), tc_fun(_1565618, tc_HOL_Obool), _1565626)), hAPP(hAPP(c_COMBB(tc_fun(_1565618, tc_HOL_Obool), tc_fun(tc_fun(_1565618, tc_HOL_Obool), tc_fun(_1565618, tc_HOL_Obool)), _1565620), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565618, tc_HOL_Obool))), _1565624))), _1565630))))], (40153 ^ _779300) ^ [_1565821, _1565823, _1565825, _1565827, _1565829] : [-(hAPP(c_Relation_Oconverse(_1565821, _1565823), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565825, tc_fun(tc_prod(_1565821, _1565823), tc_HOL_Obool)), _1565827), _1565829)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565825, tc_fun(tc_prod(_1565823, _1565821), tc_HOL_Obool)), _1565827), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1565821, _1565823), tc_HOL_Obool), tc_fun(tc_prod(_1565823, _1565821), tc_HOL_Obool), _1565825), c_Relation_Oconverse(_1565821, _1565823)), _1565829)))], (40155 ^ _779300) ^ [_1565913, _1565915, _1565917, _1565919] : [class_Complete__Lattice_Ocomplete__lattice(_1565913), -(_1565915 = c_Orderings_Obot__class_Obot(tc_fun(_1565917, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565917, _1565913), _1565915), hAPP(c_COMBK(_1565913, _1565917), _1565919)) = _1565919)], (40165 ^ _779300) ^ [_1566047, _1566049, _1566051, _1566053, _1566055] : [hBOOL(hAPP(hAPP(c_member(_1566047), _1566049), _1566051)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566053, tc_HOL_Obool)), hAPP(_1566055, _1566049)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566047, tc_fun(_1566053, tc_HOL_Obool)), _1566051), _1566055)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566047, tc_fun(_1566053, tc_HOL_Obool)), _1566051), _1566055))], (40171 ^ _779300) ^ [_1566241, _1566243, _1566245, _1566247] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566241, tc_fun(_1566243, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1566241, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1566243, tc_HOL_Obool), tc_fun(_1566243, tc_HOL_Obool), _1566241), hAPP(c_COMBC(_1566243, tc_fun(_1566243, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566243))), _1566245)), _1566247)), -(hBOOL(hAPP(hAPP(c_member(_1566243), _1566247), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566241, tc_fun(_1566243, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1566241, tc_HOL_Obool))), _1566245))))], (40177 ^ _779300) ^ [_1566460, _1566462, _1566464, _1566466] : [hBOOL(hAPP(hAPP(c_member(_1566462), _1566466), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566460, tc_fun(_1566462, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1566460, tc_HOL_Obool))), _1566464))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566460, tc_fun(_1566462, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1566460, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1566462, tc_HOL_Obool), tc_fun(_1566462, tc_HOL_Obool), _1566460), hAPP(c_COMBC(_1566462, tc_fun(_1566462, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566462))), _1566464)), _1566466)))], (40183 ^ _779300) ^ [_1566685, _1566687, _1566689, _1566691, _1566693] : [hBOOL(hAPP(hAPP(c_member(_1566685), _1566687), _1566689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1566691, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566685, tc_fun(_1566691, tc_HOL_Obool)), _1566689), _1566693)), hAPP(_1566693, _1566687))))], (40189 ^ _779300) ^ [_1566850, _1566852, _1566854, _1566856, _1566858] : [_1566850 = c_Orderings_Obot__class_Obot(tc_fun(_1566852, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566854, tc_HOL_Obool)), _1566856), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566852, tc_fun(_1566854, tc_HOL_Obool)), _1566850), _1566858)) = _1566856)], (40195 ^ _779300) ^ [_1566983, _1566985, _1566987, _1566989, _1566991] : [-(_1566983 = c_Orderings_Obot__class_Obot(tc_fun(_1566985, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566987, tc_HOL_Obool)), _1566989), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566985, tc_fun(_1566987, tc_HOL_Obool)), _1566983), _1566991)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566985, tc_fun(_1566987, tc_HOL_Obool)), _1566983), hAPP(hAPP(c_COMBB(tc_fun(_1566987, tc_HOL_Obool), tc_fun(_1566987, tc_HOL_Obool), _1566985), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566987, tc_HOL_Obool)), _1566989)), _1566991)))], (40201 ^ _779300) ^ [_1567109, _1567111, _1567113, _1567115, _1567117] : [_1567109 = c_Orderings_Obot__class_Obot(tc_fun(_1567111, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567113, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567111, tc_fun(_1567113, tc_HOL_Obool)), _1567109), _1567115)), _1567117) = _1567117)], (40207 ^ _779300) ^ [_1567242, _1567244, _1567246, _1567248, _1567250] : [-(_1567242 = c_Orderings_Obot__class_Obot(tc_fun(_1567244, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567246, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567244, tc_fun(_1567246, tc_HOL_Obool)), _1567242), _1567248)), _1567250) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567244, tc_fun(_1567246, tc_HOL_Obool)), _1567242), hAPP(hAPP(c_COMBC(_1567244, tc_fun(_1567246, tc_HOL_Obool), tc_fun(_1567246, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1567246, tc_HOL_Obool), tc_fun(tc_fun(_1567246, tc_HOL_Obool), tc_fun(_1567246, tc_HOL_Obool)), _1567244), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567246, tc_HOL_Obool))), _1567248)), _1567250)))], (40213 ^ _779300) ^ [_1567369, _1567371, _1567373, _1567375, _1567377] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567369, tc_fun(_1567371, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1567369), _1567373), _1567375)), _1567377) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567371, tc_HOL_Obool)), hAPP(_1567377, _1567373)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567369, tc_fun(_1567371, tc_HOL_Obool)), _1567375), _1567377)))], (40215 ^ _779300) ^ [_1567446, _1567448, _1567450, _1567452] : [-(hAPP(c_Set_OCollect(_1567446), hAPP(hAPP(c_COMBB(tc_fun(_1567448, tc_HOL_Obool), tc_HOL_Obool, _1567446), c_HOL_OAll(_1567448)), hAPP(hAPP(c_COMBB(tc_fun(_1567448, tc_HOL_Obool), tc_fun(_1567448, tc_HOL_Obool), _1567446), hAPP(c_COMBS(_1567448, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1567448), c_fimplies), hAPP(hAPP(c_COMBC(_1567448, tc_fun(_1567448, tc_HOL_Obool), tc_HOL_Obool), c_member(_1567448)), _1567450)))), _1567452))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567448, tc_fun(_1567446, tc_HOL_Obool)), _1567450), hAPP(hAPP(c_COMBB(tc_fun(_1567446, tc_HOL_Obool), tc_fun(_1567446, tc_HOL_Obool), _1567448), c_Set_OCollect(_1567446)), hAPP(c_COMBC(_1567446, _1567448, tc_HOL_Obool), _1567452))))], (40217 ^ _779300) ^ [_1567580, _1567582, _1567584, _1567586, _1567588] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567580, tc_fun(_1567582, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567580, tc_HOL_Obool)), _1567584), _1567586)), _1567588) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567582, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567580, tc_fun(_1567582, tc_HOL_Obool)), _1567584), _1567588)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567580, tc_fun(_1567582, tc_HOL_Obool)), _1567586), _1567588)))], (40219 ^ _779300) ^ [_1567669, _1567671, _1567673, _1567675, _1567677] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1567669, tc_fun(_1567671, tc_HOL_Obool)), _1567673), hAPP(hAPP(c_COMBB(tc_fun(_1567671, tc_HOL_Obool), tc_fun(_1567671, tc_HOL_Obool), _1567669), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567671, tc_HOL_Obool)), _1567675)), _1567677)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567671, tc_HOL_Obool)), _1567675), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567669, tc_fun(_1567671, tc_HOL_Obool)), _1567673), _1567677)))], (40221 ^ _779300) ^ [_1567759, _1567761, _1567763, _1567765, _1567767] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567759, tc_HOL_Obool)), _1567761), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567763, tc_fun(_1567759, tc_HOL_Obool)), _1567765), _1567767)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1567763, tc_fun(_1567759, tc_HOL_Obool)), _1567765), hAPP(hAPP(c_COMBB(tc_fun(_1567759, tc_HOL_Obool), tc_fun(_1567759, tc_HOL_Obool), _1567763), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567759, tc_HOL_Obool)), _1567761)), _1567767)))], (40223 ^ _779300) ^ [_1567849, _1567851, _1567853, _1567855, _1567857, _1567859] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567849, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1567851, _1567849, _1567853), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567855, tc_fun(_1567851, tc_HOL_Obool)), _1567857), _1567859))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567855, tc_fun(_1567849, tc_HOL_Obool)), _1567857), hAPP(hAPP(c_COMBB(tc_fun(_1567851, tc_HOL_Obool), tc_fun(_1567849, tc_HOL_Obool), _1567855), c_Relation_OImage(_1567851, _1567849, _1567853)), _1567859)))))], (40225 ^ _779300) ^ [_1567943, _1567945, _1567947, _1567949] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1567943, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1567945, tc_fun(_1567943, tc_HOL_Obool)), _1567947), _1567949)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567945, tc_fun(_1567943, tc_HOL_Obool)), _1567947), hAPP(hAPP(c_COMBB(tc_fun(_1567943, tc_HOL_Obool), tc_fun(_1567943, tc_HOL_Obool), _1567945), c_Groups_Ouminus__class_Ouminus(tc_fun(_1567943, tc_HOL_Obool))), _1567949)))], (40227 ^ _779300) ^ [_1568025, _1568027, _1568029, _1568031] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1568025, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568027, tc_fun(_1568025, tc_HOL_Obool)), _1568029), _1568031)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1568027, tc_fun(_1568025, tc_HOL_Obool)), _1568029), hAPP(hAPP(c_COMBB(tc_fun(_1568025, tc_HOL_Obool), tc_fun(_1568025, tc_HOL_Obool), _1568027), c_Groups_Ouminus__class_Ouminus(tc_fun(_1568025, tc_HOL_Obool))), _1568031)))], (40229 ^ _779300) ^ [_1568107, _1568109, _1568111, _1568113, _1568115] : [class_Complete__Lattice_Ocomplete__lattice(_1568107), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1568109, tc_HOL_Obool)), _1568111), _1568113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1568107), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568109, _1568107), _1568113), _1568115)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568109, _1568107), _1568111), _1568115))))], (40239 ^ _779300) ^ [_1568316, _1568318, _1568320, _1568322] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568316, tc_fun(_1568318, tc_HOL_Obool)), _1568320), _1568322) = hAPP(c_Set_OCollect(_1568318), hAPP(hAPP(c_COMBB(tc_fun(_1568316, tc_HOL_Obool), tc_HOL_Obool, _1568318), c_HOL_OAll(_1568316)), hAPP(hAPP(c_COMBB(tc_fun(_1568316, tc_HOL_Obool), tc_fun(_1568316, tc_HOL_Obool), _1568318), hAPP(c_COMBS(_1568316, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1568316), c_fimplies), hAPP(hAPP(c_COMBC(_1568316, tc_fun(_1568316, tc_HOL_Obool), tc_HOL_Obool), c_member(_1568316)), _1568320)))), hAPP(hAPP(c_COMBC(_1568318, tc_fun(_1568316, tc_fun(_1568318, tc_HOL_Obool)), tc_fun(_1568316, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1568318, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1568316, tc_fun(_1568318, tc_HOL_Obool)), tc_fun(_1568316, tc_HOL_Obool)), _1568318), c_COMBB(tc_fun(_1568318, tc_HOL_Obool), tc_HOL_Obool, _1568316)), c_member(_1568318))), _1568322)))))], (40241 ^ _779300) ^ [_1568499, _1568501, _1568503, _1568505, _1568507] : [_1568499 = c_Orderings_Obot__class_Obot(tc_fun(_1568501, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568501, tc_fun(_1568503, tc_HOL_Obool)), _1568499), hAPP(hAPP(c_COMBB(tc_fun(_1568503, tc_HOL_Obool), tc_fun(_1568503, tc_HOL_Obool), _1568501), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568503, tc_HOL_Obool)), _1568505)), _1568507)) = c_Orderings_Otop__class_Otop(tc_fun(_1568503, tc_HOL_Obool)))], (40247 ^ _779300) ^ [_1568668, _1568670, _1568672, _1568674, _1568676] : [-(_1568668 = c_Orderings_Obot__class_Obot(tc_fun(_1568670, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568670, tc_fun(_1568672, tc_HOL_Obool)), _1568668), hAPP(hAPP(c_COMBB(tc_fun(_1568672, tc_HOL_Obool), tc_fun(_1568672, tc_HOL_Obool), _1568670), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568672, tc_HOL_Obool)), _1568674)), _1568676)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568672, tc_HOL_Obool)), _1568674), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568670, tc_fun(_1568672, tc_HOL_Obool)), _1568668), _1568676)))], (40253 ^ _779300) ^ [_1568794, _1568796, _1568798, _1568800, _1568802] : [_1568794 = c_Orderings_Obot__class_Obot(tc_fun(_1568796, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568796, tc_fun(_1568798, tc_HOL_Obool)), _1568794), hAPP(hAPP(c_COMBC(_1568796, tc_fun(_1568798, tc_HOL_Obool), tc_fun(_1568798, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568798, tc_HOL_Obool), tc_fun(tc_fun(_1568798, tc_HOL_Obool), tc_fun(_1568798, tc_HOL_Obool)), _1568796), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568798, tc_HOL_Obool))), _1568800)), _1568802)) = c_Orderings_Otop__class_Otop(tc_fun(_1568798, tc_HOL_Obool)))], (40259 ^ _779300) ^ [_1569001, _1569003, _1569005, _1569007, _1569009] : [-(_1569001 = c_Orderings_Obot__class_Obot(tc_fun(_1569003, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569003, tc_fun(_1569005, tc_HOL_Obool)), _1569001), hAPP(hAPP(c_COMBC(_1569003, tc_fun(_1569005, tc_HOL_Obool), tc_fun(_1569005, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569005, tc_HOL_Obool), tc_fun(tc_fun(_1569005, tc_HOL_Obool), tc_fun(_1569005, tc_HOL_Obool)), _1569003), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1569005, tc_HOL_Obool))), _1569007)), _1569009)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1569005, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569003, tc_fun(_1569005, tc_HOL_Obool)), _1569001), _1569007)), _1569009))], (40265 ^ _779300) ^ [_1569146, _1569148, _1569150, _1569152, _1569154] : [_1569146 = c_Orderings_Obot__class_Obot(tc_fun(_1569148, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569150, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569148, tc_fun(_1569150, tc_HOL_Obool)), _1569146), _1569152)), _1569154) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569150, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1569150, tc_HOL_Obool))), _1569154))], (40271 ^ _779300) ^ [_1569311, _1569313, _1569315, _1569317, _1569319] : [-(_1569311 = c_Orderings_Obot__class_Obot(tc_fun(_1569313, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569315, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569313, tc_fun(_1569315, tc_HOL_Obool)), _1569311), _1569317)), _1569319) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569313, tc_fun(_1569315, tc_HOL_Obool)), _1569311), hAPP(hAPP(c_COMBC(_1569313, tc_fun(_1569315, tc_HOL_Obool), tc_fun(_1569315, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569315, tc_HOL_Obool), tc_fun(tc_fun(_1569315, tc_HOL_Obool), tc_fun(_1569315, tc_HOL_Obool)), _1569313), c_Groups_Ominus__class_Ominus(tc_fun(_1569315, tc_HOL_Obool))), _1569317)), _1569319)))], (40277 ^ _779300) ^ [_1569456, _1569458, _1569460, _1569462, _1569464] : [_1569456 = c_Orderings_Obot__class_Obot(tc_fun(_1569458, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569458, tc_fun(_1569460, tc_HOL_Obool)), _1569456), hAPP(hAPP(c_COMBC(_1569458, tc_fun(_1569460, tc_HOL_Obool), tc_fun(_1569460, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569460, tc_HOL_Obool), tc_fun(tc_fun(_1569460, tc_HOL_Obool), tc_fun(_1569460, tc_HOL_Obool)), _1569458), c_Groups_Ominus__class_Ominus(tc_fun(_1569460, tc_HOL_Obool))), _1569462)), _1569464)) = c_Orderings_Otop__class_Otop(tc_fun(_1569460, tc_HOL_Obool)))], (40283 ^ _779300) ^ [_1569663, _1569665, _1569667, _1569669, _1569671] : [-(_1569663 = c_Orderings_Obot__class_Obot(tc_fun(_1569665, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569665, tc_fun(_1569667, tc_HOL_Obool)), _1569663), hAPP(hAPP(c_COMBC(_1569665, tc_fun(_1569667, tc_HOL_Obool), tc_fun(_1569667, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569667, tc_HOL_Obool), tc_fun(tc_fun(_1569667, tc_HOL_Obool), tc_fun(_1569667, tc_HOL_Obool)), _1569665), c_Groups_Ominus__class_Ominus(tc_fun(_1569667, tc_HOL_Obool))), _1569669)), _1569671)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569667, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569665, tc_fun(_1569667, tc_HOL_Obool)), _1569663), _1569669)), _1569671))], (40289 ^ _779300) ^ [_1569808, _1569810, _1569812, _1569814, _1569816] : [_1569808 = c_Orderings_Obot__class_Obot(tc_fun(_1569810, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569812, tc_HOL_Obool)), _1569814), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1569810, tc_fun(_1569812, tc_HOL_Obool)), _1569808), _1569816)) = _1569814)], (40295 ^ _779300) ^ [_1569941, _1569943, _1569945, _1569947, _1569949] : [-(_1569941 = c_Orderings_Obot__class_Obot(tc_fun(_1569943, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569945, tc_HOL_Obool)), _1569947), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1569943, tc_fun(_1569945, tc_HOL_Obool)), _1569941), _1569949)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569943, tc_fun(_1569945, tc_HOL_Obool)), _1569941), hAPP(hAPP(c_COMBB(tc_fun(_1569945, tc_HOL_Obool), tc_fun(_1569945, tc_HOL_Obool), _1569943), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569945, tc_HOL_Obool)), _1569947)), _1569949)))], (40301 ^ _779300) ^ [_1570049, _1570051, _1570053, _1570055, _1570057, _1570059] : [c_Finite__Set_Ofun__left__comm(_1570049, _1570051, _1570053), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570049), _1570055)), -(hAPP(hAPP(_1570053, _1570057), hAPP(hAPP(c_Finite__Set_Ofold(_1570049, _1570051, _1570053), _1570059), _1570055)) = hAPP(hAPP(c_Finite__Set_Ofold(_1570049, _1570051, _1570053), hAPP(hAPP(_1570053, _1570057), _1570059)), _1570055))], (40311 ^ _779300) ^ [_1570268, _1570270, _1570272, _1570274, _1570276] : [class_Complete__Lattice_Ocomplete__lattice(_1570268), hBOOL(hAPP(hAPP(c_member(_1570270), _1570272), _1570274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1570268), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1570270, _1570268), _1570274), _1570276)), hAPP(_1570276, _1570272))))], (40321 ^ _779300) ^ [_1570459, _1570461, _1570463, _1570465, _1570467, _1570469] : [c_Finite__Set_Ofun__left__comm(_1570459, _1570461, _1570463), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1570459, _1570461, _1570463, _1570465, _1570467), _1570469)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1570459, _1570461, _1570463), _1570465), _1570467) = _1570469)], (40331 ^ _779300) ^ [] : [-(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)))], (40333 ^ _779300) ^ [_1570678, _1570680, _1570682, _1570684, _1570686] : [_1570678 = c_Orderings_Obot__class_Obot(tc_fun(_1570680, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1570680, tc_fun(_1570682, tc_HOL_Obool)), _1570678), hAPP(hAPP(c_COMBB(tc_fun(_1570682, tc_HOL_Obool), tc_fun(_1570682, tc_HOL_Obool), _1570680), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1570682, tc_HOL_Obool)), _1570684)), _1570686)) = c_Orderings_Otop__class_Otop(tc_fun(_1570682, tc_HOL_Obool)))], (40339 ^ _779300) ^ [_1570847, _1570849, _1570851, _1570853, _1570855] : [-(_1570847 = c_Orderings_Obot__class_Obot(tc_fun(_1570849, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1570849, tc_fun(_1570851, tc_HOL_Obool)), _1570847), hAPP(hAPP(c_COMBB(tc_fun(_1570851, tc_HOL_Obool), tc_fun(_1570851, tc_HOL_Obool), _1570849), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1570851, tc_HOL_Obool)), _1570853)), _1570855)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1570851, tc_HOL_Obool)), _1570853), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1570849, tc_fun(_1570851, tc_HOL_Obool)), _1570847), _1570855)))], (40345 ^ _779300) ^ [_1570955, _1570957, _1570959, _1570961, _1570963, _1570965] : [c_Relation_Osingle__valued(_1570955, _1570957, hAPP(c_Relation_Oconverse(_1570957, _1570955), _1570959)), -(_1570961 = c_Orderings_Obot__class_Obot(tc_fun(_1570963, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1570957, _1570955, _1570959), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1570963, tc_fun(_1570957, tc_HOL_Obool)), _1570961), _1570965)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1570963, tc_fun(_1570955, tc_HOL_Obool)), _1570961), hAPP(hAPP(c_COMBB(tc_fun(_1570957, tc_HOL_Obool), tc_fun(_1570955, tc_HOL_Obool), _1570963), c_Relation_OImage(_1570957, _1570955, _1570959)), _1570965)))], (40355 ^ _779300) ^ [_1571181, _1571183, _1571185, _1571187, _1571189] : [class_Complete__Lattice_Ocomplete__lattice(_1571181), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571183), _1571185)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1571181), _1571187), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1571183, _1571181), _1571185), _1571189)) = hAPP(hAPP(c_Finite__Set_Ofold(_1571183, _1571181, hAPP(hAPP(c_COMBB(_1571181, tc_fun(_1571181, _1571181), _1571183), c_Lattices_Osemilattice__inf__class_Oinf(_1571181)), _1571189)), _1571187), _1571185))], (40365 ^ _779300) ^ [_1571412, _1571414, _1571416, _1571418, _1571420] : [c_Finite__Set_Ofun__left__comm(_1571412, _1571414, _1571416), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571412), _1571418)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1571412, _1571414, _1571416, _1571420, _1571418), hAPP(hAPP(c_Finite__Set_Ofold(_1571412, _1571414, _1571416), _1571420), _1571418))))], (40375 ^ _779300) ^ [_1571599, _1571601, _1571603, _1571605, _1571607, _1571609] : [c_Finite__Set_Ofun__left__comm(_1571599, _1571601, _1571603), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571599), _1571605)), -(hBOOL(hAPP(hAPP(c_member(_1571599), _1571607), _1571605))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1571599, _1571601, _1571603), _1571609), hAPP(hAPP(c_Set_Oinsert(_1571599), _1571607), _1571605)) = hAPP(hAPP(_1571603, _1571607), hAPP(hAPP(c_Finite__Set_Ofold(_1571599, _1571601, _1571603), _1571609), _1571605)))], (40389 ^ _779300) ^ [_1571851, _1571853, _1571855, _1571857, _1571859, _1571861] : [c_Finite__Set_Ofun__left__comm(_1571851, _1571853, _1571855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571851), _1571857)), -(hBOOL(hAPP(hAPP(c_member(_1571851), _1571859), _1571857))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1571851, _1571853, _1571855), _1571861), hAPP(hAPP(c_Set_Oinsert(_1571851), _1571859), _1571857)) = hAPP(hAPP(c_Finite__Set_Ofold(_1571851, _1571853, _1571855), hAPP(hAPP(_1571855, _1571859), _1571861)), _1571857))], (40403 ^ _779300) ^ [_1572103, _1572105, _1572107, _1572109, _1572111, _1572113, _1572115] : [c_Finite__Set_Ofun__left__comm(_1572103, _1572105, _1572107), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1572103, _1572105, _1572107, _1572109, _1572111), _1572113)), hBOOL(hAPP(hAPP(c_member(_1572103), _1572115), _1572111)), 40415 ^ _779300 : [(40416 ^ _779300) ^ [] : [-(_1572113 = hAPP(hAPP(_1572107, _1572115), 40414 ^ [_1572103, _1572105, _1572107, _1572109, _1572111, _1572113, _1572115]))], (40418 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1572103, _1572105, _1572107, _1572109, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1572103, tc_HOL_Obool)), _1572111), hAPP(hAPP(c_Set_Oinsert(_1572103), _1572115), c_Orderings_Obot__class_Obot(tc_fun(_1572103, tc_HOL_Obool))))), 40414 ^ [_1572103, _1572105, _1572107, _1572109, _1572111, _1572113, _1572115])))]]], (40420 ^ _779300) ^ [_1572487, _1572489] : [class_Complete__Lattice_Ocomplete__lattice(_1572487), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572487), _1572489)), -(c_Complete__Lattice_OInf__class_OInf(_1572487, _1572489) = hAPP(hAPP(c_Finite__Set_Ofold(_1572487, _1572487, c_Lattices_Osemilattice__inf__class_Oinf(_1572487)), c_Orderings_Otop__class_Otop(_1572487)), _1572489))], (40430 ^ _779300) ^ [_1572656, _1572658] : [class_Complete__Lattice_Ocomplete__lattice(_1572656), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572656), _1572658)), -(c_Complete__Lattice_OSup__class_OSup(_1572656, _1572658) = hAPP(hAPP(c_Finite__Set_Ofold(_1572656, _1572656, c_Lattices_Osemilattice__sup__class_Osup(_1572656)), c_Orderings_Obot__class_Obot(_1572656)), _1572658))], (40440 ^ _779300) ^ [_1572825, _1572827] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1572825), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1572825, tc_HOL_Obool), _1572827)))), 40441 ^ _779300 : [(40442 ^ _779300) ^ [_1572889] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1572825, tc_HOL_Obool)), _1572889), _1572827)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572825), _1572889))]]], (40450 ^ _779300) ^ [_1573033, _1573035, _1573037, _1573039] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1573033, tc_HOL_Obool)), _1573035), _1573037)), hBOOL(hAPP(hAPP(c_member(_1573033), _1573039), _1573035)), -(hBOOL(hAPP(hAPP(c_member(_1573033), _1573039), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1573033, tc_HOL_Obool), _1573037))))], (40460 ^ _779300) ^ [_1573230, _1573232, _1573234, _1573236] : [hBOOL(hAPP(hAPP(c_member(_1573230), _1573232), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1573230, tc_HOL_Obool), _1573234))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1573230, tc_HOL_Obool)), _1573236), _1573234)), -(hBOOL(hAPP(hAPP(c_member(_1573230), _1573232), _1573236)))], (40470 ^ _779300) ^ [_1573427, _1573429, _1573431, _1573433] : [hBOOL(hAPP(hAPP(c_member(_1573427), _1573429), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1573427, tc_HOL_Obool), _1573431))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1573427, tc_HOL_Obool)), _1573433), _1573431)), -(hBOOL(hAPP(hAPP(c_member(_1573427), _1573429), _1573433)))], (40490 ^ _779300) ^ [_1573901, _1573903, _1573905, _1573907, _1573909, _1573911, _1573913] : [40492 ^ _779300 : [(40493 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1573901), 40491 ^ [_1573901, _1573903, _1573905, _1573907, _1573909, _1573911, _1573913]), _1573907)))], (40495 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1573909, 40491 ^ [_1573901, _1573903, _1573905, _1573907, _1573909, _1573911, _1573913]), _1573911), _1573913))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1573901, tc_fun(_1573903, tc_fun(_1573905, tc_HOL_Obool))), _1573907), _1573909), _1573911), _1573913)))], (40480 ^ _779300) ^ [_1573654, _1573656, _1573658, _1573660, _1573662, _1573664, _1573666] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1573654, tc_fun(_1573656, tc_fun(_1573658, tc_HOL_Obool))), _1573660), _1573662), _1573664), _1573666)), 40483 ^ _779300 : [(40484 ^ _779300) ^ [_1573782] : [hBOOL(hAPP(hAPP(c_member(_1573654), _1573782), _1573660)), -(hBOOL(hAPP(hAPP(hAPP(_1573662, _1573782), _1573664), _1573666)))]]], (40509 ^ _779300) ^ [_1574403, _1574405, _1574407, _1574409, _1574411] : [40511 ^ _779300 : [(40512 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1574403), 40510 ^ [_1574403, _1574405, _1574407, _1574409, _1574411]), _1574407)))], (40514 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1574409, 40510 ^ [_1574403, _1574405, _1574407, _1574409, _1574411]), _1574411))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574403, tc_fun(_1574405, tc_HOL_Obool)), _1574407), _1574409), _1574411)))], (40499 ^ _779300) ^ [_1574185, _1574187, _1574189, _1574191, _1574193] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574185, tc_fun(_1574187, tc_HOL_Obool)), _1574189), _1574191), _1574193)), 40502 ^ _779300 : [(40503 ^ _779300) ^ [_1574294] : [hBOOL(hAPP(hAPP(c_member(_1574185), _1574294), _1574189)), -(hBOOL(hAPP(hAPP(_1574191, _1574294), _1574193)))]]], (40518 ^ _779300) ^ [_1574626, _1574628, _1574630, _1574632] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1574626, tc_HOL_Obool), tc_fun(_1574628, tc_HOL_Obool)), _1574630), hAPP(hAPP(c_COMBC(tc_fun(_1574626, tc_HOL_Obool), tc_fun(_1574626, tc_fun(_1574628, tc_HOL_Obool)), tc_fun(_1574628, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574626, tc_fun(_1574628, tc_HOL_Obool))), _1574632)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574626, tc_fun(_1574628, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1574626, tc_HOL_Obool), _1574630)), _1574632))], (40520 ^ _779300) ^ [_1574716, _1574718, _1574720, _1574722] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574716, tc_fun(_1574718, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1574716, tc_HOL_Obool), _1574720)), _1574722) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1574716, tc_HOL_Obool), tc_fun(_1574718, tc_HOL_Obool)), _1574720), hAPP(hAPP(c_COMBC(tc_fun(_1574716, tc_HOL_Obool), tc_fun(_1574716, tc_fun(_1574718, tc_HOL_Obool)), tc_fun(_1574718, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574716, tc_fun(_1574718, tc_HOL_Obool))), _1574722)))], (40522 ^ _779300) ^ [_1574806, _1574808, _1574810, _1574812] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574806, tc_fun(_1574808, tc_HOL_Obool)), _1574810), _1574812) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1574808, tc_HOL_Obool), hAPP(c_Set_Oimage(_1574806, tc_fun(_1574808, tc_HOL_Obool), _1574812), _1574810)))], (40524 ^ _779300) ^ [_1574863, _1574865, _1574867, _1574869] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1574863, tc_HOL_Obool), hAPP(c_Set_Oimage(_1574865, tc_fun(_1574863, tc_HOL_Obool), _1574867), _1574869)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574865, tc_fun(_1574863, tc_HOL_Obool)), _1574869), _1574867))], (40526 ^ _779300) ^ [_1574920, _1574922, _1574924] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574920, tc_HOL_Obool)), _1574922), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1574920, tc_HOL_Obool), _1574924)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1574920, tc_HOL_Obool), tc_fun(_1574920, tc_HOL_Obool)), _1574924), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574920, tc_HOL_Obool)), _1574922)))], (40538 ^ _779300) ^ [_1575273, _1575275, _1575277] : [40540 ^ _779300 : [(40541 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1575273, tc_HOL_Obool)), 40539 ^ [_1575273, _1575275, _1575277]), _1575275)))], (40543 ^ _779300) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1575273, tc_HOL_Obool)), 40539 ^ [_1575273, _1575275, _1575277]), _1575277) = c_Orderings_Obot__class_Obot(tc_fun(_1575273, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1575273, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1575273, tc_HOL_Obool), _1575275)), _1575277) = c_Orderings_Obot__class_Obot(tc_fun(_1575273, tc_HOL_Obool)))], (40528 ^ _779300) ^ [_1575005, _1575007, _1575009] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1575005, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1575005, tc_HOL_Obool), _1575007)), _1575009) = c_Orderings_Obot__class_Obot(tc_fun(_1575005, tc_HOL_Obool)), 40531 ^ _779300 : [(40532 ^ _779300) ^ [_1575140] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1575005, tc_HOL_Obool)), _1575140), _1575007)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1575005, tc_HOL_Obool)), _1575140), _1575009) = c_Orderings_Obot__class_Obot(tc_fun(_1575005, tc_HOL_Obool)))]]], (40547 ^ _779300) ^ [_1575536, _1575538, _1575540] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1575536, tc_HOL_Obool)), _1575538), _1575540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575536, tc_HOL_Obool)), _1575538), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1575536, tc_HOL_Obool), _1575540))))], (40553 ^ _779300) ^ [_1575667, _1575669, _1575671] : [class_Complete__Lattice_Ocomplete__lattice(_1575667), class_Orderings_Olinorder(_1575667), 40560 ^ _779300 : [(40561 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575667), _1575669), c_Complete__Lattice_OSup__class_OSup(_1575667, _1575671))), 40565 ^ _779300 : [(40566 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1575667), 40564 ^ [_1575667, _1575669, _1575671]), _1575671)))], (40568 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575667), _1575669), 40564 ^ [_1575667, _1575669, _1575671])))]]], (40570 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575667), _1575669), c_Complete__Lattice_OSup__class_OSup(_1575667, _1575671)))), 40571 ^ _779300 : [(40572 ^ _779300) ^ [_1575973] : [hBOOL(hAPP(hAPP(c_member(_1575667), _1575973), _1575671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575667), _1575669), _1575973))]]]]], (40580 ^ _779300) ^ [_1576127, _1576129, _1576131] : [class_Complete__Lattice_Ocomplete__lattice(_1576127), class_Orderings_Olinorder(_1576127), 40587 ^ _779300 : [(40588 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1576127), c_Complete__Lattice_OInf__class_OInf(_1576127, _1576129)), _1576131)), 40592 ^ _779300 : [(40593 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576127), 40591 ^ [_1576127, _1576129, _1576131]), _1576129)))], (40595 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1576127), 40591 ^ [_1576127, _1576129, _1576131]), _1576131)))]]], (40597 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1576127), c_Complete__Lattice_OInf__class_OInf(_1576127, _1576129)), _1576131))), 40598 ^ _779300 : [(40599 ^ _779300) ^ [_1576433] : [hBOOL(hAPP(hAPP(c_member(_1576127), _1576433), _1576129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1576127), _1576433), _1576131))]]]]], (40607 ^ _779300) ^ [_1576587, _1576589, _1576591] : [class_Complete__Lattice_Ocomplete__lattice(_1576587), 40610 ^ _779300 : [(40621 ^ _779300) ^ [] : [40623 ^ _779300 : [(40624 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576587), 40622 ^ [_1576587, _1576589, _1576591]), _1576591)))], (40626 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576587), _1576589), 40622 ^ [_1576587, _1576589, _1576591]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576587), _1576589), c_Complete__Lattice_OInf__class_OInf(_1576587, _1576591))))], (40611 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576587), _1576589), c_Complete__Lattice_OInf__class_OInf(_1576587, _1576591))), 40614 ^ _779300 : [(40615 ^ _779300) ^ [_1576745] : [hBOOL(hAPP(hAPP(c_member(_1576587), _1576745), _1576591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576587), _1576589), _1576745)))]]]]], (40630 ^ _779300) ^ [_1577021, _1577023, _1577025] : [class_Complete__Lattice_Ocomplete__lattice(_1577021), 40633 ^ _779300 : [(40644 ^ _779300) ^ [] : [40646 ^ _779300 : [(40647 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1577021), 40645 ^ [_1577021, _1577023, _1577025]), _1577023)))], (40649 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577021), 40645 ^ [_1577021, _1577023, _1577025]), _1577025))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577021), c_Complete__Lattice_OSup__class_OSup(_1577021, _1577023)), _1577025)))], (40634 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577021), c_Complete__Lattice_OSup__class_OSup(_1577021, _1577023)), _1577025)), 40637 ^ _779300 : [(40638 ^ _779300) ^ [_1577179] : [hBOOL(hAPP(hAPP(c_member(_1577021), _1577179), _1577023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1577021), _1577179), _1577025)))]]]]], (40653 ^ _779300) ^ [_1577455, _1577457] : [-(hAPP(c_Relation_OField(_1577455), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1577455, _1577455), tc_HOL_Obool), _1577457)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577455, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1577455, _1577455), tc_HOL_Obool), tc_fun(_1577455, tc_HOL_Obool), c_Relation_OField(_1577455)), _1577457)))], (40655 ^ _779300) ^ [_1577518, _1577520] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577518, tc_HOL_Obool), hAPP(c_Set_OPow(_1577518), _1577520)) = _1577520)], (40657 ^ _779300) ^ [_1577554, _1577556, _1577558, _1577560] : [-(hAPP(c_Set_Oimage(_1577554, _1577556, _1577558), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577554, tc_HOL_Obool), _1577560)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577554, tc_HOL_Obool), tc_fun(_1577556, tc_HOL_Obool)), _1577560), c_Set_Oimage(_1577554, _1577556, _1577558)))], (40659 ^ _779300) ^ [_1577615, _1577617, _1577619, _1577621] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1577615, _1577617), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577615, tc_HOL_Obool), _1577619)), _1577621) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577615, tc_HOL_Obool), tc_fun(tc_prod(_1577615, _1577617), tc_HOL_Obool)), _1577619), hAPP(hAPP(c_COMBC(tc_fun(_1577615, tc_HOL_Obool), tc_fun(_1577615, tc_fun(_1577617, tc_HOL_Obool)), tc_fun(tc_prod(_1577615, _1577617), tc_HOL_Obool)), c_Product__Type_OSigma(_1577615, _1577617)), _1577621)))], (40661 ^ _779300) ^ [_1577705, _1577707, _1577709, _1577711] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577705, tc_fun(_1577707, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577705, tc_HOL_Obool), _1577709)), _1577711) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577705, tc_HOL_Obool), tc_fun(_1577707, tc_HOL_Obool)), _1577709), hAPP(hAPP(c_COMBC(tc_fun(_1577705, tc_HOL_Obool), tc_fun(_1577705, tc_fun(_1577707, tc_HOL_Obool)), tc_fun(_1577707, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577705, tc_fun(_1577707, tc_HOL_Obool))), _1577711)))], (40663 ^ _779300) ^ [_1577795, _1577797, _1577799, _1577801] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577795, tc_HOL_Obool), tc_fun(_1577797, tc_HOL_Obool)), _1577799), hAPP(hAPP(c_COMBC(tc_fun(_1577795, tc_HOL_Obool), tc_fun(_1577795, tc_fun(_1577797, tc_HOL_Obool)), tc_fun(_1577797, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577795, tc_fun(_1577797, tc_HOL_Obool))), _1577801)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577795, tc_fun(_1577797, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577795, tc_HOL_Obool), _1577799)), _1577801))], (40665 ^ _779300) ^ [_1577885, _1577887, _1577889] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577885, tc_HOL_Obool)), _1577887), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577885, tc_HOL_Obool), _1577889)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577885, tc_HOL_Obool), tc_fun(_1577885, tc_HOL_Obool)), _1577889), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577885, tc_HOL_Obool)), _1577887)))], (40667 ^ _779300) ^ [_1577952, _1577954, _1577956] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577952, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577952, tc_HOL_Obool), _1577954)), _1577956) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577952, tc_HOL_Obool), tc_fun(_1577952, tc_HOL_Obool)), _1577954), hAPP(hAPP(c_COMBC(tc_fun(_1577952, tc_HOL_Obool), tc_fun(_1577952, tc_HOL_Obool), tc_fun(_1577952, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577952, tc_HOL_Obool))), _1577956)))], (40669 ^ _779300) ^ [_1578035, _1578037, _1578039] : [-(hAPP(c_Relation_ORange(_1578035, _1578037), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1578035, _1578037), tc_HOL_Obool), _1578039)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1578035, _1578037), tc_HOL_Obool), tc_fun(_1578037, tc_HOL_Obool)), _1578039), c_Relation_ORange(_1578035, _1578037)))], (40671 ^ _779300) ^ [_1578098, _1578100, _1578102] : [-(hAPP(c_Relation_ODomain(_1578098, _1578100), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1578098, _1578100), tc_HOL_Obool), _1578102)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1578098, _1578100), tc_HOL_Obool), tc_fun(_1578098, tc_HOL_Obool)), _1578102), c_Relation_ODomain(_1578098, _1578100)))], (40673 ^ _779300) ^ [_1578161, _1578163, _1578165, _1578167] : [-(hAPP(c_Set_Ovimage(_1578161, _1578163, _1578165), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578163, tc_HOL_Obool), _1578167)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1578163, tc_HOL_Obool), tc_fun(_1578161, tc_HOL_Obool)), _1578167), c_Set_Ovimage(_1578161, _1578163, _1578165)))], (40675 ^ _779300) ^ [_1578222, _1578224] : [class_Complete__Lattice_Ocomplete__lattice(_1578222), -(c_Complete__Lattice_OInf__class_OInf(_1578222, _1578224) = c_Complete__Lattice_OSup__class_OSup(_1578222, hAPP(c_Set_OCollect(_1578222), hAPP(hAPP(c_COMBB(tc_fun(_1578222, tc_HOL_Obool), tc_HOL_Obool, _1578222), c_HOL_OAll(_1578222)), hAPP(hAPP(c_COMBB(tc_fun(_1578222, tc_HOL_Obool), tc_fun(_1578222, tc_HOL_Obool), _1578222), hAPP(c_COMBS(_1578222, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578222), c_fimplies), hAPP(hAPP(c_COMBC(_1578222, tc_fun(_1578222, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578222)), _1578224)))), c_Orderings_Oord__class_Oless__eq(_1578222))))))], (40681 ^ _779300) ^ [_1578449, _1578451] : [class_Complete__Lattice_Ocomplete__lattice(_1578449), -(c_Complete__Lattice_OSup__class_OSup(_1578449, _1578451) = c_Complete__Lattice_OInf__class_OInf(_1578449, hAPP(c_Set_OCollect(_1578449), hAPP(hAPP(c_COMBB(tc_fun(_1578449, tc_HOL_Obool), tc_HOL_Obool, _1578449), c_HOL_OAll(_1578449)), hAPP(hAPP(c_COMBB(tc_fun(_1578449, tc_HOL_Obool), tc_fun(_1578449, tc_HOL_Obool), _1578449), hAPP(c_COMBS(_1578449, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578449), c_fimplies), hAPP(hAPP(c_COMBC(_1578449, tc_fun(_1578449, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578449)), _1578451)))), hAPP(c_COMBC(_1578449, _1578449, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1578449)))))))], (40687 ^ _779300) ^ [_1578690, _1578692, _1578694] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1578690, tc_HOL_Obool)), _1578692), _1578694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578690, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1578690, tc_HOL_Obool), _1578694)), _1578692)))], (40693 ^ _779300) ^ [_1578821] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578821, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1578821, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1578821, tc_HOL_Obool)))], (40695 ^ _779300) ^ [_1578863, _1578865, _1578867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1578863, tc_HOL_Obool), tc_HOL_Obool)), _1578865), _1578867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578863, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578863, tc_HOL_Obool), _1578865)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578863, tc_HOL_Obool), _1578867))))], (40701 ^ _779300) ^ [_1579012, _1579014, _1579016] : [c_Equiv__Relations_Oequiv(_1579012, _1579014, _1579016), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579012, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1579012), _1579014), _1579016)) = _1579014)], (40707 ^ _779300) ^ [_1579121, _1579123, _1579125] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579121, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1579121, tc_HOL_Obool)), _1579123), _1579125)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1579121, tc_HOL_Obool)), _1579123), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579121, tc_HOL_Obool), _1579125)))], (40709 ^ _779300) ^ [_1579182, _1579184] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1579182), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579182, tc_HOL_Obool), _1579184))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1579182, tc_HOL_Obool)), _1579184)))], (40715 ^ _779300) ^ [_1579293, _1579295] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1579293, tc_HOL_Obool), tc_HOL_Obool)), _1579295), hAPP(c_Set_OPow(_1579293), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579293, tc_HOL_Obool), _1579295)))))], (40717 ^ _779300) ^ [_1579342, _1579344, _1579346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1579342, tc_HOL_Obool), tc_HOL_Obool)), _1579344), _1579346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579342, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579342, tc_HOL_Obool), _1579346)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579342, tc_HOL_Obool), _1579344))))], (40723 ^ _779300) ^ [_1579491] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579491, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1579491, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1579491, tc_HOL_Obool)))], (40725 ^ _779300) ^ [_1579533, _1579535] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579533, tc_HOL_Obool), _1579535) = hAPP(c_Set_OCollect(_1579533), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1579533, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1579533), c_HOL_OAll(tc_fun(_1579533, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1579533, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1579533, tc_HOL_Obool), tc_HOL_Obool), _1579533), hAPP(c_COMBS(tc_fun(_1579533, 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(_1579533, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1579533, tc_HOL_Obool), tc_fun(tc_fun(_1579533, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1579533, tc_HOL_Obool))), _1579535)))), c_member(_1579533)))))], (40727 ^ _779300) ^ [_1579661] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579661, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1579661, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1579661, tc_HOL_Obool)))], (40729 ^ _779300) ^ [_1579703, _1579705, _1579707] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579703, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1579703, tc_HOL_Obool), tc_HOL_Obool)), _1579705), _1579707)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1579703, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579703, tc_HOL_Obool), _1579705)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579703, tc_HOL_Obool), _1579707)))], (40731 ^ _779300) ^ [_1579773, _1579775, _1579777] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579773, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1579773, tc_HOL_Obool)), _1579775), _1579777)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1579773, tc_HOL_Obool)), _1579775), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579773, tc_HOL_Obool), _1579777)))], (40733 ^ _779300) ^ [_1579834, _1579836, _1579838, _1579840] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579834, tc_HOL_Obool), hAPP(c_Set_Oimage(_1579836, tc_fun(_1579834, tc_HOL_Obool), _1579838), _1579840)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1579836, tc_fun(_1579834, tc_HOL_Obool)), _1579840), _1579838))], (40735 ^ _779300) ^ [_1579891, _1579893, _1579895, _1579897] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1579891, tc_fun(_1579893, tc_HOL_Obool)), _1579895), _1579897) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579893, tc_HOL_Obool), hAPP(c_Set_Oimage(_1579891, tc_fun(_1579893, tc_HOL_Obool), _1579897), _1579895)))], (40737 ^ _779300) ^ [_1579948, _1579950, _1579952] : [class_Complete__Lattice_Ocomplete__lattice(_1579948), hBOOL(hAPP(hAPP(c_member(_1579948), _1579950), _1579952)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1579948), _1579950), c_Complete__Lattice_OSup__class_OSup(_1579948, _1579952))))], (40747 ^ _779300) ^ [_1580113] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580113, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1580113, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1580113, tc_HOL_Obool)))], (40749 ^ _779300) ^ [_1580155, _1580157, _1580159] : [class_Complete__Lattice_Ocomplete__lattice(_1580155), hBOOL(hAPP(hAPP(c_member(_1580155), _1580157), _1580159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1580155), c_Complete__Lattice_OInf__class_OInf(_1580155, _1580159)), _1580157)))], (40759 ^ _779300) ^ [_1580320] : [class_Complete__Lattice_Ocomplete__lattice(_1580320), -(c_Complete__Lattice_OSup__class_OSup(_1580320, c_Orderings_Obot__class_Obot(tc_fun(_1580320, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1580320))], (40765 ^ _779300) ^ [_1580413, _1580415, _1580417] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580413, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1580413, tc_HOL_Obool), tc_HOL_Obool)), _1580415), _1580417)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1580413, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580413, tc_HOL_Obool), _1580415)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580413, tc_HOL_Obool), _1580417)))], (40767 ^ _779300) ^ [_1580483, _1580485] : [class_Complete__Lattice_Ocomplete__lattice(_1580483), -(c_Complete__Lattice_OSup__class_OSup(_1580483, hAPP(hAPP(c_Set_Oinsert(_1580483), _1580485), c_Orderings_Obot__class_Obot(tc_fun(_1580483, tc_HOL_Obool)))) = _1580485)], (40773 ^ _779300) ^ [_1580590, _1580592, _1580594] : [class_Complete__Lattice_Ocomplete__lattice(_1580590), -(c_Complete__Lattice_OSup__class_OSup(_1580590, hAPP(hAPP(c_Set_Oinsert(_1580590), _1580592), _1580594)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1580590), _1580592), c_Complete__Lattice_OSup__class_OSup(_1580590, _1580594)))], (40779 ^ _779300) ^ [_1580711, _1580713, _1580715, _1580717, _1580719] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1580711, tc_fun(_1580713, tc_HOL_Obool)), _1580715), hAPP(hAPP(c_COMBS(_1580711, tc_fun(_1580713, tc_HOL_Obool), tc_fun(_1580713, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1580713, tc_HOL_Obool), tc_fun(tc_fun(_1580713, tc_HOL_Obool), tc_fun(_1580713, tc_HOL_Obool)), _1580711), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1580713, tc_HOL_Obool))), _1580717)), _1580719)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1580713, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580713, tc_HOL_Obool), hAPP(c_Set_Oimage(_1580711, tc_fun(_1580713, tc_HOL_Obool), _1580717), _1580715))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580713, tc_HOL_Obool), hAPP(c_Set_Oimage(_1580711, tc_fun(_1580713, tc_HOL_Obool), _1580719), _1580715))))], (40781 ^ _779300) ^ [_1580840, _1580842] : [class_Complete__Lattice_Ocomplete__lattice(_1580840), -(c_Complete__Lattice_OInf__class_OInf(_1580840, hAPP(hAPP(c_Set_Oinsert(_1580840), _1580842), c_Orderings_Obot__class_Obot(tc_fun(_1580840, tc_HOL_Obool)))) = _1580842)], (40787 ^ _779300) ^ [_1580947] : [class_Complete__Lattice_Ocomplete__lattice(_1580947), -(c_Complete__Lattice_OSup__class_OSup(_1580947, c_Orderings_Otop__class_Otop(tc_fun(_1580947, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1580947))], (40793 ^ _779300) ^ [_1581040] : [class_Complete__Lattice_Ocomplete__lattice(_1581040), -(c_Complete__Lattice_OInf__class_OInf(_1581040, c_Orderings_Obot__class_Obot(tc_fun(_1581040, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1581040))], (40799 ^ _779300) ^ [_1581133] : [class_Complete__Lattice_Ocomplete__lattice(_1581133), -(c_Complete__Lattice_OInf__class_OInf(_1581133, c_Orderings_Otop__class_Otop(tc_fun(_1581133, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1581133))], (40805 ^ _779300) ^ [_1581226, _1581228, _1581230] : [class_Complete__Lattice_Ocomplete__lattice(_1581226), -(c_Complete__Lattice_OInf__class_OInf(_1581226, hAPP(hAPP(c_Set_Oinsert(_1581226), _1581228), _1581230)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1581226), _1581228), c_Complete__Lattice_OInf__class_OInf(_1581226, _1581230)))], (40811 ^ _779300) ^ [_1581347, _1581349, _1581351] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1581347, tc_HOL_Obool)), _1581349), _1581351) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581347, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1581347, tc_HOL_Obool)), _1581349), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1581347, tc_HOL_Obool)), _1581351), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1581347, tc_HOL_Obool), tc_HOL_Obool))))))], (40813 ^ _779300) ^ [_1581421, _1581423, _1581425, _1581427, _1581429] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1581421, tc_fun(_1581423, tc_HOL_Obool)), _1581425), hAPP(hAPP(c_COMBS(_1581421, tc_fun(_1581423, tc_HOL_Obool), tc_fun(_1581423, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581423, tc_HOL_Obool), tc_fun(tc_fun(_1581423, tc_HOL_Obool), tc_fun(_1581423, tc_HOL_Obool)), _1581421), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1581423, tc_HOL_Obool))), _1581427)), _1581429)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1581423, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581423, tc_HOL_Obool), hAPP(c_Set_Oimage(_1581421, tc_fun(_1581423, tc_HOL_Obool), _1581427), _1581425))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581423, tc_HOL_Obool), hAPP(c_Set_Oimage(_1581421, tc_fun(_1581423, tc_HOL_Obool), _1581429), _1581425))))], (40815 ^ _779300) ^ [_1581550, _1581552, _1581554] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1581550, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581550, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1581550, tc_HOL_Obool), tc_HOL_Obool)), _1581552), _1581554))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1581550, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581550, tc_HOL_Obool), _1581552)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581550, tc_HOL_Obool), _1581554)))))], (40817 ^ _779300) ^ [_1581630, _1581632, _1581634] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1581630, tc_HOL_Obool)), _1581632), _1581634) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1581630, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1581630, tc_HOL_Obool)), _1581632), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1581630, tc_HOL_Obool)), _1581634), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1581630, tc_HOL_Obool), tc_HOL_Obool))))))], (40819 ^ _779300) ^ [_1581704, _1581706, _1581708] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1581704, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1581704, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1581704, tc_HOL_Obool), _1581706)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1581704, tc_HOL_Obool), _1581708))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1581704, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1581704, tc_HOL_Obool), tc_HOL_Obool)), _1581706), _1581708)))))], (40821 ^ _779300) ^ [_1581784, _1581786, _1581788] : [class_Complete__Lattice_Ocomplete__lattice(_1581784), -(c_Complete__Lattice_OSup__class_OSup(_1581784, hAPP(hAPP(c_Set_Oinsert(_1581784), _1581786), hAPP(hAPP(c_Set_Oinsert(_1581784), _1581788), c_Orderings_Obot__class_Obot(tc_fun(_1581784, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1581784), _1581786), _1581788))], (40827 ^ _779300) ^ [_1581925, _1581927, _1581929] : [class_Complete__Lattice_Ocomplete__lattice(_1581925), -(c_Complete__Lattice_OInf__class_OInf(_1581925, hAPP(hAPP(c_Set_Oinsert(_1581925), _1581927), hAPP(hAPP(c_Set_Oinsert(_1581925), _1581929), c_Orderings_Obot__class_Obot(tc_fun(_1581925, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1581925), _1581927), _1581929))], (40833 ^ _779300) ^ [_1582066, _1582068, _1582070] : [class_Complete__Lattice_Ocomplete__lattice(_1582066), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582066), _1582068)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1582066), _1582070), c_Complete__Lattice_OSup__class_OSup(_1582066, _1582068)) = hAPP(hAPP(c_Finite__Set_Ofold(_1582066, _1582066, c_Lattices_Osemilattice__sup__class_Osup(_1582066)), _1582070), _1582068))], (40843 ^ _779300) ^ [_1582251, _1582253] : [class_Complete__Lattice_Ocomplete__lattice(_1582251), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582251), _1582253)), -(_1582253 = c_Orderings_Obot__class_Obot(tc_fun(_1582251, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1582251, _1582253) = c_Complete__Lattice_OSup__class_OSup(_1582251, _1582253))], (40857 ^ _779300) ^ [_1582423, _1582425, _1582427] : [class_Complete__Lattice_Ocomplete__lattice(_1582423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582423), _1582425)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1582423), _1582427), c_Complete__Lattice_OInf__class_OInf(_1582423, _1582425)) = hAPP(hAPP(c_Finite__Set_Ofold(_1582423, _1582423, c_Lattices_Osemilattice__inf__class_Oinf(_1582423)), _1582427), _1582425))], (40867 ^ _779300) ^ [_1582608, _1582610] : [class_Complete__Lattice_Ocomplete__lattice(_1582608), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582608), _1582610)), -(_1582610 = c_Orderings_Obot__class_Obot(tc_fun(_1582608, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1582608, _1582610) = c_Complete__Lattice_OInf__class_OInf(_1582608, _1582610))], (40881 ^ _779300) ^ [_1582780, _1582782, _1582784, _1582786, _1582788, _1582790, _1582792, _1582794] : [c_Fun_Oinj__on(_1582780, _1582782, _1582784, _1582786), 40887 ^ _779300 : [(40888 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1582788), 40886 ^ [_1582780, _1582782, _1582784, _1582786, _1582788, _1582790, _1582792, _1582794]), _1582790)))], (40890 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1582780, tc_HOL_Obool)), hAPP(_1582792, 40886 ^ [_1582780, _1582782, _1582784, _1582786, _1582788, _1582790, _1582792, _1582794])), _1582786))]], hBOOL(hAPP(hAPP(c_member(_1582788), _1582794), _1582790)), -(hAPP(c_Set_Oimage(_1582780, _1582782, _1582784), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1582788, tc_fun(_1582780, tc_HOL_Obool)), _1582790), _1582792)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1582788, tc_fun(_1582782, tc_HOL_Obool)), _1582790), hAPP(hAPP(c_COMBB(tc_fun(_1582780, tc_HOL_Obool), tc_fun(_1582782, tc_HOL_Obool), _1582788), c_Set_Oimage(_1582780, _1582782, _1582784)), _1582792)))], (40898 ^ _779300) ^ [_1583269, _1583271, _1583273] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1583269, tc_HOL_Obool)), _1583271)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583269), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1583269, tc_HOL_Obool), _1583271))), 40908 ^ _779300 : [(40909 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1583269, tc_HOL_Obool)), 40907 ^ [_1583269, _1583271, _1583273]), _1583271)))], (40911 ^ _779300) ^ [] : [hAPP(c_Finite__Set_Ocard(_1583269), 40907 ^ [_1583269, _1583271, _1583273]) = _1583273]], 40915 ^ _779300 : [(40916 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1583269, tc_HOL_Obool)), 40914 ^ [_1583269, _1583271, _1583273]), _1583271)))], (40919 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1583269, tc_HOL_Obool)), 40917 ^ [_1583269, _1583271, _1583273]), _1583271)))], (40921 ^ _779300) ^ [] : [40914 ^ [_1583269, _1583271, _1583273] = 40917 ^ [_1583269, _1583271, _1583273]], (40923 ^ _779300) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1583269, tc_HOL_Obool)), 40914 ^ [_1583269, _1583271, _1583273]), 40917 ^ [_1583269, _1583271, _1583273]) = c_Orderings_Obot__class_Obot(tc_fun(_1583269, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1583273), hAPP(c_Finite__Set_Ocard(tc_fun(_1583269, tc_HOL_Obool)), _1583271)) = hAPP(c_Finite__Set_Ocard(_1583269), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1583269, tc_HOL_Obool), _1583271)))], (40927 ^ _779300) ^ [_1584051, _1584053] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1584051, tc_HOL_Obool), _1584053) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1584051, tc_HOL_Obool), tc_fun(_1584051, tc_HOL_Obool)), _1584053), c_COMBI(tc_fun(_1584051, tc_HOL_Obool))))], (40929 ^ _779300) ^ [_1584102, _1584104] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1584102, tc_HOL_Obool), _1584104) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1584102, tc_HOL_Obool), tc_fun(_1584102, tc_HOL_Obool)), _1584104), c_COMBI(tc_fun(_1584102, tc_HOL_Obool))))], (40931 ^ _779300) ^ [_1584153, _1584155] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1584153, tc_HOL_Obool)), _1584155)), 40937 ^ _779300 : [(40938 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1584153, tc_HOL_Obool)), 40936 ^ [_1584153, _1584155]), _1584155)))], (40940 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1584153), 40936 ^ [_1584153, _1584155]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1584153), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1584153, tc_HOL_Obool), _1584155))))], (40944 ^ _779300) ^ [_1584411, _1584413, _1584415] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1584411, tc_HOL_Obool)), _1584413), _1584415))), 40950 ^ _779300 : [(40951 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1584411, tc_HOL_Obool)), 40949 ^ [_1584411, _1584413, _1584415]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1584411, tc_HOL_Obool)), _1584413), _1584415))))], (40954 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1584411, tc_HOL_Obool)), 40952 ^ [_1584411, _1584413, _1584415]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1584411, tc_HOL_Obool)), _1584413), _1584415))))], (40956 ^ _779300) ^ [] : [40949 ^ [_1584411, _1584413, _1584415] = 40952 ^ [_1584411, _1584413, _1584415]], (40958 ^ _779300) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1584411, tc_HOL_Obool)), 40949 ^ [_1584411, _1584413, _1584415]), 40952 ^ [_1584411, _1584413, _1584415]) = c_Orderings_Obot__class_Obot(tc_fun(_1584411, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1584411, tc_HOL_Obool)), _1584413), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1584411, tc_HOL_Obool), _1584415)) = c_Orderings_Obot__class_Obot(tc_fun(_1584411, tc_HOL_Obool)))], (40962 ^ _779300) ^ [_1585004, _1585006, _1585008, _1585010] : [-(_1585004 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1585006, tc_HOL_Obool), tc_HOL_Obool))), 40968 ^ _779300 : [(40969 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1585006, tc_HOL_Obool)), 40967 ^ [_1585004, _1585006, _1585008, _1585010]), _1585004)))], (40971 ^ _779300) ^ [] : [c_Fun_Oinj__on(_1585006, _1585008, _1585010, 40967 ^ [_1585004, _1585006, _1585008, _1585010])]], -(c_Fun_Oinj__on(_1585006, _1585008, _1585010, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1585006, tc_HOL_Obool), _1585004)))], (40975 ^ _779300) ^ [_1585265, _1585267, _1585269] : [40977 ^ _779300 : [(40978 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1585265, tc_HOL_Obool)), 40976 ^ [_1585265, _1585267, _1585269]), _1585267)))], (40980 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1585265, tc_HOL_Obool)), 40976 ^ [_1585265, _1585267, _1585269]), _1585269))]], -(_1585267 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1585265, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1585265, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1585265, tc_HOL_Obool), _1585267)), _1585269)))], (40988 ^ _779300) ^ [_1585526, _1585528, _1585530, _1585532, _1585534, _1585536] : [-(_1585526 = c_Orderings_Obot__class_Obot(tc_fun(_1585528, tc_HOL_Obool))), 40994 ^ _779300 : [(40995 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1585528), 40993 ^ [_1585526, _1585528, _1585530, _1585532, _1585534, _1585536]), _1585526)))], (40997 ^ _779300) ^ [] : [c_Fun_Oinj__on(_1585530, _1585532, _1585534, hAPP(_1585536, 40993 ^ [_1585526, _1585528, _1585530, _1585532, _1585534, _1585536]))]], -(c_Fun_Oinj__on(_1585530, _1585532, _1585534, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1585528, tc_fun(_1585530, tc_HOL_Obool)), _1585526), _1585536)))], (41001 ^ _779300) ^ [_1585818, _1585820, _1585822, _1585824, _1585826, _1585828, _1585830] : [c_Finite__Set_Ofun__left__comm(_1585818, _1585820, _1585822), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1585818, _1585820, _1585822, _1585824, hAPP(hAPP(c_Set_Oinsert(_1585818), _1585826), _1585828)), _1585830)), -(hBOOL(hAPP(hAPP(c_member(_1585818), _1585826), _1585828))), 41013 ^ _779300 : [(41014 ^ _779300) ^ [] : [-(_1585830 = hAPP(hAPP(_1585822, _1585826), 41012 ^ [_1585818, _1585820, _1585822, _1585824, _1585826, _1585828, _1585830]))], (41016 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1585818, _1585820, _1585822, _1585824, _1585828), 41012 ^ [_1585818, _1585820, _1585822, _1585824, _1585826, _1585828, _1585830])))]]], (41018 ^ _779300) ^ [_1586144, _1586146, _1586148, _1586150] : [class_Orderings_Olinorder(_1586144), hBOOL(hAPP(c_Finite__Set_Ofinite(_1586144), _1586146)), 41028 ^ _779300 : [(41029 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1586144), 41027 ^ [_1586144, _1586146, _1586148, _1586150]), _1586146)))], (41031 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1586144), 41027 ^ [_1586144, _1586146, _1586148, _1586150]), _1586148))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1586144), hAPP(hAPP(c_Finite__Set_Ofold(_1586144, _1586144, c_Orderings_Oord__class_Omax(_1586144)), _1586150), _1586146)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1586144), _1586148), _1586150))))], (41035 ^ _779300) ^ [_1586508, _1586510, _1586512, _1586514] : [class_Orderings_Olinorder(_1586508), hBOOL(hAPP(c_Finite__Set_Ofinite(_1586508), _1586510)), 41045 ^ _779300 : [(41046 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1586508), 41044 ^ [_1586508, _1586510, _1586512, _1586514]), _1586510)))], (41048 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1586508), _1586512), 41044 ^ [_1586508, _1586510, _1586512, _1586514]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1586508), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1586508), _1586512), _1586514)), hAPP(hAPP(c_Finite__Set_Ofold(_1586508, _1586508, c_Orderings_Oord__class_Omin(_1586508)), _1586514), _1586510))))], (41052 ^ _779300) ^ [_1586872, _1586874, _1586876] : [41054 ^ _779300 : [(41055 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1586872, tc_HOL_Obool)), 41053 ^ [_1586872, _1586874, _1586876]), _1586874)))], (41057 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1586872), _1586876), 41053 ^ [_1586872, _1586874, _1586876]))]], -(hBOOL(hAPP(hAPP(c_member(_1586872), _1586876), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1586872, tc_HOL_Obool), _1586874))))], (41061 ^ _779300) ^ [_1587088, _1587090, _1587092, _1587094] : [class_Lattices_Osemilattice__inf(_1587088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1587088), _1587090)), 41071 ^ _779300 : [(41072 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1587088), 41070 ^ [_1587088, _1587090, _1587092, _1587094]), _1587090)))], (41074 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1587088), _1587092), 41070 ^ [_1587088, _1587090, _1587092, _1587094]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1587088), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1587088), _1587092), _1587094)), hAPP(hAPP(c_Finite__Set_Ofold(_1587088, _1587088, c_Lattices_Osemilattice__inf__class_Oinf(_1587088)), _1587094), _1587090))))], (41078 ^ _779300) ^ [_1587452, _1587454, _1587456, _1587458] : [class_Lattices_Osemilattice__sup(_1587452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1587452), _1587454)), 41088 ^ _779300 : [(41089 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1587452), 41087 ^ [_1587452, _1587454, _1587456, _1587458]), _1587454)))], (41091 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1587452), 41087 ^ [_1587452, _1587454, _1587456, _1587458]), _1587456))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1587452), hAPP(hAPP(c_Finite__Set_Ofold(_1587452, _1587452, c_Lattices_Osemilattice__sup__class_Osup(_1587452)), _1587458), _1587454)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1587452), _1587456), _1587458))))], (41095 ^ _779300) ^ [_1587816, _1587818, _1587820] : [class_Divides_Osemiring__div(_1587816), -(_1587818 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1587816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1587816), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1587816), _1587818), _1587820)), _1587820)), c_Divides_Odiv__class_Omod(_1587816, _1587818, _1587820)))], (41118 ^ _779300) ^ [_1588483, _1588485] : [-(c_Wellfounded_Owf(_1588483, _1588485)), 41121 ^ _779300 : [(41122 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588483), 41120 ^ [_1588483, _1588485]), 41119 ^ [_1588483, _1588485])))], (41124 ^ _779300) ^ [_1588703] : [hBOOL(hAPP(hAPP(c_member(_1588483), _1588703), 41119 ^ [_1588483, _1588485])), 41128 ^ _779300 : [(41129 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588483, _1588483)), hAPP(hAPP(c_Product__Type_OPair(_1588483, _1588483), 41127 ^ [_1588483, _1588485, _1588703]), _1588703)), _1588485)))], (41131 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588483), 41127 ^ [_1588483, _1588485, _1588703]), 41119 ^ [_1588483, _1588485])))]]]]], (41101 ^ _779300) ^ [_1587964, _1587966] : [c_Wellfounded_Owf(_1587964, _1587966), 41104 ^ _779300 : [(41105 ^ _779300) ^ [_1588096] : [41106 ^ _779300 : [(41107 ^ _779300) ^ [_1588201] : [hBOOL(hAPP(hAPP(c_member(_1587964), _1588201), _1588096))]], 41109 ^ _779300 : [(41110 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1587964), 41108 ^ [_1587964, _1587966, _1588096]), _1588096)))], (41112 ^ _779300) ^ [_1588323] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587964, _1587964)), hAPP(hAPP(c_Product__Type_OPair(_1587964, _1587964), _1588323), 41108 ^ [_1587964, _1587966, _1588096])), _1587966)), hBOOL(hAPP(hAPP(c_member(_1587964), _1588323), _1588096))]]]]], (41135 ^ _779300) ^ [_1588959, _1588961] : [-(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)))), _1588959)) = 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)))), _1588961))), 41137 ^ _779300 : [(41138 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41136 ^ [_1588959, _1588961])))], (41140 ^ _779300) ^ [] : [41141 ^ _779300 : [(41142 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1588959, 41136 ^ [_1588959, _1588961])))], (41144 ^ _779300) ^ [] : [hBOOL(hAPP(_1588961, 41136 ^ [_1588959, _1588961]))]], 41145 ^ _779300 : [(41146 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1588961, 41136 ^ [_1588959, _1588961])))], (41148 ^ _779300) ^ [] : [hBOOL(hAPP(_1588959, 41136 ^ [_1588959, _1588961]))]]]]], (41152 ^ _779300) ^ [_1589280, _1589282, _1589284, _1589286, _1589288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1589280, tc_HOL_Obool)), _1589282), _1589284)), 41158 ^ _779300 : [(41159 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589280), 41157 ^ [_1589280, _1589282, _1589284, _1589286, _1589288]), _1589282)))], (41161 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1589286, 41157 ^ [_1589280, _1589282, _1589284, _1589286, _1589288])))], (41163 ^ _779300) ^ [] : [hBOOL(hAPP(_1589288, 41157 ^ [_1589280, _1589282, _1589284, _1589286, _1589288]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1589280, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589280, tc_HOL_Obool)), _1589282), hAPP(c_Set_OCollect(_1589280), _1589286))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589280, tc_HOL_Obool)), _1589284), hAPP(c_Set_OCollect(_1589280), _1589288)))))], (41167 ^ _779300) ^ [_1589680, _1589682, _1589684] : [hBOOL(hAPP(hAPP(c_member(_1589680), _1589682), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1589680, tc_HOL_Obool), _1589684))), 41171 ^ _779300 : [(41172 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589680), _1589682), 41170 ^ [_1589680, _1589682, _1589684])))], (41174 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1589680, tc_HOL_Obool)), 41170 ^ [_1589680, _1589682, _1589684]), _1589684)))]]], (41176 ^ _779300) ^ [_1589872, _1589874, _1589876, _1589878] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589872, _1589874)), _1589876), hAPP(c_Relation_Oconverse(_1589874, _1589872), _1589878))), 41181 ^ _779300 : [(41182 ^ _779300) ^ [] : [-(_1589876 = hAPP(hAPP(c_Product__Type_OPair(_1589872, _1589874), 41180 ^ [_1589872, _1589874, _1589876, _1589878]), 41179 ^ [_1589872, _1589874, _1589876, _1589878]))], (41184 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589874, _1589872)), hAPP(hAPP(c_Product__Type_OPair(_1589874, _1589872), 41179 ^ [_1589872, _1589874, _1589876, _1589878]), 41180 ^ [_1589872, _1589874, _1589876, _1589878])), _1589878)))]]], (41186 ^ _779300) ^ [_1590125, _1590127, _1590129, _1590131, _1590133, _1590135] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590125, _1590127)), _1590129), hAPP(hAPP(c_Relation_Orel__comp(_1590125, _1590131, _1590127), _1590133), _1590135))), 41192 ^ _779300 : [(41193 ^ _779300) ^ [] : [-(_1590129 = hAPP(hAPP(c_Product__Type_OPair(_1590125, _1590127), 41189 ^ [_1590125, _1590127, _1590129, _1590131, _1590133, _1590135]), 41191 ^ [_1590125, _1590127, _1590129, _1590131, _1590133, _1590135]))], (41195 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590125, _1590131)), hAPP(hAPP(c_Product__Type_OPair(_1590125, _1590131), 41189 ^ [_1590125, _1590127, _1590129, _1590131, _1590133, _1590135]), 41190 ^ [_1590125, _1590127, _1590129, _1590131, _1590133, _1590135])), _1590133)))], (41197 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590131, _1590127)), hAPP(hAPP(c_Product__Type_OPair(_1590131, _1590127), 41190 ^ [_1590125, _1590127, _1590129, _1590131, _1590133, _1590135]), 41191 ^ [_1590125, _1590127, _1590129, _1590131, _1590133, _1590135])), _1590135)))]]], (41199 ^ _779300) ^ [_1590503, _1590505, _1590507] : [-(c_Nitpick_Oplus__frac(_1590503, _1590505, _1590507) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1590503), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1590503), _1590505), hAPP(c_Nitpick_Odenom(_1590503), _1590507))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1590503), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1590503), tc_Int_Oint), c_Nitpick_Ofrac(_1590503)), 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(_1590503), _1590505))), 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(_1590503), _1590505))))), 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(_1590503), _1590507))), 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(_1590503), _1590507)))))), c_COMBI(tc_Int_Oint))))], (41201 ^ _779300) ^ [_1590634, _1590636, _1590638, _1590640] : [class_Rings_Olinordered__semidom(_1590634), 41207 ^ _779300 : [(41208 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590636), 41206 ^ [_1590634, _1590636, _1590638, _1590640]), _1590638)))], (41210 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1590634), c_Groups_Ozero__class_Ozero(_1590634)), hAPP(_1590640, 41206 ^ [_1590634, _1590636, _1590638, _1590640])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1590634), c_Groups_Ozero__class_Ozero(_1590634)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1590636, _1590634), _1590640), _1590638))))], (41214 ^ _779300) ^ [_1590930, _1590932, _1590934] : [-(c_Nitpick_Otimes__frac(_1590930, _1590932, _1590934) = hAPP(hAPP(c_Nitpick_Ofrac(_1590930), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1590930), _1590932)), hAPP(c_Nitpick_Onum(_1590930), _1590934))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1590930), _1590932)), hAPP(c_Nitpick_Odenom(_1590930), _1590934))))], (41216 ^ _779300) ^ [_1591001, _1591003, _1591005] : [-(c_Nitpick_Oof__frac(_1591003, _1591001, _1591005) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1591001), hAPP(c_Int_Oring__1__class_Oof__int(_1591001), hAPP(c_Nitpick_Onum(_1591003), _1591005))), hAPP(c_Int_Oring__1__class_Oof__int(_1591001), hAPP(c_Nitpick_Odenom(_1591003), _1591005)))), class_Rings_Oinverse(_1591001), class_Rings_Oring__1(_1591001)], (41226 ^ _779300) ^ [_1591194, _1591196] : [-(c_Nitpick_Oinverse__frac(_1591194, _1591196) = hAPP(hAPP(c_Nitpick_Ofrac(_1591194), hAPP(c_Nitpick_Odenom(_1591194), _1591196)), hAPP(c_Nitpick_Onum(_1591194), _1591196)))], (41228 ^ _779300) ^ [_1591240, _1591242] : [-(c_Nitpick_Ouminus__frac(_1591240, _1591242) = c_Nitpick_OAbs__Frac(_1591240, 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(_1591240), _1591242))), hAPP(c_Nitpick_Odenom(_1591240), _1591242))))], (41230 ^ _779300) ^ [_1591308, _1591310, _1591312] : [c_Nitpick_Oless__frac(_1591308, _1591310, _1591312), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591308), c_Nitpick_Oplus__frac(_1591308, _1591310, c_Nitpick_Ouminus__frac(_1591308, _1591312)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41236 ^ _779300) ^ [_1591419, _1591421, _1591423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591419), c_Nitpick_Oplus__frac(_1591419, _1591421, c_Nitpick_Ouminus__frac(_1591419, _1591423)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1591419, _1591421, _1591423))], (41242 ^ _779300) ^ [_1591554, _1591556, _1591558] : [c_Nitpick_Oless__eq__frac(_1591554, _1591556, _1591558), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591554), c_Nitpick_Oplus__frac(_1591554, _1591556, c_Nitpick_Ouminus__frac(_1591554, _1591558)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41248 ^ _779300) ^ [_1591665, _1591667, _1591669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591665), c_Nitpick_Oplus__frac(_1591665, _1591667, c_Nitpick_Ouminus__frac(_1591665, _1591669)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1591665, _1591667, _1591669))], (41254 ^ _779300) ^ [_1591782] : [-(c_Nitpick_Odenom(_1591782) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1591782, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1591782)))], (41256 ^ _779300) ^ [_1591817] : [-(c_Nitpick_Onum(_1591817) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1591817, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1591817)))], (41258 ^ _779300) ^ [_1591852, _1591854, _1591856] : [-(c_Product__Type_Ointernal__split(_1591852, _1591854, _1591856) = c_Product__Type_Oprod_Oprod__case(_1591852, _1591854, _1591856))], (41260 ^ _779300) ^ [_1591887, _1591889, _1591891, _1591893] : [class_Rings_Olinordered__semidom(_1591887), 41266 ^ _779300 : [(41267 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591889), 41265 ^ [_1591887, _1591889, _1591891, _1591893]), _1591891)))], (41269 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1591887), c_Groups_Ozero__class_Ozero(_1591887)), hAPP(_1591893, 41265 ^ [_1591887, _1591889, _1591891, _1591893])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1591887), c_Groups_Ozero__class_Ozero(_1591887)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1591889, _1591887), _1591893), _1591891))))], (41273 ^ _779300) ^ [_1592183, _1592185, _1592187, _1592189, _1592191, _1592193] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1592183, _1592185, _1592187), _1592189), hAPP(hAPP(c_Product__Type_OPair(_1592183, _1592185), _1592191), _1592193)) = hAPP(hAPP(_1592189, _1592191), _1592193))], (41275 ^ _779300) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41277 ^ _779300) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41279 ^ _779300) ^ [_1592277, _1592279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41280 ^ [_1592277, _1592279]), hAPP(_1592277, 41280 ^ [_1592277, _1592279]))), -(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)), _1592277)), _1592279)))))], (41286 ^ _779300) ^ [_1592437, _1592439] : [-(c_List_Olenlex(_1592437, _1592439) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1592437)), tc_List_Olist(_1592437)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1592437), c_Wellfounded_Oless__than, c_List_Olex(_1592437, _1592439))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592437), tc_List_Olist(_1592437), tc_prod(tc_Nat_Onat, tc_List_Olist(_1592437))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1592437), tc_prod(tc_Nat_Onat, tc_List_Olist(_1592437))), tc_List_Olist(_1592437)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1592437))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592437)))), c_COMBI(tc_List_Olist(_1592437)))))], (41288 ^ _779300) ^ [_1592544, _1592546, _1592548] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592544)), _1592546) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592544)), _1592548)), _1592546 = _1592548], (41294 ^ _779300) ^ [_1592636, _1592638, _1592640, _1592642, _1592644] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1592636), tc_List_Olist(_1592636))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1592636), tc_List_Olist(_1592636)), _1592638), _1592640)), hAPP(c_List_Olexn(_1592636, _1592642), _1592644))), 41297 ^ _779300 : [(41298 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592636)), _1592638) = _1592644)], (41300 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592636)), _1592640) = _1592644)]]], (41302 ^ _779300) ^ [_1592839, _1592841] : [-(c_List_Olenlex(_1592839, _1592841) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1592839), tc_List_Olist(_1592839))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1592839), tc_List_Olist(_1592839), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592839), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592839), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool)), tc_List_Olist(_1592839)), c_COMBS(tc_List_Olist(_1592839), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592839), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1592839)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1592839)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592839), tc_fun(tc_List_Olist(_1592839), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1592839), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool)), tc_List_Olist(_1592839)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1592839))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1592839)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1592839))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592839)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592839), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592839), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool)), tc_List_Olist(_1592839)), c_COMBS(tc_List_Olist(_1592839), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592839), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1592839)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1592839)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592839), tc_fun(tc_List_Olist(_1592839), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1592839), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool)), tc_List_Olist(_1592839)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1592839))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1592839)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1592839))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592839)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592839), tc_fun(tc_prod(tc_List_Olist(_1592839), tc_List_Olist(_1592839)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592839), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592839), tc_List_Olist(_1592839)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592839), tc_List_Olist(_1592839)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592839), tc_HOL_Obool)), tc_List_Olist(_1592839)), c_COMBC(tc_List_Olist(_1592839), tc_fun(tc_prod(tc_List_Olist(_1592839), tc_List_Olist(_1592839)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592839), tc_prod(tc_List_Olist(_1592839), tc_List_Olist(_1592839))), tc_fun(tc_List_Olist(_1592839), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592839), tc_List_Olist(_1592839)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1592839)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1592839), tc_List_Olist(_1592839)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592839), tc_List_Olist(_1592839)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1592839)), c_member(tc_prod(tc_List_Olist(_1592839), tc_List_Olist(_1592839))))), c_Product__Type_OPair(tc_List_Olist(_1592839), tc_List_Olist(_1592839))))), c_List_Olex(_1592839, _1592841)))))))], (41304 ^ _779300) ^ [_1593395, _1593397, _1593399] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593395)), c_List_Osublist(_1593395, _1593397, _1593399)) = 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(_1593395)), _1593397)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1593399)))))], (41306 ^ _779300) ^ [_1593461, _1593463, _1593465] : [-(hAPP(c_List_Olexn(_1593461, _1593463), hAPP(c_Nat_OSuc, _1593465)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1593461), tc_List_Olist(_1593461)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1593461, tc_List_Olist(_1593461)), tc_prod(_1593461, tc_List_Olist(_1593461))), tc_prod(tc_List_Olist(_1593461), tc_List_Olist(_1593461)), c_Product__Type_Omap__pair(tc_prod(_1593461, tc_List_Olist(_1593461)), tc_List_Olist(_1593461), tc_prod(_1593461, tc_List_Olist(_1593461)), tc_List_Olist(_1593461), hAPP(c_Product__Type_Oprod_Oprod__case(_1593461, tc_List_Olist(_1593461), tc_List_Olist(_1593461)), c_List_Olist_OCons(_1593461)), hAPP(c_Product__Type_Oprod_Oprod__case(_1593461, tc_List_Olist(_1593461), tc_List_Olist(_1593461)), c_List_Olist_OCons(_1593461)))), c_Wellfounded_Olex__prod(_1593461, tc_List_Olist(_1593461), _1593463, hAPP(c_List_Olexn(_1593461, _1593463), _1593465)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1593461), tc_List_Olist(_1593461))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1593461), tc_List_Olist(_1593461), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593461), tc_fun(tc_List_Olist(_1593461), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593461), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593461), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593461), tc_HOL_Obool)), tc_List_Olist(_1593461)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1593461))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593461)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593461), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593461)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593461)))), hAPP(c_Nat_OSuc, _1593465))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593461), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593461)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593461)))), hAPP(c_Nat_OSuc, _1593465)))))))], (41308 ^ _779300) ^ [_1593752, _1593754, _1593756, _1593758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593752)), _1593754)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593752)), _1593756))), _1593754 = hAPP(hAPP(c_List_Olist_OCons(_1593752), _1593758), _1593756)], (41314 ^ _779300) ^ [_1593912, _1593914, _1593916, _1593918, _1593920] : [hAPP(hAPP(c_List_Olist_OCons(_1593912), _1593914), _1593916) = hAPP(hAPP(c_List_Olist_OCons(_1593912), _1593918), _1593920), 41317 ^ _779300 : [(41318 ^ _779300) ^ [] : [-(_1593914 = _1593918)], (41320 ^ _779300) ^ [] : [-(_1593916 = _1593920)]]], (41322 ^ _779300) ^ [_1594049, _1594051, _1594053, _1594055, _1594057] : [-(hAPP(hAPP(c_List_Olist_OCons(_1594049), _1594051), _1594053) = hAPP(hAPP(c_List_Olist_OCons(_1594049), _1594055), _1594057)), _1594051 = _1594055, _1594053 = _1594057], (41332 ^ _779300) ^ [_1594239, _1594241, _1594243] : [hAPP(hAPP(c_List_Olist_OCons(_1594239), _1594241), _1594243) = _1594243], (41334 ^ _779300) ^ [_1594289, _1594291, _1594293] : [_1594289 = hAPP(hAPP(c_List_Olist_OCons(_1594291), _1594293), _1594289)], (41336 ^ _779300) ^ [_1594324, _1594326, _1594328] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594324)), hAPP(hAPP(c_List_Olist_OCons(_1594324), _1594326), _1594328)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594324)), _1594328)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41338 ^ _779300) ^ [_1594406, _1594408, _1594410, _1594412, _1594414, _1594416] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594406), tc_List_Olist(_1594406))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594406), tc_List_Olist(_1594406)), hAPP(hAPP(c_List_Olist_OCons(_1594406), _1594408), _1594410)), hAPP(hAPP(c_List_Olist_OCons(_1594406), _1594412), _1594414))), c_List_Olex(_1594406, _1594416))), 41343 ^ _779300 : [(41344 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594406, _1594406)), hAPP(hAPP(c_Product__Type_OPair(_1594406, _1594406), _1594408), _1594412)), _1594416)))], (41346 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594406)), _1594410) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594406)), _1594414))]], 41347 ^ _779300 : [(41348 ^ _779300) ^ [] : [-(_1594408 = _1594412)], (41350 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594406), tc_List_Olist(_1594406))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594406), tc_List_Olist(_1594406)), _1594410), _1594414)), c_List_Olex(_1594406, _1594416))))]]], (41352 ^ _779300) ^ [_1594804, _1594806, _1594808, _1594810, _1594812, _1594814] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594804), tc_List_Olist(_1594804))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594804), tc_List_Olist(_1594804)), hAPP(hAPP(c_List_Olist_OCons(_1594804), _1594806), _1594808)), hAPP(hAPP(c_List_Olist_OCons(_1594804), _1594810), _1594812))), c_List_Olex(_1594804, _1594814)))), 41353 ^ _779300 : [(41354 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594804, _1594804)), hAPP(hAPP(c_Product__Type_OPair(_1594804, _1594804), _1594806), _1594810)), _1594814)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594804)), _1594808) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594804)), _1594812)], (41360 ^ _779300) ^ [] : [_1594806 = _1594810, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594804), tc_List_Olist(_1594804))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594804), tc_List_Olist(_1594804)), _1594808), _1594812)), c_List_Olex(_1594804, _1594814)))]]], (41368 ^ _779300) ^ [_1595260, _1595262, _1595264] : [-(c_List_Oset__Cons(_1595260, _1595262, _1595264) = hAPP(c_Set_OCollect(tc_List_Olist(_1595260)), hAPP(hAPP(c_COMBB(tc_fun(_1595260, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1595260)), c_HOL_OEx(_1595260)), hAPP(hAPP(c_COMBB(tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool)), tc_fun(_1595260, tc_HOL_Obool), tc_List_Olist(_1595260)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), tc_HOL_Obool, _1595260), c_HOL_OEx(tc_List_Olist(_1595260)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595260), tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool)), tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595260, tc_fun(tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool))), tc_fun(tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool)), tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool))), tc_List_Olist(_1595260)), c_COMBS(_1595260, tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1595260, tc_fun(tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool))), tc_List_Olist(_1595260)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595260), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool)), _1595260), c_COMBS(tc_List_Olist(_1595260), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool)), tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1595260)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595260), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1595260), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1595260)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595260), tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_List_Olist(_1595260))), tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1595260), tc_List_Olist(_1595260)), tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool)), tc_fun(tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_List_Olist(_1595260))), tc_fun(_1595260, tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool))), tc_List_Olist(_1595260)), c_COMBB(tc_fun(tc_List_Olist(_1595260), tc_List_Olist(_1595260)), tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), _1595260)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1595260), tc_List_Olist(_1595260)), tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool)), tc_List_Olist(_1595260)), c_COMBB(tc_List_Olist(_1595260), tc_HOL_Obool, tc_List_Olist(_1595260))), c_fequal))), c_List_Olist_OCons(_1595260)))))), hAPP(hAPP(c_COMBC(_1595260, tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool)), _1595260), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1595260))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1595260), c_fconj), hAPP(hAPP(c_COMBC(_1595260, tc_fun(_1595260, tc_HOL_Obool), tc_HOL_Obool), c_member(_1595260)), _1595262)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595260), tc_fun(tc_List_Olist(_1595260), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1595260))), _1595264)))))))], (41370 ^ _779300) ^ [_1595810, _1595812, _1595814, _1595816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1595810), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1595812), _1595814))), -(hAPP(c_Random_Opick(_1595812, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1595812)), _1595814), _1595816)), _1595810) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1595812), _1595814))], (41376 ^ _779300) ^ [_1595953, _1595955, _1595957, _1595959] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1595953), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1595955), _1595957)))), -(hAPP(c_Random_Opick(_1595955, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1595955)), _1595957), _1595959)), _1595953) = hAPP(c_Random_Opick(_1595955, _1595959), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1595953), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1595955), _1595957))))], (41382 ^ _779300) ^ [_1596041, _1596043, _1596045] : [-(c_Random_Oselect__weight(_1596041, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1596041)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1596041), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1596043)), _1596045)) = c_Random_Oselect__weight(_1596041, _1596045))], (41384 ^ _779300) ^ [_1596121, _1596123, _1596125, _1596127, _1596129, _1596131] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596121), tc_List_Olist(_1596121))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596121), tc_List_Olist(_1596121)), hAPP(hAPP(c_List_Olist_OCons(_1596121), _1596123), _1596125)), hAPP(hAPP(c_List_Olist_OCons(_1596121), _1596127), _1596129))), c_List_Olexord(_1596121, _1596131))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596121, _1596121)), hAPP(hAPP(c_Product__Type_OPair(_1596121, _1596121), _1596123), _1596127)), _1596131))), 41391 ^ _779300 : [(41392 ^ _779300) ^ [] : [-(_1596123 = _1596127)], (41394 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596121), tc_List_Olist(_1596121))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596121), tc_List_Olist(_1596121)), _1596125), _1596129)), c_List_Olexord(_1596121, _1596131))))]]], (41396 ^ _779300) ^ [_1596448, _1596450, _1596452, _1596454, _1596456, _1596458] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596448), tc_List_Olist(_1596448))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596448), tc_List_Olist(_1596448)), hAPP(hAPP(c_List_Olist_OCons(_1596448), _1596450), _1596452)), hAPP(hAPP(c_List_Olist_OCons(_1596448), _1596454), _1596456))), c_List_Olexord(_1596448, _1596458)))), 41397 ^ _779300 : [(41398 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596448, _1596448)), hAPP(hAPP(c_Product__Type_OPair(_1596448, _1596448), _1596450), _1596454)), _1596458))], (41400 ^ _779300) ^ [] : [_1596450 = _1596454, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596448), tc_List_Olist(_1596448))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596448), tc_List_Olist(_1596448)), _1596452), _1596456)), c_List_Olexord(_1596448, _1596458)))]]], (41408 ^ _779300) ^ [_1596842, _1596844, _1596846, _1596848] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596842), tc_List_Olist(_1596842))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596842), tc_List_Olist(_1596842)), _1596844), _1596846)), c_List_Olex(_1596842, _1596848))), 41411 ^ _779300 : [(41412 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596842), tc_List_Olist(_1596842))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596842), tc_List_Olist(_1596842)), _1596844), _1596846)), c_List_Olexord(_1596842, _1596848))))], (41414 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596842)), _1596844) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596842)), _1596846))]]], (41416 ^ _779300) ^ [_1597093, _1597095, _1597097, _1597099] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597093), tc_List_Olist(_1597093))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597093), tc_List_Olist(_1597093)), _1597095), _1597097)), c_List_Olex(_1597093, _1597099)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597093), tc_List_Olist(_1597093))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597093), tc_List_Olist(_1597093)), _1597095), _1597097)), c_List_Olexord(_1597093, _1597099))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597093)), _1597095) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597093)), _1597097)], (41426 ^ _779300) ^ [_1597380, _1597382, _1597384, _1597386, _1597388, _1597390] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597380, _1597380)), hAPP(hAPP(c_Product__Type_OPair(_1597380, _1597380), _1597382), _1597384)), c_Transitive__Closure_Ortrancl(_1597380, _1597386))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597380), tc_List_Olist(_1597380))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597380), tc_List_Olist(_1597380)), _1597388), _1597390)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597380), c_List_Olistrel1(_1597380, _1597386)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597380), tc_List_Olist(_1597380))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597380), tc_List_Olist(_1597380)), hAPP(hAPP(c_List_Olist_OCons(_1597380), _1597382), _1597388)), hAPP(hAPP(c_List_Olist_OCons(_1597380), _1597384), _1597390))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597380), c_List_Olistrel1(_1597380, _1597386)))))], (41436 ^ _779300) ^ [_1597741, _1597743, _1597745, _1597747] : [-(c_List_Olist_Olist__size(_1597741, _1597743, hAPP(hAPP(c_List_Olist_OCons(_1597741), _1597745), _1597747)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1597743, _1597745)), c_List_Olist_Olist__size(_1597741, _1597743, _1597747))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41438 ^ _779300) ^ [_1597801, _1597803, _1597805, _1597807] : [hBOOL(hAPP(hAPP(c_member(_1597801), _1597803), c_Wellfounded_Oacc(_1597801, _1597805))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1597801)), _1597807), c_Wellfounded_Oacc(tc_List_Olist(_1597801), c_List_Olistrel1(_1597801, _1597805)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1597801)), hAPP(hAPP(c_List_Olist_OCons(_1597801), _1597803), _1597807)), c_Wellfounded_Oacc(tc_List_Olist(_1597801), c_List_Olistrel1(_1597801, _1597805)))))], (41448 ^ _779300) ^ [_1598042, _1598044] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1598042), tc_List_Olist(_1598042)), tc_HOL_Obool)), c_List_Olistrel1(_1598042, c_Transitive__Closure_Ortrancl(_1598042, _1598044))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598042), c_List_Olistrel1(_1598042, _1598044)))))], (41450 ^ _779300) ^ [_1598098, _1598100] : [-(c_List_Olistrel1(_1598098, hAPP(c_Relation_Oconverse(_1598098, _1598098), _1598100)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1598098), tc_List_Olist(_1598098)), c_List_Olistrel1(_1598098, _1598100)))], (41452 ^ _779300) ^ [_1598145, _1598147, _1598149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598145, _1598145), tc_HOL_Obool)), _1598147), _1598149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1598145), tc_List_Olist(_1598145)), tc_HOL_Obool)), c_List_Olistrel1(_1598145, _1598147)), c_List_Olistrel1(_1598145, _1598149))))], (41458 ^ _779300) ^ [_1598296, _1598298, _1598300, _1598302, _1598304] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598296), tc_List_Olist(_1598296))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598296), tc_List_Olist(_1598296)), _1598298), _1598300)), c_List_Olistrel1(_1598296, _1598302))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598296), tc_List_Olist(_1598296))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598296), tc_List_Olist(_1598296)), hAPP(hAPP(c_List_Olist_OCons(_1598296), _1598304), _1598298)), hAPP(hAPP(c_List_Olist_OCons(_1598296), _1598304), _1598300))), c_List_Olistrel1(_1598296, _1598302))))], (41464 ^ _779300) ^ [_1598531, _1598533, _1598535, _1598537, _1598539] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598531), tc_List_Olist(_1598531))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598531), tc_List_Olist(_1598531)), _1598533), _1598535)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598531), c_List_Olistrel1(_1598531, _1598537)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598531), tc_List_Olist(_1598531))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598531), tc_List_Olist(_1598531)), hAPP(hAPP(c_List_Olist_OCons(_1598531), _1598539), _1598533)), hAPP(hAPP(c_List_Olist_OCons(_1598531), _1598539), _1598535))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598531), c_List_Olistrel1(_1598531, _1598537)))))], (41470 ^ _779300) ^ [_1598786, _1598788, _1598790, _1598792] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598786), tc_List_Olist(_1598786))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598786), tc_List_Olist(_1598786)), _1598788), _1598790)), c_List_Olistrel1(_1598786, _1598792))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598786)), _1598788) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598786)), _1598790))], (41476 ^ _779300) ^ [_1598955, _1598957, _1598959, _1598961] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598955), tc_List_Olist(_1598955))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598955), tc_List_Olist(_1598955)), _1598957), _1598959)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598955), c_List_Olistrel1(_1598955, _1598961)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598955)), _1598957) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598955)), _1598959))], (41482 ^ _779300) ^ [_1599155, _1599157, _1599159, _1599161] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599155), tc_List_Olist(_1599155))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599155), tc_List_Olist(_1599155)), _1599157), _1599159)), c_List_Olistrel1(_1599155, hAPP(c_Relation_Oconverse(_1599155, _1599155), _1599161)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599155), tc_List_Olist(_1599155))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599155), tc_List_Olist(_1599155)), _1599157), _1599159)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1599155), tc_List_Olist(_1599155)), c_List_Olistrel1(_1599155, _1599161)))))], (41488 ^ _779300) ^ [_1599384, _1599386, _1599388, _1599390] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599384), tc_List_Olist(_1599384))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599384), tc_List_Olist(_1599384)), _1599386), _1599388)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1599384), tc_List_Olist(_1599384)), c_List_Olistrel1(_1599384, _1599390)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599384), tc_List_Olist(_1599384))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599384), tc_List_Olist(_1599384)), _1599386), _1599388)), c_List_Olistrel1(_1599384, hAPP(c_Relation_Oconverse(_1599384, _1599384), _1599390)))))], (41494 ^ _779300) ^ [_1599646, _1599648, _1599650, _1599652, _1599654, _1599656] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599646), tc_List_Olist(_1599646))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599646), tc_List_Olist(_1599646)), hAPP(hAPP(c_List_Olist_OCons(_1599646), _1599648), _1599650)), hAPP(hAPP(c_List_Olist_OCons(_1599646), _1599652), _1599654))), c_List_Olistrel1(_1599646, _1599656))), 41499 ^ _779300 : [(41500 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599646, _1599646)), hAPP(hAPP(c_Product__Type_OPair(_1599646, _1599646), _1599648), _1599652)), _1599656)))], (41502 ^ _779300) ^ [] : [-(_1599650 = _1599654)]], 41503 ^ _779300 : [(41504 ^ _779300) ^ [] : [-(_1599648 = _1599652)], (41506 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599646), tc_List_Olist(_1599646))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599646), tc_List_Olist(_1599646)), _1599650), _1599654)), c_List_Olistrel1(_1599646, _1599656))))]]], (41508 ^ _779300) ^ [_1600016, _1600018, _1600020, _1600022, _1600024, _1600026] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600016), tc_List_Olist(_1600016))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600016), tc_List_Olist(_1600016)), hAPP(hAPP(c_List_Olist_OCons(_1600016), _1600018), _1600020)), hAPP(hAPP(c_List_Olist_OCons(_1600016), _1600022), _1600024))), c_List_Olistrel1(_1600016, _1600026)))), 41509 ^ _779300 : [(41510 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600016, _1600016)), hAPP(hAPP(c_Product__Type_OPair(_1600016, _1600016), _1600018), _1600022)), _1600026)), _1600020 = _1600024], (41516 ^ _779300) ^ [] : [_1600018 = _1600022, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600016), tc_List_Olist(_1600016))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600016), tc_List_Olist(_1600016)), _1600020), _1600024)), c_List_Olistrel1(_1600016, _1600026)))]]], (41524 ^ _779300) ^ [_1600444, _1600446, _1600448, _1600450, _1600452] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600444, _1600444)), hAPP(hAPP(c_Product__Type_OPair(_1600444, _1600444), _1600446), _1600448)), _1600450)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600444), tc_List_Olist(_1600444))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600444), tc_List_Olist(_1600444)), hAPP(hAPP(c_List_Olist_OCons(_1600444), _1600446), _1600452)), hAPP(hAPP(c_List_Olist_OCons(_1600444), _1600448), _1600452))), c_List_Olistrel1(_1600444, _1600450))))], (41530 ^ _779300) ^ [_1600657, _1600659, _1600661, _1600663] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1600657), tc_List_Olist(_1600657), c_List_Olistrel(_1600657, _1600659)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1600657)), hAPP(hAPP(c_List_Olist_OCons(_1600657), _1600661), _1600663)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1600657), tc_HOL_Obool)))) = c_List_Oset__Cons(_1600657, hAPP(c_Relation_OImage(_1600657, _1600657, _1600659), hAPP(hAPP(c_Set_Oinsert(_1600657), _1600661), c_Orderings_Obot__class_Obot(tc_fun(_1600657, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1600657), tc_List_Olist(_1600657), c_List_Olistrel(_1600657, _1600659)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1600657)), _1600663), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1600657), tc_HOL_Obool))))))], (41532 ^ _779300) ^ [_1600780, _1600782, _1600784, _1600786] : [41535 ^ _779300 : [(41536 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600780, _1600780)), hAPP(hAPP(c_Product__Type_OPair(_1600780, _1600780), 41533 ^ [_1600780, _1600782, _1600784, _1600786]), 41534 ^ [_1600780, _1600782, _1600784, _1600786])), _1600782))], (41538 ^ _779300) ^ [] : [41533 ^ [_1600780, _1600782, _1600784, _1600786] = 41534 ^ [_1600780, _1600782, _1600784, _1600786]], (41540 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600780, _1600780)), hAPP(hAPP(c_Product__Type_OPair(_1600780, _1600780), 41534 ^ [_1600780, _1600782, _1600784, _1600786]), 41533 ^ [_1600780, _1600782, _1600784, _1600786])), _1600782))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600780), tc_List_Olist(_1600780))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600780), tc_List_Olist(_1600780)), _1600784), _1600786)), c_List_Olexord(_1600780, _1600782)))), -(_1600784 = _1600786), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600780), tc_List_Olist(_1600780))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600780), tc_List_Olist(_1600780)), _1600786), _1600784)), c_List_Olexord(_1600780, _1600782))))], (41552 ^ _779300) ^ [_1601327, _1601329, _1601331] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601327), tc_List_Olist(_1601327))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601327), tc_List_Olist(_1601327)), _1601329), _1601329)), c_List_Olistrel(_1601327, c_Transitive__Closure_Ortrancl(_1601327, _1601331)))))], (41554 ^ _779300) ^ [_1601387, _1601389, _1601391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601387, _1601387), tc_HOL_Obool)), _1601389), _1601391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1601387), tc_List_Olist(_1601387)), tc_HOL_Obool)), c_List_Olistrel(_1601387, _1601389)), c_List_Olistrel(_1601387, _1601391))))], (41560 ^ _779300) ^ [_1601538, _1601540] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1601538), tc_List_Olist(_1601538)), tc_HOL_Obool)), c_List_Olistrel(_1601538, _1601540)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1601538), c_List_Olistrel1(_1601538, _1601540)))))], (41562 ^ _779300) ^ [_1601591, _1601593, _1601595, _1601597] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601591), tc_List_Olist(_1601591))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601591), tc_List_Olist(_1601591)), _1601593), _1601595)), c_List_Olistrel(_1601591, _1601597))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601591)), _1601593) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601591)), _1601595))], (41568 ^ _779300) ^ [_1601760, _1601762, _1601764, _1601766, _1601768] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601760), tc_List_Olist(_1601760))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601760), tc_List_Olist(_1601760)), _1601762), _1601764)), c_List_Olistrel(_1601760, c_Transitive__Closure_Ortrancl(_1601760, _1601766)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601760), tc_List_Olist(_1601760))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601760), tc_List_Olist(_1601760)), _1601764), _1601768)), c_List_Olistrel(_1601760, c_Transitive__Closure_Ortrancl(_1601760, _1601766)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601760), tc_List_Olist(_1601760))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601760), tc_List_Olist(_1601760)), _1601762), _1601768)), c_List_Olistrel(_1601760, c_Transitive__Closure_Ortrancl(_1601760, _1601766)))))], (41578 ^ _779300) ^ [_1602099, _1602101] : [-(c_List_Olistrel(_1602099, c_Transitive__Closure_Ortrancl(_1602099, _1602101)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1602099), c_List_Olistrel1(_1602099, _1602101)))], (41580 ^ _779300) ^ [_1602138, _1602140, _1602142, _1602144] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602138), tc_List_Olist(_1602138))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602138), tc_List_Olist(_1602138)), _1602140), _1602142)), c_List_Olistrel1(_1602138, _1602144))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602138), tc_List_Olist(_1602138))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602138), tc_List_Olist(_1602138)), _1602140), _1602142)), c_List_Olistrel(_1602138, c_Transitive__Closure_Ortrancl(_1602138, _1602144)))))], (41586 ^ _779300) ^ [_1602345, _1602347, _1602349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602345, _1602345), tc_HOL_Obool)), _1602347), _1602349)), c_Relation_Orefl__on(_1602345, c_Orderings_Otop__class_Otop(tc_fun(_1602345, tc_HOL_Obool)), _1602349), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1602345), tc_List_Olist(_1602345)), tc_HOL_Obool)), c_List_Olistrel1(_1602345, _1602347)), c_List_Olistrel(_1602345, _1602349))))], (41596 ^ _779300) ^ [_1602562, _1602564, _1602566, _1602568] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602562), tc_List_Olist(_1602562))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602562), tc_List_Olist(_1602562)), _1602564), _1602566)), c_List_Olistrel(_1602562, _1602568))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602562), tc_List_Olist(_1602562))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602562), tc_List_Olist(_1602562)), _1602564), _1602566)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1602562), c_List_Olistrel1(_1602562, _1602568)))))], (41602 ^ _779300) ^ [_1602773, _1602775, _1602777, _1602779, _1602781, _1602783] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602773, _1602773)), hAPP(hAPP(c_Product__Type_OPair(_1602773, _1602773), _1602775), _1602777)), _1602779)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602773), tc_List_Olist(_1602773))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602773), tc_List_Olist(_1602773)), _1602781), _1602783)), c_List_Olistrel(_1602773, _1602779))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602773), tc_List_Olist(_1602773))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602773), tc_List_Olist(_1602773)), hAPP(hAPP(c_List_Olist_OCons(_1602773), _1602775), _1602781)), hAPP(hAPP(c_List_Olist_OCons(_1602773), _1602777), _1602783))), c_List_Olistrel(_1602773, _1602779))))], (41612 ^ _779300) ^ [_1603129, _1603131, _1603133, _1603135] : [c_List_Olistrelp(_1603129, hAPP(hAPP(c_COMBC(_1603129, tc_fun(tc_prod(_1603129, _1603129), tc_HOL_Obool), tc_fun(_1603129, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603129, tc_fun(tc_fun(tc_prod(_1603129, _1603129), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1603129, _1603129), tc_HOL_Obool), tc_fun(_1603129, tc_HOL_Obool)), _1603129), c_COMBC(_1603129, tc_fun(tc_prod(_1603129, _1603129), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603129, tc_prod(_1603129, _1603129)), tc_fun(_1603129, tc_fun(tc_fun(tc_prod(_1603129, _1603129), tc_HOL_Obool), tc_HOL_Obool)), _1603129), hAPP(c_COMBB(tc_prod(_1603129, _1603129), tc_fun(tc_fun(tc_prod(_1603129, _1603129), tc_HOL_Obool), tc_HOL_Obool), _1603129), c_member(tc_prod(_1603129, _1603129)))), c_Product__Type_OPair(_1603129, _1603129)))), _1603131), _1603133, _1603135), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603129), tc_List_Olist(_1603129))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603129), tc_List_Olist(_1603129)), _1603133), _1603135)), c_List_Olistrel(_1603129, _1603131))))], (41618 ^ _779300) ^ [_1603506, _1603508, _1603510, _1603512] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603506), tc_List_Olist(_1603506))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603506), tc_List_Olist(_1603506)), _1603510), _1603512)), c_List_Olistrel(_1603506, _1603508))), -(c_List_Olistrelp(_1603506, hAPP(hAPP(c_COMBC(_1603506, tc_fun(tc_prod(_1603506, _1603506), tc_HOL_Obool), tc_fun(_1603506, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603506, tc_fun(tc_fun(tc_prod(_1603506, _1603506), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1603506, _1603506), tc_HOL_Obool), tc_fun(_1603506, tc_HOL_Obool)), _1603506), c_COMBC(_1603506, tc_fun(tc_prod(_1603506, _1603506), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603506, tc_prod(_1603506, _1603506)), tc_fun(_1603506, tc_fun(tc_fun(tc_prod(_1603506, _1603506), tc_HOL_Obool), tc_HOL_Obool)), _1603506), hAPP(c_COMBB(tc_prod(_1603506, _1603506), tc_fun(tc_fun(tc_prod(_1603506, _1603506), tc_HOL_Obool), tc_HOL_Obool), _1603506), c_member(tc_prod(_1603506, _1603506)))), c_Product__Type_OPair(_1603506, _1603506)))), _1603508), _1603510, _1603512))], (41624 ^ _779300) ^ [_1603889, _1603891, _1603893, _1603895, _1603897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603889), tc_List_Olist(_1603889))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603889), tc_List_Olist(_1603889)), hAPP(hAPP(c_List_Olist_OCons(_1603889), _1603891), _1603893)), _1603895)), c_List_Olistrel(_1603889, _1603897))), 41629 ^ _779300 : [(41630 ^ _779300) ^ [] : [-(_1603895 = hAPP(hAPP(c_List_Olist_OCons(_1603889), 41627 ^ [_1603889, _1603891, _1603893, _1603895, _1603897]), 41628 ^ [_1603889, _1603891, _1603893, _1603895, _1603897]))], (41632 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603889, _1603889)), hAPP(hAPP(c_Product__Type_OPair(_1603889, _1603889), _1603891), 41627 ^ [_1603889, _1603891, _1603893, _1603895, _1603897])), _1603897)))], (41634 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603889), tc_List_Olist(_1603889))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603889), tc_List_Olist(_1603889)), _1603893), 41628 ^ [_1603889, _1603891, _1603893, _1603895, _1603897])), c_List_Olistrel(_1603889, _1603897))))]]], (41636 ^ _779300) ^ [_1604305, _1604307, _1604309, _1604311, _1604313, _1604315] : [c_List_Olistrelp(_1604305, _1604307, hAPP(hAPP(c_List_Olist_OCons(_1604305), _1604309), _1604311), hAPP(hAPP(c_List_Olist_OCons(_1604305), _1604313), _1604315)), 41639 ^ _779300 : [(41640 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1604307, _1604309), _1604313)))], (41642 ^ _779300) ^ [] : [-(c_List_Olistrelp(_1604305, _1604307, _1604311, _1604315))]]], (41644 ^ _779300) ^ [_1604462, _1604464, _1604466, _1604468, _1604470, _1604472] : [-(c_List_Olistrelp(_1604462, _1604464, hAPP(hAPP(c_List_Olist_OCons(_1604462), _1604466), _1604468), hAPP(hAPP(c_List_Olist_OCons(_1604462), _1604470), _1604472))), hBOOL(hAPP(hAPP(_1604464, _1604466), _1604470)), c_List_Olistrelp(_1604462, _1604464, _1604468, _1604472)], (41654 ^ _779300) ^ [_1604659, _1604661, _1604663, _1604665, _1604667, _1604669] : [hBOOL(hAPP(hAPP(_1604659, _1604661), _1604663)), c_List_Olistrelp(_1604665, _1604659, _1604667, _1604669), -(c_List_Olistrelp(_1604665, _1604659, hAPP(hAPP(c_List_Olist_OCons(_1604665), _1604661), _1604667), hAPP(hAPP(c_List_Olist_OCons(_1604665), _1604663), _1604669)))], (41664 ^ _779300) ^ [_1604854, _1604856, _1604858, _1604860, _1604862] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604854), tc_List_Olist(_1604854))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604854), tc_List_Olist(_1604854)), _1604856), hAPP(hAPP(c_List_Olist_OCons(_1604854), _1604858), _1604860))), c_List_Olistrel(_1604854, _1604862))), 41669 ^ _779300 : [(41670 ^ _779300) ^ [] : [-(_1604856 = hAPP(hAPP(c_List_Olist_OCons(_1604854), 41667 ^ [_1604854, _1604856, _1604858, _1604860, _1604862]), 41668 ^ [_1604854, _1604856, _1604858, _1604860, _1604862]))], (41672 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604854, _1604854)), hAPP(hAPP(c_Product__Type_OPair(_1604854, _1604854), 41667 ^ [_1604854, _1604856, _1604858, _1604860, _1604862]), _1604858)), _1604862)))], (41674 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604854), tc_List_Olist(_1604854))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604854), tc_List_Olist(_1604854)), 41668 ^ [_1604854, _1604856, _1604858, _1604860, _1604862]), _1604860)), c_List_Olistrel(_1604854, _1604862))))]]], (41676 ^ _779300) ^ [_1605243, _1605245, _1605247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1605243, _1605243), tc_HOL_Obool)), _1605245), hAPP(hAPP(c_Product__Type_OSigma(_1605243, _1605243), _1605247), hAPP(c_COMBK(tc_fun(_1605243, tc_HOL_Obool), _1605243), _1605247)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1605243), tc_List_Olist(_1605243)), tc_HOL_Obool)), c_List_Olistrel(_1605243, _1605245)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1605243), tc_List_Olist(_1605243)), c_List_Olists(_1605243, _1605247)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1605243), tc_HOL_Obool), tc_List_Olist(_1605243)), c_List_Olists(_1605243, _1605247))))))], (41682 ^ _779300) ^ [_1605488] : [-(c_List_Olists(_1605488, c_Orderings_Otop__class_Otop(tc_fun(_1605488, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1605488), tc_HOL_Obool)))], (41684 ^ _779300) ^ [_1605526, _1605528, _1605530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605526, tc_HOL_Obool)), _1605528), _1605530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1605526), tc_HOL_Obool)), c_List_Olists(_1605526, _1605528)), c_List_Olists(_1605526, _1605530))))], (41690 ^ _779300) ^ [_1605661, _1605663, _1605665] : [c_Equiv__Relations_Oequiv(_1605661, _1605663, _1605665), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1605661), c_List_Olists(_1605661, _1605663), c_List_Olistrel(_1605661, _1605665)))], (41696 ^ _779300) ^ [_1605760, _1605762, _1605764] : [c_Relation_Orefl__on(_1605760, _1605762, _1605764), -(c_Relation_Orefl__on(tc_List_Olist(_1605760), c_List_Olists(_1605760, _1605762), c_List_Olistrel(_1605760, _1605764)))], (41702 ^ _779300) ^ [_1605880, _1605882, _1605884, _1605886] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605880)), hAPP(hAPP(c_List_Olist_OCons(_1605880), _1605882), _1605884)), c_List_Olists(_1605880, _1605886))), 41705 ^ _779300 : [(41706 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605880), _1605882), _1605886)))], (41708 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605880)), _1605884), c_List_Olists(_1605880, _1605886))))]]], (41710 ^ _779300) ^ [_1606061, _1606063, _1606065, _1606067] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606061)), hAPP(hAPP(c_List_Olist_OCons(_1606061), _1606063), _1606065)), c_List_Olists(_1606061, _1606067)))), hBOOL(hAPP(hAPP(c_member(_1606061), _1606063), _1606067)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606061)), _1606065), c_List_Olists(_1606061, _1606067)))], (41720 ^ _779300) ^ [_1606278, _1606280, _1606282] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606278)), _1606280), c_List_Olists(_1606278, c_Wellfounded_Oacc(_1606278, _1606282)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606278)), _1606280), c_Wellfounded_Oacc(tc_List_Olist(_1606278), c_List_Olistrel1(_1606278, _1606282)))))], (41726 ^ _779300) ^ [_1606421, _1606423, _1606425] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606421)), _1606423), c_Wellfounded_Oacc(tc_List_Olist(_1606421), c_List_Olistrel1(_1606421, _1606425)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606421)), _1606423), c_List_Olists(_1606421, c_Wellfounded_Oacc(_1606421, _1606425)))))], (41732 ^ _779300) ^ [_1606585, _1606587, _1606589, _1606591] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606585), tc_List_Olist(_1606585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606585), tc_List_Olist(_1606585)), _1606587), _1606589)), c_List_Olistrel(_1606585, _1606591))), 41735 ^ _779300 : [(41736 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606585)), _1606587) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606585)), _1606589))], (41738 ^ _779300) ^ [_1606814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1606814), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606585)), _1606587))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606585, _1606585)), hAPP(hAPP(c_Product__Type_OPair(_1606585, _1606585), hAPP(hAPP(c_List_Onth(_1606585), _1606587), _1606814)), hAPP(hAPP(c_List_Onth(_1606585), _1606589), _1606814))), _1606591)))]]], (41744 ^ _779300) ^ [_1606993, _1606995, _1606997, _1606999] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606993), tc_List_Olist(_1606993))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606993), tc_List_Olist(_1606993)), _1606995), _1606997)), c_List_Olistrel(_1606993, _1606999)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606993)), _1606995) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606993)), _1606997), 41750 ^ _779300 : [(41751 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41749 ^ [_1606993, _1606995, _1606997, _1606999]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606993)), _1606995))))], (41753 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606993, _1606993)), hAPP(hAPP(c_Product__Type_OPair(_1606993, _1606993), hAPP(hAPP(c_List_Onth(_1606993), _1606995), 41749 ^ [_1606993, _1606995, _1606997, _1606999])), hAPP(hAPP(c_List_Onth(_1606993), _1606997), 41749 ^ [_1606993, _1606995, _1606997, _1606999]))), _1606999))]]], (41757 ^ _779300) ^ [_1607436, _1607438, _1607440] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607436, _1607436)), hAPP(hAPP(c_Product__Type_OPair(_1607436, _1607436), 41758 ^ [_1607436, _1607438, _1607440]), 41758 ^ [_1607436, _1607438, _1607440])), _1607438))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607436), tc_List_Olist(_1607436))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607436), tc_List_Olist(_1607436)), _1607440), _1607440)), c_List_Olexord(_1607436, _1607438)))], (41764 ^ _779300) ^ [_1607620] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1607620)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1607620), tc_HOL_Obool))))], (41766 ^ _779300) ^ [_1607674, _1607676, _1607678] : [_1607674 = _1607676, 41769 ^ _779300 : [(41770 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607678)), _1607674) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607678)), _1607676))], (41772 ^ _779300) ^ [_1607822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1607822), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607678)), _1607674))), -(hAPP(hAPP(c_List_Onth(_1607678), _1607674), _1607822) = hAPP(hAPP(c_List_Onth(_1607678), _1607676), _1607822))]]], (41778 ^ _779300) ^ [_1607961, _1607963, _1607965] : [-(_1607961 = _1607963), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607965)), _1607961) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607965)), _1607963), 41784 ^ _779300 : [(41785 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41783 ^ [_1607961, _1607963, _1607965]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607965)), _1607961))))], (41787 ^ _779300) ^ [] : [hAPP(hAPP(c_List_Onth(_1607965), _1607961), 41783 ^ [_1607961, _1607963, _1607965]) = hAPP(hAPP(c_List_Onth(_1607965), _1607963), 41783 ^ [_1607961, _1607963, _1607965])]]], (41791 ^ _779300) ^ [_1608276, _1608278, _1608280] : [-(hAPP(hAPP(c_List_Onth(_1608276), hAPP(hAPP(c_List_Olist_OCons(_1608276), _1608278), _1608280)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1608278)], (41793 ^ _779300) ^ [_1608319, _1608321, _1608323, _1608325] : [-(hAPP(hAPP(c_List_Onth(_1608319), hAPP(hAPP(c_List_Olist_OCons(_1608319), _1608321), _1608323)), hAPP(c_Nat_OSuc, _1608325)) = hAPP(hAPP(c_List_Onth(_1608319), _1608323), _1608325))], (41795 ^ _779300) ^ [_1608375, _1608377, _1608379, _1608381] : [-(hAPP(hAPP(c_List_Onth(_1608375), hAPP(hAPP(c_List_Olist_OCons(_1608375), _1608377), _1608379)), _1608381) = c_Nat_Onat_Onat__case(_1608375, _1608377, hAPP(c_List_Onth(_1608375), _1608379), _1608381))], (41797 ^ _779300) ^ [_1608445, _1608447, _1608449, _1608451] : [_1608445 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1608447), hAPP(hAPP(c_List_Olist_OCons(_1608447), _1608449), _1608451)), _1608445) = _1608449)], (41803 ^ _779300) ^ [_1608552, _1608554, _1608556, _1608558] : [-(_1608552 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1608554), hAPP(hAPP(c_List_Olist_OCons(_1608554), _1608556), _1608558)), _1608552) = hAPP(hAPP(c_List_Onth(_1608554), _1608558), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1608552), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41809 ^ _779300) ^ [_1608639, _1608641, _1608643, _1608645] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608639) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1608641), hAPP(hAPP(c_List_Olist_OCons(_1608641), _1608643), _1608645)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608639)) = _1608643)], (41815 ^ _779300) ^ [_1608758, _1608760, _1608762, _1608764] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608758) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1608760), hAPP(hAPP(c_List_Olist_OCons(_1608760), _1608762), _1608764)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608758)) = hAPP(hAPP(c_List_Onth(_1608760), _1608764), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608758)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41821 ^ _779300) ^ [_1608860, _1608862, _1608864, _1608866] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608860), tc_List_Olist(_1608860))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608860), tc_List_Olist(_1608860)), _1608862), _1608864)), c_List_Olexord(_1608860, _1608866))), 41826 ^ _779300 : [(41827 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608860)), _1608862)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608860)), _1608864))))], (41829 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1608860), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608860)), _1608862)), _1608864) = _1608862)]], 41831 ^ _779300 : [(41832 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41830 ^ [_1608860, _1608862, _1608864, _1608866]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608860)), _1608862)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608860)), _1608864)))))], (41834 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1608860), 41830 ^ [_1608860, _1608862, _1608864, _1608866]), _1608862) = hAPP(hAPP(c_List_Otake(_1608860), 41830 ^ [_1608860, _1608862, _1608864, _1608866]), _1608864))], (41836 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608860, _1608860)), hAPP(hAPP(c_Product__Type_OPair(_1608860, _1608860), hAPP(hAPP(c_List_Onth(_1608860), _1608862), 41830 ^ [_1608860, _1608862, _1608864, _1608866])), hAPP(hAPP(c_List_Onth(_1608860), _1608864), 41830 ^ [_1608860, _1608862, _1608864, _1608866]))), _1608866)))]]], (41838 ^ _779300) ^ [_1609400, _1609402, _1609404, _1609406] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609400), tc_List_Olist(_1609400))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609400), tc_List_Olist(_1609400)), _1609402), _1609404)), c_List_Olexord(_1609400, _1609406)))), 41839 ^ _779300 : [(41840 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609400)), _1609402)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609400)), _1609404))), hAPP(hAPP(c_List_Otake(_1609400), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609400)), _1609402)), _1609404) = _1609402], (41846 ^ _779300) ^ [_1609707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1609707), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609400)), _1609402)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609400)), _1609404)))), hAPP(hAPP(c_List_Otake(_1609400), _1609707), _1609402) = hAPP(hAPP(c_List_Otake(_1609400), _1609707), _1609404), hBOOL(hAPP(hAPP(c_member(tc_prod(_1609400, _1609400)), hAPP(hAPP(c_Product__Type_OPair(_1609400, _1609400), hAPP(hAPP(c_List_Onth(_1609400), _1609402), _1609707)), hAPP(hAPP(c_List_Onth(_1609400), _1609404), _1609707))), _1609406))]]], (41858 ^ _779300) ^ [_1610061, _1610063, _1610065] : [-(hAPP(c_List_Oset(_1610061), c_List_Osublist(_1610061, _1610063, _1610065)) = hAPP(c_Set_OCollect(_1610061), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1610061), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1610061, 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)), _1610061), 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)), _1610061), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1610061, tc_fun(tc_Nat_Onat, _1610061), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1610061, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1610061), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1610061), c_COMBB(_1610061, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1610061), _1610063))))), 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(_1610061)), _1610063)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1610065))))))], (41860 ^ _779300) ^ [_1610205, _1610207] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1610205), hAPP(c_List_Oset(_1610205), _1610207))))], (41862 ^ _779300) ^ [_1610239, _1610241, _1610243] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610239, tc_HOL_Obool)), hAPP(c_List_Oset(_1610239), _1610241)), hAPP(c_List_Oset(_1610239), hAPP(hAPP(c_List_Olist_OCons(_1610239), _1610243), _1610241)))))], (41864 ^ _779300) ^ [_1610294, _1610296, _1610298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610294)), _1610296)), _1610298)), -(hAPP(hAPP(c_List_Otake(_1610294), _1610298), _1610296) = _1610296)], (41870 ^ _779300) ^ [_1610413, _1610415, _1610417] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610413, tc_HOL_Obool)), hAPP(c_List_Oset(_1610413), hAPP(hAPP(c_List_Otake(_1610413), _1610415), _1610417))), hAPP(c_List_Oset(_1610413), _1610417))))], (41872 ^ _779300) ^ [_1610468, _1610470, _1610472, _1610474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1610468), _1610470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610472, tc_HOL_Obool)), hAPP(c_List_Oset(_1610472), hAPP(hAPP(c_List_Otake(_1610472), _1610468), _1610474))), hAPP(c_List_Oset(_1610472), hAPP(hAPP(c_List_Otake(_1610472), _1610470), _1610474)))))], (41878 ^ _779300) ^ [_1610631, _1610633, _1610635] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610631, tc_HOL_Obool)), hAPP(c_List_Oset(_1610631), c_List_Osublist(_1610631, _1610633, _1610635))), hAPP(c_List_Oset(_1610631), _1610633))))], (41880 ^ _779300) ^ [_1610682, _1610684, _1610686, _1610688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610682), _1610684)), -(hAPP(hAPP(c_List_Onth(_1610686), hAPP(hAPP(c_List_Otake(_1610686), _1610684), _1610688)), _1610682) = hAPP(hAPP(c_List_Onth(_1610686), _1610688), _1610682))], (41886 ^ _779300) ^ [_1610820, _1610822, _1610824, _1610826] : [-(hBOOL(hAPP(hAPP(c_member(_1610820), _1610822), hAPP(c_List_Oset(_1610820), _1610824)))), hBOOL(hAPP(hAPP(c_member(_1610820), _1610822), hAPP(c_List_Oset(_1610820), c_List_Osublist(_1610820, _1610824, _1610826))))], (41892 ^ _779300) ^ [_1610944, _1610946, _1610948, _1610950] : [hBOOL(hAPP(hAPP(c_member(_1610944), _1610946), hAPP(c_List_Oset(_1610944), hAPP(hAPP(c_List_Otake(_1610944), _1610948), _1610950)))), -(hBOOL(hAPP(hAPP(c_member(_1610944), _1610946), hAPP(c_List_Oset(_1610944), _1610950))))], (41898 ^ _779300) ^ [_1611089, _1611091, _1611093, _1611095] : [hBOOL(hAPP(hAPP(c_member(_1611089), _1611091), hAPP(c_List_Oset(_1611089), c_List_Osublist(_1611089, _1611093, _1611095)))), -(hBOOL(hAPP(hAPP(c_member(_1611089), _1611091), hAPP(c_List_Oset(_1611089), _1611093))))], (41904 ^ _779300) ^ [_1611226, _1611228, _1611230, _1611232] : [hBOOL(hAPP(hAPP(c_member(_1611226), _1611228), hAPP(c_List_Oset(_1611226), hAPP(hAPP(c_List_Olist_OCons(_1611226), _1611230), _1611232)))), -(_1611228 = _1611230), -(hBOOL(hAPP(hAPP(c_member(_1611226), _1611228), hAPP(c_List_Oset(_1611226), _1611232))))], (41914 ^ _779300) ^ [_1611384, _1611386, _1611388, _1611390] : [-(hAPP(hAPP(c_List_Otake(_1611384), hAPP(c_Nat_OSuc, _1611386)), hAPP(hAPP(c_List_Olist_OCons(_1611384), _1611388), _1611390)) = hAPP(hAPP(c_List_Olist_OCons(_1611384), _1611388), hAPP(hAPP(c_List_Otake(_1611384), _1611386), _1611390)))], (41916 ^ _779300) ^ [_1611448, _1611450, _1611452] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611448)), hAPP(hAPP(c_List_Otake(_1611448), _1611450), _1611452)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611448)), _1611452)), _1611450))], (41918 ^ _779300) ^ [_1611503, _1611505, _1611507, _1611509] : [-(hAPP(hAPP(c_List_Otake(_1611503), _1611505), hAPP(hAPP(c_List_Otake(_1611503), _1611507), _1611509)) = hAPP(hAPP(c_List_Otake(_1611503), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1611505), _1611507)), _1611509))], (41920 ^ _779300) ^ [_1611562, _1611564, _1611566] : [-(hAPP(c_List_Oset(_1611562), hAPP(hAPP(c_List_Olist_OCons(_1611562), _1611564), _1611566)) = hAPP(hAPP(c_Set_Oinsert(_1611562), _1611564), hAPP(c_List_Oset(_1611562), _1611566)))], (41922 ^ _779300) ^ [_1611615, _1611617, _1611619] : [-(c_List_Osublist(_1611615, _1611617, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1611619)) = hAPP(hAPP(c_List_Otake(_1611615), _1611619), _1611617))], (41924 ^ _779300) ^ [_1611657, _1611659] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1611657), hAPP(c_List_Oset(_1611657), _1611659))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611657)), _1611659))))], (41926 ^ _779300) ^ [_1611722, _1611724, _1611726] : [41928 ^ _779300 : [(41929 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611722), 41927 ^ [_1611722, _1611724, _1611726]), hAPP(c_List_Oset(_1611722), _1611724))))], (41931 ^ _779300) ^ [] : [hBOOL(hAPP(_1611726, 41927 ^ [_1611722, _1611724, _1611726]))]], 41932 ^ _779300 : [(41933 ^ _779300) ^ [_1611906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1611906), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611722)), _1611724))), -(hBOOL(hAPP(_1611726, hAPP(hAPP(c_List_Onth(_1611722), _1611724), _1611906))))]]], (41939 ^ _779300) ^ [_1612033, _1612035, _1612037] : [41941 ^ _779300 : [(41942 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41940 ^ [_1612033, _1612035, _1612037]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612033)), _1612035))))], (41944 ^ _779300) ^ [] : [hBOOL(hAPP(_1612037, hAPP(hAPP(c_List_Onth(_1612033), _1612035), 41940 ^ [_1612033, _1612035, _1612037])))]], 41945 ^ _779300 : [(41946 ^ _779300) ^ [_1612235] : [hBOOL(hAPP(hAPP(c_member(_1612033), _1612235), hAPP(c_List_Oset(_1612033), _1612035))), -(hBOOL(hAPP(_1612037, _1612235)))]]], (41952 ^ _779300) ^ [_1612352, _1612354, _1612356, _1612358, _1612360] : [hBOOL(hAPP(hAPP(c_member(_1612352), _1612354), hAPP(c_List_Oset(_1612352), _1612356))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612358), hAPP(_1612360, _1612354))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612358), c_List_Olist_Olist__size(_1612352, _1612360, _1612356))))], (41962 ^ _779300) ^ [_1612551, _1612553, _1612555, _1612557, _1612559] : [hBOOL(hAPP(hAPP(c_member(_1612551), _1612553), hAPP(c_List_Oset(_1612551), _1612555))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1612557), hAPP(_1612559, _1612553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1612557), c_List_Olist_Olist__size(_1612551, _1612559, _1612555))))], (41982 ^ _779300) ^ [_1612995, _1612997, _1612999] : [41984 ^ _779300 : [(41985 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612995), 41983 ^ [_1612995, _1612997, _1612999]), hAPP(c_List_Oset(_1612995), _1612997))))], (41987 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1612995), 41983 ^ [_1612995, _1612997, _1612999]), _1612999))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612995)), _1612997), c_List_Olists(_1612995, _1612999))))], (41972 ^ _779300) ^ [_1612768, _1612770, _1612772] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612768)), _1612770), c_List_Olists(_1612768, _1612772))), 41975 ^ _779300 : [(41976 ^ _779300) ^ [_1612876] : [hBOOL(hAPP(hAPP(c_member(_1612768), _1612876), hAPP(c_List_Oset(_1612768), _1612770))), -(hBOOL(hAPP(hAPP(c_member(_1612768), _1612876), _1612772)))]]], (41991 ^ _779300) ^ [_1613215, _1613217, _1613219] : [hBOOL(hAPP(hAPP(c_member(_1613215), _1613217), hAPP(c_List_Oset(_1613215), _1613219))), -(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(_1613215)), _1613219))))], (41997 ^ _779300) ^ [_1613336, _1613338, _1613340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613336), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613338)), _1613340))), -(hBOOL(hAPP(hAPP(c_member(_1613338), hAPP(hAPP(c_List_Onth(_1613338), _1613340), _1613336)), hAPP(c_List_Oset(_1613338), _1613340))))], (42003 ^ _779300) ^ [_1613497, _1613499, _1613501] : [hBOOL(hAPP(hAPP(c_member(_1613497), _1613499), hAPP(c_List_Oset(_1613497), _1613501))), 42007 ^ _779300 : [(42008 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42006 ^ [_1613497, _1613499, _1613501]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613497)), _1613501))))], (42010 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1613497), _1613501), 42006 ^ [_1613497, _1613499, _1613501]) = _1613499)]]], (42012 ^ _779300) ^ [_1613685, _1613687, _1613689] : [-(hBOOL(hAPP(hAPP(c_member(_1613685), _1613687), hAPP(c_List_Oset(_1613685), _1613689)))), 42013 ^ _779300 : [(42014 ^ _779300) ^ [_1613759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613759), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613685)), _1613689))), hAPP(hAPP(c_List_Onth(_1613685), _1613689), _1613759) = _1613687]]], (42022 ^ _779300) ^ [_1613921, _1613923] : [-(c_List_Olists(_1613921, _1613923) = hAPP(c_Set_OCollect(tc_List_Olist(_1613921)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613921), tc_fun(_1613921, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1613921, tc_HOL_Obool), tc_fun(tc_fun(_1613921, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1613921)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1613921, tc_HOL_Obool))), c_List_Oset(_1613921))), _1613923)))], (42024 ^ _779300) ^ [_1613999, _1614001] : [-(hAPP(c_List_Oset(_1613999), _1614001) = hAPP(c_Set_OCollect(_1613999), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1613999), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1613999, 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)), _1613999), 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)), _1613999), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1613999, tc_fun(tc_Nat_Onat, _1613999), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1613999, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1613999), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1613999), c_COMBB(_1613999, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1613999), _1614001))))), 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(_1613999)), _1614001))))))], (42026 ^ _779300) ^ [_1614125, _1614127, _1614129] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1614125), _1614127)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1614125)), hAPP(c_Set_OCollect(tc_List_Olist(_1614125)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1614125), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1614125)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614125), tc_fun(_1614125, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614125, tc_HOL_Obool), tc_fun(tc_fun(_1614125, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614125)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614125, tc_HOL_Obool))), c_List_Oset(_1614125))), _1614127))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614125), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1614125)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1614125)))), _1614129))))))], (42032 ^ _779300) ^ [_1614428, _1614430, _1614432] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1614428), _1614430)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1614428)), hAPP(c_Set_OCollect(tc_List_Olist(_1614428)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1614428), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1614428)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614428), tc_fun(_1614428, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614428, tc_HOL_Obool), tc_fun(tc_fun(_1614428, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614428)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614428, tc_HOL_Obool))), c_List_Oset(_1614428))), _1614430))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614428), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1614428)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1614428)))), _1614432))))))], (42038 ^ _779300) ^ [_1614752, _1614754, _1614756, _1614758] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614752), tc_List_Olist(_1614752))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614752), tc_List_Olist(_1614752)), _1614754), _1614756)), c_List_Olistrel(_1614752, _1614758))), 42041 ^ _779300 : [(42042 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614752)), _1614754) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614752)), _1614756))], (42044 ^ _779300) ^ [_1615088] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614752, _1614752)), _1615088), hAPP(c_List_Oset(tc_prod(_1614752, _1614752)), hAPP(hAPP(c_List_Ozip(_1614752, _1614752), _1614754), _1614756)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1614752, _1614752, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1614752, tc_fun(tc_prod(_1614752, _1614752), tc_HOL_Obool), tc_fun(_1614752, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614752, tc_fun(tc_fun(tc_prod(_1614752, _1614752), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1614752, _1614752), tc_HOL_Obool), tc_fun(_1614752, tc_HOL_Obool)), _1614752), c_COMBC(_1614752, tc_fun(tc_prod(_1614752, _1614752), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614752, tc_prod(_1614752, _1614752)), tc_fun(_1614752, tc_fun(tc_fun(tc_prod(_1614752, _1614752), tc_HOL_Obool), tc_HOL_Obool)), _1614752), hAPP(c_COMBB(tc_prod(_1614752, _1614752), tc_fun(tc_fun(tc_prod(_1614752, _1614752), tc_HOL_Obool), tc_HOL_Obool), _1614752), c_member(tc_prod(_1614752, _1614752)))), c_Product__Type_OPair(_1614752, _1614752)))), _1614758)), _1615088)))]]], (42050 ^ _779300) ^ [_1615481, _1615483, _1615485, _1615487] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615481), tc_List_Olist(_1615481))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615481), tc_List_Olist(_1615481)), _1615483), _1615485)), c_List_Olistrel(_1615481, _1615487)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615481)), _1615483) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615481)), _1615485), 42056 ^ _779300 : [(42057 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615481, _1615481)), 42055 ^ [_1615481, _1615483, _1615485, _1615487]), hAPP(c_List_Oset(tc_prod(_1615481, _1615481)), hAPP(hAPP(c_List_Ozip(_1615481, _1615481), _1615483), _1615485)))))], (42059 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1615481, _1615481, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1615481, tc_fun(tc_prod(_1615481, _1615481), tc_HOL_Obool), tc_fun(_1615481, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615481, tc_fun(tc_fun(tc_prod(_1615481, _1615481), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1615481, _1615481), tc_HOL_Obool), tc_fun(_1615481, tc_HOL_Obool)), _1615481), c_COMBC(_1615481, tc_fun(tc_prod(_1615481, _1615481), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615481, tc_prod(_1615481, _1615481)), tc_fun(_1615481, tc_fun(tc_fun(tc_prod(_1615481, _1615481), tc_HOL_Obool), tc_HOL_Obool)), _1615481), hAPP(c_COMBB(tc_prod(_1615481, _1615481), tc_fun(tc_fun(tc_prod(_1615481, _1615481), tc_HOL_Obool), tc_HOL_Obool), _1615481), c_member(tc_prod(_1615481, _1615481)))), c_Product__Type_OPair(_1615481, _1615481)))), _1615487)), 42055 ^ [_1615481, _1615483, _1615485, _1615487]))]]], (42063 ^ _779300) ^ [_1616219, _1616221, _1616223, _1616225] : [-(hAPP(c_List_Oset(tc_prod(_1616219, _1616221)), hAPP(hAPP(c_List_Ozip(_1616219, _1616221), _1616223), _1616225)) = hAPP(c_Set_OCollect(tc_prod(_1616219, _1616221)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1616219, _1616221)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1616219, _1616221), 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(_1616219, _1616221)), 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(_1616219, _1616221)), 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(_1616219, _1616221), tc_fun(tc_Nat_Onat, tc_prod(_1616219, _1616221)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1616219, _1616221), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1616219, _1616221)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1616219, _1616221)), c_COMBB(tc_prod(_1616219, _1616221), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1616221, tc_prod(_1616219, _1616221)), hAPP(hAPP(c_COMBB(_1616219, tc_fun(_1616221, tc_prod(_1616219, _1616221)), tc_Nat_Onat), c_Product__Type_OPair(_1616219, _1616221)), hAPP(c_List_Onth(_1616219), _1616223))), hAPP(c_List_Onth(_1616221), _1616225)))))), 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(_1616219)), _1616223)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616221)), _1616225)))))))], (42065 ^ _779300) ^ [_1616444, _1616446, _1616448, _1616450, _1616452] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1616444, _1616446)), _1616448), hAPP(hAPP(c_List_Ozip(_1616444, _1616446), _1616450), _1616452)) = hAPP(hAPP(c_List_Ozip(_1616444, _1616446), hAPP(hAPP(c_List_Otake(_1616444), _1616448), _1616450)), hAPP(hAPP(c_List_Otake(_1616446), _1616448), _1616452)))], (42067 ^ _779300) ^ [_1616520, _1616522, _1616524, _1616526] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1616520, _1616522))), hAPP(hAPP(c_List_Ozip(_1616520, _1616522), _1616524), _1616526)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616520)), _1616524)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616522)), _1616526)))], (42069 ^ _779300) ^ [_1616588, _1616590, _1616592, _1616594, _1616596, _1616598] : [-(hAPP(hAPP(c_List_Ozip(_1616588, _1616590), hAPP(hAPP(c_List_Olist_OCons(_1616588), _1616592), _1616594)), hAPP(hAPP(c_List_Olist_OCons(_1616590), _1616596), _1616598)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1616588, _1616590)), hAPP(hAPP(c_Product__Type_OPair(_1616588, _1616590), _1616592), _1616596)), hAPP(hAPP(c_List_Ozip(_1616588, _1616590), _1616594), _1616598)))], (42071 ^ _779300) ^ [_1616693, _1616695, _1616697] : [_1616693 = _1616695, 42074 ^ _779300 : [(42075 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616697)), _1616693) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616697)), _1616695))], (42077 ^ _779300) ^ [_1616849] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616697, _1616697)), _1616849), hAPP(c_List_Oset(tc_prod(_1616697, _1616697)), hAPP(hAPP(c_List_Ozip(_1616697, _1616697), _1616693), _1616695)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1616697, _1616697, tc_HOL_Obool), c_fequal), _1616849)))]]], (42083 ^ _779300) ^ [_1617004, _1617006, _1617008] : [-(_1617004 = _1617006), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617008)), _1617004) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617008)), _1617006), 42089 ^ _779300 : [(42090 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617008, _1617008)), 42088 ^ [_1617004, _1617006, _1617008]), hAPP(c_List_Oset(tc_prod(_1617008, _1617008)), hAPP(hAPP(c_List_Ozip(_1617008, _1617008), _1617004), _1617006)))))], (42092 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1617008, _1617008, tc_HOL_Obool), c_fequal), 42088 ^ [_1617004, _1617006, _1617008]))]]], (42096 ^ _779300) ^ [_1617318, _1617320, _1617322, _1617324, _1617326, _1617328] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617318, _1617320)), hAPP(hAPP(c_Product__Type_OPair(_1617318, _1617320), _1617322), _1617324)), hAPP(c_List_Oset(tc_prod(_1617318, _1617320)), hAPP(hAPP(c_List_Ozip(_1617318, _1617320), _1617326), _1617328)))), 42099 ^ _779300 : [(42100 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617318), _1617322), hAPP(c_List_Oset(_1617318), _1617326))))], (42102 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617320), _1617324), hAPP(c_List_Oset(_1617320), _1617328))))]]], (42104 ^ _779300) ^ [_1617553, _1617555, _1617557, _1617559, _1617561, _1617563] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617553, _1617555)), hAPP(hAPP(c_Product__Type_OPair(_1617553, _1617555), _1617557), _1617559)), hAPP(c_List_Oset(tc_prod(_1617553, _1617555)), hAPP(hAPP(c_List_Ozip(_1617553, _1617555), _1617561), _1617563)))), -(hBOOL(hAPP(hAPP(c_member(_1617555), _1617559), hAPP(c_List_Oset(_1617555), _1617563))))], (42110 ^ _779300) ^ [_1617734, _1617736, _1617738, _1617740, _1617742, _1617744] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617734, _1617736)), hAPP(hAPP(c_Product__Type_OPair(_1617734, _1617736), _1617738), _1617740)), hAPP(c_List_Oset(tc_prod(_1617734, _1617736)), hAPP(hAPP(c_List_Ozip(_1617734, _1617736), _1617742), _1617744)))), -(hBOOL(hAPP(hAPP(c_member(_1617734), _1617738), hAPP(c_List_Oset(_1617734), _1617742))))], (42116 ^ _779300) ^ [_1617936, _1617938, _1617940, _1617942] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617936, _1617936)), hAPP(hAPP(c_Product__Type_OPair(_1617936, _1617936), _1617938), _1617940)), hAPP(c_List_Oset(tc_prod(_1617936, _1617936)), hAPP(hAPP(c_List_Ozip(_1617936, _1617936), _1617942), _1617942)))), 42119 ^ _779300 : [(42120 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617936), _1617938), hAPP(c_List_Oset(_1617936), _1617942))))], (42122 ^ _779300) ^ [] : [-(_1617938 = _1617940)]]], (42124 ^ _779300) ^ [_1618135, _1618137, _1618139, _1618141] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618135, _1618135)), hAPP(hAPP(c_Product__Type_OPair(_1618135, _1618135), _1618137), _1618139)), hAPP(c_List_Oset(tc_prod(_1618135, _1618135)), hAPP(hAPP(c_List_Ozip(_1618135, _1618135), _1618141), _1618141))))), hBOOL(hAPP(hAPP(c_member(_1618135), _1618137), hAPP(c_List_Oset(_1618135), _1618141))), _1618137 = _1618139], (42134 ^ _779300) ^ [_1618370, _1618372, _1618374, _1618376, _1618378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618370), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618372)), _1618374))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618370), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618376)), _1618378))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1618372, _1618376)), hAPP(hAPP(c_List_Ozip(_1618372, _1618376), _1618374), _1618378)), _1618370) = hAPP(hAPP(c_Product__Type_OPair(_1618372, _1618376), hAPP(hAPP(c_List_Onth(_1618372), _1618374), _1618370)), hAPP(hAPP(c_List_Onth(_1618376), _1618378), _1618370)))], (42144 ^ _779300) ^ [_1618649, _1618651] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1618649, _1618651) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1618649), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1618651), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42146 ^ _779300) ^ [_1618696, _1618698] : [class_Groups_Ocomm__monoid__add(_1618696), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1618696), _1618698) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1618696), hAPP(c_List_Onth(_1618696), _1618698)), 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(_1618696)), _1618698))))], (42152 ^ _779300) ^ [_1618829, _1618831] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1618829, _1618831) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1618829, _1618831)))], (42154 ^ _779300) ^ [_1618864, _1618866] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1618864, _1618866)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1618864, _1618866))], (42166 ^ _779300) ^ [_1619079] : [42168 ^ _779300 : [(42169 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42167 ^ [_1619079]), hAPP(c_List_Oset(tc_Nat_Onat), _1619079))))], (42171 ^ _779300) ^ [] : [42167 ^ [_1619079] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619079) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42156 ^ _779300) ^ [_1618911] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1618911) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42159 ^ _779300 : [(42160 ^ _779300) ^ [_1618986] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1618986), hAPP(c_List_Oset(tc_Nat_Onat), _1618911))), -(_1618986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42175 ^ _779300) ^ [_1619235, _1619237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619235), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1619237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1619237), _1619235)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619237))))], (42181 ^ _779300) ^ [_1619356, _1619358, _1619360] : [class_Groups_Omonoid__add(_1619356), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1619356), hAPP(hAPP(c_List_Olist_OCons(_1619356), _1619358), _1619360)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1619356), _1619358), hAPP(c_List_Omonoid__add__class_Olistsum(_1619356), _1619360)))], (42187 ^ _779300) ^ [_1619485, _1619487] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1619485), _1619487) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619485, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1619487), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42189 ^ _779300) ^ [_1619528, _1619530] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1619528, _1619530) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1619528), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1619530)))], (42191 ^ _779300) ^ [_1619581] : [c_List_Onat__list(_1619581), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1619581)))], (42197 ^ _779300) ^ [_1619654] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1619654)), -(c_List_Onat__list(_1619654))], (42203 ^ _779300) ^ [_1619733, _1619735, _1619737, _1619739] : [42205 ^ _779300 : [(42206 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1619733), 42204 ^ [_1619733, _1619735, _1619737, _1619739]), hAPP(c_List_Oset(_1619733), _1619735))))], (42208 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1619737, 42204 ^ [_1619733, _1619735, _1619737, _1619739])), hAPP(_1619739, 42204 ^ [_1619733, _1619735, _1619737, _1619739])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1619733, _1619737, _1619735)), c_List_Olist_Olist__size(_1619733, _1619739, _1619735))))], (42212 ^ _779300) ^ [_1619983, _1619985, _1619987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619983), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1619985))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1619985), _1619983), _1619987)) = 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), _1619985)), _1619987)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1619985), _1619983)))], (42218 ^ _779300) ^ [_1620144, _1620146, _1620148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1620144), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620146)), _1620148))), -(c_List_Obutlast(_1620146, hAPP(hAPP(c_List_Otake(_1620146), _1620144), _1620148)) = hAPP(hAPP(c_List_Otake(_1620146), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1620144), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1620148))], (42224 ^ _779300) ^ [_1620297, _1620299, _1620301, _1620303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620297)), _1620299)), _1620301)), -(hAPP(hAPP(c_List_Olist__update(_1620297, _1620299), _1620301), _1620303) = _1620299)], (42230 ^ _779300) ^ [_1620420, _1620422, _1620424] : [-(hAPP(hAPP(c_List_Olist__update(_1620420, _1620422), _1620424), hAPP(hAPP(c_List_Onth(_1620420), _1620422), _1620424)) = _1620422)], (42232 ^ _779300) ^ [_1620460, _1620462, _1620464, _1620466, _1620468] : [-(_1620460 = _1620462), -(hAPP(hAPP(c_List_Onth(_1620464), hAPP(hAPP(c_List_Olist__update(_1620464, _1620466), _1620460), _1620468)), _1620462) = hAPP(hAPP(c_List_Onth(_1620464), _1620466), _1620462))], (42238 ^ _779300) ^ [_1620542, _1620544, _1620546, _1620548] : [_1620542 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620544)), _1620546)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1620544, hAPP(hAPP(c_List_Olist__update(_1620544, _1620546), _1620542), _1620548)) = c_List_Obutlast(_1620544, _1620546))], (42244 ^ _779300) ^ [_1620673, _1620675, _1620677, _1620679] : [-(_1620673 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620675)), _1620677)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1620675, hAPP(hAPP(c_List_Olist__update(_1620675, _1620677), _1620673), _1620679)) = hAPP(hAPP(c_List_Olist__update(_1620675, c_List_Obutlast(_1620675, _1620677)), _1620673), _1620679))], (42250 ^ _779300) ^ [_1620752, _1620754, _1620756, _1620758] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620752)), hAPP(hAPP(c_List_Olist__update(_1620752, _1620754), _1620756), _1620758)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620752)), _1620754))], (42252 ^ _779300) ^ [_1620804, _1620806, _1620808, _1620810, _1620812, _1620814, _1620816] : [-(hAPP(hAPP(c_List_Ozip(_1620804, _1620806), hAPP(hAPP(c_List_Olist__update(_1620804, _1620808), _1620810), _1620812)), hAPP(hAPP(c_List_Olist__update(_1620806, _1620814), _1620810), _1620816)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1620804, _1620806), hAPP(hAPP(c_List_Ozip(_1620804, _1620806), _1620808), _1620814)), _1620810), hAPP(hAPP(c_Product__Type_OPair(_1620804, _1620806), _1620812), _1620816)))], (42254 ^ _779300) ^ [_1620896, _1620898, _1620900, _1620902, _1620904, _1620906] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1620896, _1620898), hAPP(hAPP(c_List_Ozip(_1620896, _1620898), _1620900), _1620902)), _1620904), _1620906) = hAPP(hAPP(c_List_Ozip(_1620896, _1620898), hAPP(hAPP(c_List_Olist__update(_1620896, _1620900), _1620904), hAPP(c_Product__Type_Ofst(_1620896, _1620898), _1620906))), hAPP(hAPP(c_List_Olist__update(_1620898, _1620902), _1620904), hAPP(c_Product__Type_Osnd(_1620896, _1620898), _1620906))))], (42256 ^ _779300) ^ [_1620985, _1620987, _1620989, _1620991, _1620993, _1620995] : [-(_1620985 = _1620987), -(hAPP(hAPP(c_List_Olist__update(_1620989, hAPP(hAPP(c_List_Olist__update(_1620989, _1620991), _1620985), _1620993)), _1620987), _1620995) = hAPP(hAPP(c_List_Olist__update(_1620989, hAPP(hAPP(c_List_Olist__update(_1620989, _1620991), _1620987), _1620995)), _1620985), _1620993))], (42262 ^ _779300) ^ [_1621065, _1621067, _1621069, _1621071, _1621073] : [-(hAPP(hAPP(c_List_Olist__update(_1621065, hAPP(hAPP(c_List_Olist__update(_1621065, _1621067), _1621069), _1621071)), _1621069), _1621073) = hAPP(hAPP(c_List_Olist__update(_1621065, _1621067), _1621069), _1621073))], (42264 ^ _779300) ^ [_1621123, _1621125, _1621127, _1621129, _1621131] : [-(hAPP(hAPP(c_List_Olist__update(_1621123, hAPP(hAPP(c_List_Olist_OCons(_1621123), _1621125), _1621127)), _1621129), _1621131) = c_Nat_Onat_Onat__case(tc_List_Olist(_1621123), hAPP(hAPP(c_List_Olist_OCons(_1621123), _1621131), _1621127), hAPP(hAPP(c_COMBB(tc_List_Olist(_1621123), tc_List_Olist(_1621123), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1621123), _1621125)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1621123, tc_List_Olist(_1621123)), c_List_Olist__update(_1621123, _1621127)), _1621131)), _1621129))], (42266 ^ _779300) ^ [_1621220, _1621222, _1621224, _1621226] : [-(hAPP(hAPP(c_List_Olist__update(_1621220, hAPP(hAPP(c_List_Olist_OCons(_1621220), _1621222), _1621224)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1621226) = hAPP(hAPP(c_List_Olist_OCons(_1621220), _1621226), _1621224))], (42268 ^ _779300) ^ [_1621274, _1621276, _1621278, _1621280, _1621282] : [-(hAPP(hAPP(c_List_Olist__update(_1621274, hAPP(hAPP(c_List_Olist_OCons(_1621274), _1621276), _1621278)), hAPP(c_Nat_OSuc, _1621280)), _1621282) = hAPP(hAPP(c_List_Olist_OCons(_1621274), _1621276), hAPP(hAPP(c_List_Olist__update(_1621274, _1621278), _1621280), _1621282)))], (42270 ^ _779300) ^ [_1621342, _1621344, _1621346] : [hBOOL(hAPP(hAPP(c_member(_1621342), _1621344), hAPP(c_List_Oset(_1621342), c_List_Obutlast(_1621342, _1621346)))), -(hBOOL(hAPP(hAPP(c_member(_1621342), _1621344), hAPP(c_List_Oset(_1621342), _1621346))))], (42276 ^ _779300) ^ [_1621475, _1621477, _1621479, _1621481, _1621483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621475, tc_HOL_Obool)), hAPP(c_List_Oset(_1621475), _1621477)), _1621479)), hBOOL(hAPP(hAPP(c_member(_1621475), _1621481), _1621479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621475, tc_HOL_Obool)), hAPP(c_List_Oset(_1621475), hAPP(hAPP(c_List_Olist__update(_1621475, _1621477), _1621483), _1621481))), _1621479)))], (42286 ^ _779300) ^ [_1621708, _1621710, _1621712, _1621714] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621708, tc_HOL_Obool)), hAPP(c_List_Oset(_1621708), hAPP(hAPP(c_List_Olist__update(_1621708, _1621710), _1621712), _1621714))), hAPP(hAPP(c_Set_Oinsert(_1621708), _1621714), hAPP(c_List_Oset(_1621708), _1621710)))))], (42288 ^ _779300) ^ [_1621774, _1621776, _1621778, _1621780, _1621782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1621774), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621776)), _1621778))), 42291 ^ _779300 : [(42292 ^ _779300) ^ [] : [_1621774 = _1621780, -(hAPP(hAPP(c_List_Onth(_1621776), hAPP(hAPP(c_List_Olist__update(_1621776, _1621778), _1621774), _1621782)), _1621780) = _1621782)], (42298 ^ _779300) ^ [] : [-(_1621774 = _1621780), -(hAPP(hAPP(c_List_Onth(_1621776), hAPP(hAPP(c_List_Olist__update(_1621776, _1621778), _1621774), _1621782)), _1621780) = hAPP(hAPP(c_List_Onth(_1621776), _1621778), _1621780))]]], (42304 ^ _779300) ^ [_1622070, _1622072, _1622074, _1622076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622070), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622072)), _1622074))), 42307 ^ _779300 : [(42308 ^ _779300) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1622072, _1622074), _1622070), _1622076) = _1622074, -(hAPP(hAPP(c_List_Onth(_1622072), _1622074), _1622070) = _1622076)], (42314 ^ _779300) ^ [] : [hAPP(hAPP(c_List_Onth(_1622072), _1622074), _1622070) = _1622076, -(hAPP(hAPP(c_List_Olist__update(_1622072, _1622074), _1622070), _1622076) = _1622074)]]], (42320 ^ _779300) ^ [_1622364, _1622366, _1622368, _1622370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622364), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622366)), _1622368))), -(hAPP(hAPP(c_List_Onth(_1622366), hAPP(hAPP(c_List_Olist__update(_1622366, _1622368), _1622364), _1622370)), _1622364) = _1622370)], (42326 ^ _779300) ^ [_1622503, _1622505, _1622507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622503), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622505)), _1622507))), -(hAPP(hAPP(c_List_Otake(_1622505), _1622503), c_List_Obutlast(_1622505, _1622507)) = hAPP(hAPP(c_List_Otake(_1622505), _1622503), _1622507))], (42332 ^ _779300) ^ [_1622644, _1622646] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622644)), c_List_Obutlast(_1622644, _1622646)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622644)), _1622646)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42334 ^ _779300) ^ [_1622692, _1622694, _1622696, _1622698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622692), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622694)), _1622696))), -(hBOOL(hAPP(hAPP(c_member(_1622694), _1622698), hAPP(c_List_Oset(_1622694), hAPP(hAPP(c_List_Olist__update(_1622694, _1622696), _1622692), _1622698)))))], (42340 ^ _779300) ^ [_1622839, _1622841] : [-(c_List_Obutlast(_1622839, _1622841) = hAPP(hAPP(c_List_Otake(_1622839), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622839)), _1622841)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1622841))], (42342 ^ _779300) ^ [_1622909, _1622911, _1622913, _1622915] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622909), tc_List_Olist(_1622909))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622909), tc_List_Olist(_1622909)), _1622911), _1622913)), c_List_Olistrel1(_1622909, _1622915))), 42347 ^ _779300 : [(42348 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622909, _1622909)), hAPP(hAPP(c_Product__Type_OPair(_1622909, _1622909), hAPP(hAPP(c_List_Onth(_1622909), _1622911), 42346 ^ [_1622909, _1622911, _1622913, _1622915])), 42345 ^ [_1622909, _1622911, _1622913, _1622915])), _1622915)))], (42350 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42346 ^ [_1622909, _1622911, _1622913, _1622915]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622909)), _1622911))))], (42352 ^ _779300) ^ [] : [-(_1622913 = hAPP(hAPP(c_List_Olist__update(_1622909, _1622911), 42346 ^ [_1622909, _1622911, _1622913, _1622915]), 42345 ^ [_1622909, _1622911, _1622913, _1622915]))]]], (42354 ^ _779300) ^ [_1623257, _1623259, _1623261, _1623263] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623257), tc_List_Olist(_1623257))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623257), tc_List_Olist(_1623257)), _1623259), _1623261)), c_List_Olistrel1(_1623257, _1623263)))), 42355 ^ _779300 : [(42356 ^ _779300) ^ [_1623390, _1623392] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623257, _1623257)), hAPP(hAPP(c_Product__Type_OPair(_1623257, _1623257), hAPP(hAPP(c_List_Onth(_1623257), _1623259), _1623390)), _1623392)), _1623263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623390), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623257)), _1623259))), _1623261 = hAPP(hAPP(c_List_Olist__update(_1623257, _1623259), _1623390), _1623392)]]], (42368 ^ _779300) ^ [_1623690, _1623692, _1623694, _1623696] : [hBOOL(hAPP(c_List_Odistinct(_1623690), _1623692)), -(hBOOL(hAPP(hAPP(c_member(_1623690), _1623694), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1623690, tc_HOL_Obool)), hAPP(c_List_Oset(_1623690), _1623692)), hAPP(hAPP(c_Set_Oinsert(_1623690), hAPP(hAPP(c_List_Onth(_1623690), _1623692), _1623696)), c_Orderings_Obot__class_Obot(tc_fun(_1623690, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1623690), hAPP(hAPP(c_List_Olist__update(_1623690, _1623692), _1623696), _1623694))))], (42378 ^ _779300) ^ [_1623908, _1623910] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1623908, _1623910))))], (42380 ^ _779300) ^ [_1623938, _1623940, _1623942] : [hBOOL(hAPP(c_List_Odistinct(_1623938), _1623940)), -(hBOOL(hAPP(c_List_Odistinct(_1623938), hAPP(hAPP(c_List_Otake(_1623938), _1623942), _1623940))))], (42386 ^ _779300) ^ [_1624049, _1624051, _1624053] : [hBOOL(hAPP(c_List_Odistinct(_1624049), _1624051)), -(hBOOL(hAPP(c_List_Odistinct(_1624049), c_List_Osublist(_1624049, _1624051, _1624053))))], (42392 ^ _779300) ^ [_1624152, _1624154, _1624156, _1624158] : [hBOOL(hAPP(c_List_Odistinct(_1624152), _1624154)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1624156, _1624152)), hAPP(hAPP(c_List_Ozip(_1624156, _1624152), _1624158), _1624154))))], (42398 ^ _779300) ^ [_1624273, _1624275, _1624277, _1624279] : [hBOOL(hAPP(c_List_Odistinct(_1624273), _1624275)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1624273, _1624277)), hAPP(hAPP(c_List_Ozip(_1624273, _1624277), _1624275), _1624279))))], (42404 ^ _779300) ^ [_1624412, _1624414, _1624416] : [hBOOL(hAPP(c_List_Odistinct(_1624412), hAPP(hAPP(c_List_Olist_OCons(_1624412), _1624414), _1624416))), 42407 ^ _779300 : [(42408 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1624412), _1624414), hAPP(c_List_Oset(_1624412), _1624416)))], (42410 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1624412), _1624416)))]]], (42412 ^ _779300) ^ [_1624579, _1624581, _1624583] : [-(hBOOL(hAPP(c_List_Odistinct(_1624579), hAPP(hAPP(c_List_Olist_OCons(_1624579), _1624581), _1624583)))), -(hBOOL(hAPP(hAPP(c_member(_1624579), _1624581), hAPP(c_List_Oset(_1624579), _1624583)))), hBOOL(hAPP(c_List_Odistinct(_1624579), _1624583))], (42422 ^ _779300) ^ [_1624773, _1624775] : [hBOOL(hAPP(c_List_Odistinct(_1624773), _1624775)), -(hAPP(c_Finite__Set_Ocard(_1624773), hAPP(c_List_Oset(_1624773), _1624775)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624773)), _1624775))], (42428 ^ _779300) ^ [_1624892, _1624894] : [hAPP(c_Finite__Set_Ocard(_1624892), hAPP(c_List_Oset(_1624892), _1624894)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624892)), _1624894), -(hBOOL(hAPP(c_List_Odistinct(_1624892), _1624894)))], (42452 ^ _779300) ^ [_1625486, _1625488] : [42454 ^ _779300 : [(42455 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42453 ^ [_1625486, _1625488]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625486)), _1625488))))], (42458 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42456 ^ [_1625486, _1625488]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625486)), _1625488))))], (42460 ^ _779300) ^ [] : [42453 ^ [_1625486, _1625488] = 42456 ^ [_1625486, _1625488]], (42462 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1625486), _1625488), 42453 ^ [_1625486, _1625488]) = hAPP(hAPP(c_List_Onth(_1625486), _1625488), 42456 ^ [_1625486, _1625488]))]], -(hBOOL(hAPP(c_List_Odistinct(_1625486), _1625488)))], (42434 ^ _779300) ^ [_1625026, _1625028] : [hBOOL(hAPP(c_List_Odistinct(_1625026), _1625028)), 42437 ^ _779300 : [(42438 ^ _779300) ^ [_1625158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625158), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625026)), _1625028))), 42441 ^ _779300 : [(42442 ^ _779300) ^ [_1625285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625285), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625026)), _1625028))), -(_1625158 = _1625285), hAPP(hAPP(c_List_Onth(_1625026), _1625028), _1625158) = hAPP(hAPP(c_List_Onth(_1625026), _1625028), _1625285)]]]]], (42466 ^ _779300) ^ [_1625918, _1625920, _1625922, _1625924] : [hBOOL(hAPP(c_List_Odistinct(_1625918), _1625920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625922), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625918)), _1625920))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625924), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625918)), _1625920))), 42477 ^ _779300 : [(42478 ^ _779300) ^ [] : [hAPP(hAPP(c_List_Onth(_1625918), _1625920), _1625922) = hAPP(hAPP(c_List_Onth(_1625918), _1625920), _1625924), -(_1625922 = _1625924)], (42484 ^ _779300) ^ [] : [_1625922 = _1625924, -(hAPP(hAPP(c_List_Onth(_1625918), _1625920), _1625922) = hAPP(hAPP(c_List_Onth(_1625918), _1625920), _1625924))]]], (42490 ^ _779300) ^ [_1626353, _1626355] : [class_Groups_Ocomm__monoid__add(_1626353), hBOOL(hAPP(c_List_Odistinct(_1626353), _1626355)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1626353), _1626355) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1626353, _1626353), c_COMBI(_1626353)), hAPP(c_List_Oset(_1626353), _1626355)))], (42500 ^ _779300) ^ [_1626539, _1626541] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1626539), _1626541)), -(c_Nitpick_Ocard_H(_1626539, _1626541) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626539)), c_Hilbert__Choice_OEps(tc_List_Olist(_1626539), hAPP(hAPP(c_COMBS(tc_List_Olist(_1626539), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1626539)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1626539), tc_fun(_1626539, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1626539, tc_HOL_Obool), tc_fun(tc_fun(_1626539, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1626539)), c_fequal), c_List_Oset(_1626539))), _1626541))), c_List_Odistinct(_1626539)))))], (42506 ^ _779300) ^ [_1626776, _1626778] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1626776), _1626778))), -(c_Nitpick_Ocard_H(_1626776, _1626778) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42512 ^ _779300) ^ [_1626821, _1626823, _1626825, _1626827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1626821), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626823)), _1626825))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1626821), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626823)), _1626827))), 42522 ^ _779300 : [(42523 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42521 ^ [_1626821, _1626823, _1626825, _1626827]), _1626821)))], (42525 ^ _779300) ^ [] : [hAPP(hAPP(c_List_Onth(_1626823), _1626825), 42521 ^ [_1626821, _1626823, _1626825, _1626827]) = hAPP(hAPP(c_List_Onth(_1626823), _1626827), 42521 ^ [_1626821, _1626823, _1626825, _1626827])]], -(hAPP(hAPP(c_List_Otake(_1626823), _1626821), _1626825) = hAPP(hAPP(c_List_Otake(_1626823), _1626821), _1626827))], (42529 ^ _779300) ^ [_1627238, _1627240, _1627242] : [hBOOL(hAPP(c_List_Odistinct(_1627238), _1627240)), -(hAPP(c_List_Oset(_1627238), c_List_Oremove1(_1627238, _1627242, _1627240)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627238, tc_HOL_Obool)), hAPP(c_List_Oset(_1627238), _1627240)), hAPP(hAPP(c_Set_Oinsert(_1627238), _1627242), c_Orderings_Obot__class_Obot(tc_fun(_1627238, tc_HOL_Obool)))))], (42535 ^ _779300) ^ [_1627416, _1627418, _1627420, _1627422] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627416) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1627418), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627416)), hAPP(hAPP(c_List_Olist_OCons(_1627418), _1627420), _1627422)) = c_List_Olist_ONil(_1627418))], (42541 ^ _779300) ^ [_1627539, _1627541, _1627543, _1627545] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627539) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1627541), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627539)), hAPP(hAPP(c_List_Olist_OCons(_1627541), _1627543), _1627545)) = hAPP(hAPP(c_List_Olist_OCons(_1627541), _1627543), hAPP(hAPP(c_List_Otake(_1627541), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627539)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1627545)))], (42547 ^ _779300) ^ [_1627628, _1627630] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1627628)), c_List_Olist_ONil(_1627628)), c_List_Olists(_1627628, _1627630))))], (42549 ^ _779300) ^ [_1627667, _1627669, _1627671] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627667), tc_List_Olist(_1627667))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627667), tc_List_Olist(_1627667)), _1627669), c_List_Olist_ONil(_1627667))), c_List_Olistrel(_1627667, _1627671))), -(_1627669 = c_List_Olist_ONil(_1627667))], (42555 ^ _779300) ^ [_1627814, _1627816, _1627818] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627814), tc_List_Olist(_1627814))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627814), tc_List_Olist(_1627814)), c_List_Olist_ONil(_1627814)), _1627816)), c_List_Olistrel(_1627814, _1627818))), -(_1627816 = c_List_Olist_ONil(_1627814))], (42561 ^ _779300) ^ [_1627960, _1627962] : [-(_1627960 = c_List_Olist_ONil(_1627962)), hBOOL(hAPP(c_List_Odistinct(_1627962), _1627960)), -(hBOOL(hAPP(c_List_Odistinct(_1627962), c_List_Obutlast(_1627962, _1627960))))], (42571 ^ _779300) ^ [_1628111] : [-(hBOOL(hAPP(c_List_Odistinct(_1628111), c_List_Olist_ONil(_1628111))))], (42573 ^ _779300) ^ [_1628140, _1628142, _1628144] : [hBOOL(hAPP(c_List_Odistinct(_1628140), _1628142)), -(hBOOL(hAPP(c_List_Odistinct(_1628140), c_List_Oremove1(_1628140, _1628144, _1628142))))], (42579 ^ _779300) ^ [_1628243] : [-(c_List_Obutlast(_1628243, c_List_Olist_ONil(_1628243)) = c_List_Olist_ONil(_1628243))], (42581 ^ _779300) ^ [_1628285, _1628287, _1628289] : [_1628285 = c_List_Olist_ONil(_1628287), -(c_List_Obutlast(_1628287, hAPP(hAPP(c_List_Olist_OCons(_1628287), _1628289), _1628285)) = c_List_Olist_ONil(_1628287))], (42587 ^ _779300) ^ [_1628388, _1628390, _1628392] : [-(_1628388 = c_List_Olist_ONil(_1628390)), -(c_List_Obutlast(_1628390, hAPP(hAPP(c_List_Olist_OCons(_1628390), _1628392), _1628388)) = hAPP(hAPP(c_List_Olist_OCons(_1628390), _1628392), c_List_Obutlast(_1628390, _1628388)))], (42593 ^ _779300) ^ [_1628467, _1628469, _1628471, _1628473] : [_1628467 = _1628469, -(c_List_Oremove1(_1628471, _1628467, hAPP(hAPP(c_List_Olist_OCons(_1628471), _1628469), _1628473)) = _1628473)], (42599 ^ _779300) ^ [_1628566, _1628568, _1628570, _1628572] : [-(_1628566 = _1628568), -(c_List_Oremove1(_1628570, _1628566, hAPP(hAPP(c_List_Olist_OCons(_1628570), _1628568), _1628572)) = hAPP(hAPP(c_List_Olist_OCons(_1628570), _1628568), c_List_Oremove1(_1628570, _1628566, _1628572)))], (42605 ^ _779300) ^ [_1628647, _1628649, _1628651] : [hAPP(hAPP(c_List_Olist_OCons(_1628647), _1628649), _1628651) = c_List_Olist_ONil(_1628647)], (42607 ^ _779300) ^ [_1628699, _1628701, _1628703] : [c_List_Olist_ONil(_1628699) = hAPP(hAPP(c_List_Olist_OCons(_1628699), _1628701), _1628703)], (42609 ^ _779300) ^ [_1628736, _1628738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1628736), _1628738)), -(c_List_Oupto(_1628738, _1628736) = c_List_Olist_ONil(tc_Int_Oint))], (42615 ^ _779300) ^ [_1628829, _1628831] : [-(hAPP(hAPP(c_List_Otake(_1628829), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1628831) = c_List_Olist_ONil(_1628829))], (42627 ^ _779300) ^ [_1628994, _1628996, _1628998] : [42628 ^ _779300 : [(42629 ^ _779300) ^ [] : [_1628996 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42631 ^ _779300) ^ [] : [_1628998 = c_List_Olist_ONil(_1628994)]], -(hAPP(hAPP(c_List_Otake(_1628994), _1628996), _1628998) = c_List_Olist_ONil(_1628994))], (42617 ^ _779300) ^ [_1628882, _1628884, _1628886] : [hAPP(hAPP(c_List_Otake(_1628882), _1628884), _1628886) = c_List_Olist_ONil(_1628882), -(_1628884 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1628886 = c_List_Olist_ONil(_1628882))], (42635 ^ _779300) ^ [_1629137, _1629139] : [-(hAPP(hAPP(c_List_Otake(_1629137), _1629139), c_List_Olist_ONil(_1629137)) = c_List_Olist_ONil(_1629137))], (42637 ^ _779300) ^ [_1629174, _1629176] : [-(c_List_Osublist(_1629174, c_List_Olist_ONil(_1629174), _1629176) = c_List_Olist_ONil(_1629174))], (42639 ^ _779300) ^ [_1629207, _1629209] : [-(c_List_Oremove1(_1629207, _1629209, c_List_Olist_ONil(_1629207)) = c_List_Olist_ONil(_1629207))], (42641 ^ _779300) ^ [_1629240, _1629242, _1629244, _1629246] : [-(c_List_Oremove1(_1629240, _1629242, c_List_Oremove1(_1629240, _1629244, _1629246)) = c_List_Oremove1(_1629240, _1629244, c_List_Oremove1(_1629240, _1629242, _1629246)))], (42643 ^ _779300) ^ [_1629285, _1629287] : [-(c_List_Olistrelp(_1629285, _1629287, c_List_Olist_ONil(_1629285), c_List_Olist_ONil(_1629285)))], (42645 ^ _779300) ^ [_1629316, _1629318] : [-(c_List_Olistrelp(_1629316, _1629318, c_List_Olist_ONil(_1629316), c_List_Olist_ONil(_1629316)))], (42647 ^ _779300) ^ [_1629347, _1629349, _1629351] : [-(hAPP(hAPP(c_List_Ozip(_1629347, _1629349), _1629351), c_List_Olist_ONil(_1629349)) = c_List_Olist_ONil(tc_prod(_1629347, _1629349)))], (42649 ^ _779300) ^ [_1629390, _1629392, _1629394] : [-(hAPP(hAPP(c_List_Ozip(_1629390, _1629392), c_List_Olist_ONil(_1629390)), _1629394) = c_List_Olist_ONil(tc_prod(_1629390, _1629392)))], (42651 ^ _779300) ^ [_1629433] : [class_Groups_Omonoid__add(_1629433), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1629433), c_List_Olist_ONil(_1629433)) = c_Groups_Ozero__class_Ozero(_1629433))], (42657 ^ _779300) ^ [_1629524] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629524)), c_List_Olist_ONil(_1629524)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42659 ^ _779300) ^ [_1629571, _1629573] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629571)), _1629573) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1629573 = c_List_Olist_ONil(_1629571))], (42665 ^ _779300) ^ [_1629662, _1629664] : [_1629664 = c_List_Olist_ONil(_1629662), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629662)), _1629664) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42671 ^ _779300) ^ [_1629759] : [-(hAPP(c_List_Oset(_1629759), c_List_Olist_ONil(_1629759)) = c_Orderings_Obot__class_Obot(tc_fun(_1629759, tc_HOL_Obool)))], (42673 ^ _779300) ^ [_1629809, _1629811] : [c_Orderings_Obot__class_Obot(tc_fun(_1629809, tc_HOL_Obool)) = hAPP(c_List_Oset(_1629809), _1629811), -(_1629811 = c_List_Olist_ONil(_1629809))], (42679 ^ _779300) ^ [_1629906, _1629908] : [_1629908 = c_List_Olist_ONil(_1629906), -(c_Orderings_Obot__class_Obot(tc_fun(_1629906, tc_HOL_Obool)) = hAPP(c_List_Oset(_1629906), _1629908))], (42685 ^ _779300) ^ [_1630024, _1630026] : [hAPP(c_List_Oset(_1630024), _1630026) = c_Orderings_Obot__class_Obot(tc_fun(_1630024, tc_HOL_Obool)), -(_1630026 = c_List_Olist_ONil(_1630024))], (42691 ^ _779300) ^ [_1630121, _1630123] : [_1630123 = c_List_Olist_ONil(_1630121), -(hAPP(c_List_Oset(_1630121), _1630123) = c_Orderings_Obot__class_Obot(tc_fun(_1630121, tc_HOL_Obool)))], (42697 ^ _779300) ^ [_1630245, _1630247, _1630249, _1630251] : [hAPP(hAPP(c_List_Olist__update(_1630245, _1630247), _1630249), _1630251) = c_List_Olist_ONil(_1630245), -(_1630247 = c_List_Olist_ONil(_1630245))], (42703 ^ _779300) ^ [_1630348, _1630350, _1630352, _1630354] : [_1630350 = c_List_Olist_ONil(_1630348), -(hAPP(hAPP(c_List_Olist__update(_1630348, _1630350), _1630352), _1630354) = c_List_Olist_ONil(_1630348))], (42709 ^ _779300) ^ [_1630457, _1630459, _1630461] : [-(hAPP(hAPP(c_List_Olist__update(_1630457, c_List_Olist_ONil(_1630457)), _1630459), _1630461) = c_List_Olist_ONil(_1630457))], (42711 ^ _779300) ^ [_1630497, _1630499, _1630501] : [-(hAPP(hAPP(c_List_Olist__update(_1630497, c_List_Olist_ONil(_1630497)), _1630499), _1630501) = c_List_Olist_ONil(_1630497))], (42713 ^ _779300) ^ [_1630537, _1630539] : [-(c_List_Olist_Olist__size(_1630537, _1630539, c_List_Olist_ONil(_1630537)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42715 ^ _779300) ^ [_1630564, _1630566, _1630568] : [-(hBOOL(hAPP(hAPP(c_member(_1630564), _1630566), hAPP(c_List_Oset(_1630564), _1630568)))), -(c_List_Oremove1(_1630564, _1630566, _1630568) = _1630568)], (42721 ^ _779300) ^ [_1630617, _1630619, _1630621, _1630623] : [-(hBOOL(hAPP(hAPP(c_member(_1630617), _1630619), hAPP(c_List_Oset(_1630617), _1630621)))), hBOOL(hAPP(hAPP(c_member(_1630617), _1630619), hAPP(c_List_Oset(_1630617), c_List_Oremove1(_1630617, _1630623, _1630621))))], (42727 ^ _779300) ^ [_1630740, _1630742, _1630744, _1630746] : [-(_1630740 = _1630742), 42730 ^ _779300 : [(42731 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630744), _1630740), hAPP(c_List_Oset(_1630744), c_List_Oremove1(_1630744, _1630742, _1630746)))), -(hBOOL(hAPP(hAPP(c_member(_1630744), _1630740), hAPP(c_List_Oset(_1630744), _1630746))))], (42737 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630744), _1630740), hAPP(c_List_Oset(_1630744), _1630746))), -(hBOOL(hAPP(hAPP(c_member(_1630744), _1630740), hAPP(c_List_Oset(_1630744), c_List_Oremove1(_1630744, _1630742, _1630746)))))]]], (42743 ^ _779300) ^ [_1631041, _1631043] : [-(c_List_Osublist(_1631041, _1631043, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1631041))], (42745 ^ _779300) ^ [_1631072, _1631074, _1631076] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1631072, tc_HOL_Obool)), hAPP(c_List_Oset(_1631072), c_List_Oremove1(_1631072, _1631074, _1631076))), hAPP(c_List_Oset(_1631072), _1631076))))], (42747 ^ _779300) ^ [_1631138, _1631140] : [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(_1631138)), _1631140))), _1631140 = c_List_Olist_ONil(_1631138)], (42753 ^ _779300) ^ [_1631232, _1631234] : [-(_1631234 = c_List_Olist_ONil(_1631232)), -(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(_1631232)), _1631234))))], (42759 ^ _779300) ^ [_1631281, _1631283, _1631285] : [-(hAPP(hAPP(c_List_Otake(_1631281), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1631281), _1631283), _1631285)) = hAPP(hAPP(c_List_Olist_OCons(_1631281), _1631283), c_List_Olist_ONil(_1631281)))], (42761 ^ _779300) ^ [_1631349, _1631351, _1631353] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631349), tc_List_Olist(_1631349))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631349), tc_List_Olist(_1631349)), _1631351), c_List_Olist_ONil(_1631349))), c_List_Olistrel1(_1631349, _1631353)))], (42763 ^ _779300) ^ [_1631423, _1631425, _1631427] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631423), tc_List_Olist(_1631423))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631423), tc_List_Olist(_1631423)), c_List_Olist_ONil(_1631423)), _1631425)), c_List_Olistrel1(_1631423, _1631427)))], (42765 ^ _779300) ^ [_1631482, _1631484] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631482), tc_List_Olist(_1631482))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631482), tc_List_Olist(_1631482)), c_List_Olist_ONil(_1631482)), c_List_Olist_ONil(_1631482))), c_List_Olistrel(_1631482, _1631484))))], (42767 ^ _779300) ^ [_1631556, _1631558, _1631560] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631556), tc_List_Olist(_1631556))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631556), tc_List_Olist(_1631556)), _1631558), c_List_Olist_ONil(_1631556))), c_List_Olexord(_1631556, _1631560)))], (42769 ^ _779300) ^ [_1631630, _1631632, _1631634] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631630), tc_List_Olist(_1631630))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631630), tc_List_Olist(_1631630)), _1631632), c_List_Olist_ONil(_1631630))), c_List_Olex(_1631630, _1631634)))], (42771 ^ _779300) ^ [_1631704, _1631706, _1631708] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631704), tc_List_Olist(_1631704))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631704), tc_List_Olist(_1631704)), c_List_Olist_ONil(_1631704)), _1631706)), c_List_Olex(_1631704, _1631708)))], (42773 ^ _779300) ^ [_1631763, _1631765, _1631767, _1631769] : [-(hAPP(hAPP(c_List_Otake(_1631763), _1631765), hAPP(hAPP(c_List_Olist_OCons(_1631763), _1631767), _1631769)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1631763), c_List_Olist_ONil(_1631763), hAPP(hAPP(c_COMBB(tc_List_Olist(_1631763), tc_List_Olist(_1631763), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1631763), _1631767)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1631763), tc_List_Olist(_1631763)), c_List_Otake(_1631763)), _1631769)), _1631765))], (42775 ^ _779300) ^ [_1631861, _1631863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1631861), _1631863)), -(c_List_Oupto(_1631861, _1631863) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1631861), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1631861), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1631863)))], (42781 ^ _779300) ^ [_1631978, _1631980] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1631978), _1631980))), -(c_List_Oupto(_1631978, _1631980) = c_List_Olist_ONil(tc_Int_Oint))], (42787 ^ _779300) ^ [_1632036, _1632038, _1632040] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1632036)), -(c_List_Osublist(_1632038, hAPP(hAPP(c_List_Olist_OCons(_1632038), _1632040), c_List_Olist_ONil(_1632038)), _1632036) = hAPP(hAPP(c_List_Olist_OCons(_1632038), _1632040), c_List_Olist_ONil(_1632038)))], (42793 ^ _779300) ^ [_1632161, _1632163, _1632165] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1632161))), -(c_List_Osublist(_1632163, hAPP(hAPP(c_List_Olist_OCons(_1632163), _1632165), c_List_Olist_ONil(_1632163)), _1632161) = c_List_Olist_ONil(_1632163))], (42799 ^ _779300) ^ [_1632219] : [-(c_List_Olists(_1632219, c_Orderings_Obot__class_Obot(tc_fun(_1632219, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632219)), c_List_Olist_ONil(_1632219)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632219), tc_HOL_Obool))))], (42801 ^ _779300) ^ [_1632284, _1632286, _1632288, _1632290] : [_1632284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1632286), _1632284), hAPP(hAPP(c_List_Olist_OCons(_1632286), _1632288), _1632290)) = c_List_Olist_ONil(_1632286))], (42807 ^ _779300) ^ [_1632395, _1632397, _1632399, _1632401] : [-(_1632395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1632397), _1632395), hAPP(hAPP(c_List_Olist_OCons(_1632397), _1632399), _1632401)) = hAPP(hAPP(c_List_Olist_OCons(_1632397), _1632399), hAPP(hAPP(c_List_Otake(_1632397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1632395), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1632401)))], (42813 ^ _779300) ^ [_1632484, _1632486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632484)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632486))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632484), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632486)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632484)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632484)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632486))))], (42819 ^ _779300) ^ [_1632643, _1632645] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632643)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632645)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632643), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632645)) = c_List_Olist_ONil(tc_Int_Oint))], (42825 ^ _779300) ^ [_1632701, _1632703] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1632701), tc_List_Olist(_1632701), c_List_Olistrel(_1632701, _1632703)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632701)), c_List_Olist_ONil(_1632701)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632701), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632701)), c_List_Olist_ONil(_1632701)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632701), tc_HOL_Obool))))], (42827 ^ _779300) ^ [_1632778, _1632780] : [-(c_List_Oset__Cons(_1632778, _1632780, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632778)), c_List_Olist_ONil(_1632778)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632778), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1632778, tc_List_Olist(_1632778), hAPP(hAPP(c_COMBC(_1632778, tc_List_Olist(_1632778), tc_List_Olist(_1632778)), c_List_Olist_OCons(_1632778)), c_List_Olist_ONil(_1632778))), _1632780))], (42829 ^ _779300) ^ [_1632865, _1632867, _1632869] : [hBOOL(hAPP(hAPP(c_member(_1632865), _1632867), hAPP(c_List_Oset(_1632865), _1632869))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632865)), c_List_Oremove1(_1632865, _1632867, _1632869)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632865)), _1632869)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42835 ^ _779300) ^ [_1633010, _1633012, _1633014] : [-(hBOOL(hAPP(hAPP(c_member(_1633010), _1633012), hAPP(c_List_Oset(_1633010), _1633014)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633010)), c_List_Oremove1(_1633010, _1633012, _1633014)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633010)), _1633014))], (42841 ^ _779300) ^ [_1633080, _1633082] : [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), _1633080), _1633082))), 42844 ^ _779300 : [(42845 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1633080), _1633082)), -(c_List_Oupto(_1633080, _1633082) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1633080), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1633080), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1633082)))], (42851 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1633080), _1633082))), -(c_List_Oupto(_1633080, _1633082) = c_List_Olist_ONil(tc_Int_Oint))]]], (42857 ^ _779300) ^ [_1633330, _1633332, _1633334] : [-(_1633330 = c_List_Olist_ONil(_1633332)), -(hBOOL(hAPP(hAPP(c_member(_1633332), hAPP(c_Product__Type_Ofst(_1633332, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1633332, _1633330), _1633334))), hAPP(c_List_Oset(_1633332), _1633330))))], (42863 ^ _779300) ^ [_1633394] : [-(c_List_Olistset(_1633394, c_List_Olist_ONil(tc_fun(_1633394, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633394)), c_List_Olist_ONil(_1633394)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633394), tc_HOL_Obool))))], (42865 ^ _779300) ^ [_1633444, _1633446, _1633448, _1633450, _1633452] : [-(hAPP(hAPP(c_List_Ozip(_1633444, _1633446), hAPP(hAPP(c_List_Olist_OCons(_1633444), _1633448), _1633450)), _1633452) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1633444, _1633446)), _1633446, c_List_Olist_ONil(tc_prod(_1633444, _1633446)), hAPP(hAPP(c_COMBC(_1633446, tc_fun(tc_List_Olist(_1633446), tc_List_Olist(tc_prod(_1633444, _1633446))), tc_fun(tc_List_Olist(_1633446), tc_List_Olist(tc_prod(_1633444, _1633446)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1633444, _1633446)), tc_List_Olist(tc_prod(_1633444, _1633446))), tc_fun(tc_fun(tc_List_Olist(_1633446), tc_List_Olist(tc_prod(_1633444, _1633446))), tc_fun(tc_List_Olist(_1633446), tc_List_Olist(tc_prod(_1633444, _1633446)))), _1633446), c_COMBB(tc_List_Olist(tc_prod(_1633444, _1633446)), tc_List_Olist(tc_prod(_1633444, _1633446)), tc_List_Olist(_1633446))), hAPP(hAPP(c_COMBB(tc_prod(_1633444, _1633446), tc_fun(tc_List_Olist(tc_prod(_1633444, _1633446)), tc_List_Olist(tc_prod(_1633444, _1633446))), _1633446), c_List_Olist_OCons(tc_prod(_1633444, _1633446))), hAPP(c_Product__Type_OPair(_1633444, _1633446), _1633448)))), hAPP(c_List_Ozip(_1633444, _1633446), _1633450))), _1633452))], (42867 ^ _779300) ^ [_1633645, _1633647, _1633649, _1633651, _1633653, _1633655] : [-(hAPP(c_List_Olist_Olist__case(_1633645, _1633647, _1633649, _1633651), hAPP(hAPP(c_List_Olist_OCons(_1633647), _1633653), _1633655)) = hAPP(hAPP(_1633651, _1633653), _1633655))], (42869 ^ _779300) ^ [_1633700, _1633702, _1633704, _1633706] : [-(hAPP(c_List_Olist_Olist__case(_1633700, _1633702, _1633704, _1633706), c_List_Olist_ONil(_1633702)) = _1633704)], (42871 ^ _779300) ^ [_1633739, _1633741, _1633743] : [-(c_List_Olistset(_1633739, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1633739, tc_HOL_Obool)), _1633741), _1633743)) = c_List_Oset__Cons(_1633739, _1633741, c_List_Olistset(_1633739, _1633743)))], (42873 ^ _779300) ^ [_1633787, _1633789, _1633791, _1633793, _1633795] : [-(hAPP(hAPP(c_List_Ozip(_1633787, _1633789), _1633791), hAPP(hAPP(c_List_Olist_OCons(_1633789), _1633793), _1633795)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1633787, _1633789)), _1633787, c_List_Olist_ONil(tc_prod(_1633787, _1633789)), hAPP(hAPP(c_COMBC(_1633787, tc_fun(tc_List_Olist(_1633787), tc_List_Olist(tc_prod(_1633787, _1633789))), tc_fun(tc_List_Olist(_1633787), tc_List_Olist(tc_prod(_1633787, _1633789)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1633787, _1633789)), tc_List_Olist(tc_prod(_1633787, _1633789))), tc_fun(tc_fun(tc_List_Olist(_1633787), tc_List_Olist(tc_prod(_1633787, _1633789))), tc_fun(tc_List_Olist(_1633787), tc_List_Olist(tc_prod(_1633787, _1633789)))), _1633787), c_COMBB(tc_List_Olist(tc_prod(_1633787, _1633789)), tc_List_Olist(tc_prod(_1633787, _1633789)), tc_List_Olist(_1633787))), hAPP(hAPP(c_COMBB(tc_prod(_1633787, _1633789), tc_fun(tc_List_Olist(tc_prod(_1633787, _1633789)), tc_List_Olist(tc_prod(_1633787, _1633789))), _1633787), c_List_Olist_OCons(tc_prod(_1633787, _1633789))), hAPP(hAPP(c_COMBC(_1633787, _1633789, tc_prod(_1633787, _1633789)), c_Product__Type_OPair(_1633787, _1633789)), _1633793)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1633787), tc_List_Olist(_1633789), tc_List_Olist(tc_prod(_1633787, _1633789))), c_List_Ozip(_1633787, _1633789)), _1633795))), _1633791))], (42875 ^ _779300) ^ [_1634014, _1634016, _1634018] : [class_Orderings_Olinorder(_1634014), hBOOL(hAPP(c_Finite__Set_Ofinite(_1634014), _1634016)), -(c_List_Olinorder__class_Osorted__list__of__set(_1634014, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1634014, tc_HOL_Obool)), _1634016), hAPP(hAPP(c_Set_Oinsert(_1634014), _1634018), c_Orderings_Obot__class_Obot(tc_fun(_1634014, tc_HOL_Obool))))) = c_List_Oremove1(_1634014, _1634018, c_List_Olinorder__class_Osorted__list__of__set(_1634014, _1634016)))], (42885 ^ _779300) ^ [_1634221, _1634223, _1634225] : [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), _1634221), _1634223))), -(hBOOL(hAPP(hAPP(_1634225, _1634221), _1634223))), 42892 ^ _779300 : [(42893 ^ _779300) ^ [] : [-(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), 42890 ^ [_1634221, _1634223, _1634225]), 42891 ^ [_1634221, _1634223, _1634225]))))], (42901 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1634225, 42890 ^ [_1634221, _1634223, _1634225]), 42891 ^ [_1634221, _1634223, _1634225]))], (42895 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 42890 ^ [_1634221, _1634223, _1634225]), 42891 ^ [_1634221, _1634223, _1634225])), -(hBOOL(hAPP(hAPP(_1634225, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 42890 ^ [_1634221, _1634223, _1634225]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 42891 ^ [_1634221, _1634223, _1634225])))]]], (42905 ^ _779300) ^ [_1634712] : [class_Orderings_Olinorder(_1634712), -(c_List_Olinorder__class_Osorted__list__of__set(_1634712, c_Orderings_Obot__class_Obot(tc_fun(_1634712, tc_HOL_Obool))) = c_List_Olist_ONil(_1634712))], (42911 ^ _779300) ^ [_1634823, _1634825, _1634827, _1634829, _1634831] : [_1634823 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1634825, _1634827, _1634829), _1634823), _1634831) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634827), _1634825), c_List_Olist_ONil(_1634827)), _1634831))], (42917 ^ _779300) ^ [_1634946, _1634948, _1634950, _1634952, _1634954] : [-(_1634946 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1634948, _1634950, _1634952), _1634946), _1634954) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1634950), _1634948), tc_prod(_1634950, _1634948), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634950), _1634948), c_List_Olist_ONil(_1634950)), _1634954), hAPP(c_Product__Type_Oprod_Oprod__case(_1634950, _1634948, tc_prod(tc_List_Olist(_1634950), _1634948)), hAPP(hAPP(c_COMBC(_1634950, tc_fun(_1634948, tc_prod(tc_List_Olist(_1634950), _1634948)), tc_fun(_1634948, tc_prod(tc_List_Olist(_1634950), _1634948))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1634950), _1634948), tc_prod(tc_List_Olist(_1634950), _1634948)), tc_fun(tc_fun(_1634948, tc_prod(tc_List_Olist(_1634950), _1634948)), tc_fun(_1634948, tc_prod(tc_List_Olist(_1634950), _1634948))), _1634950), c_COMBB(tc_prod(tc_List_Olist(_1634950), _1634948), tc_prod(tc_List_Olist(_1634950), _1634948), _1634948)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1634950), tc_fun(_1634948, tc_prod(tc_List_Olist(_1634950), _1634948))), tc_fun(tc_prod(tc_List_Olist(_1634950), _1634948), tc_prod(tc_List_Olist(_1634950), _1634948)), _1634950), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1634950), _1634948, tc_prod(tc_List_Olist(_1634950), _1634948))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1634950), tc_List_Olist(_1634950)), tc_fun(tc_List_Olist(_1634950), tc_fun(_1634948, tc_prod(tc_List_Olist(_1634950), _1634948))), _1634950), hAPP(c_COMBB(tc_List_Olist(_1634950), tc_fun(_1634948, tc_prod(tc_List_Olist(_1634950), _1634948)), tc_List_Olist(_1634950)), c_Product__Type_OPair(tc_List_Olist(_1634950), _1634948))), c_List_Olist_OCons(_1634950))))), hAPP(c_Lazy__Sequence_Oanamorph(_1634948, _1634950, _1634952), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1634946), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1634952, _1634954)))], (42923 ^ _779300) ^ [_1635240, _1635242, _1635244, _1635246] : [-(c_List_Osublist(_1635240, hAPP(hAPP(c_List_Olist_OCons(_1635240), _1635242), _1635244), _1635246) = hAPP(hAPP(c_List_Oappend(_1635240), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1635240)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1635246)), hAPP(hAPP(c_List_Olist_OCons(_1635240), _1635242), c_List_Olist_ONil(_1635240))), c_List_Olist_ONil(_1635240))), c_List_Osublist(_1635240, _1635244, 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)), _1635246)))))], (42925 ^ _779300) ^ [_1635351, _1635353, _1635355, _1635357, _1635359] : [hAPP(hAPP(c_List_Oappend(_1635351), _1635353), hAPP(hAPP(c_List_Olist_OCons(_1635351), _1635355), c_List_Olist_ONil(_1635351))) = hAPP(hAPP(c_List_Oappend(_1635351), _1635357), hAPP(hAPP(c_List_Olist_OCons(_1635351), _1635359), c_List_Olist_ONil(_1635351))), 42928 ^ _779300 : [(42929 ^ _779300) ^ [] : [-(_1635353 = _1635357)], (42931 ^ _779300) ^ [] : [-(_1635355 = _1635359)]]], (42933 ^ _779300) ^ [_1635528, _1635530, _1635532, _1635534, _1635536] : [-(hAPP(hAPP(c_List_Oappend(_1635528), _1635530), hAPP(hAPP(c_List_Olist_OCons(_1635528), _1635532), c_List_Olist_ONil(_1635528))) = hAPP(hAPP(c_List_Oappend(_1635528), _1635534), hAPP(hAPP(c_List_Olist_OCons(_1635528), _1635536), c_List_Olist_ONil(_1635528)))), _1635530 = _1635534, _1635532 = _1635536], (42943 ^ _779300) ^ [_1635767, _1635769, _1635771, _1635773, _1635775] : [hAPP(hAPP(c_List_Olist_OCons(_1635767), _1635769), _1635771) = hAPP(hAPP(c_List_Oappend(_1635767), _1635773), _1635775), 42948 ^ _779300 : [(42949 ^ _779300) ^ [] : [-(_1635773 = c_List_Olist_ONil(_1635767))], (42951 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1635767), _1635769), _1635771) = _1635775)]], 42953 ^ _779300 : [(42954 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1635767), _1635769), 42952 ^ [_1635767, _1635769, _1635771, _1635773, _1635775]) = _1635773)], (42956 ^ _779300) ^ [] : [-(_1635771 = hAPP(hAPP(c_List_Oappend(_1635767), 42952 ^ [_1635767, _1635769, _1635771, _1635773, _1635775]), _1635775))]]], (42958 ^ _779300) ^ [_1636060, _1636062, _1636064, _1636066, _1636068] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636060), _1636062), _1636064) = hAPP(hAPP(c_List_Oappend(_1636060), _1636066), _1636068)), 42959 ^ _779300 : [(42960 ^ _779300) ^ [] : [_1636066 = c_List_Olist_ONil(_1636060), hAPP(hAPP(c_List_Olist_OCons(_1636060), _1636062), _1636064) = _1636068], (42966 ^ _779300) ^ [_1636243] : [hAPP(hAPP(c_List_Olist_OCons(_1636060), _1636062), _1636243) = _1636066, _1636064 = hAPP(hAPP(c_List_Oappend(_1636060), _1636243), _1636068)]]], (42974 ^ _779300) ^ [_1636431, _1636433, _1636435, _1636437, _1636439] : [hAPP(hAPP(c_List_Oappend(_1636431), _1636433), _1636435) = hAPP(hAPP(c_List_Olist_OCons(_1636431), _1636437), _1636439), 42979 ^ _779300 : [(42980 ^ _779300) ^ [] : [-(_1636433 = c_List_Olist_ONil(_1636431))], (42982 ^ _779300) ^ [] : [-(_1636435 = hAPP(hAPP(c_List_Olist_OCons(_1636431), _1636437), _1636439))]], 42984 ^ _779300 : [(42985 ^ _779300) ^ [] : [-(_1636433 = hAPP(hAPP(c_List_Olist_OCons(_1636431), _1636437), 42983 ^ [_1636431, _1636433, _1636435, _1636437, _1636439]))], (42987 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1636431), 42983 ^ [_1636431, _1636433, _1636435, _1636437, _1636439]), _1636435) = _1636439)]]], (42989 ^ _779300) ^ [_1636724, _1636726, _1636728, _1636730, _1636732] : [-(hAPP(hAPP(c_List_Oappend(_1636724), _1636726), _1636728) = hAPP(hAPP(c_List_Olist_OCons(_1636724), _1636730), _1636732)), 42990 ^ _779300 : [(42991 ^ _779300) ^ [] : [_1636726 = c_List_Olist_ONil(_1636724), _1636728 = hAPP(hAPP(c_List_Olist_OCons(_1636724), _1636730), _1636732)], (42997 ^ _779300) ^ [_1636907] : [_1636726 = hAPP(hAPP(c_List_Olist_OCons(_1636724), _1636730), _1636907), hAPP(hAPP(c_List_Oappend(_1636724), _1636907), _1636728) = _1636732]]], (43005 ^ _779300) ^ [_1637071, _1637073, _1637075, _1637077, _1637079, _1637081] : [hAPP(hAPP(c_List_Olist_OCons(_1637071), _1637073), _1637075) = _1637077, _1637079 = hAPP(hAPP(c_List_Oappend(_1637071), _1637075), _1637081), -(hAPP(hAPP(c_List_Olist_OCons(_1637071), _1637073), _1637079) = hAPP(hAPP(c_List_Oappend(_1637071), _1637077), _1637081))], (43015 ^ _779300) ^ [_1637280, _1637282, _1637284, _1637286] : [-(hAPP(hAPP(c_List_Oappend(_1637280), hAPP(hAPP(c_List_Olist_OCons(_1637280), _1637282), _1637284)), _1637286) = hAPP(hAPP(c_List_Olist_OCons(_1637280), _1637282), hAPP(hAPP(c_List_Oappend(_1637280), _1637284), _1637286)))], (43017 ^ _779300) ^ [_1637362, _1637364, _1637366, _1637368] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637362)), hAPP(hAPP(c_List_Oappend(_1637362), _1637364), _1637366)), c_List_Olists(_1637362, _1637368))), 43020 ^ _779300 : [(43021 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637362)), _1637364), c_List_Olists(_1637362, _1637368))))], (43023 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637362)), _1637366), c_List_Olists(_1637362, _1637368))))]]], (43025 ^ _779300) ^ [_1637553, _1637555, _1637557, _1637559] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637553)), hAPP(hAPP(c_List_Oappend(_1637553), _1637555), _1637557)), c_List_Olists(_1637553, _1637559)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637553)), _1637555), c_List_Olists(_1637553, _1637559))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637553)), _1637557), c_List_Olists(_1637553, _1637559)))], (43035 ^ _779300) ^ [_1637780, _1637782, _1637784, _1637786] : [-(hAPP(hAPP(c_List_Oappend(_1637780), hAPP(hAPP(c_List_Oappend(_1637780), _1637782), _1637784)), _1637786) = hAPP(hAPP(c_List_Oappend(_1637780), _1637782), hAPP(hAPP(c_List_Oappend(_1637780), _1637784), _1637786)))], (43037 ^ _779300) ^ [_1637865, _1637867, _1637869, _1637871, _1637873] : [hAPP(hAPP(c_List_Oappend(_1637865), _1637867), _1637869) = hAPP(hAPP(c_List_Oappend(_1637865), _1637871), _1637873), 43043 ^ _779300 : [(43044 ^ _779300) ^ [] : [-(_1637867 = hAPP(hAPP(c_List_Oappend(_1637865), _1637871), 43040 ^ [_1637865, _1637867, _1637869, _1637871, _1637873]))], (43046 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1637865), 43040 ^ [_1637865, _1637867, _1637869, _1637871, _1637873]), _1637869) = _1637873)]], 43047 ^ _779300 : [(43048 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1637865), _1637867), 43040 ^ [_1637865, _1637867, _1637869, _1637871, _1637873]) = _1637871)], (43050 ^ _779300) ^ [] : [-(_1637869 = hAPP(hAPP(c_List_Oappend(_1637865), 43040 ^ [_1637865, _1637867, _1637869, _1637871, _1637873]), _1637873))]]], (43052 ^ _779300) ^ [_1638196, _1638198, _1638200, _1638202, _1638204] : [-(hAPP(hAPP(c_List_Oappend(_1638196), _1638198), _1638200) = hAPP(hAPP(c_List_Oappend(_1638196), _1638202), _1638204)), 43053 ^ _779300 : [(43054 ^ _779300) ^ [_1638308] : [_1638198 = hAPP(hAPP(c_List_Oappend(_1638196), _1638202), _1638308), hAPP(hAPP(c_List_Oappend(_1638196), _1638308), _1638200) = _1638204], (43060 ^ _779300) ^ [_1638420] : [hAPP(hAPP(c_List_Oappend(_1638196), _1638198), _1638420) = _1638202, _1638200 = hAPP(hAPP(c_List_Oappend(_1638196), _1638420), _1638204)]]], (43068 ^ _779300) ^ [_1638605, _1638607, _1638609, _1638611] : [hAPP(hAPP(c_List_Oappend(_1638605), _1638607), _1638609) = hAPP(hAPP(c_List_Oappend(_1638605), _1638607), _1638611), -(_1638609 = _1638611)], (43074 ^ _779300) ^ [_1638714, _1638716, _1638718, _1638720] : [_1638718 = _1638720, -(hAPP(hAPP(c_List_Oappend(_1638714), _1638716), _1638718) = hAPP(hAPP(c_List_Oappend(_1638714), _1638716), _1638720))], (43080 ^ _779300) ^ [_1638850, _1638852, _1638854, _1638856] : [hAPP(hAPP(c_List_Oappend(_1638850), _1638852), _1638854) = hAPP(hAPP(c_List_Oappend(_1638850), _1638856), _1638854), -(_1638852 = _1638856)], (43086 ^ _779300) ^ [_1638959, _1638961, _1638963, _1638965] : [_1638961 = _1638965, -(hAPP(hAPP(c_List_Oappend(_1638959), _1638961), _1638963) = hAPP(hAPP(c_List_Oappend(_1638959), _1638965), _1638963))], (43092 ^ _779300) ^ [_1639074, _1639076, _1639078, _1639080, _1639082, _1639084] : [hAPP(hAPP(c_List_Oappend(_1639074), _1639076), _1639078) = _1639080, _1639082 = hAPP(hAPP(c_List_Oappend(_1639074), _1639078), _1639084), -(hAPP(hAPP(c_List_Oappend(_1639074), _1639076), _1639082) = hAPP(hAPP(c_List_Oappend(_1639074), _1639080), _1639084))], (43102 ^ _779300) ^ [_1639283, _1639285, _1639287] : [class_Groups_Omonoid__add(_1639283), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1639283), hAPP(hAPP(c_List_Oappend(_1639283), _1639285), _1639287)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1639283), hAPP(c_List_Omonoid__add__class_Olistsum(_1639283), _1639285)), hAPP(c_List_Omonoid__add__class_Olistsum(_1639283), _1639287)))], (43108 ^ _779300) ^ [_1639422, _1639424, _1639426] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639422)), hAPP(hAPP(c_List_Oappend(_1639422), _1639424), _1639426)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639422)), _1639424)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639422)), _1639426)))], (43110 ^ _779300) ^ [_1639484, _1639486, _1639488, _1639490, _1639492, _1639494] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639484)), _1639486) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639488)), _1639490), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639484)), _1639492) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639488)), _1639494), -(hAPP(hAPP(c_List_Ozip(_1639484, _1639488), hAPP(hAPP(c_List_Oappend(_1639484), _1639486), _1639492)), hAPP(hAPP(c_List_Oappend(_1639488), _1639490), _1639494)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1639484, _1639488)), hAPP(hAPP(c_List_Ozip(_1639484, _1639488), _1639486), _1639490)), hAPP(hAPP(c_List_Ozip(_1639484, _1639488), _1639492), _1639494)))], (43120 ^ _779300) ^ [_1639793, _1639795, _1639797] : [-(hAPP(c_List_Oset(_1639793), hAPP(hAPP(c_List_Oappend(_1639793), _1639795), _1639797)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1639793, tc_HOL_Obool)), hAPP(c_List_Oset(_1639793), _1639795)), hAPP(c_List_Oset(_1639793), _1639797)))], (43122 ^ _779300) ^ [_1639854, _1639856, _1639858] : [_1639854 = _1639856, -(_1639854 = hAPP(hAPP(c_List_Oappend(_1639858), c_List_Olist_ONil(_1639858)), _1639856))], (43128 ^ _779300) ^ [_1639971, _1639973, _1639975] : [hAPP(hAPP(c_List_Oappend(_1639971), _1639973), _1639975) = _1639975, -(_1639973 = c_List_Olist_ONil(_1639971))], (43134 ^ _779300) ^ [_1640066, _1640068, _1640070] : [_1640068 = c_List_Olist_ONil(_1640066), -(hAPP(hAPP(c_List_Oappend(_1640066), _1640068), _1640070) = _1640070)], (43140 ^ _779300) ^ [_1640185, _1640187, _1640189] : [hAPP(hAPP(c_List_Oappend(_1640185), _1640187), _1640189) = _1640187, -(_1640189 = c_List_Olist_ONil(_1640185))], (43146 ^ _779300) ^ [_1640280, _1640282, _1640284] : [_1640284 = c_List_Olist_ONil(_1640280), -(hAPP(hAPP(c_List_Oappend(_1640280), _1640282), _1640284) = _1640282)], (43152 ^ _779300) ^ [_1640399, _1640401, _1640403] : [hAPP(hAPP(c_List_Oappend(_1640399), _1640401), _1640403) = c_List_Olist_ONil(_1640399), 43155 ^ _779300 : [(43156 ^ _779300) ^ [] : [-(_1640401 = c_List_Olist_ONil(_1640399))], (43158 ^ _779300) ^ [] : [-(_1640403 = c_List_Olist_ONil(_1640399))]]], (43160 ^ _779300) ^ [_1640528, _1640530, _1640532] : [-(hAPP(hAPP(c_List_Oappend(_1640528), _1640530), _1640532) = c_List_Olist_ONil(_1640528)), _1640530 = c_List_Olist_ONil(_1640528), _1640532 = c_List_Olist_ONil(_1640528)], (43170 ^ _779300) ^ [_1640709, _1640711, _1640713] : [_1640709 = hAPP(hAPP(c_List_Oappend(_1640711), _1640713), _1640709), -(_1640713 = c_List_Olist_ONil(_1640711))], (43176 ^ _779300) ^ [_1640804, _1640806, _1640808] : [_1640808 = c_List_Olist_ONil(_1640806), -(_1640804 = hAPP(hAPP(c_List_Oappend(_1640806), _1640808), _1640804))], (43182 ^ _779300) ^ [_1640923, _1640925, _1640927] : [_1640923 = hAPP(hAPP(c_List_Oappend(_1640925), _1640923), _1640927), -(_1640927 = c_List_Olist_ONil(_1640925))], (43188 ^ _779300) ^ [_1641018, _1641020, _1641022] : [_1641022 = c_List_Olist_ONil(_1641020), -(_1641018 = hAPP(hAPP(c_List_Oappend(_1641020), _1641018), _1641022))], (43194 ^ _779300) ^ [_1641119, _1641121] : [-(hAPP(hAPP(c_List_Oappend(_1641119), _1641121), c_List_Olist_ONil(_1641119)) = _1641121)], (43196 ^ _779300) ^ [_1641172, _1641174, _1641176] : [c_List_Olist_ONil(_1641172) = hAPP(hAPP(c_List_Oappend(_1641172), _1641174), _1641176), 43199 ^ _779300 : [(43200 ^ _779300) ^ [] : [-(_1641174 = c_List_Olist_ONil(_1641172))], (43202 ^ _779300) ^ [] : [-(_1641176 = c_List_Olist_ONil(_1641172))]]], (43204 ^ _779300) ^ [_1641301, _1641303, _1641305] : [-(c_List_Olist_ONil(_1641301) = hAPP(hAPP(c_List_Oappend(_1641301), _1641303), _1641305)), _1641303 = c_List_Olist_ONil(_1641301), _1641305 = c_List_Olist_ONil(_1641301)], (43214 ^ _779300) ^ [_1641464, _1641466] : [-(hAPP(hAPP(c_List_Oappend(_1641464), c_List_Olist_ONil(_1641464)), _1641466) = _1641466)], (43216 ^ _779300) ^ [_1641511, _1641513, _1641515] : [_1641511 = c_List_Olist_ONil(_1641513), -(c_List_Obutlast(_1641513, hAPP(hAPP(c_List_Oappend(_1641513), _1641515), _1641511)) = c_List_Obutlast(_1641513, _1641515))], (43222 ^ _779300) ^ [_1641616, _1641618, _1641620] : [-(_1641616 = c_List_Olist_ONil(_1641618)), -(c_List_Obutlast(_1641618, hAPP(hAPP(c_List_Oappend(_1641618), _1641620), _1641616)) = hAPP(hAPP(c_List_Oappend(_1641618), _1641620), c_List_Obutlast(_1641618, _1641616)))], (43228 ^ _779300) ^ [_1641680, _1641682, _1641684, _1641686] : [-(hAPP(hAPP(c_List_Onth(_1641680), hAPP(hAPP(c_List_Oappend(_1641680), _1641682), hAPP(hAPP(c_List_Olist_OCons(_1641680), _1641684), _1641686))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641680)), _1641682)) = _1641684)], (43230 ^ _779300) ^ [_1641740, _1641742, _1641744, _1641746] : [-(hAPP(hAPP(c_List_Onth(_1641740), hAPP(hAPP(c_List_Oappend(_1641740), _1641742), _1641744)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641740)), _1641742)), _1641746)) = hAPP(hAPP(c_List_Onth(_1641740), _1641744), _1641746))], (43232 ^ _779300) ^ [_1641806, _1641808, _1641810, _1641812] : [-(hAPP(hAPP(c_List_Otake(_1641806), _1641808), hAPP(hAPP(c_List_Oappend(_1641806), _1641810), _1641812)) = hAPP(hAPP(c_List_Oappend(_1641806), hAPP(hAPP(c_List_Otake(_1641806), _1641808), _1641810)), hAPP(hAPP(c_List_Otake(_1641806), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1641808), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641806)), _1641810))), _1641812)))], (43234 ^ _779300) ^ [_1641888, _1641890, _1641892, _1641894, _1641896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641888), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641890)), _1641892))), -(hAPP(hAPP(c_List_Olist__update(_1641890, hAPP(hAPP(c_List_Oappend(_1641890), _1641892), _1641894)), _1641888), _1641896) = hAPP(hAPP(c_List_Oappend(_1641890), hAPP(hAPP(c_List_Olist__update(_1641890, _1641892), _1641888), _1641896)), _1641894))], (43240 ^ _779300) ^ [_1642063, _1642065, _1642067, _1642069, _1642071] : [-(hAPP(hAPP(c_List_Olist__update(_1642063, hAPP(hAPP(c_List_Oappend(_1642063), _1642065), hAPP(hAPP(c_List_Olist_OCons(_1642063), _1642067), _1642069))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642063)), _1642065)), _1642071) = hAPP(hAPP(c_List_Oappend(_1642063), _1642065), hAPP(hAPP(c_List_Olist_OCons(_1642063), _1642071), _1642069)))], (43242 ^ _779300) ^ [_1642157, _1642159, _1642161, _1642163] : [hBOOL(hAPP(hAPP(c_member(_1642157), _1642159), hAPP(c_List_Oset(_1642157), _1642161))), -(c_List_Oremove1(_1642157, _1642159, hAPP(hAPP(c_List_Oappend(_1642157), _1642161), _1642163)) = hAPP(hAPP(c_List_Oappend(_1642157), c_List_Oremove1(_1642157, _1642159, _1642161)), _1642163))], (43248 ^ _779300) ^ [_1642304, _1642306, _1642308, _1642310] : [-(hBOOL(hAPP(hAPP(c_member(_1642304), _1642306), hAPP(c_List_Oset(_1642304), _1642308)))), -(c_List_Oremove1(_1642304, _1642306, hAPP(hAPP(c_List_Oappend(_1642304), _1642308), _1642310)) = hAPP(hAPP(c_List_Oappend(_1642304), _1642308), c_List_Oremove1(_1642304, _1642306, _1642310)))], (43254 ^ _779300) ^ [_1642382, _1642384, _1642386, _1642388] : [43255 ^ _779300 : [(43256 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642382), _1642384), hAPP(c_List_Oset(_1642382), c_List_Obutlast(_1642382, _1642386))))], (43258 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642382), _1642384), hAPP(c_List_Oset(_1642382), c_List_Obutlast(_1642382, _1642388))))]], -(hBOOL(hAPP(hAPP(c_member(_1642382), _1642384), hAPP(c_List_Oset(_1642382), c_List_Obutlast(_1642382, hAPP(hAPP(c_List_Oappend(_1642382), _1642386), _1642388))))))], (43262 ^ _779300) ^ [_1642607, _1642609, _1642611] : [-(c_List_Obutlast(_1642607, hAPP(hAPP(c_List_Oappend(_1642607), _1642609), hAPP(hAPP(c_List_Olist_OCons(_1642607), _1642611), c_List_Olist_ONil(_1642607)))) = _1642609)], (43264 ^ _779300) ^ [_1642655, _1642657, _1642659, _1642661, _1642663, _1642665] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642655), tc_List_Olist(_1642655))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642655), tc_List_Olist(_1642655)), hAPP(hAPP(c_List_Oappend(_1642655), _1642657), _1642663)), hAPP(hAPP(c_List_Oappend(_1642655), _1642659), _1642665))), c_List_Olistrel1(_1642655, _1642661)))), 43265 ^ _779300 : [(43266 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642655), tc_List_Olist(_1642655))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642655), tc_List_Olist(_1642655)), _1642657), _1642659)), c_List_Olistrel1(_1642655, _1642661))), _1642663 = _1642665], (43272 ^ _779300) ^ [] : [_1642657 = _1642659, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642655), tc_List_Olist(_1642655))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642655), tc_List_Olist(_1642655)), _1642663), _1642665)), c_List_Olistrel1(_1642655, _1642661)))]]], (43280 ^ _779300) ^ [_1643103, _1643105, _1643107, _1643109, _1643111] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643103), tc_List_Olist(_1643103))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643103), tc_List_Olist(_1643103)), _1643105), _1643107)), c_List_Olexord(_1643103, _1643109))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643103), tc_List_Olist(_1643103))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643103), tc_List_Olist(_1643103)), hAPP(hAPP(c_List_Oappend(_1643103), _1643111), _1643105)), hAPP(hAPP(c_List_Oappend(_1643103), _1643111), _1643107))), c_List_Olexord(_1643103, _1643109))))], (43286 ^ _779300) ^ [_1643356, _1643358, _1643360] : [hBOOL(hAPP(c_List_Odistinct(_1643356), hAPP(hAPP(c_List_Oappend(_1643356), _1643358), _1643360))), 43289 ^ _779300 : [(43290 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643356), _1643358)))], (43292 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643356), _1643360)))], (43294 ^ _779300) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643356, tc_HOL_Obool)), hAPP(c_List_Oset(_1643356), _1643358)), hAPP(c_List_Oset(_1643356), _1643360)) = c_Orderings_Obot__class_Obot(tc_fun(_1643356, tc_HOL_Obool)))]]], (43296 ^ _779300) ^ [_1643573, _1643575, _1643577] : [-(hBOOL(hAPP(c_List_Odistinct(_1643573), hAPP(hAPP(c_List_Oappend(_1643573), _1643575), _1643577)))), hBOOL(hAPP(c_List_Odistinct(_1643573), _1643575)), hBOOL(hAPP(c_List_Odistinct(_1643573), _1643577)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643573, tc_HOL_Obool)), hAPP(c_List_Oset(_1643573), _1643575)), hAPP(c_List_Oset(_1643573), _1643577)) = c_Orderings_Obot__class_Obot(tc_fun(_1643573, tc_HOL_Obool))], (43310 ^ _779300) ^ [_1643869, _1643871, _1643873, _1643875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1643869), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643871)), _1643873))), -(hAPP(hAPP(c_List_Onth(_1643871), hAPP(hAPP(c_List_Oappend(_1643871), _1643873), _1643875)), _1643869) = hAPP(hAPP(c_List_Onth(_1643871), _1643873), _1643869))], (43316 ^ _779300) ^ [_1644016, _1644018, _1644020, _1644022] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644016), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644018)), _1644020)))), -(hAPP(hAPP(c_List_Onth(_1644018), hAPP(hAPP(c_List_Oappend(_1644018), _1644020), _1644022)), _1644016) = hAPP(hAPP(c_List_Onth(_1644018), _1644022), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644016), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644018)), _1644020))))], (43322 ^ _779300) ^ [_1644125, _1644127, _1644129, _1644131, _1644133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644125), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644127)), _1644129))), -(hAPP(hAPP(c_List_Olist__update(_1644127, hAPP(hAPP(c_List_Oappend(_1644127), _1644129), _1644131)), _1644125), _1644133) = hAPP(hAPP(c_List_Oappend(_1644127), hAPP(hAPP(c_List_Olist__update(_1644127, _1644129), _1644125), _1644133)), _1644131))], (43328 ^ _779300) ^ [_1644294, _1644296, _1644298, _1644300, _1644302] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644294), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644296)), _1644298)))), -(hAPP(hAPP(c_List_Olist__update(_1644296, hAPP(hAPP(c_List_Oappend(_1644296), _1644298), _1644300)), _1644294), _1644302) = hAPP(hAPP(c_List_Oappend(_1644296), _1644298), hAPP(hAPP(c_List_Olist__update(_1644296, _1644300), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644294), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644296)), _1644298))), _1644302)))], (43334 ^ _779300) ^ [_1644397, _1644399, _1644401, _1644403] : [-(c_List_Osublist(_1644397, hAPP(hAPP(c_List_Oappend(_1644397), _1644399), _1644401), _1644403) = hAPP(hAPP(c_List_Oappend(_1644397), c_List_Osublist(_1644397, _1644399, _1644403)), c_List_Osublist(_1644397, _1644401, 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(_1644397)), _1644399)))), _1644403)))))], (43336 ^ _779300) ^ [_1644476, _1644478, _1644480, _1644482, _1644484, _1644486, _1644488, _1644490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644476, _1644476)), hAPP(hAPP(c_Product__Type_OPair(_1644476, _1644476), _1644478), _1644480)), _1644482)), _1644484 = hAPP(hAPP(c_List_Oappend(_1644476), _1644486), hAPP(hAPP(c_List_Olist_OCons(_1644476), _1644478), _1644488)), _1644490 = hAPP(hAPP(c_List_Oappend(_1644476), _1644486), hAPP(hAPP(c_List_Olist_OCons(_1644476), _1644480), _1644488)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644476), tc_List_Olist(_1644476))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644476), tc_List_Olist(_1644476)), _1644484), _1644490)), c_List_Olistrel1(_1644476, _1644482))))], (43350 ^ _779300) ^ [_1644855, _1644857, _1644859, _1644861, _1644863, _1644865, _1644867] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644855, _1644855)), hAPP(hAPP(c_Product__Type_OPair(_1644855, _1644855), _1644857), _1644859)), _1644861)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644855), tc_List_Olist(_1644855))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644855), tc_List_Olist(_1644855)), hAPP(hAPP(c_List_Oappend(_1644855), _1644863), hAPP(hAPP(c_List_Olist_OCons(_1644855), _1644857), _1644865))), hAPP(hAPP(c_List_Oappend(_1644855), _1644863), hAPP(hAPP(c_List_Olist_OCons(_1644855), _1644859), _1644867)))), c_List_Olexord(_1644855, _1644861))))], (43356 ^ _779300) ^ [_1645104, _1645106, _1645108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645104), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645106)), _1645108))), -(hAPP(hAPP(c_List_Otake(_1645106), hAPP(c_Nat_OSuc, _1645104)), _1645108) = hAPP(hAPP(c_List_Oappend(_1645106), hAPP(hAPP(c_List_Otake(_1645106), _1645104), _1645108)), hAPP(hAPP(c_List_Olist_OCons(_1645106), hAPP(hAPP(c_List_Onth(_1645106), _1645108), _1645104)), c_List_Olist_ONil(_1645106))))], (43362 ^ _779300) ^ [_1645324, _1645326, _1645328, _1645330, _1645332, _1645334] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645324), tc_List_Olist(_1645324))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645324), tc_List_Olist(_1645324)), hAPP(hAPP(c_List_Oappend(_1645324), _1645326), hAPP(hAPP(c_List_Olist_OCons(_1645324), _1645328), c_List_Olist_ONil(_1645324)))), hAPP(hAPP(c_List_Oappend(_1645324), _1645330), hAPP(hAPP(c_List_Olist_OCons(_1645324), _1645332), c_List_Olist_ONil(_1645324))))), c_List_Olistrel1(_1645324, _1645334))), 43367 ^ _779300 : [(43368 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645324), tc_List_Olist(_1645324))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645324), tc_List_Olist(_1645324)), _1645326), _1645330)), c_List_Olistrel1(_1645324, _1645334))))], (43370 ^ _779300) ^ [] : [-(_1645328 = _1645332)]], 43371 ^ _779300 : [(43372 ^ _779300) ^ [] : [-(_1645326 = _1645330)], (43374 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1645324, _1645324)), hAPP(hAPP(c_Product__Type_OPair(_1645324, _1645324), _1645328), _1645332)), _1645334)))]]], (43376 ^ _779300) ^ [_1645734, _1645736, _1645738, _1645740, _1645742, _1645744] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645734), tc_List_Olist(_1645734))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645734), tc_List_Olist(_1645734)), hAPP(hAPP(c_List_Oappend(_1645734), _1645736), hAPP(hAPP(c_List_Olist_OCons(_1645734), _1645738), c_List_Olist_ONil(_1645734)))), hAPP(hAPP(c_List_Oappend(_1645734), _1645740), hAPP(hAPP(c_List_Olist_OCons(_1645734), _1645742), c_List_Olist_ONil(_1645734))))), c_List_Olistrel1(_1645734, _1645744)))), 43377 ^ _779300 : [(43378 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645734), tc_List_Olist(_1645734))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645734), tc_List_Olist(_1645734)), _1645736), _1645740)), c_List_Olistrel1(_1645734, _1645744))), _1645738 = _1645742], (43384 ^ _779300) ^ [] : [_1645736 = _1645740, hBOOL(hAPP(hAPP(c_member(tc_prod(_1645734, _1645734)), hAPP(hAPP(c_Product__Type_OPair(_1645734, _1645734), _1645738), _1645742)), _1645744))]]], (43392 ^ _779300) ^ [_1646202, _1646204, _1646206, _1646208] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646202), tc_List_Olist(_1646202))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646202), tc_List_Olist(_1646202)), _1646204), _1646206)), c_List_Olistrel1(_1646202, _1646208))), 43397 ^ _779300 : [(43398 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646202, _1646202)), hAPP(hAPP(c_Product__Type_OPair(_1646202, _1646202), 43395 ^ [_1646202, _1646204, _1646206, _1646208]), 43396 ^ [_1646202, _1646204, _1646206, _1646208])), _1646208)))], (43402 ^ _779300) ^ [] : [-(_1646204 = hAPP(hAPP(c_List_Oappend(_1646202), 43399 ^ [_1646202, _1646204, _1646206, _1646208]), hAPP(hAPP(c_List_Olist_OCons(_1646202), 43395 ^ [_1646202, _1646204, _1646206, _1646208]), 43400 ^ [_1646202, _1646204, _1646206, _1646208])))], (43404 ^ _779300) ^ [] : [-(_1646206 = hAPP(hAPP(c_List_Oappend(_1646202), 43399 ^ [_1646202, _1646204, _1646206, _1646208]), hAPP(hAPP(c_List_Olist_OCons(_1646202), 43396 ^ [_1646202, _1646204, _1646206, _1646208]), 43400 ^ [_1646202, _1646204, _1646206, _1646208])))]]], (43406 ^ _779300) ^ [_1646607, _1646609, _1646611, _1646613, _1646615] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646607), tc_List_Olist(_1646607))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646607), tc_List_Olist(_1646607)), hAPP(hAPP(c_List_Oappend(_1646607), _1646609), _1646611)), hAPP(hAPP(c_List_Oappend(_1646607), _1646609), _1646613))), c_List_Olexord(_1646607, _1646615))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646607, _1646607)), hAPP(hAPP(c_Product__Type_OPair(_1646607, _1646607), 43411 ^ [_1646607, _1646609, _1646611, _1646613, _1646615]), 43411 ^ [_1646607, _1646609, _1646611, _1646613, _1646615])), _1646615))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646607), tc_List_Olist(_1646607))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646607), tc_List_Olist(_1646607)), _1646611), _1646613)), c_List_Olexord(_1646607, _1646615))))], (43417 ^ _779300) ^ [_1646926, _1646928] : [-(hAPP(c_List_Orotate1(_1646926), _1646928) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1646926), _1646926, c_List_Olist_ONil(_1646926), hAPP(hAPP(c_COMBB(tc_List_Olist(_1646926), tc_fun(tc_List_Olist(_1646926), tc_List_Olist(_1646926)), _1646926), hAPP(c_COMBC(tc_List_Olist(_1646926), tc_List_Olist(_1646926), tc_List_Olist(_1646926)), c_List_Oappend(_1646926))), hAPP(hAPP(c_COMBC(_1646926, tc_List_Olist(_1646926), tc_List_Olist(_1646926)), c_List_Olist_OCons(_1646926)), c_List_Olist_ONil(_1646926)))), _1646928))], (43419 ^ _779300) ^ [_1647020, _1647022, _1647024, _1647026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647020), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647022)), _1647024))), -(hAPP(hAPP(c_List_Olist__update(_1647022, _1647024), _1647020), _1647026) = hAPP(hAPP(c_List_Oappend(_1647022), hAPP(hAPP(c_List_Otake(_1647022), _1647020), _1647024)), hAPP(hAPP(c_List_Olist_OCons(_1647022), _1647026), hAPP(hAPP(c_List_Odrop(_1647022), hAPP(c_Nat_OSuc, _1647020)), _1647024))))], (43425 ^ _779300) ^ [_1647213, _1647215, _1647217] : [-(hAPP(hAPP(c_List_Oappend(_1647213), hAPP(hAPP(c_List_Otake(_1647213), _1647215), _1647217)), hAPP(hAPP(c_List_Odrop(_1647213), _1647215), _1647217)) = _1647217)], (43427 ^ _779300) ^ [_1647264, _1647266, _1647268, _1647270] : [-(hAPP(hAPP(c_List_Odrop(_1647264), hAPP(c_Nat_OSuc, _1647266)), hAPP(hAPP(c_List_Olist_OCons(_1647264), _1647268), _1647270)) = hAPP(hAPP(c_List_Odrop(_1647264), _1647266), _1647270))], (43429 ^ _779300) ^ [_1647320, _1647322, _1647324] : [-(hAPP(hAPP(c_List_Odrop(_1647320), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1647320), _1647322), _1647324)) = _1647324)], (43431 ^ _779300) ^ [_1647363, _1647365, _1647367, _1647369, _1647371] : [hAPP(hAPP(c_List_Odrop(_1647363), _1647365), _1647367) = hAPP(hAPP(c_List_Olist_OCons(_1647363), _1647369), _1647371), -(hAPP(hAPP(c_List_Onth(_1647363), _1647367), _1647365) = _1647369)], (43437 ^ _779300) ^ [_1647509, _1647511] : [hBOOL(hAPP(c_List_Odistinct(_1647509), hAPP(c_List_Orotate1(_1647509), _1647511))), -(hBOOL(hAPP(c_List_Odistinct(_1647509), _1647511)))], (43443 ^ _779300) ^ [_1647608, _1647610] : [hBOOL(hAPP(c_List_Odistinct(_1647608), _1647610)), -(hBOOL(hAPP(c_List_Odistinct(_1647608), hAPP(c_List_Orotate1(_1647608), _1647610))))], (43449 ^ _779300) ^ [_1647713, _1647715, _1647717] : [hBOOL(hAPP(c_List_Odistinct(_1647713), _1647715)), -(hBOOL(hAPP(c_List_Odistinct(_1647713), hAPP(hAPP(c_List_Odrop(_1647713), _1647717), _1647715))))], (43455 ^ _779300) ^ [_1647824, _1647826, _1647828] : [-(hAPP(hAPP(c_List_Odrop(_1647824), _1647826), c_List_Obutlast(_1647824, _1647828)) = c_List_Obutlast(_1647824, hAPP(hAPP(c_List_Odrop(_1647824), _1647826), _1647828)))], (43457 ^ _779300) ^ [_1647873, _1647875, _1647877] : [-(c_List_Obutlast(_1647873, hAPP(hAPP(c_List_Odrop(_1647873), _1647875), _1647877)) = hAPP(hAPP(c_List_Odrop(_1647873), _1647875), c_List_Obutlast(_1647873, _1647877)))], (43459 ^ _779300) ^ [_1647922, _1647924, _1647926, _1647928] : [-(hAPP(hAPP(c_List_Otake(_1647922), _1647924), hAPP(hAPP(c_List_Odrop(_1647922), _1647926), _1647928)) = hAPP(hAPP(c_List_Odrop(_1647922), _1647926), hAPP(hAPP(c_List_Otake(_1647922), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1647924), _1647926)), _1647928)))], (43461 ^ _779300) ^ [_1647989, _1647991, _1647993, _1647995] : [-(hAPP(hAPP(c_List_Odrop(_1647989), _1647991), hAPP(hAPP(c_List_Otake(_1647989), _1647993), _1647995)) = hAPP(hAPP(c_List_Otake(_1647989), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1647993), _1647991)), hAPP(hAPP(c_List_Odrop(_1647989), _1647991), _1647995)))], (43463 ^ _779300) ^ [_1648056, _1648058, _1648060, _1648062] : [-(hAPP(hAPP(c_List_Odrop(_1648056), _1648058), hAPP(hAPP(c_List_Odrop(_1648056), _1648060), _1648062)) = hAPP(hAPP(c_List_Odrop(_1648056), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1648058), _1648060)), _1648062))], (43465 ^ _779300) ^ [_1648115, _1648117] : [-(hAPP(hAPP(c_List_Odrop(_1648115), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1648117) = _1648117)], (43467 ^ _779300) ^ [_1648148, _1648150, _1648152, _1648154, _1648156] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1648148, _1648150)), _1648152), hAPP(hAPP(c_List_Ozip(_1648148, _1648150), _1648154), _1648156)) = hAPP(hAPP(c_List_Ozip(_1648148, _1648150), hAPP(hAPP(c_List_Odrop(_1648148), _1648152), _1648154)), hAPP(hAPP(c_List_Odrop(_1648150), _1648152), _1648156)))], (43469 ^ _779300) ^ [_1648224, _1648226] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648224)), hAPP(c_List_Orotate1(_1648224), _1648226)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648224)), _1648226))], (43471 ^ _779300) ^ [_1648268, _1648270, _1648272] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648268)), hAPP(hAPP(c_List_Odrop(_1648268), _1648270), _1648272)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648268)), _1648272)), _1648270))], (43473 ^ _779300) ^ [_1648323, _1648325] : [-(hAPP(c_List_Oset(_1648323), hAPP(c_List_Orotate1(_1648323), _1648325)) = hAPP(c_List_Oset(_1648323), _1648325))], (43475 ^ _779300) ^ [_1648363, _1648365, _1648367, _1648369] : [hBOOL(hAPP(hAPP(c_member(_1648363), _1648365), hAPP(c_List_Oset(_1648363), hAPP(hAPP(c_List_Odrop(_1648363), _1648367), _1648369)))), -(hBOOL(hAPP(hAPP(c_member(_1648363), _1648365), hAPP(c_List_Oset(_1648363), _1648369))))], (43481 ^ _779300) ^ [_1648508, _1648510, _1648512] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648508, tc_HOL_Obool)), hAPP(c_List_Oset(_1648508), hAPP(hAPP(c_List_Odrop(_1648508), _1648510), _1648512))), hAPP(c_List_Oset(_1648508), _1648512))))], (43483 ^ _779300) ^ [_1648578, _1648580] : [hAPP(c_List_Orotate1(_1648578), _1648580) = c_List_Olist_ONil(_1648578), -(_1648580 = c_List_Olist_ONil(_1648578))], (43489 ^ _779300) ^ [_1648669, _1648671] : [_1648671 = c_List_Olist_ONil(_1648669), -(hAPP(c_List_Orotate1(_1648669), _1648671) = c_List_Olist_ONil(_1648669))], (43495 ^ _779300) ^ [_1648766, _1648768] : [-(hAPP(hAPP(c_List_Odrop(_1648766), _1648768), c_List_Olist_ONil(_1648766)) = c_List_Olist_ONil(_1648766))], (43497 ^ _779300) ^ [_1648803, _1648805, _1648807, _1648809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1648803), _1648805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648807, tc_HOL_Obool)), hAPP(c_List_Oset(_1648807), hAPP(hAPP(c_List_Odrop(_1648807), _1648805), _1648809))), hAPP(c_List_Oset(_1648807), hAPP(hAPP(c_List_Odrop(_1648807), _1648803), _1648809)))))], (43503 ^ _779300) ^ [_1648984, _1648986, _1648988] : [hAPP(hAPP(c_List_Odrop(_1648984), _1648986), _1648988) = c_List_Olist_ONil(_1648984), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648984)), _1648988)), _1648986)))], (43509 ^ _779300) ^ [_1649103, _1649105, _1649107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649103)), _1649107)), _1649105)), -(hAPP(hAPP(c_List_Odrop(_1649103), _1649105), _1649107) = c_List_Olist_ONil(_1649103))], (43515 ^ _779300) ^ [_1649228, _1649230, _1649232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649228)), _1649230)), _1649232)), -(hAPP(hAPP(c_List_Odrop(_1649228), _1649232), _1649230) = c_List_Olist_ONil(_1649228))], (43521 ^ _779300) ^ [_1649351, _1649353, _1649355, _1649357] : [-(hAPP(hAPP(c_List_Odrop(_1649351), _1649353), hAPP(hAPP(c_List_Oappend(_1649351), _1649355), _1649357)) = hAPP(hAPP(c_List_Oappend(_1649351), hAPP(hAPP(c_List_Odrop(_1649351), _1649353), _1649355)), hAPP(hAPP(c_List_Odrop(_1649351), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1649353), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649351)), _1649355))), _1649357)))], (43523 ^ _779300) ^ [_1649454, _1649456, _1649458, _1649460] : [hAPP(hAPP(c_List_Oappend(_1649454), _1649456), _1649458) = _1649460, 43526 ^ _779300 : [(43527 ^ _779300) ^ [] : [-(_1649456 = hAPP(hAPP(c_List_Otake(_1649454), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649454)), _1649456)), _1649460))], (43529 ^ _779300) ^ [] : [-(_1649458 = hAPP(hAPP(c_List_Odrop(_1649454), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649454)), _1649456)), _1649460))]]], (43531 ^ _779300) ^ [_1649633, _1649635, _1649637, _1649639] : [-(hAPP(hAPP(c_List_Oappend(_1649633), _1649635), _1649637) = _1649639), _1649635 = hAPP(hAPP(c_List_Otake(_1649633), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649633)), _1649635)), _1649639), _1649637 = hAPP(hAPP(c_List_Odrop(_1649633), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649633)), _1649635)), _1649639)], (43541 ^ _779300) ^ [_1649848, _1649850, _1649852, _1649854] : [-(hAPP(hAPP(c_List_Odrop(_1649848), _1649850), hAPP(hAPP(c_List_Olist_OCons(_1649848), _1649852), _1649854)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1649848), hAPP(hAPP(c_List_Olist_OCons(_1649848), _1649852), _1649854), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1649848), tc_List_Olist(_1649848)), c_List_Odrop(_1649848)), _1649854), _1649850))], (43543 ^ _779300) ^ [_1649939, _1649941, _1649943, _1649945] : [_1649939 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1649941), _1649939), hAPP(hAPP(c_List_Olist_OCons(_1649941), _1649943), _1649945)) = hAPP(hAPP(c_List_Olist_OCons(_1649941), _1649943), _1649945))], (43549 ^ _779300) ^ [_1650062, _1650064, _1650066, _1650068] : [-(_1650062 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1650064), _1650062), hAPP(hAPP(c_List_Olist_OCons(_1650064), _1650066), _1650068)) = hAPP(hAPP(c_List_Odrop(_1650064), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1650062), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1650068))], (43555 ^ _779300) ^ [_1650134, _1650136, _1650138, _1650140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650134), _1650136)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650138)), _1650140))), -(hAPP(hAPP(c_List_Onth(_1650138), hAPP(hAPP(c_List_Odrop(_1650138), _1650134), _1650140)), _1650136) = hAPP(hAPP(c_List_Onth(_1650138), _1650140), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650134), _1650136)))], (43561 ^ _779300) ^ [_1650335, _1650337, _1650339, _1650341, _1650343] : [hAPP(hAPP(c_List_Oappend(_1650335), _1650337), _1650339) = hAPP(hAPP(c_List_Oappend(_1650335), _1650341), _1650343), 43564 ^ _779300 : [(43565 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650335)), _1650337)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650335)), _1650341))), 43568 ^ _779300 : [(43569 ^ _779300) ^ [] : [-(_1650337 = hAPP(hAPP(c_List_Otake(_1650335), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650335)), _1650337)), _1650341))], (43571 ^ _779300) ^ [] : [-(_1650339 = hAPP(hAPP(c_List_Oappend(_1650335), hAPP(hAPP(c_List_Odrop(_1650335), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650335)), _1650337)), _1650341)), _1650343))]]], (43573 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650335)), _1650337)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650335)), _1650341)))), 43576 ^ _779300 : [(43577 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1650335), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650335)), _1650341)), _1650337) = _1650341)], (43579 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1650335), hAPP(hAPP(c_List_Odrop(_1650335), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650335)), _1650341)), _1650337)), _1650339) = _1650343)]]]]], (43581 ^ _779300) ^ [_1650848, _1650850, _1650852, _1650854, _1650856] : [-(hAPP(hAPP(c_List_Oappend(_1650848), _1650850), _1650852) = hAPP(hAPP(c_List_Oappend(_1650848), _1650854), _1650856)), 43584 ^ _779300 : [(43585 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650848)), _1650850)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650848)), _1650854))))], (43587 ^ _779300) ^ [] : [_1650850 = hAPP(hAPP(c_List_Otake(_1650848), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650848)), _1650850)), _1650854), _1650852 = hAPP(hAPP(c_List_Oappend(_1650848), hAPP(hAPP(c_List_Odrop(_1650848), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650848)), _1650850)), _1650854)), _1650856)]], 43592 ^ _779300 : [(43593 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650848)), _1650850)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650848)), _1650854)))], (43595 ^ _779300) ^ [] : [hAPP(hAPP(c_List_Otake(_1650848), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650848)), _1650854)), _1650850) = _1650854, hAPP(hAPP(c_List_Oappend(_1650848), hAPP(hAPP(c_List_Odrop(_1650848), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650848)), _1650854)), _1650850)), _1650852) = _1650856]]], (43603 ^ _779300) ^ [_1651436, _1651438, _1651440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651436), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651438)), _1651440))), -(hAPP(hAPP(c_List_Olist_OCons(_1651438), hAPP(hAPP(c_List_Onth(_1651438), _1651440), _1651436)), hAPP(hAPP(c_List_Odrop(_1651438), hAPP(c_Nat_OSuc, _1651436)), _1651440)) = hAPP(hAPP(c_List_Odrop(_1651438), _1651436), _1651440))], (43609 ^ _779300) ^ [_1651607, _1651609, _1651611, _1651613] : [-(hAPP(c_List_Orotate1(_1651607), c_List_Olist_ONil(_1651607)) = c_List_Olist_ONil(_1651607))], (43611 ^ _779300) ^ [_1651642, _1651644, _1651646, _1651648] : [-(hAPP(c_List_Orotate1(_1651644), hAPP(hAPP(c_List_Olist_OCons(_1651644), _1651646), _1651648)) = hAPP(hAPP(c_List_Oappend(_1651644), _1651648), hAPP(hAPP(c_List_Olist_OCons(_1651644), _1651646), c_List_Olist_ONil(_1651644))))], (43613 ^ _779300) ^ [_1651719, _1651721, _1651723, _1651725] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1651721), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651719)), hAPP(hAPP(c_List_Olist_OCons(_1651721), _1651723), _1651725)) = hAPP(hAPP(c_List_Olist_OCons(_1651721), _1651723), _1651725))], (43619 ^ _779300) ^ [_1651854, _1651856, _1651858, _1651860] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651854) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1651856), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651854)), hAPP(hAPP(c_List_Olist_OCons(_1651856), _1651858), _1651860)) = hAPP(hAPP(c_List_Odrop(_1651856), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651854)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1651860))], (43625 ^ _779300) ^ [_1651935, _1651937, _1651939, _1651941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1651935), _1651937)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651939)), _1651941))), -(hAPP(hAPP(c_List_Otake(_1651939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1651935), _1651937)), _1651941) = hAPP(hAPP(c_List_Oappend(_1651939), hAPP(hAPP(c_List_Otake(_1651939), _1651935), _1651941)), hAPP(hAPP(c_List_Otake(_1651939), _1651937), hAPP(hAPP(c_List_Odrop(_1651939), _1651935), _1651941))))], (43631 ^ _779300) ^ [_1652144, _1652146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652144)), _1652146)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1652144), _1652146) = _1652146)], (43637 ^ _779300) ^ [_1652255, _1652257, _1652259, _1652261, _1652263] : [-(hAPP(hAPP(c_List_Ozip(_1652255, _1652257), _1652259), hAPP(hAPP(c_List_Oappend(_1652257), _1652261), _1652263)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652255, _1652257)), hAPP(hAPP(c_List_Ozip(_1652255, _1652257), hAPP(hAPP(c_List_Otake(_1652255), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652257)), _1652261)), _1652259)), _1652261)), hAPP(hAPP(c_List_Ozip(_1652255, _1652257), hAPP(hAPP(c_List_Odrop(_1652255), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652257)), _1652261)), _1652259)), _1652263)))], (43639 ^ _779300) ^ [_1652362, _1652364, _1652366, _1652368, _1652370] : [-(hAPP(hAPP(c_List_Ozip(_1652362, _1652364), hAPP(hAPP(c_List_Oappend(_1652362), _1652366), _1652368)), _1652370) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652362, _1652364)), hAPP(hAPP(c_List_Ozip(_1652362, _1652364), _1652366), hAPP(hAPP(c_List_Otake(_1652364), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652362)), _1652366)), _1652370))), hAPP(hAPP(c_List_Ozip(_1652362, _1652364), _1652368), hAPP(hAPP(c_List_Odrop(_1652364), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652362)), _1652366)), _1652370))))], (43641 ^ _779300) ^ [_1652469, _1652471, _1652473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652469), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652471)), _1652473))), -(_1652473 = hAPP(hAPP(c_List_Oappend(_1652471), hAPP(hAPP(c_List_Otake(_1652471), _1652469), _1652473)), hAPP(hAPP(c_List_Olist_OCons(_1652471), hAPP(hAPP(c_List_Onth(_1652471), _1652473), _1652469)), hAPP(hAPP(c_List_Odrop(_1652471), hAPP(c_Nat_OSuc, _1652469)), _1652473))))], (43647 ^ _779300) ^ [_1652658, _1652660, _1652662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652658), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652660)), _1652662))), -(hAPP(hAPP(c_List_Oappend(_1652660), hAPP(hAPP(c_List_Otake(_1652660), _1652658), _1652662)), hAPP(hAPP(c_List_Olist_OCons(_1652660), hAPP(c_List_Ohd(_1652660), hAPP(hAPP(c_List_Odrop(_1652660), _1652658), _1652662))), c_List_Olist_ONil(_1652660))) = hAPP(hAPP(c_List_Otake(_1652660), hAPP(c_Nat_OSuc, _1652658)), _1652662))], (43653 ^ _779300) ^ [_1652860, _1652862, _1652864] : [-(_1652860 = c_List_Olist_ONil(_1652862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652864), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652862)), _1652860))), -(hAPP(c_List_Ohd(_1652862), hAPP(hAPP(c_List_Odrop(_1652862), _1652864), _1652860)) = hAPP(hAPP(c_List_Onth(_1652862), _1652860), _1652864))], (43663 ^ _779300) ^ [_1653059, _1653061, _1653063] : [-(hAPP(c_List_Ohd(_1653059), hAPP(hAPP(c_List_Olist_OCons(_1653059), _1653061), _1653063)) = _1653061)], (43665 ^ _779300) ^ [_1653111, _1653113, _1653115] : [_1653111 = c_List_Olist_ONil(_1653113), -(hAPP(c_List_Ohd(_1653113), hAPP(hAPP(c_List_Oappend(_1653113), _1653111), _1653115)) = hAPP(c_List_Ohd(_1653113), _1653115))], (43671 ^ _779300) ^ [_1653224, _1653226, _1653228] : [-(_1653224 = c_List_Olist_ONil(_1653226)), -(hAPP(c_List_Ohd(_1653226), hAPP(hAPP(c_List_Oappend(_1653226), _1653224), _1653228)) = hAPP(c_List_Ohd(_1653226), _1653224))], (43677 ^ _779300) ^ [_1653280, _1653282, _1653284] : [-(_1653280 = c_List_Olist_ONil(_1653282)), -(hAPP(c_List_Ohd(_1653282), hAPP(hAPP(c_List_Oappend(_1653282), _1653280), _1653284)) = hAPP(c_List_Ohd(_1653282), _1653280))], (43683 ^ _779300) ^ [_1653334, _1653336] : [-(_1653334 = c_List_Olist_ONil(_1653336)), -(hBOOL(hAPP(hAPP(c_member(_1653336), hAPP(c_List_Ohd(_1653336), _1653334)), hAPP(c_List_Oset(_1653336), _1653334))))], (43689 ^ _779300) ^ [_1653385, _1653387] : [-(_1653385 = c_List_Olist_ONil(_1653387)), -(hAPP(c_List_Ohd(_1653387), _1653385) = hAPP(hAPP(c_List_Onth(_1653387), _1653385), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (43695 ^ _779300) ^ [_1653432, _1653434] : [-(_1653432 = c_List_Olist_ONil(_1653434)), -(hAPP(c_List_Orotate1(_1653434), _1653432) = hAPP(hAPP(c_List_Oappend(_1653434), hAPP(c_List_Otl(_1653434), _1653432)), hAPP(hAPP(c_List_Olist_OCons(_1653434), hAPP(c_List_Ohd(_1653434), _1653432)), c_List_Olist_ONil(_1653434))))], (43701 ^ _779300) ^ [_1653499, _1653501, _1653503] : [-(_1653499 = c_List_Olist_ONil(_1653501)), -(hAPP(c_List_Ohd(_1653501), hAPP(c_List_Orotate(_1653501, _1653503), _1653499)) = hAPP(hAPP(c_List_Onth(_1653501), _1653499), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1653503, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653501)), _1653499))))], (43707 ^ _779300) ^ [_1653569, _1653571, _1653573] : [-(hAPP(c_List_Otl(_1653569), hAPP(hAPP(c_List_Odrop(_1653569), _1653571), _1653573)) = hAPP(hAPP(c_List_Odrop(_1653569), _1653571), hAPP(c_List_Otl(_1653569), _1653573)))], (43709 ^ _779300) ^ [_1653622, _1653624, _1653626] : [-(hAPP(hAPP(c_List_Odrop(_1653622), _1653624), hAPP(c_List_Otl(_1653622), _1653626)) = hAPP(c_List_Otl(_1653622), hAPP(hAPP(c_List_Odrop(_1653622), _1653624), _1653626)))], (43711 ^ _779300) ^ [_1653675, _1653677, _1653679] : [-(hAPP(c_List_Otl(_1653675), hAPP(hAPP(c_List_Olist_OCons(_1653675), _1653677), _1653679)) = _1653679)], (43713 ^ _779300) ^ [_1653733, _1653735, _1653737] : [hBOOL(hAPP(c_List_Odistinct(_1653733), hAPP(c_List_Orotate(_1653733, _1653735), _1653737))), -(hBOOL(hAPP(c_List_Odistinct(_1653733), _1653737)))], (43719 ^ _779300) ^ [_1653836, _1653838, _1653840] : [hBOOL(hAPP(c_List_Odistinct(_1653836), _1653840)), -(hBOOL(hAPP(c_List_Odistinct(_1653836), hAPP(c_List_Orotate(_1653836, _1653838), _1653840))))], (43725 ^ _779300) ^ [_1653945, _1653947] : [hBOOL(hAPP(c_List_Odistinct(_1653945), _1653947)), -(hBOOL(hAPP(c_List_Odistinct(_1653945), hAPP(c_List_Otl(_1653945), _1653947))))], (43731 ^ _779300) ^ [_1654048, _1654050, _1654052] : [-(c_List_Orotate(_1654048, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1654050), _1654052)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1654048), tc_List_Olist(_1654048), tc_List_Olist(_1654048), c_List_Orotate(_1654048, _1654050)), c_List_Orotate(_1654048, _1654052)))], (43733 ^ _779300) ^ [_1654104, _1654106, _1654108, _1654110] : [-(hAPP(c_List_Orotate(_1654104, _1654106), hAPP(c_List_Orotate(_1654104, _1654108), _1654110)) = hAPP(c_List_Orotate(_1654104, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1654106), _1654108)), _1654110))], (43735 ^ _779300) ^ [_1654157] : [-(c_List_Orotate(_1654157, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1654157)))], (43737 ^ _779300) ^ [_1654187, _1654189, _1654191] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654187)), hAPP(c_List_Orotate(_1654187, _1654189), _1654191)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654187)), _1654191))], (43739 ^ _779300) ^ [_1654234, _1654236, _1654238] : [-(hAPP(c_List_Oset(_1654234), hAPP(c_List_Orotate(_1654234, _1654236), _1654238)) = hAPP(c_List_Oset(_1654234), _1654238))], (43741 ^ _779300) ^ [_1654295, _1654297, _1654299] : [hAPP(c_List_Orotate(_1654295, _1654297), _1654299) = c_List_Olist_ONil(_1654295), -(_1654299 = c_List_Olist_ONil(_1654295))], (43747 ^ _779300) ^ [_1654390, _1654392, _1654394] : [_1654394 = c_List_Olist_ONil(_1654390), -(hAPP(c_List_Orotate(_1654390, _1654392), _1654394) = c_List_Olist_ONil(_1654390))], (43753 ^ _779300) ^ [_1654491] : [-(hAPP(c_List_Otl(_1654491), c_List_Olist_ONil(_1654491)) = c_List_Olist_ONil(_1654491))], (43755 ^ _779300) ^ [_1654523, _1654525, _1654527] : [-(hAPP(c_List_Orotate1(_1654523), hAPP(c_List_Orotate(_1654523, _1654525), _1654527)) = hAPP(c_List_Orotate(_1654523, _1654525), hAPP(c_List_Orotate1(_1654523), _1654527)))], (43757 ^ _779300) ^ [_1654572, _1654574] : [-(c_List_Orotate(_1654572, _1654574) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1654572), tc_List_Olist(_1654572)), _1654574), c_List_Orotate1(_1654572)))], (43759 ^ _779300) ^ [_1654611, _1654613, _1654615] : [-(_1654611 = c_List_Olist_ONil(_1654613)), -(hAPP(c_List_Otl(_1654613), hAPP(hAPP(c_List_Oappend(_1654613), _1654611), _1654615)) = hAPP(hAPP(c_List_Oappend(_1654613), hAPP(c_List_Otl(_1654613), _1654611)), _1654615))], (43765 ^ _779300) ^ [_1654677, _1654679, _1654681] : [-(hAPP(hAPP(c_List_Otake(_1654677), _1654679), hAPP(c_List_Otl(_1654677), _1654681)) = hAPP(c_List_Otl(_1654677), hAPP(hAPP(c_List_Otake(_1654677), hAPP(c_Nat_OSuc, _1654679)), _1654681)))], (43767 ^ _779300) ^ [_1654733, _1654735, _1654737] : [-(hAPP(c_List_Orotate(_1654733, _1654735), _1654737) = hAPP(c_List_Orotate(_1654733, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1654735, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654733)), _1654737))), _1654737))], (43769 ^ _779300) ^ [_1654783, _1654785, _1654787] : [-(hAPP(hAPP(c_List_Odrop(_1654783), hAPP(c_Nat_OSuc, _1654785)), _1654787) = hAPP(hAPP(c_List_Odrop(_1654783), _1654785), hAPP(c_List_Otl(_1654783), _1654787)))], (43771 ^ _779300) ^ [_1654834, _1654836, _1654838] : [-(hAPP(c_List_Orotate(_1654834, hAPP(c_Nat_OSuc, _1654836)), _1654838) = hAPP(c_List_Orotate1(_1654834), hAPP(c_List_Orotate(_1654834, _1654836), _1654838)))], (43773 ^ _779300) ^ [_1654881, _1654883, _1654885] : [-(hAPP(c_List_Otl(_1654881), hAPP(hAPP(c_List_Oappend(_1654881), _1654883), _1654885)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1654881), _1654881, hAPP(c_List_Otl(_1654881), _1654885), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1654881), tc_List_Olist(_1654881)), _1654881), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654881), tc_List_Olist(_1654881), tc_List_Olist(_1654881)), c_List_Oappend(_1654881)), _1654885))), _1654883))], (43775 ^ _779300) ^ [_1654967, _1654969, _1654971] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1654967, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654969)), _1654971)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1654969, _1654967), _1654971) = _1654971)], (43781 ^ _779300) ^ [_1655080, _1655082, _1655084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655080)), _1655082)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1655080, _1655084), _1655082) = _1655082)], (43787 ^ _779300) ^ [_1655195, _1655197] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655195)), hAPP(c_List_Otl(_1655195), _1655197)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655195)), _1655197)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43789 ^ _779300) ^ [_1655245, _1655247, _1655249] : [-(hAPP(c_List_Otl(_1655245), hAPP(hAPP(c_List_Otake(_1655245), _1655247), _1655249)) = hAPP(hAPP(c_List_Otake(_1655245), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655247), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1655245), _1655249)))], (43791 ^ _779300) ^ [_1655300, _1655302, _1655304] : [-(_1655300 = c_List_Olist_ONil(_1655302)), -(hAPP(hAPP(c_List_Otake(_1655302), hAPP(c_Nat_OSuc, _1655304)), _1655300) = hAPP(hAPP(c_List_Olist_OCons(_1655302), hAPP(c_List_Ohd(_1655302), _1655300)), hAPP(hAPP(c_List_Otake(_1655302), _1655304), hAPP(c_List_Otl(_1655302), _1655300))))], (43797 ^ _779300) ^ [_1655377, _1655379, _1655381] : [-(hAPP(c_List_Orotate(_1655377, _1655379), _1655381) = hAPP(hAPP(c_List_Oappend(_1655377), hAPP(hAPP(c_List_Odrop(_1655377), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655379, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655377)), _1655381))), _1655381)), hAPP(hAPP(c_List_Otake(_1655377), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655379, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655377)), _1655381))), _1655381)))], (43799 ^ _779300) ^ [_1655456, _1655458] : [class_Lattices_Oab__semigroup__idem__mult(_1655456), -(_1655458 = c_List_Olist_ONil(_1655456)), -(hAPP(c_Finite__Set_Ofold1(_1655456, c_Groups_Otimes__class_Otimes(_1655456)), hAPP(c_List_Oset(_1655456), _1655458)) = hAPP(c_List_Ofoldl(_1655456, _1655456, c_Groups_Otimes__class_Otimes(_1655456), hAPP(c_List_Ohd(_1655456), _1655458)), hAPP(c_List_Otl(_1655456), _1655458)))], (43809 ^ _779300) ^ [_1655616, _1655618, _1655620, _1655622] : [43810 ^ _779300 : [(43811 ^ _779300) ^ [_1655713, _1655715] : [_1655616 = hAPP(hAPP(c_List_Olist_OCons(_1655618), _1655715), _1655713)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655618), tc_List_Olist(_1655618))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655618), tc_List_Olist(_1655618)), _1655620), hAPP(hAPP(c_List_Oappend(_1655618), _1655620), _1655616))), c_List_Olexord(_1655618, _1655622))))], (43815 ^ _779300) ^ [_1655812, _1655814, _1655816, _1655818] : [-(hAPP(c_List_Ofoldl(_1655812, _1655814, _1655816, _1655818), c_List_Olist_ONil(_1655814)) = _1655818)], (43817 ^ _779300) ^ [_1655851, _1655853, _1655855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655851), _1655853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655851), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1655853), _1655855))))], (43823 ^ _779300) ^ [_1655966, _1655968, _1655970] : [class_Groups_Omonoid__add(_1655966), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655966), _1655968), hAPP(c_List_Ofoldl(_1655966, _1655966, c_Groups_Oplus__class_Oplus(_1655966), c_Groups_Ozero__class_Ozero(_1655966)), _1655970)) = hAPP(c_List_Ofoldl(_1655966, _1655966, c_Groups_Oplus__class_Oplus(_1655966), _1655968), _1655970))], (43829 ^ _779300) ^ [_1656103, _1656105, _1656107, _1656109] : [class_Groups_Osemigroup__add(_1656103), -(hAPP(c_List_Ofoldl(_1656103, _1656103, c_Groups_Oplus__class_Oplus(_1656103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656103), _1656105), _1656107)), _1656109) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656103), _1656105), hAPP(c_List_Ofoldl(_1656103, _1656103, c_Groups_Oplus__class_Oplus(_1656103), _1656107), _1656109)))], (43835 ^ _779300) ^ [_1656254, _1656256, _1656258, _1656260, _1656262, _1656264] : [-(hAPP(c_List_Ofoldl(_1656254, _1656256, _1656258, _1656260), hAPP(hAPP(c_List_Olist_OCons(_1656256), _1656262), _1656264)) = hAPP(c_List_Ofoldl(_1656254, _1656256, _1656258, hAPP(hAPP(_1656258, _1656260), _1656262)), _1656264))], (43837 ^ _779300) ^ [_1656317, _1656319, _1656321, _1656323, _1656325, _1656327] : [-(hAPP(c_List_Ofoldl(_1656317, _1656319, _1656321, _1656323), hAPP(hAPP(c_List_Oappend(_1656319), _1656325), _1656327)) = hAPP(c_List_Ofoldl(_1656317, _1656319, _1656321, hAPP(c_List_Ofoldl(_1656317, _1656319, _1656321, _1656323), _1656325)), _1656327))], (43839 ^ _779300) ^ [_1656382] : [class_Groups_Omonoid__add(_1656382), -(c_List_Omonoid__add__class_Olistsum(_1656382) = c_List_Ofoldl(_1656382, _1656382, c_Groups_Oplus__class_Oplus(_1656382), c_Groups_Ozero__class_Ozero(_1656382)))], (43845 ^ _779300) ^ [_1656492, _1656494] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656492), _1656494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43848 ^ _779300 : [(43849 ^ _779300) ^ [] : [-(_1656492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43851 ^ _779300) ^ [_1656606] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1656606), hAPP(c_List_Oset(tc_Nat_Onat), _1656494))), -(_1656606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43857 ^ _779300) ^ [_1656703, _1656705] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656703), _1656705) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1656703 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43863 ^ _779300 : [(43864 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43862 ^ [_1656703, _1656705]), hAPP(c_List_Oset(tc_Nat_Onat), _1656705))))], (43866 ^ _779300) ^ [] : [43862 ^ [_1656703, _1656705] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43870 ^ _779300) ^ [_1656929, _1656931, _1656933, _1656935, _1656937] : [c_Finite__Set_Ofun__left__comm__idem(_1656929, _1656931, _1656933), -(hAPP(hAPP(c_Finite__Set_Ofold(_1656929, _1656931, _1656933), _1656935), hAPP(c_List_Oset(_1656929), _1656937)) = hAPP(c_List_Ofoldl(_1656931, _1656929, hAPP(c_COMBC(_1656929, _1656931, _1656931), _1656933), _1656935), _1656937))], (43876 ^ _779300) ^ [_1657074, _1657076] : [class_Complete__Lattice_Ocomplete__lattice(_1657074), -(c_Complete__Lattice_OSup__class_OSup(_1657074, hAPP(c_List_Oset(_1657074), _1657076)) = hAPP(c_List_Ofoldl(_1657074, _1657074, c_Lattices_Osemilattice__sup__class_Osup(_1657074), c_Orderings_Obot__class_Obot(_1657074)), _1657076))], (43882 ^ _779300) ^ [_1657189, _1657191] : [class_Complete__Lattice_Ocomplete__lattice(_1657189), -(c_Complete__Lattice_OInf__class_OInf(_1657189, hAPP(c_List_Oset(_1657189), _1657191)) = hAPP(c_List_Ofoldl(_1657189, _1657189, c_Lattices_Osemilattice__inf__class_Oinf(_1657189), c_Orderings_Otop__class_Otop(_1657189)), _1657191))], (43888 ^ _779300) ^ [_1657304, _1657306, _1657308] : [class_Lattices_Olattice(_1657304), -(c_Big__Operators_Olattice__class_OSup__fin(_1657304, hAPP(c_List_Oset(_1657304), hAPP(hAPP(c_List_Olist_OCons(_1657304), _1657306), _1657308))) = hAPP(c_List_Ofoldl(_1657304, _1657304, c_Lattices_Osemilattice__sup__class_Osup(_1657304), _1657306), _1657308))], (43894 ^ _779300) ^ [_1657433, _1657435, _1657437] : [class_Lattices_Olattice(_1657433), -(c_Big__Operators_Olattice__class_OInf__fin(_1657433, hAPP(c_List_Oset(_1657433), hAPP(hAPP(c_List_Olist_OCons(_1657433), _1657435), _1657437))) = hAPP(c_List_Ofoldl(_1657433, _1657433, c_Lattices_Osemilattice__inf__class_Oinf(_1657433), _1657435), _1657437))], (43900 ^ _779300) ^ [_1657562, _1657564, _1657566] : [class_Orderings_Olinorder(_1657562), -(c_Big__Operators_Olinorder__class_OMin(_1657562, hAPP(c_List_Oset(_1657562), hAPP(hAPP(c_List_Olist_OCons(_1657562), _1657564), _1657566))) = hAPP(c_List_Ofoldl(_1657562, _1657562, c_Orderings_Oord__class_Omin(_1657562), _1657564), _1657566))], (43906 ^ _779300) ^ [_1657691, _1657693, _1657695] : [class_Orderings_Olinorder(_1657691), -(c_Big__Operators_Olinorder__class_OMax(_1657691, hAPP(c_List_Oset(_1657691), hAPP(hAPP(c_List_Olist_OCons(_1657691), _1657693), _1657695))) = hAPP(c_List_Ofoldl(_1657691, _1657691, c_Orderings_Oord__class_Omax(_1657691), _1657693), _1657695))], (43912 ^ _779300) ^ [_1657820, _1657822, _1657824] : [class_Orderings_Olinorder(_1657820), -(c_Big__Operators_Olattice_OInf__fin(_1657820, c_Orderings_Oord__class_Omin(_1657820), hAPP(c_List_Oset(_1657820), hAPP(hAPP(c_List_Olist_OCons(_1657820), _1657822), _1657824))) = hAPP(c_List_Ofoldl(_1657820, _1657820, c_Orderings_Oord__class_Omin(_1657820), _1657822), _1657824))], (43918 ^ _779300) ^ [_1657955, _1657957, _1657959] : [class_Orderings_Olinorder(_1657955), -(c_Big__Operators_Olattice_OSup__fin(_1657955, c_Orderings_Oord__class_Omax(_1657955), hAPP(c_List_Oset(_1657955), hAPP(hAPP(c_List_Olist_OCons(_1657955), _1657957), _1657959))) = hAPP(c_List_Ofoldl(_1657955, _1657955, c_Orderings_Oord__class_Omax(_1657955), _1657957), _1657959))], (43924 ^ _779300) ^ [_1658090, _1658092, _1658094, _1658096] : [class_Complete__Lattice_Ocomplete__lattice(_1658090), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1658092, _1658090), hAPP(c_List_Oset(_1658092), _1658094)), _1658096) = hAPP(c_List_Ofoldl(_1658090, _1658092, hAPP(c_COMBC(_1658092, _1658090, _1658090), hAPP(hAPP(c_COMBB(_1658090, tc_fun(_1658090, _1658090), _1658092), c_Lattices_Osemilattice__sup__class_Osup(_1658090)), _1658096)), c_Orderings_Obot__class_Obot(_1658090)), _1658094))], (43930 ^ _779300) ^ [_1658261, _1658263, _1658265, _1658267] : [class_Complete__Lattice_Ocomplete__lattice(_1658261), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658263, _1658261), hAPP(c_List_Oset(_1658263), _1658265)), _1658267) = hAPP(c_List_Ofoldl(_1658261, _1658263, hAPP(c_COMBC(_1658263, _1658261, _1658261), hAPP(hAPP(c_COMBB(_1658261, tc_fun(_1658261, _1658261), _1658263), c_Lattices_Osemilattice__inf__class_Oinf(_1658261)), _1658267)), c_Orderings_Otop__class_Otop(_1658261)), _1658265))], (43936 ^ _779300) ^ [_1658432, _1658434] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1658432), hAPP(c_List_Oset(tc_Nat_Onat), _1658434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1658432), 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)), _1658434))))], (43942 ^ _779300) ^ [_1658541, _1658543, _1658545] : [class_Orderings_Olinorder(_1658541), hBOOL(hAPP(c_Finite__Set_Ofinite(_1658541), _1658543)), -(c_List_Olinorder__class_Osorted__list__of__set(_1658541, hAPP(hAPP(c_Set_Oinsert(_1658541), _1658545), _1658543)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658541, _1658541, c_COMBI(_1658541)), _1658545), c_List_Olinorder__class_Osorted__list__of__set(_1658541, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1658541, tc_HOL_Obool)), _1658543), hAPP(hAPP(c_Set_Oinsert(_1658541), _1658545), c_Orderings_Obot__class_Obot(tc_fun(_1658541, tc_HOL_Obool)))))))], (43952 ^ _779300) ^ [_1658798, _1658800, _1658802] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658798), tc_List_Olist(_1658798))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658798), tc_List_Olist(_1658798)), c_List_Olist_ONil(_1658798)), _1658800)), c_List_Olexord(_1658798, _1658802))), -(_1658800 = hAPP(hAPP(c_List_Olist_OCons(_1658798), 43955 ^ [_1658798, _1658800, _1658802]), 43956 ^ [_1658798, _1658800, _1658802]))], (43960 ^ _779300) ^ [_1658981, _1658983, _1658985] : [43961 ^ _779300 : [(43962 ^ _779300) ^ [_1659070, _1659072] : [_1658983 = hAPP(hAPP(c_List_Olist_OCons(_1658981), _1659072), _1659070)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658981), tc_List_Olist(_1658981))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658981), tc_List_Olist(_1658981)), c_List_Olist_ONil(_1658981)), _1658983)), c_List_Olexord(_1658981, _1658985))))], (43966 ^ _779300) ^ [_1659165, _1659167, _1659169, _1659171, _1659173, _1659175] : [class_Orderings_Olinorder(_1659165), 43969 ^ _779300 : [(43970 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659165), hAPP(_1659167, _1659169)), hAPP(_1659167, _1659171))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659173, _1659165, _1659167), _1659169), hAPP(hAPP(c_List_Olist_OCons(_1659173), _1659171), _1659175)) = hAPP(hAPP(c_List_Olist_OCons(_1659173), _1659169), hAPP(hAPP(c_List_Olist_OCons(_1659173), _1659171), _1659175)))], (43976 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659165), hAPP(_1659167, _1659169)), hAPP(_1659167, _1659171)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659173, _1659165, _1659167), _1659169), hAPP(hAPP(c_List_Olist_OCons(_1659173), _1659171), _1659175)) = hAPP(hAPP(c_List_Olist_OCons(_1659173), _1659171), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659173, _1659165, _1659167), _1659169), _1659175)))]]], (43982 ^ _779300) ^ [_1659547, _1659549, _1659551, _1659553] : [class_Orderings_Olinorder(_1659547), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659549, _1659547, _1659551), _1659553), c_List_Olist_ONil(_1659549)) = hAPP(hAPP(c_List_Olist_OCons(_1659549), _1659553), c_List_Olist_ONil(_1659549)))], (43988 ^ _779300) ^ [_1659670, _1659672, _1659674, _1659676, _1659678] : [class_Orderings_Olinorder(_1659670), -(hAPP(c_List_Oset(_1659672), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659672, _1659670, _1659674), _1659676), _1659678)) = hAPP(hAPP(c_Set_Oinsert(_1659672), _1659676), hAPP(c_List_Oset(_1659672), _1659678)))], (43994 ^ _779300) ^ [_1659807, _1659809, _1659811, _1659813, _1659815] : [class_Orderings_Olinorder(_1659807), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659809)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659809, _1659807, _1659811), _1659813), _1659815)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659809)), _1659815)))], (44000 ^ _779300) ^ [_1659942] : [class_Orderings_Olinorder(_1659942), -(c_Finite__Set_Ofun__left__comm(_1659942, tc_List_Olist(_1659942), c_List_Olinorder__class_Oinsort__key(_1659942, _1659942, c_COMBI(_1659942))))], (44006 ^ _779300) ^ [_1660033, _1660035, _1660037, _1660039] : [class_Orderings_Olinorder(_1660033), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660033, _1660033, c_COMBI(_1660033)), _1660035), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660033, _1660033, c_COMBI(_1660033)), _1660037), _1660039)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660033, _1660033, c_COMBI(_1660033)), _1660037), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660033, _1660033, c_COMBI(_1660033)), _1660035), _1660039)))], (44012 ^ _779300) ^ [_1660208, _1660210, _1660212, _1660214, _1660216, _1660218] : [class_Orderings_Olinorder(_1660208), -(hAPP(_1660210, _1660212) = hAPP(_1660210, _1660214)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660216, _1660208, _1660210), _1660214), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660216, _1660208, _1660210), _1660212), _1660218)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660216, _1660208, _1660210), _1660212), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660216, _1660208, _1660210), _1660214), _1660218)))], (44022 ^ _779300) ^ [_1660398, _1660400, _1660402] : [class_Orderings_Olinorder(_1660398), -(c_List_Oremove1(_1660398, _1660400, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660398, _1660398, c_COMBI(_1660398)), _1660400), _1660402)) = _1660402)], (44028 ^ _779300) ^ [_1660507, _1660509, _1660511, _1660513, _1660515] : [class_Orderings_Olinorder(_1660507), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660509, _1660507, _1660511), _1660513), _1660515) = c_List_Olist_ONil(_1660509)], (44034 ^ _779300) ^ [_1660613, _1660615, _1660617, _1660619, _1660621] : [class_Orderings_Olinorder(_1660613), 44037 ^ _779300 : [(44038 ^ _779300) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1660615), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660615, _1660613, _1660617), _1660619), _1660621))), 44041 ^ _779300 : [(44042 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1660615), _1660619), hAPP(c_List_Oset(_1660615), _1660621)))], (44044 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1660615), _1660621)))]]], (44046 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1660615), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660615, _1660613, _1660617), _1660619), _1660621)))), -(hBOOL(hAPP(hAPP(c_member(_1660615), _1660619), hAPP(c_List_Oset(_1660615), _1660621)))), hBOOL(hAPP(c_List_Odistinct(_1660615), _1660621))]]], (44056 ^ _779300) ^ [_1661015, _1661017, _1661019, _1661021, _1661023] : [class_Orderings_Olinorder(_1661015), -(hBOOL(hAPP(hAPP(c_member(_1661015), hAPP(_1661017, _1661019)), hAPP(c_Set_Oimage(_1661021, _1661015, _1661017), hAPP(c_List_Oset(_1661021), _1661023))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661021, _1661015, _1661017, _1661019, _1661023) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661021, _1661015, _1661017), _1661019), _1661023))], (44066 ^ _779300) ^ [_1661187, _1661189, _1661191] : [class_Orderings_Olinorder(_1661187), -(hBOOL(hAPP(hAPP(c_member(_1661187), _1661189), hAPP(c_List_Oset(_1661187), _1661191)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661187, _1661187, c_COMBI(_1661187), _1661189, _1661191) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661187, _1661187, c_COMBI(_1661187)), _1661189), _1661191))], (44076 ^ _779300) ^ [_1661343, _1661345, _1661347, _1661349, _1661351] : [class_Orderings_Olinorder(_1661343), hBOOL(hAPP(c_List_Odistinct(_1661345), _1661347)), -(hBOOL(hAPP(c_List_Odistinct(_1661345), c_List_Olinorder__class_Oinsort__insert__key(_1661345, _1661343, _1661349, _1661351, _1661347))))], (44086 ^ _779300) ^ [_1661510, _1661512, _1661514] : [class_Orderings_Olinorder(_1661510), hBOOL(hAPP(hAPP(c_member(_1661510), _1661512), hAPP(c_List_Oset(_1661510), _1661514))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661510, _1661510, c_COMBI(_1661510), _1661512, _1661514) = _1661514)], (44096 ^ _779300) ^ [_1661681, _1661683, _1661685] : [class_Orderings_Olinorder(_1661681), -(hAPP(c_List_Oset(_1661681), c_List_Olinorder__class_Oinsort__insert__key(_1661681, _1661681, c_COMBI(_1661681), _1661683, _1661685)) = hAPP(hAPP(c_Set_Oinsert(_1661681), _1661683), hAPP(c_List_Oset(_1661681), _1661685)))], (44102 ^ _779300) ^ [_1661810, _1661812, _1661814, _1661816, _1661818] : [class_Orderings_Olinorder(_1661810), hBOOL(hAPP(hAPP(c_member(_1661810), hAPP(_1661812, _1661814)), hAPP(c_Set_Oimage(_1661816, _1661810, _1661812), hAPP(c_List_Oset(_1661816), _1661818)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661816, _1661810, _1661812, _1661814, _1661818) = _1661818)], (44112 ^ _779300) ^ [_1662004, _1662006, _1662008, _1662010] : [-(_1662004 = c_List_Olist_ONil(_1662006)), 44115 ^ _779300 : [(44116 ^ _779300) ^ [] : [_1662008 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662006)), _1662004)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1662006, hAPP(hAPP(c_List_Olist__update(_1662006, _1662004), _1662008), _1662010)) = _1662010)], (44122 ^ _779300) ^ [] : [-(_1662008 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662006)), _1662004)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1662006, hAPP(hAPP(c_List_Olist__update(_1662006, _1662004), _1662008), _1662010)) = c_List_Olast(_1662006, _1662004))]]], (44128 ^ _779300) ^ [_1662290, _1662292] : [-(_1662290 = c_List_Olist_ONil(_1662292)), -(c_List_Olast(_1662292, _1662290) = hAPP(hAPP(c_List_Onth(_1662292), _1662290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662292)), _1662290)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (44134 ^ _779300) ^ [_1662352, _1662354, _1662356] : [_1662352 = c_List_Olist_ONil(_1662354), -(c_List_Olast(_1662354, hAPP(hAPP(c_List_Olist_OCons(_1662354), _1662356), _1662352)) = _1662356)], (44140 ^ _779300) ^ [_1662453, _1662455, _1662457] : [-(_1662453 = c_List_Olist_ONil(_1662455)), -(c_List_Olast(_1662455, hAPP(hAPP(c_List_Olist_OCons(_1662455), _1662457), _1662453)) = c_List_Olast(_1662455, _1662453))], (44146 ^ _779300) ^ [_1662519, _1662521, _1662523] : [_1662519 = c_List_Olist_ONil(_1662521), -(c_List_Olast(_1662521, hAPP(hAPP(c_List_Olist_OCons(_1662521), _1662523), _1662519)) = _1662523)], (44152 ^ _779300) ^ [_1662618, _1662620, _1662622] : [-(_1662618 = c_List_Olist_ONil(_1662620)), -(c_List_Olast(_1662620, hAPP(hAPP(c_List_Olist_OCons(_1662620), _1662622), _1662618)) = c_List_Olast(_1662620, _1662618))], (44158 ^ _779300) ^ [_1662674, _1662676, _1662678] : [_1662674 = c_List_Olist_ONil(_1662676), -(c_List_Olast(_1662676, hAPP(hAPP(c_List_Oappend(_1662676), _1662678), _1662674)) = c_List_Olast(_1662676, _1662678))], (44164 ^ _779300) ^ [_1662781, _1662783, _1662785] : [-(_1662781 = c_List_Olist_ONil(_1662783)), -(c_List_Olast(_1662783, hAPP(hAPP(c_List_Oappend(_1662783), _1662785), _1662781)) = c_List_Olast(_1662783, _1662781))], (44170 ^ _779300) ^ [_1662847, _1662849, _1662851] : [_1662847 = c_List_Olist_ONil(_1662849), -(c_List_Olast(_1662849, hAPP(hAPP(c_List_Oappend(_1662849), _1662851), _1662847)) = c_List_Olast(_1662849, _1662851))], (44176 ^ _779300) ^ [_1662952, _1662954, _1662956] : [-(_1662952 = c_List_Olist_ONil(_1662954)), -(c_List_Olast(_1662954, hAPP(hAPP(c_List_Oappend(_1662954), _1662956), _1662952)) = c_List_Olast(_1662954, _1662952))], (44182 ^ _779300) ^ [_1663004, _1663006] : [-(_1663004 = c_List_Olist_ONil(_1663006)), -(hBOOL(hAPP(hAPP(c_member(_1663006), c_List_Olast(_1663006, _1663004)), hAPP(c_List_Oset(_1663006), _1663004))))], (44188 ^ _779300) ^ [_1663057, _1663059, _1663061] : [-(c_List_Olast(_1663057, hAPP(hAPP(c_List_Oappend(_1663057), _1663059), hAPP(hAPP(c_List_Olist_OCons(_1663057), _1663061), c_List_Olist_ONil(_1663057)))) = _1663061)], (44190 ^ _779300) ^ [_1663105, _1663107, _1663109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663105), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663107)), _1663109))), -(c_List_Olast(_1663107, hAPP(hAPP(c_List_Odrop(_1663107), _1663105), _1663109)) = c_List_Olast(_1663107, _1663109))], (44196 ^ _779300) ^ [_1663257, _1663259, _1663261, _1663263] : [hAPP(hAPP(c_List_Oappend(_1663257), _1663259), hAPP(hAPP(c_List_Olist_OCons(_1663257), _1663261), c_List_Olist_ONil(_1663257))) = _1663263, 44199 ^ _779300 : [(44200 ^ _779300) ^ [] : [_1663263 = c_List_Olist_ONil(_1663257)], (44202 ^ _779300) ^ [] : [-(c_List_Obutlast(_1663257, _1663263) = _1663259)], (44204 ^ _779300) ^ [] : [-(c_List_Olast(_1663257, _1663263) = _1663261)]]], (44206 ^ _779300) ^ [_1663446, _1663448, _1663450, _1663452] : [-(hAPP(hAPP(c_List_Oappend(_1663446), _1663448), hAPP(hAPP(c_List_Olist_OCons(_1663446), _1663450), c_List_Olist_ONil(_1663446))) = _1663452), -(_1663452 = c_List_Olist_ONil(_1663446)), c_List_Obutlast(_1663446, _1663452) = _1663448, c_List_Olast(_1663446, _1663452) = _1663450], (44220 ^ _779300) ^ [_1663692, _1663694] : [-(_1663692 = c_List_Olist_ONil(_1663694)), -(hAPP(hAPP(c_List_Oappend(_1663694), c_List_Obutlast(_1663694, _1663692)), hAPP(hAPP(c_List_Olist_OCons(_1663694), c_List_Olast(_1663694, _1663692)), c_List_Olist_ONil(_1663694))) = _1663692)], (44226 ^ _779300) ^ [_1663772, _1663774, _1663776] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663772)), _1663774), c_List_Olists(_1663772, _1663776))), -(_1663774 = c_List_Olist_ONil(_1663772)), 44235 ^ _779300 : [(44236 ^ _779300) ^ [] : [-(_1663774 = hAPP(hAPP(c_List_Olist_OCons(_1663772), 44233 ^ [_1663772, _1663774, _1663776]), 44234 ^ [_1663772, _1663774, _1663776]))], (44238 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1663772), 44233 ^ [_1663772, _1663774, _1663776]), _1663776)))], (44240 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663772)), 44234 ^ [_1663772, _1663774, _1663776]), c_List_Olists(_1663772, _1663776))))]]], (44242 ^ _779300) ^ [_1664055, _1664057, _1664059] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664055)), _1664057), c_List_Olists(_1664055, _1664059)))), 44243 ^ _779300 : [(44244 ^ _779300) ^ [] : [_1664057 = c_List_Olist_ONil(_1664055)], (44246 ^ _779300) ^ [_1664183, _1664185] : [_1664057 = hAPP(hAPP(c_List_Olist_OCons(_1664055), _1664185), _1664183), hBOOL(hAPP(hAPP(c_member(_1664055), _1664185), _1664059)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664055)), _1664183), c_List_Olists(_1664055, _1664059)))]]], (44258 ^ _779300) ^ [_1664417, _1664419] : [-(_1664417 = c_List_Olist_ONil(_1664419)), -(c_Random_Oselect__weight(_1664419, hAPP(hAPP(c_List_Omap(_1664419, tc_prod(tc_Code__Numeral_Ocode__numeral, _1664419)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1664419), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1664417)) = c_Random_Oselect(_1664419, _1664417))], (44264 ^ _779300) ^ [_1664479, _1664481, _1664483] : [c_Fun_Oinj__on(_1664479, _1664481, _1664483, c_Orderings_Otop__class_Otop(tc_fun(_1664479, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1664479), tc_List_Olist(_1664481), hAPP(c_List_Omap(_1664479, _1664481), _1664483), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1664479), tc_HOL_Obool))))], (44270 ^ _779300) ^ [_1664606, _1664608, _1664610, _1664612] : [-(_1664606 = c_List_Olist_ONil(_1664608)), -(c_List_Olast(_1664610, hAPP(hAPP(c_List_Omap(_1664608, _1664610), _1664612), _1664606)) = hAPP(_1664612, c_List_Olast(_1664608, _1664606)))], (44276 ^ _779300) ^ [_1664666, _1664668, _1664670, _1664672, _1664674, _1664676, _1664678] : [-(hAPP(c_List_Ofoldl(_1664666, _1664668, _1664670, _1664672), hAPP(hAPP(c_List_Omap(_1664674, _1664668), _1664676), _1664678)) = hAPP(c_List_Ofoldl(_1664666, _1664674, hAPP(hAPP(c_COMBC(_1664666, tc_fun(_1664674, _1664668), tc_fun(_1664674, _1664666)), hAPP(hAPP(c_COMBB(tc_fun(_1664668, _1664666), tc_fun(tc_fun(_1664674, _1664668), tc_fun(_1664674, _1664666)), _1664666), c_COMBB(_1664668, _1664666, _1664674)), _1664670)), _1664676), _1664672), _1664678))], (44278 ^ _779300) ^ [_1664768, _1664770, _1664772, _1664774] : [-(hAPP(hAPP(c_List_Omap(_1664768, _1664770), _1664772), hAPP(c_List_Otl(_1664768), _1664774)) = hAPP(c_List_Otl(_1664770), hAPP(hAPP(c_List_Omap(_1664768, _1664770), _1664772), _1664774)))], (44280 ^ _779300) ^ [_1664825, _1664827, _1664829, _1664831, _1664833] : [-(hAPP(c_List_Orotate(_1664825, _1664827), hAPP(hAPP(c_List_Omap(_1664829, _1664825), _1664831), _1664833)) = hAPP(hAPP(c_List_Omap(_1664829, _1664825), _1664831), hAPP(c_List_Orotate(_1664829, _1664827), _1664833)))], (44282 ^ _779300) ^ [_1664886, _1664888, _1664890, _1664892, _1664894, _1664896, _1664898, _1664900] : [-(hAPP(hAPP(c_List_Ozip(_1664886, _1664888), hAPP(hAPP(c_List_Omap(_1664890, _1664886), _1664892), _1664894)), hAPP(hAPP(c_List_Omap(_1664896, _1664888), _1664898), _1664900)) = hAPP(hAPP(c_List_Omap(tc_prod(_1664890, _1664896), tc_prod(_1664886, _1664888)), hAPP(c_Product__Type_Oprod_Oprod__case(_1664890, _1664896, tc_prod(_1664886, _1664888)), hAPP(hAPP(c_COMBC(_1664890, tc_fun(_1664896, _1664888), tc_fun(_1664896, tc_prod(_1664886, _1664888))), hAPP(hAPP(c_COMBB(tc_fun(_1664888, tc_prod(_1664886, _1664888)), tc_fun(tc_fun(_1664896, _1664888), tc_fun(_1664896, tc_prod(_1664886, _1664888))), _1664890), c_COMBB(_1664888, tc_prod(_1664886, _1664888), _1664896)), hAPP(hAPP(c_COMBB(_1664886, tc_fun(_1664888, tc_prod(_1664886, _1664888)), _1664890), c_Product__Type_OPair(_1664886, _1664888)), _1664892))), _1664898))), hAPP(hAPP(c_List_Ozip(_1664890, _1664896), _1664894), _1664900)))], (44284 ^ _779300) ^ [_1665057, _1665059, _1665061, _1665063, _1665065, _1665067] : [-(hAPP(hAPP(c_List_Ozip(_1665057, _1665059), hAPP(hAPP(c_List_Omap(_1665061, _1665057), _1665063), _1665065)), _1665067) = hAPP(hAPP(c_List_Omap(tc_prod(_1665061, _1665059), tc_prod(_1665057, _1665059)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665061, _1665059, tc_prod(_1665057, _1665059)), hAPP(hAPP(c_COMBB(_1665057, tc_fun(_1665059, tc_prod(_1665057, _1665059)), _1665061), c_Product__Type_OPair(_1665057, _1665059)), _1665063))), hAPP(hAPP(c_List_Ozip(_1665061, _1665059), _1665065), _1665067)))], (44286 ^ _779300) ^ [_1665161, _1665163, _1665165, _1665167, _1665169, _1665171, _1665173, _1665175] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1665161, _1665163), _1665165), _1665167), hAPP(hAPP(c_List_Ozip(_1665161, _1665163), hAPP(hAPP(c_List_Omap(_1665169, _1665161), _1665171), _1665173)), _1665175)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665169, _1665163), _1665165), hAPP(c_Product__Type_Oprod_Oprod__case(_1665169, _1665163, _1665165), hAPP(hAPP(c_COMBB(tc_fun(_1665163, tc_prod(_1665161, _1665163)), tc_fun(_1665163, _1665165), _1665169), hAPP(c_COMBB(tc_prod(_1665161, _1665163), _1665165, _1665163), _1665167)), hAPP(hAPP(c_COMBB(_1665161, tc_fun(_1665163, tc_prod(_1665161, _1665163)), _1665169), c_Product__Type_OPair(_1665161, _1665163)), _1665171)))), hAPP(hAPP(c_List_Ozip(_1665169, _1665163), _1665173), _1665175)))], (44288 ^ _779300) ^ [_1665304, _1665306, _1665308, _1665310, _1665312, _1665314, _1665316, _1665318] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1665304, _1665306), _1665308), _1665310), hAPP(hAPP(c_List_Ozip(_1665304, _1665306), _1665312), hAPP(hAPP(c_List_Omap(_1665314, _1665306), _1665316), _1665318))) = hAPP(hAPP(c_List_Omap(tc_prod(_1665304, _1665314), _1665308), hAPP(c_Product__Type_Oprod_Oprod__case(_1665304, _1665314, _1665308), hAPP(hAPP(c_COMBB(tc_fun(_1665314, tc_prod(_1665304, _1665306)), tc_fun(_1665314, _1665308), _1665304), hAPP(c_COMBB(tc_prod(_1665304, _1665306), _1665308, _1665314), _1665310)), hAPP(hAPP(c_COMBC(_1665304, tc_fun(_1665314, _1665306), tc_fun(_1665314, tc_prod(_1665304, _1665306))), hAPP(hAPP(c_COMBB(tc_fun(_1665306, tc_prod(_1665304, _1665306)), tc_fun(tc_fun(_1665314, _1665306), tc_fun(_1665314, tc_prod(_1665304, _1665306))), _1665304), c_COMBB(_1665306, tc_prod(_1665304, _1665306), _1665314)), c_Product__Type_OPair(_1665304, _1665306))), _1665316)))), hAPP(hAPP(c_List_Ozip(_1665304, _1665314), _1665312), _1665318)))], (44290 ^ _779300) ^ [_1665485, _1665487, _1665489, _1665491, _1665493, _1665495] : [-(hAPP(hAPP(c_List_Ozip(_1665485, _1665487), _1665489), hAPP(hAPP(c_List_Omap(_1665491, _1665487), _1665493), _1665495)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665485, _1665491), tc_prod(_1665485, _1665487)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665485, _1665491, tc_prod(_1665485, _1665487)), hAPP(hAPP(c_COMBC(_1665485, tc_fun(_1665491, _1665487), tc_fun(_1665491, tc_prod(_1665485, _1665487))), hAPP(hAPP(c_COMBB(tc_fun(_1665487, tc_prod(_1665485, _1665487)), tc_fun(tc_fun(_1665491, _1665487), tc_fun(_1665491, tc_prod(_1665485, _1665487))), _1665485), c_COMBB(_1665487, tc_prod(_1665485, _1665487), _1665491)), c_Product__Type_OPair(_1665485, _1665487))), _1665493))), hAPP(hAPP(c_List_Ozip(_1665485, _1665491), _1665489), _1665495)))], (44292 ^ _779300) ^ [_1665627, _1665629] : [-(hAPP(hAPP(c_List_Ozip(_1665627, _1665627), _1665629), _1665629) = hAPP(hAPP(c_List_Omap(_1665627, tc_prod(_1665627, _1665627)), hAPP(hAPP(c_COMBS(_1665627, _1665627, tc_prod(_1665627, _1665627)), c_Product__Type_OPair(_1665627, _1665627)), c_COMBI(_1665627))), _1665629))], (44294 ^ _779300) ^ [_1665712, _1665714, _1665716, _1665718] : [c_List_Olist_ONil(_1665712) = hAPP(hAPP(c_List_Omap(_1665714, _1665712), _1665716), _1665718), -(_1665718 = c_List_Olist_ONil(_1665714))], (44300 ^ _779300) ^ [_1665815, _1665817, _1665819, _1665821] : [_1665821 = c_List_Olist_ONil(_1665817), -(c_List_Olist_ONil(_1665815) = hAPP(hAPP(c_List_Omap(_1665817, _1665815), _1665819), _1665821))], (44306 ^ _779300) ^ [_1665924, _1665926, _1665928] : [-(hAPP(hAPP(c_List_Omap(_1665924, _1665926), _1665928), c_List_Olist_ONil(_1665924)) = c_List_Olist_ONil(_1665926))], (44308 ^ _779300) ^ [_1665985, _1665987, _1665989, _1665991] : [hAPP(hAPP(c_List_Omap(_1665985, _1665987), _1665989), _1665991) = c_List_Olist_ONil(_1665987), -(_1665991 = c_List_Olist_ONil(_1665985))], (44314 ^ _779300) ^ [_1666088, _1666090, _1666092, _1666094] : [_1666094 = c_List_Olist_ONil(_1666088), -(hAPP(hAPP(c_List_Omap(_1666088, _1666090), _1666092), _1666094) = c_List_Olist_ONil(_1666090))], (44320 ^ _779300) ^ [_1666197, _1666199, _1666201, _1666203, _1666205, _1666207] : [-(hAPP(hAPP(c_List_Omap(_1666197, _1666199), _1666201), hAPP(hAPP(c_List_Olist__update(_1666197, _1666203), _1666205), _1666207)) = hAPP(hAPP(c_List_Olist__update(_1666199, hAPP(hAPP(c_List_Omap(_1666197, _1666199), _1666201), _1666203)), _1666205), hAPP(_1666201, _1666207)))], (44332 ^ _779300) ^ [_1666537, _1666539, _1666541, _1666543, _1666545] : [44334 ^ _779300 : [(44335 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1666537), 44333 ^ [_1666537, _1666539, _1666541, _1666543, _1666545]), hAPP(c_List_Oset(_1666537), _1666543))))], (44337 ^ _779300) ^ [] : [hAPP(_1666541, 44333 ^ [_1666537, _1666539, _1666541, _1666543, _1666545]) = hAPP(_1666545, 44333 ^ [_1666537, _1666539, _1666541, _1666543, _1666545])]], -(hAPP(hAPP(c_List_Omap(_1666537, _1666539), _1666541), _1666543) = hAPP(hAPP(c_List_Omap(_1666537, _1666539), _1666545), _1666543))], (44322 ^ _779300) ^ [_1666293, _1666295, _1666297, _1666299, _1666301] : [hAPP(hAPP(c_List_Omap(_1666293, _1666295), _1666297), _1666299) = hAPP(hAPP(c_List_Omap(_1666293, _1666295), _1666301), _1666299), 44325 ^ _779300 : [(44326 ^ _779300) ^ [_1666416] : [hBOOL(hAPP(hAPP(c_member(_1666293), _1666416), hAPP(c_List_Oset(_1666293), _1666299))), -(hAPP(_1666297, _1666416) = hAPP(_1666301, _1666416))]]], (44341 ^ _779300) ^ [_1666794, _1666796, _1666798, _1666800, _1666802, _1666804, _1666806] : [hAPP(hAPP(c_List_Omap(_1666794, _1666796), _1666798), _1666800) = hAPP(hAPP(c_List_Omap(_1666802, _1666796), _1666804), _1666806), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666794)), _1666800) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666802)), _1666806))], (44347 ^ _779300) ^ [_1666945, _1666947, _1666949, _1666951] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666945)), hAPP(hAPP(c_List_Omap(_1666947, _1666945), _1666949), _1666951)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666947)), _1666951))], (44349 ^ _779300) ^ [_1666997, _1666999, _1667001] : [class_Groups_Omonoid__add(_1666997), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1666997), hAPP(hAPP(c_List_Omap(_1666999, _1666997), hAPP(c_COMBK(_1666997, _1666999), c_Groups_Ozero__class_Ozero(_1666997))), _1667001)) = c_Groups_Ozero__class_Ozero(_1666997))], (44355 ^ _779300) ^ [_1667122, _1667124, _1667126, _1667128, _1667130] : [class_Rings_Osemiring__0(_1667122), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667122), hAPP(hAPP(c_List_Omap(_1667124, _1667122), hAPP(hAPP(c_COMBB(_1667122, _1667122, _1667124), hAPP(c_Groups_Otimes__class_Otimes(_1667122), _1667126)), _1667128)), _1667130)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1667122), _1667126), hAPP(c_List_Omonoid__add__class_Olistsum(_1667122), hAPP(hAPP(c_List_Omap(_1667124, _1667122), _1667128), _1667130))))], (44361 ^ _779300) ^ [_1667305, _1667307, _1667309, _1667311, _1667313] : [class_Rings_Osemiring__0(_1667305), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667305), hAPP(hAPP(c_List_Omap(_1667307, _1667305), hAPP(hAPP(c_COMBC(_1667307, _1667305, _1667305), hAPP(hAPP(c_COMBB(_1667305, tc_fun(_1667305, _1667305), _1667307), c_Groups_Otimes__class_Otimes(_1667305)), _1667309)), _1667311)), _1667313)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1667305), hAPP(c_List_Omonoid__add__class_Olistsum(_1667305), hAPP(hAPP(c_List_Omap(_1667307, _1667305), _1667309), _1667313))), _1667311))], (44367 ^ _779300) ^ [_1667508, _1667510, _1667512, _1667514, _1667516] : [class_Groups_Oab__group__add(_1667508), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667508), hAPP(hAPP(c_List_Omap(_1667510, _1667508), hAPP(hAPP(c_COMBS(_1667510, _1667508, _1667508), hAPP(hAPP(c_COMBB(_1667508, tc_fun(_1667508, _1667508), _1667510), c_Groups_Ominus__class_Ominus(_1667508)), _1667512)), _1667514)), _1667516)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1667508), hAPP(c_List_Omonoid__add__class_Olistsum(_1667508), hAPP(hAPP(c_List_Omap(_1667510, _1667508), _1667512), _1667516))), hAPP(c_List_Omonoid__add__class_Olistsum(_1667508), hAPP(hAPP(c_List_Omap(_1667510, _1667508), _1667514), _1667516))))], (44373 ^ _779300) ^ [_1667739, _1667741, _1667743, _1667745, _1667747] : [class_Groups_Ocomm__monoid__add(_1667739), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667739), hAPP(hAPP(c_List_Omap(_1667741, _1667739), hAPP(hAPP(c_COMBS(_1667741, _1667739, _1667739), hAPP(hAPP(c_COMBB(_1667739, tc_fun(_1667739, _1667739), _1667741), c_Groups_Oplus__class_Oplus(_1667739)), _1667743)), _1667745)), _1667747)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1667739), hAPP(c_List_Omonoid__add__class_Olistsum(_1667739), hAPP(hAPP(c_List_Omap(_1667741, _1667739), _1667743), _1667747))), hAPP(c_List_Omonoid__add__class_Olistsum(_1667739), hAPP(hAPP(c_List_Omap(_1667741, _1667739), _1667745), _1667747))))], (44379 ^ _779300) ^ [_1667970, _1667972, _1667974, _1667976, _1667978] : [c_Fun_Oinj__on(_1667970, _1667972, _1667974, c_Orderings_Otop__class_Otop(tc_fun(_1667970, tc_HOL_Obool))), 44382 ^ _779300 : [(44383 ^ _779300) ^ [] : [hAPP(hAPP(c_List_Omap(_1667970, _1667972), _1667974), _1667976) = hAPP(hAPP(c_List_Omap(_1667970, _1667972), _1667974), _1667978), -(_1667976 = _1667978)], (44389 ^ _779300) ^ [] : [_1667976 = _1667978, -(hAPP(hAPP(c_List_Omap(_1667970, _1667972), _1667974), _1667976) = hAPP(hAPP(c_List_Omap(_1667970, _1667972), _1667974), _1667978))]]], (44395 ^ _779300) ^ [_1668263, _1668265, _1668267, _1668269, _1668271] : [hAPP(hAPP(c_List_Omap(_1668263, _1668265), _1668267), _1668269) = hAPP(hAPP(c_List_Omap(_1668263, _1668265), _1668267), _1668271), c_Fun_Oinj__on(_1668263, _1668265, _1668267, c_Orderings_Otop__class_Otop(tc_fun(_1668263, tc_HOL_Obool))), -(_1668269 = _1668271)], (44405 ^ _779300) ^ [_1668454, _1668456] : [-(hAPP(hAPP(c_List_Omap(_1668454, _1668454), c_COMBI(_1668454)), _1668456) = _1668456)], (44407 ^ _779300) ^ [_1668490, _1668492, _1668494, _1668496, _1668498] : [-(hAPP(hAPP(c_List_Otake(_1668490), _1668492), hAPP(hAPP(c_List_Omap(_1668494, _1668490), _1668496), _1668498)) = hAPP(hAPP(c_List_Omap(_1668494, _1668490), _1668496), hAPP(hAPP(c_List_Otake(_1668494), _1668492), _1668498)))], (44409 ^ _779300) ^ [_1668555, _1668557, _1668559, _1668561] : [-(hAPP(hAPP(c_List_Omap(_1668555, _1668557), _1668559), c_List_Obutlast(_1668555, _1668561)) = c_List_Obutlast(_1668557, hAPP(hAPP(c_List_Omap(_1668555, _1668557), _1668559), _1668561)))], (44411 ^ _779300) ^ [_1668608, _1668610, _1668612, _1668614] : [-(hAPP(c_List_Oset(_1668608), hAPP(hAPP(c_List_Omap(_1668610, _1668608), _1668612), _1668614)) = hAPP(c_Set_Oimage(_1668610, _1668608, _1668612), hAPP(c_List_Oset(_1668610), _1668614)))], (44413 ^ _779300) ^ [_1668663, _1668665, _1668667, _1668669, _1668671] : [-(hAPP(hAPP(c_List_Omap(_1668663, _1668665), _1668667), hAPP(hAPP(c_List_Olist_OCons(_1668663), _1668669), _1668671)) = hAPP(hAPP(c_List_Olist_OCons(_1668665), hAPP(_1668667, _1668669)), hAPP(hAPP(c_List_Omap(_1668663, _1668665), _1668667), _1668671)))], (44415 ^ _779300) ^ [_1668731, _1668733, _1668735, _1668737, _1668739] : [-(hAPP(hAPP(c_List_Omap(_1668731, _1668733), _1668735), hAPP(hAPP(c_List_Oappend(_1668731), _1668737), _1668739)) = hAPP(hAPP(c_List_Oappend(_1668733), hAPP(hAPP(c_List_Omap(_1668731, _1668733), _1668735), _1668737)), hAPP(hAPP(c_List_Omap(_1668731, _1668733), _1668735), _1668739)))], (44417 ^ _779300) ^ [_1668801, _1668803, _1668805, _1668807] : [-(_1668801 = c_List_Olist_ONil(_1668803)), -(hAPP(c_List_Ohd(_1668805), hAPP(hAPP(c_List_Omap(_1668803, _1668805), _1668807), _1668801)) = hAPP(_1668807, hAPP(c_List_Ohd(_1668803), _1668801)))], (44423 ^ _779300) ^ [_1668865, _1668867, _1668869, _1668871, _1668873] : [-(hAPP(hAPP(c_List_Odrop(_1668865), _1668867), hAPP(hAPP(c_List_Omap(_1668869, _1668865), _1668871), _1668873)) = hAPP(hAPP(c_List_Omap(_1668869, _1668865), _1668871), hAPP(hAPP(c_List_Odrop(_1668869), _1668867), _1668873)))], (44425 ^ _779300) ^ [_1668930, _1668932, _1668934, _1668936, _1668938, _1668940] : [-(hAPP(hAPP(c_List_Omap(_1668930, _1668932), _1668934), hAPP(hAPP(c_List_Omap(_1668936, _1668930), _1668938), _1668940)) = hAPP(hAPP(c_List_Omap(_1668936, _1668932), hAPP(c_Fun_Ocomp(_1668930, _1668932, _1668936, _1668934), _1668938)), _1668940))], (44427 ^ _779300) ^ [_1668998, _1669000, _1669002, _1669004, _1669006, _1669008] : [-(hAPP(hAPP(c_List_Omap(_1668998, _1669000), _1669002), hAPP(hAPP(c_List_Omap(_1669004, _1668998), _1669006), _1669008)) = hAPP(hAPP(c_List_Omap(_1669004, _1669000), hAPP(c_Fun_Ocomp(_1668998, _1669000, _1669004, _1669002), _1669006)), _1669008))], (44429 ^ _779300) ^ [_1669066, _1669068, _1669070, _1669072, _1669074] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1669066), tc_List_Olist(_1669068), tc_List_Olist(_1669070), hAPP(c_List_Omap(_1669066, _1669068), _1669072)), hAPP(c_List_Omap(_1669070, _1669066), _1669074)) = hAPP(c_List_Omap(_1669070, _1669068), hAPP(c_Fun_Ocomp(_1669066, _1669068, _1669070, _1669072), _1669074)))], (44431 ^ _779300) ^ [_1669137, _1669139, _1669141, _1669143, _1669145] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1669137), tc_List_Olist(_1669139), tc_List_Olist(_1669141), hAPP(c_List_Omap(_1669137, _1669139), _1669143)), hAPP(c_List_Omap(_1669141, _1669137), _1669145)) = hAPP(c_List_Omap(_1669141, _1669139), hAPP(c_Fun_Ocomp(_1669137, _1669139, _1669141, _1669143), _1669145)))], (44433 ^ _779300) ^ [_1669208] : [-(hAPP(c_List_Omap(_1669208, _1669208), c_COMBI(_1669208)) = c_Fun_Oid(tc_List_Olist(_1669208)))], (44435 ^ _779300) ^ [_1669243, _1669245, _1669247, _1669249, _1669251] : [-(c_List_Olist_Olist__size(_1669243, _1669245, hAPP(hAPP(c_List_Omap(_1669247, _1669243), _1669249), _1669251)) = c_List_Olist_Olist__size(_1669247, hAPP(c_Fun_Ocomp(_1669243, tc_Nat_Onat, _1669247, _1669245), _1669249), _1669251))], (44437 ^ _779300) ^ [_1669299] : [-(hAPP(c_List_Omap(_1669299, _1669299), c_Fun_Oid(_1669299)) = c_Fun_Oid(tc_List_Olist(_1669299)))], (44439 ^ _779300) ^ [_1669334, _1669336, _1669338, _1669340, _1669342] : [hAPP(hAPP(c_List_Omap(_1669334, _1669336), _1669338), _1669340) = hAPP(hAPP(c_List_Omap(_1669334, _1669336), _1669338), _1669342), c_Fun_Oinj__on(_1669334, _1669336, _1669338, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669334, tc_HOL_Obool)), hAPP(c_List_Oset(_1669334), _1669340)), hAPP(c_List_Oset(_1669334), _1669342))), -(_1669340 = _1669342)], (44449 ^ _779300) ^ [_1669557, _1669559, _1669561, _1669563, _1669565] : [c_Fun_Oinj__on(_1669557, _1669559, _1669561, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669557, tc_HOL_Obool)), hAPP(c_List_Oset(_1669557), _1669563)), hAPP(c_List_Oset(_1669557), _1669565))), 44452 ^ _779300 : [(44453 ^ _779300) ^ [] : [hAPP(hAPP(c_List_Omap(_1669557, _1669559), _1669561), _1669563) = hAPP(hAPP(c_List_Omap(_1669557, _1669559), _1669561), _1669565), -(_1669563 = _1669565)], (44459 ^ _779300) ^ [] : [_1669563 = _1669565, -(hAPP(hAPP(c_List_Omap(_1669557, _1669559), _1669561), _1669563) = hAPP(hAPP(c_List_Omap(_1669557, _1669559), _1669561), _1669565))]]], (44465 ^ _779300) ^ [_1669882, _1669884, _1669886, _1669888, _1669890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669882), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669884)), _1669886))), -(hAPP(hAPP(c_List_Onth(_1669888), hAPP(hAPP(c_List_Omap(_1669884, _1669888), _1669890), _1669886)), _1669882) = hAPP(_1669890, hAPP(hAPP(c_List_Onth(_1669884), _1669886), _1669882)))], (44471 ^ _779300) ^ [_1670041, _1670043, _1670045, _1670047, _1670049, _1670051] : [-(hBOOL(hAPP(hAPP(c_member(_1670041), _1670043), hAPP(c_List_Oset(_1670041), _1670045)))), -(hAPP(hAPP(c_List_Omap(_1670041, _1670047), c_Fun_Ofun__upd(_1670041, _1670047, _1670049, _1670043, _1670051)), _1670045) = hAPP(hAPP(c_List_Omap(_1670041, _1670047), _1670049), _1670045))], (44477 ^ _779300) ^ [_1670142, _1670144, _1670146, _1670148] : [hBOOL(hAPP(c_List_Odistinct(_1670142), hAPP(hAPP(c_List_Omap(_1670144, _1670142), _1670146), _1670148))), 44480 ^ _779300 : [(44481 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1670144), _1670148)))], (44483 ^ _779300) ^ [] : [-(c_Fun_Oinj__on(_1670144, _1670142, _1670146, hAPP(c_List_Oset(_1670144), _1670148)))]]], (44485 ^ _779300) ^ [_1670293, _1670295, _1670297, _1670299] : [-(hBOOL(hAPP(c_List_Odistinct(_1670293), hAPP(hAPP(c_List_Omap(_1670295, _1670293), _1670297), _1670299)))), hBOOL(hAPP(c_List_Odistinct(_1670295), _1670299)), c_Fun_Oinj__on(_1670295, _1670293, _1670297, hAPP(c_List_Oset(_1670295), _1670299))], (44495 ^ _779300) ^ [_1670480, _1670482] : [class_Groups_Oordered__ab__group__add__abs(_1670480), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670480), hAPP(c_Groups_Oabs__class_Oabs(_1670480), hAPP(c_List_Omonoid__add__class_Olistsum(_1670480), _1670482))), hAPP(c_List_Omonoid__add__class_Olistsum(_1670480), hAPP(hAPP(c_List_Omap(_1670480, _1670480), c_Groups_Oabs__class_Oabs(_1670480)), _1670482)))))], (44501 ^ _779300) ^ [_1670621, _1670623, _1670625, _1670627] : [class_Groups_Oab__group__add(_1670621), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1670621), hAPP(c_List_Omonoid__add__class_Olistsum(_1670621), hAPP(hAPP(c_List_Omap(_1670623, _1670621), _1670625), _1670627))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1670621), hAPP(hAPP(c_List_Omap(_1670623, _1670621), hAPP(c_Fun_Ocomp(_1670621, _1670621, _1670623, c_Groups_Ouminus__class_Ouminus(_1670621)), _1670625)), _1670627)))], (44507 ^ _779300) ^ [_1670786, _1670788, _1670790, _1670792] : [c_Fun_Oinj__on(_1670786, _1670788, _1670790, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670786, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1670786), tc_fun(_1670786, tc_HOL_Obool), c_List_Oset(_1670786)), _1670792))), -(c_Fun_Oinj__on(tc_List_Olist(_1670786), tc_List_Olist(_1670788), hAPP(c_List_Omap(_1670786, _1670788), _1670790), _1670792))], (44513 ^ _779300) ^ [_1670935, _1670937, _1670939] : [c_Fun_Oinj__on(tc_List_Olist(_1670935), tc_List_Olist(_1670937), hAPP(c_List_Omap(_1670935, _1670937), _1670939), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1670935), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1670935, _1670937, _1670939, c_Orderings_Otop__class_Otop(tc_fun(_1670935, tc_HOL_Obool))))], (44519 ^ _779300) ^ [_1671084, _1671086, _1671088] : [c_Fun_Oinj__on(tc_List_Olist(_1671084), tc_List_Olist(_1671086), hAPP(c_List_Omap(_1671084, _1671086), _1671088), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671084), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1671084, _1671086, _1671088, c_Orderings_Otop__class_Otop(tc_fun(_1671084, tc_HOL_Obool))))], (44525 ^ _779300) ^ [_1671211, _1671213, _1671215] : [c_Fun_Oinj__on(_1671211, _1671213, _1671215, c_Orderings_Otop__class_Otop(tc_fun(_1671211, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1671211), tc_List_Olist(_1671213), hAPP(c_List_Omap(_1671211, _1671213), _1671215), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671211), tc_HOL_Obool))))], (44531 ^ _779300) ^ [_1671344, _1671346, _1671348, _1671350] : [class_Groups_Ocomm__monoid__add(_1671344), hBOOL(hAPP(c_List_Odistinct(_1671346), _1671348)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671344), hAPP(hAPP(c_List_Omap(_1671346, _1671344), _1671350), _1671348)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1671346, _1671344), _1671350), hAPP(c_List_Oset(_1671346), _1671348)))], (44541 ^ _779300) ^ [_1671543, _1671545, _1671547, _1671549] : [class_Rings_Osemiring__1(_1671543), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671543), hAPP(hAPP(c_List_Omap(_1671545, _1671543), hAPP(c_COMBK(_1671543, _1671545), _1671547)), _1671549)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1671543), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1671543), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671545)), _1671549))), _1671547))], (44547 ^ _779300) ^ [_1671702, _1671704, _1671706, _1671708, _1671710] : [class_Groups_Ocomm__monoid__add(_1671702), hBOOL(hAPP(hAPP(c_member(_1671704), _1671706), hAPP(c_List_Oset(_1671704), _1671708))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671702), hAPP(hAPP(c_List_Omap(_1671704, _1671702), _1671710), _1671708)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1671702), hAPP(_1671710, _1671706)), hAPP(c_List_Omonoid__add__class_Olistsum(_1671702), hAPP(hAPP(c_List_Omap(_1671704, _1671702), _1671710), c_List_Oremove1(_1671704, _1671706, _1671708)))))], (44557 ^ _779300) ^ [_1671951, _1671953, _1671955, _1671957] : [class_Groups_Ocomm__monoid__add(_1671951), 44560 ^ _779300 : [(44561 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1671953), _1671955)), -(c_Nitpick_Osetsum_H(_1671953, _1671951, _1671957, _1671955) = hAPP(c_List_Omonoid__add__class_Olistsum(_1671951), hAPP(hAPP(c_List_Omap(_1671953, _1671951), _1671957), c_Hilbert__Choice_OEps(tc_List_Olist(_1671953), hAPP(hAPP(c_COMBS(tc_List_Olist(_1671953), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1671953)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1671953), tc_fun(_1671953, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1671953, tc_HOL_Obool), tc_fun(tc_fun(_1671953, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1671953)), c_fequal), c_List_Oset(_1671953))), _1671955))), c_List_Odistinct(_1671953))))))], (44567 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1671953), _1671955))), -(c_Nitpick_Osetsum_H(_1671953, _1671951, _1671957, _1671955) = c_Groups_Ozero__class_Ozero(_1671951))]]], (44573 ^ _779300) ^ [_1672339, _1672341, _1672343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672339), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672341)), _1672343))), -(hAPP(c_Random_Opick(_1672341, hAPP(hAPP(c_List_Omap(_1672341, tc_prod(tc_Code__Numeral_Ocode__numeral, _1672341)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1672341), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1672343)), hAPP(c_Code__Numeral_Oof__nat, _1672339)) = hAPP(hAPP(c_List_Onth(_1672341), _1672343), _1672339))], (44579 ^ _779300) ^ [_1672512, _1672514] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1672512)), hAPP(c_Code__Numeral_Oof__nat, _1672514)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1672512), _1672514)))], (44581 ^ _779300) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (44583 ^ _779300) ^ [_1672591, _1672593] : [hAPP(c_Code__Numeral_Oof__nat, _1672591) = hAPP(c_Code__Numeral_Oof__nat, _1672593), -(_1672591 = _1672593)], (44589 ^ _779300) ^ [_1672676, _1672678] : [_1672676 = _1672678, -(hAPP(c_Code__Numeral_Oof__nat, _1672676) = hAPP(c_Code__Numeral_Oof__nat, _1672678))], (44595 ^ _779300) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44597 ^ _779300) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44599 ^ _779300) ^ [_1672818, _1672820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1672818)), hAPP(c_Code__Numeral_Oof__nat, _1672820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672818), _1672820)))], (44605 ^ _779300) ^ [_1672923, _1672925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672923), _1672925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1672923)), hAPP(c_Code__Numeral_Oof__nat, _1672925))))], (44611 ^ _779300) ^ [_1673034, _1673036] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1673034), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1673036), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 44618 ^ _779300 : [(44619 ^ _779300) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1673034) = hAPP(c_Code__Numeral_Oof__nat, _1673036), -(_1673034 = _1673036)], (44625 ^ _779300) ^ [] : [_1673034 = _1673036, -(hAPP(c_Code__Numeral_Oof__nat, _1673034) = hAPP(c_Code__Numeral_Oof__nat, _1673036))]]], (44631 ^ _779300) ^ [_1673331, _1673333, _1673335, _1673337] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673331)), _1673333) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673335)), _1673337), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673331, _1673335), _1673331), c_Product__Type_Ofst(_1673331, _1673335)), hAPP(hAPP(c_List_Ozip(_1673331, _1673335), _1673333), _1673337)) = _1673333)], (44637 ^ _779300) ^ [_1673488, _1673490, _1673492, _1673494] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673488)), _1673490) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673492)), _1673494), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673488, _1673492), _1673492), c_Product__Type_Osnd(_1673488, _1673492)), hAPP(hAPP(c_List_Ozip(_1673488, _1673492), _1673490), _1673494)) = _1673494)], (44643 ^ _779300) ^ [] : [-(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))], (44645 ^ _779300) ^ [_1673663, _1673665, _1673667] : [-(hAPP(hAPP(c_List_Ozip(_1673663, _1673665), hAPP(hAPP(c_List_Omap(tc_prod(_1673663, _1673665), _1673663), c_Product__Type_Ofst(_1673663, _1673665)), _1673667)), hAPP(hAPP(c_List_Omap(tc_prod(_1673663, _1673665), _1673665), c_Product__Type_Osnd(_1673663, _1673665)), _1673667)) = _1673667)], (44647 ^ _779300) ^ [_1673729, _1673731] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673729)), hAPP(c_Code__Numeral_Oof__nat, _1673731)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1673729), _1673731)))], (44649 ^ _779300) ^ [_1673790, _1673792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673790)), hAPP(c_Code__Numeral_Oof__nat, _1673792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1673790), _1673792)))], (44655 ^ _779300) ^ [_1673895, _1673897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1673895), _1673897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673895)), hAPP(c_Code__Numeral_Oof__nat, _1673897))))], (44661 ^ _779300) ^ [_1674006, _1674008, _1674010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1674006), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674008), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1674008)), _1674010)))), -(hBOOL(hAPP(hAPP(c_member(_1674008), hAPP(c_Random_Opick(_1674008, _1674010), _1674006)), hAPP(c_List_Oset(_1674008), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674008), _1674008), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1674008)), _1674010)))))], (44667 ^ _779300) ^ [_1674197, _1674199, _1674201, _1674203, _1674205] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674197)), _1674199) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674201)), _1674203), 44670 ^ _779300 : [(44671 ^ _779300) ^ [] : [hAPP(hAPP(c_List_Ozip(_1674197, _1674201), _1674199), _1674203) = _1674205, 44674 ^ _779300 : [(44675 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674197, _1674201), _1674197), c_Product__Type_Ofst(_1674197, _1674201)), _1674205) = _1674199)], (44677 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674197, _1674201), _1674201), c_Product__Type_Osnd(_1674197, _1674201)), _1674205) = _1674203)]]], (44679 ^ _779300) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1674197, _1674201), _1674199), _1674203) = _1674205), hAPP(hAPP(c_List_Omap(tc_prod(_1674197, _1674201), _1674197), c_Product__Type_Ofst(_1674197, _1674201)), _1674205) = _1674199, hAPP(hAPP(c_List_Omap(tc_prod(_1674197, _1674201), _1674201), c_Product__Type_Osnd(_1674197, _1674201)), _1674205) = _1674203]]], (44689 ^ _779300) ^ [_1674645, _1674647, _1674649] : [-(c_List_Olist_Olist__size(_1674645, _1674647, _1674649) = 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(_1674645, tc_Nat_Onat), _1674647), _1674649))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674645)), _1674649)))], (44691 ^ _779300) ^ [_1674707] : [-(_1674707 = 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)), _1674707)))], (44697 ^ _779300) ^ [_1674739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1674739)), _1674739 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44703 ^ _779300) ^ [_1674821, _1674823, _1674825, _1674827] : [class_Groups_Ocomm__monoid__add(_1674821), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1674821), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1674821), _1674823), c_List_Oupto(_1674825, _1674827))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1674821), _1674823), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1674825, _1674827))))], (44709 ^ _779300) ^ [_1674964, _1674966, _1674968, _1674970] : [class_Groups_Ocomm__monoid__add(_1674964), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1674964), _1674966), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1674968, _1674970))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1674964), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1674964), _1674966), c_List_Oupto(_1674968, _1674970))))], (44715 ^ _779300) ^ [_1675107, _1675109, _1675111] : [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, _1675107), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1675107)), _1675109)))), -(hBOOL(hAPP(hAPP(c_member(_1675107), hAPP(c_Product__Type_Ofst(_1675107, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1675107, _1675109), _1675111))), hAPP(c_List_Oset(_1675107), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1675107), _1675107), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1675107)), _1675109)))))], (44721 ^ _779300) ^ [_1675304, _1675306] : [-(c_Random_Oselect__weight(_1675304, _1675306) = 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(_1675304, 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, _1675304), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1675304)), _1675306)))), hAPP(hAPP(c_COMBB(_1675304, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675304, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1675304, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1675304, _1675306))))], (44723 ^ _779300) ^ [_1675388, _1675390] : [-(c_Random_Oselect(_1675388, _1675390) = 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(_1675388, 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(_1675388)), _1675390)))), hAPP(hAPP(c_COMBB(_1675388, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675388, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1675388, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1675388, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1675388), _1675390)), c_Code__Numeral_Onat__of))))], (44725 ^ _779300) ^ [_1675476, _1675478] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1675476)), hAPP(c_Code__Numeral_Oof__nat, _1675478)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1675476), _1675478)))], (44727 ^ _779300) ^ [_1675522] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1675522)) = _1675522)], (44729 ^ _779300) ^ [_1675551] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1675551)) = _1675551)], (44731 ^ _779300) ^ [_1675580] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1675580)) = _1675580)], (44733 ^ _779300) ^ [_1675624, _1675626] : [hAPP(c_Code__Numeral_Onat__of, _1675624) = hAPP(c_Code__Numeral_Onat__of, _1675626), -(_1675624 = _1675626)], (44739 ^ _779300) ^ [_1675709, _1675711] : [_1675709 = _1675711, -(hAPP(c_Code__Numeral_Onat__of, _1675709) = hAPP(c_Code__Numeral_Onat__of, _1675711))], (44745 ^ _779300) ^ [_1675815, _1675817] : [hAPP(c_Code__Numeral_Onat__of, _1675815) = hAPP(c_Code__Numeral_Onat__of, _1675817), -(_1675815 = _1675817)], (44751 ^ _779300) ^ [_1675900, _1675902] : [_1675900 = _1675902, -(hAPP(c_Code__Numeral_Onat__of, _1675900) = hAPP(c_Code__Numeral_Onat__of, _1675902))], (44757 ^ _779300) ^ [_1675991, _1675993] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1675991), _1675993) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1675991)), hAPP(c_Code__Numeral_Onat__of, _1675993))))], (44759 ^ _779300) ^ [] : [-(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))))], (44761 ^ _779300) ^ [_1676070, _1676072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1676070), _1676072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676070)), hAPP(c_Code__Numeral_Onat__of, _1676072))))], (44767 ^ _779300) ^ [_1676175, _1676177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676175)), hAPP(c_Code__Numeral_Onat__of, _1676177))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1676175), _1676177)))], (44773 ^ _779300) ^ [_1676286] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676286)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (44775 ^ _779300) ^ [_1676317] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1676317)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1676317))], (44777 ^ _779300) ^ [] : [-(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))], (44779 ^ _779300) ^ [_1676382, _1676384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1676382), _1676384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676382)), hAPP(c_Code__Numeral_Onat__of, _1676384))))], (44785 ^ _779300) ^ [_1676487, _1676489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676487)), hAPP(c_Code__Numeral_Onat__of, _1676489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1676487), _1676489)))], (44791 ^ _779300) ^ [_1676598] : [-(hAPP(c_Code__Numeral_Onat__of, _1676598) = c_Code__Numeral_Onat__of__aux(_1676598, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44793 ^ _779300) ^ [_1676627, _1676629] : [-(c_Code__Numeral_Onat__of__aux(_1676627, _1676629) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676627)), _1676629))], (44795 ^ _779300) ^ [_1676664] : [-(c_Code__Numeral_OSuc__code__numeral(_1676664) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1676664))))], (44797 ^ _779300) ^ [_1676698, _1676700] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1676698), _1676700) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676698)), hAPP(c_Code__Numeral_Onat__of, _1676700))))], (44799 ^ _779300) ^ [_1676744] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1676744), 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, _1676744)) = _1676744)], (44805 ^ _779300) ^ [_1676841, _1676843] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1676841), _1676843) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676841)), hAPP(c_Code__Numeral_Onat__of, _1676843))))], (44807 ^ _779300) ^ [_1676887, _1676889] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1676887), _1676889) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676887)), hAPP(c_Code__Numeral_Onat__of, _1676889))))], (44809 ^ _779300) ^ [_1676933, _1676935] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1676933), _1676935) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1676933), _1676935))], (44811 ^ _779300) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (44813 ^ _779300) ^ [_1676988, _1676990] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1676988, _1676990) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1676988), hAPP(c_Code__Numeral_Onat__of, _1676990))))], (44815 ^ _779300) ^ [_1677026] : [-(_1677026 = 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, _1677026)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1677026))))], (44821 ^ _779300) ^ [_1677077, _1677079, _1677081, _1677083, _1677085] : [class_Groups_Omonoid__add(_1677077), class_Groups_Oordered__ab__semigroup__add(_1677077), 44831 ^ _779300 : [(44832 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1677079), 44830 ^ [_1677077, _1677079, _1677081, _1677083, _1677085]), hAPP(c_List_Oset(_1677079), _1677081))))], (44834 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1677077), hAPP(_1677083, 44830 ^ [_1677077, _1677079, _1677081, _1677083, _1677085])), hAPP(_1677085, 44830 ^ [_1677077, _1677079, _1677081, _1677083, _1677085])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1677077), hAPP(c_List_Omonoid__add__class_Olistsum(_1677077), hAPP(hAPP(c_List_Omap(_1677079, _1677077), _1677083), _1677081))), hAPP(c_List_Omonoid__add__class_Olistsum(_1677077), hAPP(hAPP(c_List_Omap(_1677079, _1677077), _1677085), _1677081)))))], (44838 ^ _779300) ^ [_1677501, _1677503] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1677501), _1677503) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1677501, 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)))), _1677503))))], (44840 ^ _779300) ^ [_1677539, _1677541, _1677543, _1677545, _1677547] : [c_List_Opartition(_1677539, _1677541, _1677543) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1677539), tc_List_Olist(_1677539)), _1677545), _1677547), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1677539, tc_HOL_Obool)), hAPP(c_List_Oset(_1677539), _1677545)), hAPP(c_List_Oset(_1677539), _1677547)) = hAPP(c_List_Oset(_1677539), _1677543))], (44846 ^ _779300) ^ [_1677708, _1677710, _1677712] : [-(c_List_Olistsp(_1677708, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1677708, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1677708, tc_fun(_1677708, tc_HOL_Obool), tc_HOL_Obool), c_member(_1677708)), _1677710)), hAPP(hAPP(c_COMBC(_1677708, tc_fun(_1677708, tc_HOL_Obool), tc_HOL_Obool), c_member(_1677708)), _1677712))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1677708), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677708), tc_fun(tc_List_Olist(_1677708), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1677708))), c_List_Olists(_1677708, _1677710))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677708), tc_fun(tc_List_Olist(_1677708), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1677708))), c_List_Olists(_1677708, _1677712))))], (44848 ^ _779300) ^ [_1677840, _1677842] : [-(hBOOL(hAPP(c_List_Olistsp(_1677840, _1677842), c_List_Olist_ONil(_1677840))))], (44850 ^ _779300) ^ [_1677872, _1677874] : [-(hBOOL(hAPP(c_List_Olistsp(_1677872, _1677874), c_List_Olist_ONil(_1677872))))], (44862 ^ _779300) ^ [_1678120, _1678122, _1678124] : [44864 ^ _779300 : [(44865 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678120), 44863 ^ [_1678120, _1678122, _1678124]), hAPP(c_List_Oset(_1678120), _1678124))))], (44867 ^ _779300) ^ [] : [hBOOL(hAPP(_1678122, 44863 ^ [_1678120, _1678122, _1678124]))]], -(hBOOL(hAPP(c_List_Olistsp(_1678120, _1678122), _1678124)))], (44852 ^ _779300) ^ [_1677922, _1677924, _1677926] : [hBOOL(hAPP(c_List_Olistsp(_1677922, _1677924), _1677926)), 44855 ^ _779300 : [(44856 ^ _779300) ^ [_1678011] : [hBOOL(hAPP(hAPP(c_member(_1677922), _1678011), hAPP(c_List_Oset(_1677922), _1677926))), -(hBOOL(hAPP(_1677924, _1678011)))]]], (44871 ^ _779300) ^ [_1678331, _1678333, _1678335, _1678337] : [hBOOL(hAPP(c_List_Olistsp(_1678331, hAPP(hAPP(c_COMBS(_1678331, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1678331), c_fconj), _1678333)), _1678335)), _1678337)), 44874 ^ _779300 : [(44875 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1678331, _1678333), _1678337)))], (44877 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1678331, _1678335), _1678337)))]]], (44879 ^ _779300) ^ [_1678504, _1678506, _1678508, _1678510] : [-(hBOOL(hAPP(c_List_Olistsp(_1678504, hAPP(hAPP(c_COMBS(_1678504, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1678504), c_fconj), _1678506)), _1678508)), _1678510))), hBOOL(hAPP(c_List_Olistsp(_1678504, _1678506), _1678510)), hBOOL(hAPP(c_List_Olistsp(_1678504, _1678508), _1678510))], (44889 ^ _779300) ^ [_1678713, _1678715, _1678717, _1678719] : [hBOOL(hAPP(c_List_Olistsp(_1678713, _1678715), _1678717)), hBOOL(hAPP(c_List_Olistsp(_1678713, _1678719), _1678717)), -(hBOOL(hAPP(c_List_Olistsp(_1678713, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1678713, tc_HOL_Obool)), _1678715), _1678719)), _1678717)))], (44899 ^ _779300) ^ [_1678902, _1678904, _1678906] : [-(c_List_Olistsp(_1678902, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1678902, tc_HOL_Obool)), _1678904), _1678906)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1678902), tc_HOL_Obool)), c_List_Olistsp(_1678902, _1678904)), c_List_Olistsp(_1678902, _1678906)))], (44901 ^ _779300) ^ [_1678983, _1678985, _1678987, _1678989] : [hBOOL(hAPP(c_List_Olistsp(_1678983, _1678985), hAPP(hAPP(c_List_Olist_OCons(_1678983), _1678987), _1678989))), 44904 ^ _779300 : [(44905 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1678985, _1678987)))], (44907 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1678983, _1678985), _1678989)))]]], (44909 ^ _779300) ^ [_1679126, _1679128, _1679130, _1679132] : [-(hBOOL(hAPP(c_List_Olistsp(_1679126, _1679128), hAPP(hAPP(c_List_Olist_OCons(_1679126), _1679130), _1679132)))), hBOOL(hAPP(_1679128, _1679130)), hBOOL(hAPP(c_List_Olistsp(_1679126, _1679128), _1679132))], (44919 ^ _779300) ^ [_1679326, _1679328, _1679330, _1679332] : [hBOOL(hAPP(c_List_Olistsp(_1679326, _1679328), hAPP(hAPP(c_List_Oappend(_1679326), _1679330), _1679332))), 44922 ^ _779300 : [(44923 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1679326, _1679328), _1679330)))], (44925 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1679326, _1679328), _1679332)))]]], (44927 ^ _779300) ^ [_1679475, _1679477, _1679479, _1679481] : [-(hBOOL(hAPP(c_List_Olistsp(_1679475, _1679477), hAPP(hAPP(c_List_Oappend(_1679475), _1679479), _1679481)))), hBOOL(hAPP(c_List_Olistsp(_1679475, _1679477), _1679479)), hBOOL(hAPP(c_List_Olistsp(_1679475, _1679477), _1679481))], (44937 ^ _779300) ^ [_1679660, _1679662, _1679664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1679660, tc_HOL_Obool)), _1679662), _1679664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1679660), tc_HOL_Obool)), c_List_Olistsp(_1679660, _1679662)), c_List_Olistsp(_1679660, _1679664))))], (44943 ^ _779300) ^ [_1679795, _1679797, _1679799, _1679801, _1679803] : [c_List_Opartition(_1679795, _1679797, _1679799) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679795), tc_List_Olist(_1679795)), _1679801), _1679803), 44946 ^ _779300 : [(44947 ^ _779300) ^ [_1679948] : [hBOOL(hAPP(hAPP(c_member(_1679795), _1679948), hAPP(c_List_Oset(_1679795), _1679801))), -(hBOOL(hAPP(_1679797, _1679948)))], (44953 ^ _779300) ^ [_1680057] : [hBOOL(hAPP(hAPP(c_member(_1679795), _1680057), hAPP(c_List_Oset(_1679795), _1679803))), hBOOL(hAPP(_1679797, _1680057))]]], (44959 ^ _779300) ^ [_1680177, _1680179] : [-(c_List_Opartition(_1680177, _1680179, c_List_Olist_ONil(_1680177)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1680177), tc_List_Olist(_1680177)), c_List_Olist_ONil(_1680177)), c_List_Olist_ONil(_1680177)))], (44961 ^ _779300) ^ [_1680243, _1680245, _1680247] : [hBOOL(hAPP(c_List_Olistsp(_1680243, hAPP(hAPP(c_COMBC(_1680243, tc_fun(_1680243, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680243)), _1680245)), _1680247)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680243)), _1680247), c_List_Olists(_1680243, _1680245))))], (44967 ^ _779300) ^ [_1680382, _1680384, _1680386] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680382)), _1680386), c_List_Olists(_1680382, _1680384))), -(hBOOL(hAPP(c_List_Olistsp(_1680382, hAPP(hAPP(c_COMBC(_1680382, tc_fun(_1680382, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680382)), _1680384)), _1680386)))], (44973 ^ _779300) ^ [_1680527, _1680529, _1680531, _1680533] : [-(c_List_Opartition(_1680527, _1680529, hAPP(hAPP(c_List_Olist_OCons(_1680527), _1680531), _1680533)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1680527), tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1680527), tc_fun(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527))), tc_fun(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1680527), tc_fun(tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)))), tc_fun(tc_fun(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527))), tc_fun(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)))), tc_List_Olist(_1680527)), c_COMBS(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527))), tc_fun(tc_List_Olist(_1680527), tc_fun(tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)))), tc_List_Olist(_1680527)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)), tc_fun(tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527))), tc_List_Olist(_1680527)), hAPP(c_If(tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527))), hAPP(_1680529, _1680531)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1680527), tc_fun(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527))), tc_List_Olist(_1680527)), c_Product__Type_OPair(tc_List_Olist(_1680527), tc_List_Olist(_1680527))), hAPP(c_List_Olist_OCons(_1680527), _1680531))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1680527), tc_fun(tc_List_Olist(_1680527), tc_List_Olist(_1680527)), tc_fun(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527))), tc_fun(tc_fun(tc_List_Olist(_1680527), tc_List_Olist(_1680527)), tc_fun(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)))), tc_List_Olist(_1680527)), c_COMBB(tc_List_Olist(_1680527), tc_prod(tc_List_Olist(_1680527), tc_List_Olist(_1680527)), tc_List_Olist(_1680527))), c_Product__Type_OPair(tc_List_Olist(_1680527), tc_List_Olist(_1680527)))), hAPP(c_List_Olist_OCons(_1680527), _1680531)))), c_List_Opartition(_1680527, _1680529, _1680533)))], (44975 ^ _779300) ^ [_1680946, _1680948, _1680950, _1680952] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680946)), _1680948), c_List_Olists(_1680946, _1680950))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680946)), _1680948), c_List_Olists(_1680946, _1680952))), -(hBOOL(hAPP(c_List_Olistsp(_1680946, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680946, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1680946, tc_fun(_1680946, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680946)), _1680950)), hAPP(hAPP(c_COMBC(_1680946, tc_fun(_1680946, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680946)), _1680952))), _1680948)))], (44985 ^ _779300) ^ [_1681223, _1681225, _1681227, _1681229, _1681231] : [-(c_Enum_Oproduct(_1681223, _1681225, hAPP(hAPP(c_List_Olist_OCons(_1681223), _1681227), _1681229), _1681231) = hAPP(hAPP(c_List_Oappend(tc_prod(_1681223, _1681225)), hAPP(hAPP(c_List_Omap(_1681225, tc_prod(_1681223, _1681225)), hAPP(c_Product__Type_OPair(_1681223, _1681225), _1681227)), _1681231)), c_Enum_Oproduct(_1681223, _1681225, _1681229, _1681231)))], (44987 ^ _779300) ^ [_1681325, _1681327, _1681329, _1681331, _1681333] : [c_List_Olist__all2(_1681325, _1681327, _1681329, _1681331, _1681333), 44990 ^ _779300 : [(44991 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681325)), _1681331) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681327)), _1681333))], (44993 ^ _779300) ^ [_1681491] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681325, _1681327)), _1681491), hAPP(c_List_Oset(tc_prod(_1681325, _1681327)), hAPP(hAPP(c_List_Ozip(_1681325, _1681327), _1681331), _1681333)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1681325, _1681327, tc_HOL_Obool), _1681329), _1681491)))]]], (44999 ^ _779300) ^ [_1681650, _1681652, _1681654, _1681656, _1681658] : [-(c_List_Olist__all2(_1681650, _1681652, _1681654, _1681656, _1681658)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681650)), _1681656) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681652)), _1681658), 45005 ^ _779300 : [(45006 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1681650, _1681652)), 45004 ^ [_1681650, _1681652, _1681654, _1681656, _1681658]), hAPP(c_List_Oset(tc_prod(_1681650, _1681652)), hAPP(hAPP(c_List_Ozip(_1681650, _1681652), _1681656), _1681658)))))], (45008 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1681650, _1681652, tc_HOL_Obool), _1681654), 45004 ^ [_1681650, _1681652, _1681654, _1681656, _1681658]))]]], (45012 ^ _779300) ^ [_1682021, _1682023, _1682025, _1682027, _1682029, _1682031, _1682033] : [c_List_Olist__all2(_1682021, _1682023, _1682025, _1682027, hAPP(hAPP(c_List_Omap(_1682029, _1682023), _1682031), _1682033)), -(c_List_Olist__all2(_1682021, _1682029, hAPP(hAPP(c_COMBC(_1682021, tc_fun(_1682029, _1682023), tc_fun(_1682029, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682023, tc_HOL_Obool), tc_fun(tc_fun(_1682029, _1682023), tc_fun(_1682029, tc_HOL_Obool)), _1682021), c_COMBB(_1682023, tc_HOL_Obool, _1682029)), _1682025)), _1682031), _1682027, _1682033))], (45018 ^ _779300) ^ [_1682218, _1682220, _1682222, _1682224, _1682226, _1682228, _1682230] : [c_List_Olist__all2(_1682218, _1682226, hAPP(hAPP(c_COMBC(_1682218, tc_fun(_1682226, _1682220), tc_fun(_1682226, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682220, tc_HOL_Obool), tc_fun(tc_fun(_1682226, _1682220), tc_fun(_1682226, tc_HOL_Obool)), _1682218), c_COMBB(_1682220, tc_HOL_Obool, _1682226)), _1682222)), _1682228), _1682224, _1682230), -(c_List_Olist__all2(_1682218, _1682220, _1682222, _1682224, hAPP(hAPP(c_List_Omap(_1682226, _1682220), _1682228), _1682230)))], (45024 ^ _779300) ^ [_1682451, _1682453, _1682455, _1682457, _1682459, _1682461, _1682463] : [c_List_Olist__all2(_1682451, _1682453, _1682455, hAPP(hAPP(c_List_Omap(_1682457, _1682451), _1682459), _1682461), _1682463), -(c_List_Olist__all2(_1682457, _1682453, hAPP(hAPP(c_COMBB(_1682451, tc_fun(_1682453, tc_HOL_Obool), _1682457), _1682455), _1682459), _1682461, _1682463))], (45030 ^ _779300) ^ [_1682590, _1682592, _1682594, _1682596, _1682598, _1682600, _1682602] : [c_List_Olist__all2(_1682596, _1682592, hAPP(hAPP(c_COMBB(_1682590, tc_fun(_1682592, tc_HOL_Obool), _1682596), _1682594), _1682598), _1682600, _1682602), -(c_List_Olist__all2(_1682590, _1682592, _1682594, hAPP(hAPP(c_List_Omap(_1682596, _1682590), _1682598), _1682600), _1682602))], (45036 ^ _779300) ^ [_1682735, _1682737, _1682739, _1682741, _1682743, _1682745] : [c_List_Olist__all2(_1682735, _1682737, _1682739, _1682741, _1682743), -(c_List_Olist__all2(_1682735, _1682737, _1682739, hAPP(hAPP(c_List_Odrop(_1682735), _1682745), _1682741), hAPP(hAPP(c_List_Odrop(_1682737), _1682745), _1682743)))], (45042 ^ _779300) ^ [_1682864, _1682866, _1682868, _1682870, _1682872, _1682874, _1682876] : [c_List_Olist__all2(_1682864, _1682866, _1682868, _1682870, _1682872), c_List_Olist__all2(_1682864, _1682866, _1682868, _1682874, _1682876), -(c_List_Olist__all2(_1682864, _1682866, _1682868, hAPP(hAPP(c_List_Oappend(_1682864), _1682870), _1682874), hAPP(hAPP(c_List_Oappend(_1682866), _1682872), _1682876)))], (45052 ^ _779300) ^ [_1683063, _1683065, _1683067, _1683069, _1683071, _1683073, _1683075] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683063)), _1683065) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683067)), _1683069), 45055 ^ _779300 : [(45056 ^ _779300) ^ [] : [c_List_Olist__all2(_1683063, _1683067, _1683071, hAPP(hAPP(c_List_Oappend(_1683063), _1683065), _1683073), hAPP(hAPP(c_List_Oappend(_1683067), _1683069), _1683075)), 45059 ^ _779300 : [(45060 ^ _779300) ^ [] : [-(c_List_Olist__all2(_1683063, _1683067, _1683071, _1683065, _1683069))], (45062 ^ _779300) ^ [] : [-(c_List_Olist__all2(_1683063, _1683067, _1683071, _1683073, _1683075))]]], (45064 ^ _779300) ^ [] : [-(c_List_Olist__all2(_1683063, _1683067, _1683071, hAPP(hAPP(c_List_Oappend(_1683063), _1683065), _1683073), hAPP(hAPP(c_List_Oappend(_1683067), _1683069), _1683075))), c_List_Olist__all2(_1683063, _1683067, _1683071, _1683065, _1683069), c_List_Olist__all2(_1683063, _1683067, _1683071, _1683073, _1683075)]]], (45074 ^ _779300) ^ [_1683515, _1683517, _1683519, _1683521, _1683523, _1683525, _1683527] : [c_List_Olist__all2(_1683515, _1683517, _1683519, hAPP(hAPP(c_List_Olist_OCons(_1683515), _1683521), _1683523), hAPP(hAPP(c_List_Olist_OCons(_1683517), _1683525), _1683527)), 45077 ^ _779300 : [(45078 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1683519, _1683521), _1683525)))], (45080 ^ _779300) ^ [] : [-(c_List_Olist__all2(_1683515, _1683517, _1683519, _1683523, _1683527))]]], (45082 ^ _779300) ^ [_1683678, _1683680, _1683682, _1683684, _1683686, _1683688, _1683690] : [-(c_List_Olist__all2(_1683678, _1683680, _1683682, hAPP(hAPP(c_List_Olist_OCons(_1683678), _1683684), _1683686), hAPP(hAPP(c_List_Olist_OCons(_1683680), _1683688), _1683690))), hBOOL(hAPP(hAPP(_1683682, _1683684), _1683688)), c_List_Olist__all2(_1683678, _1683680, _1683682, _1683686, _1683690)], (45092 ^ _779300) ^ [_1683883, _1683885, _1683887, _1683889, _1683891, _1683893] : [c_List_Olist__all2(_1683883, _1683885, _1683887, _1683889, _1683891), -(c_List_Olist__all2(_1683883, _1683885, _1683887, hAPP(hAPP(c_List_Otake(_1683883), _1683893), _1683889), hAPP(hAPP(c_List_Otake(_1683885), _1683893), _1683891)))], (45098 ^ _779300) ^ [_1684030, _1684032, _1684034] : [_1684030 = _1684032, -(c_List_Olist__all2(_1684034, _1684034, c_fequal, _1684030, _1684032))], (45104 ^ _779300) ^ [_1684111, _1684113, _1684115] : [c_List_Olist__all2(_1684115, _1684115, c_fequal, _1684111, _1684113), -(_1684111 = _1684113)], (45110 ^ _779300) ^ [_1684198, _1684200, _1684202, _1684204, _1684206] : [c_List_Olist__all2(_1684198, _1684200, _1684202, _1684204, _1684206), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684198)), _1684204) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684200)), _1684206))], (45116 ^ _779300) ^ [_1684336, _1684338, _1684340, _1684342] : [c_List_Olist__all2(_1684336, _1684338, _1684340, _1684342, c_List_Olist_ONil(_1684338)), -(_1684342 = c_List_Olist_ONil(_1684336))], (45122 ^ _779300) ^ [_1684427, _1684429, _1684431, _1684433] : [_1684433 = c_List_Olist_ONil(_1684427), -(c_List_Olist__all2(_1684427, _1684429, _1684431, _1684433, c_List_Olist_ONil(_1684429)))], (45128 ^ _779300) ^ [_1684545, _1684547, _1684549, _1684551] : [c_List_Olist__all2(_1684545, _1684547, _1684549, c_List_Olist_ONil(_1684545), _1684551), -(_1684551 = c_List_Olist_ONil(_1684547))], (45134 ^ _779300) ^ [_1684636, _1684638, _1684640, _1684642] : [_1684642 = c_List_Olist_ONil(_1684638), -(c_List_Olist__all2(_1684636, _1684638, _1684640, c_List_Olist_ONil(_1684636), _1684642))], (45140 ^ _779300) ^ [_1684733, _1684735, _1684737] : [-(c_Enum_Oproduct(_1684733, _1684735, c_List_Olist_ONil(_1684733), _1684737) = c_List_Olist_ONil(tc_prod(_1684733, _1684735)))], (45142 ^ _779300) ^ [_1684796, _1684798, _1684800, _1684802, _1684804] : [c_List_Olist__all2(_1684796, _1684798, _1684800, _1684802, _1684804), 45145 ^ _779300 : [(45146 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684796)), _1684802) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684798)), _1684804))], (45148 ^ _779300) ^ [_1684959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684959), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684796)), _1684802))), -(hBOOL(hAPP(hAPP(_1684800, hAPP(hAPP(c_List_Onth(_1684796), _1684802), _1684959)), hAPP(hAPP(c_List_Onth(_1684798), _1684804), _1684959))))]]], (45154 ^ _779300) ^ [_1685112, _1685114, _1685116, _1685118, _1685120] : [-(c_List_Olist__all2(_1685112, _1685114, _1685116, _1685118, _1685120)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685112)), _1685118) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685114)), _1685120), 45160 ^ _779300 : [(45161 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45159 ^ [_1685112, _1685114, _1685116, _1685118, _1685120]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685112)), _1685118))))], (45163 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1685116, hAPP(hAPP(c_List_Onth(_1685112), _1685118), 45159 ^ [_1685112, _1685114, _1685116, _1685118, _1685120])), hAPP(hAPP(c_List_Onth(_1685114), _1685120), 45159 ^ [_1685112, _1685114, _1685116, _1685118, _1685120])))]]], (45167 ^ _779300) ^ [_1685472, _1685474, _1685476, _1685478, _1685480, _1685482] : [c_List_Olist__all2(_1685472, _1685474, _1685476, _1685478, _1685480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685482), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685472)), _1685478))), -(hBOOL(hAPP(hAPP(_1685476, hAPP(hAPP(c_List_Onth(_1685472), _1685478), _1685482)), hAPP(hAPP(c_List_Onth(_1685474), _1685480), _1685482))))], (45177 ^ _779300) ^ [_1685689, _1685691, _1685693, _1685695, _1685697, _1685699] : [c_List_Olist__all2(_1685689, _1685691, _1685693, _1685695, _1685697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685699), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685691)), _1685697))), -(hBOOL(hAPP(hAPP(_1685693, hAPP(hAPP(c_List_Onth(_1685689), _1685695), _1685699)), hAPP(hAPP(c_List_Onth(_1685691), _1685697), _1685699))))], (45187 ^ _779300) ^ [_1685906, _1685908, _1685910, _1685912, _1685914, _1685916, _1685918, _1685920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685906), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685908)), _1685910))), c_List_Olist__all2(_1685908, _1685912, _1685914, _1685910, _1685916), hBOOL(hAPP(hAPP(_1685914, _1685918), _1685920)), -(c_List_Olist__all2(_1685908, _1685912, _1685914, hAPP(hAPP(c_List_Olist__update(_1685908, _1685910), _1685906), _1685918), hAPP(hAPP(c_List_Olist__update(_1685912, _1685916), _1685906), _1685920)))], (45201 ^ _779300) ^ [_1686205, _1686207, _1686209, _1686211, _1686213, _1686215, _1686217, _1686219] : [c_List_Olist__all2(_1686205, _1686207, _1686209, _1686211, _1686213), hBOOL(hAPP(hAPP(_1686209, _1686215), _1686217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686219), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686207)), _1686213))), -(c_List_Olist__all2(_1686205, _1686207, _1686209, hAPP(hAPP(c_List_Olist__update(_1686205, _1686211), _1686219), _1686215), hAPP(hAPP(c_List_Olist__update(_1686207, _1686213), _1686219), _1686217)))], (45215 ^ _779300) ^ [_1686504, _1686506, _1686508, _1686510] : [hBOOL(hAPP(c_List_Odistinct(_1686504), _1686506)), hBOOL(hAPP(c_List_Odistinct(_1686508), _1686510)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1686504, _1686508)), c_Enum_Oproduct(_1686504, _1686508, _1686506, _1686510))))], (45225 ^ _779300) ^ [_1686681, _1686683, _1686685, _1686687] : [-(hAPP(c_List_Oset(tc_prod(_1686681, _1686683)), c_Enum_Oproduct(_1686681, _1686683, _1686685, _1686687)) = hAPP(hAPP(c_Product__Type_OSigma(_1686681, _1686683), hAPP(c_List_Oset(_1686681), _1686685)), hAPP(c_COMBK(tc_fun(_1686683, tc_HOL_Obool), _1686681), hAPP(c_List_Oset(_1686683), _1686687))))], (45227 ^ _779300) ^ [_1686751, _1686753] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1686751), tc_fun(_1686751, tc_HOL_Obool), c_List_Oset(_1686751)), hAPP(c_List_Oset(tc_List_Olist(_1686751)), c_Enum_Osublists(_1686751, _1686753))) = hAPP(c_Set_OPow(_1686751), hAPP(c_List_Oset(_1686751), _1686753)))], (45229 ^ _779300) ^ [_1686810, _1686812] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1686810))), c_Enum_Osublists(_1686810, _1686812)) = 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(_1686810)), _1686812)))], (45231 ^ _779300) ^ [_1686857] : [-(c_Enum_Osublists(_1686857, c_List_Olist_ONil(_1686857)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1686857)), c_List_Olist_ONil(_1686857)), c_List_Olist_ONil(tc_List_Olist(_1686857))))], (45233 ^ _779300) ^ [_1686901, _1686903, _1686905] : [-(c_Enum_Osublists(_1686901, hAPP(hAPP(c_List_Olist_OCons(_1686901), _1686903), _1686905)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1686901)), tc_List_Olist(tc_List_Olist(_1686901))), c_Enum_Osublists(_1686901, _1686905)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1686901)), tc_List_Olist(tc_List_Olist(_1686901)), tc_List_Olist(tc_List_Olist(_1686901))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1686901)), tc_fun(tc_List_Olist(tc_List_Olist(_1686901)), tc_List_Olist(tc_List_Olist(_1686901))), tc_List_Olist(tc_List_Olist(_1686901))), c_List_Oappend(tc_List_Olist(_1686901))), hAPP(c_List_Omap(tc_List_Olist(_1686901), tc_List_Olist(_1686901)), hAPP(c_List_Olist_OCons(_1686901), _1686903)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1686901))))))], (45235 ^ _779300) ^ [_1687035, _1687037] : [hBOOL(hAPP(c_List_Odistinct(_1687035), _1687037)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1687035, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1687035), tc_fun(_1687035, tc_HOL_Obool)), c_List_Oset(_1687035)), c_Enum_Osublists(_1687035, _1687037)))))], (45241 ^ _779300) ^ [_1687172, _1687174, _1687176] : [-(hAPP(c_List_Oset(tc_List_Olist(_1687172)), c_Enum_On__lists(_1687172, _1687174, _1687176)) = hAPP(c_Set_OCollect(tc_List_Olist(_1687172)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1687172), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1687172)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687172), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1687172)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1687172)))), _1687174))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687172), tc_fun(_1687172, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1687172, tc_HOL_Obool), tc_fun(tc_fun(_1687172, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1687172)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1687172, tc_HOL_Obool))), c_List_Oset(_1687172))), hAPP(c_List_Oset(_1687172), _1687176)))))], (45243 ^ _779300) ^ [_1687317, _1687319] : [-(c_Enum_Oenum__the(_1687317, _1687319) = c_HOL_OThe(_1687317, _1687319))], (45245 ^ _779300) ^ [_1687348, _1687350, _1687352] : [hBOOL(hAPP(c_List_Odistinct(_1687348), _1687350)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1687348)), c_Enum_On__lists(_1687348, _1687352, _1687350))))], (45251 ^ _779300) ^ [_1687455, _1687457] : [-(c_Enum_On__lists(_1687455, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1687457) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687455)), c_List_Olist_ONil(_1687455)), c_List_Olist_ONil(tc_List_Olist(_1687455))))], (45253 ^ _779300) ^ [_1687509, _1687511] : [_1687509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1687511, _1687509, c_List_Olist_ONil(_1687511)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687511)), c_List_Olist_ONil(_1687511)), c_List_Olist_ONil(tc_List_Olist(_1687511))))], (45259 ^ _779300) ^ [_1687624, _1687626] : [-(_1687624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1687626, _1687624, c_List_Olist_ONil(_1687626)) = c_List_Olist_ONil(tc_List_Olist(_1687626)))], (45265 ^ _779300) ^ [_1687672, _1687674, _1687676] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1687672))), c_Enum_On__lists(_1687672, _1687674, _1687676)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687672)), _1687676)), _1687674))], (45267 ^ _779300) ^ [_1687725, _1687727, _1687729, _1687731] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1687725)), _1687727), hAPP(c_List_Oset(tc_List_Olist(_1687725)), c_Enum_On__lists(_1687725, _1687729, _1687731)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687725)), _1687727) = _1687729)], (45273 ^ _779300) ^ [_1687860, _1687862, _1687864, _1687866, _1687868] : [45275 ^ _779300 : [(45276 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1687860, _1687862)), 45274 ^ [_1687860, _1687862, _1687864, _1687866, _1687868]), hAPP(c_List_Oset(tc_prod(_1687860, _1687862)), hAPP(hAPP(c_List_Ozip(_1687860, _1687862), _1687864), _1687866)))))], (45278 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1687860, _1687862, tc_HOL_Obool), _1687868), 45274 ^ [_1687860, _1687862, _1687864, _1687866, _1687868]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687860)), _1687864) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687862)), _1687866), -(c_List_Olist__all2(_1687860, _1687862, _1687868, _1687864, _1687866))], (45286 ^ _779300) ^ [_1688199, _1688201, _1688203, _1688205] : [45288 ^ _779300 : [(45289 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45287 ^ [_1688199, _1688201, _1688203, _1688205]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688199)), _1688201))))], (45291 ^ _779300) ^ [] : [hBOOL(hAPP(_1688203, hAPP(hAPP(c_List_Onth(_1688199), _1688201), 45287 ^ [_1688199, _1688201, _1688203, _1688205])))]], hBOOL(hAPP(hAPP(c_member(_1688199), _1688205), hAPP(c_List_Oset(_1688199), _1688201))), -(hBOOL(hAPP(_1688203, _1688205)))], (45299 ^ _779300) ^ [_1688495, _1688497, _1688499, _1688501, _1688503] : [c_Finite__Set_Ofun__left__comm(_1688495, _1688497, _1688499), -(hAPP(hAPP(c_Finite__Set_Ofold(_1688495, _1688497, _1688499), _1688501), hAPP(c_List_Oset(_1688495), _1688503)) = hAPP(c_List_Ofoldl(_1688497, _1688495, hAPP(c_COMBC(_1688495, _1688497, _1688497), _1688499), _1688501), c_List_Oremdups(_1688495, _1688503)))], (45305 ^ _779300) ^ [_1688646, _1688648, _1688650, _1688652, _1688654] : [c_Fun_Oinj__on(_1688646, _1688648, _1688650, hAPP(hAPP(c_Set_Oinsert(_1688646), _1688652), hAPP(c_List_Oset(_1688646), _1688654))), -(hAPP(hAPP(c_List_Omap(_1688646, _1688648), _1688650), hAPP(c_List_OremoveAll(_1688646, _1688652), _1688654)) = hAPP(c_List_OremoveAll(_1688648, hAPP(_1688650, _1688652)), hAPP(hAPP(c_List_Omap(_1688646, _1688648), _1688650), _1688654)))], (45311 ^ _779300) ^ [_1688825, _1688827] : [-(hBOOL(hAPP(c_List_Odistinct(_1688825), c_List_Oremdups(_1688825, _1688827))))], (45313 ^ _779300) ^ [_1688857, _1688859] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688857)), c_List_Oremdups(_1688857, _1688859))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688857)), _1688859))))], (45315 ^ _779300) ^ [_1688919, _1688921] : [c_List_Oremdups(_1688919, _1688921) = _1688921, -(hBOOL(hAPP(c_List_Odistinct(_1688919), _1688921)))], (45321 ^ _779300) ^ [_1689006, _1689008] : [hBOOL(hAPP(c_List_Odistinct(_1689006), _1689008)), -(c_List_Oremdups(_1689006, _1689008) = _1689008)], (45327 ^ _779300) ^ [_1689099, _1689101, _1689103] : [hBOOL(hAPP(c_List_Odistinct(_1689099), _1689101)), -(hBOOL(hAPP(c_List_Odistinct(_1689099), hAPP(c_List_OremoveAll(_1689099, _1689103), _1689101))))], (45333 ^ _779300) ^ [_1689206, _1689208] : [hBOOL(hAPP(c_List_Odistinct(_1689206), _1689208)), -(c_List_Oremdups(_1689206, _1689208) = _1689208)], (45339 ^ _779300) ^ [_1689297, _1689299] : [-(hAPP(c_List_Oset(_1689297), c_List_Oremdups(_1689297, _1689299)) = hAPP(c_List_Oset(_1689297), _1689299))], (45341 ^ _779300) ^ [_1689350, _1689352] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689350)), c_List_Oremdups(_1689350, _1689352)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689350)), _1689352), -(c_List_Oremdups(_1689350, _1689352) = _1689352)], (45347 ^ _779300) ^ [_1689463, _1689465] : [c_List_Oremdups(_1689463, _1689465) = _1689465, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689463)), c_List_Oremdups(_1689463, _1689465)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689463)), _1689465))], (45353 ^ _779300) ^ [_1689582, _1689584] : [-(c_List_Oremdups(_1689582, c_List_Oremdups(_1689582, _1689584)) = c_List_Oremdups(_1689582, _1689584))], (45355 ^ _779300) ^ [_1689616] : [-(c_List_Oremdups(_1689616, c_List_Olist_ONil(_1689616)) = c_List_Olist_ONil(_1689616))], (45357 ^ _779300) ^ [_1689661, _1689663] : [c_List_Olist_ONil(_1689661) = c_List_Oremdups(_1689661, _1689663), -(_1689663 = c_List_Olist_ONil(_1689661))], (45363 ^ _779300) ^ [_1689748, _1689750] : [_1689750 = c_List_Olist_ONil(_1689748), -(c_List_Olist_ONil(_1689748) = c_List_Oremdups(_1689748, _1689750))], (45369 ^ _779300) ^ [_1689841, _1689843] : [-(hAPP(c_List_OremoveAll(_1689841, _1689843), c_List_Olist_ONil(_1689841)) = c_List_Olist_ONil(_1689841))], (45371 ^ _779300) ^ [_1689891, _1689893] : [c_List_Oremdups(_1689891, _1689893) = c_List_Olist_ONil(_1689891), -(_1689893 = c_List_Olist_ONil(_1689891))], (45377 ^ _779300) ^ [_1689978, _1689980] : [_1689980 = c_List_Olist_ONil(_1689978), -(c_List_Oremdups(_1689978, _1689980) = c_List_Olist_ONil(_1689978))], (45383 ^ _779300) ^ [_1690086, _1690088, _1690090, _1690092] : [_1690086 = _1690088, -(hAPP(c_List_OremoveAll(_1690090, _1690086), hAPP(hAPP(c_List_Olist_OCons(_1690090), _1690088), _1690092)) = hAPP(c_List_OremoveAll(_1690090, _1690086), _1690092))], (45389 ^ _779300) ^ [_1690201, _1690203, _1690205, _1690207] : [-(_1690201 = _1690203), -(hAPP(c_List_OremoveAll(_1690205, _1690201), hAPP(hAPP(c_List_Olist_OCons(_1690205), _1690203), _1690207)) = hAPP(hAPP(c_List_Olist_OCons(_1690205), _1690203), hAPP(c_List_OremoveAll(_1690205, _1690201), _1690207)))], (45395 ^ _779300) ^ [_1690271, _1690273, _1690275, _1690277] : [-(hAPP(c_List_OremoveAll(_1690271, _1690273), hAPP(hAPP(c_List_Oappend(_1690271), _1690275), _1690277)) = hAPP(hAPP(c_List_Oappend(_1690271), hAPP(c_List_OremoveAll(_1690271, _1690273), _1690275)), hAPP(c_List_OremoveAll(_1690271, _1690273), _1690277)))], (45397 ^ _779300) ^ [_1690334, _1690336, _1690338, _1690340] : [-(c_List_Oremdups(_1690334, hAPP(hAPP(c_List_Omap(_1690336, _1690334), _1690338), c_List_Oremdups(_1690336, _1690340))) = c_List_Oremdups(_1690334, hAPP(hAPP(c_List_Omap(_1690336, _1690334), _1690338), _1690340)))], (45399 ^ _779300) ^ [_1690390, _1690392, _1690394] : [hBOOL(hAPP(c_List_Odistinct(_1690390), _1690392)), -(c_List_Oremove1(_1690390, _1690394, c_List_Oremdups(_1690390, _1690392)) = c_List_Oremdups(_1690390, c_List_Oremove1(_1690390, _1690394, _1690392)))], (45405 ^ _779300) ^ [_1690501, _1690503, _1690505] : [-(hBOOL(hAPP(hAPP(c_member(_1690501), _1690503), hAPP(c_List_Oset(_1690501), _1690505)))), -(hAPP(c_List_OremoveAll(_1690501, _1690503), _1690505) = _1690505)], (45411 ^ _779300) ^ [_1690557, _1690559, _1690561] : [hBOOL(hAPP(c_List_Odistinct(_1690557), _1690559)), -(c_List_Oremove1(_1690557, _1690561, _1690559) = hAPP(c_List_OremoveAll(_1690557, _1690561), _1690559))], (45417 ^ _779300) ^ [_1690676, _1690678, _1690680] : [hBOOL(hAPP(hAPP(c_member(_1690676), _1690678), hAPP(c_List_Oset(_1690676), _1690680))), -(c_List_Oremdups(_1690676, hAPP(hAPP(c_List_Olist_OCons(_1690676), _1690678), _1690680)) = c_List_Oremdups(_1690676, _1690680))], (45423 ^ _779300) ^ [_1690801, _1690803, _1690805] : [-(hBOOL(hAPP(hAPP(c_member(_1690801), _1690803), hAPP(c_List_Oset(_1690801), _1690805)))), -(c_List_Oremdups(_1690801, hAPP(hAPP(c_List_Olist_OCons(_1690801), _1690803), _1690805)) = hAPP(hAPP(c_List_Olist_OCons(_1690801), _1690803), c_List_Oremdups(_1690801, _1690805)))], (45429 ^ _779300) ^ [_1690875, _1690877] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690875)), c_List_Oremdups(_1690875, _1690877)) = hAPP(c_Finite__Set_Ocard(_1690875), hAPP(c_List_Oset(_1690875), _1690877)))], (45431 ^ _779300) ^ [_1690920, _1690922, _1690924, _1690926, _1690928] : [c_Fun_Oinj__on(_1690920, _1690922, _1690924, c_Orderings_Otop__class_Otop(tc_fun(_1690920, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1690920, _1690922), _1690924), hAPP(c_List_OremoveAll(_1690920, _1690926), _1690928)) = hAPP(c_List_OremoveAll(_1690922, hAPP(_1690924, _1690926)), hAPP(hAPP(c_List_Omap(_1690920, _1690922), _1690924), _1690928)))], (45437 ^ _779300) ^ [_1691083, _1691085, _1691087] : [-(hAPP(c_List_Oset(_1691083), hAPP(c_List_OremoveAll(_1691083, _1691085), _1691087)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1691083, tc_HOL_Obool)), hAPP(c_List_Oset(_1691083), _1691087)), hAPP(hAPP(c_Set_Oinsert(_1691083), _1691085), c_Orderings_Obot__class_Obot(tc_fun(_1691083, tc_HOL_Obool)))))], (45439 ^ _779300) ^ [_1691150, _1691152] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691150)), c_List_Oremdups(_1691150, c_List_Oconcat(_1691150, _1691152))) = hAPP(c_Finite__Set_Ocard(_1691150), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1691150), tc_fun(_1691150, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1691150)), _1691152)), c_List_Oset(_1691150))))], (45441 ^ _779300) ^ [_1691216, _1691218] : [class_Orderings_Olinorder(_1691216), -(c_List_Olinorder__class_Osorted__list__of__set(_1691216, hAPP(c_List_Oset(_1691216), _1691218)) = c_List_Olinorder__class_Osort__key(_1691216, _1691216, c_COMBI(_1691216), c_List_Oremdups(_1691216, _1691218)))], (45447 ^ _779300) ^ [_1691327, _1691329] : [-(c_List_Oconcat(_1691327, _1691329) = hAPP(c_List_Ofoldl(tc_List_Olist(_1691327), tc_List_Olist(_1691327), c_List_Oappend(_1691327), c_List_Olist_ONil(_1691327)), _1691329))], (45449 ^ _779300) ^ [_1691371, _1691373, _1691375] : [class_Orderings_Olinorder(_1691371), -(c_List_Olinorder__class_Osort__key(_1691373, _1691371, _1691375, c_List_Olist_ONil(_1691373)) = c_List_Olist_ONil(_1691373))], (45455 ^ _779300) ^ [_1691466, _1691468, _1691470] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1691466), tc_List_Olist(_1691466), c_List_Oappend(_1691466), _1691468), _1691470) = hAPP(hAPP(c_List_Oappend(_1691466), _1691468), c_List_Oconcat(_1691466, _1691470)))], (45457 ^ _779300) ^ [_1691518, _1691520, _1691522, _1691524] : [class_Orderings_Olinorder(_1691518), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691520)), c_List_Olinorder__class_Osort__key(_1691520, _1691518, _1691522, _1691524)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691520)), _1691524))], (45463 ^ _779300) ^ [_1691635, _1691637, _1691639, _1691641] : [class_Orderings_Olinorder(_1691635), -(hAPP(c_List_Oset(_1691637), c_List_Olinorder__class_Osort__key(_1691637, _1691635, _1691639, _1691641)) = hAPP(c_List_Oset(_1691637), _1691641))], (45469 ^ _779300) ^ [_1691744, _1691746, _1691748, _1691750] : [class_Orderings_Olinorder(_1691744), 45472 ^ _779300 : [(45473 ^ _779300) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1691746), c_List_Olinorder__class_Osort__key(_1691746, _1691744, _1691748, _1691750))), -(hBOOL(hAPP(c_List_Odistinct(_1691746), _1691750)))], (45479 ^ _779300) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1691746), _1691750)), -(hBOOL(hAPP(c_List_Odistinct(_1691746), c_List_Olinorder__class_Osort__key(_1691746, _1691744, _1691748, _1691750))))]]], (45485 ^ _779300) ^ [_1692000] : [-(c_List_Oconcat(_1692000, c_List_Olist_ONil(tc_List_Olist(_1692000))) = c_List_Olist_ONil(_1692000))], (45487 ^ _779300) ^ [_1692032, _1692034, _1692036] : [-(c_List_Oconcat(_1692032, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1692032)), _1692034), _1692036)) = hAPP(hAPP(c_List_Oappend(_1692032), _1692034), c_List_Oconcat(_1692032, _1692036)))], (45499 ^ _779300) ^ [_1692304, _1692306] : [45501 ^ _779300 : [(45502 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692304)), 45500 ^ [_1692304, _1692306]), hAPP(c_List_Oset(tc_List_Olist(_1692304)), _1692306))))], (45504 ^ _779300) ^ [] : [45500 ^ [_1692304, _1692306] = c_List_Olist_ONil(_1692304)]], -(c_List_Olist_ONil(_1692304) = c_List_Oconcat(_1692304, _1692306))], (45489 ^ _779300) ^ [_1692098, _1692100] : [c_List_Olist_ONil(_1692098) = c_List_Oconcat(_1692098, _1692100), 45492 ^ _779300 : [(45493 ^ _779300) ^ [_1692189] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692098)), _1692189), hAPP(c_List_Oset(tc_List_Olist(_1692098)), _1692100))), -(_1692189 = c_List_Olist_ONil(_1692098))]]], (45518 ^ _779300) ^ [_1692716, _1692718] : [45520 ^ _779300 : [(45521 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692716)), 45519 ^ [_1692716, _1692718]), hAPP(c_List_Oset(tc_List_Olist(_1692716)), _1692718))))], (45523 ^ _779300) ^ [] : [45519 ^ [_1692716, _1692718] = c_List_Olist_ONil(_1692716)]], -(c_List_Oconcat(_1692716, _1692718) = c_List_Olist_ONil(_1692716))], (45508 ^ _779300) ^ [_1692510, _1692512] : [c_List_Oconcat(_1692510, _1692512) = c_List_Olist_ONil(_1692510), 45511 ^ _779300 : [(45512 ^ _779300) ^ [_1692601] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692510)), _1692601), hAPP(c_List_Oset(tc_List_Olist(_1692510)), _1692512))), -(_1692601 = c_List_Olist_ONil(_1692510))]]], (45527 ^ _779300) ^ [_1692907, _1692909, _1692911, _1692913] : [-(hAPP(hAPP(c_List_Omap(_1692907, _1692909), _1692911), c_List_Oconcat(_1692907, _1692913)) = c_List_Oconcat(_1692909, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692907), tc_List_Olist(_1692909)), hAPP(c_List_Omap(_1692907, _1692909), _1692911)), _1692913)))], (45529 ^ _779300) ^ [_1692970, _1692972] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692970)), c_List_Oconcat(_1692970, _1692972)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692970), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1692970))), _1692972)))], (45531 ^ _779300) ^ [_1693023, _1693025] : [-(hAPP(c_List_Oset(_1693023), c_List_Oconcat(_1693023, _1693025)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1693023), tc_fun(_1693023, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1693023)), _1693025)), c_List_Oset(_1693023)))], (45533 ^ _779300) ^ [_1693079, _1693081, _1693083, _1693085, _1693087] : [class_Orderings_Olinorder(_1693079), -(c_List_Olinorder__class_Osort__key(_1693081, _1693079, _1693083, hAPP(hAPP(c_List_Olist_OCons(_1693081), _1693085), _1693087)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1693081, _1693079, _1693083), _1693085), c_List_Olinorder__class_Osort__key(_1693081, _1693079, _1693083, _1693087)))], (45539 ^ _779300) ^ [_1693216, _1693218, _1693220] : [-(c_List_Oconcat(_1693216, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1693216)), _1693218), _1693220)) = hAPP(hAPP(c_List_Oappend(_1693216), c_List_Oconcat(_1693216, _1693218)), c_List_Oconcat(_1693216, _1693220)))], (45541 ^ _779300) ^ [_1693270, _1693272] : [class_Orderings_Olinorder(_1693270), -(c_List_Olinorder__class_Osort__key(_1693270, _1693270, c_COMBI(_1693270), _1693272) = hAPP(c_List_Ofoldl(tc_List_Olist(_1693270), _1693270, hAPP(c_COMBC(_1693270, tc_List_Olist(_1693270), tc_List_Olist(_1693270)), c_List_Olinorder__class_Oinsort__key(_1693270, _1693270, c_COMBI(_1693270))), c_List_Olist_ONil(_1693270)), _1693272))], (45547 ^ _779300) ^ [_1693417, _1693419, _1693421] : [c_List_Oconcat(_1693417, _1693419) = c_List_Oconcat(_1693417, _1693421), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693417))), _1693419) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693417))), _1693421), 45557 ^ _779300 : [(45558 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693417), tc_List_Olist(_1693417))), 45556 ^ [_1693417, _1693419, _1693421]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1693417), tc_List_Olist(_1693417))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1693417), tc_List_Olist(_1693417)), _1693419), _1693421)))))], (45560 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1693417), tc_List_Olist(_1693417), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1693417), tc_fun(tc_List_Olist(_1693417), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693417), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1693417), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693417), tc_HOL_Obool)), tc_List_Olist(_1693417)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1693417))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1693417)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1693417))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1693417)))), 45556 ^ [_1693417, _1693419, _1693421]))]], -(_1693419 = _1693421)], (45564 ^ _779300) ^ [_1694058, _1694060, _1694062] : [45566 ^ _779300 : [(45567 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694058), tc_List_Olist(_1694058))), 45565 ^ [_1694058, _1694060, _1694062]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1694058), tc_List_Olist(_1694058))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1694058), tc_List_Olist(_1694058)), _1694060), _1694062)))))], (45569 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1694058), tc_List_Olist(_1694058), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694058), tc_fun(tc_List_Olist(_1694058), tc_Nat_Onat), tc_fun(tc_List_Olist(_1694058), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1694058), tc_Nat_Onat), tc_fun(tc_List_Olist(_1694058), tc_HOL_Obool)), tc_List_Olist(_1694058)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1694058))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1694058)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1694058))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1694058)))), 45565 ^ [_1694058, _1694060, _1694062]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694058))), _1694060) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694058))), _1694062), 45574 ^ _779300 : [(45575 ^ _779300) ^ [] : [c_List_Oconcat(_1694058, _1694060) = c_List_Oconcat(_1694058, _1694062), -(_1694060 = _1694062)], (45581 ^ _779300) ^ [] : [_1694060 = _1694062, -(c_List_Oconcat(_1694058, _1694060) = c_List_Oconcat(_1694058, _1694062))]]], (45587 ^ _779300) ^ [_1694785, _1694787, _1694789, _1694791] : [-(c_List_Oconcat(_1694785, hAPP(hAPP(c_List_Omap(_1694787, tc_List_Olist(_1694785)), hAPP(hAPP(c_COMBC(_1694787, tc_List_Olist(_1694785), tc_List_Olist(_1694785)), hAPP(hAPP(c_COMBB(_1694785, tc_fun(tc_List_Olist(_1694785), tc_List_Olist(_1694785)), _1694787), c_List_Olist_OCons(_1694785)), _1694789)), c_List_Olist_ONil(_1694785))), _1694791)) = hAPP(hAPP(c_List_Omap(_1694787, _1694785), _1694789), _1694791))], (45589 ^ _779300) ^ [_1694872, _1694874, _1694876] : [-(c_Enum_On__lists(_1694872, hAPP(c_Nat_OSuc, _1694874), _1694876) = c_List_Oconcat(tc_List_Olist(_1694872), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694872), tc_List_Olist(tc_List_Olist(_1694872))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694872), tc_List_Olist(_1694872), tc_List_Olist(tc_List_Olist(_1694872))), hAPP(hAPP(c_COMBB(tc_fun(_1694872, tc_List_Olist(_1694872)), tc_fun(tc_List_Olist(_1694872), tc_List_Olist(tc_List_Olist(_1694872))), tc_List_Olist(_1694872)), c_List_Omap(_1694872, tc_List_Olist(_1694872))), hAPP(c_COMBC(_1694872, tc_List_Olist(_1694872), tc_List_Olist(_1694872)), c_List_Olist_OCons(_1694872)))), _1694876)), c_Enum_On__lists(_1694872, _1694874, _1694876))))], (45591 ^ _779300) ^ [_1694992, _1694994, _1694996, _1694998] : [-(c_List_Otranspose(_1694992, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1694992)), hAPP(hAPP(c_List_Olist_OCons(_1694992), _1694994), _1694996)), _1694998)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1694992)), hAPP(hAPP(c_List_Olist_OCons(_1694992), _1694994), c_List_Oconcat(_1694992, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694992), tc_List_Olist(_1694992)), c_List_Olist_Olist__case(tc_List_Olist(_1694992), _1694992, c_List_Olist_ONil(_1694992), hAPP(hAPP(c_COMBB(tc_List_Olist(_1694992), tc_fun(tc_List_Olist(_1694992), tc_List_Olist(_1694992)), _1694992), c_COMBK(tc_List_Olist(_1694992), tc_List_Olist(_1694992))), hAPP(hAPP(c_COMBC(_1694992, tc_List_Olist(_1694992), tc_List_Olist(_1694992)), c_List_Olist_OCons(_1694992)), c_List_Olist_ONil(_1694992))))), _1694998)))), c_List_Otranspose(_1694992, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1694992)), _1694996), c_List_Oconcat(tc_List_Olist(_1694992), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694992), tc_List_Olist(tc_List_Olist(_1694992))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1694992)), _1694992, c_List_Olist_ONil(tc_List_Olist(_1694992)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1694992), tc_List_Olist(tc_List_Olist(_1694992))), _1694992), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694992), tc_List_Olist(tc_List_Olist(_1694992)), tc_List_Olist(tc_List_Olist(_1694992))), c_List_Olist_OCons(tc_List_Olist(_1694992))), c_List_Olist_ONil(tc_List_Olist(_1694992)))))), _1694998))))))], (45593 ^ _779300) ^ [_1695218, _1695220] : [-(c_List_Oconcat(_1695218, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695218), tc_List_Olist(_1695218)), c_List_Olist_Olist__case(tc_List_Olist(_1695218), _1695218, c_List_Olist_ONil(_1695218), hAPP(hAPP(c_COMBB(tc_List_Olist(_1695218), tc_fun(tc_List_Olist(_1695218), tc_List_Olist(_1695218)), _1695218), c_COMBK(tc_List_Olist(_1695218), tc_List_Olist(_1695218))), hAPP(hAPP(c_COMBC(_1695218, tc_List_Olist(_1695218), tc_List_Olist(_1695218)), c_List_Olist_OCons(_1695218)), c_List_Olist_ONil(_1695218))))), _1695220)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695218), _1695218), c_List_Ohd(_1695218)), hAPP(c_List_Ofilter(tc_List_Olist(_1695218), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1695218)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695218), tc_List_Olist(_1695218), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1695218)))), _1695220)))], (45595 ^ _779300) ^ [_1695361, _1695363, _1695365] : [-(hAPP(c_List_Ofilter(_1695361, _1695363), c_List_Oconcat(_1695361, _1695365)) = c_List_Oconcat(_1695361, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695361), tc_List_Olist(_1695361)), c_List_Ofilter(_1695361, _1695363)), _1695365)))], (45597 ^ _779300) ^ [_1695416, _1695418, _1695420, _1695422, _1695424] : [class_Orderings_Olinorder(_1695416), -(hAPP(c_List_Ofilter(_1695418, _1695420), c_List_Olinorder__class_Osort__key(_1695418, _1695416, _1695422, _1695424)) = c_List_Olinorder__class_Osort__key(_1695418, _1695416, _1695422, hAPP(c_List_Ofilter(_1695418, _1695420), _1695424)))], (45603 ^ _779300) ^ [_1695541, _1695543, _1695545] : [hBOOL(hAPP(c_List_Odistinct(_1695541), _1695543)), -(hBOOL(hAPP(c_List_Odistinct(_1695541), hAPP(c_List_Ofilter(_1695541, _1695545), _1695543))))], (45609 ^ _779300) ^ [_1695648, _1695650, _1695652] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695648)), hAPP(c_List_Ofilter(_1695648, _1695650), _1695652))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695648)), hAPP(c_List_Ofilter(_1695648, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1695648), c_fNot), _1695650)), _1695652))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695648)), _1695652))], (45611 ^ _779300) ^ [_1695724, _1695726, _1695728] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1695724, tc_HOL_Obool)), hAPP(c_List_Oset(_1695724), hAPP(c_List_Ofilter(_1695724, _1695726), _1695728))), hAPP(c_List_Oset(_1695724), _1695728))))], (45623 ^ _779300) ^ [_1695995, _1695997, _1695999] : [45625 ^ _779300 : [(45626 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1695995), 45624 ^ [_1695995, _1695997, _1695999]), hAPP(c_List_Oset(_1695995), _1695999))))], (45628 ^ _779300) ^ [] : [hBOOL(hAPP(_1695997, 45624 ^ [_1695995, _1695997, _1695999]))]], -(hAPP(c_List_Ofilter(_1695995, _1695997), _1695999) = _1695999)], (45613 ^ _779300) ^ [_1695795, _1695797, _1695799] : [hAPP(c_List_Ofilter(_1695795, _1695797), _1695799) = _1695799, 45616 ^ _779300 : [(45617 ^ _779300) ^ [_1695886] : [hBOOL(hAPP(hAPP(c_member(_1695795), _1695886), hAPP(c_List_Oset(_1695795), _1695799))), -(hBOOL(hAPP(_1695797, _1695886)))]]], (45632 ^ _779300) ^ [_1696187, _1696189, _1696191] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696187)), hAPP(c_List_Ofilter(_1696187, _1696189), _1696191))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696187)), _1696191))))], (45634 ^ _779300) ^ [_1696239, _1696241, _1696243] : [-(c_List_Opartition(_1696239, _1696241, _1696243) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1696239), tc_List_Olist(_1696239)), hAPP(c_List_Ofilter(_1696239, _1696241), _1696243)), hAPP(c_List_Ofilter(_1696239, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1696239, c_fNot), _1696241)), _1696243)))], (45636 ^ _779300) ^ [_1696303, _1696305, _1696307] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1696303), tc_List_Olist(_1696303)), c_List_Opartition(_1696303, _1696305, _1696307)) = hAPP(c_List_Ofilter(_1696303, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1696303, c_fNot), _1696305)), _1696307))], (45638 ^ _779300) ^ [_1696358, _1696360, _1696362] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1696358), tc_List_Olist(_1696358)), c_List_Opartition(_1696358, _1696360, _1696362)) = hAPP(c_List_Ofilter(_1696358, _1696360), _1696362))], (45640 ^ _779300) ^ [_1696405, _1696407, _1696409, _1696411] : [-(hAPP(c_List_Ofilter(_1696405, _1696407), hAPP(c_List_Ofilter(_1696405, _1696409), _1696411)) = hAPP(c_List_Ofilter(_1696405, hAPP(hAPP(c_COMBS(_1696405, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1696405), c_fconj), _1696409)), _1696407)), _1696411))], (45642 ^ _779300) ^ [_1696468, _1696470, _1696472, _1696474] : [-(hBOOL(hAPP(_1696468, _1696470))), -(c_List_Oremove1(_1696472, _1696470, hAPP(c_List_Ofilter(_1696472, _1696468), _1696474)) = hAPP(c_List_Ofilter(_1696472, _1696468), _1696474))], (45648 ^ _779300) ^ [_1696526, _1696528, _1696530, _1696532] : [-(hAPP(c_List_Ofilter(_1696526, _1696528), c_List_Oremove1(_1696526, _1696530, _1696532)) = c_List_Oremove1(_1696526, _1696530, hAPP(c_List_Ofilter(_1696526, _1696528), _1696532)))], (45650 ^ _779300) ^ [_1696575, _1696577, _1696579, _1696581, _1696583, _1696585] : [class_Orderings_Olinorder(_1696575), -(hBOOL(hAPP(_1696577, _1696579))), -(hAPP(c_List_Ofilter(_1696581, _1696577), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696581, _1696575, _1696583), _1696579), _1696585)) = hAPP(c_List_Ofilter(_1696581, _1696577), _1696585))], (45660 ^ _779300) ^ [_1696721, _1696723, _1696725, _1696727, _1696729] : [-(hAPP(c_List_Ofilter(_1696721, _1696723), hAPP(hAPP(c_List_Omap(_1696725, _1696721), _1696727), _1696729)) = hAPP(hAPP(c_List_Omap(_1696725, _1696721), _1696727), hAPP(c_List_Ofilter(_1696725, hAPP(c_Fun_Ocomp(_1696721, tc_HOL_Obool, _1696725, _1696723), _1696727)), _1696729)))], (45662 ^ _779300) ^ [_1696790] : [-(c_List_Otranspose(_1696790, c_List_Olist_ONil(tc_List_Olist(_1696790))) = c_List_Olist_ONil(tc_List_Olist(_1696790)))], (45664 ^ _779300) ^ [_1696824, _1696826] : [-(hAPP(c_List_Ofilter(_1696824, _1696826), c_List_Olist_ONil(_1696824)) = c_List_Olist_ONil(_1696824))], (45666 ^ _779300) ^ [_1696874, _1696876, _1696878, _1696880] : [hBOOL(hAPP(_1696874, _1696876)), -(hAPP(c_List_Ofilter(_1696878, _1696874), hAPP(hAPP(c_List_Olist_OCons(_1696878), _1696876), _1696880)) = hAPP(hAPP(c_List_Olist_OCons(_1696878), _1696876), hAPP(c_List_Ofilter(_1696878, _1696874), _1696880)))], (45672 ^ _779300) ^ [_1697009, _1697011, _1697013, _1697015] : [-(hBOOL(hAPP(_1697009, _1697011))), -(hAPP(c_List_Ofilter(_1697013, _1697009), hAPP(hAPP(c_List_Olist_OCons(_1697013), _1697011), _1697015)) = hAPP(c_List_Ofilter(_1697013, _1697009), _1697015))], (45678 ^ _779300) ^ [_1697073, _1697075, _1697077, _1697079] : [-(hAPP(c_List_Ofilter(_1697073, _1697075), hAPP(hAPP(c_List_Oappend(_1697073), _1697077), _1697079)) = hAPP(hAPP(c_List_Oappend(_1697073), hAPP(c_List_Ofilter(_1697073, _1697075), _1697077)), hAPP(c_List_Ofilter(_1697073, _1697075), _1697079)))], (45690 ^ _779300) ^ [_1697359, _1697361, _1697363] : [45692 ^ _779300 : [(45693 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1697359), 45691 ^ [_1697359, _1697361, _1697363]), hAPP(c_List_Oset(_1697359), _1697363))))], (45695 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1697361, 45691 ^ [_1697359, _1697361, _1697363])))]], -(hAPP(c_List_Ofilter(_1697359, _1697361), _1697363) = c_List_Olist_ONil(_1697359))], (45680 ^ _779300) ^ [_1697154, _1697156, _1697158] : [hAPP(c_List_Ofilter(_1697154, _1697156), _1697158) = c_List_Olist_ONil(_1697154), 45683 ^ _779300 : [(45684 ^ _779300) ^ [_1697251] : [hBOOL(hAPP(hAPP(c_member(_1697154), _1697251), hAPP(c_List_Oset(_1697154), _1697158))), hBOOL(hAPP(_1697156, _1697251))]]], (45699 ^ _779300) ^ [_1697476, _1697478, _1697480, _1697482, _1697484] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697476)), hAPP(c_List_Ofilter(_1697476, _1697478), hAPP(hAPP(c_List_Omap(_1697480, _1697476), _1697482), _1697484))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697480)), hAPP(c_List_Ofilter(_1697480, hAPP(c_Fun_Ocomp(_1697476, tc_HOL_Obool, _1697480, _1697478), _1697482)), _1697484)))], (45701 ^ _779300) ^ [_1697546, _1697548, _1697550, _1697552] : [-(hBOOL(hAPP(_1697546, _1697548))), -(hAPP(c_List_OremoveAll(_1697550, _1697548), hAPP(c_List_Ofilter(_1697550, _1697546), _1697552)) = hAPP(c_List_Ofilter(_1697550, _1697546), _1697552))], (45707 ^ _779300) ^ [_1697606, _1697608, _1697610] : [-(c_List_Oremdups(_1697606, hAPP(c_List_Ofilter(_1697606, _1697608), _1697610)) = hAPP(c_List_Ofilter(_1697606, _1697608), c_List_Oremdups(_1697606, _1697610)))], (45709 ^ _779300) ^ [_1697651, _1697653] : [-(c_List_OremoveAll(_1697651, _1697653) = c_List_Ofilter(_1697651, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1697651), c_fNot), hAPP(c_fequal, _1697653))))], (45711 ^ _779300) ^ [_1697695, _1697697] : [-(c_List_Otranspose(_1697695, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1697695)), c_List_Olist_ONil(_1697695)), _1697697)) = c_List_Otranspose(_1697695, _1697697))], (45713 ^ _779300) ^ [_1697738, _1697740, _1697742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697738), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1697740))), c_List_Otranspose(_1697740, _1697742)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1697740)), c_List_Otranspose(_1697740, _1697742)), _1697738) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1697740), _1697740), hAPP(hAPP(c_COMBC(tc_List_Olist(_1697740), tc_Nat_Onat, _1697740), c_List_Onth(_1697740)), _1697738)), hAPP(c_List_Ofilter(tc_List_Olist(_1697740), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1697740)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697738)), c_Nat_Osize__class_Osize(tc_List_Olist(_1697740)))), _1697742)))], (45719 ^ _779300) ^ [_1697981, _1697983, _1697985, _1697987] : [-(c_List_Otranspose(_1697981, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1697983), tc_List_Olist(_1697981)), hAPP(c_List_Omap(_1697983, _1697981), _1697985)), _1697987)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1697983), tc_List_Olist(_1697981)), hAPP(c_List_Omap(_1697983, _1697981), _1697985)), c_List_Otranspose(_1697983, _1697987)))], (45721 ^ _779300) ^ [_1698054, _1698056, _1698058] : [-(hAPP(c_List_Oset(_1698054), hAPP(c_List_Ofilter(_1698054, _1698056), _1698058)) = hAPP(c_Set_OCollect(_1698054), hAPP(hAPP(c_COMBS(_1698054, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1698054), c_fconj), hAPP(hAPP(c_COMBC(_1698054, tc_fun(_1698054, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698054)), hAPP(c_List_Oset(_1698054), _1698058)))), _1698056)))], (45723 ^ _779300) ^ [_1698137, _1698139, _1698141, _1698143] : [hBOOL(hAPP(hAPP(c_member(_1698137), _1698139), hAPP(c_List_Oset(_1698137), _1698141))), -(hBOOL(hAPP(_1698143, _1698139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698137)), hAPP(c_List_Ofilter(_1698137, _1698143), _1698141))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698137)), _1698141))))], (45733 ^ _779300) ^ [_1698311, _1698313, _1698315] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1698311, tc_HOL_Obool)), hAPP(c_List_Oset(_1698311), _1698313)), hAPP(hAPP(c_Set_Oinsert(_1698311), _1698315), c_Orderings_Obot__class_Obot(tc_fun(_1698311, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1698311), hAPP(c_List_Ofilter(_1698311, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698311), c_fNot), hAPP(hAPP(c_COMBC(_1698311, _1698311, tc_HOL_Obool), c_fequal), _1698315))), _1698313)))], (45735 ^ _779300) ^ [_1698398, _1698400, _1698402] : [hBOOL(hAPP(c_List_Odistinct(_1698398), _1698400)), -(hAPP(c_List_Ofilter(_1698398, hAPP(hAPP(c_COMBC(_1698398, tc_fun(_1698398, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698398)), hAPP(c_List_Oset(_1698398), c_List_Osublist(_1698398, _1698400, _1698402)))), _1698400) = c_List_Osublist(_1698398, _1698400, _1698402))], (45751 ^ _779300) ^ [_1698778, _1698780] : [45753 ^ _779300 : [(45754 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698778)), 45752 ^ [_1698778, _1698780]), hAPP(c_List_Oset(tc_List_Olist(_1698778)), _1698780))))], (45756 ^ _779300) ^ [] : [45752 ^ [_1698778, _1698780] = c_List_Olist_ONil(_1698778)]], -(c_List_Otranspose(_1698778, _1698780) = c_List_Olist_ONil(tc_List_Olist(_1698778)))], (45741 ^ _779300) ^ [_1698568, _1698570] : [c_List_Otranspose(_1698568, _1698570) = c_List_Olist_ONil(tc_List_Olist(_1698568)), 45744 ^ _779300 : [(45745 ^ _779300) ^ [_1698663] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698568)), _1698663), hAPP(c_List_Oset(tc_List_Olist(_1698568)), _1698570))), -(_1698663 = c_List_Olist_ONil(_1698568))]]], (45760 ^ _779300) ^ [_1698973, _1698975, _1698977] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698973)), hAPP(c_List_Ofilter(_1698973, _1698975), _1698977)) = 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(_1698973)), _1698977)))), hAPP(hAPP(c_COMBB(_1698973, tc_HOL_Obool, tc_Nat_Onat), _1698975), hAPP(c_List_Onth(_1698973), _1698977))))))], (45762 ^ _779300) ^ [_1699053, _1699055] : [-(c_List_Oconcat(tc_List_Olist(_1699053), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699053), tc_List_Olist(tc_List_Olist(_1699053))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1699053)), _1699053, c_List_Olist_ONil(tc_List_Olist(_1699053)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1699053), tc_List_Olist(tc_List_Olist(_1699053))), _1699053), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699053), tc_List_Olist(tc_List_Olist(_1699053)), tc_List_Olist(tc_List_Olist(_1699053))), c_List_Olist_OCons(tc_List_Olist(_1699053))), c_List_Olist_ONil(tc_List_Olist(_1699053)))))), _1699055)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699053), tc_List_Olist(_1699053)), c_List_Otl(_1699053)), hAPP(c_List_Ofilter(tc_List_Olist(_1699053), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1699053)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699053), tc_List_Olist(_1699053), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1699053)))), _1699055)))], (45764 ^ _779300) ^ [_1699205, _1699207, _1699209, _1699211] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1699205)), c_List_Otranspose__rel(_1699205)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699205)), hAPP(hAPP(c_List_Olist_OCons(_1699205), _1699207), _1699209)), _1699211))), -(c_List_Otranspose(_1699205, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699205)), hAPP(hAPP(c_List_Olist_OCons(_1699205), _1699207), _1699209)), _1699211)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699205)), hAPP(hAPP(c_List_Olist_OCons(_1699205), _1699207), c_List_Oconcat(_1699205, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699205), tc_List_Olist(_1699205)), c_List_Olist_Olist__case(tc_List_Olist(_1699205), _1699205, c_List_Olist_ONil(_1699205), hAPP(hAPP(c_COMBB(tc_List_Olist(_1699205), tc_fun(tc_List_Olist(_1699205), tc_List_Olist(_1699205)), _1699205), c_COMBK(tc_List_Olist(_1699205), tc_List_Olist(_1699205))), hAPP(hAPP(c_COMBC(_1699205, tc_List_Olist(_1699205), tc_List_Olist(_1699205)), c_List_Olist_OCons(_1699205)), c_List_Olist_ONil(_1699205))))), _1699211)))), c_List_Otranspose(_1699205, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699205)), _1699209), c_List_Oconcat(tc_List_Olist(_1699205), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699205), tc_List_Olist(tc_List_Olist(_1699205))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1699205)), _1699205, c_List_Olist_ONil(tc_List_Olist(_1699205)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1699205), tc_List_Olist(tc_List_Olist(_1699205))), _1699205), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699205), tc_List_Olist(tc_List_Olist(_1699205)), tc_List_Olist(tc_List_Olist(_1699205))), c_List_Olist_OCons(tc_List_Olist(_1699205))), c_List_Olist_ONil(tc_List_Olist(_1699205)))))), _1699211))))))], (45770 ^ _779300) ^ [_1699738, _1699740] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1699738)), c_List_Otranspose__rel(_1699738)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699738)), c_List_Olist_ONil(_1699738)), _1699740))), -(c_List_Otranspose(_1699738, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699738)), c_List_Olist_ONil(_1699738)), _1699740)) = c_List_Otranspose(_1699738, _1699740))], (45776 ^ _779300) ^ [_1699897, _1699899, _1699901, _1699903] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1699897, tc_Nat_Onat), _1699897), c_Product__Type_Ofst(_1699897, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1699897, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1699897, tc_Nat_Onat)), _1699899), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1699897, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1699897, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1699897, tc_Nat_Onat), _1699901), _1699903))) = hAPP(hAPP(c_List_Omap(tc_prod(_1699897, tc_Nat_Onat), _1699897), c_Product__Type_Ofst(_1699897, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1699897, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1699897, tc_Nat_Onat)), _1699899), c_Product__Type_Osnd(_1699897, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1699897, tc_Nat_Onat), _1699901), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1699903)))))], (45778 ^ _779300) ^ [_1700040, _1700042] : [-(c_Random_Oselect__weight(_1700040, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1700040), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1700040, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1700040, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1700040)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1700042)) = c_Random_Oselect__weight(_1700040, _1700042))], (45780 ^ _779300) ^ [_1700103, _1700105] : [-(c_Random_Opick(_1700103, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1700103), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1700103, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1700103, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1700103)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1700105)) = c_Random_Opick(_1700103, _1700105))], (45782 ^ _779300) ^ [_1700166] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1700166)), c_List_Otranspose__rel(_1700166)), c_List_Olist_ONil(tc_List_Olist(_1700166)))), -(c_List_Otranspose(_1700166, c_List_Olist_ONil(tc_List_Olist(_1700166))) = c_List_Olist_ONil(tc_List_Olist(_1700166)))], (45788 ^ _779300) ^ [_1700293, _1700295] : [-(c_List_Ofoldr(tc_List_Olist(_1700293), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700293)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700293))), c_List_Otranspose(_1700293, _1700295), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1700293))), hAPP(c_List_Ofilter(tc_List_Olist(_1700293), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700293)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700293), tc_List_Olist(_1700293), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700293)))), _1700295)))], (45790 ^ _779300) ^ [_1700390, _1700392, _1700394, _1700396] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700390)), _1700392))), c_List_Ofoldr(tc_List_Olist(_1700394), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700394)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700394))), _1700396, 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(_1700390)), _1700392)), c_List_Ofoldr(tc_List_Olist(_1700394), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700394)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700394), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700394)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700394)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1700394), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700394)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700394), tc_List_Olist(_1700394), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700394)))), _1700396), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (45792 ^ _779300) ^ [_1700559, _1700561, _1700563, _1700565] : [-(c_List_Ofoldr(_1700559, _1700561, _1700563, c_List_Olist_ONil(_1700559), _1700565) = _1700565)], (45794 ^ _779300) ^ [_1700596, _1700598, _1700600, _1700602, _1700604, _1700606] : [-(c_List_Ofoldr(_1700596, _1700598, _1700600, hAPP(hAPP(c_List_Olist_OCons(_1700596), _1700602), _1700604), _1700606) = hAPP(hAPP(_1700600, _1700602), c_List_Ofoldr(_1700596, _1700598, _1700600, _1700604, _1700606)))], (45796 ^ _779300) ^ [_1700655, _1700657, _1700659, _1700661, _1700663, _1700665] : [-(c_List_Ofoldr(_1700655, _1700657, _1700659, hAPP(hAPP(c_List_Oappend(_1700655), _1700661), _1700663), _1700665) = c_List_Ofoldr(_1700655, _1700657, _1700659, _1700661, c_List_Ofoldr(_1700655, _1700657, _1700659, _1700663, _1700665)))], (45798 ^ _779300) ^ [_1700714, _1700716, _1700718] : [class_Groups_Oab__semigroup__add(_1700714), -(c_List_Ofoldr(_1700714, _1700714, c_Groups_Oplus__class_Oplus(_1700714), _1700716, _1700718) = hAPP(c_List_Ofoldl(_1700714, _1700714, c_Groups_Oplus__class_Oplus(_1700714), _1700718), _1700716))], (45804 ^ _779300) ^ [_1700827, _1700829, _1700831, _1700833, _1700835, _1700837, _1700839] : [-(c_List_Ofoldr(_1700827, _1700829, _1700831, hAPP(hAPP(c_List_Omap(_1700833, _1700827), _1700835), _1700837), _1700839) = c_List_Ofoldr(_1700833, _1700829, hAPP(c_Fun_Ocomp(_1700827, tc_fun(_1700829, _1700829), _1700833, _1700831), _1700835), _1700837, _1700839))], (45806 ^ _779300) ^ [_1700894, _1700896, _1700898] : [class_Groups_Omonoid__add(_1700894), -(hAPP(c_List_Ofoldl(_1700894, _1700894, c_Groups_Oplus__class_Oplus(_1700894), _1700896), _1700898) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1700894), _1700896), c_List_Ofoldr(_1700894, _1700894, c_Groups_Oplus__class_Oplus(_1700894), _1700898, c_Groups_Ozero__class_Ozero(_1700894))))], (45812 ^ _779300) ^ [_1701027, _1701029] : [class_Groups_Omonoid__add(_1701027), -(hAPP(c_List_Ofoldl(_1701027, _1701027, c_Groups_Oplus__class_Oplus(_1701027), c_Groups_Ozero__class_Ozero(_1701027)), _1701029) = c_List_Ofoldr(_1701027, _1701027, c_Groups_Oplus__class_Oplus(_1701027), _1701029, c_Groups_Ozero__class_Ozero(_1701027)))], (45818 ^ _779300) ^ [_1701146, _1701148] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1701146))), c_List_Otranspose(_1701146, _1701148)) = c_List_Ofoldr(tc_List_Olist(_1701146), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1701146)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1701146))), _1701148, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45820 ^ _779300) ^ [_1701207, _1701209, _1701211] : [-(c_List_Osublist(_1701207, _1701209, _1701211) = hAPP(hAPP(c_List_Omap(tc_prod(_1701207, tc_Nat_Onat), _1701207), c_Product__Type_Ofst(_1701207, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701207, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701207, 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(_1701207, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701207, tc_Nat_Onat))), _1701211)), hAPP(hAPP(c_List_Ozip(_1701207, tc_Nat_Onat), _1701209), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701207)), _1701209))))))], (45822 ^ _779300) ^ [_1701310, _1701312, _1701314, _1701316] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1701310, tc_Nat_Onat), _1701310), c_Product__Type_Ofst(_1701310, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701310, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701310, 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(_1701310, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701310, tc_Nat_Onat))), _1701312)), hAPP(hAPP(c_List_Ozip(_1701310, tc_Nat_Onat), _1701314), c_List_Oupt(_1701316, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701316), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701310)), _1701314)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1701310, tc_Nat_Onat), _1701310), c_Product__Type_Ofst(_1701310, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701310, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701310, 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(_1701310, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1701310, 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(_1701310, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1701310, tc_Nat_Onat))), _1701316))), _1701312)), hAPP(hAPP(c_List_Ozip(_1701310, tc_Nat_Onat), _1701314), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701310)), _1701314))))))], (45824 ^ _779300) ^ [_1701515, _1701517] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701515, _1701517)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1701515), _1701517))], (45826 ^ _779300) ^ [_1701552, _1701554] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1701552), _1701554) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701552, _1701554)))], (45828 ^ _779300) ^ [_1701598, _1701600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701598), _1701600)), -(c_List_Oupt(_1701598, hAPP(c_Nat_OSuc, _1701600)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701598, _1701600)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1701600), c_List_Olist_ONil(tc_Nat_Onat))))], (45834 ^ _779300) ^ [_1701721, _1701723] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701721), _1701723))), -(c_List_Oupt(_1701721, hAPP(c_Nat_OSuc, _1701723)) = c_List_Olist_ONil(tc_Nat_Onat))], (45840 ^ _779300) ^ [_1701770, _1701772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701770), _1701772)), -(c_List_Oupt(_1701770, hAPP(c_Nat_OSuc, _1701772)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701770, _1701772)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1701772), c_List_Olist_ONil(tc_Nat_Onat))))], (45846 ^ _779300) ^ [_1701899, _1701901, _1701903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701899), _1701901)), -(c_List_Oupt(_1701899, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701901), _1701903)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701899, _1701901)), c_List_Oupt(_1701901, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701901), _1701903))))], (45852 ^ _779300) ^ [_1702051, _1702053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702051), _1702053)), -(c_List_Oupt(_1702051, _1702053) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702051), c_List_Oupt(hAPP(c_Nat_OSuc, _1702051), _1702053)))], (45858 ^ _779300) ^ [_1702162, _1702164] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702162), _1702164))), -(c_List_Oupt(_1702162, _1702164) = c_List_Olist_ONil(tc_Nat_Onat))], (45864 ^ _779300) ^ [_1702208, _1702210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702208), _1702210)), -(c_List_Oupt(_1702208, _1702210) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702208), c_List_Oupt(hAPP(c_Nat_OSuc, _1702208), _1702210)))], (45870 ^ _779300) ^ [_1702325, _1702327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702325), _1702327)), -(c_List_Oupt(_1702327, _1702325) = c_List_Olist_ONil(tc_Nat_Onat))], (45886 ^ _779300) ^ [_1702535, _1702537] : [45887 ^ _779300 : [(45888 ^ _779300) ^ [] : [_1702537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45890 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702537), _1702535))]], -(c_List_Oupt(_1702535, _1702537) = c_List_Olist_ONil(tc_Nat_Onat))], (45876 ^ _779300) ^ [_1702433, _1702435] : [c_List_Oupt(_1702433, _1702435) = c_List_Olist_ONil(tc_Nat_Onat), -(_1702435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702435), _1702433)))], (45894 ^ _779300) ^ [_1702668] : [-(c_List_Oupt(_1702668, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (45896 ^ _779300) ^ [_1702694, _1702696, _1702698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702694), _1702696)), _1702698)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1702696), c_List_Oupt(_1702694, _1702698)) = c_List_Oupt(_1702694, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702694), _1702696)))], (45902 ^ _779300) ^ [_1702831, _1702833] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1702831), _1702833)) = c_List_Oupt(_1702831, _1702833))], (45904 ^ _779300) ^ [_1702868, _1702870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702868), _1702870)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1702868, _1702870)) = _1702868)], (45910 ^ _779300) ^ [_1702967, _1702969, _1702971] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1702967), c_List_Oupt(_1702969, _1702971)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702969), _1702967), _1702971))], (45912 ^ _779300) ^ [_1703012, _1703014] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1703012, _1703014))))], (45914 ^ _779300) ^ [_1703042, _1703044] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1703042, _1703044)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1703044), _1703042))], (45916 ^ _779300) ^ [_1703088, _1703090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703088)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703090))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703088), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703090)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703088)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703088)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703090))))], (45922 ^ _779300) ^ [_1703241, _1703243] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703241)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703243)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703241), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703243)) = c_List_Olist_ONil(tc_Nat_Onat))], (45928 ^ _779300) ^ [_1703320, _1703322, _1703324, _1703326] : [c_List_Oupt(_1703320, _1703322) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703324), _1703326), 45931 ^ _779300 : [(45932 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703320), _1703322)))], (45934 ^ _779300) ^ [] : [-(_1703320 = _1703324)], (45936 ^ _779300) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703320), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703322) = _1703326)]]], (45938 ^ _779300) ^ [_1703493, _1703495, _1703497, _1703499] : [-(c_List_Oupt(_1703493, _1703495) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703497), _1703499)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703493), _1703495)), _1703493 = _1703497, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703493), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703495) = _1703499], (45952 ^ _779300) ^ [_1703734, _1703736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703734), _1703736)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1703734, _1703736)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1703736), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45958 ^ _779300) ^ [_1703845, _1703847] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1703845, _1703847)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1703845), hAPP(c_Nat_OSuc, _1703847)))], (45960 ^ _779300) ^ [_1703885, _1703887] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1703885, _1703887) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1703885, hAPP(c_Nat_OSuc, _1703887))))], (45962 ^ _779300) ^ [_1703923] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1703923) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1703923)))], (45964 ^ _779300) ^ [_1703955, _1703957, _1703959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703955), _1703957)), _1703959)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1703955, _1703959)), _1703957) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703955), _1703957))], (45970 ^ _779300) ^ [_1704086, _1704088] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1704086, _1704088) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1704086), hAPP(c_Nat_OSuc, _1704088))))], (45972 ^ _779300) ^ [_1704127, _1704129] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1704127, _1704129) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1704127), _1704129)))], (45974 ^ _779300) ^ [_1704165] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1704165) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1704165))))], (45976 ^ _779300) ^ [_1704200, _1704202] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704200), hAPP(c_List_Onth(_1704200), _1704202)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704200)), _1704202))) = _1704202)], (45978 ^ _779300) ^ [_1704249, _1704251, _1704253, _1704255] : [class_Groups_Ocomm__monoid__add(_1704249), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704249), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704249), _1704251), c_List_Oupt(_1704253, _1704255))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704249), _1704251), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704253, _1704255))))], (45984 ^ _779300) ^ [_1704392, _1704394, _1704396, _1704398] : [class_Groups_Ocomm__monoid__add(_1704392), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704392), _1704394), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704396, _1704398))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1704392), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704392), _1704394), c_List_Oupt(_1704396, _1704398))))], (45990 ^ _779300) ^ [_1704535, _1704537, _1704539, _1704541, _1704543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704535), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1704537), _1704539))), -(hAPP(hAPP(c_List_Onth(_1704541), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704541), _1704543), c_List_Oupt(_1704539, _1704537))), _1704535) = hAPP(_1704543, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704539), _1704535)))], (45996 ^ _779300) ^ [_1704698, _1704700, _1704702] : [45997 ^ _779300 : [(45998 ^ _779300) ^ [] : [-(_1704698 = c_List_Olist_ONil(tc_List_Olist(_1704700)))], (46000 ^ _779300) ^ [] : [_1704702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 46004 ^ _779300 : [(46005 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46003 ^ [_1704698, _1704700, _1704702]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1704700))), _1704698))))], (46007 ^ _779300) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704700)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1704700)), _1704698), 46003 ^ [_1704698, _1704700, _1704702])) = _1704702]], -(c_List_Otranspose(_1704700, _1704698) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1704700)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1704700)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1704700), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1704700)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1704700)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1704700), hAPP(hAPP(c_COMBB(tc_List_Olist(_1704700), tc_fun(tc_Nat_Onat, _1704700), tc_Nat_Onat), c_List_Onth(_1704700)), hAPP(c_List_Onth(tc_List_Olist(_1704700)), _1704698))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1704700))), _1704698)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1704702)))], (46011 ^ _779300) ^ [_1705208, _1705210, _1705212, _1705214, _1705216] : [class_Orderings_Olinorder(_1705208), hBOOL(hAPP(hAPP(c_member(_1705210), _1705212), hAPP(c_List_Oset(_1705210), _1705214))), c_List_Olinorder__class_Osorted(_1705208, hAPP(hAPP(c_List_Omap(_1705210, _1705208), _1705216), _1705214)), hAPP(c_List_Ohd(_1705210), hAPP(c_List_Ofilter(_1705210, hAPP(hAPP(c_COMBB(_1705208, tc_HOL_Obool, _1705210), hAPP(c_fequal, hAPP(_1705216, _1705212))), _1705216)), _1705214)) = _1705212, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705210, _1705208, _1705216), _1705212), c_List_Oremove1(_1705210, _1705212, _1705214)) = _1705214)], (46029 ^ _779300) ^ [_1705587] : [class_Orderings_Olinorder(_1705587), -(c_List_Olinorder__class_Osorted(_1705587, c_List_Olist_ONil(_1705587)))], (46035 ^ _779300) ^ [_1705664, _1705666] : [class_Orderings_Olinorder(_1705664), -(c_List_Olinorder__class_Osorted(_1705664, hAPP(hAPP(c_List_Olist_OCons(_1705664), _1705666), c_List_Olist_ONil(_1705664))))], (46041 ^ _779300) ^ [_1705759, _1705761] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1705759, _1705761)))], (46043 ^ _779300) ^ [_1705787, _1705789] : [class_Orderings_Olinorder(_1705787), -(c_List_Olinorder__class_Osorted(_1705787, c_List_Olinorder__class_Osort__key(_1705787, _1705787, c_COMBI(_1705787), _1705789)))], (46049 ^ _779300) ^ [_1705876, _1705878, _1705880] : [class_Orderings_Olinorder(_1705876), c_List_Olinorder__class_Osorted(_1705876, _1705878), -(c_List_Olinorder__class_Osorted(_1705876, c_List_Olinorder__class_Oinsort__insert__key(_1705876, _1705876, c_COMBI(_1705876), _1705880, _1705878)))], (46059 ^ _779300) ^ [_1706023, _1706025, _1706027] : [class_Orderings_Olinorder(_1706023), c_List_Olinorder__class_Osorted(_1706023, _1706025), -(c_List_Olinorder__class_Osorted(_1706023, hAPP(hAPP(c_List_Odrop(_1706023), _1706027), _1706025)))], (46069 ^ _779300) ^ [_1706170, _1706172] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1706170, _1706172)))], (46071 ^ _779300) ^ [_1706198, _1706200, _1706202] : [class_Orderings_Olinorder(_1706198), c_List_Olinorder__class_Osorted(_1706198, _1706200), -(c_List_Olinorder__class_Osorted(_1706198, hAPP(hAPP(c_List_Otake(_1706198), _1706202), _1706200)))], (46081 ^ _779300) ^ [_1706345, _1706347, _1706349] : [class_Orderings_Olinorder(_1706345), c_List_Olinorder__class_Osorted(_1706345, _1706347), -(c_List_Olinorder__class_Osorted(_1706345, c_List_Oremove1(_1706345, _1706349, _1706347)))], (46091 ^ _779300) ^ [_1706484, _1706486] : [class_Orderings_Olinorder(_1706484), c_List_Olinorder__class_Osorted(_1706484, _1706486), -(c_List_Olinorder__class_Osorted(_1706484, hAPP(c_List_Otl(_1706484), _1706486)))], (46101 ^ _779300) ^ [_1706621, _1706623, _1706625] : [class_Orderings_Olinorder(_1706621), 46104 ^ _779300 : [(46105 ^ _779300) ^ [] : [c_List_Olinorder__class_Osorted(_1706621, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706621, _1706621, c_COMBI(_1706621)), _1706623), _1706625)), -(c_List_Olinorder__class_Osorted(_1706621, _1706625))], (46111 ^ _779300) ^ [] : [c_List_Olinorder__class_Osorted(_1706621, _1706625), -(c_List_Olinorder__class_Osorted(_1706621, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706621, _1706621, c_COMBI(_1706621)), _1706623), _1706625)))]]], (46117 ^ _779300) ^ [_1706868, _1706870] : [class_Orderings_Olinorder(_1706868), -(_1706870 = c_List_Olist_ONil(_1706868)), c_List_Olinorder__class_Osorted(_1706868, _1706870), -(c_List_Olinorder__class_Osorted(_1706868, c_List_Obutlast(_1706868, _1706870)))], (46131 ^ _779300) ^ [_1707060] : [class_Orderings_Olinorder(_1707060), -(c_List_Olinorder__class_Osorted(_1707060, c_List_Olist_ONil(_1707060)))], (46137 ^ _779300) ^ [_1707137, _1707139, _1707141, _1707143] : [class_Orderings_Olinorder(_1707137), 46140 ^ _779300 : [(46141 ^ _779300) ^ [] : [c_List_Olinorder__class_Osorted(_1707137, hAPP(hAPP(c_List_Olist_OCons(_1707137), _1707139), hAPP(hAPP(c_List_Olist_OCons(_1707137), _1707141), _1707143))), 46144 ^ _779300 : [(46145 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707137), _1707139), _1707141)))], (46147 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1707137, hAPP(hAPP(c_List_Olist_OCons(_1707137), _1707141), _1707143)))]]], (46149 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1707137, hAPP(hAPP(c_List_Olist_OCons(_1707137), _1707139), hAPP(hAPP(c_List_Olist_OCons(_1707137), _1707141), _1707143)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707137), _1707139), _1707141)), c_List_Olinorder__class_Osorted(_1707137, hAPP(hAPP(c_List_Olist_OCons(_1707137), _1707141), _1707143))]]], (46159 ^ _779300) ^ [_1707523, _1707525, _1707527, _1707529] : [class_Orderings_Olinorder(_1707523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707523), _1707525), _1707527)), c_List_Olinorder__class_Osorted(_1707523, hAPP(hAPP(c_List_Olist_OCons(_1707523), _1707527), _1707529)), -(c_List_Olinorder__class_Osorted(_1707523, hAPP(hAPP(c_List_Olist_OCons(_1707523), _1707525), hAPP(hAPP(c_List_Olist_OCons(_1707523), _1707527), _1707529))))], (46173 ^ _779300) ^ [_1707776, _1707778] : [class_Orderings_Olinorder(_1707776), c_List_Olinorder__class_Osorted(_1707776, _1707778), -(c_List_Olinorder__class_Osorted(_1707776, c_List_Oremdups(_1707776, _1707778)))], (46183 ^ _779300) ^ [_1707909, _1707911, _1707913] : [class_Orderings_Olinorder(_1707909), c_List_Olinorder__class_Osorted(_1707909, _1707911), hBOOL(hAPP(c_List_Odistinct(_1707909), _1707911)), c_List_Olinorder__class_Osorted(_1707909, _1707913), hBOOL(hAPP(c_List_Odistinct(_1707909), _1707913)), hAPP(c_List_Oset(_1707909), _1707911) = hAPP(c_List_Oset(_1707909), _1707913), -(_1707911 = _1707913)], (46209 ^ _779300) ^ [_1708292, _1708294, _1708296, _1708298] : [class_Orderings_Olinorder(_1708292), -(c_List_Olinorder__class_Osorted(_1708292, hAPP(hAPP(c_List_Omap(_1708294, _1708292), _1708296), c_List_Olinorder__class_Osort__key(_1708294, _1708292, _1708296, _1708298))))], (46215 ^ _779300) ^ [_1708399, _1708401, _1708403, _1708405, _1708407] : [class_Orderings_Olinorder(_1708399), c_List_Olinorder__class_Osorted(_1708399, hAPP(hAPP(c_List_Omap(_1708401, _1708399), _1708403), _1708405)), -(c_List_Olinorder__class_Osorted(_1708399, hAPP(hAPP(c_List_Omap(_1708401, _1708399), _1708403), c_List_Olinorder__class_Oinsort__insert__key(_1708401, _1708399, _1708403, _1708407, _1708405))))], (46225 ^ _779300) ^ [_1708586, _1708588, _1708590, _1708592, _1708594] : [class_Orderings_Olinorder(_1708586), c_List_Olinorder__class_Osorted(_1708586, hAPP(hAPP(c_List_Omap(_1708588, _1708586), _1708590), _1708592)), -(c_List_Olinorder__class_Osorted(_1708586, hAPP(hAPP(c_List_Omap(_1708588, _1708586), _1708590), c_List_Oremove1(_1708588, _1708594, _1708592))))], (46235 ^ _779300) ^ [_1708769, _1708771, _1708773, _1708775, _1708777] : [class_Orderings_Olinorder(_1708769), 46238 ^ _779300 : [(46239 ^ _779300) ^ [] : [c_List_Olinorder__class_Osorted(_1708769, hAPP(hAPP(c_List_Omap(_1708771, _1708769), _1708773), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1708771, _1708769, _1708773), _1708775), _1708777))), -(c_List_Olinorder__class_Osorted(_1708769, hAPP(hAPP(c_List_Omap(_1708771, _1708769), _1708773), _1708777)))], (46245 ^ _779300) ^ [] : [c_List_Olinorder__class_Osorted(_1708769, hAPP(hAPP(c_List_Omap(_1708771, _1708769), _1708773), _1708777)), -(c_List_Olinorder__class_Osorted(_1708769, hAPP(hAPP(c_List_Omap(_1708771, _1708769), _1708773), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1708771, _1708769, _1708773), _1708775), _1708777))))]]], (46251 ^ _779300) ^ [_1709076, _1709078, _1709080, _1709082, _1709084] : [class_Orderings_Olinorder(_1709076), c_List_Olinorder__class_Osorted(_1709076, hAPP(hAPP(c_List_Omap(_1709078, _1709076), _1709080), _1709082)), -(c_List_Olinorder__class_Osorted(_1709076, hAPP(hAPP(c_List_Omap(_1709078, _1709076), _1709080), hAPP(c_List_Ofilter(_1709078, _1709084), _1709082))))], (46261 ^ _779300) ^ [_1709263, _1709265, _1709267, _1709269, _1709271] : [class_Orderings_Olinorder(_1709263), -(c_List_Olinorder__class_Osorted(_1709263, hAPP(hAPP(c_List_Omap(_1709265, _1709263), _1709267), hAPP(c_List_Ofilter(_1709265, hAPP(hAPP(c_COMBC(_1709265, _1709263, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1709263, tc_fun(_1709263, tc_HOL_Obool), _1709265), c_fequal), _1709267)), hAPP(_1709269, _1709271))), _1709271))))], (46267 ^ _779300) ^ [_1709426, _1709428, _1709430] : [class_Orderings_Olinorder(_1709426), -(c_List_Olinorder__class_Osorted(_1709426, hAPP(c_List_Ofilter(_1709426, hAPP(hAPP(c_COMBC(_1709426, _1709426, tc_HOL_Obool), c_fequal), hAPP(_1709428, _1709430))), _1709430)))], (46273 ^ _779300) ^ [_1709541, _1709543, _1709545] : [class_Orderings_Olinorder(_1709541), 46276 ^ _779300 : [(46277 ^ _779300) ^ [] : [c_List_Olinorder__class_Osorted(_1709541, hAPP(hAPP(c_List_Olist_OCons(_1709541), _1709543), _1709545)), 46280 ^ _779300 : [(46281 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709541, _1709545))], (46283 ^ _779300) ^ [_1709727] : [hBOOL(hAPP(hAPP(c_member(_1709541), _1709727), hAPP(c_List_Oset(_1709541), _1709545))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709541), _1709543), _1709727)))]]], (46289 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709541, hAPP(hAPP(c_List_Olist_OCons(_1709541), _1709543), _1709545))), c_List_Olinorder__class_Osorted(_1709541, _1709545), 46295 ^ _779300 : [(46296 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709541), 46294 ^ [_1709541, _1709543, _1709545]), hAPP(c_List_Oset(_1709541), _1709545))))], (46298 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709541), _1709543), 46294 ^ [_1709541, _1709543, _1709545]))]]]]], (46302 ^ _779300) ^ [_1710066, _1710068, _1710070] : [class_Orderings_Olinorder(_1710066), 46305 ^ _779300 : [(46306 ^ _779300) ^ [] : [c_List_Olinorder__class_Osorted(_1710066, hAPP(hAPP(c_List_Oappend(_1710066), _1710068), _1710070)), 46309 ^ _779300 : [(46310 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710066, _1710068))], (46312 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710066, _1710070))], (46314 ^ _779300) ^ [_1710302] : [hBOOL(hAPP(hAPP(c_member(_1710066), _1710302), hAPP(c_List_Oset(_1710066), _1710068))), 46317 ^ _779300 : [(46318 ^ _779300) ^ [_1710412] : [hBOOL(hAPP(hAPP(c_member(_1710066), _1710412), hAPP(c_List_Oset(_1710066), _1710070))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710066), _1710302), _1710412)))]]]]], (46324 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710066, hAPP(hAPP(c_List_Oappend(_1710066), _1710068), _1710070))), c_List_Olinorder__class_Osorted(_1710066, _1710068), c_List_Olinorder__class_Osorted(_1710066, _1710070), 46334 ^ _779300 : [(46335 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710066), 46333 ^ [_1710066, _1710068, _1710070]), hAPP(c_List_Oset(_1710066), _1710068))))], (46338 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710066), 46336 ^ [_1710066, _1710068, _1710070]), hAPP(c_List_Oset(_1710066), _1710070))))], (46340 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710066), 46333 ^ [_1710066, _1710068, _1710070]), 46336 ^ [_1710066, _1710068, _1710070]))]]]]], (46344 ^ _779300) ^ [_1710914, _1710916, _1710918, _1710920, _1710922, _1710924] : [class_Orderings_Olinorder(_1710914), c_List_Olinorder__class_Osorted(_1710914, hAPP(hAPP(c_List_Omap(_1710916, _1710914), _1710918), _1710920)), hBOOL(hAPP(_1710922, _1710924)), -(hAPP(c_List_Ofilter(_1710916, _1710922), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710916, _1710914, _1710918), _1710924), _1710920)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710916, _1710914, _1710918), _1710924), hAPP(c_List_Ofilter(_1710916, _1710922), _1710920)))], (46358 ^ _779300) ^ [_1711203, _1711205, _1711207] : [class_Orderings_Olinorder(_1711203), 46361 ^ _779300 : [(46362 ^ _779300) ^ [] : [c_List_Olinorder__class_Osorted(_1711203, hAPP(hAPP(c_List_Olist_OCons(_1711203), _1711205), _1711207)), 46365 ^ _779300 : [(46372 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711203, _1711207))], (46366 ^ _779300) ^ [_1711371] : [hBOOL(hAPP(hAPP(c_member(_1711203), _1711371), hAPP(c_List_Oset(_1711203), _1711207))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711203), _1711205), _1711371)))]]], (46374 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711203, hAPP(hAPP(c_List_Olist_OCons(_1711203), _1711205), _1711207))), 46378 ^ _779300 : [(46379 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1711203), 46377 ^ [_1711203, _1711205, _1711207]), hAPP(c_List_Oset(_1711203), _1711207))))], (46381 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711203), _1711205), 46377 ^ [_1711203, _1711205, _1711207]))]], c_List_Olinorder__class_Osorted(_1711203, _1711207)]]], (46387 ^ _779300) ^ [_1711729, _1711731] : [class_Orderings_Olinorder(_1711729), hBOOL(hAPP(c_Finite__Set_Ofinite(_1711729), _1711731)), 46394 ^ _779300 : [(46395 ^ _779300) ^ [] : [-(hAPP(c_List_Oset(_1711729), c_List_Olinorder__class_Osorted__list__of__set(_1711729, _1711731)) = _1711731)], (46397 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711729, c_List_Olinorder__class_Osorted__list__of__set(_1711729, _1711731)))], (46399 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1711729), c_List_Olinorder__class_Osorted__list__of__set(_1711729, _1711731))))]]], (46401 ^ _779300) ^ [_1711950, _1711952, _1711954] : [class_Orderings_Olinorder(_1711950), hBOOL(hAPP(hAPP(c_member(_1711950), _1711952), hAPP(c_List_Oset(_1711950), _1711954))), c_List_Olinorder__class_Osorted(_1711950, _1711954), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1711950, _1711950, c_COMBI(_1711950)), _1711952), c_List_Oremove1(_1711950, _1711952, _1711954)) = _1711954)], (46415 ^ _779300) ^ [_1712191, _1712193, _1712195, _1712197] : [class_Orderings_Olinorder(_1712191), c_List_Olinorder__class_Osorted(_1712191, _1712193), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712195), _1712197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712197), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712191)), _1712193))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712191), hAPP(hAPP(c_List_Onth(_1712191), _1712193), _1712195)), hAPP(hAPP(c_List_Onth(_1712191), _1712193), _1712197))))], (46433 ^ _779300) ^ [_1712518, _1712520] : [class_Orderings_Olinorder(_1712518), 46436 ^ _779300 : [(46451 ^ _779300) ^ [] : [46453 ^ _779300 : [(46454 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46452 ^ [_1712518, _1712520]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712518)), _1712520))))], (46457 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46455 ^ [_1712518, _1712520]), 46452 ^ [_1712518, _1712520])))], (46459 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712518), hAPP(hAPP(c_List_Onth(_1712518), _1712520), 46455 ^ [_1712518, _1712520])), hAPP(hAPP(c_List_Onth(_1712518), _1712520), 46452 ^ [_1712518, _1712520])))]], -(c_List_Olinorder__class_Osorted(_1712518, _1712520))], (46437 ^ _779300) ^ [] : [c_List_Olinorder__class_Osorted(_1712518, _1712520), 46440 ^ _779300 : [(46441 ^ _779300) ^ [_1712689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712689), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712518)), _1712520))), 46444 ^ _779300 : [(46445 ^ _779300) ^ [_1712806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712806), _1712689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712518), hAPP(hAPP(c_List_Onth(_1712518), _1712520), _1712806)), hAPP(hAPP(c_List_Onth(_1712518), _1712520), _1712689))))]]]]]]], (46463 ^ _779300) ^ [_1713242, _1713244, _1713246, _1713248, _1713250] : [class_Orderings_Olinorder(_1713242), c_Fun_Oinj__on(_1713244, _1713242, _1713246, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1713244, tc_HOL_Obool)), hAPP(c_List_Oset(_1713244), _1713248)), hAPP(c_List_Oset(_1713244), _1713250))), c_List_Olinorder__class_Osorted(_1713242, hAPP(hAPP(c_List_Omap(_1713244, _1713242), _1713246), _1713248)), hBOOL(hAPP(c_List_Odistinct(_1713242), hAPP(hAPP(c_List_Omap(_1713244, _1713242), _1713246), _1713248))), c_List_Olinorder__class_Osorted(_1713242, hAPP(hAPP(c_List_Omap(_1713244, _1713242), _1713246), _1713250)), hBOOL(hAPP(c_List_Odistinct(_1713242), hAPP(hAPP(c_List_Omap(_1713244, _1713242), _1713246), _1713250))), hAPP(c_List_Oset(_1713244), _1713248) = hAPP(c_List_Oset(_1713244), _1713250), -(_1713248 = _1713250)], (46493 ^ _779300) ^ [_1713825, _1713827, _1713829] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1713825), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1713825))), _1713827))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713829), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1713825))), _1713827))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1713825), _1713825), hAPP(hAPP(c_COMBC(tc_List_Olist(_1713825), tc_Nat_Onat, _1713825), c_List_Onth(_1713825)), _1713829)), hAPP(c_List_Ofilter(tc_List_Olist(_1713825), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1713825)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713829)), c_Nat_Osize__class_Osize(tc_List_Olist(_1713825)))), c_List_Otranspose(_1713825, _1713827))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1713825)), _1713827), _1713829))], (46503 ^ _779300) ^ [_1714152, _1714154, _1714156, _1714158] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714152), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1714152))), _1714154))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714156), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714152))), c_List_Otranspose(_1714152, _1714154)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714158), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714152))), hAPP(c_List_Ofilter(tc_List_Olist(_1714152), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714152)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714156)), c_Nat_Osize__class_Osize(tc_List_Olist(_1714152)))), _1714154)))), -(hAPP(hAPP(c_List_Onth(_1714152), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714152)), c_List_Otranspose(_1714152, _1714154)), _1714156)), _1714158) = hAPP(hAPP(c_List_Onth(_1714152), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714152)), _1714154), _1714158)), _1714156))], (46517 ^ _779300) ^ [_1714575, _1714577] : [-(c_Fun_Oinj__on(tc_List_Olist(_1714575), tc_List_Olist(_1714575), c_List_Orev(_1714575), _1714577))], (46519 ^ _779300) ^ [_1714623, _1714625] : [hBOOL(hAPP(c_List_Odistinct(_1714623), hAPP(c_List_Orev(_1714623), _1714625))), -(hBOOL(hAPP(c_List_Odistinct(_1714623), _1714625)))], (46525 ^ _779300) ^ [_1714722, _1714724] : [hBOOL(hAPP(c_List_Odistinct(_1714722), _1714724)), -(hBOOL(hAPP(c_List_Odistinct(_1714722), hAPP(c_List_Orev(_1714722), _1714724))))], (46531 ^ _779300) ^ [_1714827] : [-(hAPP(c_List_Orev(_1714827), c_List_Olist_ONil(_1714827)) = c_List_Olist_ONil(_1714827))], (46533 ^ _779300) ^ [_1714874, _1714876] : [c_List_Olist_ONil(_1714874) = hAPP(c_List_Orev(_1714874), _1714876), -(_1714876 = c_List_Olist_ONil(_1714874))], (46539 ^ _779300) ^ [_1714965, _1714967] : [_1714967 = c_List_Olist_ONil(_1714965), -(c_List_Olist_ONil(_1714965) = hAPP(c_List_Orev(_1714965), _1714967))], (46545 ^ _779300) ^ [_1715077, _1715079] : [hAPP(c_List_Orev(_1715077), _1715079) = c_List_Olist_ONil(_1715077), -(_1715079 = c_List_Olist_ONil(_1715077))], (46551 ^ _779300) ^ [_1715168, _1715170] : [_1715170 = c_List_Olist_ONil(_1715168), -(hAPP(c_List_Orev(_1715168), _1715170) = c_List_Olist_ONil(_1715168))], (46557 ^ _779300) ^ [_1715283, _1715285, _1715287] : [hAPP(c_List_Orev(_1715283), _1715285) = hAPP(hAPP(c_List_Olist_OCons(_1715283), _1715287), c_List_Olist_ONil(_1715283)), -(_1715285 = hAPP(hAPP(c_List_Olist_OCons(_1715283), _1715287), c_List_Olist_ONil(_1715283)))], (46563 ^ _779300) ^ [_1715408, _1715410, _1715412] : [_1715410 = hAPP(hAPP(c_List_Olist_OCons(_1715408), _1715412), c_List_Olist_ONil(_1715408)), -(hAPP(c_List_Orev(_1715408), _1715410) = hAPP(hAPP(c_List_Olist_OCons(_1715408), _1715412), c_List_Olist_ONil(_1715408)))], (46569 ^ _779300) ^ [_1715557, _1715559, _1715561] : [hAPP(hAPP(c_List_Olist_OCons(_1715557), _1715559), c_List_Olist_ONil(_1715557)) = hAPP(c_List_Orev(_1715557), _1715561), -(_1715561 = hAPP(hAPP(c_List_Olist_OCons(_1715557), _1715559), c_List_Olist_ONil(_1715557)))], (46575 ^ _779300) ^ [_1715682, _1715684, _1715686] : [_1715686 = hAPP(hAPP(c_List_Olist_OCons(_1715682), _1715684), c_List_Olist_ONil(_1715682)), -(hAPP(hAPP(c_List_Olist_OCons(_1715682), _1715684), c_List_Olist_ONil(_1715682)) = hAPP(c_List_Orev(_1715682), _1715686))], (46581 ^ _779300) ^ [_1715813, _1715815, _1715817] : [-(hAPP(c_List_Orev(_1715813), hAPP(hAPP(c_List_Oappend(_1715813), _1715815), _1715817)) = hAPP(hAPP(c_List_Oappend(_1715813), hAPP(c_List_Orev(_1715813), _1715817)), hAPP(c_List_Orev(_1715813), _1715815)))], (46583 ^ _779300) ^ [_1715871, _1715873] : [-(hAPP(c_List_Orev(_1715871), c_List_Oconcat(_1715871, _1715873)) = c_List_Oconcat(_1715871, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715871), tc_List_Olist(_1715871)), c_List_Orev(_1715871)), hAPP(c_List_Orev(tc_List_Olist(_1715871)), _1715873))))], (46585 ^ _779300) ^ [_1715929, _1715931, _1715933, _1715935] : [-(hAPP(c_List_Orev(_1715929), hAPP(hAPP(c_List_Omap(_1715931, _1715929), _1715933), _1715935)) = hAPP(hAPP(c_List_Omap(_1715931, _1715929), _1715933), hAPP(c_List_Orev(_1715931), _1715935)))], (46587 ^ _779300) ^ [_1715986, _1715988, _1715990] : [-(hAPP(c_List_Orev(_1715986), hAPP(c_List_Ofilter(_1715986, _1715988), _1715990)) = hAPP(c_List_Ofilter(_1715986, _1715988), hAPP(c_List_Orev(_1715986), _1715990)))], (46589 ^ _779300) ^ [_1716035, _1716037, _1716039, _1716041] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716035)), _1716037) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716039)), _1716041), -(hAPP(hAPP(c_List_Ozip(_1716035, _1716039), hAPP(c_List_Orev(_1716035), _1716037)), hAPP(c_List_Orev(_1716039), _1716041)) = hAPP(c_List_Orev(tc_prod(_1716035, _1716039)), hAPP(hAPP(c_List_Ozip(_1716035, _1716039), _1716037), _1716041)))], (46595 ^ _779300) ^ [_1716216, _1716218] : [-(hAPP(c_List_Oset(_1716216), hAPP(c_List_Orev(_1716216), _1716218)) = hAPP(c_List_Oset(_1716216), _1716218))], (46597 ^ _779300) ^ [_1716280, _1716282, _1716284, _1716286, _1716288] : [c_List_Olist__all2(_1716280, _1716282, _1716284, hAPP(c_List_Orev(_1716280), _1716286), _1716288), -(c_List_Olist__all2(_1716280, _1716282, _1716284, _1716286, hAPP(c_List_Orev(_1716282), _1716288)))], (46603 ^ _779300) ^ [_1716391, _1716393, _1716395, _1716397, _1716399] : [c_List_Olist__all2(_1716391, _1716393, _1716395, _1716397, hAPP(c_List_Orev(_1716393), _1716399)), -(c_List_Olist__all2(_1716391, _1716393, _1716395, hAPP(c_List_Orev(_1716391), _1716397), _1716399))], (46609 ^ _779300) ^ [_1716532, _1716534, _1716536, _1716538, _1716540] : [c_List_Olist__all2(_1716532, _1716534, _1716536, hAPP(c_List_Orev(_1716532), _1716538), hAPP(c_List_Orev(_1716534), _1716540)), -(c_List_Olist__all2(_1716532, _1716534, _1716536, _1716538, _1716540))], (46615 ^ _779300) ^ [_1716643, _1716645, _1716647, _1716649, _1716651] : [c_List_Olist__all2(_1716643, _1716645, _1716647, _1716649, _1716651), -(c_List_Olist__all2(_1716643, _1716645, _1716647, hAPP(c_List_Orev(_1716643), _1716649), hAPP(c_List_Orev(_1716645), _1716651)))], (46621 ^ _779300) ^ [_1716778, _1716780, _1716782] : [hAPP(c_List_Orev(_1716778), _1716780) = hAPP(c_List_Orev(_1716778), _1716782), -(_1716780 = _1716782)], (46627 ^ _779300) ^ [_1716873, _1716875, _1716877] : [_1716875 = _1716877, -(hAPP(c_List_Orev(_1716873), _1716875) = hAPP(c_List_Orev(_1716873), _1716877))], (46633 ^ _779300) ^ [_1716992, _1716994, _1716996] : [hAPP(c_List_Orev(_1716992), _1716994) = _1716996, -(_1716994 = hAPP(c_List_Orev(_1716992), _1716996))], (46639 ^ _779300) ^ [_1717087, _1717089, _1717091] : [_1717089 = hAPP(c_List_Orev(_1717087), _1717091), -(hAPP(c_List_Orev(_1717087), _1717089) = _1717091)], (46645 ^ _779300) ^ [_1717188, _1717190] : [-(hAPP(c_List_Orev(_1717188), hAPP(c_List_Orev(_1717188), _1717190)) = _1717190)], (46647 ^ _779300) ^ [_1717223, _1717225] : [class_Groups_Ocomm__monoid__add(_1717223), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717223), hAPP(c_List_Orev(_1717223), _1717225)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1717223), _1717225))], (46653 ^ _779300) ^ [_1717328, _1717330] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717328)), hAPP(c_List_Orev(_1717328), _1717330)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717328)), _1717330))], (46655 ^ _779300) ^ [_1717372, _1717374, _1717376, _1717378, _1717380] : [-(c_List_Ofoldr(_1717372, _1717374, _1717376, _1717378, _1717380) = hAPP(c_List_Ofoldl(_1717374, _1717372, hAPP(c_COMBC(_1717372, _1717374, _1717374), _1717376), _1717380), hAPP(c_List_Orev(_1717372), _1717378)))], (46657 ^ _779300) ^ [_1717429, _1717431, _1717433, _1717435, _1717437] : [-(hAPP(c_List_Ofoldl(_1717429, _1717431, _1717433, _1717435), _1717437) = c_List_Ofoldr(_1717431, _1717429, hAPP(c_COMBC(_1717429, _1717431, _1717429), _1717433), hAPP(c_List_Orev(_1717431), _1717437), _1717435))], (46659 ^ _779300) ^ [_1717486, _1717488, _1717490] : [-(hAPP(c_List_Orev(_1717486), hAPP(hAPP(c_List_Olist_OCons(_1717486), _1717488), _1717490)) = hAPP(hAPP(c_List_Oappend(_1717486), hAPP(c_List_Orev(_1717486), _1717490)), hAPP(hAPP(c_List_Olist_OCons(_1717486), _1717488), c_List_Olist_ONil(_1717486))))], (46661 ^ _779300) ^ [_1717570, _1717572, _1717574, _1717576] : [hAPP(c_List_Orev(_1717570), _1717572) = hAPP(hAPP(c_List_Olist_OCons(_1717570), _1717574), _1717576), -(_1717572 = hAPP(hAPP(c_List_Oappend(_1717570), hAPP(c_List_Orev(_1717570), _1717576)), hAPP(hAPP(c_List_Olist_OCons(_1717570), _1717574), c_List_Olist_ONil(_1717570))))], (46667 ^ _779300) ^ [_1717719, _1717721, _1717723, _1717725] : [_1717721 = hAPP(hAPP(c_List_Oappend(_1717719), hAPP(c_List_Orev(_1717719), _1717725)), hAPP(hAPP(c_List_Olist_OCons(_1717719), _1717723), c_List_Olist_ONil(_1717719))), -(hAPP(c_List_Orev(_1717719), _1717721) = hAPP(hAPP(c_List_Olist_OCons(_1717719), _1717723), _1717725))], (46673 ^ _779300) ^ [_1717870, _1717872] : [-(_1717870 = c_List_Olist_ONil(_1717872)), -(c_List_Olast(_1717872, hAPP(c_List_Orev(_1717872), _1717870)) = hAPP(c_List_Ohd(_1717872), _1717870))], (46679 ^ _779300) ^ [_1717917, _1717919] : [-(_1717917 = c_List_Olist_ONil(_1717919)), -(hAPP(c_List_Ohd(_1717919), hAPP(c_List_Orev(_1717919), _1717917)) = c_List_Olast(_1717919, _1717917))], (46685 ^ _779300) ^ [_1717968, _1717970] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1717968), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1717968))), c_List_Otranspose(_1717968, _1717970)))))], (46687 ^ _779300) ^ [_1718014, _1718016] : [-(hAPP(c_List_Orev(_1718014), _1718016) = hAPP(c_List_Ofoldl(tc_List_Olist(_1718014), _1718014, hAPP(c_COMBC(_1718014, tc_List_Olist(_1718014), tc_List_Olist(_1718014)), c_List_Olist_OCons(_1718014)), c_List_Olist_ONil(_1718014)), _1718016))], (46689 ^ _779300) ^ [_1718069, _1718071, _1718073] : [-(hAPP(c_List_Orev(_1718069), hAPP(hAPP(c_List_Odrop(_1718069), _1718071), _1718073)) = hAPP(hAPP(c_List_Otake(_1718069), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718069)), _1718073)), _1718071)), hAPP(c_List_Orev(_1718069), _1718073)))], (46691 ^ _779300) ^ [_1718135, _1718137, _1718139] : [-(hAPP(c_List_Orev(_1718135), hAPP(hAPP(c_List_Otake(_1718135), _1718137), _1718139)) = hAPP(hAPP(c_List_Odrop(_1718135), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718135)), _1718139)), _1718137)), hAPP(c_List_Orev(_1718135), _1718139)))], (46693 ^ _779300) ^ [_1718201, _1718203, _1718205] : [-(hAPP(c_List_Orotate(_1718201, _1718203), hAPP(c_List_Orev(_1718201), _1718205)) = hAPP(c_List_Orev(_1718201), hAPP(c_List_Orotate(_1718201, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718201)), _1718205)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1718203, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718201)), _1718205)))), _1718205)))], (46695 ^ _779300) ^ [_1718274, _1718276, _1718278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718274), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718276)), _1718278))), -(hAPP(hAPP(c_List_Onth(_1718276), hAPP(c_List_Orev(_1718276), _1718278)), _1718274) = hAPP(hAPP(c_List_Onth(_1718276), _1718278), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718276)), _1718278)), hAPP(c_Nat_OSuc, _1718274))))], (46701 ^ _779300) ^ [_1718451, _1718453, _1718455, _1718457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718451), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718453)), _1718455))), -(hAPP(c_List_Orev(_1718453), hAPP(hAPP(c_List_Olist__update(_1718453, _1718455), _1718451), _1718457)) = hAPP(hAPP(c_List_Olist__update(_1718453, hAPP(c_List_Orev(_1718453), _1718455)), 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(_1718453)), _1718455)), _1718451)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1718457))], (46707 ^ _779300) ^ [_1718650, _1718652, _1718654, _1718656] : [class_Orderings_Olinorder(_1718650), c_List_Olinorder__class_Osorted(_1718650, hAPP(c_List_Orev(_1718650), _1718652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718654), _1718656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718656), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718650)), _1718652))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1718650), hAPP(hAPP(c_List_Onth(_1718650), _1718652), _1718656)), hAPP(hAPP(c_List_Onth(_1718650), _1718652), _1718654))))], (46725 ^ _779300) ^ [_1718987, _1718989, _1718991] : [class_Orderings_Olinorder(_1718987), c_List_Olinorder__class_Osorted(_1718987, hAPP(c_List_Orev(_1718987), _1718989)), 46732 ^ _779300 : [(46733 ^ _779300) ^ [] : [_1718989 = c_List_Olist_ONil(_1718987), -(c_List_Ofoldr(_1718987, _1718987, c_Orderings_Oord__class_Omax(_1718987), _1718989, _1718991) = _1718991)], (46739 ^ _779300) ^ [] : [-(_1718989 = c_List_Olist_ONil(_1718987)), -(c_List_Ofoldr(_1718987, _1718987, c_Orderings_Oord__class_Omax(_1718987), _1718989, _1718991) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1718987), hAPP(hAPP(c_List_Onth(_1718987), _1718989), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1718991))]]], (46745 ^ _779300) ^ [_1719301, _1719303] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719301), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719301))), _1719303))), 46748 ^ _779300 : [(46749 ^ _779300) ^ [] : [_1719303 = c_List_Olist_ONil(tc_List_Olist(_1719301)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719301))), c_List_Otranspose(_1719301, _1719303)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46755 ^ _779300) ^ [] : [-(_1719303 = c_List_Olist_ONil(tc_List_Olist(_1719301))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719301))), c_List_Otranspose(_1719301, _1719303)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719301)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719301)), _1719303), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (46761 ^ _779300) ^ [_1719611, _1719613, _1719615] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719611), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719611))), _1719613))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719615), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719611))), _1719613))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719611))), hAPP(c_List_Ofilter(tc_List_Olist(_1719611), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1719611)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719615)), c_Nat_Osize__class_Osize(tc_List_Olist(_1719611)))), c_List_Otranspose(_1719611, _1719613))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719611)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719611)), _1719613), _1719615)))], (46771 ^ _779300) ^ [_1719920, _1719922] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719920), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719920))), _1719922))), -(c_List_Otranspose(_1719920, c_List_Otranspose(_1719920, _1719922)) = c_List_OtakeWhile(tc_List_Olist(_1719920), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1719920)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719920), tc_List_Olist(_1719920), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1719920))), _1719922))], (46777 ^ _779300) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (46779 ^ _779300) ^ [_1720131, _1720133, _1720135] : [class_Orderings_Olinorder(_1720131), c_List_Olinorder__class_Osorted(_1720131, _1720133), -(c_List_Olinorder__class_Osorted(_1720131, c_List_OtakeWhile(_1720131, _1720135, _1720133)))], (46789 ^ _779300) ^ [_1720270, _1720272, _1720274] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720270)), c_List_OtakeWhile(_1720270, _1720272, _1720274))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720270)), _1720274))))], (46801 ^ _779300) ^ [_1720534, _1720536, _1720538] : [46803 ^ _779300 : [(46804 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720534), 46802 ^ [_1720534, _1720536, _1720538]), hAPP(c_List_Oset(_1720534), _1720538))))], (46806 ^ _779300) ^ [] : [hBOOL(hAPP(_1720536, 46802 ^ [_1720534, _1720536, _1720538]))]], -(c_List_OtakeWhile(_1720534, _1720536, _1720538) = _1720538)], (46791 ^ _779300) ^ [_1720338, _1720340, _1720342] : [c_List_OtakeWhile(_1720338, _1720340, _1720342) = _1720342, 46794 ^ _779300 : [(46795 ^ _779300) ^ [_1720425] : [hBOOL(hAPP(hAPP(c_member(_1720338), _1720425), hAPP(c_List_Oset(_1720338), _1720342))), -(hBOOL(hAPP(_1720340, _1720425)))]]], (46810 ^ _779300) ^ [_1720722, _1720724, _1720726, _1720728] : [hBOOL(hAPP(hAPP(c_member(_1720722), _1720724), hAPP(c_List_Oset(_1720722), c_List_OtakeWhile(_1720722, _1720726, _1720728)))), 46813 ^ _779300 : [(46814 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720722), _1720724), hAPP(c_List_Oset(_1720722), _1720728))))], (46816 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1720726, _1720724)))]]], (46818 ^ _779300) ^ [_1720889, _1720891, _1720893, _1720895, _1720897] : [-(hAPP(hAPP(c_List_Ozip(_1720889, _1720891), _1720893), c_List_OtakeWhile(_1720891, _1720895, _1720897)) = c_List_OtakeWhile(tc_prod(_1720889, _1720891), hAPP(c_Fun_Ocomp(_1720891, tc_HOL_Obool, tc_prod(_1720889, _1720891), _1720895), c_Product__Type_Osnd(_1720889, _1720891)), hAPP(hAPP(c_List_Ozip(_1720889, _1720891), _1720893), _1720897)))], (46820 ^ _779300) ^ [_1720963, _1720965, _1720967, _1720969, _1720971] : [-(hAPP(hAPP(c_List_Ozip(_1720963, _1720965), c_List_OtakeWhile(_1720963, _1720967, _1720969)), _1720971) = c_List_OtakeWhile(tc_prod(_1720963, _1720965), hAPP(c_Fun_Ocomp(_1720963, tc_HOL_Obool, tc_prod(_1720963, _1720965), _1720967), c_Product__Type_Ofst(_1720963, _1720965)), hAPP(hAPP(c_List_Ozip(_1720963, _1720965), _1720969), _1720971)))], (46822 ^ _779300) ^ [_1721037, _1721039, _1721041, _1721043, _1721045] : [-(c_List_OtakeWhile(_1721037, _1721039, hAPP(hAPP(c_List_Omap(_1721041, _1721037), _1721043), _1721045)) = hAPP(hAPP(c_List_Omap(_1721041, _1721037), _1721043), c_List_OtakeWhile(_1721041, hAPP(c_Fun_Ocomp(_1721037, tc_HOL_Obool, _1721041, _1721039), _1721043), _1721045)))], (46824 ^ _779300) ^ [_1721098, _1721100, _1721102, _1721104, _1721106] : [-(hBOOL(hAPP(_1721098, _1721100))), -(c_List_OtakeWhile(_1721102, _1721098, hAPP(hAPP(c_List_Oappend(_1721102), _1721104), hAPP(hAPP(c_List_Olist_OCons(_1721102), _1721100), _1721106))) = c_List_OtakeWhile(_1721102, _1721098, _1721104))], (46830 ^ _779300) ^ [_1721181, _1721183, _1721185, _1721187] : [hBOOL(hAPP(_1721181, _1721183)), -(c_List_OtakeWhile(_1721185, _1721181, hAPP(hAPP(c_List_Olist_OCons(_1721185), _1721183), _1721187)) = hAPP(hAPP(c_List_Olist_OCons(_1721185), _1721183), c_List_OtakeWhile(_1721185, _1721181, _1721187)))], (46836 ^ _779300) ^ [_1721308, _1721310, _1721312, _1721314] : [-(hBOOL(hAPP(_1721308, _1721310))), -(c_List_OtakeWhile(_1721312, _1721308, hAPP(hAPP(c_List_Olist_OCons(_1721312), _1721310), _1721314)) = c_List_Olist_ONil(_1721312))], (46842 ^ _779300) ^ [_1721366, _1721368] : [-(c_List_OtakeWhile(_1721366, _1721368, c_List_Olist_ONil(_1721366)) = c_List_Olist_ONil(_1721366))], (46844 ^ _779300) ^ [_1721399, _1721401, _1721403] : [-(c_List_OtakeWhile(_1721399, _1721401, _1721403) = hAPP(hAPP(c_List_Otake(_1721399), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721399)), c_List_OtakeWhile(_1721399, _1721401, _1721403))), _1721403))], (46846 ^ _779300) ^ [_1721449, _1721451, _1721453] : [hBOOL(hAPP(c_List_Odistinct(_1721449), _1721451)), -(hBOOL(hAPP(c_List_Odistinct(_1721449), c_List_OtakeWhile(_1721449, _1721453, _1721451))))], (46852 ^ _779300) ^ [_1721552] : [-(c_List_Oreturn__list(_1721552) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1721552))], (46854 ^ _779300) ^ [_1721580, _1721582, _1721584, _1721586, _1721588] : [hBOOL(hAPP(hAPP(c_member(_1721580), _1721582), hAPP(c_List_Oset(_1721580), _1721584))), -(hBOOL(hAPP(_1721586, _1721582))), -(c_List_OtakeWhile(_1721580, _1721586, hAPP(hAPP(c_List_Oappend(_1721580), _1721584), _1721588)) = c_List_OtakeWhile(_1721580, _1721586, _1721584))], (46864 ^ _779300) ^ [_1721738, _1721740, _1721742, _1721744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721738), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721740)), c_List_OtakeWhile(_1721740, _1721742, _1721744)))), -(hAPP(hAPP(c_List_Onth(_1721740), c_List_OtakeWhile(_1721740, _1721742, _1721744)), _1721738) = hAPP(hAPP(c_List_Onth(_1721740), _1721744), _1721738))], (46870 ^ _779300) ^ [_1721891, _1721893, _1721895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721891)), c_List_OtakeWhile(_1721891, _1721893, _1721895))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721891)), _1721895))), hBOOL(hAPP(_1721893, hAPP(hAPP(c_List_Onth(_1721891), _1721895), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721891)), c_List_OtakeWhile(_1721891, _1721893, _1721895)))))], (46876 ^ _779300) ^ [_1722058, _1722060] : [-(_1722058 = c_List_Olist_ONil(_1722060)), hBOOL(hAPP(c_List_Odistinct(_1722060), _1722058)), -(c_List_OtakeWhile(_1722060, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722060), c_fNot), hAPP(hAPP(c_COMBC(_1722060, _1722060, tc_HOL_Obool), c_fequal), c_List_Olast(_1722060, _1722058))), _1722058) = c_List_Obutlast(_1722060, _1722058))], (46886 ^ _779300) ^ [_1722255, _1722257, _1722259, _1722261, _1722263] : [class_Orderings_Olinorder(_1722255), c_List_Olinorder__class_Osorted(_1722255, hAPP(c_List_Orev(_1722255), hAPP(hAPP(c_List_Omap(_1722257, _1722255), _1722259), _1722261))), -(hAPP(c_List_Ofilter(_1722257, hAPP(hAPP(c_COMBB(_1722255, tc_HOL_Obool, _1722257), hAPP(c_Orderings_Oord__class_Oless(_1722255), _1722263)), _1722259)), _1722261) = c_List_OtakeWhile(_1722257, hAPP(hAPP(c_COMBB(_1722255, tc_HOL_Obool, _1722257), hAPP(c_Orderings_Oord__class_Oless(_1722255), _1722263)), _1722259), _1722261))], (46896 ^ _779300) ^ [_1722502] : [c_List_Onat__list(_1722502), -(c_List_Oembed__list(c_List_Oreturn__list(_1722502)) = _1722502)], (46902 ^ _779300) ^ [_1722583, _1722585] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1722583), _1722585) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1722583)), c_List_Oembed__list(_1722585))))], (46904 ^ _779300) ^ [_1722626] : [-(c_List_Oembed__list(_1722626) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1722626))], (46906 ^ _779300) ^ [_1722654, _1722656, _1722658] : [hBOOL(hAPP(c_List_Odistinct(_1722654), _1722656)), hBOOL(hAPP(hAPP(c_member(_1722654), _1722658), hAPP(c_List_Oset(_1722654), _1722656))), -(c_List_OtakeWhile(_1722654, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722654), c_fNot), hAPP(hAPP(c_COMBC(_1722654, _1722654, tc_HOL_Obool), c_fequal), _1722658)), hAPP(c_List_Orev(_1722654), _1722656)) = hAPP(c_List_Orev(_1722654), hAPP(c_List_Otl(_1722654), c_List_OdropWhile(_1722654, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722654), c_fNot), hAPP(hAPP(c_COMBC(_1722654, _1722654, tc_HOL_Obool), c_fequal), _1722658)), _1722656))))], (46916 ^ _779300) ^ [_1722945, _1722947, _1722949] : [hBOOL(hAPP(c_List_Odistinct(_1722945), _1722947)), hBOOL(hAPP(hAPP(c_member(_1722945), _1722949), hAPP(c_List_Oset(_1722945), _1722947))), -(c_List_OdropWhile(_1722945, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722945), c_fNot), hAPP(hAPP(c_COMBC(_1722945, _1722945, tc_HOL_Obool), c_fequal), _1722949)), hAPP(c_List_Orev(_1722945), _1722947)) = hAPP(hAPP(c_List_Olist_OCons(_1722945), _1722949), hAPP(c_List_Orev(_1722945), c_List_OtakeWhile(_1722945, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722945), c_fNot), hAPP(hAPP(c_COMBC(_1722945, _1722945, tc_HOL_Obool), c_fequal), _1722949)), _1722947))))], (46926 ^ _779300) ^ [_1723242, _1723244, _1723246] : [-(hAPP(hAPP(c_List_Oappend(_1723242), c_List_OtakeWhile(_1723242, _1723244, _1723246)), c_List_OdropWhile(_1723242, _1723244, _1723246)) = _1723246)], (46928 ^ _779300) ^ [_1723285, _1723287, _1723289] : [class_Orderings_Olinorder(_1723285), c_List_Olinorder__class_Osorted(_1723285, _1723287), -(c_List_Olinorder__class_Osorted(_1723285, c_List_OdropWhile(_1723285, _1723289, _1723287)))], (46938 ^ _779300) ^ [_1723424, _1723426, _1723428] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723424)), c_List_OdropWhile(_1723424, _1723426, _1723428))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723424)), _1723428))))], (46950 ^ _779300) ^ [_1723692, _1723694, _1723696] : [46952 ^ _779300 : [(46953 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1723692), 46951 ^ [_1723692, _1723694, _1723696]), hAPP(c_List_Oset(_1723692), _1723696))))], (46955 ^ _779300) ^ [] : [hBOOL(hAPP(_1723694, 46951 ^ [_1723692, _1723694, _1723696]))]], -(c_List_OdropWhile(_1723692, _1723694, _1723696) = c_List_Olist_ONil(_1723692))], (46940 ^ _779300) ^ [_1723492, _1723494, _1723496] : [c_List_OdropWhile(_1723492, _1723494, _1723496) = c_List_Olist_ONil(_1723492), 46943 ^ _779300 : [(46944 ^ _779300) ^ [_1723583] : [hBOOL(hAPP(hAPP(c_member(_1723492), _1723583), hAPP(c_List_Oset(_1723492), _1723496))), -(hBOOL(hAPP(_1723494, _1723583)))]]], (46959 ^ _779300) ^ [_1723899, _1723901, _1723903, _1723905] : [hBOOL(hAPP(_1723899, _1723901)), -(c_List_OdropWhile(_1723903, _1723899, hAPP(hAPP(c_List_Olist_OCons(_1723903), _1723901), _1723905)) = c_List_OdropWhile(_1723903, _1723899, _1723905))], (46965 ^ _779300) ^ [_1724010, _1724012, _1724014, _1724016] : [-(hBOOL(hAPP(_1724010, _1724012))), -(c_List_OdropWhile(_1724014, _1724010, hAPP(hAPP(c_List_Olist_OCons(_1724014), _1724012), _1724016)) = hAPP(hAPP(c_List_Olist_OCons(_1724014), _1724012), _1724016))], (46971 ^ _779300) ^ [_1724074, _1724076] : [-(c_List_OdropWhile(_1724074, _1724076, c_List_Olist_ONil(_1724074)) = c_List_Olist_ONil(_1724074))], (46973 ^ _779300) ^ [_1724107, _1724109, _1724111] : [hBOOL(hAPP(c_List_Odistinct(_1724107), _1724109)), -(hBOOL(hAPP(c_List_Odistinct(_1724107), c_List_OdropWhile(_1724107, _1724111, _1724109))))], (46979 ^ _779300) ^ [_1724209, _1724211, _1724213] : [-(c_List_OdropWhile(_1724209, _1724211, _1724213) = c_List_Olist_ONil(_1724209)), hBOOL(hAPP(_1724211, hAPP(c_List_Ohd(_1724209), c_List_OdropWhile(_1724209, _1724211, _1724213))))], (46985 ^ _779300) ^ [_1724315, _1724317, _1724319, _1724321, _1724323] : [-(c_List_OdropWhile(_1724315, _1724317, hAPP(hAPP(c_List_Omap(_1724319, _1724315), _1724321), _1724323)) = hAPP(hAPP(c_List_Omap(_1724319, _1724315), _1724321), c_List_OdropWhile(_1724319, hAPP(c_Fun_Ocomp(_1724315, tc_HOL_Obool, _1724319, _1724317), _1724321), _1724323)))], (46987 ^ _779300) ^ [_1724380, _1724382, _1724384, _1724386, _1724388] : [hBOOL(hAPP(hAPP(c_member(_1724380), _1724382), hAPP(c_List_Oset(_1724380), _1724384))), -(hBOOL(hAPP(_1724386, _1724382))), -(c_List_OdropWhile(_1724380, _1724386, hAPP(hAPP(c_List_Oappend(_1724380), _1724384), _1724388)) = hAPP(hAPP(c_List_Oappend(_1724380), c_List_OdropWhile(_1724380, _1724386, _1724384)), _1724388))], (46997 ^ _779300) ^ [_1724578, _1724580, _1724582, _1724584, _1724586] : [c_List_OdropWhile(_1724578, _1724580, _1724582) = hAPP(hAPP(c_List_Olist_OCons(_1724578), _1724584), _1724586), 47000 ^ _779300 : [(47001 ^ _779300) ^ [] : [-(_1724582 = hAPP(hAPP(c_List_Oappend(_1724578), c_List_OtakeWhile(_1724578, _1724580, _1724582)), hAPP(hAPP(c_List_Olist_OCons(_1724578), _1724584), _1724586)))], (47003 ^ _779300) ^ [] : [hBOOL(hAPP(_1724580, _1724584))]]], (47005 ^ _779300) ^ [_1724759, _1724761, _1724763, _1724765, _1724767] : [-(c_List_OdropWhile(_1724759, _1724761, _1724763) = hAPP(hAPP(c_List_Olist_OCons(_1724759), _1724765), _1724767)), _1724763 = hAPP(hAPP(c_List_Oappend(_1724759), c_List_OtakeWhile(_1724759, _1724761, _1724763)), hAPP(hAPP(c_List_Olist_OCons(_1724759), _1724765), _1724767)), -(hBOOL(hAPP(_1724761, _1724765)))], (47015 ^ _779300) ^ [_1724973, _1724975, _1724977] : [-(c_List_OdropWhile(_1724973, _1724975, _1724977) = hAPP(hAPP(c_List_Odrop(_1724973), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724973)), c_List_OtakeWhile(_1724973, _1724975, _1724977))), _1724977))], (47017 ^ _779300) ^ [_1725023, _1725025, _1725027, _1725029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725023), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725025)), c_List_OdropWhile(_1725025, _1725027, _1725029)))), -(hAPP(hAPP(c_List_Onth(_1725025), c_List_OdropWhile(_1725025, _1725027, _1725029)), _1725023) = hAPP(hAPP(c_List_Onth(_1725025), _1725029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1725023), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725025)), c_List_OtakeWhile(_1725025, _1725027, _1725029)))))], (47023 ^ _779300) ^ [_1725210, _1725212, _1725214, _1725216, _1725218] : [class_Groups_Omonoid__add(_1725210), 47029 ^ _779300 : [(47030 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725212), 47028 ^ [_1725210, _1725212, _1725214, _1725216, _1725218]), hAPP(c_List_Oset(_1725212), _1725214))))], (47032 ^ _779300) ^ [] : [hBOOL(hAPP(_1725216, 47028 ^ [_1725210, _1725212, _1725214, _1725216, _1725218]))], (47034 ^ _779300) ^ [] : [hAPP(_1725218, 47028 ^ [_1725210, _1725212, _1725214, _1725216, _1725218]) = c_Groups_Ozero__class_Ozero(_1725210)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1725210), hAPP(hAPP(c_List_Omap(_1725212, _1725210), _1725218), hAPP(c_List_Ofilter(_1725212, _1725216), _1725214))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1725210), hAPP(hAPP(c_List_Omap(_1725212, _1725210), _1725218), _1725214)))], (47038 ^ _779300) ^ [_1725601, _1725603] : [class_Orderings_Olinorder(_1725601), 47045 ^ _779300 : [(47046 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47043 ^ [_1725601, _1725603]), 47044 ^ [_1725601, _1725603])))], (47048 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47044 ^ [_1725601, _1725603]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725601)), _1725603))))], (47050 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1725601), hAPP(hAPP(c_List_Onth(_1725601), _1725603), 47043 ^ [_1725601, _1725603])), hAPP(hAPP(c_List_Onth(_1725601), _1725603), 47044 ^ [_1725601, _1725603])))]], -(c_List_Olinorder__class_Osorted(_1725601, _1725603))], (47054 ^ _779300) ^ [_1725972, _1725974, _1725976] : [47056 ^ _779300 : [(47057 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725972), 47055 ^ [_1725972, _1725974, _1725976]), hAPP(c_List_Oset(_1725972), c_List_OdropWhile(_1725972, _1725974, _1725976)))))], (47059 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1725974, 47055 ^ [_1725972, _1725974, _1725976])))]], -(c_List_OtakeWhile(_1725972, _1725974, _1725976) = hAPP(c_List_Ofilter(_1725972, _1725974), _1725976))], (47063 ^ _779300) ^ [_1726093, _1726095, _1726097, _1726099] : [47065 ^ _779300 : [(47066 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47064 ^ [_1726093, _1726095, _1726097, _1726099]), _1726093)))], (47068 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47064 ^ [_1726093, _1726095, _1726097, _1726099]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726095)), _1726097))))], (47070 ^ _779300) ^ [] : [hBOOL(hAPP(_1726099, hAPP(hAPP(c_List_Onth(_1726095), _1726097), 47064 ^ [_1726093, _1726095, _1726097, _1726099])))]], 47073 ^ _779300 : [(47074 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726093), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726095)), _1726097))))], (47076 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1726099, hAPP(hAPP(c_List_Onth(_1726095), _1726097), _1726093))))]], -(c_List_OtakeWhile(_1726095, _1726099, _1726097) = hAPP(hAPP(c_List_Otake(_1726095), _1726093), _1726097))], (47080 ^ _779300) ^ [_1726497, _1726499, _1726501, _1726503] : [47082 ^ _779300 : [(47083 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47081 ^ [_1726497, _1726499, _1726501, _1726503]), _1726497)))], (47085 ^ _779300) ^ [] : [hBOOL(hAPP(_1726499, hAPP(hAPP(c_List_Onth(_1726501), _1726503), 47081 ^ [_1726497, _1726499, _1726501, _1726503])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1726497), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726501)), _1726503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1726497), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726501)), c_List_OtakeWhile(_1726501, _1726499, _1726503)))))], (47093 ^ _779300) ^ [_1726805, _1726807] : [class_Orderings_Olinorder(_1726805), 47096 ^ _779300 : [(47097 ^ _779300) ^ [] : [c_List_Olinorder__class_Osorted(_1726805, _1726807), -(_1726807 = c_List_Olist_ONil(_1726805)), 47106 ^ _779300 : [(47107 ^ _779300) ^ [] : [-(_1726807 = hAPP(hAPP(c_List_Olist_OCons(_1726805), 47105 ^ [_1726805, _1726807]), 47104 ^ [_1726805, _1726807]))], (47115 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726805, 47104 ^ [_1726805, _1726807]))], (47109 ^ _779300) ^ [_1727139] : [hBOOL(hAPP(hAPP(c_member(_1726805), _1727139), hAPP(c_List_Oset(_1726805), 47104 ^ [_1726805, _1726807]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726805), 47105 ^ [_1726805, _1726807]), _1727139)))]]], (47117 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726805, _1726807)), 47118 ^ _779300 : [(47119 ^ _779300) ^ [] : [_1726807 = c_List_Olist_ONil(_1726805)], (47121 ^ _779300) ^ [_1727365, _1727367] : [_1726807 = hAPP(hAPP(c_List_Olist_OCons(_1726805), _1727365), _1727367), 47127 ^ _779300 : [(47128 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726805), 47126 ^ [_1726805, _1726807, _1727365, _1727367]), hAPP(c_List_Oset(_1726805), _1727367))))], (47130 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726805), _1727365), 47126 ^ [_1726805, _1726807, _1727365, _1727367]))]], c_List_Olinorder__class_Osorted(_1726805, _1727367)]]]]], (47136 ^ _779300) ^ [_1727686, _1727688, _1727690] : [hBOOL(hAPP(hAPP(c_member(_1727686), _1727688), hAPP(c_List_Oset(_1727686), _1727690))), -(c_List_Oinsert(_1727686, _1727688, _1727690) = _1727690)], (47142 ^ _779300) ^ [_1727791, _1727793, _1727795] : [-(hBOOL(hAPP(hAPP(c_member(_1727791), _1727793), hAPP(c_List_Oset(_1727791), _1727795)))), -(c_List_Oinsert(_1727791, _1727793, _1727795) = hAPP(hAPP(c_List_Olist_OCons(_1727791), _1727793), _1727795))], (47148 ^ _779300) ^ [_1727851, _1727853, _1727855] : [-(hBOOL(hAPP(hAPP(c_member(_1727851), _1727853), hAPP(c_List_Oset(_1727851), _1727855)))), -(c_List_Oinsert(_1727851, _1727853, _1727855) = hAPP(hAPP(c_List_Olist_OCons(_1727851), _1727853), _1727855))], (47154 ^ _779300) ^ [_1727913, _1727915, _1727917] : [-(c_List_Oinsert(_1727913, _1727915, c_List_Oremdups(_1727913, _1727917)) = c_List_Oremdups(_1727913, c_List_Oinsert(_1727913, _1727915, _1727917)))], (47156 ^ _779300) ^ [_1727954, _1727956, _1727958] : [hBOOL(hAPP(c_List_Odistinct(_1727954), _1727956)), -(hBOOL(hAPP(c_List_Odistinct(_1727954), c_List_Oinsert(_1727954, _1727958, _1727956))))], (47162 ^ _779300) ^ [_1728057, _1728059, _1728061] : [hBOOL(hAPP(hAPP(c_member(_1728057), _1728059), hAPP(c_List_Oset(_1728057), _1728061))), -(c_List_Oinsert(_1728057, _1728059, _1728061) = _1728061)], (47168 ^ _779300) ^ [_1728168, _1728170, _1728172] : [-(hAPP(c_List_Oset(_1728168), c_List_Oinsert(_1728168, _1728170, _1728172)) = hAPP(hAPP(c_Set_Oinsert(_1728168), _1728170), hAPP(c_List_Oset(_1728168), _1728172)))], (47170 ^ _779300) ^ [_1728217, _1728219] : [-(c_List_Oinsert(_1728217, _1728219, c_List_Olist_ONil(_1728217)) = hAPP(hAPP(c_List_Olist_OCons(_1728217), _1728219), c_List_Olist_ONil(_1728217)))], (47172 ^ _779300) ^ [_1728258, _1728260, _1728262, _1728264] : [-(c_List_Oconcat(_1728258, hAPP(hAPP(c_List_Omap(_1728260, tc_List_Olist(_1728258)), _1728262), _1728264)) = c_List_Omaps(_1728260, _1728258, _1728262, _1728264))], (47174 ^ _779300) ^ [_1728306, _1728308, _1728310, _1728312] : [-(c_List_Omaps(_1728306, _1728308, _1728310, _1728312) = c_List_Oconcat(_1728308, hAPP(hAPP(c_List_Omap(_1728306, tc_List_Olist(_1728308)), _1728310), _1728312)))], (47176 ^ _779300) ^ [_1728354, _1728356, _1728358] : [-(c_List_Omaps(_1728354, _1728356, _1728358, c_List_Olist_ONil(_1728354)) = c_List_Olist_ONil(_1728356))], (47178 ^ _779300) ^ [_1728390, _1728392, _1728394, _1728396, _1728398] : [-(c_List_Omaps(_1728390, _1728392, _1728394, hAPP(hAPP(c_List_Olist_OCons(_1728390), _1728396), _1728398)) = hAPP(hAPP(c_List_Oappend(_1728392), hAPP(_1728394, _1728396)), c_List_Omaps(_1728390, _1728392, _1728394, _1728398)))], (47180 ^ _779300) ^ [_1728450, _1728452] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1728450)), _1728452)), 47186 ^ _779300 : [(47187 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728450)), 47185 ^ [_1728450, _1728452]), hAPP(c_List_Oset(tc_List_Olist(_1728450)), _1728452))))], (47189 ^ _779300) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1728450), 47185 ^ [_1728450, _1728452]))]], 47193 ^ _779300 : [(47194 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728450)), 47192 ^ [_1728450, _1728452]), hAPP(c_List_Oset(tc_List_Olist(_1728450)), _1728452))))], (47197 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728450)), 47195 ^ [_1728450, _1728452]), hAPP(c_List_Oset(tc_List_Olist(_1728450)), _1728452))))], (47199 ^ _779300) ^ [] : [47192 ^ [_1728450, _1728452] = 47195 ^ [_1728450, _1728452]], (47201 ^ _779300) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1728450, tc_HOL_Obool)), hAPP(c_List_Oset(_1728450), 47192 ^ [_1728450, _1728452])), hAPP(c_List_Oset(_1728450), 47195 ^ [_1728450, _1728452])) = c_Orderings_Obot__class_Obot(tc_fun(_1728450, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1728450), c_List_Oconcat(_1728450, _1728452))))], (47205 ^ _779300) ^ [_1729167, _1729169, _1729171, _1729173, _1729175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1729167, _1729169)), hAPP(_1729167, _1729171))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1729173, _1729173)), hAPP(hAPP(c_Product__Type_OPair(_1729173, _1729173), _1729169), _1729171)), c_List_Omeasures(_1729173, _1729175))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729173, _1729173)), hAPP(hAPP(c_Product__Type_OPair(_1729173, _1729173), _1729169), _1729171)), c_List_Omeasures(_1729173, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729173, tc_Nat_Onat)), _1729167), _1729175)))))], (47215 ^ _779300) ^ [_1729440, _1729442] : [-(c_Wellfounded_Owf(_1729440, c_List_Omeasures(_1729440, _1729442)))], (47217 ^ _779300) ^ [_1729483, _1729485, _1729487] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729483, _1729483)), hAPP(hAPP(c_Product__Type_OPair(_1729483, _1729483), _1729485), _1729487)), c_List_Omeasures(_1729483, c_List_Olist_ONil(tc_fun(_1729483, tc_Nat_Onat)))))], (47219 ^ _779300) ^ [_1729537, _1729539] : [-(c_List_Omeasures(_1729537, _1729539) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1729537), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1729537, tc_List_Olist(tc_fun(_1729537, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1729537, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1729537, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1729537), c_List_Omap(tc_fun(_1729537, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1729537, tc_Nat_Onat), _1729537, tc_Nat_Onat), c_COMBI(tc_fun(_1729537, tc_Nat_Onat))))), _1729539)))], (47221 ^ _779300) ^ [_1729634, _1729636, _1729638, _1729640, _1729642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1729634, _1729636)), hAPP(_1729634, _1729638))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729640, _1729640)), hAPP(hAPP(c_Product__Type_OPair(_1729640, _1729640), _1729636), _1729638)), c_List_Omeasures(_1729640, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729640, tc_Nat_Onat)), _1729634), _1729642)))))], (47227 ^ _779300) ^ [_1729829, _1729831, _1729833, _1729835, _1729837] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729829, _1729829)), hAPP(hAPP(c_Product__Type_OPair(_1729829, _1729829), _1729831), _1729833)), c_List_Omeasures(_1729829, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729829, tc_Nat_Onat)), _1729835), _1729837)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1729835, _1729831)), hAPP(_1729835, _1729833)))), 47234 ^ _779300 : [(47235 ^ _779300) ^ [] : [-(hAPP(_1729835, _1729831) = hAPP(_1729835, _1729833))], (47237 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729829, _1729829)), hAPP(hAPP(c_Product__Type_OPair(_1729829, _1729829), _1729831), _1729833)), c_List_Omeasures(_1729829, _1729837))))]]], (47239 ^ _779300) ^ [_1730108, _1730110, _1730112, _1730114, _1730116] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730108, _1730108)), hAPP(hAPP(c_Product__Type_OPair(_1730108, _1730108), _1730110), _1730112)), c_List_Omeasures(_1730108, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1730108, tc_Nat_Onat)), _1730114), _1730116))))), 47240 ^ _779300 : [(47241 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1730114, _1730110)), hAPP(_1730114, _1730112)))], (47243 ^ _779300) ^ [] : [hAPP(_1730114, _1730110) = hAPP(_1730114, _1730112), hBOOL(hAPP(hAPP(c_member(tc_prod(_1730108, _1730108)), hAPP(hAPP(c_Product__Type_OPair(_1730108, _1730108), _1730110), _1730112)), c_List_Omeasures(_1730108, _1730116)))]]], (47251 ^ _779300) ^ [_1730431, _1730433, _1730435, _1730437, _1730439, _1730441, _1730443, _1730445] : [47253 ^ _779300 : [(47254 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730431), 47252 ^ [_1730431, _1730433, _1730435, _1730437, _1730439, _1730441, _1730443, _1730445]), hAPP(c_List_Oset(_1730431), _1730433))))], (47256 ^ _779300) ^ [] : [hAPP(c_Fun_Ocomp(_1730435, _1730435, _1730437, hAPP(_1730439, 47252 ^ [_1730431, _1730433, _1730435, _1730437, _1730439, _1730441, _1730443, _1730445])), _1730441) = hAPP(c_Fun_Ocomp(_1730437, _1730435, _1730437, _1730441), hAPP(_1730443, 47252 ^ [_1730431, _1730433, _1730435, _1730437, _1730439, _1730441, _1730443, _1730445]))]], -(hAPP(c_List_Ofoldl(_1730435, _1730431, hAPP(c_COMBC(_1730431, _1730435, _1730435), _1730439), hAPP(_1730441, _1730445)), _1730433) = hAPP(_1730441, hAPP(c_List_Ofoldl(_1730437, _1730431, hAPP(c_COMBC(_1730431, _1730437, _1730437), _1730443), _1730445), _1730433)))], (47260 ^ _779300) ^ [_1730800, _1730802, _1730804, _1730806] : [class_Orderings_Oorder(_1730800), class_Enum_Oenum(_1730802), 47267 ^ _779300 : [(47268 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1730802, _1730800)), _1730804), _1730806)), 47271 ^ _779300 : [(47272 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730802, _1730800)), _1730804), _1730806)))], (47274 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1730802), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1730802), c_fNot), hAPP(hAPP(c_COMBS(_1730802, _1730800, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1730800, tc_fun(_1730800, tc_HOL_Obool), _1730802), c_fequal), _1730804)), _1730806)))))]]], (47276 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1730802, _1730800)), _1730804), _1730806))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730802, _1730800)), _1730804), _1730806)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1730802), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1730802), c_fNot), hAPP(hAPP(c_COMBS(_1730802, _1730800, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1730800, tc_fun(_1730800, tc_HOL_Obool), _1730802), c_fequal), _1730804)), _1730806))))]]], (47286 ^ _779300) ^ [_1731320, _1731322, _1731324] : [class_Enum_Oenum(_1731320), class_Enum_Oenum(_1731322), 47293 ^ _779300 : [(47294 ^ _779300) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731322, _1731320)), _1731324)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731322), hAPP(hAPP(c_COMBB(tc_fun(_1731320, tc_HOL_Obool), tc_HOL_Obool, _1731322), c_Enum_Oenum__class_Oenum__ex(_1731320)), hAPP(hAPP(c_COMBB(tc_fun(_1731320, tc_prod(_1731322, _1731320)), tc_fun(_1731320, tc_HOL_Obool), _1731322), hAPP(c_COMBB(tc_prod(_1731322, _1731320), tc_HOL_Obool, _1731320), _1731324)), c_Product__Type_OPair(_1731322, _1731320))))))], (47300 ^ _779300) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731322), hAPP(hAPP(c_COMBB(tc_fun(_1731320, tc_HOL_Obool), tc_HOL_Obool, _1731322), c_Enum_Oenum__class_Oenum__ex(_1731320)), hAPP(hAPP(c_COMBB(tc_fun(_1731320, tc_prod(_1731322, _1731320)), tc_fun(_1731320, tc_HOL_Obool), _1731322), hAPP(c_COMBB(tc_prod(_1731322, _1731320), tc_HOL_Obool, _1731320), _1731324)), c_Product__Type_OPair(_1731322, _1731320))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731322, _1731320)), _1731324)))]]], (47306 ^ _779300) ^ [_1731759, _1731761] : [class_Enum_Oenum(_1731759), 47309 ^ _779300 : [(47310 ^ _779300) ^ [] : [47311 ^ _779300 : [(47312 ^ _779300) ^ [_1731861] : [hBOOL(hAPP(_1731761, _1731861))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731759), _1731761)))], (47316 ^ _779300) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731759), _1731761)), -(hBOOL(hAPP(_1731761, 47319 ^ [_1731759, _1731761])))]]], (47323 ^ _779300) ^ [_1732002, _1732004] : [class_Enum_Oenum(_1732002), 47326 ^ _779300 : [(47327 ^ _779300) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732002), _1732004)), -(hBOOL(hAPP(_1732004, 47330 ^ [_1732002, _1732004])))], (47334 ^ _779300) ^ [] : [47335 ^ _779300 : [(47336 ^ _779300) ^ [_1732182] : [hBOOL(hAPP(_1732004, _1732182))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732002), _1732004)))]]], (47340 ^ _779300) ^ [_1732245, _1732247, _1732249, _1732251, _1732253] : [47341 ^ _779300 : [(47342 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732245)), hAPP(hAPP(c_List_Otake(_1732245), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732245)), _1732247)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732249)), _1732251))), _1732247)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732249)), hAPP(hAPP(c_List_Otake(_1732249), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732245)), _1732247)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732249)), _1732251))), _1732251)))], (47344 ^ _779300) ^ [] : [hBOOL(hAPP(_1732253, hAPP(hAPP(c_List_Ozip(_1732245, _1732249), hAPP(hAPP(c_List_Otake(_1732245), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732245)), _1732247)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732249)), _1732251))), _1732247)), hAPP(hAPP(c_List_Otake(_1732249), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732245)), _1732247)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732249)), _1732251))), _1732251))))]], -(hBOOL(hAPP(_1732253, hAPP(hAPP(c_List_Ozip(_1732245, _1732249), _1732247), _1732251))))], (47348 ^ _779300) ^ [_1732657, _1732659, _1732661, _1732663] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1732657, _1732659, _1732661, _1732663) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1732657, _1732659), _1732661), _1732663)))], (47350 ^ _779300) ^ [_1732702, _1732704, _1732706, _1732708] : [47352 ^ _779300 : [(47353 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1732702), 47351 ^ [_1732702, _1732704, _1732706, _1732708]), hAPP(c_List_Oset(_1732702), _1732704))))], (47355 ^ _779300) ^ [] : [hBOOL(hAPP(_1732706, 47351 ^ [_1732702, _1732704, _1732706, _1732708]))]], -(c_List_OdropWhile(_1732702, _1732706, hAPP(hAPP(c_List_Oappend(_1732702), _1732704), _1732708)) = c_List_OdropWhile(_1732702, _1732706, _1732708))], (47359 ^ _779300) ^ [_1732920, _1732922, _1732924, _1732926, _1732928] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732920)), _1732922) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732924)), _1732926), 47365 ^ _779300 : [(47366 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47364 ^ [_1732920, _1732922, _1732924, _1732926, _1732928]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732920)), _1732922))))], (47368 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1732928, hAPP(hAPP(c_List_Onth(_1732920), _1732922), 47364 ^ [_1732920, _1732922, _1732924, _1732926, _1732928])), hAPP(hAPP(c_List_Onth(_1732924), _1732926), 47364 ^ [_1732920, _1732922, _1732924, _1732926, _1732928])))]], -(c_List_Olist__all2(_1732920, _1732924, _1732928, _1732922, _1732926))], (47372 ^ _779300) ^ [_1733278, _1733280] : [class_Orderings_Olinorder(_1733278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1733278), _1733280)), 47380 ^ _779300 : [(47381 ^ _779300) ^ [] : [-(hAPP(c_List_Oset(_1733278), 47379 ^ [_1733278, _1733280]) = _1733280)], (47383 ^ _779300) ^ [] : [-(c_List_Olinorder__class_Osorted(_1733278, 47379 ^ [_1733278, _1733280]))], (47385 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1733278), 47379 ^ [_1733278, _1733280])))], (47387 ^ _779300) ^ [_1733604] : [-(_1733604 = 47379 ^ [_1733278, _1733280]), hAPP(c_List_Oset(_1733278), _1733604) = _1733280, c_List_Olinorder__class_Osorted(_1733278, _1733604), hBOOL(hAPP(c_List_Odistinct(_1733278), _1733604))]]], (47401 ^ _779300) ^ [_1733835, _1733837, _1733839, _1733841] : [47403 ^ _779300 : [(47404 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733835), 47402 ^ [_1733835, _1733837, _1733839, _1733841]), hAPP(c_List_Oset(_1733835), _1733837))))], (47406 ^ _779300) ^ [] : [hBOOL(hAPP(_1733839, 47402 ^ [_1733835, _1733837, _1733839, _1733841]))]], -(c_List_OtakeWhile(_1733835, _1733839, hAPP(hAPP(c_List_Oappend(_1733835), _1733837), _1733841)) = hAPP(hAPP(c_List_Oappend(_1733835), _1733837), c_List_OtakeWhile(_1733835, _1733839, _1733841)))], (47410 ^ _779300) ^ [_1734069, _1734071, _1734073, _1734075, _1734077] : [class_Orderings_Olinorder(_1734069), 47416 ^ _779300 : [(47417 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734071), 47415 ^ [_1734069, _1734071, _1734073, _1734075, _1734077]), hAPP(c_List_Oset(_1734071), _1734073))))], (47419 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1734069), hAPP(_1734075, _1734077)), hAPP(_1734075, 47415 ^ [_1734069, _1734071, _1734073, _1734075, _1734077])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1734071, _1734069, _1734075), _1734077), _1734073) = hAPP(hAPP(c_List_Olist_OCons(_1734071), _1734077), _1734073))], (47423 ^ _779300) ^ [_1734412, _1734414, _1734416, _1734418, _1734420] : [hAPP(c_List_Ofilter(_1734412, _1734414), _1734416) = hAPP(hAPP(c_List_Olist_OCons(_1734412), _1734418), _1734420), 47428 ^ _779300 : [(47429 ^ _779300) ^ [] : [-(_1734416 = hAPP(hAPP(c_List_Oappend(_1734412), 47426 ^ [_1734412, _1734414, _1734416, _1734418, _1734420]), hAPP(hAPP(c_List_Olist_OCons(_1734412), _1734418), 47427 ^ [_1734412, _1734414, _1734416, _1734418, _1734420])))], (47437 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1734414, _1734418)))], (47439 ^ _779300) ^ [] : [-(_1734420 = hAPP(c_List_Ofilter(_1734412, _1734414), 47427 ^ [_1734412, _1734414, _1734416, _1734418, _1734420]))], (47431 ^ _779300) ^ [_1734726] : [hBOOL(hAPP(hAPP(c_member(_1734412), _1734726), hAPP(c_List_Oset(_1734412), 47426 ^ [_1734412, _1734414, _1734416, _1734418, _1734420]))), hBOOL(hAPP(_1734414, _1734726))]]], (47441 ^ _779300) ^ [_1734930, _1734932, _1734934, _1734936, _1734938] : [-(hAPP(c_List_Ofilter(_1734930, _1734932), _1734934) = hAPP(hAPP(c_List_Olist_OCons(_1734930), _1734936), _1734938)), 47442 ^ _779300 : [(47443 ^ _779300) ^ [_1735058, _1735060] : [_1734934 = hAPP(hAPP(c_List_Oappend(_1734930), _1735060), hAPP(hAPP(c_List_Olist_OCons(_1734930), _1734936), _1735058)), 47449 ^ _779300 : [(47450 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734930), 47448 ^ [_1734930, _1734932, _1734934, _1734936, _1734938, _1735058, _1735060]), hAPP(c_List_Oset(_1734930), _1735060))))], (47452 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1734932, 47448 ^ [_1734930, _1734932, _1734934, _1734936, _1734938, _1735058, _1735060])))]], hBOOL(hAPP(_1734932, _1734936)), _1734938 = hAPP(c_List_Ofilter(_1734930, _1734932), _1735058)]]], (47462 ^ _779300) ^ [_1735480, _1735482, _1735484, _1735486, _1735488] : [hAPP(hAPP(c_List_Olist_OCons(_1735480), _1735482), _1735484) = hAPP(c_List_Ofilter(_1735480, _1735486), _1735488), 47467 ^ _779300 : [(47468 ^ _779300) ^ [] : [-(_1735488 = hAPP(hAPP(c_List_Oappend(_1735480), 47465 ^ [_1735480, _1735482, _1735484, _1735486, _1735488]), hAPP(hAPP(c_List_Olist_OCons(_1735480), _1735482), 47466 ^ [_1735480, _1735482, _1735484, _1735486, _1735488])))], (47476 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1735486, _1735482)))], (47478 ^ _779300) ^ [] : [-(_1735484 = hAPP(c_List_Ofilter(_1735480, _1735486), 47466 ^ [_1735480, _1735482, _1735484, _1735486, _1735488]))], (47470 ^ _779300) ^ [_1735794] : [hBOOL(hAPP(hAPP(c_member(_1735480), _1735794), hAPP(c_List_Oset(_1735480), 47465 ^ [_1735480, _1735482, _1735484, _1735486, _1735488]))), hBOOL(hAPP(_1735486, _1735794))]]], (47480 ^ _779300) ^ [_1735998, _1736000, _1736002, _1736004, _1736006] : [-(hAPP(hAPP(c_List_Olist_OCons(_1735998), _1736000), _1736002) = hAPP(c_List_Ofilter(_1735998, _1736004), _1736006)), 47481 ^ _779300 : [(47482 ^ _779300) ^ [_1736126, _1736128] : [_1736006 = hAPP(hAPP(c_List_Oappend(_1735998), _1736128), hAPP(hAPP(c_List_Olist_OCons(_1735998), _1736000), _1736126)), 47488 ^ _779300 : [(47489 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735998), 47487 ^ [_1735998, _1736000, _1736002, _1736004, _1736006, _1736126, _1736128]), hAPP(c_List_Oset(_1735998), _1736128))))], (47491 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1736004, 47487 ^ [_1735998, _1736000, _1736002, _1736004, _1736006, _1736126, _1736128])))]], hBOOL(hAPP(_1736004, _1736000)), _1736002 = hAPP(c_List_Ofilter(_1735998, _1736004), _1736126)]]], (47501 ^ _779300) ^ [_1736524, _1736526, _1736528, _1736530] : [class_Orderings_Oorder(_1736524), class_Enum_Oenum(_1736526), 47508 ^ _779300 : [(47509 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736526, _1736524)), _1736528), _1736530)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736526), hAPP(hAPP(c_COMBS(_1736526, _1736524, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736524, tc_fun(_1736524, tc_HOL_Obool), _1736526), c_Orderings_Oord__class_Oless__eq(_1736524)), _1736528)), _1736530))))], (47515 ^ _779300) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736526), hAPP(hAPP(c_COMBS(_1736526, _1736524, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736524, tc_fun(_1736524, tc_HOL_Obool), _1736526), c_Orderings_Oord__class_Oless__eq(_1736524)), _1736528)), _1736530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736526, _1736524)), _1736528), _1736530)))]]], (47521 ^ _779300) ^ [_1736914, _1736916] : [class_Enum_Oenum(_1736914), 47524 ^ _779300 : [(47525 ^ _779300) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736914), _1736916)), 47528 ^ _779300 : [(47529 ^ _779300) ^ [_1737040] : [-(hBOOL(hAPP(_1736916, _1737040)))]]], (47531 ^ _779300) ^ [] : [hBOOL(hAPP(_1736916, 47532 ^ [_1736914, _1736916])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736914), _1736916)))]]], (47538 ^ _779300) ^ [_1737167, _1737169] : [class_Enum_Oenum(_1737167), 47541 ^ _779300 : [(47542 ^ _779300) ^ [] : [hBOOL(hAPP(_1737169, 47543 ^ [_1737167, _1737169])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737167), _1737169)))], (47549 ^ _779300) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737167), _1737169)), 47552 ^ _779300 : [(47553 ^ _779300) ^ [_1737385] : [-(hBOOL(hAPP(_1737169, _1737385)))]]]]], (47555 ^ _779300) ^ [_1737420, _1737422, _1737424] : [class_Enum_Oenum(_1737420), class_Enum_Oenum(_1737422), 47562 ^ _779300 : [(47563 ^ _779300) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1737422, _1737420)), _1737424)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737422), hAPP(hAPP(c_COMBB(tc_fun(_1737420, tc_HOL_Obool), tc_HOL_Obool, _1737422), c_Enum_Oenum__class_Oenum__all(_1737420)), hAPP(hAPP(c_COMBB(tc_fun(_1737420, tc_prod(_1737422, _1737420)), tc_fun(_1737420, tc_HOL_Obool), _1737422), hAPP(c_COMBB(tc_prod(_1737422, _1737420), tc_HOL_Obool, _1737420), _1737424)), c_Product__Type_OPair(_1737422, _1737420))))))], (47569 ^ _779300) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737422), hAPP(hAPP(c_COMBB(tc_fun(_1737420, tc_HOL_Obool), tc_HOL_Obool, _1737422), c_Enum_Oenum__class_Oenum__all(_1737420)), hAPP(hAPP(c_COMBB(tc_fun(_1737420, tc_prod(_1737422, _1737420)), tc_fun(_1737420, tc_HOL_Obool), _1737422), hAPP(c_COMBB(tc_prod(_1737422, _1737420), tc_HOL_Obool, _1737420), _1737424)), c_Product__Type_OPair(_1737422, _1737420))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1737422, _1737420)), _1737424)))]]], (47575 ^ _779300) ^ [_1737859, _1737861, _1737863, _1737865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737859), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737861)), _1737863))), 47581 ^ _779300 : [(47582 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737861), 47580 ^ [_1737859, _1737861, _1737863, _1737865]), hAPP(c_List_Oset(_1737861), _1737863))))], (47584 ^ _779300) ^ [] : [hBOOL(hAPP(_1737865, 47580 ^ [_1737859, _1737861, _1737863, _1737865]))]], -(hBOOL(hAPP(_1737865, hAPP(hAPP(c_List_Onth(_1737861), _1737863), _1737859))))], (47588 ^ _779300) ^ [_1738145, _1738147, _1738149] : [class_Orderings_Olinorder(_1738145), 47594 ^ _779300 : [(47595 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738145), 47593 ^ [_1738145, _1738147, _1738149]), hAPP(c_List_Oset(_1738145), _1738147))))], (47597 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1738145), _1738149), 47593 ^ [_1738145, _1738147, _1738149]))]], c_List_Olinorder__class_Osorted(_1738145, _1738147), -(c_List_Olinorder__class_Osorted(_1738145, hAPP(hAPP(c_List_Olist_OCons(_1738145), _1738149), _1738147)))], (47605 ^ _779300) ^ [_1738479, _1738481, _1738483] : [c_List_Olist__ex(_1738479, _1738481, _1738483), 47609 ^ _779300 : [(47610 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47608 ^ [_1738479, _1738481, _1738483]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738479)), _1738483))))], (47612 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1738481, hAPP(hAPP(c_List_Onth(_1738479), _1738483), 47608 ^ [_1738479, _1738481, _1738483]))))]]], (47614 ^ _779300) ^ [_1738649, _1738651, _1738653] : [-(c_List_Olist__ex(_1738649, _1738651, _1738653)), 47615 ^ _779300 : [(47616 ^ _779300) ^ [_1738714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738714), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738649)), _1738653))), hBOOL(hAPP(_1738651, hAPP(hAPP(c_List_Onth(_1738649), _1738653), _1738714)))]]], (47624 ^ _779300) ^ [_1738887, _1738889, _1738891] : [hBOOL(hAPP(hAPP(c_member(_1738887), _1738889), hAPP(c_List_Oset(_1738887), _1738891))), -(_1738891 = hAPP(hAPP(c_List_Oappend(_1738887), 47627 ^ [_1738887, _1738889, _1738891]), hAPP(hAPP(c_List_Olist_OCons(_1738887), _1738889), 47628 ^ [_1738887, _1738889, _1738891])))], (47632 ^ _779300) ^ [_1739046, _1739048, _1739050] : [47633 ^ _779300 : [(47634 ^ _779300) ^ [_1739123, _1739125] : [_1739050 = hAPP(hAPP(c_List_Oappend(_1739046), _1739125), hAPP(hAPP(c_List_Olist_OCons(_1739046), _1739048), _1739123))]], -(hBOOL(hAPP(hAPP(c_member(_1739046), _1739048), hAPP(c_List_Oset(_1739046), _1739050))))], (47638 ^ _779300) ^ [_1739218, _1739220] : [c_List_Olist__ex(_1739218, _1739220, c_List_Olist_ONil(_1739218))], (47650 ^ _779300) ^ [_1739379, _1739381, _1739383, _1739385] : [47651 ^ _779300 : [(47652 ^ _779300) ^ [] : [c_List_Olist__ex(_1739379, _1739381, _1739383)], (47654 ^ _779300) ^ [] : [c_List_Olist__ex(_1739379, _1739381, _1739385)]], -(c_List_Olist__ex(_1739379, _1739381, hAPP(hAPP(c_List_Oappend(_1739379), _1739383), _1739385)))], (47640 ^ _779300) ^ [_1739267, _1739269, _1739271, _1739273] : [c_List_Olist__ex(_1739267, _1739269, hAPP(hAPP(c_List_Oappend(_1739267), _1739271), _1739273)), -(c_List_Olist__ex(_1739267, _1739269, _1739271)), -(c_List_Olist__ex(_1739267, _1739269, _1739273))], (47658 ^ _779300) ^ [_1739540, _1739542, _1739544] : [c_List_Olist__ex(_1739540, _1739542, _1739544), 47662 ^ _779300 : [(47663 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739540), 47661 ^ [_1739540, _1739542, _1739544]), hAPP(c_List_Oset(_1739540), _1739544))))], (47665 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1739542, 47661 ^ [_1739540, _1739542, _1739544])))]]], (47667 ^ _779300) ^ [_1739694, _1739696, _1739698] : [-(c_List_Olist__ex(_1739694, _1739696, _1739698)), 47668 ^ _779300 : [(47669 ^ _779300) ^ [_1739751] : [hBOOL(hAPP(hAPP(c_member(_1739694), _1739751), hAPP(c_List_Oset(_1739694), _1739698))), hBOOL(hAPP(_1739696, _1739751))]]], (47677 ^ _779300) ^ [_1739908, _1739910, _1739912] : [c_List_Olist__ex(_1739908, _1739910, hAPP(c_List_Orev(_1739908), _1739912)), -(c_List_Olist__ex(_1739908, _1739910, _1739912))], (47683 ^ _779300) ^ [_1739997, _1739999, _1740001] : [c_List_Olist__ex(_1739997, _1739999, _1740001), -(c_List_Olist__ex(_1739997, _1739999, hAPP(c_List_Orev(_1739997), _1740001)))], (47699 ^ _779300) ^ [_1740227, _1740229, _1740231, _1740233] : [47700 ^ _779300 : [(47701 ^ _779300) ^ [] : [hBOOL(hAPP(_1740229, _1740231))], (47703 ^ _779300) ^ [] : [c_List_Olist__ex(_1740227, _1740229, _1740233)]], -(c_List_Olist__ex(_1740227, _1740229, hAPP(hAPP(c_List_Olist_OCons(_1740227), _1740231), _1740233)))], (47689 ^ _779300) ^ [_1740113, _1740115, _1740117, _1740119] : [c_List_Olist__ex(_1740113, _1740115, hAPP(hAPP(c_List_Olist_OCons(_1740113), _1740117), _1740119)), -(hBOOL(hAPP(_1740115, _1740117))), -(c_List_Olist__ex(_1740113, _1740115, _1740119))], (47707 ^ _779300) ^ [_1740390, _1740392, _1740394] : [hBOOL(hAPP(hAPP(c_member(_1740390), _1740392), hAPP(c_List_Oset(_1740390), _1740394))), 47712 ^ _779300 : [(47713 ^ _779300) ^ [] : [-(_1740394 = hAPP(hAPP(c_List_Oappend(_1740390), 47710 ^ [_1740390, _1740392, _1740394]), hAPP(hAPP(c_List_Olist_OCons(_1740390), _1740392), 47711 ^ [_1740390, _1740392, _1740394])))], (47715 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1740390), _1740392), hAPP(c_List_Oset(_1740390), 47710 ^ [_1740390, _1740392, _1740394])))]]], (47717 ^ _779300) ^ [_1740645, _1740647, _1740649] : [-(hBOOL(hAPP(hAPP(c_member(_1740645), _1740647), hAPP(c_List_Oset(_1740645), _1740649)))), 47718 ^ _779300 : [(47719 ^ _779300) ^ [_1740734] : [47720 ^ _779300 : [(47721 ^ _779300) ^ [_1740807] : [_1740649 = hAPP(hAPP(c_List_Oappend(_1740645), _1740734), hAPP(hAPP(c_List_Olist_OCons(_1740645), _1740647), _1740807))]], -(hBOOL(hAPP(hAPP(c_member(_1740645), _1740647), hAPP(c_List_Oset(_1740645), _1740734))))]]], (47727 ^ _779300) ^ [_1740946, _1740948, _1740950] : [hBOOL(hAPP(hAPP(c_member(_1740946), _1740948), hAPP(c_List_Oset(_1740946), _1740950))), 47732 ^ _779300 : [(47733 ^ _779300) ^ [] : [-(_1740950 = hAPP(hAPP(c_List_Oappend(_1740946), 47730 ^ [_1740946, _1740948, _1740950]), hAPP(hAPP(c_List_Olist_OCons(_1740946), _1740948), 47731 ^ [_1740946, _1740948, _1740950])))], (47735 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1740946), _1740948), hAPP(c_List_Oset(_1740946), 47731 ^ [_1740946, _1740948, _1740950])))]]], (47737 ^ _779300) ^ [_1741201, _1741203, _1741205] : [-(hBOOL(hAPP(hAPP(c_member(_1741201), _1741203), hAPP(c_List_Oset(_1741201), _1741205)))), 47738 ^ _779300 : [(47739 ^ _779300) ^ [_1741290, _1741292] : [_1741205 = hAPP(hAPP(c_List_Oappend(_1741201), _1741292), hAPP(hAPP(c_List_Olist_OCons(_1741201), _1741203), _1741290)), -(hBOOL(hAPP(hAPP(c_member(_1741201), _1741203), hAPP(c_List_Oset(_1741201), _1741290))))]]], (47757 ^ _779300) ^ [_1741705, _1741707, _1741709] : [47759 ^ _779300 : [(47760 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47758 ^ [_1741705, _1741707, _1741709]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741705)), _1741709))))], (47762 ^ _779300) ^ [] : [hBOOL(hAPP(_1741707, hAPP(hAPP(c_List_Onth(_1741705), _1741709), 47758 ^ [_1741705, _1741707, _1741709])))]], -(c_List_Olist__all(_1741705, _1741707, _1741709))], (47747 ^ _779300) ^ [_1741491, _1741493, _1741495] : [c_List_Olist__all(_1741491, _1741493, _1741495), 47750 ^ _779300 : [(47751 ^ _779300) ^ [_1741580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741580), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741491)), _1741495))), -(hBOOL(hAPP(_1741493, hAPP(hAPP(c_List_Onth(_1741491), _1741495), _1741580))))]]], (47766 ^ _779300) ^ [] : [-(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))))], (47768 ^ _779300) ^ [_1741931, _1741933] : [-(c_List_Olist__all(_1741931, _1741933, c_List_Olist_ONil(_1741931)))], (47770 ^ _779300) ^ [_1741980, _1741982, _1741984, _1741986] : [c_List_Olist__all(_1741980, _1741982, hAPP(hAPP(c_List_Oappend(_1741980), _1741984), _1741986)), 47773 ^ _779300 : [(47774 ^ _779300) ^ [] : [-(c_List_Olist__all(_1741980, _1741982, _1741984))], (47776 ^ _779300) ^ [] : [-(c_List_Olist__all(_1741980, _1741982, _1741986))]]], (47778 ^ _779300) ^ [_1742105, _1742107, _1742109, _1742111] : [-(c_List_Olist__all(_1742105, _1742107, hAPP(hAPP(c_List_Oappend(_1742105), _1742109), _1742111))), c_List_Olist__all(_1742105, _1742107, _1742109), c_List_Olist__all(_1742105, _1742107, _1742111)], (47788 ^ _779300) ^ [_1742266] : [class_Nat_Osize(_1742266), -(c_FunDef_Ois__measure(_1742266, c_Nat_Osize__class_Osize(_1742266)))], (47794 ^ _779300) ^ [_1742343, _1742345] : [-(c_FunDef_Ois__measure(_1742343, _1742345))], (47796 ^ _779300) ^ [_1742368, _1742370] : [-(c_FunDef_Ois__measure(_1742368, _1742370))], (47798 ^ _779300) ^ [_1742393, _1742395] : [-(c_FunDef_Ois__measure(_1742393, _1742395))], (47810 ^ _779300) ^ [_1742626, _1742628, _1742630] : [47812 ^ _779300 : [(47813 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742626), 47811 ^ [_1742626, _1742628, _1742630]), hAPP(c_List_Oset(_1742626), _1742630))))], (47815 ^ _779300) ^ [] : [hBOOL(hAPP(_1742628, 47811 ^ [_1742626, _1742628, _1742630]))]], -(c_List_Olist__all(_1742626, _1742628, _1742630))], (47800 ^ _779300) ^ [_1742436, _1742438, _1742440] : [c_List_Olist__all(_1742436, _1742438, _1742440), 47803 ^ _779300 : [(47804 ^ _779300) ^ [_1742517] : [hBOOL(hAPP(hAPP(c_member(_1742436), _1742517), hAPP(c_List_Oset(_1742436), _1742440))), -(hBOOL(hAPP(_1742438, _1742517)))]]], (47819 ^ _779300) ^ [_1742808, _1742810, _1742812] : [c_FunDef_Ois__measure(_1742808, _1742810), -(c_FunDef_Ois__measure(tc_prod(_1742808, _1742812), hAPP(hAPP(c_COMBB(_1742808, tc_Nat_Onat, tc_prod(_1742808, _1742812)), _1742810), c_Product__Type_Ofst(_1742808, _1742812))))], (47825 ^ _779300) ^ [_1742925, _1742927, _1742929] : [c_FunDef_Ois__measure(_1742925, _1742927), -(c_FunDef_Ois__measure(tc_prod(_1742929, _1742925), hAPP(hAPP(c_COMBB(_1742925, tc_Nat_Onat, tc_prod(_1742929, _1742925)), _1742927), c_Product__Type_Osnd(_1742929, _1742925))))], (47831 ^ _779300) ^ [_1743060, _1743062, _1743064] : [c_List_Olist__all(_1743060, _1743062, hAPP(c_List_Orev(_1743060), _1743064)), -(c_List_Olist__all(_1743060, _1743062, _1743064))], (47837 ^ _779300) ^ [_1743149, _1743151, _1743153] : [c_List_Olist__all(_1743149, _1743151, _1743153), -(c_List_Olist__all(_1743149, _1743151, hAPP(c_List_Orev(_1743149), _1743153)))], (47843 ^ _779300) ^ [_1743265, _1743267, _1743269, _1743271] : [c_List_Olist__all(_1743265, _1743267, hAPP(hAPP(c_List_Olist_OCons(_1743265), _1743269), _1743271)), 47846 ^ _779300 : [(47847 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1743267, _1743269)))], (47849 ^ _779300) ^ [] : [-(c_List_Olist__all(_1743265, _1743267, _1743271))]]], (47851 ^ _779300) ^ [_1743392, _1743394, _1743396, _1743398] : [-(c_List_Olist__all(_1743392, _1743394, hAPP(hAPP(c_List_Olist_OCons(_1743392), _1743396), _1743398))), hBOOL(hAPP(_1743394, _1743396)), c_List_Olist__all(_1743392, _1743394, _1743398)], (47861 ^ _779300) ^ [_1743573, _1743575, _1743577] : [47863 ^ _779300 : [(47864 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743573), 47862 ^ [_1743573, _1743575, _1743577]), hAPP(c_List_Oset(_1743573), _1743575))))], (47866 ^ _779300) ^ [] : [hBOOL(hAPP(_1743577, 47862 ^ [_1743573, _1743575, _1743577]))]], -(c_List_Olist__all(_1743573, _1743577, _1743575))], (47870 ^ _779300) ^ [_1743749, _1743751, _1743753] : [c_List_Olist__all(_1743749, _1743753, _1743751), 47873 ^ _779300 : [(47874 ^ _779300) ^ [_1743830] : [hBOOL(hAPP(hAPP(c_member(_1743749), _1743830), hAPP(c_List_Oset(_1743749), _1743751))), -(hBOOL(hAPP(_1743753, _1743830)))]]], (47890 ^ _779300) ^ [_1744153, _1744155, _1744157] : [47892 ^ _779300 : [(47893 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744153), 47891 ^ [_1744153, _1744155, _1744157]), hAPP(c_List_Oset(_1744153), _1744157))))], (47895 ^ _779300) ^ [] : [hBOOL(hAPP(_1744155, 47891 ^ [_1744153, _1744155, _1744157]))]], -(c_List_Olist__all(_1744153, _1744155, _1744157))], (47880 ^ _779300) ^ [_1743963, _1743965, _1743967] : [c_List_Olist__all(_1743963, _1743965, _1743967), 47883 ^ _779300 : [(47884 ^ _779300) ^ [_1744044] : [hBOOL(hAPP(hAPP(c_member(_1743963), _1744044), hAPP(c_List_Oset(_1743963), _1743967))), -(hBOOL(hAPP(_1743965, _1744044)))]]], (47915 ^ _779300) ^ [_1744632, _1744634, _1744636, _1744638] : [-(c_List_Olist__ex1(_1744632, _1744634, hAPP(hAPP(c_List_Olist_OCons(_1744632), _1744636), _1744638))), 47918 ^ _779300 : [(47919 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1744634, _1744636)))], (47921 ^ _779300) ^ [] : [c_List_Olist__all(_1744632, hAPP(hAPP(c_COMBS(_1744632, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1744632), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1744632), c_fNot), _1744634))), hAPP(c_fequal, _1744636)), _1744638)]], 47922 ^ _779300 : [(47923 ^ _779300) ^ [] : [hBOOL(hAPP(_1744634, _1744636))], (47925 ^ _779300) ^ [] : [c_List_Olist__ex1(_1744632, _1744634, _1744638)]]], (47899 ^ _779300) ^ [_1744356, _1744358, _1744360, _1744362] : [c_List_Olist__ex1(_1744356, _1744358, hAPP(hAPP(c_List_Olist_OCons(_1744356), _1744360), _1744362)), 47902 ^ _779300 : [(47903 ^ _779300) ^ [] : [hBOOL(hAPP(_1744358, _1744360)), -(c_List_Olist__all(_1744356, hAPP(hAPP(c_COMBS(_1744356, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1744356), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1744356), c_fNot), _1744358))), hAPP(c_fequal, _1744360)), _1744362))], (47909 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1744358, _1744360))), -(c_List_Olist__ex1(_1744356, _1744358, _1744362))]]], (47929 ^ _779300) ^ [] : [-(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)))], (47931 ^ _779300) ^ [_1744970, _1744972] : [c_List_Olist__ex1(_1744970, _1744972, c_List_Olist_ONil(_1744970))], (47933 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47935 ^ _779300) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47937 ^ _779300) ^ [_1745052, _1745054, _1745056] : [c_List_Olist__ex1(_1745052, _1745054, _1745056), 47941 ^ _779300 : [(47942 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745052), 47940 ^ [_1745052, _1745054, _1745056]), hAPP(c_List_Oset(_1745052), _1745056))))], (47944 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1745054, 47940 ^ [_1745052, _1745054, _1745056])))], (47946 ^ _779300) ^ [_1745298] : [-(_1745298 = 47940 ^ [_1745052, _1745054, _1745056]), hBOOL(hAPP(hAPP(c_member(_1745052), _1745298), hAPP(c_List_Oset(_1745052), _1745056))), hBOOL(hAPP(_1745054, _1745298))]]], (47956 ^ _779300) ^ [_1745485, _1745487, _1745489] : [-(c_List_Olist__ex1(_1745485, _1745487, _1745489)), 47957 ^ _779300 : [(47958 ^ _779300) ^ [_1745579] : [hBOOL(hAPP(hAPP(c_member(_1745485), _1745579), hAPP(c_List_Oset(_1745485), _1745489))), hBOOL(hAPP(_1745487, _1745579)), 47966 ^ _779300 : [(47967 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745485), 47965 ^ [_1745485, _1745487, _1745489, _1745579]), hAPP(c_List_Oset(_1745485), _1745489))))], (47969 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1745487, 47965 ^ [_1745485, _1745487, _1745489, _1745579])))], (47971 ^ _779300) ^ [] : [47965 ^ [_1745485, _1745487, _1745489, _1745579] = _1745579]]]]], (47975 ^ _779300) ^ [_1745932, _1745934, _1745936, _1745938, _1745940] : [_1745932 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1745934, _1745936, _1745938, _1745940), _1745932) = c_Lazy__Sequence_Ohit__bound(_1745936))], (47981 ^ _779300) ^ [_1746029, _1746031, _1746033, _1746035, _1746037] : [-(_1746029 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1746031, _1746033, _1746035, _1746037), _1746029) = c_Lazy__Sequence_Ohb__bind(_1746031, _1746033, hAPP(_1746035, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1746029), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1746031, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746033))), _1746037), _1746029)))], (47987 ^ _779300) ^ [_1746127, _1746129, _1746131, _1746133, _1746135] : [_1746127 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1746129, _1746131, _1746133, _1746135), _1746127) = c_Lazy__Sequence_Oempty(_1746131))], (47993 ^ _779300) ^ [_1746224, _1746226, _1746228, _1746230, _1746232] : [-(_1746224 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1746226, _1746228, _1746230, _1746232), _1746224) = hAPP(c_Lazy__Sequence_Obind(_1746226, _1746228, hAPP(_1746230, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1746224), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1746226, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746228)), _1746232), _1746224)))], (47999 ^ _779300) ^ [_1746304, _1746306, _1746308, _1746310, _1746312, _1746314, _1746316] : [-(c_New__Random__Sequence_Opos__decr__bind(_1746304, _1746306, _1746308, _1746310, _1746312, _1746314, _1746316) = c_New__DSequence_Opos__decr__bind(_1746304, _1746306, hAPP(hAPP(hAPP(_1746308, _1746312), _1746314), _1746316), hAPP(hAPP(c_COMBC(_1746304, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746306))), hAPP(hAPP(c_COMBC(_1746304, 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(_1746306)))), hAPP(hAPP(c_COMBC(_1746304, 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(_1746306))))), _1746310), _1746312)), _1746314)), _1746316)))], (48001 ^ _779300) ^ [_1746415, _1746417, _1746419, _1746421, _1746423, _1746425, _1746427] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1746415, _1746417, _1746419, _1746421, _1746423, _1746425, _1746427) = c_New__DSequence_Oneg__decr__bind(_1746415, _1746417, hAPP(hAPP(hAPP(_1746419, _1746423), _1746425), _1746427), hAPP(hAPP(c_COMBC(_1746415, 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(_1746417)))), hAPP(hAPP(c_COMBC(_1746415, 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(_1746417))))), hAPP(hAPP(c_COMBC(_1746415, 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(_1746417)))))), _1746421), _1746423)), _1746425)), _1746427)))], (48003 ^ _779300) ^ [_1746532, _1746534, _1746536, _1746538, _1746540] : [-(hAPP(c_New__DSequence_Oneg__bind(_1746532, _1746534, _1746536, _1746538), _1746540) = c_Lazy__Sequence_Ohb__bind(_1746532, _1746534, hAPP(_1746536, _1746540), hAPP(hAPP(c_COMBC(_1746532, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746534))), _1746538), _1746540)))], (48005 ^ _779300) ^ [_1746593, _1746595] : [-(hAPP(c_New__DSequence_Opos__empty(_1746593), _1746595) = c_Lazy__Sequence_Oempty(_1746593))], (48007 ^ _779300) ^ [_1746625, _1746627, _1746629, _1746631] : [-(c_New__Random__Sequence_Opos__empty(_1746625, _1746627, _1746629, _1746631) = c_New__DSequence_Opos__empty(_1746625))], (48009 ^ _779300) ^ [_1746661, _1746663, _1746665, _1746667, _1746669, _1746671, _1746673] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1746661, _1746663, _1746665, _1746667), _1746669), _1746671), _1746673) = c_New__DSequence_Oneg__bind(_1746661, _1746663, hAPP(hAPP(hAPP(_1746665, _1746669), _1746671), _1746673), hAPP(hAPP(c_COMBC(_1746661, 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(_1746663)))), hAPP(hAPP(c_COMBC(_1746661, 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(_1746663))))), hAPP(hAPP(c_COMBC(_1746661, 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(_1746663)))))), _1746667), _1746669)), _1746671)), _1746673)))], (48011 ^ _779300) ^ [_1746784, _1746786, _1746788, _1746790, _1746792] : [-(hAPP(c_New__DSequence_Opos__bind(_1746784, _1746786, _1746788, _1746790), _1746792) = hAPP(c_Lazy__Sequence_Obind(_1746784, _1746786, hAPP(_1746788, _1746792)), hAPP(hAPP(c_COMBC(_1746784, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746786)), _1746790), _1746792)))], (48013 ^ _779300) ^ [_1746845, _1746847, _1746849, _1746851] : [-(c_New__Random__Sequence_Oneg__map(_1746845, _1746847, _1746849, _1746851) = c_New__Random__Sequence_Oneg__bind(_1746845, _1746847, _1746851, hAPP(c_Fun_Ocomp(_1746847, 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(_1746847)))))), _1746845, c_New__Random__Sequence_Oneg__single(_1746847)), _1746849)))], (48015 ^ _779300) ^ [_1746910, _1746912, _1746914, _1746916, _1746918] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1746910), _1746912), _1746914), _1746916), _1746918) = c_New__DSequence_Oneg__single(_1746910, _1746912))], (48017 ^ _779300) ^ [_1746958, _1746960, _1746962, _1746964, _1746966, _1746968, _1746970] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1746958, _1746960, _1746962, _1746964), _1746966), _1746968), _1746970) = c_New__DSequence_Opos__bind(_1746958, _1746960, hAPP(hAPP(hAPP(_1746962, _1746966), _1746968), _1746970), hAPP(hAPP(c_COMBC(_1746958, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746960))), hAPP(hAPP(c_COMBC(_1746958, 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(_1746960)))), hAPP(hAPP(c_COMBC(_1746958, 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(_1746960))))), _1746964), _1746966)), _1746968)), _1746970)))], (48019 ^ _779300) ^ [_1747075, _1747077, _1747079] : [-(hAPP(c_New__DSequence_Oneg__single(_1747075, _1747077), _1747079) = c_Lazy__Sequence_Ohb__single(_1747075, _1747077))], (48021 ^ _779300) ^ [_1747111, _1747113, _1747115, _1747117] : [-(c_New__Random__Sequence_Opos__map(_1747111, _1747113, _1747115, _1747117) = c_New__Random__Sequence_Opos__bind(_1747111, _1747113, _1747117, hAPP(c_Fun_Ocomp(_1747113, 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(_1747113))))), _1747111, c_New__Random__Sequence_Opos__single(_1747113)), _1747115)))], (48023 ^ _779300) ^ [_1747174, _1747176, _1747178, _1747180, _1747182] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1747174), _1747176), _1747178), _1747180), _1747182) = c_New__DSequence_Opos__single(_1747174, _1747176))], (48025 ^ _779300) ^ [_1747222, _1747224, _1747226] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747222)), c_List_Osplice(_1747222, _1747224, _1747226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747222)), _1747224)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747222)), _1747226)))], (48027 ^ _779300) ^ [_1747280, _1747282, _1747284, _1747286, _1747288] : [-(c_List_Osplice(_1747280, hAPP(hAPP(c_List_Olist_OCons(_1747280), _1747282), _1747284), hAPP(hAPP(c_List_Olist_OCons(_1747280), _1747286), _1747288)) = hAPP(hAPP(c_List_Olist_OCons(_1747280), _1747282), hAPP(hAPP(c_List_Olist_OCons(_1747280), _1747286), c_List_Osplice(_1747280, _1747284, _1747288))))], (48029 ^ _779300) ^ [_1747351, _1747353] : [-(c_List_Osplice(_1747351, _1747353, c_List_Olist_ONil(_1747351)) = _1747353)], (48031 ^ _779300) ^ [_1747382, _1747384] : [-(c_List_Osplice(_1747382, c_List_Olist_ONil(_1747382), _1747384) = _1747384)], (48033 ^ _779300) ^ [_1747413, _1747415, _1747417] : [-(c_List_Osplice(_1747413, hAPP(hAPP(c_List_Olist_OCons(_1747413), _1747415), _1747417), c_List_Olist_ONil(_1747413)) = hAPP(hAPP(c_List_Olist_OCons(_1747413), _1747415), _1747417))], (48035 ^ _779300) ^ [_1747462, _1747464, _1747466] : [-(hAPP(c_New__DSequence_Opos__single(_1747462, _1747464), _1747466) = hAPP(c_Lazy__Sequence_Osingle(_1747462), _1747464))], (48037 ^ _779300) ^ [_1747515, _1747517] : [c_Wellfounded_Oacyclic(_1747515, hAPP(c_Set_OCollect(tc_prod(_1747515, _1747515)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747515, _1747515, tc_HOL_Obool), c_Predicate_Oconversep(_1747515, _1747515, _1747517)))), -(c_Wellfounded_Oacyclic(_1747515, hAPP(c_Set_OCollect(tc_prod(_1747515, _1747515)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747515, _1747515, tc_HOL_Obool), _1747517))))], (48043 ^ _779300) ^ [_1747656, _1747658] : [c_Wellfounded_Oacyclic(_1747656, hAPP(c_Set_OCollect(tc_prod(_1747656, _1747656)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747656, _1747656, tc_HOL_Obool), _1747658))), -(c_Wellfounded_Oacyclic(_1747656, hAPP(c_Set_OCollect(tc_prod(_1747656, _1747656)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747656, _1747656, tc_HOL_Obool), c_Predicate_Oconversep(_1747656, _1747656, _1747658)))))], (48049 ^ _779300) ^ [_1747803, _1747805, _1747807, _1747809] : [-(c_Predicate_Oconversep(_1747803, _1747805, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1747803, tc_fun(_1747805, tc_HOL_Obool))), _1747807), _1747809)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1747805, tc_fun(_1747803, tc_HOL_Obool))), c_Predicate_Oconversep(_1747803, _1747805, _1747807)), c_Predicate_Oconversep(_1747803, _1747805, _1747809)))], (48051 ^ _779300) ^ [_1747872, _1747874, _1747876, _1747878] : [-(c_Predicate_Oconversep(_1747872, _1747874, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1747872, tc_fun(_1747874, tc_HOL_Obool))), _1747876), _1747878)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1747874, tc_fun(_1747872, tc_HOL_Obool))), c_Predicate_Oconversep(_1747872, _1747874, _1747876)), c_Predicate_Oconversep(_1747872, _1747874, _1747878)))], (48053 ^ _779300) ^ [_1747941, _1747943, _1747945, _1747947, _1747949] : [-(c_Predicate_Oconversep(_1747941, _1747943, c_Predicate_Opred__comp(_1747941, _1747945, _1747943, _1747947, _1747949)) = c_Predicate_Opred__comp(_1747943, _1747945, _1747941, c_Predicate_Oconversep(_1747945, _1747943, _1747949), c_Predicate_Oconversep(_1747941, _1747945, _1747947)))], (48055 ^ _779300) ^ [_1747996] : [-(c_Predicate_Oconversep(_1747996, _1747996, c_fequal) = c_fequal)], (48057 ^ _779300) ^ [_1748023, _1748025, _1748027] : [-(c_Predicate_Oconversep(_1748023, _1748025, c_Predicate_Oconversep(_1748025, _1748023, _1748027)) = _1748027)], (48059 ^ _779300) ^ [_1748082, _1748084, _1748086, _1748088, _1748090] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748082, _1748084, _1748086), _1748088), _1748090)), -(hBOOL(hAPP(hAPP(_1748086, _1748090), _1748088)))], (48065 ^ _779300) ^ [_1748189, _1748191, _1748193, _1748195, _1748197] : [hBOOL(hAPP(hAPP(_1748193, _1748197), _1748195)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748189, _1748191, _1748193), _1748195), _1748197)))], (48071 ^ _779300) ^ [_1748326, _1748328, _1748330, _1748332, _1748334] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748326, _1748328, _1748330), _1748332), _1748334)), -(hBOOL(hAPP(hAPP(_1748330, _1748334), _1748332)))], (48077 ^ _779300) ^ [_1748433, _1748435, _1748437, _1748439, _1748441] : [hBOOL(hAPP(hAPP(_1748437, _1748441), _1748439)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748433, _1748435, _1748437), _1748439), _1748441)))], (48083 ^ _779300) ^ [_1748546, _1748548, _1748550, _1748552, _1748554] : [hBOOL(hAPP(hAPP(_1748546, _1748548), _1748550)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748552, _1748554, _1748546), _1748550), _1748548)))], (48089 ^ _779300) ^ [_1748657, _1748659, _1748661, _1748663, _1748665] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748657, _1748659, _1748661), _1748663), _1748665)), -(hBOOL(hAPP(hAPP(_1748661, _1748665), _1748663)))], (48095 ^ _779300) ^ [_1748786, _1748788, _1748790] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748786, _1748786, hAPP(hAPP(c_COMBB(tc_fun(_1748786, tc_HOL_Obool), tc_fun(_1748786, tc_HOL_Obool), _1748786), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1748786), c_fNot)), c_fequal)), _1748788), _1748790)), _1748788 = _1748790], (48101 ^ _779300) ^ [_1748924, _1748926, _1748928] : [-(_1748926 = _1748928), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748924, _1748924, hAPP(hAPP(c_COMBB(tc_fun(_1748924, tc_HOL_Obool), tc_fun(_1748924, tc_HOL_Obool), _1748924), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1748924), c_fNot)), c_fequal)), _1748926), _1748928)))], (48107 ^ _779300) ^ [_1749020, _1749022, _1749024, _1749026, _1749028] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749020, _1749022, hAPP(hAPP(c_COMBC(_1749020, tc_fun(tc_prod(_1749020, _1749022), tc_HOL_Obool), tc_fun(_1749022, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749022, tc_fun(tc_fun(tc_prod(_1749020, _1749022), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1749020, _1749022), tc_HOL_Obool), tc_fun(_1749022, tc_HOL_Obool)), _1749020), c_COMBC(_1749022, tc_fun(tc_prod(_1749020, _1749022), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749022, tc_prod(_1749020, _1749022)), tc_fun(_1749022, tc_fun(tc_fun(tc_prod(_1749020, _1749022), tc_HOL_Obool), tc_HOL_Obool)), _1749020), hAPP(c_COMBB(tc_prod(_1749020, _1749022), tc_fun(tc_fun(tc_prod(_1749020, _1749022), tc_HOL_Obool), tc_HOL_Obool), _1749022), c_member(tc_prod(_1749020, _1749022)))), c_Product__Type_OPair(_1749020, _1749022)))), _1749024)), _1749026), _1749028)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1749022, _1749020)), hAPP(hAPP(c_Product__Type_OPair(_1749022, _1749020), _1749026), _1749028)), hAPP(c_Relation_Oconverse(_1749020, _1749022), _1749024))))], (48113 ^ _779300) ^ [_1749403, _1749405, _1749407, _1749409, _1749411] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1749405, _1749403)), hAPP(hAPP(c_Product__Type_OPair(_1749405, _1749403), _1749409), _1749411)), hAPP(c_Relation_Oconverse(_1749403, _1749405), _1749407))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749403, _1749405, hAPP(hAPP(c_COMBC(_1749403, tc_fun(tc_prod(_1749403, _1749405), tc_HOL_Obool), tc_fun(_1749405, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749405, tc_fun(tc_fun(tc_prod(_1749403, _1749405), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1749403, _1749405), tc_HOL_Obool), tc_fun(_1749405, tc_HOL_Obool)), _1749403), c_COMBC(_1749405, tc_fun(tc_prod(_1749403, _1749405), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749405, tc_prod(_1749403, _1749405)), tc_fun(_1749405, tc_fun(tc_fun(tc_prod(_1749403, _1749405), tc_HOL_Obool), tc_HOL_Obool)), _1749403), hAPP(c_COMBB(tc_prod(_1749403, _1749405), tc_fun(tc_fun(tc_prod(_1749403, _1749405), tc_HOL_Obool), tc_HOL_Obool), _1749405), c_member(tc_prod(_1749403, _1749405)))), c_Product__Type_OPair(_1749403, _1749405)))), _1749407)), _1749409), _1749411)))], (48119 ^ _779300) ^ [_1749792, _1749794, _1749796, _1749798] : [-(c_Lazy__Sequence_Oproduct(_1749792, _1749794, _1749796, _1749798) = hAPP(c_Lazy__Sequence_Obind(_1749792, tc_prod(_1749792, _1749794), _1749796), hAPP(hAPP(c_COMBB(tc_fun(_1749794, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749792, _1749794))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749792, _1749794)), _1749792), c_Lazy__Sequence_Obind(_1749794, tc_prod(_1749792, _1749794), _1749798)), hAPP(hAPP(c_COMBB(tc_fun(_1749794, tc_prod(_1749792, _1749794)), tc_fun(_1749794, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749792, _1749794))), _1749792), hAPP(c_COMBB(tc_prod(_1749792, _1749794), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749792, _1749794)), _1749794), c_Lazy__Sequence_Osingle(tc_prod(_1749792, _1749794)))), c_Product__Type_OPair(_1749792, _1749794)))))], (48121 ^ _779300) ^ [_1749909, _1749911, _1749913] : [-(_1749909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1749911), c_List_Oreplicate(_1749911, _1749909, _1749913)) = c_List_Oreplicate(_1749911, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1749909), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1749913))], (48127 ^ _779300) ^ [_1749966, _1749968, _1749970] : [-(c_List_Oreplicate(_1749966, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749966)), hAPP(c_List_Ofilter(_1749966, hAPP(c_fequal, _1749968)), _1749970)), _1749968) = hAPP(c_List_Ofilter(_1749966, hAPP(c_fequal, _1749968)), _1749970))], (48129 ^ _779300) ^ [_1750022, _1750024, _1750026] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750022)), c_List_Oreplicate(_1750022, _1750024, _1750026)) = _1750024)], (48131 ^ _779300) ^ [_1750060, _1750062, _1750064, _1750066] : [-(hAPP(hAPP(c_List_Omap(_1750060, _1750062), hAPP(c_COMBK(_1750062, _1750060), _1750064)), _1750066) = c_List_Oreplicate(_1750062, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750060)), _1750066), _1750064))], (48133 ^ _779300) ^ [_1750115, _1750117, _1750119, _1750121] : [-(hAPP(hAPP(c_List_Oappend(_1750115), c_List_Oreplicate(_1750115, _1750117, _1750119)), hAPP(hAPP(c_List_Olist_OCons(_1750115), _1750119), _1750121)) = hAPP(hAPP(c_List_Olist_OCons(_1750115), _1750119), hAPP(hAPP(c_List_Oappend(_1750115), c_List_Oreplicate(_1750115, _1750117, _1750119)), _1750121)))], (48135 ^ _779300) ^ [_1750184, _1750186, _1750188] : [-(c_List_Oreplicate(_1750184, hAPP(c_Nat_OSuc, _1750186), _1750188) = hAPP(hAPP(c_List_Olist_OCons(_1750184), _1750188), c_List_Oreplicate(_1750184, _1750186, _1750188)))], (48137 ^ _779300) ^ [_1750230, _1750232, _1750234] : [-(hAPP(c_List_Orev(_1750230), c_List_Oreplicate(_1750230, _1750232, _1750234)) = c_List_Oreplicate(_1750230, _1750232, _1750234))], (48139 ^ _779300) ^ [_1750270, _1750272, _1750274, _1750276] : [-(hAPP(hAPP(c_List_Odrop(_1750270), _1750272), c_List_Oreplicate(_1750270, _1750274, _1750276)) = c_List_Oreplicate(_1750270, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1750274), _1750272), _1750276))], (48141 ^ _779300) ^ [_1750317, _1750319, _1750321] : [-(_1750317 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1750319), c_List_Oreplicate(_1750319, _1750317, _1750321)) = _1750321)], (48147 ^ _779300) ^ [_1750360, _1750362, _1750364] : [-(_1750360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1750362, c_List_Oreplicate(_1750362, _1750360, _1750364)) = _1750364)], (48153 ^ _779300) ^ [_1750405, _1750407, _1750409, _1750411] : [-(hAPP(hAPP(c_List_Otake(_1750405), _1750407), c_List_Oreplicate(_1750405, _1750409, _1750411)) = c_List_Oreplicate(_1750405, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750407), _1750409), _1750411))], (48155 ^ _779300) ^ [_1750456, _1750458, _1750460, _1750462, _1750464, _1750466] : [-(hAPP(hAPP(c_List_Ozip(_1750456, _1750458), c_List_Oreplicate(_1750456, _1750460, _1750462)), c_List_Oreplicate(_1750458, _1750464, _1750466)) = c_List_Oreplicate(tc_prod(_1750456, _1750458), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750460), _1750464), hAPP(hAPP(c_Product__Type_OPair(_1750456, _1750458), _1750462), _1750466)))], (48157 ^ _779300) ^ [_1750549, _1750551, _1750553, _1750555] : [48159 ^ _779300 : [(48160 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750549), 48158 ^ [_1750549, _1750551, _1750553, _1750555]), hAPP(c_List_Oset(_1750549), c_List_Oreplicate(_1750549, _1750551, _1750553)))))], (48162 ^ _779300) ^ [] : [hBOOL(hAPP(_1750555, 48158 ^ [_1750549, _1750551, _1750553, _1750555]))]], -(hBOOL(hAPP(_1750555, _1750553))), -(_1750551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48170 ^ _779300) ^ [_1750756, _1750758, _1750760, _1750762] : [48171 ^ _779300 : [(48172 ^ _779300) ^ [] : [hBOOL(hAPP(_1750762, _1750760))], (48174 ^ _779300) ^ [] : [_1750758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48175 ^ _779300 : [(48176 ^ _779300) ^ [_1750881] : [hBOOL(hAPP(hAPP(c_member(_1750756), _1750881), hAPP(c_List_Oset(_1750756), c_List_Oreplicate(_1750756, _1750758, _1750760)))), -(hBOOL(hAPP(_1750762, _1750881)))]]], (48182 ^ _779300) ^ [_1751029, _1751031, _1751033, _1751035] : [48189 ^ _779300 : [(48190 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1751035, _1751033)))], (48192 ^ _779300) ^ [] : [_1751031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48183 ^ _779300 : [(48184 ^ _779300) ^ [_1751101] : [hBOOL(hAPP(hAPP(c_member(_1751029), _1751101), hAPP(c_List_Oset(_1751029), c_List_Oreplicate(_1751029, _1751031, _1751033)))), hBOOL(hAPP(_1751035, _1751101))]]], (48194 ^ _779300) ^ [_1751271, _1751273, _1751275, _1751277] : [48202 ^ _779300 : [(48203 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751271), 48201 ^ [_1751271, _1751273, _1751275, _1751277]), hAPP(c_List_Oset(_1751271), c_List_Oreplicate(_1751271, _1751273, _1751275)))))], (48205 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1751277, 48201 ^ [_1751271, _1751273, _1751275, _1751277])))]], hBOOL(hAPP(_1751277, _1751275)), -(_1751273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48207 ^ _779300) ^ [_1751530, _1751532, _1751534, _1751536, _1751538] : [c_List_Oreplicate(_1751530, _1751532, _1751534) = c_List_Oreplicate(_1751530, _1751536, _1751538), 48210 ^ _779300 : [(48211 ^ _779300) ^ [] : [-(_1751532 = _1751536)], (48213 ^ _779300) ^ [] : [-(_1751532 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1751534 = _1751538)]]], (48219 ^ _779300) ^ [_1751666, _1751668, _1751670, _1751672, _1751674] : [-(c_List_Oreplicate(_1751666, _1751668, _1751670) = c_List_Oreplicate(_1751666, _1751672, _1751674)), _1751668 = _1751672, 48224 ^ _779300 : [(48225 ^ _779300) ^ [] : [_1751668 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48227 ^ _779300) ^ [] : [_1751670 = _1751674]]], (48231 ^ _779300) ^ [_1751865, _1751867, _1751869, _1751871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751865), _1751867)), -(hAPP(hAPP(c_List_Onth(_1751869), c_List_Oreplicate(_1751869, _1751867, _1751871)), _1751865) = _1751871)], (48237 ^ _779300) ^ [_1751980, _1751982, _1751984, _1751986] : [-(c_List_Oreplicate(_1751980, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1751982), _1751984), _1751986) = hAPP(hAPP(c_List_Oappend(_1751980), c_List_Oreplicate(_1751980, _1751982, _1751986)), c_List_Oreplicate(_1751980, _1751984, _1751986)))], (48239 ^ _779300) ^ [_1752035, _1752037, _1752039, _1752041] : [-(hAPP(hAPP(c_List_Oappend(_1752035), c_List_Oreplicate(_1752035, _1752037, _1752039)), c_List_Oreplicate(_1752035, _1752041, _1752039)) = hAPP(hAPP(c_List_Oappend(_1752035), c_List_Oreplicate(_1752035, _1752041, _1752039)), c_List_Oreplicate(_1752035, _1752037, _1752039)))], (48241 ^ _779300) ^ [_1752111, _1752113, _1752115, _1752117] : [hBOOL(hAPP(_1752111, _1752113)), -(hAPP(c_List_Ofilter(_1752115, _1752111), c_List_Oreplicate(_1752115, _1752117, _1752113)) = c_List_Oreplicate(_1752115, _1752117, _1752113))], (48247 ^ _779300) ^ [_1752218, _1752220, _1752222, _1752224] : [-(hBOOL(hAPP(_1752218, _1752220))), -(hAPP(c_List_Ofilter(_1752222, _1752218), c_List_Oreplicate(_1752222, _1752224, _1752220)) = c_List_Olist_ONil(_1752222))], (48253 ^ _779300) ^ [_1752274, _1752276] : [-(c_List_Oconcat(_1752274, c_List_Oreplicate(tc_List_Olist(_1752274), _1752276, c_List_Olist_ONil(_1752274))) = c_List_Olist_ONil(_1752274))], (48255 ^ _779300) ^ [_1752330, _1752332, _1752334] : [c_List_Oreplicate(_1752330, _1752332, _1752334) = c_List_Olist_ONil(_1752330), -(_1752332 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48261 ^ _779300) ^ [_1752417, _1752419, _1752421] : [_1752419 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1752417, _1752419, _1752421) = c_List_Olist_ONil(_1752417))], (48267 ^ _779300) ^ [_1752528, _1752530, _1752532] : [c_List_Olist_ONil(_1752528) = c_List_Oreplicate(_1752528, _1752530, _1752532), -(_1752530 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48273 ^ _779300) ^ [_1752615, _1752617, _1752619] : [_1752617 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1752615) = c_List_Oreplicate(_1752615, _1752617, _1752619))], (48279 ^ _779300) ^ [_1752708, _1752710] : [-(c_List_Oreplicate(_1752708, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1752710) = c_List_Olist_ONil(_1752708))], (48281 ^ _779300) ^ [_1752739, _1752741, _1752743, _1752745, _1752747] : [-(hAPP(hAPP(c_List_Omap(_1752739, _1752741), _1752743), c_List_Oreplicate(_1752739, _1752745, _1752747)) = c_List_Oreplicate(_1752741, _1752745, hAPP(_1752743, _1752747)))], (48283 ^ _779300) ^ [_1752811, _1752813, _1752815, _1752817] : [hBOOL(hAPP(hAPP(c_member(_1752811), _1752813), hAPP(c_List_Oset(_1752811), c_List_Oreplicate(_1752811, _1752815, _1752817)))), 48286 ^ _779300 : [(48287 ^ _779300) ^ [] : [-(_1752813 = _1752817)], (48289 ^ _779300) ^ [] : [_1752815 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (48291 ^ _779300) ^ [_1752954, _1752956, _1752958, _1752960] : [-(hBOOL(hAPP(hAPP(c_member(_1752954), _1752956), hAPP(c_List_Oset(_1752954), c_List_Oreplicate(_1752954, _1752958, _1752960))))), _1752956 = _1752960, -(_1752958 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48301 ^ _779300) ^ [_1753128, _1753130, _1753132] : [-(hAPP(hAPP(c_List_Oappend(_1753128), c_List_Oreplicate(_1753128, _1753130, _1753132)), hAPP(hAPP(c_List_Olist_OCons(_1753128), _1753132), c_List_Olist_ONil(_1753128))) = hAPP(hAPP(c_List_Olist_OCons(_1753128), _1753132), c_List_Oreplicate(_1753128, _1753130, _1753132)))], (48303 ^ _779300) ^ [_1753189, _1753191, _1753193] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1753189), hAPP(c_COMBK(_1753189, tc_Nat_Onat), _1753191)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1753193)) = c_List_Oreplicate(_1753189, _1753193, _1753191))], (48305 ^ _779300) ^ [_1753234, _1753236, _1753238] : [-(_1753234 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753236), c_List_Oreplicate(_1753236, _1753234, _1753238)) = hAPP(hAPP(c_Set_Oinsert(_1753236), _1753238), c_Orderings_Obot__class_Obot(tc_fun(_1753236, tc_HOL_Obool))))], (48311 ^ _779300) ^ [_1753306, _1753308, _1753310] : [_1753306 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1753308), c_List_Oreplicate(_1753308, _1753306, _1753310)) = c_Orderings_Obot__class_Obot(tc_fun(_1753308, tc_HOL_Obool)))], (48317 ^ _779300) ^ [_1753407, _1753409, _1753411] : [-(_1753407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753409), c_List_Oreplicate(_1753409, _1753407, _1753411)) = hAPP(hAPP(c_Set_Oinsert(_1753409), _1753411), c_Orderings_Obot__class_Obot(tc_fun(_1753409, tc_HOL_Obool))))], (48323 ^ _779300) ^ [_1753469, _1753471, _1753473] : [-(hAPP(c_List_Oset(_1753469), c_List_Oreplicate(_1753469, hAPP(c_Nat_OSuc, _1753471), _1753473)) = hAPP(hAPP(c_Set_Oinsert(_1753469), _1753473), c_Orderings_Obot__class_Obot(tc_fun(_1753469, tc_HOL_Obool))))], (48325 ^ _779300) ^ [_1753521, _1753523] : [class_Lazy__Sequence_Osmall__lazy(_1753521), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1753521), _1753523) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1753521), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1753521)), c_List_Olist_ONil(_1753521)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753521))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1753523)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1753521, tc_List_Olist(_1753521)), tc_List_Olist(_1753521), c_Lazy__Sequence_Oproduct(_1753521, tc_List_Olist(_1753521), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753521, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1753523), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1753521), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1753523), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1753521, tc_List_Olist(_1753521), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753521))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1753521), tc_List_Olist(_1753521)), tc_fun(tc_List_Olist(_1753521), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753521))), _1753521), hAPP(c_COMBB(tc_List_Olist(_1753521), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753521)), tc_List_Olist(_1753521)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1753521)))), c_List_Olist_OCons(_1753521))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1753521)))))], (48331 ^ _779300) ^ [_1753882, _1753884] : [-(c_Predicate_Opred__comp(_1753882, _1753882, _1753882, c_fequal, c_Predicate_Opred__comp(_1753882, _1753882, _1753882, _1753884, c_fequal)) = _1753884)], (48333 ^ _779300) ^ [_1753919, _1753921, _1753923] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1753919, _1753921), _1753923) = c_Lazy__Sequence_Oproduct(_1753919, _1753921, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753919, _1753923), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753921, _1753923))), class_Lazy__Sequence_Osmall__lazy(_1753919), class_Lazy__Sequence_Osmall__lazy(_1753921)], (48343 ^ _779300) ^ [_1754082, _1754084, _1754086, _1754088] : [-(hAPP(c_New__DSequence_Opos__union(_1754082, _1754084, _1754086), _1754088) = c_Lazy__Sequence_Oappend(_1754082, hAPP(_1754084, _1754088), hAPP(_1754086, _1754088)))], (48345 ^ _779300) ^ [_1754128, _1754130, _1754132] : [class_Fields_Olinordered__field(_1754128), 48351 ^ _779300 : [(48352 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1754128), c_Groups_Ozero__class_Ozero(_1754128)), 48350 ^ [_1754128, _1754130, _1754132])))], (48354 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1754128), _1754130), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1754128), _1754132), 48350 ^ [_1754128, _1754130, _1754132])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1754128), _1754130), _1754132)))], (48358 ^ _779300) ^ [_1754406, _1754408, _1754410, _1754412, _1754414, _1754416] : [-(c_New__Random__Sequence_Opos__union(_1754406, _1754408, _1754410, _1754412, _1754414, _1754416) = c_New__DSequence_Opos__union(_1754406, hAPP(hAPP(hAPP(_1754408, _1754412), _1754414), _1754416), hAPP(hAPP(hAPP(_1754410, _1754412), _1754414), _1754416)))], (48360 ^ _779300) ^ [_1754477, _1754479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754477), _1754479)), -(c_Lazy__Sequence_Osmall__lazy_H(_1754477, _1754479) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (48366 ^ _779300) ^ [_1754564, _1754566] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754564), _1754566))), -(c_Lazy__Sequence_Osmall__lazy_H(_1754564, _1754566) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1754566), c_Lazy__Sequence_Osmall__lazy_H(_1754564, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1754566), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48372 ^ _779300) ^ [_1754626] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1754626) = c_Lazy__Sequence_Osmall__lazy_H(_1754626, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1754626)))], (48374 ^ _779300) ^ [_1754658, _1754660] : [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), _1754658), _1754660))), 48377 ^ _779300 : [(48378 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754658), _1754660)), -(c_Lazy__Sequence_Osmall__lazy_H(_1754658, _1754660) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (48384 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754658), _1754660))), -(c_Lazy__Sequence_Osmall__lazy_H(_1754658, _1754660) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1754660), c_Lazy__Sequence_Osmall__lazy_H(_1754658, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1754660), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (48390 ^ _779300) ^ [_1754914, _1754916, _1754918] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754914)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1754914, _1754916, _1754918)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754914)), _1754918)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48392 ^ _779300) ^ [_1754965, _1754967, _1754969, _1754971] : [-(c_Lazy__Sequence_Oappend(_1754965, c_Lazy__Sequence_Olazy__sequence_OInsert(_1754965, _1754967, _1754969), _1754971) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754965, _1754967, c_Lazy__Sequence_Oappend(_1754965, _1754969, _1754971)))], (48394 ^ _779300) ^ [_1755034, _1755036, _1755038, _1755040, _1755042] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1755034, _1755036, _1755038) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1755034, _1755040, _1755042), 48397 ^ _779300 : [(48398 ^ _779300) ^ [] : [-(_1755036 = _1755040)], (48400 ^ _779300) ^ [] : [-(_1755038 = _1755042)]]], (48402 ^ _779300) ^ [_1755155, _1755157, _1755159, _1755161, _1755163] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1755155, _1755157, _1755159) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1755155, _1755161, _1755163)), _1755157 = _1755161, _1755159 = _1755163], (48412 ^ _779300) ^ [_1755314, _1755316, _1755318, _1755320] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755314, _1755316), c_Lazy__Sequence_Olazy__sequence_OInsert(_1755314, _1755318, _1755320)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1755316, _1755318)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755314, _1755316), _1755320))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48414 ^ _779300) ^ [_1755374, _1755376, _1755378] : [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), _1755374), _1755376))), -(hBOOL(hAPP(hAPP(_1755378, _1755374), _1755376))), 48421 ^ _779300 : [(48422 ^ _779300) ^ [] : [-(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), 48419 ^ [_1755374, _1755376, _1755378]), 48420 ^ [_1755374, _1755376, _1755378]))))], (48430 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1755378, 48419 ^ [_1755374, _1755376, _1755378]), 48420 ^ [_1755374, _1755376, _1755378]))], (48424 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48419 ^ [_1755374, _1755376, _1755378]), 48420 ^ [_1755374, _1755376, _1755378]))), -(hBOOL(hAPP(hAPP(_1755378, 48419 ^ [_1755374, _1755376, _1755378]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48420 ^ [_1755374, _1755376, _1755378]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (48434 ^ _779300) ^ [_1755826, _1755828] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1755826)), _1755828) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1755826, tc_Lazy__Sequence_Olazy__sequence(_1755826)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1755826, tc_Lazy__Sequence_Olazy__sequence(_1755826), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755826), tc_Nat_Onat), _1755826), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1755826), 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(_1755826)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1755826)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1755826), _1755828)))], (48436 ^ _779300) ^ [_1755922, _1755924, _1755926] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755922, _1755924), _1755926) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1755922, tc_Lazy__Sequence_Olazy__sequence(_1755922)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1755922, tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1755922, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_Nat_Onat)), _1755922), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1755922), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1755922)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1755922, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755922), tc_Nat_Onat)), _1755922), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1755922))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1755922), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1755924))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755922, _1755924))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1755922), _1755926)))], (48438 ^ _779300) ^ [_1756115, _1756117, _1756119, _1756121, _1756123] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1756115, _1756117, _1756119, _1756121, _1756123) = c_Option_Ooption_Ooption__case(_1756115, tc_prod(_1756117, tc_Lazy__Sequence_Olazy__sequence(_1756117)), _1756119, hAPP(c_Product__Type_Oprod_Oprod__case(_1756117, tc_Lazy__Sequence_Olazy__sequence(_1756117), _1756115), _1756121), hAPP(c_Lazy__Sequence_Oyield(_1756117), _1756123)))], (48440 ^ _779300) ^ [_1756177] : [-(c_Lazy__Sequence_Oyieldn(_1756177) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1756177), _1756177, c_Lazy__Sequence_Oyield(_1756177)))], (48442 ^ _779300) ^ [_1756210, _1756212, _1756214, _1756216, _1756218, _1756220] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1756210, _1756212, _1756214, _1756216, c_Lazy__Sequence_Olazy__sequence_OInsert(_1756212, _1756218, _1756220)) = hAPP(hAPP(_1756216, _1756218), _1756220))], (48444 ^ _779300) ^ [_1756259, _1756261, _1756263, _1756265, _1756267] : [48446 ^ _779300 : [(48447 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756259), 48445 ^ [_1756259, _1756261, _1756263, _1756265, _1756267]), _1756261)))], (48449 ^ _779300) ^ [] : [c_Relation_Orefl__on(_1756263, hAPP(_1756265, 48445 ^ [_1756259, _1756261, _1756263, _1756265, _1756267]), hAPP(_1756267, 48445 ^ [_1756259, _1756261, _1756263, _1756265, _1756267]))]], -(c_Relation_Orefl__on(_1756263, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756259, tc_fun(_1756263, tc_HOL_Obool)), _1756261), _1756265), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756259, tc_fun(tc_prod(_1756263, _1756263), tc_HOL_Obool)), _1756261), _1756267)))], (48453 ^ _779300) ^ [_1756545, _1756547, _1756549] : [hBOOL(hAPP(hAPP(c_member(_1756545), _1756547), hAPP(c_List_Oset(_1756545), _1756549))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756545), _1756549), _1756547)))], (48459 ^ _779300) ^ [_1756658, _1756660, _1756662] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756658), _1756662), _1756660)), -(hBOOL(hAPP(hAPP(c_member(_1756658), _1756660), hAPP(c_List_Oset(_1756658), _1756662))))], (48475 ^ _779300) ^ [_1756932, _1756934, _1756936, _1756938] : [48476 ^ _779300 : [(48477 ^ _779300) ^ [] : [_1756934 = _1756938], (48479 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756932), _1756936), _1756938))]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1756932), hAPP(hAPP(c_List_Olist_OCons(_1756932), _1756934), _1756936)), _1756938)))], (48465 ^ _779300) ^ [_1756798, _1756800, _1756802, _1756804] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756798), hAPP(hAPP(c_List_Olist_OCons(_1756798), _1756800), _1756802)), _1756804)), -(_1756800 = _1756804), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756798), _1756802), _1756804)))], (48483 ^ _779300) ^ [_1757097] : [-(c_List_Omember(_1757097) = c_List_Oset(_1757097))], (48485 ^ _779300) ^ [_1757136, _1757138] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757136), c_List_Olist_ONil(_1757136)), _1757138))], (48487 ^ _779300) ^ [_1757188, _1757190, _1757192] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757188), _1757190), _1757192)), -(hBOOL(hAPP(hAPP(c_member(_1757188), _1757192), hAPP(c_List_Oset(_1757188), _1757190))))], (48493 ^ _779300) ^ [_1757301, _1757303, _1757305] : [hBOOL(hAPP(hAPP(c_member(_1757301), _1757305), hAPP(c_List_Oset(_1757301), _1757303))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1757301), _1757303), _1757305)))], (48499 ^ _779300) ^ [_1757438, _1757440, _1757442] : [c_List_Olist__ex1(_1757438, _1757440, _1757442), 48503 ^ _779300 : [(48504 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757438), 48502 ^ [_1757438, _1757440, _1757442]), hAPP(c_List_Oset(_1757438), _1757442))))], (48506 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1757440, 48502 ^ [_1757438, _1757440, _1757442])))], (48508 ^ _779300) ^ [_1757684] : [-(_1757684 = 48502 ^ [_1757438, _1757440, _1757442]), hBOOL(hAPP(hAPP(c_member(_1757438), _1757684), hAPP(c_List_Oset(_1757438), _1757442))), hBOOL(hAPP(_1757440, _1757684))]]], (48518 ^ _779300) ^ [_1757871, _1757873, _1757875] : [-(c_List_Olist__ex1(_1757871, _1757873, _1757875)), 48519 ^ _779300 : [(48520 ^ _779300) ^ [_1757965] : [hBOOL(hAPP(hAPP(c_member(_1757871), _1757965), hAPP(c_List_Oset(_1757871), _1757875))), hBOOL(hAPP(_1757873, _1757965)), 48528 ^ _779300 : [(48529 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757871), 48527 ^ [_1757871, _1757873, _1757875, _1757965]), hAPP(c_List_Oset(_1757871), _1757875))))], (48531 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1757873, 48527 ^ [_1757871, _1757873, _1757875, _1757965])))], (48533 ^ _779300) ^ [] : [48527 ^ [_1757871, _1757873, _1757875, _1757965] = _1757965]]]]], (48537 ^ _779300) ^ [_1758300, _1758302, _1758304, _1758306] : [class_Groups_Ocomm__monoid__add(_1758300), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1758302, tc_HOL_Obool)), _1758304)), 48547 ^ _779300 : [(48548 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758302, tc_HOL_Obool)), 48546 ^ [_1758300, _1758302, _1758304, _1758306]), _1758304)))], (48550 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1758302), 48546 ^ [_1758300, _1758302, _1758304, _1758306]))]], 48554 ^ _779300 : [(48555 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758302, tc_HOL_Obool)), 48553 ^ [_1758300, _1758302, _1758304, _1758306]), _1758304)))], (48558 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758302, tc_HOL_Obool)), 48556 ^ [_1758300, _1758302, _1758304, _1758306]), _1758304)))], (48560 ^ _779300) ^ [] : [48553 ^ [_1758300, _1758302, _1758304, _1758306] = 48556 ^ [_1758300, _1758302, _1758304, _1758306]], (48563 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758302), 48561 ^ [_1758300, _1758302, _1758304, _1758306]), 48553 ^ [_1758300, _1758302, _1758304, _1758306])))], (48565 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758302), 48561 ^ [_1758300, _1758302, _1758304, _1758306]), 48556 ^ [_1758300, _1758302, _1758304, _1758306])))], (48567 ^ _779300) ^ [] : [hAPP(_1758306, 48561 ^ [_1758300, _1758302, _1758304, _1758306]) = c_Groups_Ozero__class_Ozero(_1758300)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1758302, _1758300), _1758306), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1758302, tc_HOL_Obool), _1758304)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1758302, tc_HOL_Obool), _1758300), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1758302, _1758300), _1758306)), _1758304))], (48571 ^ _779300) ^ [_1759309, _1759311, _1759313] : [-(c_FunDef_OTHE__default(_1759311, _1759313, _1759309) = c_HOL_OThe(_1759311, _1759309)), 48572 ^ _779300 : [(48573 ^ _779300) ^ [_1759373] : [hBOOL(hAPP(_1759309, _1759373)), 48577 ^ _779300 : [(48578 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1759309, 48576 ^ [_1759309, _1759311, _1759313, _1759373])))], (48580 ^ _779300) ^ [] : [48576 ^ [_1759309, _1759311, _1759313, _1759373] = _1759373]]]]], (48584 ^ _779300) ^ [_1759567, _1759569, _1759571] : [-(c_FunDef_OTHE__default(_1759569, _1759571, _1759567) = _1759571), 48586 ^ _779300 : [(48587 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1759567, 48585 ^ [_1759567, _1759569, _1759571])))], (48589 ^ _779300) ^ [_1759689] : [hBOOL(hAPP(_1759567, _1759689)), -(_1759689 = 48585 ^ [_1759567, _1759569, _1759571])]]], (48597 ^ _779300) ^ [_1759828, _1759830, _1759832, _1759834, _1759836, _1759838, _1759840] : [48599 ^ _779300 : [(48600 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759828), 48598 ^ [_1759828, _1759830, _1759832, _1759834, _1759836, _1759838, _1759840]), _1759830)))], (48602 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1759832, 48598 ^ [_1759828, _1759830, _1759832, _1759834, _1759836, _1759838, _1759840]), _1759834), _1759836))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1759828, tc_fun(_1759838, tc_fun(_1759840, tc_HOL_Obool))), _1759830), _1759832), _1759834), _1759836)))], (48606 ^ _779300) ^ [_1760086, _1760088, _1760090, _1760092, _1760094, _1760096, _1760098] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1760086, tc_fun(_1760088, tc_fun(_1760090, tc_HOL_Obool))), _1760092), _1760094), _1760096), _1760098)), 48610 ^ _779300 : [(48611 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760086), 48609 ^ [_1760086, _1760088, _1760090, _1760092, _1760094, _1760096, _1760098]), _1760092)))], (48613 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1760094, 48609 ^ [_1760086, _1760088, _1760090, _1760092, _1760094, _1760096, _1760098]), _1760096), _1760098)))]]], (48615 ^ _779300) ^ [_1760312, _1760314] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1760312)), _1760314)), 48619 ^ _779300 : [(48620 ^ _779300) ^ [_1760413] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1760312)), _1760413), _1760314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760312)), _1760413)), 48618 ^ [_1760312, _1760314])))]]], (48626 ^ _779300) ^ [_1760552, _1760554] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1760552, _1760554), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760552)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48628 ^ _779300) ^ [_1760585] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1760585)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760585)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48630 ^ _779300) ^ [_1760617, _1760619] : [-(c_Lazy__Sequence_Oappend(_1760617, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760617), _1760619) = _1760619)], (48632 ^ _779300) ^ [_1760663, _1760665, _1760667] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760663) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1760663, _1760665, _1760667)], (48634 ^ _779300) ^ [_1760711, _1760713, _1760715] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1760711, _1760713, _1760715) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760711)], (48636 ^ _779300) ^ [_1760744, _1760746, _1760748, _1760750] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1760744, _1760746, _1760748, _1760750, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760746)) = _1760748)], (48638 ^ _779300) ^ [_1760799, _1760801, _1760803] : [c_List_Olist__ex(tc_Int_Oint, _1760799, c_List_Oupto(_1760801, _1760803)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1760799), _1760801, _1760803)], (48644 ^ _779300) ^ [_1760889, _1760891, _1760893] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1760889), _1760891, _1760893)), -(c_List_Olist__ex(tc_Int_Oint, _1760889, c_List_Oupto(_1760891, _1760893)))], (48650 ^ _779300) ^ [_1760955, _1760957, _1760959] : [c_List_Olist__all(tc_Int_Oint, _1760955, c_List_Oupto(_1760957, _1760959)), -(c_List_Oall__interval__int(_1760955, _1760957, _1760959))], (48656 ^ _779300) ^ [_1761040, _1761042, _1761044] : [c_List_Oall__interval__int(_1761040, _1761042, _1761044), -(c_List_Olist__all(tc_Int_Oint, _1761040, c_List_Oupto(_1761042, _1761044)))], (48672 ^ _779300) ^ [_1761330, _1761332, _1761334] : [48674 ^ _779300 : [(48675 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 48673 ^ [_1761330, _1761332, _1761334]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1761332, _1761334))))], (48677 ^ _779300) ^ [] : [hBOOL(hAPP(_1761330, 48673 ^ [_1761330, _1761332, _1761334]))]], -(c_List_Oall__interval__int(_1761330, _1761332, _1761334))], (48662 ^ _779300) ^ [_1761149, _1761151, _1761153] : [c_List_Oall__interval__int(_1761149, _1761151, _1761153), 48665 ^ _779300 : [(48666 ^ _779300) ^ [_1761227] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1761227), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1761151, _1761153))), -(hBOOL(hAPP(_1761149, _1761227)))]]], (48681 ^ _779300) ^ [_1761506, _1761508, _1761510, _1761512] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761506, _1761508, _1761510, c_Code__Numeral_OSuc__code__numeral(_1761512)) = hAPP(hAPP(_1761510, _1761512), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761506, _1761508, _1761510, _1761512)))], (48683 ^ _779300) ^ [_1761568, _1761570, _1761572, _1761574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761568), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1761570, _1761572, _1761568, _1761574) = 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(_1761570)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1761570)))], (48689 ^ _779300) ^ [_1761699, _1761701, _1761703, _1761705] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761699), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1761701, _1761703, _1761699, _1761705) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1761701, 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(_1761701)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1761703, _1761705)), 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(_1761701)))), 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(_1761701)))), 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(_1761701)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1761701, 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(_1761701)))), 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(_1761701)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1761701, _1761703, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1761699), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1761705))), 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(_1761701)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761701))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761701)))), 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(_1761701)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1761701, 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(_1761701)))), 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(_1761701)))), 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(_1761701))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761701)))), 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(_1761701)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761701)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761701))))), tc_prod(_1761701, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1761701)), hAPP(hAPP(c_COMBB(_1761701, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761701)))), tc_prod(_1761701, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1761701)), c_Product__Type_Ofst(_1761701, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (48695 ^ _779300) ^ [_1762078, _1762080, _1762082] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1762078, _1762080, _1762082, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1762080)], (48697 ^ _779300) ^ [_1762110, _1762112, _1762114] : [-(c_Random__Sequence_Oempty(_1762110, _1762112, _1762114) = 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(_1762110)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1762110)))], (48699 ^ _779300) ^ [_1762159, _1762161, _1762163, _1762165] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1762159), _1762161), _1762163), _1762165) = 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(_1762159)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1762159), _1762161)))], (48701 ^ _779300) ^ [_1762220, _1762222, _1762224, _1762226] : [-(c_Random__Sequence_Omap(_1762220, _1762222, _1762224, _1762226) = c_Random__Sequence_Obind(_1762220, _1762222, _1762226, hAPP(c_Fun_Ocomp(_1762222, 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(_1762222)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1762220, c_Random__Sequence_Osingle(_1762222)), _1762224)))], (48703 ^ _779300) ^ [_1762291, _1762293, _1762295, _1762297, _1762299, _1762301, _1762303] : [hBOOL(hAPP(hAPP(_1762291, hAPP(c_Product__Type_Osnd(_1762293, _1762295), _1762297)), hAPP(c_Product__Type_Ofst(_1762293, _1762295), _1762297))), 48710 ^ _779300 : [(48711 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1762291, 48709 ^ [_1762291, _1762293, _1762295, _1762297, _1762299, _1762301, _1762303]), 48708 ^ [_1762291, _1762293, _1762295, _1762297, _1762299, _1762301, _1762303])))], (48713 ^ _779300) ^ [] : [hBOOL(hAPP(_1762299, hAPP(hAPP(_1762301, 48708 ^ [_1762291, _1762293, _1762295, _1762297, _1762299, _1762301, _1762303]), 48709 ^ [_1762291, _1762293, _1762295, _1762297, _1762299, _1762301, _1762303])))]], -(hBOOL(hAPP(_1762299, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1762293, _1762295, _1762303), _1762301), _1762297))))], (48717 ^ _779300) ^ [_1762688, _1762690, _1762692, _1762694] : [-(hAPP(c_Relation_OImage(_1762688, _1762690, hAPP(c_Set_OCollect(tc_prod(_1762688, _1762690)), hAPP(c_Product__Type_Oprod_Oprod__case(_1762688, _1762690, tc_HOL_Obool), _1762692))), _1762694) = hAPP(c_Set_OCollect(_1762690), hAPP(hAPP(c_COMBB(tc_fun(_1762688, tc_HOL_Obool), tc_HOL_Obool, _1762690), c_HOL_OEx(_1762688)), hAPP(hAPP(c_COMBB(tc_fun(_1762688, tc_HOL_Obool), tc_fun(_1762688, tc_HOL_Obool), _1762690), hAPP(c_COMBS(_1762688, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1762688), c_fconj), hAPP(hAPP(c_COMBC(_1762688, tc_fun(_1762688, tc_HOL_Obool), tc_HOL_Obool), c_member(_1762688)), _1762694)))), hAPP(c_COMBC(_1762688, _1762690, tc_HOL_Obool), _1762692)))))], (48719 ^ _779300) ^ [_1762814, _1762816, _1762818, _1762820, _1762822] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762814), tc_List_Olist(_1762814))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762814), tc_List_Olist(_1762814)), _1762816), _1762818)), c_List_Olexord(_1762814, _1762820))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762814), tc_List_Olist(_1762814))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762814), tc_List_Olist(_1762814)), _1762818), _1762822)), c_List_Olexord(_1762814, _1762820))), c_Relation_Otrans(_1762814, _1762820), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762814), tc_List_Olist(_1762814))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762814), tc_List_Olist(_1762814)), _1762816), _1762822)), c_List_Olexord(_1762814, _1762820))))], (48733 ^ _779300) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (48735 ^ _779300) ^ [_1763211, _1763213, _1763215, _1763217] : [c_Relation_Otrans(_1763211, _1763213), c_Relation_Otrans(_1763215, _1763217), -(c_Relation_Otrans(tc_prod(_1763211, _1763215), c_Wellfounded_Olex__prod(_1763211, _1763215, _1763213, _1763217)))], (48759 ^ _779300) ^ [_1763821, _1763823] : [48762 ^ _779300 : [(48763 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763821, _1763821)), hAPP(hAPP(c_Product__Type_OPair(_1763821, _1763821), 48760 ^ [_1763821, _1763823]), 48761 ^ [_1763821, _1763823])), _1763823)))], (48766 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763821, _1763821)), hAPP(hAPP(c_Product__Type_OPair(_1763821, _1763821), 48761 ^ [_1763821, _1763823]), 48764 ^ [_1763821, _1763823])), _1763823)))], (48768 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763821, _1763821)), hAPP(hAPP(c_Product__Type_OPair(_1763821, _1763821), 48760 ^ [_1763821, _1763823]), 48764 ^ [_1763821, _1763823])), _1763823))]], -(c_Relation_Otrans(_1763821, _1763823))], (48745 ^ _779300) ^ [_1763379, _1763381] : [c_Relation_Otrans(_1763379, _1763381), 48748 ^ _779300 : [(48749 ^ _779300) ^ [_1763515, _1763517] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763379, _1763379)), hAPP(hAPP(c_Product__Type_OPair(_1763379, _1763379), _1763517), _1763515)), _1763381)), 48752 ^ _779300 : [(48753 ^ _779300) ^ [_1763658] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763379, _1763379)), hAPP(hAPP(c_Product__Type_OPair(_1763379, _1763379), _1763515), _1763658)), _1763381)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763379, _1763379)), hAPP(hAPP(c_Product__Type_OPair(_1763379, _1763379), _1763517), _1763658)), _1763381)))]]]]], (48772 ^ _779300) ^ [_1764241, _1764243, _1764245, _1764247, _1764249] : [c_Relation_Otrans(_1764241, _1764243), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764241, _1764241)), hAPP(hAPP(c_Product__Type_OPair(_1764241, _1764241), _1764245), _1764247)), _1764243)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764241, _1764241)), hAPP(hAPP(c_Product__Type_OPair(_1764241, _1764241), _1764247), _1764249)), _1764243)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764241, _1764241)), hAPP(hAPP(c_Product__Type_OPair(_1764241, _1764241), _1764245), _1764249)), _1764243)))], (48786 ^ _779300) ^ [_1764554, _1764556] : [c_Relation_Otrans(_1764554, _1764556), -(c_Relation_Otrans(_1764554, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1764554, _1764554), tc_HOL_Obool)), _1764556), c_Relation_OId(_1764554))))], (48792 ^ _779300) ^ [_1764663, _1764665, _1764667, _1764669] : [c_Relation_Otrans(_1764663, _1764665), -(c_Relation_Otrans(_1764667, hAPP(hAPP(c_Relation_Oinv__image(_1764663, _1764667), _1764665), _1764669)))], (48798 ^ _779300) ^ [_1764762, _1764764] : [c_Relation_Otrans(_1764762, _1764764), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1764762, _1764762), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1764762, _1764762, _1764762), _1764764), _1764764)), _1764764)))], (48804 ^ _779300) ^ [_1764885] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1764885, tc_HOL_Obool) = c_Set_OBex(_1764885))], (48806 ^ _779300) ^ [_1764913, _1764915, _1764917] : [c_Relation_Otrans(_1764913, _1764915), c_Relation_Otrans(_1764913, _1764917), -(c_Relation_Otrans(_1764913, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1764913, _1764913), tc_HOL_Obool)), _1764915), _1764917)))], (48827 ^ _779300) ^ [_1765289, _1765291] : [48828 ^ _779300 : [(48829 ^ _779300) ^ [_1765355] : [hBOOL(hAPP(_1765291, _1765355))]], 48831 ^ _779300 : [(48832 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765289), 48830 ^ [_1765289, _1765291]), c_Orderings_Otop__class_Otop(tc_fun(_1765289, tc_HOL_Obool)))))], (48834 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1765291, 48830 ^ [_1765289, _1765291])))]]], (48816 ^ _779300) ^ [_1765089, _1765091] : [-(hBOOL(hAPP(_1765091, 48823 ^ [_1765089, _1765091]))), 48817 ^ _779300 : [(48818 ^ _779300) ^ [_1765150] : [hBOOL(hAPP(hAPP(c_member(_1765089), _1765150), c_Orderings_Otop__class_Otop(tc_fun(_1765089, tc_HOL_Obool)))), hBOOL(hAPP(_1765091, _1765150))]]], (48836 ^ _779300) ^ [_1765458, _1765460, _1765462, _1765464] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765458), _1765460)), 48839 ^ _779300 : [(48850 ^ _779300) ^ [] : [48852 ^ _779300 : [(48853 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765458), 48851 ^ [_1765458, _1765460, _1765462, _1765464]), _1765460)))], (48855 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765462), hAPP(c_Set_OCollect(_1765462), hAPP(hAPP(c_COMBC(_1765462, _1765458, tc_HOL_Obool), _1765464), 48851 ^ [_1765458, _1765460, _1765462, _1765464]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1765462), hAPP(c_Set_OCollect(_1765462), hAPP(hAPP(c_COMBB(tc_fun(_1765458, tc_HOL_Obool), tc_HOL_Obool, _1765462), c_HOL_OEx(_1765458)), hAPP(hAPP(c_COMBB(tc_fun(_1765458, tc_HOL_Obool), tc_fun(_1765458, tc_HOL_Obool), _1765462), hAPP(c_COMBS(_1765458, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765458), c_fconj), hAPP(hAPP(c_COMBC(_1765458, tc_fun(_1765458, tc_HOL_Obool), tc_HOL_Obool), c_member(_1765458)), _1765460)))), _1765464))))))], (48840 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765462), hAPP(c_Set_OCollect(_1765462), hAPP(hAPP(c_COMBB(tc_fun(_1765458, tc_HOL_Obool), tc_HOL_Obool, _1765462), c_HOL_OEx(_1765458)), hAPP(hAPP(c_COMBB(tc_fun(_1765458, tc_HOL_Obool), tc_fun(_1765458, tc_HOL_Obool), _1765462), hAPP(c_COMBS(_1765458, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765458), c_fconj), hAPP(hAPP(c_COMBC(_1765458, tc_fun(_1765458, tc_HOL_Obool), tc_HOL_Obool), c_member(_1765458)), _1765460)))), _1765464))))), 48843 ^ _779300 : [(48844 ^ _779300) ^ [_1765766] : [hBOOL(hAPP(hAPP(c_member(_1765458), _1765766), _1765460)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1765462), hAPP(c_Set_OCollect(_1765462), hAPP(hAPP(c_COMBC(_1765462, _1765458, tc_HOL_Obool), _1765464), _1765766)))))]]]]], (48859 ^ _779300) ^ [_1766162, _1766164] : [c_Relation_Otrans(_1766162, _1766164), -(c_Relation_Otrans(tc_List_Olist(_1766162), c_List_Olistrel(_1766162, _1766164)))], (48865 ^ _779300) ^ [_1766249, _1766251, _1766253] : [hBOOL(hAPP(hAPP(c_member(_1766251), _1766249), c_Orderings_Obot__class_Obot(tc_fun(_1766251, tc_HOL_Obool)))), hBOOL(hAPP(_1766253, _1766249))], (48871 ^ _779300) ^ [_1766370, _1766372] : [c_Relation_Otrans(_1766370, hAPP(c_Relation_Oconverse(_1766370, _1766370), _1766372)), -(c_Relation_Otrans(_1766370, _1766372))], (48877 ^ _779300) ^ [_1766455, _1766457] : [c_Relation_Otrans(_1766455, _1766457), -(c_Relation_Otrans(_1766455, hAPP(c_Relation_Oconverse(_1766455, _1766455), _1766457)))], (48883 ^ _779300) ^ [_1766546, _1766548] : [c_Relation_Otrans(_1766546, _1766548), -(c_Relation_Otrans(tc_List_Olist(_1766546), c_List_Olexord(_1766546, _1766548)))], (48889 ^ _779300) ^ [_1766633] : [-(c_Relation_Otrans(tc_fun(_1766633, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1766633)))], (48891 ^ _779300) ^ [_1766661] : [-(c_Relation_Otrans(_1766661, c_Relation_OId(_1766661)))], (48893 ^ _779300) ^ [_1766686, _1766688] : [-(c_Relation_Otrans(_1766686, c_Relation_OId__on(_1766686, _1766688)))], (48895 ^ _779300) ^ [_1766714, _1766716] : [c_Relation_Otrans(_1766714, _1766716), -(c_Transitive__Closure_Otrancl(_1766714, _1766716) = _1766716)], (48901 ^ _779300) ^ [_1766797, _1766799] : [-(c_Relation_Otrans(_1766797, c_Transitive__Closure_Otrancl(_1766797, _1766799)))], (48903 ^ _779300) ^ [_1766825, _1766827] : [-(c_Relation_Otrans(_1766825, c_Transitive__Closure_Ortrancl(_1766825, _1766827)))], (48905 ^ _779300) ^ [_1766853, _1766855] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1766853, tc_HOL_Obool), _1766855) = hAPP(c_Set_OCollect(_1766853), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1766853, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1766853), c_HOL_OEx(tc_fun(_1766853, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1766853, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1766853, tc_HOL_Obool), tc_HOL_Obool), _1766853), hAPP(c_COMBS(tc_fun(_1766853, 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(_1766853, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1766853, tc_HOL_Obool), tc_fun(tc_fun(_1766853, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1766853, tc_HOL_Obool))), _1766855)))), c_member(_1766853)))))], (48907 ^ _779300) ^ [_1766999, _1767001, _1767003] : [c_List_Olist__ex(_1766999, _1767001, _1767003), 48911 ^ _779300 : [(48912 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766999), 48910 ^ [_1766999, _1767001, _1767003]), hAPP(c_List_Oset(_1766999), _1767003))))], (48914 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1767001, 48910 ^ [_1766999, _1767001, _1767003])))]]], (48916 ^ _779300) ^ [_1767153, _1767155, _1767157] : [-(c_List_Olist__ex(_1767153, _1767155, _1767157)), 48917 ^ _779300 : [(48918 ^ _779300) ^ [_1767210] : [hBOOL(hAPP(hAPP(c_member(_1767153), _1767210), hAPP(c_List_Oset(_1767153), _1767157))), hBOOL(hAPP(_1767155, _1767210))]]], (48936 ^ _779300) ^ [_1767557, _1767559, _1767561] : [c_List_Olist__ex(_1767557, _1767561, _1767559), 48940 ^ _779300 : [(48941 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767557), 48939 ^ [_1767557, _1767559, _1767561]), hAPP(c_List_Oset(_1767557), _1767559))))], (48943 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1767561, 48939 ^ [_1767557, _1767559, _1767561])))]]], (48926 ^ _779300) ^ [_1767367, _1767369, _1767371] : [-(c_List_Olist__ex(_1767367, _1767371, _1767369)), 48927 ^ _779300 : [(48928 ^ _779300) ^ [_1767424] : [hBOOL(hAPP(hAPP(c_member(_1767367), _1767424), hAPP(c_List_Oset(_1767367), _1767369))), hBOOL(hAPP(_1767371, _1767424))]]], (48945 ^ _779300) ^ [_1767717, _1767719, _1767721, _1767723] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1767717, tc_fun(_1767719, tc_HOL_Obool)), _1767721), _1767723) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1767719, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1767719, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1767717, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1767719, tc_HOL_Obool)), c_HOL_OEx(_1767717)), hAPP(hAPP(c_COMBB(tc_fun(_1767717, tc_HOL_Obool), tc_fun(_1767717, tc_HOL_Obool), tc_fun(_1767719, tc_HOL_Obool)), hAPP(c_COMBS(_1767717, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1767717), c_fconj), hAPP(hAPP(c_COMBC(_1767717, tc_fun(_1767717, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767717)), _1767721)))), hAPP(hAPP(c_COMBC(tc_fun(_1767719, tc_HOL_Obool), tc_fun(_1767717, tc_fun(_1767719, tc_HOL_Obool)), tc_fun(_1767717, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767719, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1767717, tc_fun(_1767719, tc_HOL_Obool)), tc_fun(_1767717, tc_HOL_Obool)), tc_fun(_1767719, tc_HOL_Obool)), c_COMBB(tc_fun(_1767719, tc_HOL_Obool), tc_HOL_Obool, _1767717)), c_fequal)), _1767723))))))], (48947 ^ _779300) ^ [_1767901, _1767903, _1767905, _1767907] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1767901, tc_fun(_1767903, tc_HOL_Obool)), _1767905), _1767907) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1767903, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1767903, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1767901, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1767903, tc_HOL_Obool)), c_HOL_OEx(_1767901)), hAPP(hAPP(c_COMBB(tc_fun(_1767901, tc_HOL_Obool), tc_fun(_1767901, tc_HOL_Obool), tc_fun(_1767903, tc_HOL_Obool)), hAPP(c_COMBS(_1767901, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1767901), c_fconj), hAPP(hAPP(c_COMBC(_1767901, tc_fun(_1767901, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767901)), _1767905)))), hAPP(hAPP(c_COMBC(tc_fun(_1767903, tc_HOL_Obool), tc_fun(_1767901, tc_fun(_1767903, tc_HOL_Obool)), tc_fun(_1767901, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767903, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1767901, tc_fun(_1767903, tc_HOL_Obool)), tc_fun(_1767901, tc_HOL_Obool)), tc_fun(_1767903, tc_HOL_Obool)), c_COMBB(tc_fun(_1767903, tc_HOL_Obool), tc_HOL_Obool, _1767901)), c_fequal)), _1767907))))))], (48949 ^ _779300) ^ [_1768085, _1768087, _1768089, _1768091] : [class_Complete__Lattice_Ocomplete__lattice(_1768085), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1768087, _1768085), _1768089), _1768091) = c_Complete__Lattice_OSup__class_OSup(_1768085, hAPP(c_Set_OCollect(_1768085), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768087, _1768085), tc_HOL_Obool), tc_HOL_Obool, _1768085), c_HOL_OEx(tc_fun(_1768087, _1768085))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768087, _1768085), tc_HOL_Obool), tc_fun(tc_fun(_1768087, _1768085), tc_HOL_Obool), _1768085), hAPP(c_COMBS(tc_fun(_1768087, _1768085), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768087, _1768085)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768087, _1768085), tc_fun(tc_fun(_1768087, _1768085), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768087, _1768085))), _1768089)))), hAPP(hAPP(c_COMBC(_1768085, tc_fun(tc_fun(_1768087, _1768085), _1768085), tc_fun(tc_fun(_1768087, _1768085), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768085, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768087, _1768085), _1768085), tc_fun(tc_fun(_1768087, _1768085), tc_HOL_Obool)), _1768085), c_COMBB(_1768085, tc_HOL_Obool, tc_fun(_1768087, _1768085))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768087, _1768085), _1768087, _1768085), c_COMBI(tc_fun(_1768087, _1768085))), _1768091)))))))], (48955 ^ _779300) ^ [_1768528, _1768530, _1768532, _1768534] : [class_Complete__Lattice_Ocomplete__lattice(_1768528), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1768530, _1768528), _1768532), _1768534) = c_Complete__Lattice_OSup__class_OSup(_1768528, hAPP(c_Set_OCollect(_1768528), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768530, _1768528), tc_HOL_Obool), tc_HOL_Obool, _1768528), c_HOL_OEx(tc_fun(_1768530, _1768528))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768530, _1768528), tc_HOL_Obool), tc_fun(tc_fun(_1768530, _1768528), tc_HOL_Obool), _1768528), hAPP(c_COMBS(tc_fun(_1768530, _1768528), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768530, _1768528)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768530, _1768528), tc_fun(tc_fun(_1768530, _1768528), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768530, _1768528))), _1768532)))), hAPP(hAPP(c_COMBC(_1768528, tc_fun(tc_fun(_1768530, _1768528), _1768528), tc_fun(tc_fun(_1768530, _1768528), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768528, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768530, _1768528), _1768528), tc_fun(tc_fun(_1768530, _1768528), tc_HOL_Obool)), _1768528), c_COMBB(_1768528, tc_HOL_Obool, tc_fun(_1768530, _1768528))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768530, _1768528), _1768530, _1768528), c_COMBI(tc_fun(_1768530, _1768528))), _1768534)))))))], (48961 ^ _779300) ^ [_1768971, _1768973, _1768975, _1768977] : [class_Complete__Lattice_Ocomplete__lattice(_1768971), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1768973, _1768971), _1768975), _1768977) = c_Complete__Lattice_OInf__class_OInf(_1768971, hAPP(c_Set_OCollect(_1768971), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768973, _1768971), tc_HOL_Obool), tc_HOL_Obool, _1768971), c_HOL_OEx(tc_fun(_1768973, _1768971))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768973, _1768971), tc_HOL_Obool), tc_fun(tc_fun(_1768973, _1768971), tc_HOL_Obool), _1768971), hAPP(c_COMBS(tc_fun(_1768973, _1768971), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768973, _1768971)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768973, _1768971), tc_fun(tc_fun(_1768973, _1768971), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768973, _1768971))), _1768975)))), hAPP(hAPP(c_COMBC(_1768971, tc_fun(tc_fun(_1768973, _1768971), _1768971), tc_fun(tc_fun(_1768973, _1768971), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768971, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768973, _1768971), _1768971), tc_fun(tc_fun(_1768973, _1768971), tc_HOL_Obool)), _1768971), c_COMBB(_1768971, tc_HOL_Obool, tc_fun(_1768973, _1768971))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768973, _1768971), _1768973, _1768971), c_COMBI(tc_fun(_1768973, _1768971))), _1768977)))))))], (48967 ^ _779300) ^ [_1769414, _1769416, _1769418, _1769420] : [class_Complete__Lattice_Ocomplete__lattice(_1769414), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1769416, _1769414), _1769418), _1769420) = c_Complete__Lattice_OInf__class_OInf(_1769414, hAPP(c_Set_OCollect(_1769414), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769416, _1769414), tc_HOL_Obool), tc_HOL_Obool, _1769414), c_HOL_OEx(tc_fun(_1769416, _1769414))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769416, _1769414), tc_HOL_Obool), tc_fun(tc_fun(_1769416, _1769414), tc_HOL_Obool), _1769414), hAPP(c_COMBS(tc_fun(_1769416, _1769414), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1769416, _1769414)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1769416, _1769414), tc_fun(tc_fun(_1769416, _1769414), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1769416, _1769414))), _1769418)))), hAPP(hAPP(c_COMBC(_1769414, tc_fun(tc_fun(_1769416, _1769414), _1769414), tc_fun(tc_fun(_1769416, _1769414), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769414, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1769416, _1769414), _1769414), tc_fun(tc_fun(_1769416, _1769414), tc_HOL_Obool)), _1769414), c_COMBB(_1769414, tc_HOL_Obool, tc_fun(_1769416, _1769414))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1769416, _1769414), _1769416, _1769414), c_COMBI(tc_fun(_1769416, _1769414))), _1769420)))))))], (48973 ^ _779300) ^ [_1769857, _1769859, _1769861, _1769863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1769857), _1769859)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1769857), _1769861)), -(_1769861 = c_Orderings_Obot__class_Obot(tc_fun(_1769857, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1769857, _1769863, _1769859, _1769861)), 48987 ^ _779300 : [(48988 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769857), 48986 ^ [_1769857, _1769859, _1769861, _1769863]), _1769859)))], (48990 ^ _779300) ^ [_1770202] : [hBOOL(hAPP(hAPP(c_member(_1769857), _1770202), _1769861)), hBOOL(hAPP(hAPP(_1769863, 48986 ^ [_1769857, _1769859, _1769861, _1769863]), _1770202))]]], (48998 ^ _779300) ^ [_1770383, _1770385] : [c_Predicate_Otransp(_1770383, _1770385), -(c_Relation_Otrans(_1770383, hAPP(c_Set_OCollect(tc_prod(_1770383, _1770383)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770383, _1770383, tc_HOL_Obool), _1770385))))], (49004 ^ _779300) ^ [_1770486, _1770488] : [c_Relation_Otrans(_1770486, hAPP(c_Set_OCollect(tc_prod(_1770486, _1770486)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770486, _1770486, tc_HOL_Obool), _1770488))), -(c_Predicate_Otransp(_1770486, _1770488))], (49010 ^ _779300) ^ [_1770595, _1770597, _1770599, _1770601, _1770603] : [c_Predicate_Otransp(_1770595, _1770597), hBOOL(hAPP(hAPP(_1770597, _1770599), _1770601)), hBOOL(hAPP(hAPP(_1770597, _1770601), _1770603)), -(hBOOL(hAPP(hAPP(_1770597, _1770599), _1770603)))], (49024 ^ _779300) ^ [_1770824, _1770826] : [c_Equiv__Relations_Oequivp(_1770824, _1770826), 49027 ^ _779300 : [(49028 ^ _779300) ^ [] : [-(c_Predicate_Oreflp(_1770824, _1770826))], (49030 ^ _779300) ^ [] : [-(c_Predicate_Osymp(_1770824, _1770826))], (49032 ^ _779300) ^ [] : [-(c_Predicate_Otransp(_1770824, _1770826))]]], (49034 ^ _779300) ^ [_1770955, _1770957] : [c_Predicate_Oreflp(_1770955, _1770957), c_Predicate_Osymp(_1770955, _1770957), c_Predicate_Otransp(_1770955, _1770957), -(c_Equiv__Relations_Oequivp(_1770955, _1770957))], (49048 ^ _779300) ^ [_1771136, _1771138, _1771140, _1771142] : [c_Predicate_Osymp(_1771136, _1771138), hBOOL(hAPP(hAPP(_1771138, _1771140), _1771142)), -(hBOOL(hAPP(hAPP(_1771138, _1771142), _1771140)))], (49058 ^ _779300) ^ [_1771308, _1771310] : [c_Equiv__Relations_Oequivp(_1771308, _1771310), 49061 ^ _779300 : [(49062 ^ _779300) ^ [] : [-(c_Predicate_Oreflp(_1771308, _1771310))], (49064 ^ _779300) ^ [] : [-(c_Predicate_Osymp(_1771308, _1771310))], (49066 ^ _779300) ^ [] : [-(c_Predicate_Otransp(_1771308, _1771310))]]], (49068 ^ _779300) ^ [_1771431, _1771433] : [-(c_Equiv__Relations_Oequivp(_1771431, _1771433)), c_Predicate_Oreflp(_1771431, _1771433), c_Predicate_Osymp(_1771431, _1771433), c_Predicate_Otransp(_1771431, _1771433)], (49082 ^ _779300) ^ [_1771635, _1771637, _1771639, _1771641] : [c_Wellfounded_Omax__extp(_1771635, _1771637, _1771639, _1771641), 49085 ^ _779300 : [(49086 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1771635), _1771639)))], (49088 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1771635), _1771641)))], (49090 ^ _779300) ^ [] : [_1771641 = c_Orderings_Obot__class_Obot(tc_fun(_1771635, tc_HOL_Obool))], (49092 ^ _779300) ^ [_1771851] : [hBOOL(hAPP(hAPP(c_member(_1771635), _1771851), _1771639)), 49096 ^ _779300 : [(49097 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771635), 49095 ^ [_1771635, _1771637, _1771639, _1771641, _1771851]), _1771641)))], (49099 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1771637, _1771851), 49095 ^ [_1771635, _1771637, _1771639, _1771641, _1771851])))]]]]], (49101 ^ _779300) ^ [_1772035, _1772037, _1772039, _1772041] : [-(c_Wellfounded_Omax__extp(_1772035, _1772037, _1772039, _1772041)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1772035), _1772039)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1772035), _1772041)), -(_1772041 = c_Orderings_Obot__class_Obot(tc_fun(_1772035, tc_HOL_Obool))), 49115 ^ _779300 : [(49116 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772035), 49114 ^ [_1772035, _1772037, _1772039, _1772041]), _1772039)))], (49118 ^ _779300) ^ [_1772380] : [hBOOL(hAPP(hAPP(c_member(_1772035), _1772380), _1772041)), hBOOL(hAPP(hAPP(_1772037, 49114 ^ [_1772035, _1772037, _1772039, _1772041]), _1772380))]]], (49126 ^ _779300) ^ [_1772548, _1772550] : [c_Relation_Otrans(_1772548, _1772550), c_Relation_Oantisym(_1772548, _1772550), -(c_Relation_Otrans(_1772548, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1772548, _1772548), tc_HOL_Obool)), _1772550), c_Relation_OId(_1772548))))], (49136 ^ _779300) ^ [_1772709, _1772711] : [-(c_Relation_Oantisym(_1772709, c_Relation_OId__on(_1772709, _1772711)))], (49138 ^ _779300) ^ [_1772737, _1772739, _1772741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1772737, _1772737), tc_HOL_Obool)), _1772739), _1772741)), c_Relation_Oantisym(_1772737, _1772741), -(c_Relation_Oantisym(_1772737, _1772739))], (49148 ^ _779300) ^ [_1772896] : [-(c_Relation_Oantisym(_1772896, c_Relation_OId(_1772896)))], (49150 ^ _779300) ^ [_1772921] : [-(c_Relation_Oantisym(_1772921, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1772921, _1772921), tc_HOL_Obool))))], (49152 ^ _779300) ^ [_1772967, _1772969] : [c_Relation_Oantisym(_1772967, hAPP(c_Relation_Oconverse(_1772967, _1772967), _1772969)), -(c_Relation_Oantisym(_1772967, _1772969))], (49158 ^ _779300) ^ [_1773052, _1773054] : [c_Relation_Oantisym(_1773052, _1773054), -(c_Relation_Oantisym(_1773052, hAPP(c_Relation_Oconverse(_1773052, _1773052), _1773054)))], (49178 ^ _779300) ^ [_1773483, _1773485] : [49181 ^ _779300 : [(49182 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773483, _1773483)), hAPP(hAPP(c_Product__Type_OPair(_1773483, _1773483), 49179 ^ [_1773483, _1773485]), 49180 ^ [_1773483, _1773485])), _1773485)))], (49184 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773483, _1773483)), hAPP(hAPP(c_Product__Type_OPair(_1773483, _1773483), 49180 ^ [_1773483, _1773485]), 49179 ^ [_1773483, _1773485])), _1773485)))], (49186 ^ _779300) ^ [] : [49179 ^ [_1773483, _1773485] = 49180 ^ [_1773483, _1773485]]], -(c_Relation_Oantisym(_1773483, _1773485))], (49164 ^ _779300) ^ [_1773158, _1773160] : [c_Relation_Oantisym(_1773158, _1773160), 49167 ^ _779300 : [(49168 ^ _779300) ^ [_1773270, _1773272] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773158, _1773158)), hAPP(hAPP(c_Product__Type_OPair(_1773158, _1773158), _1773272), _1773270)), _1773160)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773158, _1773158)), hAPP(hAPP(c_Product__Type_OPair(_1773158, _1773158), _1773270), _1773272)), _1773160)), -(_1773272 = _1773270)]]], (49190 ^ _779300) ^ [_1773804, _1773806, _1773808, _1773810] : [c_Relation_Oantisym(_1773804, _1773806), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773804, _1773804)), hAPP(hAPP(c_Product__Type_OPair(_1773804, _1773804), _1773808), _1773810)), _1773806)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773804, _1773804)), hAPP(hAPP(c_Product__Type_OPair(_1773804, _1773804), _1773810), _1773808)), _1773806)), -(_1773808 = _1773810)], (49204 ^ _779300) ^ [_1774088, _1774090] : [c_Relation_Oantisym(_1774088, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774088, _1774088), tc_HOL_Obool)), _1774090), c_Relation_OId(_1774088))), -(c_Relation_Oantisym(_1774088, _1774090))], (49210 ^ _779300) ^ [_1774193, _1774195] : [c_Relation_Oantisym(_1774193, _1774195), -(c_Relation_Oantisym(_1774193, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774193, _1774193), tc_HOL_Obool)), _1774195), c_Relation_OId(_1774193))))], (49216 ^ _779300) ^ [_1774304, _1774306] : [c_Wellfounded_Oacyclic(_1774304, _1774306), -(c_Relation_Oantisym(_1774304, c_Transitive__Closure_Ortrancl(_1774304, _1774306)))], (49222 ^ _779300) ^ [_1774387, _1774389, _1774391, _1774393, _1774395, _1774397] : [-(c_Partial__Function_Ofun__lub(_1774387, _1774389, _1774391, _1774393, _1774395, _1774397) = hAPP(_1774393, hAPP(c_Set_OCollect(_1774387), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774391, _1774387), tc_HOL_Obool), tc_HOL_Obool, _1774387), c_HOL_OEx(tc_fun(_1774391, _1774387))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774391, _1774387), tc_HOL_Obool), tc_fun(tc_fun(_1774391, _1774387), tc_HOL_Obool), _1774387), hAPP(c_COMBS(tc_fun(_1774391, _1774387), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1774391, _1774387)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1774391, _1774387), tc_fun(tc_fun(_1774391, _1774387), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1774391, _1774387))), _1774395)))), hAPP(hAPP(c_COMBC(_1774387, tc_fun(tc_fun(_1774391, _1774387), _1774387), tc_fun(tc_fun(_1774391, _1774387), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774387, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1774391, _1774387), _1774387), tc_fun(tc_fun(_1774391, _1774387), tc_HOL_Obool)), _1774387), c_COMBB(_1774387, tc_HOL_Obool, tc_fun(_1774391, _1774387))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1774391, _1774387), _1774391, _1774387), c_COMBI(tc_fun(_1774391, _1774387))), _1774397)))))))], (49224 ^ _779300) ^ [_1774600, _1774602] : [c_Relation_Osym(_1774600, _1774602), c_Relation_Otrans(_1774600, _1774602), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1774600, _1774600), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1774600, _1774600, _1774600), hAPP(c_Relation_Oconverse(_1774600, _1774600), _1774602)), _1774602)), _1774602)))], (49244 ^ _779300) ^ [_1775065, _1775067] : [49247 ^ _779300 : [(49248 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775065, _1775065)), hAPP(hAPP(c_Product__Type_OPair(_1775065, _1775065), 49245 ^ [_1775065, _1775067]), 49246 ^ [_1775065, _1775067])), _1775067)))], (49250 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775065, _1775065)), hAPP(hAPP(c_Product__Type_OPair(_1775065, _1775065), 49246 ^ [_1775065, _1775067]), 49245 ^ [_1775065, _1775067])), _1775067))]], -(c_Relation_Osym(_1775065, _1775067))], (49234 ^ _779300) ^ [_1774802, _1774804] : [c_Relation_Osym(_1774802, _1774804), 49237 ^ _779300 : [(49238 ^ _779300) ^ [_1774908, _1774910] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774802, _1774802)), hAPP(hAPP(c_Product__Type_OPair(_1774802, _1774802), _1774910), _1774908)), _1774804)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774802, _1774802)), hAPP(hAPP(c_Product__Type_OPair(_1774802, _1774802), _1774908), _1774910)), _1774804)))]]], (49254 ^ _779300) ^ [_1775330, _1775332, _1775334, _1775336] : [c_Relation_Osym(_1775330, _1775332), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775330, _1775330)), hAPP(hAPP(c_Product__Type_OPair(_1775330, _1775330), _1775334), _1775336)), _1775332)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775330, _1775330)), hAPP(hAPP(c_Product__Type_OPair(_1775330, _1775330), _1775336), _1775334)), _1775332)))], (49264 ^ _779300) ^ [_1775543, _1775545, _1775547, _1775549] : [c_Relation_Osym(_1775543, _1775545), -(c_Relation_Osym(_1775547, hAPP(hAPP(c_Relation_Oinv__image(_1775543, _1775547), _1775545), _1775549)))], (49270 ^ _779300) ^ [_1775642, _1775644] : [-(c_Relation_Osym(_1775642, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1775642, _1775642), tc_HOL_Obool)), _1775644), hAPP(c_Relation_Oconverse(_1775642, _1775642), _1775644))))], (49272 ^ _779300) ^ [_1775687, _1775689, _1775691] : [c_Relation_Osym(_1775687, _1775689), c_Relation_Osym(_1775687, _1775691), -(c_Relation_Osym(_1775687, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1775687, _1775687), tc_HOL_Obool)), _1775689), _1775691)))], (49282 ^ _779300) ^ [_1775848, _1775850] : [c_Relation_Osym(_1775848, _1775850), -(c_Relation_Osym(tc_List_Olist(_1775848), c_List_Olistrel(_1775848, _1775850)))], (49288 ^ _779300) ^ [_1775950, _1775952] : [c_Relation_Osym(_1775950, _1775952), -(hAPP(c_Relation_Oconverse(_1775950, _1775950), _1775952) = _1775952)], (49294 ^ _779300) ^ [_1776035, _1776037] : [hAPP(c_Relation_Oconverse(_1776035, _1776035), _1776037) = _1776037, -(c_Relation_Osym(_1776035, _1776037))], (49300 ^ _779300) ^ [_1776141, _1776143] : [c_Relation_Osym(_1776141, hAPP(c_Relation_Oconverse(_1776141, _1776141), _1776143)), -(c_Relation_Osym(_1776141, _1776143))], (49306 ^ _779300) ^ [_1776226, _1776228] : [c_Relation_Osym(_1776226, _1776228), -(c_Relation_Osym(_1776226, hAPP(c_Relation_Oconverse(_1776226, _1776226), _1776228)))], (49312 ^ _779300) ^ [_1776317] : [-(c_Relation_Osym(_1776317, c_Relation_OId(_1776317)))], (49314 ^ _779300) ^ [_1776342, _1776344, _1776346] : [c_Relation_Osym(_1776342, _1776344), c_Relation_Osym(_1776342, _1776346), -(c_Relation_Osym(_1776342, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1776342, _1776342), tc_HOL_Obool)), _1776344), _1776346)))], (49324 ^ _779300) ^ [_1776503, _1776505] : [-(c_Relation_Osym(_1776503, c_Relation_OId__on(_1776503, _1776505)))], (49326 ^ _779300) ^ [_1776531, _1776533] : [c_Relation_Osym(_1776531, _1776533), -(c_Relation_Osym(_1776531, c_Transitive__Closure_Otrancl(_1776531, _1776533)))], (49332 ^ _779300) ^ [_1776614, _1776616] : [c_Relation_Osym(_1776614, _1776616), -(c_Relation_Osym(_1776614, c_Transitive__Closure_Ortrancl(_1776614, _1776616)))], (49338 ^ _779300) ^ [_1776697, _1776699] : [-(c_Relation_Osym(_1776697, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1776697, _1776697), tc_HOL_Obool)), _1776699), hAPP(c_Relation_Oconverse(_1776697, _1776697), _1776699))))], (49340 ^ _779300) ^ [_1776742, _1776744, _1776746] : [c_Equiv__Relations_Oequiv(_1776742, _1776744, _1776746), 49343 ^ _779300 : [(49344 ^ _779300) ^ [] : [-(c_Relation_Orefl__on(_1776742, _1776744, _1776746))], (49346 ^ _779300) ^ [] : [-(c_Relation_Osym(_1776742, _1776746))], (49348 ^ _779300) ^ [] : [-(c_Relation_Otrans(_1776742, _1776746))]]], (49350 ^ _779300) ^ [_1776879, _1776881, _1776883] : [c_Relation_Orefl__on(_1776879, _1776881, _1776883), c_Relation_Osym(_1776879, _1776883), c_Relation_Otrans(_1776879, _1776883), -(c_Equiv__Relations_Oequiv(_1776879, _1776881, _1776883))], (49364 ^ _779300) ^ [_1777088, _1777090, _1777092] : [c_Equiv__Relations_Oequiv(_1777088, _1777090, _1777092), 49367 ^ _779300 : [(49368 ^ _779300) ^ [] : [-(c_Relation_Orefl__on(_1777088, _1777090, _1777092))], (49370 ^ _779300) ^ [] : [-(c_Relation_Osym(_1777088, _1777092))], (49372 ^ _779300) ^ [] : [-(c_Relation_Otrans(_1777088, _1777092))]]], (49374 ^ _779300) ^ [_1777217, _1777219, _1777221] : [-(c_Equiv__Relations_Oequiv(_1777217, _1777219, _1777221)), c_Relation_Orefl__on(_1777217, _1777219, _1777221), c_Relation_Osym(_1777217, _1777221), c_Relation_Otrans(_1777217, _1777221)], (49388 ^ _779300) ^ [_1777425, _1777427] : [c_Predicate_Osymp(_1777425, _1777427), -(c_Relation_Osym(_1777425, hAPP(c_Set_OCollect(tc_prod(_1777425, _1777425)), hAPP(c_Product__Type_Oprod_Oprod__case(_1777425, _1777425, tc_HOL_Obool), _1777427))))], (49394 ^ _779300) ^ [_1777528, _1777530] : [c_Relation_Osym(_1777528, hAPP(c_Set_OCollect(tc_prod(_1777528, _1777528)), hAPP(c_Product__Type_Oprod_Oprod__case(_1777528, _1777528, tc_HOL_Obool), _1777530))), -(c_Predicate_Osymp(_1777528, _1777530))], (49400 ^ _779300) ^ [_1777637, _1777639] : [49401 ^ _779300 : [(49402 ^ _779300) ^ [_1777693] : [hBOOL(hAPP(hAPP(_1777637, _1777693), _1777693))]], c_Predicate_Osymp(_1777639, _1777637), c_Predicate_Otransp(_1777639, _1777637), -(c_Equiv__Relations_Opart__equivp(_1777639, _1777637))], (49414 ^ _779300) ^ [_1777856, _1777858] : [c_Equiv__Relations_Opart__equivp(_1777856, _1777858), 49418 ^ _779300 : [(49419 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1777858, 49417 ^ [_1777856, _1777858]), 49417 ^ [_1777856, _1777858])))], (49421 ^ _779300) ^ [] : [-(c_Predicate_Osymp(_1777856, _1777858))], (49423 ^ _779300) ^ [] : [-(c_Predicate_Otransp(_1777856, _1777858))]]], (49425 ^ _779300) ^ [_1778008, _1778010] : [-(c_Equiv__Relations_Opart__equivp(_1778008, _1778010)), 49428 ^ _779300 : [(49429 ^ _779300) ^ [_1778085] : [hBOOL(hAPP(hAPP(_1778010, _1778085), _1778085))]], c_Predicate_Osymp(_1778008, _1778010), c_Predicate_Otransp(_1778008, _1778010)], (49439 ^ _779300) ^ [_1778214, _1778216] : [c_Equiv__Relations_Oequivp(_1778214, _1778216), -(c_Equiv__Relations_Opart__equivp(_1778214, _1778216))], (49445 ^ _779300) ^ [_1778291, _1778293, _1778295, _1778297, _1778299] : [c_Equiv__Relations_Opart__equivp(_1778291, _1778293), hBOOL(hAPP(hAPP(_1778293, _1778295), _1778297)), hBOOL(hAPP(hAPP(_1778293, _1778297), _1778299)), -(hBOOL(hAPP(hAPP(_1778293, _1778295), _1778299)))], (49459 ^ _779300) ^ [_1778520, _1778522, _1778524, _1778526] : [c_Equiv__Relations_Opart__equivp(_1778520, _1778522), hBOOL(hAPP(hAPP(_1778522, _1778524), _1778526)), -(hBOOL(hAPP(hAPP(_1778522, _1778526), _1778524)))], (49500 ^ _779300) ^ [_1779273, _1779275] : [-(c_Equiv__Relations_Opart__equivp(_1779273, _1779275)), 49503 ^ _779300 : [(49504 ^ _779300) ^ [_1779393] : [hBOOL(hAPP(hAPP(_1779275, _1779393), _1779393))]], 49521 ^ _779300 : [(49522 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1779275, 49505 ^ [_1779273, _1779275]), 49505 ^ [_1779273, _1779275])))], (49524 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1779275, 49506 ^ [_1779273, _1779275]), 49506 ^ [_1779273, _1779275])))], (49526 ^ _779300) ^ [] : [-(hAPP(_1779275, 49505 ^ [_1779273, _1779275]) = hAPP(_1779275, 49506 ^ [_1779273, _1779275]))], (49528 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1779275, 49505 ^ [_1779273, _1779275]), 49506 ^ [_1779273, _1779275]))]], 49509 ^ _779300 : [(49510 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1779275, 49505 ^ [_1779273, _1779275]), 49506 ^ [_1779273, _1779275])))], (49512 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1779275, 49505 ^ [_1779273, _1779275]), 49505 ^ [_1779273, _1779275])), hBOOL(hAPP(hAPP(_1779275, 49506 ^ [_1779273, _1779275]), 49506 ^ [_1779273, _1779275])), hAPP(_1779275, 49505 ^ [_1779273, _1779275]) = hAPP(_1779275, 49506 ^ [_1779273, _1779275])]]], (49469 ^ _779300) ^ [_1778692, _1778694] : [c_Equiv__Relations_Opart__equivp(_1778692, _1778694), 49473 ^ _779300 : [(49474 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1778694, 49472 ^ [_1778692, _1778694]), 49472 ^ [_1778692, _1778694])))], (49476 ^ _779300) ^ [_1778865, _1778867] : [hBOOL(hAPP(hAPP(_1778694, _1778867), _1778865)), 49479 ^ _779300 : [(49480 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1778694, _1778867), _1778867)))], (49482 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1778694, _1778865), _1778865)))], (49484 ^ _779300) ^ [] : [-(hAPP(_1778694, _1778867) = hAPP(_1778694, _1778865))]]], (49486 ^ _779300) ^ [_1779034, _1779036] : [-(hBOOL(hAPP(hAPP(_1778694, _1779036), _1779034))), hBOOL(hAPP(hAPP(_1778694, _1779036), _1779036)), hBOOL(hAPP(hAPP(_1778694, _1779034), _1779034)), hAPP(_1778694, _1779036) = hAPP(_1778694, _1779034)]]], (49532 ^ _779300) ^ [_1779941, _1779943] : [c_Equiv__Relations_Opart__equivp(_1779941, _1779943), 49536 ^ _779300 : [(49537 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1779943, 49535 ^ [_1779941, _1779943]), 49535 ^ [_1779941, _1779943])))], (49539 ^ _779300) ^ [] : [-(c_Predicate_Osymp(_1779941, _1779943))], (49541 ^ _779300) ^ [] : [-(c_Predicate_Otransp(_1779941, _1779943))]]], (49543 ^ _779300) ^ [_1780101, _1780103] : [c_Equiv__Relations_Opart__equivp(_1780101, _1780103), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1780101, tc_HOL_Obool)), 49546 ^ [_1780101, _1780103]), hAPP(hAPP(c_COMBB(tc_fun(_1780101, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1780101, tc_HOL_Obool)), c_HOL_OEx(_1780101)), hAPP(hAPP(c_COMBB(tc_fun(_1780101, tc_HOL_Obool), tc_fun(_1780101, tc_HOL_Obool), tc_fun(_1780101, tc_HOL_Obool)), hAPP(c_COMBS(_1780101, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1780101), c_fconj), hAPP(hAPP(c_COMBS(_1780101, _1780101, tc_HOL_Obool), _1780103), c_COMBI(_1780101))))), hAPP(hAPP(c_COMBC(tc_fun(_1780101, tc_HOL_Obool), tc_fun(_1780101, tc_fun(_1780101, tc_HOL_Obool)), tc_fun(_1780101, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1780101, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1780101, tc_fun(_1780101, tc_HOL_Obool)), tc_fun(_1780101, tc_HOL_Obool)), tc_fun(_1780101, tc_HOL_Obool)), c_COMBB(tc_fun(_1780101, tc_HOL_Obool), tc_HOL_Obool, _1780101)), c_fequal)), _1780103))))))], (49550 ^ _779300) ^ [_1780480, _1780482, _1780484] : [c_Fun_Oinj__on(_1780480, _1780482, _1780484, c_Orderings_Otop__class_Otop(tc_fun(_1780480, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780482, _1780480, _1780480, c_Hilbert__Choice_Oinv__into(_1780480, _1780482, c_Orderings_Otop__class_Otop(tc_fun(_1780480, tc_HOL_Obool)), _1780484)), _1780484) = c_Fun_Oid(_1780480))], (49556 ^ _779300) ^ [_1780609, _1780611, _1780613] : [hAPP(c_Fun_Ocomp(_1780611, _1780609, _1780609, c_Hilbert__Choice_Oinv__into(_1780609, _1780611, c_Orderings_Otop__class_Otop(tc_fun(_1780609, tc_HOL_Obool)), _1780613)), _1780613) = c_Fun_Oid(_1780609), -(c_Fun_Oinj__on(_1780609, _1780611, _1780613, c_Orderings_Otop__class_Otop(tc_fun(_1780609, tc_HOL_Obool))))], (49562 ^ _779300) ^ [_1780744, _1780746, _1780748] : [c_Fun_Oinj__on(_1780744, _1780746, _1780748, c_Orderings_Otop__class_Otop(tc_fun(_1780744, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780746, _1780744, _1780744, c_Hilbert__Choice_Oinv__into(_1780744, _1780746, c_Orderings_Otop__class_Otop(tc_fun(_1780744, tc_HOL_Obool)), _1780748)), _1780748) = c_Fun_Oid(_1780744))], (49568 ^ _779300) ^ [_1780877, _1780879, _1780881, _1780883, _1780885] : [c_Fun_Oinj__on(_1780877, _1780879, _1780881, _1780883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1780877, tc_HOL_Obool)), _1780885), _1780883)), -(hAPP(c_Set_Oimage(_1780879, _1780877, c_Hilbert__Choice_Oinv__into(_1780877, _1780879, _1780883, _1780881)), hAPP(c_Set_Oimage(_1780877, _1780879, _1780881), _1780885)) = _1780885)], (49578 ^ _779300) ^ [_1781080, _1781082, _1781084, _1781086, _1781088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1781080, tc_HOL_Obool)), _1781082), hAPP(c_Set_Oimage(_1781084, _1781080, _1781086), _1781088))), -(c_Fun_Oinj__on(_1781080, _1781084, c_Hilbert__Choice_Oinv__into(_1781084, _1781080, _1781088, _1781086), _1781082))], (49584 ^ _779300) ^ [_1781211, _1781213, _1781215] : [c_Fun_Oinj__on(_1781211, _1781213, _1781215, c_Orderings_Otop__class_Otop(tc_fun(_1781211, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781213, _1781211, c_Hilbert__Choice_Oinv__into(_1781211, _1781213, c_Orderings_Otop__class_Otop(tc_fun(_1781211, tc_HOL_Obool)), _1781215)), c_Orderings_Otop__class_Otop(tc_fun(_1781213, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781211, tc_HOL_Obool)))], (49590 ^ _779300) ^ [_1781358, _1781360, _1781362, _1781364] : [c_Fun_Oinj__on(_1781358, _1781360, _1781362, c_Orderings_Otop__class_Otop(tc_fun(_1781358, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781360, _1781358, c_Hilbert__Choice_Oinv__into(_1781358, _1781360, c_Orderings_Otop__class_Otop(tc_fun(_1781358, tc_HOL_Obool)), _1781362)), hAPP(c_Set_Oimage(_1781358, _1781360, _1781362), _1781364)) = _1781364)], (49596 ^ _779300) ^ [_1781501, _1781503, _1781505, _1781507] : [c_Fun_Oinj__on(_1781501, _1781503, _1781505, c_Orderings_Otop__class_Otop(tc_fun(_1781501, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781503, _1781501, c_Hilbert__Choice_Oinv__into(_1781501, _1781503, c_Orderings_Otop__class_Otop(tc_fun(_1781501, tc_HOL_Obool)), _1781505)), hAPP(c_Set_Oimage(_1781501, _1781503, _1781505), _1781507)) = _1781507)], (49602 ^ _779300) ^ [_1781644, _1781646, _1781648] : [hAPP(c_Set_Oimage(_1781644, _1781646, _1781648), c_Orderings_Otop__class_Otop(tc_fun(_1781644, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781646, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1781646, _1781644, c_Hilbert__Choice_Oinv__into(_1781644, _1781646, c_Orderings_Otop__class_Otop(tc_fun(_1781644, tc_HOL_Obool)), _1781648), c_Orderings_Otop__class_Otop(tc_fun(_1781646, tc_HOL_Obool))))], (49608 ^ _779300) ^ [_1781791, _1781793, _1781795, _1781797, _1781799, _1781801] : [hAPP(c_Set_Oimage(_1781791, _1781793, _1781795), _1781797) = _1781799, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1781793, tc_HOL_Obool)), _1781801), _1781799)), -(hAPP(c_Set_Oimage(_1781791, _1781793, _1781795), hAPP(c_Set_Oimage(_1781793, _1781791, c_Hilbert__Choice_Oinv__into(_1781791, _1781793, _1781797, _1781795)), _1781801)) = _1781801)], (49618 ^ _779300) ^ [_1782008, _1782010, _1782012, _1782014] : [hAPP(c_Set_Oimage(_1782008, _1782010, _1782012), c_Orderings_Otop__class_Otop(tc_fun(_1782008, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782010, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1782008, _1782010, _1782012), hAPP(c_Set_Oimage(_1782010, _1782008, c_Hilbert__Choice_Oinv__into(_1782008, _1782010, c_Orderings_Otop__class_Otop(tc_fun(_1782008, tc_HOL_Obool)), _1782012)), _1782014)) = _1782014)], (49624 ^ _779300) ^ [_1782171, _1782173, _1782175, _1782177] : [hAPP(c_Set_Oimage(_1782171, _1782173, _1782175), c_Orderings_Otop__class_Otop(tc_fun(_1782171, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782173, tc_HOL_Obool)), -(hAPP(_1782175, hAPP(c_Hilbert__Choice_Oinv__into(_1782171, _1782173, c_Orderings_Otop__class_Otop(tc_fun(_1782171, tc_HOL_Obool)), _1782175), _1782177)) = _1782177)], (49630 ^ _779300) ^ [_1782336, _1782338, _1782340] : [hAPP(c_Set_Oimage(_1782336, _1782338, _1782340), c_Orderings_Otop__class_Otop(tc_fun(_1782336, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782338, tc_HOL_Obool)), 49633 ^ _779300 : [(49634 ^ _779300) ^ [_1782447] : [-(hAPP(_1782340, hAPP(c_Hilbert__Choice_Oinv__into(_1782336, _1782338, c_Orderings_Otop__class_Otop(tc_fun(_1782336, tc_HOL_Obool)), _1782340), _1782447)) = _1782447)]]], (49636 ^ _779300) ^ [_1782486, _1782488, _1782490] : [hAPP(_1782490, hAPP(c_Hilbert__Choice_Oinv__into(_1782486, _1782488, c_Orderings_Otop__class_Otop(tc_fun(_1782486, tc_HOL_Obool)), _1782490), 49637 ^ [_1782486, _1782488, _1782490])) = 49637 ^ [_1782486, _1782488, _1782490], -(hAPP(c_Set_Oimage(_1782486, _1782488, _1782490), c_Orderings_Otop__class_Otop(tc_fun(_1782486, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782488, tc_HOL_Obool)))], (49643 ^ _779300) ^ [_1782686, _1782688, _1782690, _1782692, _1782694, _1782696] : [hAPP(c_Hilbert__Choice_Oinv__into(_1782686, _1782688, _1782690, _1782692), _1782694) = hAPP(c_Hilbert__Choice_Oinv__into(_1782686, _1782688, _1782690, _1782692), _1782696), hBOOL(hAPP(hAPP(c_member(_1782688), _1782694), hAPP(c_Set_Oimage(_1782686, _1782688, _1782692), _1782690))), hBOOL(hAPP(hAPP(c_member(_1782688), _1782696), hAPP(c_Set_Oimage(_1782686, _1782688, _1782692), _1782690))), -(_1782694 = _1782696)], (49657 ^ _779300) ^ [_1782979, _1782981, _1782983, _1782985, _1782987] : [hBOOL(hAPP(hAPP(c_member(_1782979), _1782981), hAPP(c_Set_Oimage(_1782983, _1782979, _1782985), _1782987))), -(hBOOL(hAPP(hAPP(c_member(_1782983), hAPP(c_Hilbert__Choice_Oinv__into(_1782983, _1782979, _1782987, _1782985), _1782981)), _1782987)))], (49663 ^ _779300) ^ [_1783120, _1783122, _1783124, _1783126, _1783128] : [hBOOL(hAPP(hAPP(c_member(_1783120), _1783122), hAPP(c_Set_Oimage(_1783124, _1783120, _1783126), _1783128))), -(hAPP(_1783126, hAPP(c_Hilbert__Choice_Oinv__into(_1783124, _1783120, _1783128, _1783126), _1783122)) = _1783122)], (49669 ^ _779300) ^ [_1783253, _1783255, _1783257, _1783259, _1783261] : [c_Fun_Oinj__on(_1783253, _1783255, _1783257, _1783259), hBOOL(hAPP(hAPP(c_member(_1783253), _1783261), _1783259)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1783253, _1783255, _1783259, _1783257), hAPP(_1783257, _1783261)) = _1783261)], (49679 ^ _779300) ^ [_1783434, _1783436, _1783438, _1783440, _1783442, _1783444] : [c_Fun_Oinj__on(_1783434, _1783436, _1783438, _1783440), hBOOL(hAPP(hAPP(c_member(_1783434), _1783442), _1783440)), hAPP(_1783438, _1783442) = _1783444, -(hAPP(c_Hilbert__Choice_Oinv__into(_1783434, _1783436, _1783440, _1783438), _1783444) = _1783442)], (49693 ^ _779300) ^ [_1783679, _1783681, _1783683, _1783685] : [c_Fun_Oinj__on(_1783679, _1783681, _1783683, c_Orderings_Otop__class_Otop(tc_fun(_1783679, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1783679, _1783681, c_Orderings_Otop__class_Otop(tc_fun(_1783679, tc_HOL_Obool)), _1783683), hAPP(_1783683, _1783685)) = _1783685)], (49699 ^ _779300) ^ [_1783806, _1783808, _1783810, _1783812, _1783814] : [c_Fun_Oinj__on(_1783806, _1783808, _1783810, c_Orderings_Otop__class_Otop(tc_fun(_1783806, tc_HOL_Obool))), hAPP(_1783810, _1783812) = _1783814, -(hAPP(c_Hilbert__Choice_Oinv__into(_1783806, _1783808, c_Orderings_Otop__class_Otop(tc_fun(_1783806, tc_HOL_Obool)), _1783810), _1783814) = _1783812)], (49709 ^ _779300) ^ [_1783993] : [-(c_Hilbert__Choice_Oinv__into(_1783993, _1783993, c_Orderings_Otop__class_Otop(tc_fun(_1783993, tc_HOL_Obool)), c_Fun_Oid(_1783993)) = c_Fun_Oid(_1783993))], (49711 ^ _779300) ^ [_1784030, _1784032, _1784034, _1784036, _1784038] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1784030, _1784032, _1784034, _1784036), _1784038) = c_Hilbert__Choice_OEps(_1784030, hAPP(hAPP(c_COMBS(_1784030, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1784030), c_fconj), hAPP(hAPP(c_COMBC(_1784030, tc_fun(_1784030, tc_HOL_Obool), tc_HOL_Obool), c_member(_1784030)), _1784034))), hAPP(hAPP(c_COMBC(_1784030, _1784032, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1784032, tc_fun(_1784032, tc_HOL_Obool), _1784030), c_fequal), _1784036)), _1784038))))], (49713 ^ _779300) ^ [_1784130, _1784132, _1784134, _1784136] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1784130, _1784132, c_Orderings_Otop__class_Otop(tc_fun(_1784130, tc_HOL_Obool)), _1784134), _1784136) = c_Hilbert__Choice_OEps(_1784130, hAPP(hAPP(c_COMBC(_1784130, _1784132, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1784132, tc_fun(_1784132, tc_HOL_Obool), _1784130), c_fequal), _1784134)), _1784136)))], (49715 ^ _779300) ^ [_1784198, _1784200, _1784202, _1784204, _1784206] : [c_Fun_Oinj__on(_1784198, _1784200, _1784202, c_Orderings_Otop__class_Otop(tc_fun(_1784198, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1784200, _1784204, _1784198, hAPP(c_Fun_Ocomp(_1784198, _1784204, _1784200, _1784206), c_Hilbert__Choice_Oinv__into(_1784198, _1784200, c_Orderings_Otop__class_Otop(tc_fun(_1784198, tc_HOL_Obool)), _1784202))), _1784202) = _1784206)], (49721 ^ _779300) ^ [_1784347, _1784349, _1784351, _1784353, _1784355, _1784357, _1784359] : [c_Fun_Oinj__on(_1784347, _1784349, _1784351, hAPP(c_Set_Oimage(_1784353, _1784347, _1784355), _1784357)), c_Fun_Oinj__on(_1784353, _1784347, _1784355, _1784357), hBOOL(hAPP(hAPP(c_member(_1784349), _1784359), hAPP(c_Set_Oimage(_1784347, _1784349, _1784351), hAPP(c_Set_Oimage(_1784353, _1784347, _1784355), _1784357)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1784353, _1784349, _1784357, hAPP(c_Fun_Ocomp(_1784347, _1784349, _1784353, _1784351), _1784355)), _1784359) = hAPP(hAPP(c_Fun_Ocomp(_1784347, _1784353, _1784349, c_Hilbert__Choice_Oinv__into(_1784353, _1784347, _1784357, _1784355)), c_Hilbert__Choice_Oinv__into(_1784347, _1784349, hAPP(c_Set_Oimage(_1784353, _1784347, _1784355), _1784357), _1784351)), _1784359))], (49735 ^ _779300) ^ [_1784728, _1784730, _1784732] : [hAPP(c_Set_Oimage(_1784728, _1784730, _1784732), c_Orderings_Otop__class_Otop(tc_fun(_1784728, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784730, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1784728, _1784730, _1784730, _1784732), c_Hilbert__Choice_Oinv__into(_1784728, _1784730, c_Orderings_Otop__class_Otop(tc_fun(_1784728, tc_HOL_Obool)), _1784732)) = c_Fun_Oid(_1784730))], (49741 ^ _779300) ^ [_1784877, _1784879, _1784881] : [hAPP(c_Fun_Ocomp(_1784877, _1784879, _1784879, _1784881), c_Hilbert__Choice_Oinv__into(_1784877, _1784879, c_Orderings_Otop__class_Otop(tc_fun(_1784877, tc_HOL_Obool)), _1784881)) = c_Fun_Oid(_1784879), -(hAPP(c_Set_Oimage(_1784877, _1784879, _1784881), c_Orderings_Otop__class_Otop(tc_fun(_1784877, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784879, tc_HOL_Obool)))], (49747 ^ _779300) ^ [_1785032, _1785034, _1785036, _1785038, _1785040] : [c_Fun_Oinj__on(_1785032, _1785034, _1785036, c_Orderings_Otop__class_Otop(tc_fun(_1785032, tc_HOL_Obool))), 49753 ^ _779300 : [(49754 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785034), 49752 ^ [_1785032, _1785034, _1785036, _1785038, _1785040]), hAPP(c_Set_Oimage(_1785032, _1785034, _1785036), c_Orderings_Otop__class_Otop(tc_fun(_1785032, tc_HOL_Obool))))))], (49756 ^ _779300) ^ [] : [hBOOL(hAPP(_1785038, hAPP(c_Hilbert__Choice_Oinv__into(_1785032, _1785034, c_Orderings_Otop__class_Otop(tc_fun(_1785032, tc_HOL_Obool)), _1785036), 49752 ^ [_1785032, _1785034, _1785036, _1785038, _1785040])))]], -(hBOOL(hAPP(_1785038, _1785040)))], (49760 ^ _779300) ^ [_1785358, _1785360, _1785362, _1785364, _1785366, _1785368] : [class_Groups_Ocomm__monoid__mult(_1785358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1785360), _1785362)), 49770 ^ _779300 : [(49771 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785360), 49769 ^ [_1785358, _1785360, _1785362, _1785364, _1785366, _1785368]), _1785362)))], (49773 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785364), hAPP(_1785366, 49769 ^ [_1785358, _1785360, _1785362, _1785364, _1785366, _1785368])))]], 49777 ^ _779300 : [(49778 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785360), 49776 ^ [_1785358, _1785360, _1785362, _1785364, _1785366, _1785368]), _1785362)))], (49781 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785360), 49779 ^ [_1785358, _1785360, _1785362, _1785364, _1785366, _1785368]), _1785362)))], (49783 ^ _779300) ^ [] : [49776 ^ [_1785358, _1785360, _1785362, _1785364, _1785366, _1785368] = 49779 ^ [_1785358, _1785360, _1785362, _1785364, _1785366, _1785368]], (49785 ^ _779300) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785364, tc_HOL_Obool)), hAPP(_1785366, 49776 ^ [_1785358, _1785360, _1785362, _1785364, _1785366, _1785368])), hAPP(_1785366, 49779 ^ [_1785358, _1785360, _1785362, _1785364, _1785366, _1785368])) = c_Orderings_Obot__class_Obot(tc_fun(_1785364, tc_HOL_Obool))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785358, _1785364, c_Groups_Otimes__class_Otimes(_1785358)), _1785368), c_Groups_Oone__class_Oone(_1785358)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1785360, tc_fun(_1785364, tc_HOL_Obool)), _1785362), _1785366)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785358, _1785360, c_Groups_Otimes__class_Otimes(_1785358)), hAPP(hAPP(c_COMBB(tc_fun(_1785364, tc_HOL_Obool), _1785358, _1785360), hAPP(hAPP(c_Finite__Set_Ofold__image(_1785358, _1785364, c_Groups_Otimes__class_Otimes(_1785358)), _1785368), c_Groups_Oone__class_Oone(_1785358))), _1785366)), c_Groups_Oone__class_Oone(_1785358)), _1785362))], (49789 ^ _779300) ^ [_1786318, _1786320] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786318), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1786320, hAPP(c_Code__Numeral_Onat__of, 49794 ^ [_1786318, _1786320]))), -(hBOOL(hAPP(_1786320, _1786318)))], (49800 ^ _779300) ^ [_1786500] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786500), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1786500 = hAPP(c_Code__Numeral_Onat__of, 49803 ^ [_1786500]))], (49807 ^ _779300) ^ [_1786605, _1786607] : [49809 ^ _779300 : [(49810 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49808 ^ [_1786605, _1786607]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (49812 ^ _779300) ^ [] : [hBOOL(hAPP(_1786605, hAPP(c_Code__Numeral_Oof__nat, 49808 ^ [_1786605, _1786607])))]], -(hBOOL(hAPP(_1786605, _1786607)))], (49817 ^ _779300) ^ [_1786772] : [-(_1786772 = hAPP(c_Code__Numeral_Oof__nat, 49815 ^ [_1786772]))], (49819 ^ _779300) ^ [_1786800] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49815 ^ [_1786800]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (49821 ^ _779300) ^ [_1786835, _1786837, _1786839, _1786841] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1786835, _1786837, _1786839, _1786841, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1786837)) = _1786839)], (49823 ^ _779300) ^ [_1786881, _1786883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1786881), _1786883)), -(c_Quickcheck_Obeyond(_1786881, _1786883) = _1786883)], (49829 ^ _779300) ^ [_1786968, _1786970] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1786968), _1786970))), -(c_Quickcheck_Obeyond(_1786968, _1786970) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (49835 ^ _779300) ^ [_1787014] : [-(c_Quickcheck_Obeyond(_1787014, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (49837 ^ _779300) ^ [_1787040, _1787042, _1787044, _1787046, _1787048, _1787050] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1787040, _1787042, _1787044, _1787046, c_Lazy__Sequence_Olazy__sequence_OInsert(_1787042, _1787048, _1787050)) = hAPP(hAPP(hAPP(_1787046, _1787048), _1787050), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1787040, _1787042, _1787044, _1787046, _1787050)))], (49839 ^ _779300) ^ [_1787098, _1787100, _1787102, _1787104] : [c_Fun_Obij__betw(_1787098, _1787100, _1787102, c_Orderings_Otop__class_Otop(tc_fun(_1787098, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787100, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1787098, _1787100, _1787102), hAPP(c_Set_OCollect(_1787098), _1787104)) = hAPP(c_Set_OCollect(_1787100), hAPP(hAPP(c_COMBB(_1787098, tc_HOL_Obool, _1787100), _1787104), c_Hilbert__Choice_Oinv__into(_1787098, _1787100, c_Orderings_Otop__class_Otop(tc_fun(_1787098, tc_HOL_Obool)), _1787102))))], (49845 ^ _779300) ^ [_1787279, _1787281, _1787283, _1787285, _1787287, _1787289] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1787279, _1787281, _1787283, _1787285), _1787287), _1787289) = hAPP(_1787285, hAPP(hAPP(c_Product__Type_OPair(_1787279, _1787281), _1787287), _1787289)))], (49847 ^ _779300) ^ [_1787335, _1787337, _1787339, _1787341, _1787343] : [hBOOL(hAPP(_1787335, hAPP(hAPP(c_Product__Type_OPair(_1787337, _1787339), _1787341), _1787343))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1787337, _1787339, tc_HOL_Obool, _1787335), _1787341), _1787343)))], (49853 ^ _779300) ^ [_1787460, _1787462] : [-(c_Fun_Obij__betw(_1787460, _1787460, c_Fun_Oid(_1787460), _1787462, _1787462))], (49855 ^ _779300) ^ [_1787490, _1787492, _1787494] : [c_Fun_Obij__betw(_1787490, _1787492, _1787494, c_Orderings_Otop__class_Otop(tc_fun(_1787490, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787492, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1787492, _1787490, c_Orderings_Otop__class_Otop(tc_fun(_1787492, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1787490, _1787492, c_Orderings_Otop__class_Otop(tc_fun(_1787490, tc_HOL_Obool)), _1787494)) = _1787494)], (49861 ^ _779300) ^ [_1787635, _1787637, _1787639] : [c_Fun_Obij__betw(_1787635, _1787637, _1787639, c_Orderings_Otop__class_Otop(tc_fun(_1787635, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787637, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1787637, _1787635, c_Hilbert__Choice_Oinv__into(_1787635, _1787637, c_Orderings_Otop__class_Otop(tc_fun(_1787635, tc_HOL_Obool)), _1787639), c_Orderings_Otop__class_Otop(tc_fun(_1787637, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787635, tc_HOL_Obool))))], (49867 ^ _779300) ^ [_1787786, _1787788, _1787790, _1787792, _1787794, _1787796] : [c_Fun_Obij__betw(_1787786, _1787788, _1787790, _1787792, _1787794), hBOOL(hAPP(hAPP(c_member(_1787786), _1787796), _1787792)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1787788, _1787786, _1787794, c_Hilbert__Choice_Oinv__into(_1787786, _1787788, _1787792, _1787790)), _1787796) = hAPP(_1787790, _1787796))], (49877 ^ _779300) ^ [_1787983, _1787985, _1787987, _1787989, _1787991] : [c_Fun_Obij__betw(_1787983, _1787985, _1787987, _1787989, _1787991), -(c_Fun_Obij__betw(_1787985, _1787983, c_Hilbert__Choice_Oinv__into(_1787983, _1787985, _1787989, _1787987), _1787991, _1787989))], (49883 ^ _779300) ^ [_1788088, _1788090, _1788092, _1788094, _1788096] : [c_Fun_Obij__betw(_1788088, _1788090, _1788092, c_Orderings_Otop__class_Otop(tc_fun(_1788088, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788090, tc_HOL_Obool))), c_Fun_Obij__betw(_1788094, _1788088, _1788096, c_Orderings_Otop__class_Otop(tc_fun(_1788094, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788088, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1788094, _1788090, c_Orderings_Otop__class_Otop(tc_fun(_1788094, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1788088, _1788090, _1788094, _1788092), _1788096)) = hAPP(c_Fun_Ocomp(_1788088, _1788094, _1788090, c_Hilbert__Choice_Oinv__into(_1788094, _1788088, c_Orderings_Otop__class_Otop(tc_fun(_1788094, tc_HOL_Obool)), _1788096)), c_Hilbert__Choice_Oinv__into(_1788088, _1788090, c_Orderings_Otop__class_Otop(tc_fun(_1788088, tc_HOL_Obool)), _1788092)))], (49893 ^ _779300) ^ [_1788373, _1788375, _1788377, _1788379, _1788381, _1788383, _1788385, _1788387] : [c_Fun_Obij__betw(_1788373, _1788375, _1788377, _1788379, _1788381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1788373, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1788383, _1788373, _1788385), _1788387)), _1788379)), 49900 ^ _779300 : [(49901 ^ _779300) ^ [] : [c_Fun_Obij__betw(_1788383, _1788373, _1788385, _1788387, _1788379), -(c_Fun_Obij__betw(_1788383, _1788375, hAPP(c_Fun_Ocomp(_1788373, _1788375, _1788383, _1788377), _1788385), _1788387, _1788381))], (49907 ^ _779300) ^ [] : [c_Fun_Obij__betw(_1788383, _1788375, hAPP(c_Fun_Ocomp(_1788373, _1788375, _1788383, _1788377), _1788385), _1788387, _1788381), -(c_Fun_Obij__betw(_1788383, _1788373, _1788385, _1788387, _1788379))]]], (49913 ^ _779300) ^ [_1788762, _1788764, _1788766, _1788768, _1788770] : [c_Fun_Obij__betw(_1788762, _1788764, _1788766, c_Orderings_Otop__class_Otop(tc_fun(_1788762, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788764, tc_HOL_Obool))), c_Fun_Obij__betw(_1788764, _1788768, _1788770, c_Orderings_Otop__class_Otop(tc_fun(_1788764, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788768, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1788762, _1788768, hAPP(c_Fun_Ocomp(_1788764, _1788768, _1788762, _1788770), _1788766), c_Orderings_Otop__class_Otop(tc_fun(_1788762, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788768, tc_HOL_Obool))))], (49923 ^ _779300) ^ [_1788997, _1788999, _1789001, _1789003, _1789005, _1789007, _1789009, _1789011] : [c_Fun_Obij__betw(_1788997, _1788999, _1789001, _1789003, _1789005), c_Fun_Obij__betw(_1788999, _1789007, _1789009, _1789005, _1789011), -(c_Fun_Obij__betw(_1788997, _1789007, hAPP(c_Fun_Ocomp(_1788999, _1789007, _1788997, _1789009), _1789001), _1789003, _1789011))], (49933 ^ _779300) ^ [_1789210, _1789212, _1789214, _1789216, _1789218, _1789220, _1789222, _1789224] : [c_Fun_Obij__betw(_1789210, _1789212, _1789214, _1789216, _1789218), 49936 ^ _779300 : [(49937 ^ _779300) ^ [] : [c_Fun_Obij__betw(_1789212, _1789220, _1789222, _1789218, _1789224), -(c_Fun_Obij__betw(_1789210, _1789220, hAPP(c_Fun_Ocomp(_1789212, _1789220, _1789210, _1789222), _1789214), _1789216, _1789224))], (49943 ^ _779300) ^ [] : [c_Fun_Obij__betw(_1789210, _1789220, hAPP(c_Fun_Ocomp(_1789212, _1789220, _1789210, _1789222), _1789214), _1789216, _1789224), -(c_Fun_Obij__betw(_1789212, _1789220, _1789222, _1789218, _1789224))]]], (49949 ^ _779300) ^ [_1789850, _1789852, _1789854, _1789856, _1789858] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1789850, _1789852, tc_HOL_Obool, _1789854), _1789856), _1789858)), -(hBOOL(hAPP(_1789854, hAPP(hAPP(c_Product__Type_OPair(_1789850, _1789852), _1789856), _1789858))))], (49955 ^ _779300) ^ [_1790162, _1790164, _1790166, _1790168, _1790170] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1790162, _1790164, tc_HOL_Obool, _1790166), _1790168), _1790170)), -(hBOOL(hAPP(_1790166, hAPP(hAPP(c_Product__Type_OPair(_1790162, _1790164), _1790168), _1790170))))], (49961 ^ _779300) ^ [_1790473, _1790475, _1790477, _1790479, _1790481, _1790483] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1790473, _1790475, _1790477, _1790479), _1790481), _1790483) = hAPP(_1790479, hAPP(hAPP(c_Product__Type_OPair(_1790473, _1790475), _1790481), _1790483)))], (49963 ^ _779300) ^ [_1790641, _1790643, _1790645, _1790647] : [c_Fun_Obij__betw(_1790641, _1790643, _1790645, c_Orderings_Otop__class_Otop(tc_fun(_1790641, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790643, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1790641, _1790643, _1790645), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1790641, tc_HOL_Obool)), _1790647)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1790643, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1790641, _1790643, _1790645), _1790647)))], (49969 ^ _779300) ^ [_1790977, _1790979, _1790981, _1790983] : [c_Fun_Obij__betw(_1790977, _1790979, _1790981, c_Orderings_Otop__class_Otop(tc_fun(_1790977, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790979, tc_HOL_Obool))), 49972 ^ _779300 : [(49973 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1790977), hAPP(c_Set_Ovimage(_1790977, _1790979, _1790981), _1790983))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1790979), _1790983)))], (49979 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1790979), _1790983)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1790977), hAPP(c_Set_Ovimage(_1790977, _1790979, _1790981), _1790983))))]]], (49985 ^ _779300) ^ [_1791610, _1791612, _1791614, _1791616, _1791618, _1791620, _1791622] : [c_Fun_Obij__betw(_1791610, _1791612, _1791614, _1791616, _1791618), c_Fun_Obij__betw(_1791610, _1791612, _1791614, _1791620, _1791622), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1791612, tc_HOL_Obool)), _1791618), _1791622) = c_Orderings_Obot__class_Obot(tc_fun(_1791612, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1791610, _1791612, _1791614, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1791610, tc_HOL_Obool)), _1791616), _1791620), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1791612, tc_HOL_Obool)), _1791618), _1791622)))], (49999 ^ _779300) ^ [_1792232, _1792234, _1792236, _1792238, _1792240, _1792242, _1792244] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1792232, tc_HOL_Obool)), _1792234), _1792236) = c_Orderings_Obot__class_Obot(tc_fun(_1792232, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1792238, tc_HOL_Obool)), _1792240), _1792242) = c_Orderings_Obot__class_Obot(tc_fun(_1792238, tc_HOL_Obool)), c_Fun_Obij__betw(_1792232, _1792238, _1792244, _1792234, _1792240), c_Fun_Obij__betw(_1792232, _1792238, _1792244, _1792236, _1792242), -(c_Fun_Obij__betw(_1792232, _1792238, _1792244, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1792232, tc_HOL_Obool)), _1792234), _1792236), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1792238, tc_HOL_Obool)), _1792240), _1792242)))], (50017 ^ _779300) ^ [_1792896] : [-(c_Fun_Obij__betw(_1792896, _1792896, c_Fun_Oid(_1792896), c_Orderings_Otop__class_Otop(tc_fun(_1792896, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792896, tc_HOL_Obool))))], (50019 ^ _779300) ^ [_1793061, _1793063, _1793065] : [c_Fun_Obij__betw(_1793061, _1793061, c_Fun_Oid(_1793061), _1793063, _1793065), -(_1793063 = _1793065)], (50025 ^ _779300) ^ [_1793239, _1793241, _1793243] : [_1793241 = _1793243, -(c_Fun_Obij__betw(_1793239, _1793239, c_Fun_Oid(_1793239), _1793241, _1793243))], (50031 ^ _779300) ^ [_1793495, _1793497, _1793499, _1793501] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1793495), _1793497)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1793499), _1793501)), 50038 ^ _779300 : [(50039 ^ _779300) ^ [] : [50040 ^ _779300 : [(50041 ^ _779300) ^ [_1793813] : [c_Fun_Obij__betw(_1793495, _1793499, _1793813, _1793497, _1793501)]], -(hAPP(c_Finite__Set_Ocard(_1793495), _1793497) = hAPP(c_Finite__Set_Ocard(_1793499), _1793501))], (50045 ^ _779300) ^ [] : [hAPP(c_Finite__Set_Ocard(_1793495), _1793497) = hAPP(c_Finite__Set_Ocard(_1793499), _1793501), -(c_Fun_Obij__betw(_1793495, _1793499, 50048 ^ [_1793495, _1793497, _1793499, _1793501], _1793497, _1793501))]]], (50052 ^ _779300) ^ [_1794270, _1794272, _1794274, _1794276, _1794278] : [c_Fun_Obij__betw(_1794270, _1794272, _1794274, _1794276, _1794278), 50055 ^ _779300 : [(50056 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1794270), _1794276)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1794272), _1794278)))], (50062 ^ _779300) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1794272), _1794278)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1794270), _1794276)))]]], (50068 ^ _779300) ^ [_1794836, _1794838, _1794840, _1794842] : [c_Fun_Obij__betw(_1794836, _1794838, _1794840, c_Orderings_Obot__class_Obot(tc_fun(_1794836, tc_HOL_Obool)), _1794842), -(_1794842 = c_Orderings_Obot__class_Obot(tc_fun(_1794838, tc_HOL_Obool)))], (50074 ^ _779300) ^ [_1795112, _1795114, _1795116, _1795118] : [c_Fun_Obij__betw(_1795112, _1795114, _1795116, _1795118, c_Orderings_Obot__class_Obot(tc_fun(_1795114, tc_HOL_Obool))), -(_1795118 = c_Orderings_Obot__class_Obot(tc_fun(_1795112, tc_HOL_Obool)))], (50080 ^ _779300) ^ [_1795402, _1795404, _1795406, _1795408, _1795410] : [c_Fun_Obij__betw(_1795402, _1795404, _1795406, _1795408, _1795410), -(hAPP(c_Finite__Set_Ocard(_1795402), _1795408) = hAPP(c_Finite__Set_Ocard(_1795404), _1795410))], (50086 ^ _779300) ^ [_1795698, _1795700, _1795702, _1795704, _1795706] : [c_Fun_Obij__betw(_1795698, _1795700, _1795702, _1795704, _1795706), -(c_Fun_Obij__betw(_1795700, _1795698, c_Fun_Othe__inv__into(_1795698, _1795700, _1795704, _1795702), _1795706, _1795704))], (50092 ^ _779300) ^ [_1795962, _1795964, _1795966] : [c_Fun_Obij__betw(_1795962, _1795964, _1795966, c_Orderings_Otop__class_Otop(tc_fun(_1795962, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1795964, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1795962, _1795964, _1795966, c_Orderings_Otop__class_Otop(tc_fun(_1795962, tc_HOL_Obool))))], (50098 ^ _779300) ^ [_1796260, _1796262, _1796264, _1796266, _1796268] : [c_Fun_Obij__betw(_1796260, _1796262, _1796264, _1796266, _1796268), -(c_Fun_Oinj__on(_1796260, _1796262, _1796264, _1796266))], (50104 ^ _779300) ^ [_1796526, _1796528, _1796530, _1796532] : [c_Fun_Oinj__on(_1796526, _1796528, _1796530, _1796532), -(c_Fun_Obij__betw(_1796526, _1796528, _1796530, _1796532, hAPP(c_Set_Oimage(_1796526, _1796528, _1796530), _1796532)))], (50110 ^ _779300) ^ [_1796843, _1796845, _1796847, _1796849, _1796851] : [c_Fun_Obij__betw(_1796843, _1796845, _1796847, _1796849, _1796851), 50113 ^ _779300 : [(50114 ^ _779300) ^ [] : [-(c_Fun_Oinj__on(_1796843, _1796845, _1796847, _1796849))], (50116 ^ _779300) ^ [] : [-(hAPP(c_Set_Oimage(_1796843, _1796845, _1796847), _1796849) = _1796851)]]], (50118 ^ _779300) ^ [_1797128, _1797130, _1797132, _1797134, _1797136] : [-(c_Fun_Obij__betw(_1797128, _1797130, _1797132, _1797134, _1797136)), c_Fun_Oinj__on(_1797128, _1797130, _1797132, _1797134), hAPP(c_Set_Oimage(_1797128, _1797130, _1797132), _1797134) = _1797136], (50128 ^ _779300) ^ [_1797511, _1797513, _1797515, _1797517] : [c_Fun_Obij__betw(_1797511, _1797513, _1797515, _1797517, c_Orderings_Otop__class_Otop(tc_fun(_1797513, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1797511, _1797513, _1797515), c_Orderings_Otop__class_Otop(tc_fun(_1797511, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1797513, tc_HOL_Obool)))], (50134 ^ _779300) ^ [_1797797, _1797799, _1797801] : [c_Fun_Obij__betw(_1797797, _1797799, _1797801, c_Orderings_Otop__class_Otop(tc_fun(_1797797, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1797799, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1797797, _1797799, _1797801), c_Orderings_Otop__class_Otop(tc_fun(_1797797, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1797799, tc_HOL_Obool)))], (50140 ^ _779300) ^ [_1798143, _1798145, _1798147, _1798149, _1798151, _1798153, _1798155] : [c_Fun_Obij__betw(_1798143, _1798145, _1798147, _1798149, _1798151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1798143, tc_HOL_Obool)), _1798153), _1798149)), hAPP(c_Set_Oimage(_1798143, _1798145, _1798147), _1798153) = _1798155, -(c_Fun_Obij__betw(_1798143, _1798145, _1798147, _1798153, _1798155))], (50154 ^ _779300) ^ [_1798661, _1798663, _1798665] : [c_Fun_Oinj__on(_1798661, _1798663, _1798665, c_Orderings_Otop__class_Otop(tc_fun(_1798661, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1798661, _1798663, _1798665), c_Orderings_Otop__class_Otop(tc_fun(_1798661, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1798663, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1798661, _1798663, _1798665, c_Orderings_Otop__class_Otop(tc_fun(_1798661, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1798663, tc_HOL_Obool))))], (50164 ^ _779300) ^ [_1799087, _1799089, _1799091] : [c_Fun_Obij__betw(_1799087, _1799089, _1799091, c_Orderings_Otop__class_Otop(tc_fun(_1799087, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799089, tc_HOL_Obool))), 50167 ^ _779300 : [(50168 ^ _779300) ^ [] : [-(c_Fun_Oinj__on(_1799087, _1799089, _1799091, c_Orderings_Otop__class_Otop(tc_fun(_1799087, tc_HOL_Obool))))], (50170 ^ _779300) ^ [] : [-(hAPP(c_Set_Oimage(_1799087, _1799089, _1799091), c_Orderings_Otop__class_Otop(tc_fun(_1799087, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799089, tc_HOL_Obool)))]]], (50172 ^ _779300) ^ [_1799406, _1799408, _1799410] : [-(c_Fun_Obij__betw(_1799406, _1799408, _1799410, c_Orderings_Otop__class_Otop(tc_fun(_1799406, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799408, tc_HOL_Obool)))), c_Fun_Oinj__on(_1799406, _1799408, _1799410, c_Orderings_Otop__class_Otop(tc_fun(_1799406, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1799406, _1799408, _1799410), c_Orderings_Otop__class_Otop(tc_fun(_1799406, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799408, tc_HOL_Obool))], (50182 ^ _779300) ^ [_1799804, _1799806, _1799808, _1799810] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1799804, _1799806, _1799808), c_Product__Type_Ocurry(_1799804, _1799806, _1799808, _1799810)) = _1799810)], (50184 ^ _779300) ^ [_1799942, _1799944, _1799946, _1799948] : [-(c_Product__Type_Ocurry(_1799942, _1799944, _1799946, hAPP(c_Product__Type_Oprod_Oprod__case(_1799942, _1799944, _1799946), _1799948)) = _1799948)], (50186 ^ _779300) ^ [_1800123, _1800125, _1800127, _1800129, _1800131, _1800133] : [c_Fun_Obij__betw(_1800123, _1800125, _1800127, c_Orderings_Otop__class_Otop(tc_fun(_1800123, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800125, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1800123, _1800125, _1800127), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1800129, tc_fun(_1800123, tc_HOL_Obool)), _1800131), _1800133)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1800129, tc_fun(_1800125, tc_HOL_Obool)), _1800131), hAPP(hAPP(c_COMBB(tc_fun(_1800123, tc_HOL_Obool), tc_fun(_1800125, tc_HOL_Obool), _1800129), c_Set_Oimage(_1800123, _1800125, _1800127)), _1800133)))], (50192 ^ _779300) ^ [_1800527, _1800529, _1800531, _1800533, _1800535] : [c_Fun_Obij__betw(_1800527, _1800529, _1800531, c_Orderings_Otop__class_Otop(tc_fun(_1800527, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800529, tc_HOL_Obool))), 50195 ^ _779300 : [(50196 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800527, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1800527, _1800529, _1800531), _1800533)), _1800535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800529, tc_HOL_Obool)), _1800533), hAPP(c_Set_Oimage(_1800527, _1800529, _1800531), _1800535))))], (50202 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800529, tc_HOL_Obool)), _1800533), hAPP(c_Set_Oimage(_1800527, _1800529, _1800531), _1800535))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800527, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1800527, _1800529, _1800531), _1800533)), _1800535)))]]], (50208 ^ _779300) ^ [_1801191, _1801193, _1801195, _1801197] : [c_Fun_Obij__betw(_1801191, _1801193, _1801195, c_Orderings_Otop__class_Otop(tc_fun(_1801191, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1801193, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1801191, _1801193, _1801195), _1801197) = hAPP(c_Set_Oimage(_1801193, _1801191, c_Hilbert__Choice_Oinv__into(_1801191, _1801193, c_Orderings_Otop__class_Otop(tc_fun(_1801191, tc_HOL_Obool)), _1801195)), _1801197))], (50214 ^ _779300) ^ [_1801487, _1801489] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1801487), _1801489)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1801487, 50217 ^ [_1801487, _1801489], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1801487), _1801489)), _1801489))], (50221 ^ _779300) ^ [_1801854, _1801856, _1801858, _1801860, _1801862, _1801864] : [c_Fun_Oinj__on(_1801854, _1801856, _1801858, _1801860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1801856, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1801854, _1801856, _1801858), _1801860)), _1801862)), c_Fun_Oinj__on(_1801856, _1801854, _1801864, _1801862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1801854, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1801856, _1801854, _1801864), _1801862)), _1801860)), -(c_Fun_Obij__betw(_1801854, _1801856, 50236 ^ [_1801854, _1801856, _1801858, _1801860, _1801862, _1801864], _1801860, _1801862))], (50240 ^ _779300) ^ [_1802569, _1802571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802569), _1802571)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1802569, 50243 ^ [_1802569, _1802571], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1802569), _1802571)), _1802571))], (50247 ^ _779300) ^ [_1802877, _1802879] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802877), _1802879)), -(c_Fun_Obij__betw(_1802877, tc_Nat_Onat, 50250 ^ [_1802877, _1802879], _1802879, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1802877), _1802879))))], (50254 ^ _779300) ^ [_1803227, _1803229, _1803231, _1803233, _1803235] : [50256 ^ _779300 : [(50257 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803227), 50255 ^ [_1803227, _1803229, _1803231, _1803233, _1803235]), _1803229)))], (50259 ^ _779300) ^ [] : [c_Relation_Orefl__on(_1803231, hAPP(_1803233, 50255 ^ [_1803227, _1803229, _1803231, _1803233, _1803235]), hAPP(_1803235, 50255 ^ [_1803227, _1803229, _1803231, _1803233, _1803235]))]], -(c_Relation_Orefl__on(_1803231, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1803227, tc_fun(_1803231, tc_HOL_Obool)), _1803229), _1803233), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1803227, tc_fun(tc_prod(_1803231, _1803231), tc_HOL_Obool)), _1803229), _1803235)))], (50263 ^ _779300) ^ [_1803755, _1803757, _1803759] : [c_Equiv__Relations_Oequivp(_1803755, _1803757), 50266 ^ _779300 : [(50278 ^ _779300) ^ [] : [50279 ^ _779300 : [(50280 ^ _779300) ^ [_1804338] : [hBOOL(hAPP(_1803759, _1804338))]], 50282 ^ _779300 : [(50283 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803755), 50281 ^ [_1803755, _1803757, _1803759]), c_Quotient_ORespects(_1803755, _1803757))))], (50285 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1803759, 50281 ^ [_1803755, _1803757, _1803759])))]]], (50267 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1803759, 50274 ^ [_1803755, _1803757, _1803759]))), 50268 ^ _779300 : [(50269 ^ _779300) ^ [_1803986] : [hBOOL(hAPP(hAPP(c_member(_1803755), _1803986), c_Quotient_ORespects(_1803755, _1803757))), hBOOL(hAPP(_1803759, _1803986))]]]]], (50287 ^ _779300) ^ [_1804724, _1804726, _1804728] : [hBOOL(hAPP(c_Quotient_ORespects(_1804724, _1804726), _1804728)), -(hBOOL(hAPP(hAPP(_1804726, _1804728), _1804728)))], (50293 ^ _779300) ^ [_1804912, _1804914, _1804916] : [hBOOL(hAPP(hAPP(_1804914, _1804916), _1804916)), -(hBOOL(hAPP(c_Quotient_ORespects(_1804912, _1804914), _1804916)))], (50299 ^ _779300) ^ [_1805193, _1805195, _1805197] : [hBOOL(hAPP(hAPP(c_member(_1805193), _1805195), c_Quotient_ORespects(_1805193, _1805197))), -(hBOOL(hAPP(hAPP(_1805197, _1805195), _1805195)))], (50305 ^ _779300) ^ [_1805391, _1805393, _1805395] : [hBOOL(hAPP(hAPP(_1805395, _1805393), _1805393)), -(hBOOL(hAPP(hAPP(c_member(_1805391), _1805393), c_Quotient_ORespects(_1805391, _1805395))))], (50311 ^ _779300) ^ [_1805667, _1805669, _1805671, _1805673] : [c_Equiv__Relations_Oequivp(_1805667, _1805669), 50317 ^ _779300 : [(50318 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1805671, 50316 ^ [_1805667, _1805669, _1805671, _1805673])))], (50320 ^ _779300) ^ [] : [hBOOL(hAPP(_1805673, 50316 ^ [_1805667, _1805669, _1805671, _1805673]))]], 50323 ^ _779300 : [(50324 ^ _779300) ^ [_1806128] : [hBOOL(hAPP(_1805671, _1806128))]], 50326 ^ _779300 : [(50327 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805667), 50325 ^ [_1805667, _1805669, _1805671, _1805673]), c_Quotient_ORespects(_1805667, _1805669))))], (50329 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1805673, 50325 ^ [_1805667, _1805669, _1805671, _1805673])))]]], (50331 ^ _779300) ^ [_1806515, _1806517, _1806519, _1806521] : [c_Equiv__Relations_Oequivp(_1806515, _1806517), -(c_Quotient_OBabs(_1806515, _1806519, c_Quotient_ORespects(_1806515, _1806517), _1806521) = _1806521)], (50337 ^ _779300) ^ [_1806795, _1806797, _1806799, _1806801, _1806803] : [hBOOL(hAPP(hAPP(c_member(_1806795), _1806797), _1806799)), -(hAPP(c_Quotient_OBabs(_1806795, _1806801, _1806799, _1806803), _1806797) = hAPP(_1806803, _1806797))], (50343 ^ _779300) ^ [_1807073, _1807075, _1807077] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1807073, _1807073)), hAPP(hAPP(c_Product__Type_OPair(_1807073, _1807073), hAPP(_1807075, hAPP(c_Nat_OSuc, 50344 ^ [_1807073, _1807075, _1807077]))), hAPP(_1807075, 50344 ^ [_1807073, _1807075, _1807077]))), c_Transitive__Closure_Ortrancl(_1807073, _1807077))), c_Wellfounded_Owf(_1807073, c_Transitive__Closure_Otrancl(_1807073, _1807077)), 50352 ^ _779300 : [(50353 ^ _779300) ^ [_1807536] : [-(hAPP(_1807075, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50351 ^ [_1807073, _1807075, _1807077]), _1807536)) = hAPP(_1807075, 50351 ^ [_1807073, _1807075, _1807077]))]]], (50355 ^ _779300) ^ [_1807730, _1807732, _1807734, _1807736, _1807738] : [50357 ^ _779300 : [(50358 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1807730), 50356 ^ [_1807730, _1807732, _1807734, _1807736, _1807738]), _1807732)))], (50360 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1807734, tc_HOL_Obool)), _1807736), hAPP(_1807738, 50356 ^ [_1807730, _1807732, _1807734, _1807736, _1807738])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1807734, tc_HOL_Obool)), _1807736), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1807730, tc_fun(_1807734, tc_HOL_Obool)), _1807732), _1807738))))], (50364 ^ _779300) ^ [_1808293, _1808295, _1808297, _1808299, _1808301, _1808303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1808293, tc_HOL_Obool)), _1808295), _1808297)), 50370 ^ _779300 : [(50371 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808293), 50369 ^ [_1808293, _1808295, _1808297, _1808299, _1808301, _1808303]), _1808297)))], (50373 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1808299, tc_HOL_Obool)), hAPP(_1808301, 50369 ^ [_1808293, _1808295, _1808297, _1808299, _1808301, _1808303])), hAPP(_1808303, 50369 ^ [_1808293, _1808295, _1808297, _1808299, _1808301, _1808303])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1808299, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1808293, tc_fun(_1808299, tc_HOL_Obool)), _1808297), _1808301)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1808293, tc_fun(_1808299, tc_HOL_Obool)), _1808297), _1808303))))], (50377 ^ _779300) ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1809073, _1809075), tc_prod(_1809073, _1809075))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1809073, _1809075), tc_prod(_1809073, _1809075)), hAPP(hAPP(c_Product__Type_OPair(_1809073, _1809075), _1809077), _1809079)), hAPP(hAPP(c_Product__Type_OPair(_1809073, _1809075), _1809081), _1809083))), c_Transitive__Closure_Ortrancl(tc_prod(_1809073, _1809075), _1809085))), hBOOL(hAPP(hAPP(_1809087, _1809077), _1809079)), 50388 ^ _779300 : [(50389 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1809073, _1809075), tc_prod(_1809073, _1809075))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1809073, _1809075), tc_prod(_1809073, _1809075)), hAPP(hAPP(c_Product__Type_OPair(_1809073, _1809075), _1809077), _1809079)), hAPP(hAPP(c_Product__Type_OPair(_1809073, _1809075), 50386 ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087]), 50387 ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087]))), c_Transitive__Closure_Ortrancl(tc_prod(_1809073, _1809075), _1809085))))], (50393 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1809073, _1809075), tc_prod(_1809073, _1809075))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1809073, _1809075), tc_prod(_1809073, _1809075)), hAPP(hAPP(c_Product__Type_OPair(_1809073, _1809075), 50386 ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087]), 50387 ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087])), hAPP(hAPP(c_Product__Type_OPair(_1809073, _1809075), 50390 ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087]), 50391 ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087]))), _1809085)))], (50395 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1809087, 50386 ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087]), 50387 ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087])))], (50397 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1809087, 50390 ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087]), 50391 ^ [_1809073, _1809075, _1809077, _1809079, _1809081, _1809083, _1809085, _1809087]))]], -(hBOOL(hAPP(hAPP(_1809087, _1809081), _1809083)))], (50401 ^ _779300) ^ [_1811401, _1811403, _1811405, _1811407, _1811409, _1811411, _1811413] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1811401, _1811403), tc_prod(_1811401, _1811403))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1811401, _1811403), tc_prod(_1811401, _1811403)), hAPP(hAPP(c_Product__Type_OPair(_1811401, _1811403), _1811405), _1811407)), hAPP(hAPP(c_Product__Type_OPair(_1811401, _1811403), _1811409), _1811411))), c_Transitive__Closure_Ortrancl(tc_prod(_1811401, _1811403), _1811413))), -(hAPP(hAPP(c_Product__Type_OPair(_1811401, _1811403), _1811405), _1811407) = hAPP(hAPP(c_Product__Type_OPair(_1811401, _1811403), _1811409), _1811411)), 50410 ^ _779300 : [(50411 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1811401, _1811403), tc_prod(_1811401, _1811403))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1811401, _1811403), tc_prod(_1811401, _1811403)), hAPP(hAPP(c_Product__Type_OPair(_1811401, _1811403), _1811405), _1811407)), hAPP(hAPP(c_Product__Type_OPair(_1811401, _1811403), 50408 ^ [_1811401, _1811403, _1811405, _1811407, _1811409, _1811411, _1811413]), 50409 ^ [_1811401, _1811403, _1811405, _1811407, _1811409, _1811411, _1811413]))), _1811413)))], (50413 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1811401, _1811403), tc_prod(_1811401, _1811403))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1811401, _1811403), tc_prod(_1811401, _1811403)), hAPP(hAPP(c_Product__Type_OPair(_1811401, _1811403), 50408 ^ [_1811401, _1811403, _1811405, _1811407, _1811409, _1811411, _1811413]), 50409 ^ [_1811401, _1811403, _1811405, _1811407, _1811409, _1811411, _1811413])), hAPP(hAPP(c_Product__Type_OPair(_1811401, _1811403), _1811409), _1811411))), c_Transitive__Closure_Ortrancl(tc_prod(_1811401, _1811403), _1811413))))]]], (50415 ^ _779300) ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1812751, _1812753), tc_prod(_1812751, _1812753))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1812751, _1812753), tc_prod(_1812751, _1812753)), hAPP(hAPP(c_Product__Type_OPair(_1812751, _1812753), _1812755), _1812757)), hAPP(hAPP(c_Product__Type_OPair(_1812751, _1812753), _1812759), _1812761))), c_Transitive__Closure_Ortrancl(tc_prod(_1812751, _1812753), _1812763))), hBOOL(hAPP(hAPP(_1812765, _1812759), _1812761)), 50428 ^ _779300 : [(50429 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1812751, _1812753), tc_prod(_1812751, _1812753))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1812751, _1812753), tc_prod(_1812751, _1812753)), hAPP(hAPP(c_Product__Type_OPair(_1812751, _1812753), 50424 ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765]), 50425 ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765])), hAPP(hAPP(c_Product__Type_OPair(_1812751, _1812753), 50426 ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765]), 50427 ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765]))), _1812763)))], (50431 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1812751, _1812753), tc_prod(_1812751, _1812753))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1812751, _1812753), tc_prod(_1812751, _1812753)), hAPP(hAPP(c_Product__Type_OPair(_1812751, _1812753), 50426 ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765]), 50427 ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765])), hAPP(hAPP(c_Product__Type_OPair(_1812751, _1812753), _1812759), _1812761))), c_Transitive__Closure_Ortrancl(tc_prod(_1812751, _1812753), _1812763))))], (50433 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(_1812765, 50426 ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765]), 50427 ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765])))], (50435 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(_1812765, 50424 ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765]), 50425 ^ [_1812751, _1812753, _1812755, _1812757, _1812759, _1812761, _1812763, _1812765]))]], -(hBOOL(hAPP(hAPP(_1812765, _1812755), _1812757)))], (50439 ^ _779300) ^ [_1815187, _1815189, _1815191, _1815193, _1815195, _1815197] : [50442 ^ _779300 : [(50443 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1815187, _1815187)), hAPP(hAPP(c_Product__Type_OPair(_1815187, _1815187), 50440 ^ [_1815187, _1815189, _1815191, _1815193, _1815195, _1815197]), 50441 ^ [_1815187, _1815189, _1815191, _1815193, _1815195, _1815197])), _1815189)))], (50447 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1815191, _1815191)), hAPP(hAPP(c_Product__Type_OPair(_1815191, _1815191), 50444 ^ [_1815187, _1815189, _1815191, _1815193, _1815195, _1815197]), 50445 ^ [_1815187, _1815189, _1815191, _1815193, _1815195, _1815197])), _1815193)))], (50449 ^ _779300) ^ [] : [hAPP(hAPP(_1815195, 50440 ^ [_1815187, _1815189, _1815191, _1815193, _1815195, _1815197]), 50444 ^ [_1815187, _1815189, _1815191, _1815193, _1815195, _1815197]) = hAPP(hAPP(_1815195, 50441 ^ [_1815187, _1815189, _1815191, _1815193, _1815195, _1815197]), 50445 ^ [_1815187, _1815189, _1815191, _1815193, _1815195, _1815197])]], -(c_Equiv__Relations_Ocongruent2(_1815187, _1815191, _1815197, _1815189, _1815193, _1815195))], (50453 ^ _779300) ^ [_1816454, _1816456, _1816458, _1816460] : [50456 ^ _779300 : [(50457 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1816454, _1816454)), hAPP(hAPP(c_Product__Type_OPair(_1816454, _1816454), 50454 ^ [_1816454, _1816456, _1816458, _1816460]), 50455 ^ [_1816454, _1816456, _1816458, _1816460])), _1816456)))], (50459 ^ _779300) ^ [] : [hAPP(_1816458, 50454 ^ [_1816454, _1816456, _1816458, _1816460]) = hAPP(_1816458, 50455 ^ [_1816454, _1816456, _1816458, _1816460])]], -(c_Equiv__Relations_Ocongruent(_1816454, _1816460, _1816456, _1816458))], (50463 ^ _779300) ^ [_1817057, _1817059, _1817061] : [-(c_Lazy__Sequence_Oflat(_1817057, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1817057), _1817059, _1817061)) = c_Lazy__Sequence_Oappend(_1817057, _1817059, c_Lazy__Sequence_Oflat(_1817057, _1817061)))], (50465 ^ _779300) ^ [_1817227, _1817229, _1817231] : [c_List_Olist__all(tc_Nat_Onat, _1817227, c_List_Oupt(_1817229, _1817231)), -(c_List_Oall__interval__nat(_1817227, _1817229, _1817231))], (50471 ^ _779300) ^ [_1817405, _1817407, _1817409] : [c_List_Oall__interval__nat(_1817405, _1817407, _1817409), -(c_List_Olist__all(tc_Nat_Onat, _1817405, c_List_Oupt(_1817407, _1817409)))], (50477 ^ _779300) ^ [_1817604] : [-(c_Lazy__Sequence_Oflat(_1817604, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1817604))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1817604))], (50489 ^ _779300) ^ [_1818130, _1818132, _1818134] : [50491 ^ _779300 : [(50492 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50490 ^ [_1818130, _1818132, _1818134]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1818132), _1818134))))], (50494 ^ _779300) ^ [] : [hBOOL(hAPP(_1818130, 50490 ^ [_1818130, _1818132, _1818134]))]], -(c_List_Oall__interval__nat(_1818130, _1818132, _1818134))], (50479 ^ _779300) ^ [_1817763, _1817765, _1817767] : [c_List_Oall__interval__nat(_1817763, _1817765, _1817767), 50482 ^ _779300 : [(50483 ^ _779300) ^ [_1817919] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1817919), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1817765), _1817767))), -(hBOOL(hAPP(_1817763, _1817919)))]]], (50498 ^ _779300) ^ [_1818587, _1818589, _1818591] : [c_List_Olist__ex(tc_Nat_Onat, _1818587, c_List_Oupt(_1818589, _1818591)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1818587), _1818589, _1818591)], (50504 ^ _779300) ^ [_1818772, _1818774, _1818776] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1818772), _1818774, _1818776)), -(c_List_Olist__ex(tc_Nat_Onat, _1818772, c_List_Oupt(_1818774, _1818776)))], (50510 ^ _779300) ^ [_1819022, _1819024, _1819026, _1819028] : [-(hAPP(c_Lazy__Sequence_Obind(_1819022, _1819024, _1819026), _1819028) = c_Lazy__Sequence_Oflat(_1819024, c_Lazy__Sequence_Omap(_1819022, tc_Lazy__Sequence_Olazy__sequence(_1819024), _1819028, _1819026)))], (50512 ^ _779300) ^ [_1819236, _1819238, _1819240, _1819242, _1819244, _1819246, _1819248, _1819250] : [c_Finite__Set_Ofolding__image(_1819236, _1819238, _1819240, _1819242, _1819244), hBOOL(hAPP(c_Finite__Set_Ofinite(_1819238), _1819246)), 50522 ^ _779300 : [(50523 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1819238), 50521 ^ [_1819236, _1819238, _1819240, _1819242, _1819244, _1819246, _1819248, _1819250]), _1819246)))], (50525 ^ _779300) ^ [] : [hAPP(_1819248, 50521 ^ [_1819236, _1819238, _1819240, _1819242, _1819244, _1819246, _1819248, _1819250]) = hAPP(_1819250, 50521 ^ [_1819236, _1819238, _1819240, _1819242, _1819244, _1819246, _1819248, _1819250])]], -(hAPP(hAPP(_1819244, _1819248), _1819246) = hAPP(hAPP(_1819244, _1819250), _1819246))], (50529 ^ _779300) ^ [_1820036, _1820038, _1820040, _1820042, _1820044] : [-(c_Lazy__Sequence_Omap(_1820036, _1820038, _1820040, c_Lazy__Sequence_Olazy__sequence_OInsert(_1820036, _1820042, _1820044)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1820038, hAPP(_1820040, _1820042), c_Lazy__Sequence_Omap(_1820036, _1820038, _1820040, _1820044)))], (50531 ^ _779300) ^ [_1820171, _1820173, _1820175] : [-(c_Lazy__Sequence_Omap(_1820171, _1820173, _1820175, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1820171)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1820173))], (50533 ^ _779300) ^ [_1820318, _1820320, _1820322, _1820324, _1820326] : [-(c_New__DSequence_Opos__map(_1820318, _1820320, _1820322, _1820324, _1820326) = c_Lazy__Sequence_Omap(_1820318, _1820320, _1820322, hAPP(_1820324, _1820326)))], (50535 ^ _779300) ^ [_1820461, _1820463, _1820465] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1820461), _1820463)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1820461), _1820465))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1820461)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1820463), _1820465)))], (50545 ^ _779300) ^ [_1820789] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820789), _1820789)))], (50547 ^ _779300) ^ [_1820901, _1820903] : [class_Rings_Ocomm__semiring__1(_1820901), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820901), _1820903), c_Groups_Ozero__class_Ozero(_1820901))))], (50553 ^ _779300) ^ [_1821098] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1821098)))], (50555 ^ _779300) ^ [_1821207, _1821209] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821207), _1821209)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1821209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1821207), _1821209)))], (50565 ^ _779300) ^ [_1821544, _1821546, _1821548] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1821544), _1821546)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1821544), _1821548))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1821544)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821546), _1821548)))], (50575 ^ _779300) ^ [_1821915, _1821917, _1821919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1821915)), 50578 ^ _779300 : [(50579 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1821915), _1821917)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1821915), _1821919))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821917), _1821919)))], (50585 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821917), _1821919)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1821915), _1821917)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1821915), _1821919))))]]], (50591 ^ _779300) ^ [_1822503, _1822505, _1822507, _1822509, _1822511] : [class_Groups_Ocomm__monoid__mult(_1822503), class_Rings_Odvd(_1822503), hBOOL(hAPP(c_Finite__Set_Ofinite(_1822505), _1822507)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1822505, tc_HOL_Obool)), _1822509), _1822507)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822503), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1822505, _1822503), _1822511), _1822509)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1822505, _1822503), _1822511), _1822507))))], (50609 ^ _779300) ^ [_1823124, _1823126, _1823128] : [class_Divides_Osemiring__div(_1823124), class_Int_Onumber(_1823124), 50616 ^ _779300 : [(50617 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823124), hAPP(c_Int_Onumber__class_Onumber__of(_1823124), _1823126)), hAPP(c_Int_Onumber__class_Onumber__of(_1823124), _1823128))), -(c_Divides_Odiv__class_Omod(_1823124, hAPP(c_Int_Onumber__class_Onumber__of(_1823124), _1823128), hAPP(c_Int_Onumber__class_Onumber__of(_1823124), _1823126)) = c_Groups_Ozero__class_Ozero(_1823124))], (50623 ^ _779300) ^ [] : [c_Divides_Odiv__class_Omod(_1823124, hAPP(c_Int_Onumber__class_Onumber__of(_1823124), _1823128), hAPP(c_Int_Onumber__class_Onumber__of(_1823124), _1823126)) = c_Groups_Ozero__class_Ozero(_1823124), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823124), hAPP(c_Int_Onumber__class_Onumber__of(_1823124), _1823126)), hAPP(c_Int_Onumber__class_Onumber__of(_1823124), _1823128))))]]], (50629 ^ _779300) ^ [_1823818, _1823820, _1823822, _1823824] : [class_Divides_Osemiring__div(_1823818), -(_1823820 = c_Groups_Ozero__class_Ozero(_1823818)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823818), _1823820), _1823822)), 50640 ^ _779300 : [(50641 ^ _779300) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1823818), _1823822), _1823820) = _1823824, -(_1823822 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1823818), _1823824), _1823820))], (50647 ^ _779300) ^ [] : [_1823822 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1823818), _1823824), _1823820), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1823818), _1823822), _1823820) = _1823824)]]], (50653 ^ _779300) ^ [_1824613, _1824615, _1824617, _1824619, _1824621] : [class_Divides_Osemiring__div(_1824613), -(_1824615 = c_Groups_Ozero__class_Ozero(_1824613)), -(_1824617 = c_Groups_Ozero__class_Ozero(_1824613)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824613), _1824615), _1824619)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824613), _1824617), _1824621)), 50672 ^ _779300 : [(50673 ^ _779300) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824613), _1824619), _1824615) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824613), _1824621), _1824617), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824613), _1824619), _1824617) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824613), _1824615), _1824621))], (50679 ^ _779300) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824613), _1824619), _1824617) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824613), _1824615), _1824621), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824613), _1824619), _1824615) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824613), _1824621), _1824617))]]], (50685 ^ _779300) ^ [_1825675, _1825677, _1825679] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825675), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1825677), _1825679))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825675), _1825677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1825679), _1825677)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825675), _1825679)))], (50699 ^ _779300) ^ [_1826143, _1826145, _1826147] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826143), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1826145), _1826147))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826143), _1826147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1826147), _1826145)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826143), _1826145)))], (50713 ^ _779300) ^ [_1826654, _1826656, _1826658, _1826660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826654, _1826656)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826658, _1826660))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826654), _1826656)), 50720 ^ _779300 : [(50721 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826658), _1826654)))], (50723 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826656), _1826660)))]]], (50725 ^ _779300) ^ [_1827066, _1827068, _1827070, _1827072] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827066, _1827068)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827070, _1827072)))), 50726 ^ _779300 : [(50727 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827066), _1827068)))], (50729 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827070), _1827066)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827068), _1827072))]]], (50737 ^ _779300) ^ [_1827556, _1827558, _1827560, _1827562] : [class_Rings_Ocomm__semiring__1(_1827556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1827558), _1827560)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827556), hAPP(hAPP(c_Power_Opower__class_Opower(_1827556), _1827562), _1827558)), hAPP(hAPP(c_Power_Opower__class_Opower(_1827556), _1827562), _1827560))))], (50747 ^ _779300) ^ [_1827971, _1827973, _1827975, _1827977, _1827979] : [class_Rings_Ocomm__semiring__1(_1827971), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827971), _1827973), _1827975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1827977), _1827979)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827971), hAPP(hAPP(c_Power_Opower__class_Opower(_1827971), _1827973), _1827977)), hAPP(hAPP(c_Power_Opower__class_Opower(_1827971), _1827975), _1827979))))], (50761 ^ _779300) ^ [_1828511, _1828513, _1828515, _1828517, _1828519] : [class_Rings_Ocomm__semiring__1(_1828511), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828511), hAPP(hAPP(c_Power_Opower__class_Opower(_1828511), _1828513), _1828515)), _1828517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1828519), _1828515)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828511), hAPP(hAPP(c_Power_Opower__class_Opower(_1828511), _1828513), _1828519)), _1828517)))], (50775 ^ _779300) ^ [_1829038, _1829040] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1829038), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829040))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829038), _1829040)))], (50781 ^ _779300) ^ [_1829228, _1829230] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829228), _1829230)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1829228), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829230))))], (50787 ^ _779300) ^ [_1829497, _1829499] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1829497), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829499))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829499), _1829497)))], (50793 ^ _779300) ^ [_1829687, _1829689] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829689), _1829687)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1829687), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829689))))], (50799 ^ _779300) ^ [_1829956, _1829958] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1829956), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1829958))), 50802 ^ _779300 : [(50803 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829958), _1829956)))], (50805 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829956), _1829958))]]], (50807 ^ _779300) ^ [_1830232, _1830234] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1830232), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1830234)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830234), _1830232)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830232), _1830234)))], (50817 ^ _779300) ^ [_1830603, _1830605] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1830603), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1830605))), 50820 ^ _779300 : [(50821 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830603), _1830605)))], (50823 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830605), _1830603))]]], (50825 ^ _779300) ^ [_1830879, _1830881] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1830879), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1830881)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830879), _1830881)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830881), _1830879)))], (50835 ^ _779300) ^ [_1831249, _1831251, _1831253, _1831255] : [class_Divides_Osemiring__div(_1831249), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831249), _1831251), _1831253)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1831249), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1831249), _1831253), _1831251)), _1831255) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1831249), hAPP(hAPP(c_Power_Opower__class_Opower(_1831249), _1831253), _1831255)), hAPP(hAPP(c_Power_Opower__class_Opower(_1831249), _1831251), _1831255)))], (50845 ^ _779300) ^ [_1831674, _1831676, _1831678] : [class_Rings_Olinordered__idom(_1831674), hAPP(c_Groups_Oabs__class_Oabs(_1831674), _1831676) = hAPP(c_Groups_Oabs__class_Oabs(_1831674), _1831678), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831674), _1831676), _1831678)))], (50855 ^ _779300) ^ [_1832029, _1832031, _1832033] : [class_Rings_Olinordered__idom(_1832029), 50858 ^ _779300 : [(50859 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832029), hAPP(c_Groups_Oabs__class_Oabs(_1832029), _1832031)), _1832033)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832029), _1832031), _1832033)))], (50865 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832029), _1832031), _1832033)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832029), hAPP(c_Groups_Oabs__class_Oabs(_1832029), _1832031)), _1832033)))]]], (50871 ^ _779300) ^ [_1832574, _1832576, _1832578] : [class_Rings_Olinordered__idom(_1832574), 50874 ^ _779300 : [(50875 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832574), _1832576), hAPP(c_Groups_Oabs__class_Oabs(_1832574), _1832578))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832574), _1832576), _1832578)))], (50881 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832574), _1832576), _1832578)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832574), _1832576), hAPP(c_Groups_Oabs__class_Oabs(_1832574), _1832578))))]]], (50887 ^ _779300) ^ [_1833120] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1833120), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1833120 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (50893 ^ _779300) ^ [_1833286] : [_1833286 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1833286), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (50899 ^ _779300) ^ [_1833502, _1833504] : [class_Rings_Ocomm__semiring__1(_1833502), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833502), c_Groups_Oone__class_Oone(_1833502)), _1833504)))], (50905 ^ _779300) ^ [_1833728, _1833730] : [class_Rings_Ocomm__semiring__1(_1833728), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833728), c_Groups_Ozero__class_Ozero(_1833728)), _1833730)), -(_1833730 = c_Groups_Ozero__class_Ozero(_1833728))], (50915 ^ _779300) ^ [_1834075, _1834077, _1834079, _1834081] : [class_Rings_Ocomm__semiring__1(_1834075), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834075), _1834077), _1834079)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834075), _1834079), _1834081)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834075), _1834077), _1834081)))], (50929 ^ _779300) ^ [_1834531, _1834533] : [class_Rings_Ocomm__semiring__1(_1834531), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834531), _1834533), _1834533)))], (50935 ^ _779300) ^ [_1834753, _1834755] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1834753), _1834755)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1834755), _1834753))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1834755), _1834753)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1834753), _1834755)))], (50949 ^ _779300) ^ [_1835204, _1835206, _1835208] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835204), _1835206)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835206), _1835204))), 50964 ^ _779300 : [(50965 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835204), _1835208)))], (50967 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835208), _1835204))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835206), _1835208)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835208), _1835206)))], (50969 ^ _779300) ^ [_1835845, _1835847] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835845), _1835847)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835847), _1835845))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835847), _1835845)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835845), _1835847)))], (50983 ^ _779300) ^ [_1836296, _1836298, _1836300] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836296), _1836298)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836298), _1836296))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836298), _1836300)), 50994 ^ _779300 : [(50995 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836296), _1836300)))], (50997 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836300), _1836296))]]], (50999 ^ _779300) ^ [_1836845, _1836847, _1836849] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836845), _1836847)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836847), _1836845))), _1836847 = _1836849, 51010 ^ _779300 : [(51011 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836845), _1836849)))], (51013 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836849), _1836845))]]], (51015 ^ _779300) ^ [_1837370, _1837372] : [_1837372 = _1837370, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837370), _1837372)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837372), _1837370)))], (51025 ^ _779300) ^ [_1837693, _1837695] : [_1837693 = _1837695, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837693), _1837695)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837695), _1837693)))], (51035 ^ _779300) ^ [_1838016, _1838018] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838016), _1838018)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838018), _1838016))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838018), _1838016)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838016), _1838018)))], (51049 ^ _779300) ^ [_1838453, _1838455] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838453), _1838455))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838453), _1838455)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838455), _1838453)))], (51059 ^ _779300) ^ [_1838785, _1838787] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838785), _1838787)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838787), _1838785))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838787), _1838785)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838785), _1838787)))], (51073 ^ _779300) ^ [_1839222, _1839224] : [_1839222 = _1839224, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839222), _1839224)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839224), _1839222)))], (51083 ^ _779300) ^ [_1839559, _1839561, _1839563] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839559), _1839561)), 51094 ^ _779300 : [(51095 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839559), _1839563)))], (51097 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839563), _1839559))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839561), _1839563)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839563), _1839561)))], (51099 ^ _779300) ^ [_1840106, _1840108, _1840110] : [_1840106 = _1840108, 51110 ^ _779300 : [(51111 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840106), _1840110)))], (51113 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840110), _1840106))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840108), _1840110)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840110), _1840108)))], (51115 ^ _779300) ^ [_1840643, _1840645, _1840647] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840643), _1840645)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840645), _1840647)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840643), _1840647)))], (51125 ^ _779300) ^ [_1840982, _1840984] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840982), _1840984)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840984), _1840982)), -(_1840982 = _1840984)], (51135 ^ _779300) ^ [_1841301, _1841303] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841301), _1841303)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841303), _1841301)), -(_1841301 = _1841303)], (51145 ^ _779300) ^ [_1841634, _1841636, _1841638] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841634), _1841636)), _1841636 = _1841638, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841634), _1841638)))], (51155 ^ _779300) ^ [_1841977, _1841979, _1841981] : [_1841977 = _1841979, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841979), _1841981)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841977), _1841981)))], (51165 ^ _779300) ^ [_1842306, _1842308] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842306), _1842308)), -(_1842306 = _1842308), 51172 ^ _779300 : [(51173 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842306), _1842308)))], (51175 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842308), _1842306))]]], (51177 ^ _779300) ^ [_1842714, _1842716] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842714), _1842716)), 51182 ^ _779300 : [(51183 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842714), _1842716)))], (51185 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842716), _1842714))]], -(_1842714 = _1842716)], (51189 ^ _779300) ^ [_1843120, _1843122] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843120), _1843122)), 51192 ^ _779300 : [(51193 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843122), _1843120)), -(_1843122 = _1843120)], (51199 ^ _779300) ^ [] : [_1843122 = _1843120, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843122), _1843120)))]]], (51205 ^ _779300) ^ [_1843605, _1843607] : [_1843605 = _1843607, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843605), _1843607)))], (51211 ^ _779300) ^ [_1843825, _1843827] : [-(_1843825 = _1843827), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843825), _1843827)), 51218 ^ _779300 : [(51219 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843825), _1843827)))], (51221 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843827), _1843825))]]], (51223 ^ _779300) ^ [_1844262, _1844264] : [51230 ^ _779300 : [(51231 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844262), _1844264)))], (51233 ^ _779300) ^ [] : [_1844262 = _1844264]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844262), _1844264)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844264), _1844262)))], (51235 ^ _779300) ^ [_1844622, _1844624] : [51242 ^ _779300 : [(51243 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844622), _1844624)))], (51245 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844624), _1844622))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844622), _1844624)), -(_1844622 = _1844624)], (51247 ^ _779300) ^ [_1845061, _1845063] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845061), _1845063)), 51252 ^ _779300 : [(51253 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845061), _1845063)))], (51255 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845063), _1845061))]], -(_1845061 = _1845063)], (51259 ^ _779300) ^ [_1845419, _1845421] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845419), _1845421))), 51260 ^ _779300 : [(51267 ^ _779300) ^ [] : [_1845419 = _1845421], (51261 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845419), _1845421)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845421), _1845419)))]]], (51271 ^ _779300) ^ [_1845856, _1845858] : [_1845856 = _1845858, 51274 ^ _779300 : [(51275 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845856), _1845858)))], (51277 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845858), _1845856)))]]], (51279 ^ _779300) ^ [_1846113, _1846115] : [-(_1846113 = _1846115), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846113), _1846115)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846115), _1846113))], (51289 ^ _779300) ^ [_1846462, _1846464, _1846466, _1846468] : [class_Divides_Osemiring__div(_1846462), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846462), _1846464), _1846466)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846462), _1846464), _1846468)), 51300 ^ _779300 : [(51301 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846462), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1846462), _1846466), _1846464)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1846462), _1846468), _1846464))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846462), _1846466), _1846468)))], (51307 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846462), _1846466), _1846468)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846462), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1846462), _1846466), _1846464)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1846462), _1846468), _1846464))))]]], (51313 ^ _779300) ^ [_1847292, _1847294, _1847296, _1847298] : [class_Rings_Ocomm__semiring__1(_1847292), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847292), _1847294), _1847296)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847292), hAPP(hAPP(c_Power_Opower__class_Opower(_1847292), _1847294), _1847298)), hAPP(hAPP(c_Power_Opower__class_Opower(_1847292), _1847296), _1847298))))], (51323 ^ _779300) ^ [_1847697, _1847699, _1847701, _1847703] : [class_Divides_Osemiring__div(_1847697), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847697), _1847699), _1847701)), 51330 ^ _779300 : [(51331 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847697), _1847699), c_Divides_Odiv__class_Omod(_1847697, _1847703, _1847701))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847697), _1847699), _1847703)))], (51337 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847697), _1847699), _1847703)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847697), _1847699), c_Divides_Odiv__class_Omod(_1847697, _1847703, _1847701))))]]], (51343 ^ _779300) ^ [_1848380, _1848382, _1848384, _1848386] : [class_Divides_Osemiring__div(_1848380), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848380), _1848382), _1848384)), -(c_Divides_Odiv__class_Omod(_1848380, c_Divides_Odiv__class_Omod(_1848380, _1848386, _1848384), _1848382) = c_Divides_Odiv__class_Omod(_1848380, _1848386, _1848382))], (51353 ^ _779300) ^ [_1848763, _1848765, _1848767, _1848769] : [class_Divides_Osemiring__div(_1848763), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848763), _1848765), _1848767)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848763), _1848765), _1848769)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848763), _1848765), c_Divides_Odiv__class_Omod(_1848763, _1848767, _1848769))))], (51367 ^ _779300) ^ [_1849255, _1849257, _1849259, _1849261] : [class_Divides_Osemiring__div(_1849255), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849255), _1849257), c_Divides_Odiv__class_Omod(_1849255, _1849259, _1849261))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849255), _1849257), _1849261)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849255), _1849257), _1849259)))], (51381 ^ _779300) ^ [_1849733, _1849735, _1849737] : [class_Rings_Ocomm__ring__1(_1849733), 51384 ^ _779300 : [(51385 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849733), hAPP(c_Groups_Ouminus__class_Ouminus(_1849733), _1849735)), _1849737)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849733), _1849735), _1849737)))], (51391 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849733), _1849735), _1849737)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849733), hAPP(c_Groups_Ouminus__class_Ouminus(_1849733), _1849735)), _1849737)))]]], (51397 ^ _779300) ^ [_1850278, _1850280, _1850282] : [class_Rings_Ocomm__ring__1(_1850278), 51400 ^ _779300 : [(51401 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850278), _1850280), hAPP(c_Groups_Ouminus__class_Ouminus(_1850278), _1850282))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850278), _1850280), _1850282)))], (51407 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850278), _1850280), _1850282)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850278), _1850280), hAPP(c_Groups_Ouminus__class_Ouminus(_1850278), _1850282))))]]], (51413 ^ _779300) ^ [_1850837, _1850839, _1850841, _1850843] : [class_Rings_Ocomm__ring__1(_1850837), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850837), _1850839), _1850841)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850837), _1850839), _1850843)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850837), _1850839), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1850837), _1850841), _1850843))))], (51427 ^ _779300) ^ [_1851323, _1851325, _1851327] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1851323), _1851325)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1851323), _1851327)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1851323), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1851325), _1851327))))], (51437 ^ _779300) ^ [_1851688, _1851690, _1851692] : [class_Divides_Osemiring__div(_1851688), 51440 ^ _779300 : [(51441 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851688), _1851690), _1851692)), -(c_Divides_Odiv__class_Omod(_1851688, _1851692, _1851690) = c_Groups_Ozero__class_Ozero(_1851688))], (51447 ^ _779300) ^ [] : [c_Divides_Odiv__class_Omod(_1851688, _1851692, _1851690) = c_Groups_Ozero__class_Ozero(_1851688), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851688), _1851690), _1851692)))]]], (51453 ^ _779300) ^ [_1852215, _1852217, _1852219] : [class_Divides_Osemiring__div(_1852215), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852215), _1852217), _1852219)), -(c_Divides_Odiv__class_Omod(_1852215, _1852219, _1852217) = c_Groups_Ozero__class_Ozero(_1852215))], (51463 ^ _779300) ^ [_1852562, _1852564, _1852566] : [class_Divides_Oring__div(_1852562), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852562), _1852564), _1852566)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1852562), hAPP(c_Groups_Ouminus__class_Ouminus(_1852562), _1852566)), _1852564) = hAPP(c_Groups_Ouminus__class_Ouminus(_1852562), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1852562), _1852566), _1852564)))], (51473 ^ _779300) ^ [_1852949, _1852951, _1852953] : [class_Divides_Oring__div(_1852949), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852949), _1852951), _1852953)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1852949), _1852953), hAPP(c_Groups_Ouminus__class_Ouminus(_1852949), _1852951)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1852949), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1852949), _1852953), _1852951)))], (51483 ^ _779300) ^ [_1853322, _1853324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1853322)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1853322), _1853324)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853324), _1853322))], (51493 ^ _779300) ^ [_1853661] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853661), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1853661 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51499 ^ _779300) ^ [_1853827] : [_1853827 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853827), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (51505 ^ _779300) ^ [_1854071, _1854073, _1854075, _1854077] : [class_Divides_Osemiring__div(_1854071), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1854071), _1854073), _1854075)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1854071), _1854073), _1854077)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1854071), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1854071), _1854075), _1854077)), _1854073) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1854071), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1854071), _1854075), _1854073)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1854071), _1854077), _1854073)))], (51519 ^ _779300) ^ [_1854622, _1854624] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1854622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1854624), _1854622))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1854622), _1854624)))], (51525 ^ _779300) ^ [_1854816, _1854818] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1854816), _1854818)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1854816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1854818), _1854816))))], (51531 ^ _779300) ^ [_1855088, _1855090, _1855092, _1855094] : [class_Rings_Ocomm__semiring__1(_1855088), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1855088), _1855090), _1855092)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1855088), _1855090), _1855094)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1855088), _1855090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1855088), _1855092), _1855094))))], (51545 ^ _779300) ^ [_1855617, _1855619, _1855621, _1855623] : [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), _1855617, _1855619)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855621, _1855623))), 51548 ^ _779300 : [(51567 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855621), _1855623)))], (51549 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855617), _1855619)), 51552 ^ _779300 : [(51553 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855621), _1855617)))], (51555 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855619), _1855623)))], (51557 ^ _779300) ^ [] : [51558 ^ _779300 : [(51559 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855621), _1855617)))], (51561 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855617), _1855621))]], 51562 ^ _779300 : [(51563 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855619), _1855623)))], (51565 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855623), _1855619))]]]]]]], (51569 ^ _779300) ^ [_1856494, _1856496, _1856498, _1856500] : [-(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), _1856494, _1856496)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856498, _1856500)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856498), _1856500)), 51572 ^ _779300 : [(51573 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856494), _1856496)))], (51575 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856498), _1856494)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856496), _1856500)), 51582 ^ _779300 : [(51583 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856498), _1856494)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856494), _1856498)))], (51589 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856496), _1856500)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856500), _1856496)))]]]]], (51599 ^ _779300) ^ [_1857478, _1857480] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1857480, _1857478) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1857478), _1857480)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1857480), _1857478)))], (51609 ^ _779300) ^ [_1857839, _1857841] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1857839, _1857841) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1857839), _1857841))], (51615 ^ _779300) ^ [_1858022, _1858024] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1858022), _1858024))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1858022, _1858024) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51621 ^ _779300) ^ [_1858286, _1858288] : [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), _1858286, _1858288), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1858286), _1858288))], (51627 ^ _779300) ^ [_1858469, _1858471] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1858469), _1858471))), -(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), _1858469, _1858471))], (51643 ^ _779300) ^ [_1859020, _1859022] : [51644 ^ _779300 : [(51645 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859020), _1859022)))], (51647 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859022), _1859020))]], -(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)))), _1859020, _1859022))], (51633 ^ _779300) ^ [_1858733, _1858735] : [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)))), _1858733, _1858735), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1858733), _1858735)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1858735), _1858733)))], (51661 ^ _779300) ^ [_1859659, _1859661] : [51662 ^ _779300 : [(51663 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859659), _1859661)))], (51665 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859661), _1859659))]], -(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)))), _1859659, _1859661))], (51651 ^ _779300) ^ [_1859372, _1859374] : [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)))), _1859372, _1859374), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859372), _1859374)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859374), _1859372)))], (51679 ^ _779300) ^ [_1860298, _1860300] : [51680 ^ _779300 : [(51681 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860298), _1860300)))], (51683 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860300), _1860298))]], -(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)))), _1860298, _1860300) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51669 ^ _779300) ^ [_1860011, _1860013] : [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)))), _1860011, _1860013) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860011), _1860013)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860013), _1860011)))], (51697 ^ _779300) ^ [_1860937, _1860939] : [51698 ^ _779300 : [(51699 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860937), _1860939)))], (51701 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860939), _1860937))]], -(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)))), _1860937, _1860939) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51687 ^ _779300) ^ [_1860650, _1860652] : [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)))), _1860650, _1860652) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860650), _1860652)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860652), _1860650)))], (51705 ^ _779300) ^ [_1861260, _1861262] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1861260), _1861262)), -(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)))), _1861262, _1861260) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51711 ^ _779300) ^ [_1861490, _1861492] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1861490), _1861492)), -(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)))), _1861492, _1861490) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51717 ^ _779300) ^ [_1861722, _1861724] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1861722), _1861724)), -(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)))), _1861724, _1861722) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51723 ^ _779300) ^ [_1861997, _1861999, _1862001] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1861997, _1861999) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1862001), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 51726 ^ _779300 : [(51727 ^ _779300) ^ [] : [-(_1861997 = _1861999)], (51729 ^ _779300) ^ [] : [-(_1861999 = _1862001)]]], (51731 ^ _779300) ^ [_1862264, _1862266, _1862268] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1862264, _1862266) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1862268), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1862264 = _1862266, _1862266 = _1862268], (51741 ^ _779300) ^ [_1862568] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1862568, _1862568) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1862568), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51743 ^ _779300) ^ [_1862686, _1862688] : [_1862686 = _1862688, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1862686, _1862688) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1862686), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51749 ^ _779300) ^ [_1862946, _1862948, _1862950, _1862952] : [class_Rings_Ocomm__ring(_1862946), class_Rings_Odvd(_1862946), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1862946), _1862948), _1862950)), 51760 ^ _779300 : [(51761 ^ _779300) ^ [_1863385, _1863387] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1862946), _1862948), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1862946), _1863387), _1862952))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1862946), _1862948), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1862946), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1862946), _1863387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1862946), _1863385), _1862950))), _1862952))))], (51767 ^ _779300) ^ [_1863671, _1863673] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1862946), _1862948), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1862946), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1862946), _1863673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1862946), _1863671), _1862950))), _1862952))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1862946), _1862948), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1862946), _1863673), _1862952))))]]], (51773 ^ _779300) ^ [_1864046, _1864048, _1864050, _1864052] : [class_Rings_Ocomm__ring(_1864046), class_Rings_Odvd(_1864046), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864046), _1864048), _1864050)), 51784 ^ _779300 : [(51785 ^ _779300) ^ [_1864485, _1864487] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864046), _1864048), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1864046), _1864487), _1864052))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864046), _1864048), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1864046), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1864046), _1864487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1864046), _1864485), _1864050))), _1864052))))], (51791 ^ _779300) ^ [_1864771, _1864773] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864046), _1864048), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1864046), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1864046), _1864773), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1864046), _1864771), _1864050))), _1864052))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864046), _1864048), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1864046), _1864773), _1864052))))]]], (51807 ^ _779300) ^ [_1865467, _1865469, _1865471] : [51808 ^ _779300 : [(51809 ^ _779300) ^ [] : [_1865467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51811 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1865469), _1865471))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1865467), _1865469)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1865467), _1865471))))], (51797 ^ _779300) ^ [_1865161, _1865163, _1865165] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1865161), _1865163)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1865161), _1865165))), -(_1865161 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1865163), _1865165)))], (51815 ^ _779300) ^ [_1865847, _1865849, _1865851, _1865853, _1865855] : [class_Divides_Osemiring__div(_1865847), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865847), _1865849), _1865851)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865847), _1865853), _1865855)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1865847), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1865847), _1865851), _1865849)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1865847), _1865855), _1865853)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1865847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1865847), _1865851), _1865855)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1865847), _1865849), _1865853)))], (51829 ^ _779300) ^ [_1866427, _1866429, _1866431, _1866433] : [class_Divides_Osemiring__div(_1866427), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1866427), _1866429), _1866431)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1866427), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1866427), _1866431), _1866429)), _1866433) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1866427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1866427), _1866431), _1866433)), _1866429))], (51839 ^ _779300) ^ [_1866836, _1866838, _1866840] : [class_Divides_Osemiring__div(_1866836), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1866836), _1866838), _1866840)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1866836), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1866836), _1866840), _1866838)), _1866838) = _1866840)], (51849 ^ _779300) ^ [_1867217, _1867219, _1867221, _1867223] : [class_Divides_Osemiring__div(_1867217), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1867217), _1867219), _1867221)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1867217), _1867223), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1867217), _1867221), _1867219)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1867217), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1867217), _1867223), _1867221)), _1867219))], (51859 ^ _779300) ^ [_1867626, _1867628, _1867630] : [class_Divides_Osemiring__div(_1867626), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1867626), _1867628), _1867630)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1867626), _1867628), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1867626), _1867630), _1867628)) = _1867630)], (51869 ^ _779300) ^ [_1868007, _1868009, _1868011, _1868013] : [class_Rings_Ocomm__semiring__1(_1868007), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1868007), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1868007), _1868009), _1868011)), _1868013)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1868007), _1868011), _1868013)))], (51879 ^ _779300) ^ [_1868396, _1868398, _1868400, _1868402] : [class_Rings_Ocomm__semiring__1(_1868396), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1868396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1868396), _1868398), _1868400)), _1868402)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1868396), _1868398), _1868402)))], (51889 ^ _779300) ^ [_1868785, _1868787, _1868789, _1868791] : [class_Rings_Odvd(_1868785), _1868787 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1868785), _1868789), _1868791), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1868785), _1868789), _1868787)))], (51899 ^ _779300) ^ [_1869174, _1869176, _1869178, _1869180, _1869182] : [class_Rings_Ocomm__semiring__1(_1869174), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1869174), _1869176), _1869178)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1869174), _1869180), _1869182)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1869174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1869174), _1869176), _1869180)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1869174), _1869178), _1869182))))], (51913 ^ _779300) ^ [_1869704, _1869706, _1869708, _1869710] : [class_Rings_Ocomm__semiring__1(_1869704), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1869704), _1869706), _1869708)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1869704), _1869706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1869704), _1869710), _1869708))))], (51923 ^ _779300) ^ [_1870093, _1870095, _1870097, _1870099] : [class_Rings_Ocomm__semiring__1(_1870093), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870093), _1870095), _1870097)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870093), _1870095), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1870093), _1870097), _1870099))))], (51933 ^ _779300) ^ [_1870468, _1870470, _1870472] : [class_Rings_Ocomm__semiring__1(_1870468), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870468), _1870470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1870468), _1870472), _1870470))))], (51939 ^ _779300) ^ [_1870726, _1870728, _1870730] : [class_Rings_Ocomm__semiring__1(_1870726), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870726), _1870728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1870726), _1870728), _1870730))))], (51945 ^ _779300) ^ [_1870998, _1871000, _1871002, _1871004] : [class_Rings_Oidom(_1870998), 51948 ^ _779300 : [(51959 ^ _779300) ^ [] : [51960 ^ _779300 : [(51961 ^ _779300) ^ [] : [_1871002 = c_Groups_Ozero__class_Ozero(_1870998)], (51963 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870998), _1871000), _1871004))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1870998), _1871000), _1871002)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1870998), _1871004), _1871002))))], (51949 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1870998), _1871000), _1871002)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1870998), _1871004), _1871002))), -(_1871002 = c_Groups_Ozero__class_Ozero(_1870998)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870998), _1871000), _1871004)))]]], (51967 ^ _779300) ^ [_1871782, _1871784, _1871786, _1871788] : [class_Rings_Oidom(_1871782), 51970 ^ _779300 : [(51981 ^ _779300) ^ [] : [51982 ^ _779300 : [(51983 ^ _779300) ^ [] : [_1871784 = c_Groups_Ozero__class_Ozero(_1871782)], (51985 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1871782), _1871786), _1871788))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1871782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1871782), _1871784), _1871786)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1871782), _1871784), _1871788))))], (51971 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1871782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1871782), _1871784), _1871786)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1871782), _1871784), _1871788))), -(_1871784 = c_Groups_Ozero__class_Ozero(_1871782)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1871782), _1871786), _1871788)))]]], (51989 ^ _779300) ^ [_1872552, _1872554, _1872556] : [class_Rings_Odvd(_1872552), class_Rings_Osemiring__0(_1872552), 51996 ^ _779300 : [(51997 ^ _779300) ^ [] : [51998 ^ _779300 : [(51999 ^ _779300) ^ [_1872871] : [hBOOL(hAPP(_1872554, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1872552), _1872556), _1872871)))]], 52001 ^ _779300 : [(52002 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1872552), _1872556), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1872552), 52000 ^ [_1872552, _1872554, _1872556]), c_Groups_Ozero__class_Ozero(_1872552)))))], (52004 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1872554, 52000 ^ [_1872552, _1872554, _1872556])))]]], (52006 ^ _779300) ^ [] : [-(hBOOL(hAPP(_1872554, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1872552), _1872556), 52013 ^ [_1872552, _1872554, _1872556])))), 52007 ^ _779300 : [(52008 ^ _779300) ^ [_1873231] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1872552), _1872556), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1872552), _1873231), c_Groups_Ozero__class_Ozero(_1872552)))), hBOOL(hAPP(_1872554, _1873231))]]]]], (52017 ^ _779300) ^ [_1873678, _1873680, _1873682, _1873684, _1873686] : [class_Rings_Ocomm__semiring__1(_1873678), hBOOL(hAPP(c_Finite__Set_Ofinite(_1873680), _1873682)), hBOOL(hAPP(hAPP(c_member(_1873680), _1873684), _1873682)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1873678), hAPP(_1873686, _1873684)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1873680, _1873678), _1873686), _1873682))))], (52031 ^ _779300) ^ [_1874180, _1874182, _1874184] : [class_Rings_Ocomm__semiring__1(_1874180), 52036 ^ _779300 : [(52037 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1874182))], (52039 ^ _779300) ^ [] : [_1874184 = c_Groups_Oone__class_Oone(_1874180)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1874180), _1874184), hAPP(hAPP(c_Power_Opower__class_Opower(_1874180), _1874184), _1874182))))], (52043 ^ _779300) ^ [_1874601, _1874603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1874601)), 52046 ^ _779300 : [(52047 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1874601), _1874603)), _1874601)), -(_1874603 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (52053 ^ _779300) ^ [] : [_1874603 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1874601), _1874603)), _1874601)))]]], (52059 ^ _779300) ^ [_1875098, _1875100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1875098)), 52062 ^ _779300 : [(52063 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1875100), _1875098)), _1875098)), -(_1875100 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (52069 ^ _779300) ^ [] : [_1875100 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1875100), _1875098)), _1875098)))]]], (52075 ^ _779300) ^ [_1875623, _1875625, _1875627, _1875629] : [class_Orderings_Oorder(_1875623), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1875623, 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)))), _1875625), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1875623), hAPP(_1875625, _1875627)), hAPP(_1875625, _1875629)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1875627), _1875629)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1875629), _1875627)))], (52093 ^ _779300) ^ [_1876215, _1876217, _1876219, _1876221] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1876215), _1876217)), c_Equiv__Relations_Oequiv(_1876215, _1876217, _1876219), 52103 ^ _779300 : [(52104 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1876215, tc_HOL_Obool)), 52102 ^ [_1876215, _1876217, _1876219, _1876221]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1876215), _1876217), _1876219))))], (52106 ^ _779300) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1876221), hAPP(c_Finite__Set_Ocard(_1876215), 52102 ^ [_1876215, _1876217, _1876219, _1876221])))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1876221), hAPP(c_Finite__Set_Ocard(_1876215), _1876217))))], (52110 ^ _779300) ^ [_1876910, _1876912] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1876910), _1876912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1876912)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1876910), _1876912)))], (52120 ^ _779300) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (52122 ^ _779300) ^ [_1877286, _1877288] : [class_Lattices_Obounded__lattice(_1877286), -(class_Lattices_Obounded__lattice(tc_fun(_1877288, _1877286)))], (52128 ^ _779300) ^ [_1877498, _1877500] : [class_Complete__Lattice_Ocomplete__lattice(_1877498), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1877500, _1877498)))], (52134 ^ _779300) ^ [_1877710, _1877712] : [class_Lattices_Obounded__lattice(_1877710), -(class_Lattices_Obounded__lattice__top(tc_fun(_1877712, _1877710)))], (52140 ^ _779300) ^ [_1877922, _1877924] : [class_Lattices_Obounded__lattice(_1877922), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1877924, _1877922)))], (52146 ^ _779300) ^ [_1878134, _1878136] : [class_Lattices_Olattice(_1878134), -(class_Lattices_Osemilattice__sup(tc_fun(_1878136, _1878134)))], (52152 ^ _779300) ^ [_1878346, _1878348] : [class_Lattices_Olattice(_1878346), -(class_Lattices_Osemilattice__inf(tc_fun(_1878348, _1878346)))], (52158 ^ _779300) ^ [_1878558, _1878560] : [class_Lattices_Odistrib__lattice(_1878558), -(class_Lattices_Odistrib__lattice(tc_fun(_1878560, _1878558)))], (52164 ^ _779300) ^ [_1878770, _1878772] : [class_Lattices_Oboolean__algebra(_1878770), -(class_Lattices_Oboolean__algebra(tc_fun(_1878772, _1878770)))], (52170 ^ _779300) ^ [_1878982, _1878984] : [class_Orderings_Opreorder(_1878982), -(class_Orderings_Opreorder(tc_fun(_1878984, _1878982)))], (52176 ^ _779300) ^ [_1879194, _1879196] : [-(class_Finite__Set_Ofinite(tc_fun(_1879194, _1879196))), class_Finite__Set_Ofinite(_1879194), class_Finite__Set_Ofinite(_1879196)], (52186 ^ _779300) ^ [_1879493, _1879495] : [class_Lattices_Olattice(_1879493), -(class_Lattices_Olattice(tc_fun(_1879495, _1879493)))], (52192 ^ _779300) ^ [_1879705, _1879707] : [class_Orderings_Oorder(_1879705), -(class_Orderings_Oorder(tc_fun(_1879707, _1879705)))], (52198 ^ _779300) ^ [_1879917, _1879919] : [class_Orderings_Otop(_1879917), -(class_Orderings_Otop(tc_fun(_1879919, _1879917)))], (52204 ^ _779300) ^ [_1880129, _1880131] : [class_Orderings_Oord(_1880129), -(class_Orderings_Oord(tc_fun(_1880131, _1880129)))], (52210 ^ _779300) ^ [_1880341, _1880343] : [class_Orderings_Obot(_1880341), -(class_Orderings_Obot(tc_fun(_1880343, _1880341)))], (52216 ^ _779300) ^ [_1880553, _1880555] : [class_Groups_Ouminus(_1880553), -(class_Groups_Ouminus(tc_fun(_1880555, _1880553)))], (52222 ^ _779300) ^ [_1880765, _1880767] : [class_Groups_Ominus(_1880765), -(class_Groups_Ominus(tc_fun(_1880767, _1880765)))], (52228 ^ _779300) ^ [_1880977, _1880979] : [-(class_Enum_Oenum(tc_fun(_1880977, _1880979))), class_Enum_Oenum(_1880977), class_Enum_Oenum(_1880979)], (52238 ^ _779300) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (52240 ^ _779300) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (52242 ^ _779300) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (52244 ^ _779300) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (52246 ^ _779300) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (52248 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (52250 ^ _779300) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (52252 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (52254 ^ _779300) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (52256 ^ _779300) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (52258 ^ _779300) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (52260 ^ _779300) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (52262 ^ _779300) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (52264 ^ _779300) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (52266 ^ _779300) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (52268 ^ _779300) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (52270 ^ _779300) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (52272 ^ _779300) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (52274 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (52276 ^ _779300) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (52278 ^ _779300) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (52280 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (52282 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (52284 ^ _779300) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (52286 ^ _779300) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (52288 ^ _779300) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (52290 ^ _779300) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (52292 ^ _779300) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (52294 ^ _779300) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (52296 ^ _779300) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (52298 ^ _779300) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (52300 ^ _779300) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (52302 ^ _779300) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (52304 ^ _779300) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (52306 ^ _779300) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (52308 ^ _779300) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (52310 ^ _779300) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (52312 ^ _779300) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (52314 ^ _779300) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (52316 ^ _779300) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (52318 ^ _779300) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (52320 ^ _779300) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (52322 ^ _779300) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (52324 ^ _779300) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (52326 ^ _779300) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (52328 ^ _779300) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (52330 ^ _779300) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (52332 ^ _779300) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (52334 ^ _779300) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (52336 ^ _779300) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (52338 ^ _779300) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (52340 ^ _779300) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (52342 ^ _779300) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (52344 ^ _779300) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (52346 ^ _779300) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (52348 ^ _779300) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (52350 ^ _779300) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (52352 ^ _779300) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (52354 ^ _779300) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (52356 ^ _779300) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (52358 ^ _779300) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (52360 ^ _779300) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (52362 ^ _779300) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (52364 ^ _779300) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (52366 ^ _779300) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (52368 ^ _779300) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (52370 ^ _779300) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (52372 ^ _779300) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (52374 ^ _779300) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (52376 ^ _779300) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (52378 ^ _779300) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (52380 ^ _779300) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (52382 ^ _779300) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (52384 ^ _779300) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (52386 ^ _779300) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (52388 ^ _779300) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (52390 ^ _779300) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (52392 ^ _779300) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (52394 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (52396 ^ _779300) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (52398 ^ _779300) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (52400 ^ _779300) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (52402 ^ _779300) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (52404 ^ _779300) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (52406 ^ _779300) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (52408 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (52410 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (52412 ^ _779300) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (52414 ^ _779300) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (52416 ^ _779300) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (52418 ^ _779300) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (52420 ^ _779300) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (52422 ^ _779300) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (52424 ^ _779300) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (52426 ^ _779300) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (52428 ^ _779300) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (52430 ^ _779300) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (52432 ^ _779300) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (52434 ^ _779300) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (52436 ^ _779300) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (52438 ^ _779300) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (52440 ^ _779300) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (52442 ^ _779300) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (52444 ^ _779300) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (52446 ^ _779300) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (52448 ^ _779300) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (52450 ^ _779300) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (52452 ^ _779300) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (52454 ^ _779300) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (52456 ^ _779300) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (52458 ^ _779300) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (52460 ^ _779300) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (52462 ^ _779300) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (52464 ^ _779300) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (52466 ^ _779300) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (52468 ^ _779300) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (52470 ^ _779300) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (52472 ^ _779300) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (52474 ^ _779300) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (52476 ^ _779300) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (52478 ^ _779300) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (52480 ^ _779300) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (52482 ^ _779300) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (52484 ^ _779300) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (52486 ^ _779300) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (52488 ^ _779300) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (52490 ^ _779300) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (52492 ^ _779300) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (52494 ^ _779300) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (52496 ^ _779300) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (52498 ^ _779300) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (52500 ^ _779300) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (52502 ^ _779300) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (52504 ^ _779300) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (52506 ^ _779300) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (52508 ^ _779300) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (52510 ^ _779300) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (52512 ^ _779300) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (52514 ^ _779300) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (52516 ^ _779300) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (52518 ^ _779300) ^ [_1888682] : [class_Lazy__Sequence_Osmall__lazy(_1888682), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1888682)))], (52524 ^ _779300) ^ [_1888857] : [-(class_Nat_Osize(tc_List_Olist(_1888857)))], (52526 ^ _779300) ^ [_1888965, _1888967] : [-(class_Finite__Set_Ofinite(tc_sum(_1888965, _1888967))), class_Finite__Set_Ofinite(_1888965), class_Finite__Set_Ofinite(_1888967)], (52536 ^ _779300) ^ [_1889264, _1889266] : [-(class_Enum_Oenum(tc_sum(_1889264, _1889266))), class_Enum_Oenum(_1889264), class_Enum_Oenum(_1889266)], (52546 ^ _779300) ^ [_1889548, _1889550] : [-(class_Nat_Osize(tc_sum(_1889548, _1889550)))], (52548 ^ _779300) ^ [_1889645] : [class_Finite__Set_Ofinite(_1889645), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1889645)))], (52554 ^ _779300) ^ [_1889835] : [class_Enum_Oenum(_1889835), -(class_Enum_Oenum(tc_Option_Ooption(_1889835)))], (52560 ^ _779300) ^ [_1890010] : [-(class_Nat_Osize(tc_Option_Ooption(_1890010)))], (52562 ^ _779300) ^ [_1890103, _1890105] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1890103, _1890105)))], (52564 ^ _779300) ^ [_1890214, _1890216] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1890214, _1890216))), class_Lazy__Sequence_Osmall__lazy(_1890214), class_Lazy__Sequence_Osmall__lazy(_1890216)], (52574 ^ _779300) ^ [_1890513, _1890515] : [-(class_Finite__Set_Ofinite(tc_prod(_1890513, _1890515))), class_Finite__Set_Ofinite(_1890513), class_Finite__Set_Ofinite(_1890515)], (52584 ^ _779300) ^ [_1890812, _1890814] : [-(class_Enum_Oenum(tc_prod(_1890812, _1890814))), class_Enum_Oenum(_1890812), class_Enum_Oenum(_1890814)], (52594 ^ _779300) ^ [_1891096, _1891098] : [-(class_Nat_Osize(tc_prod(_1891096, _1891098)))], (52596 ^ _779300) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (52598 ^ _779300) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (52600 ^ _779300) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (52602 ^ _779300) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (52604 ^ _779300) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (52606 ^ _779300) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52608 ^ _779300) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (52610 ^ _779300) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52612 ^ _779300) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52614 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52616 ^ _779300) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52618 ^ _779300) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52620 ^ _779300) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52622 ^ _779300) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (52624 ^ _779300) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (52626 ^ _779300) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52628 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52630 ^ _779300) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (52632 ^ _779300) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (52634 ^ _779300) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (52636 ^ _779300) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52638 ^ _779300) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52640 ^ _779300) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (52642 ^ _779300) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52644 ^ _779300) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (52646 ^ _779300) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (52648 ^ _779300) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (52650 ^ _779300) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (52652 ^ _779300) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (52654 ^ _779300) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (52656 ^ _779300) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (52658 ^ _779300) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (52660 ^ _779300) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (52662 ^ _779300) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (52664 ^ _779300) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (52666 ^ _779300) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (52668 ^ _779300) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (52670 ^ _779300) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (52672 ^ _779300) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (52674 ^ _779300) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (52676 ^ _779300) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (52678 ^ _779300) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (52680 ^ _779300) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (52682 ^ _779300) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (52684 ^ _779300) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (52686 ^ _779300) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (52688 ^ _779300) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (52690 ^ _779300) ^ [_1893669] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1893669)))], (52692 ^ _779300) ^ [_1893762, _1893764] : [-(hAPP(c_COMBI(_1893762), _1893764) = _1893764)], (52694 ^ _779300) ^ [_1893889, _1893891, _1893893, _1893895] : [-(hAPP(hAPP(c_COMBK(_1893889, _1893891), _1893893), _1893895) = _1893893)], (52696 ^ _779300) ^ [_1894052, _1894054, _1894056, _1894058, _1894060, _1894062] : [-(hAPP(hAPP(hAPP(c_COMBB(_1894052, _1894054, _1894056), _1894058), _1894060), _1894062) = hAPP(_1894058, hAPP(_1894060, _1894062)))], (52698 ^ _779300) ^ [_1894229, _1894231, _1894233, _1894235, _1894237, _1894239] : [-(hAPP(hAPP(hAPP(c_COMBC(_1894229, _1894231, _1894233), _1894235), _1894237), _1894239) = hAPP(hAPP(_1894235, _1894239), _1894237))], (52700 ^ _779300) ^ [_1894406, _1894408, _1894410, _1894412, _1894414, _1894416] : [-(hAPP(hAPP(hAPP(c_COMBS(_1894406, _1894408, _1894410), _1894412), _1894414), _1894416) = hAPP(hAPP(_1894412, _1894416), hAPP(_1894414, _1894416)))], (52702 ^ _779300) ^ [_1894545, _1894547] : [hBOOL(hAPP(hAPP(c_fequal, _1894545), _1894547)), -(_1894545 = _1894547)], (52708 ^ _779300) ^ [_1894767, _1894769] : [_1894767 = _1894769, -(hBOOL(hAPP(hAPP(c_fequal, _1894767), _1894769)))], (52714 ^ _779300) ^ [] : [hBOOL(c_fFalse)], (52716 ^ _779300) ^ [] : [-(hBOOL(c_fTrue))], (52718 ^ _779300) ^ [_1895080] : [hBOOL(hAPP(c_fNot, _1895080)), hBOOL(_1895080)], (52724 ^ _779300) ^ [_1895275] : [-(hBOOL(_1895275)), -(hBOOL(hAPP(c_fNot, _1895275)))], (52730 ^ _779300) ^ [_1895486, _1895488] : [hBOOL(_1895486), hBOOL(_1895488), -(hBOOL(hAPP(hAPP(c_fconj, _1895486), _1895488)))], (52740 ^ _779300) ^ [_1895795, _1895797] : [hBOOL(hAPP(hAPP(c_fconj, _1895795), _1895797)), -(hBOOL(_1895795))], (52746 ^ _779300) ^ [_1896015, _1896017] : [hBOOL(hAPP(hAPP(c_fconj, _1896015), _1896017)), -(hBOOL(_1896017))], (52752 ^ _779300) ^ [_1896235, _1896237] : [hBOOL(_1896235), -(hBOOL(hAPP(hAPP(c_fdisj, _1896235), _1896237)))], (52758 ^ _779300) ^ [_1896455, _1896457] : [hBOOL(_1896455), -(hBOOL(hAPP(hAPP(c_fdisj, _1896457), _1896455)))], (52764 ^ _779300) ^ [_1896675, _1896677] : [hBOOL(hAPP(hAPP(c_fdisj, _1896675), _1896677)), -(hBOOL(_1896675)), -(hBOOL(_1896677))], (52774 ^ _779300) ^ [_1896983, _1896985] : [-(hBOOL(_1896983)), -(hBOOL(hAPP(hAPP(c_fimplies, _1896983), _1896985)))], (52780 ^ _779300) ^ [_1897202, _1897204] : [hBOOL(_1897202), -(hBOOL(hAPP(hAPP(c_fimplies, _1897204), _1897202)))], (52796 ^ _779300) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), v_U)))], (52798 ^ _779300) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))))], (52800 ^ _779300) ^ [] : [-(hAPP(c_Finite__Set_Ocard(t_a), v_G) = hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))], (52802 ^ _779300) ^ [] : [-(v_wt(v_c))], (52786 ^ _779300) ^ [_1897422, _1897424] : [hBOOL(hAPP(hAPP(c_fimplies, _1897422), _1897424)), hBOOL(_1897422), -(hBOOL(_1897424))]], input).
% 136.17/131.28  ncf('1',plain,[v_G = hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)],start(52804 ^ 0)).
% 136.17/131.28  ncf('1.1',plain,[-(v_G = hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)), hBOOL(hAPP(c_Finite__Set_Ofinite(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), hAPP(c_Finite__Set_Ocard(t_a), v_G)))],extension(5775 ^ 1,bind([[_870832, _870834, _870836], [t_a, hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U), v_G]]))).
% 136.17/131.28  ncf('1.1.1',plain,[-(hBOOL(hAPP(c_Finite__Set_Ofinite(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), v_U))],extension(5661 ^ 2,bind([[_868590, _868592, _868594, _868596], [tc_Com_Opname, v_U, t_a, v_mgt__call]]))).
% 136.17/131.28  ncf('1.1.1.1',plain,[-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), v_U)))],extension(52796 ^ 3)).
% 136.17/131.28  ncf('1.1.2',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))))],extension(52798 ^ 2)).
% 136.17/131.28  ncf('1.1.3',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), hAPP(c_Finite__Set_Ocard(t_a), v_G)))), 5961 : hAPP(c_Finite__Set_Ocard(t_a), v_G) = hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)), 5961 : class_Orderings_Oorder(tc_Nat_Onat)],extension(5957 ^ 2,bind([[_873734, _873736, _873738], [tc_Nat_Onat, hAPP(c_Finite__Set_Ocard(t_a), v_G), hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))]]))).
% 136.17/131.28  ncf('1.1.3.1',plain,[-(hAPP(c_Finite__Set_Ocard(t_a), v_G) = hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))],extension(52800 ^ 5)).
% 136.17/131.28  ncf('1.1.3.2',plain,[-(class_Orderings_Oorder(tc_Nat_Onat))],extension(52460 ^ 3)).
% 136.17/131.28  %-----------------------------------------------------
% 136.17/131.28  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------