Courtade–Kumar proof module `CKLaneC.RSC2.BA_0135` (transplant)
DefinitionCK_CKLaneC_RSC2_BA_0135Verbatim transplant of the Lean module CKLaneC.RSC2.BA_0135 of the machine-checked proof of the general Courtade–Kumar theorem (the most informative Boolean function conjecture), so that the complete proof can be verified on this platform.
It is the original source with only two mechanical changes. Imports of project modules are redirected to their transplanted bundles Definitions.Def_CK_*. Declarations that already exist in earlier platform definition bundles of this mission are removed, and those bundles are imported instead, so every constant keeps a single platform identity.
The module contains both definitions and the lemmas proved alongside them in the source. They are kept together so the transplant stays faithful and every proof is re-checked by the server.
Source: Z. Chen, A. Gohari, A. Javanmard, H. Lin, V. Mirrokni, C. Nair, D. P. Woodruff, A Proof of the Most Informative Boolean Function Conjecture, arXiv:2609.24931 (2026). Lean development: https://github.com/dpwoodru/general-courtade-kumar-lean (Apache-2.0), module CKLaneC.RSC2.BA_0135 from release v1.0 (sources_v3.tar.zst).
import Definitions.Def_CK_CKLaneC_RSC2_BA_0135_part00
/-! RA-stat cover batch BA_0135 (generated by tools/emit_cover2.py; compact format). -/
namespace CKLaneC.RSC2.BA_0135
open CKLaneC.TM3 CKLaneC.RSCell
noncomputable def w5 : Wit := { Z0 := { p := [[[3698284533373109319]], [[(-55379782249959919), 284483425644085332], [122675924722975680]], [[356970870123555, (-4259983249996917), 0], [(-1833599675104590), 9436609594075052], [(-1037485070139432)]], [[(-3477190623739), 27459297701811, 0, 0], [14682243339163, (-141046128854200), 0], [14823934209004, (-79806543856880)], [109355694720728]], [[38733174054, (-267476201827), 0, 0, 0], [(-190117753199), 1129403333781, 0, 0], [4183037290, 1140302631461, 0], [(-1654237533467), 8411976516979], [(-5866231904101)]]], r := 78112791926792, ok := true }, Z1 := { p := [[[4551734810305365315]], [[(-68159731999950670), 0], [150985753505200837]], [[439348763228991, 0, 0], [(-2256738061667187), 0], [(-1276904701710070)]], [[(-4279619229217), 0, 0, 0], [18070453340508, 0, 0], [18244842103389, 0], [134591624271666]], [[47671598836, 0, 0, 0, 0], [(-233991080861), 0, 0, 0], [5148353588, 0, 0], [(-2035984656575), 0], [(-7219977728124)]]], r := 60240045721908, ok := true }, Z2 := { p := [[[28870074519436263684]], [[(-183087886265263441), 284483425644085332], [(-2529350965453231174)]], [[1522200084444513, (-4259983249996917), 0], [11644531928008480, 9436609594075052], [193233708290382652]], [[(-15607216894466), 27459297701811, 0, 0], [(-88515629750295), (-141046128854200), 0], [(-978858934043175), (-79806543856880)], [(-16471088731164711)]], [[182265140098, (-267476201827), 0, 0, 0], [772653060941, 1129403333781, 0, 0], [6948682020237, 1140302631461, 0], [83315398038999, 8411976516979], [1426075874365859]]], r := 305079709773081, ok := true }, Z3 := { p := [[[52232383108711512850]], [[(-967448466592582197), 912495913731873429], [(-4343318117767650575)]], [[19186764528623321, (-23884024607540335), 0], [75895153192878319, 21820882062725925], [349339544769282505]], [[(-399926006452463), 448824797624666, 0, 0], [(-1570057892470195), (-430983127830043), 0], [(-6421294034318429), (-442430705275194)], [(-29925744300455758)]], [[8480929239069, (-9296175122624), 0, 0, 0], [33080996154907, 6528930130092, 0, 0], [132050429528102, 12728576983490, 0], [555909596691807, 24863007343780], [2610090075221421]]], r := 912899533522202, ok := true }, iE := { p := [[[38357013312096235223]], [[(-194602825166176795), 0], [(-2214659389216304005)]], [[1775587374203365, 0, 0], [11271304101592449, 0], [190572323729542985]], [[(-18483849555393), 0, 0, 0], [(-72702122126632), 0, 0], [(-977454651546537), 0], [(-16190566566609099)]], [[218715376828, 0, 0, 0, 0], [586896023671, 0, 0, 0], [7120087872746, 0, 0], [82932080322495, 0], [1411027658763315]]], r := 308016550462136, ok := true }, iHu := { p := [[[61516093303157574493]], [[(-1001076033058373867), 0], [(-4121313019214344234)]], [[20345969004956436, 0, 0], [76517040490049051, 0], [344838266037960775]], [[(-425258255022267), 0, 0, 0], [(-1552948499438488), 0, 0], [(-6393307458727267), 0], [(-29672788696744570)]], [[9032080050354, 0, 0, 0, 0], [32756547381762, 0, 0, 0], [131693747168751, 0, 0], [555181765870502, 0], [2594549293547347]]], r := 835398557052914, ok := true }, T := { p := [[[14987979559889010688]], [[0, 1152921504606846976], [0]]], r := 0, ok := true }, E := { p := [[[8871451073424095419]], [[45008964284176987, 0], [512220340407364146]], [[(-182317764222924), 0, 0], [2590562174959798, 0], [(-14502157797286485)]], [[1266565409543, 0, 0, 0], [(-17505779151248), 0, 0], [(-72069246635657), 0], [362422865694779]], [[(-14030954613), 0, 0, 0, 0], [114371729234, 0, 0, 0], [(-89434672451), 0, 0], [1938455169330, 0], [(-17164324072220)]]], r := 27781024074239, ok := true }, de := { p := [[[(-38307889393867830551)]], [[310347454444509620, 0], [1277664195570253889]], [[(-3233985610900258), 0, 0], [1585523425984457, 0], [(-54811937941264314)]], [[47767929429797, 0, 0, 0], [1967562793934, 0, 0], [8100226047754, 0], [3333051527423543]], [[(-790960970415), 0, 0, 0, 0], [2441656354, 0, 0, 0], [104512693186, 0, 0], [41382965997, 0], [(-227210921024914)]]], r := 90958344656536, ok := true }, dde := { p := [[[(-264141958110069901589)]], [[5504999506388555096, 0], [22663439526300934571]], [[(-121968273627707046), 0, 0], [(-503803752405797228), 0], [(-2067206923355482215)]], [[2692800943227491, 0, 0, 0], [11081790470408165, 0, 0], [45622436092459531, 0], [187892680382192324]], [[(-59463107809719), 0, 0, 0, 0], [(-244810401233486), 0, 0, 0], [(-1008065962858505), 0, 0], [(-4149224558872334), 0], [(-17081332705157674)]]], r := 2599137483947510, ok := true }, nJu := { p := [[[(-76615778787735661102)]], [[620694908889019240, 0], [2555328391140507778]], [[(-6467971221800516), 0, 0], [3171046851968915, 0], [(-109623875882528628)]], [[95535858859594, 0, 0, 0], [3935125587868, 0, 0], [16200452095509, 0], [6666103054847086]], [[(-1581921940829), 0, 0, 0, 0], [4883312709, 0, 0, 0], [209025386372, 0, 0], [82765931994, 0], [(-454421842049827)]]], r := 181916689313067, ok := true }, Jd1 := { p := [[[(-528283916220139803177)]], [[11009999012777110193, 0], [45326879052601869143]], [[(-243936547255414091), 0, 0], [(-1007607504811594456), 0], [(-4134413846710964430)]], [[5385601886454983, 0, 0, 0], [22163580940816330, 0, 0], [91244872184919063, 0], [375785360764384648]], [[(-118926215619438), 0, 0, 0, 0], [(-489620802466971), 0, 0, 0], [(-2016131925717009), 0, 0], [(-8298449117744667), 0], [(-34162665410315348)]]], r := 5198274967895010, ok := true }, term0 := { p := [[[6327659050664450003307]], [[(-259707419042911496755), 0], [(-995975744702091739208)]], [[8423530521432508640, 0, 0], [42503576531146573596, 0], [129412785265094607383]], [[(-245312695134942733), 0, 0, 0], [(-1390787808775063845), 0, 0], [(-5578337427792170379), 0], [(-15296080449189455133)]], [[6726660537170608, 0, 0, 0, 0], [40704910048196489, 0, 0, 0], [183264917154681374, 0, 0], [663090044929346105, 0], [1711585804309401932]]], r := 369817857656969481, ok := true }, r0 := { p := [[[335197825901817991148]], [[(-7016276799306179754), 47424445114543782973], [(-20057160562692682745)]], [[136968629628148771, (-886637445850456201), 1245425248228714355], [373367462519855625, (-3077390001997881150)], [1706099966583397411]], [[(-2616900404278858), 16171234104700191, (-8765759576196977), (-36265572597325294)], [(-6016684799594685), 56709043568183912, (-113676185405299183)], [(-32501495256370013), 255805319439276480], [(-145299942713847061)]], [[51080140865033, (-301836103500829), 28020244304450, 1367709318388978, (-22108900040704)], [98920461818944, (-911162963576573), 1834727838392540, 785286250878567], [539540099458448, (-4691743247025143), 8905360735317618], [2734225501873362, (-21911816237219177)], [12658905009288273]]], r := 105801297934582868, ok := true }, r1 := { p := [[[487703719008304902268]], [[(-9719847684840853072), 0], [(-30287735321118012934)]], [[185131467403017135, 0, 0], [558394751613097296, 0], [2551930219982471955]], [[(-3517224670197749), 0, 0, 0], [(-8924627536567790), 0, 0], [(-47750075302431809), 0], [(-217843479593346396)]], [[68869000915538, 0, 0, 0, 0], [147334613234262, 0, 0, 0], [781214782094418, 0, 0], [4034100784901224, 0], [18984312852013887]]], r := 89386233797987876, ok := true }, r2 := { p := [[[1488081908803138616963]], [[(-36251667545016251733), 35512788832694103548], [(-249963735454934433595)]], [[774384165640427181, (-648560723428490470), 106885034715334488], [6014467955444332590, (-2099016042489415676)], [32193048218559599693]], [[(-16223473566646878), 12841456053901193, 1322754143068490, (-1332557637774349)], [(-126966133928327676), 39422440122465417, (-2443862555525708)], [(-764824166968453002), 209185795619121248], [(-3756945629371355428)]], [[341262590510234, (-257222492124987), (-6387092136154), (-2724675999712), 15799566734832], [2644704272024178, (-688819576671967), 178586776024300, (-179322151889811)], [15976581922366331, (-3619524081924154), (-74738990063726)], [88279923978400140, (-18595054830234850)], [414957726943181217]]], r := 8049270208623799757, ok := true }, r3 := { p := [[[9701362870939096608374]], [[(-407880138302368596256), 261306325770543802663], [(-1730469816689821348392)]], [[13298329658353915412, (-9759045028809484076), 172641870731530220], [74747235729350842688, (-22924846839642368181)], [234995486770422390686]], [[(-388471009273296219), 313803268934531725, 5487129945472876, (-3735087991062797)], [(-2457770365772535801), 919721140453320303, (-32222557352378256)], [(-10226489847552920071), 2117580387687648449], [(-28423810796841489194)]], [[10672120912894861, (-9066066877215870), (-29565814742523), (-68096046249573), 74672002691546], [72094567790362087, (-28958421210944892), 152982066219047, 168559259221276], [337068657099624150, (-83015530519245767), (-1009128415822926)], [1241545916767383923, (-192832698742983330)], [3225909439116633317]]], r := 311456956800142184893, ok := true }, eta := { p := [[[(-2184099967170348870344)]], [[53708997687982273352, 0], [301222834342044996242]], [[(-1186001647955138051), 0, 0], [(-7367804236977345545), 0], [(-36833701666729517957)]], [[25480358306818037, 0, 0, 0], [157707836471243168, 0, 0], [885546543788194646, 0], [4171150479167783754]], [[(-546643269457689), 0, 0, 0, 0], [(-3326886560588367), 0, 0, 0], [(-18732953936364158), 0, 0], [(-99011851751755238), 0], [(-452259470249356405)]]], r := 1036634347121974485, ok := true } }
theorem sB_5 : stageB c5 w5 = true := by decide +kernel
theorem s0_5 : stageC0 w5 q5 = true := by decide +kernel
theorem s1_5 : stageC1 w5 q5 = true := by decide +kernel
theorem s2_5 : stageC2 w5 q5 = true := by decide +kernel
theorem s3_5 : stageC3 w5 q5 = true := by decide +kernel
theorem sE_5 : stageE w5 q5 = true := by decide +kernel
theorem sF_5 : stageF w5 = true := by decide +kernel
theorem ok_5 : (domOK c5 && cellCheck c5 q5) = true :=
staged_check c5 q5 w5 (by decide +kernel) sB_5 s0_5 s1_5 s2_5 s3_5 sE_5 sF_5
noncomputable def c6 : Cell := { bc := 3170534137668829184, bh := 288230376151711744, tc := 14987979559889010688, th := 1152921504606846976, sc := 6088866696204910592, sh := 252201579132747776 }
noncomputable def q6 : Cert := { V0 := [[[3445761164523268056]], [[(-98792459066746261), 251894475221618695], [108654165745027822]], [[993907157160318, (-6477289799972932), (-1430566575896190)], [(-2758650751597901), 7123868827167721], [(-1185973408356496)]], [[(-15640658029279), 33713574869756, 116979142898098, (-26059504251488)], [22938115561469, (-111687599992664), (-128656289166505)], [44939340055224, (-115802006707814)], [99209001556185]], [[298876125720, (-119199098901), (-4106140880587), 1536865511832, 523783439925], [(-479280092611), (-1850758499475), 9709834332796, (-1690279213900)], [(-604585676400), 5115368125469, (-2138968290288)], [(-2749870449207), 6971347904649], [(-5617507292327)]]], r0 := 371771619113992, V1 := [[[4187908679474858659]], [[(-117135418341140301), 0], [128828164409316220]], [[1058047836230927, 0, 0], [(-3006017395238600), 0], [(-1551811675886636)]], [[(-15236245355299), 0, 0, 0], [14885782562582, 0, 0], [61002441136586, 0], [119630070539824]], [[282380542329, 0, 0, 0, 0], [(-292011728050), 0, 0, 0], [(-860558264040), 0, 0], [(-3227144435284), 0], [(-6897832603966)]]], r1 := 274411157486388, V2 := [[[14320772022700113528]], [[(-53475315836659570), 41702499943978739], [(-382637465950313119)]], [[263609617123029, (-338506675152777), (-358580351905346)], [(-5023240247681246), 7963956759614607], [(-996831870650114)]], [[(-3726102682915), (-13299725412547), 10985312025664, 2768648399038], [34340683205575, (-72573560075095), (-100006269642879)], [(-2058576381769), 403878654693046], [(-20866042173252)]], [[79326259920, 97154997625, 30558607120, (-151909512921), (-19237442420)], [(-475694083913), (-2527252545935), 3283660437858, 981641900478], [881349046894, (-5357809175787), (-9154054761145)], [946701380442, 1468399627895], [219004521310]]], r2 := 2095819968262820, V3 := [[[16228857643330179974]], [[(-89458324745538845), 43814587295449158], [(-214180650226243593)]], [[108302898440845, 923563206781466, (-770434496803796)], [(-8397174411551435), 8600018654865771], [(-1230144040329936)]], [[133829781622, (-39118336455395), 55851796288, 12751329234025], [21395640139689, 171671436836550, (-224548248373288)], [(-23710176680326), 472412740540489], [(-6899119259089)]], [[(-4299003865), (-4528992391), 1057225437677, (-292046223223), (-201836130198)], [17397081068, (-8017047830697), 432603239497, 4878793562918], [1219452974406, 7650104974621, (-22769208912517)], [156366840529, 4514330967404], [96743649489]]], r3 := 8118686086651784, Vm := [[[14530954591246720955]], [[(-57184330902690951), 0], [(-338202936327551033)]], [[227419472698620, 0, 0], [(-5831081086375387), 0], [1908076238909036]], [[(-3111663247057), 0, 0, 0], [25336079527562, 0, 0], [(-56625516937503), 0], [41502799264223]], [[74970896363, 0, 0, 0, 0], [(-301951710986), 0, 0, 0], [64566340561, 0, 0], [(-100083632127), 0], [1149981633302]]], rm := 548000922004296 }
noncomputable def w6 : Wit := { Z0 := { p := [[[3535267064699649473]], [[(-106655689686685326), 271943620361511497], [117302323419623259]], [[1310578533743860, (-8204283822052718), 0], [(-3500775247842237), 9023255647663327], [(-993010772991715)]], [[(-24421102556087), 100813733364912, 0, 0], [52380043417120, (-269290403680173), 0], [29629004265074, (-76385444076286)], [104498106877764]], [[516512617241, (-1878546350469), 0, 0, 0], [(-1307940719599), 4029234109009, 0, 0], [(-27690198537), 2279154174236, 0], [(-3170576979745), 8038315913674], [(-5608966622724)]]], r := 90510142433423, ok := true }, Z1 := { p := [[[4351097925784183967]], [[(-131268541152843478), 0], [144372090362613241]], [[1613019733838597, 0, 0], [(-4308646458882754), 0], [(-1222167105220572)]], [[(-30056741607491), 0, 0, 0], [64467745744148, 0, 0], [36466466787784, 0], [128613054618787]], [[635707836605, 0, 0, 0, 0], [(-1609773193353), 0, 0, 0], [(-34080244353), 0, 0], [(-3902248590455), 0], [(-6903343535660)]]], r := 70451574233381, ok := true }, Z2 := { p := [[[28334103480300787038]], [[(-348714609630883191), 271943620361511497], [(-2495193763353914885)]], [[5563915273940509, (-8204283822052718), 0], [22266974144472205, 9023255647663327], [190358077433036500]], [[(-108925009932799), 100813733364912, 0, 0], [(-327850023176352), (-269290403680173), 0], [(-1877486813761429), (-76385444076286)], [(-16226333860363000)]], [[2415123921338, (-1878546350469), 0, 0, 0], [5488248768901, 4029234109009, 0, 0], [25733615760422, 2279154174236, 0], [159794879120951, 8038315913674], [1404761056553298]]], r := 353357469713205, ok := true }, Z3 := { p := [[[49492566096264707072]], [[(-1724556361251409679), 844647219259939749], [(-4128923762604344240)]], [[64002915423782386, (-42844870766527886), 0], [134594770783936188, 20583355802669423], [331193229912823414]], [[(-2500817245990596), 1498935340771007, 0, 0], [(-5226997370519307), (-790165872033702), 0], [(-11396907085242240), (-406145832979055)], [(-28355199513528758)]], [[99433474894788, (-58183985420014), 0, 0, 0], [206482588961107, 21916503178577, 0, 0], [439269087026119, 22991156092758, 0], [986105730397249, 23063798793399], [2472039216664053]]], r := 1567482479282974, ok := true }, iE := { p := [[[37788703109487447718]], [[(-368851687534015795), 0], [(-2181484365107893946)]], [[6481275032680608, 0, 0], [21700775858097446, 0], [187702402737381378]], [[(-128767858859752), 0, 0, 0], [(-270766052300500), 0, 0], [(-1872710967559555), 0], [(-15946867629253480)]], [[2893121987195, 0, 0, 0, 0], [4224295465346, 0, 0, 0], [26361701827914, 0, 0], [159151601317272, 0], [1389760624399010]]], r := 358414831573741, ok := true }, iHu := { p := [[[58685184374682651928]], [[(-1779158920055690919), 0], [(-3904907240122230660)]], [[67835056752395110, 0, 0], [136027749895061278, 0], [326772989695590730]], [[(-2658172092236832), 0, 0, 0], [(-5168863067929101), 0, 0], [(-11344647512727528), 0], [(-28104187382637325)]], [[105866440709470, 0, 0, 0, 0], [204468830943281, 0, 0, 0], [438205557225660, 0, 0], [984961086282962, 0], [2456644021484418]]], r := 1498816670177036, ok := true }, T := { p := [[[14987979559889010688]], [[0, 1152921504606846976], [0]]], r := 0, ok := true }, E := { p := [[[9004870210417600390]], [[87895622231698517, 0], [519837463512207583]], [[(-686517126696029), 0, 0], [4976968399982226, 0], [(-14719173457021315)]], [[8908460096527, 0, 0, 0], [(-66164292270199), 0, 0], [(-145217732385242), 0], [368234007022419]], [[(-185204822899), 0, 0, 0, 0], [803625996721, 0, 0, 0], [(-361764062042), 0, 0], [3871202916565, 0], [(-17431502525657)]]], r := 29218191356983, ok := true }, de := { p := [[[(-37404724016731129465)]], [[584306317079883727, 0], [1282438540084420129]], [[(-11373211186090487), 0, 0], [3194790112475343, 0], [(-54786689945341610)]], [[315261903207823, 0, 0, 0], [7958809364930, 0, 0], [17468036138612, 0], [3333185096719514]], [[(-9791380620385), 0, 0, 0, 0], [19826856939, 0, 0, 0], [427038194949, 0, 0], [95509337327, 0], [(-227210214133447)]]], r := 92585196006083, ok := true }, dde := { p := [[[(-248656485689267921702)]], [[9679932055735404982, 0], [21245565161289395341]], [[(-402487092635608493), 0, 0], [(-886767700268673297), 0], [(-1938848684898906187)]], [[16667218710065778, 0, 0, 0], [36564423235127507, 0, 0], [80251786061513605, 0], [176218326549699093]], [[(-690367748276984), 0, 0, 0, 0], [(-1515285778232108), 0, 0, 0], [(-3326616408557069), 0, 0], [(-7299388954644516), 0], [(-16020070100255199)]]], r := 3485956470799737, ok := true }, nJu := { p := [[[(-74809448033462258930)]], [[1168612634159767455, 0], [2564877080168840259]], [[(-22746422372180973), 0, 0], [6389580224950686, 0], [(-109573379890683220)]], [[630523806415647, 0, 0, 0], [15917618729860, 0, 0], [34936072277224, 0], [6666370193439029]], [[(-19582761240769), 0, 0, 0, 0], [39653713878, 0, 0, 0], [854076389899, 0, 0], [191018674655, 0], [(-454420428266893)]]], r := 185170392012156, ok := true }, Jd1 := { p := [[[(-497312971378535843404)]], [[19359864111470809965, 0], [42491130322578790683]], [[(-804974185271216986), 0, 0], [(-1773535400537346594), 0], [(-3877697369797812373)]], [[33334437420131556, 0, 0, 0], [73128846470255015, 0, 0], [160503572123027210, 0], [352436653099398186]], [[(-1380735496553967), 0, 0, 0, 0], [(-3030571556464216), 0, 0, 0], [(-6653232817114137), 0, 0], [(-14598777909289032), 0], [(-32040140200510397)]]], r := 6971912941599466, ok := true }, term0 := { p := [[[5618229951348636070159]], [[(-430257929841321981292), 0], [(-879967077021388148851)]], [[26144187438399568433, 0, 0], [70295883927674512347, 0], [114193174418111355967]], [[(-1427148052167665216), 0, 0, 0], [(-4310968706139621272), 0, 0], [(-9218606839496242627), 0], [(-13487273087726966243)]], [[73373154422921080, 0, 0, 0, 0], [236574936959777283, 0, 0, 0], [567787228183540581, 0, 0], [1095393401732242081, 0], [1508496534383886685]]], r := 540530174880132669, ok := true }, r0 := { p := [[[315314960298981719053]], [[(-12519980606813312670), 44902375558350088765], [(-18988668856845284495)]], [[463688729904073236, (-1594333114317265243), 1219373297399882367], [679530642648444021, (-2915071671746511492)], [1613218337885659442]], [[(-16686220085414540), 54976950462903797, (-17208127915345610), (-32380303411964136)], [(-20843955950855588), 103254238531183819, (-108383590196161878)], [(-58986661666016339), 242376664529093267], [(-137478763879178369)]], [[611250188497799, (-1923997136120953), 104596233459814, 2450949473922114, (-68782652274946)], [647363074189455, (-3148409442079710), 3393572574065312, 639730987682057], [1862920548152944, (-8541724317838715), 8505237664505880], [4971730988954452, (-20767576144682156)], [11979616743082150]]], r := 124176567152851068, ok := true }, r1 := { p := [[[460120655262895130292]], [[(-17394217392364513721), 0], [(-28689092846953608222)]], [[627411923245023238, 0, 0], [1017128564039925803, 0], [2415375417932245217]], [[(-22413430965981349), 0, 0, 0], [(-30904589202676414), 0, 0], [(-86785262026762086), 0], [(-206296672718234107)]], [[822836623492092, 0, 0, 0, 0], [961714486658439, 0, 0, 0], [2699768648867193, 0, 0], [7344850231481739, 0], [17980550206355733]]], r := 103254523310648162, ok := true }, r2 := { p := [[[1385884320031456843181]], [[(-64018524073802110005), 33676135642824342673], [(-232995850508619642198)]], [[2580075571109326867, (-1155860828955032108), 110799364999801261], [10637042722892141703, (-1986624346376775247)], [30033963435997230635]], [[(-101638598659568870), 43133473251389624, 2575823564107912, (-1338832192439704)], [(-423494231879181195), 71214716561068899, (-1915869335043218)], [(-1354401520127167482), 198860288582805501], [(-3507600031763034329)]], [[4012597230827681, (-1622906026660293), (-21091959856722), (-2940622853652), 15344631702857], [16575523100077888, (-2346820728836750), 347082294171136, (-184933607274834)], [53352648808908766, (-6546939683548175), (-51873025633700)], [156501368978307194, (-17722453296209904)], [387666604404530250]]], r := 9700090836677364960, ok := true }, r3 := { p := [[[8587719887348737512479]], [[(-675061486971237724367), 234627199613771162704], [(-1526550422277509189231)]], [[41240912653902515407, (-16193415186259209822), 188886656013225926], [123504376714755316718, (-20405512886620118270)], [207102792981715821141]], [[(-2258604485761111882), 975962850320484141, 10717597658521065, (-3938170889272774)], [(-7613741309932665013), 1532465292594189577, (-31677407777537247)], [(-16889138214116331337), 1890349539520539732], [(-25037897586697465177)]], [[116351758724656497, (-52833262011651218), (-56335640665645), (-134539247612151), 77717954579662], [418823096484865127, (-90167947764456864), 420518412712134, 105764179460824], [1043843279525006568, (-138108348430701128), (-1035698381431094)], [2049923885529032263, (-172098775639807236)], [2840801281865351238]]], r := 544176177307659643922, ok := true }, eta := { p := [[[(-2033000607313655751572)]], [[94452686775463954572, 0], [280454338480480292880]], [[(-3933206449895094059), 0, 0], [(-13008653571735762855), 0], [(-34335706499315871650)]], [[158855703725670582, 0, 0, 0], [524824853562596847, 0, 0], [1565806559518350808, 0], [3891675703796941491]], [[(-6396829922640585), 0, 0, 0, 0], [(-20799816005882801), 0, 0, 0], [(-62436578011693146), 0, 0], [(-175295788396136357), 0], [(-422257528244986478)]]], r := 1344528025535156830, ok := true } }
theorem sB_6 : stageB c6 w6 = true := by decide +kernel
theorem s0_6 : stageC0 w6 q6 = true := by decide +kernel
theorem s1_6 : stageC1 w6 q6 = true := by decide +kernel
theorem s2_6 : stageC2 w6 q6 = true := by decide +kernel
theorem s3_6 : stageC3 w6 q6 = true := by decide +kernel
theorem sE_6 : stageE w6 q6 = true := by decide +kernel
theorem sF_6 : stageF w6 = true := by decide +kernel
theorem ok_6 : (domOK c6 && cellCheck c6 q6) = true :=
staged_check c6 q6 w6 (by decide +kernel) sB_6 s0_6 s1_6 s2_6 s3_6 sE_6 sF_6
theorem region : RegionPosI 2882303761517117440 3458764513820540928 13835058055282163712 16140901064495857664 4323455642275676160 6341068275337658368 :=
(RegionPosI.split_s 5332261958806667264 (RegionPosI.split_s 4827858800541171712 (RegionPosI.split_s 4575657221408423936 (RegionPosI.of_check c0 q0 ok_0 2882303761517117440 3458764513820540928 13835058055282163712 16140901064495857664 4323455642275676160 4575657221408423936 (by decide +kernel)) (RegionPosI.of_check c1 q1 ok_1 2882303761517117440 3458764513820540928 13835058055282163712 16140901064495857664 4575657221408423936 4827858800541171712 (by decide +kernel))) (RegionPosI.split_s 5080060379673919488 (RegionPosI.of_check c2 q2 ok_2 2882303761517117440 3458764513820540928 13835058055282163712 16140901064495857664 4827858800541171712 5080060379673919488 (by decide +kernel)) (RegionPosI.of_check c3 q3 ok_3 2882303761517117440 3458764513820540928 13835058055282163712 16140901064495857664 5080060379673919488 5332261958806667264 (by decide +kernel)))) (RegionPosI.split_s 5836665117072162816 (RegionPosI.split_s 5584463537939415040 (RegionPosI.of_check c4 q4 ok_4 2882303761517117440 3458764513820540928 13835058055282163712 16140901064495857664 5332261958806667264 5584463537939415040 (by decide +kernel)) (RegionPosI.of_check c5 q5 ok_5 2882303761517117440 3458764513820540928 13835058055282163712 16140901064495857664 5584463537939415040 5836665117072162816 (by decide +kernel))) (RegionPosI.of_check c6 q6 ok_6 2882303761517117440 3458764513820540928 13835058055282163712 16140901064495857664 5836665117072162816 6341068275337658368 (by decide +kernel))))
end CKLaneC.RSC2.BA_0135