Courtade–Kumar proof module `CKLaneC.RSC2.S06_0011` (transplant)
DefinitionCK_CKLaneC_RSC2_S06_0011Verbatim transplant of the Lean module CKLaneC.RSC2.S06_0011 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.S06_0011 from release v1.0 (sources_v3.tar.zst).
import Definitions.Def_CK_CKLaneC_RSC2_S06_0011_part00
/-! RA-stat cover batch S06_0011 (generated by tools/emit_cover2.py; compact format). -/
namespace CKLaneC.RSC2.S06_0011
open CKLaneC.TM3 CKLaneC.RSCell
noncomputable def w6 : Wit := { Z0 := { p := [[[1610009416523690306]], [[(-26691254570639512), 322001883304738061], [9831386743851708]], [[229150345231036, (-5338250914127903), 0], [(-168162603077100), 1966277348770341], [(-153425940070346)]], [[(-2828731191640), 45830069046207, 0, 0], [1743697667288, (-33632520615420), 0], [2591581997663, (-30685188014070)], [3946913286481]], [[48733153498, (-565746238328), 0, 0, 0], [(-27781927117), 348739533457, 0, 0], [(-25049564069), 518316399532, 0], [(-66505712496), 789382657296], [(-119533651839)]]], r := 3839313148641, ok := true }, Z1 := { p := [[[2576015066437904489]], [[(-42706007313023219), 0], [15730218790162734]], [[366640552369657, 0, 0], [(-269060164923360), 0], [(-245481504112553)]], [[(-4525969906623), 0, 0, 0], [2789916267660, 0, 0], [4146531196261, 0], [6315061258370]], [[77973045597, 0, 0, 0, 0], [(-44451083386), 0, 0, 0], [(-40079302511), 0, 0], [(-106409139994), 0], [(-191253842943)]]], r := 1581970597673, ok := true }, Z2 := { p := [[[1093028131153218430965]], [[(-7920402978771197999), 322001883304738061], [(-41046441881422438287)]], [[81796129058193558, (-5338250914127903), 0], [293264557302187363, 1966277348770341], [1679258880083254292]], [[(-1158104635132547), 45830069046207, 0, 0], [(-2865901022681491), (-33632520615420), 0], [(-11957860891511249), (-30685188014070)], [(-70312849058300162)]], [[22287747041168, (-565746238328), 0, 0, 0], [38182583342899, 348739533457, 0, 0], [114837149441004, 518316399532, 0], [499682120047342, 789382657296], [2975444231601356]]], r := 424156237574894, ok := true }, Z3 := { p := [[[3188432429991845810057]], [[(-134427226750253743743), 1875836788791052222], [(-123030597251001988716)]], [[6080416639495975773, (-96566608987512230), 0], [5271039706806600447, 9395342775422479], [5080189418006051071]], [[(-280359024445539704), 4313741458703973, 0, 0], [(-239765891307184944), (-432022480324001), 0], [(-218889828680955448), (-157141876270666)], [(-213862337534747848)]], [[13042808354088439, (-198256218263612), 0, 0, 0], [11091757329805217, 18003804240755, 0, 0], [9977429428111996, 7486693890751, 0], [9245221261903512, 4109007521565], [9083933834303691]]], r := 23596089124362843, ok := true }, iE := { p := [[[1097581297970415334579]], [[(-7938287066615636524), 0], [(-41018638352182349248)]], [[82027582815687329, 0, 0], [293140715360998675, 0], [1678824985789186194]], [[(-1161799681449044), 0, 0, 0], [(-2863698794925831), 0, 0], [(-11956020774891113), 0], [(-70301687039977831)]], [[22364596337809, 0, 0, 0, 0], [38140892822130, 0, 0, 0], [114807726081477, 0, 0], [499635244374517, 0], [2975106185965409]]], r := 422212977065347, ok := true }, iHu := { p := [[[3197005179428470338441]], [[(-134700770099920226835), 0], [(-122987659656448889719)]], [[6093061902848332773, 0, 0], [5269905644335121712, 0], [5079471264945337471]], [[(-280945317156614744), 0, 0, 0], [(-239714398920263163), 0, 0], [(-218869668579361891), 0], [(-213843558986354899)]], [[13070152890413290, 0, 0, 0, 0], [11089430057725766, 0, 0, 0], [9976515102546033, 0, 0], [9244685549059680, 0], [9083359494410663]]], r := 23566424266607456, ok := true }, T := { p := [[[11529215046068469760]], [[0, 2305843009213693952], [0]]], r := 0, ok := true }, E := { p := [[[310029304936380737]], [[2242295514873691, 0], [11586367188726135]], [[(-6952531912504), 0, 0], [84795181502112, 0], [(-41206913791019)]], [[110306792521, 0, 0, 0], [(-302423299836), 0, 0], [(-276125621589), 0], [595718007134]], [[(-2626352760), 0, 0, 0, 0], [4795945464, 0, 0, 0], [(-6059470), 0, 0], [3998132230, 0], [(-12950480285)]]], r := 12642894565, ok := true }, de := { p := [[[(-102226837469747566672)]], [[633935487190054804, 0], [578810662217006560]], [[(-15086746340057457), 0, 0], [12701778593114, 0], [(-12577041844925026)]], [[478944430016435, 0, 0, 0], [278735673, 0, 0], [254497788, 0], [364552014989908]], [[(-17105158213197), 0, 0, 0, 0], [6117, 0, 0, 0], [6067849, 0, 0], [5100, 0], [(-11887565705029)]]], r := 5582407229034, ok := true }, dde := { p := [[[(-28901284235469517643568)]], [[1375617402632355523982, 0], [1255998498055628959491]], [[(-65505604519423448823), 0, 0], [(-59809477703627367875), 0], [(-54608641952865295623)]], [[3119314500619505925, 0, 0, 0], [2848069760877471932, 0, 0], [2600411520801170127, 0], [2374288780326889361]], [[(-148538785743791611), 0, 0, 0, 0], [(-135622369592174670), 0, 0, 0], [(-123829120074557624), 0, 0], [(-113061370491775409), 0], [(-103229946970736156)]]], r := 36196470174224398, ok := true }, nJu := { p := [[[(-204453674939495133343)]], [[1267870974380109609, 0], [1157621324434013121]], [[(-30173492680114914), 0, 0], [25403557186228, 0], [(-25154083689850051)]], [[957888860032871, 0, 0, 0], [557471347, 0, 0], [508995577, 0], [729104029979816]], [[(-34210316426394), 0, 0, 0, 0], [12235, 0, 0, 0], [12135699, 0, 0], [10200, 0], [(-23775131410058)]]], r := 11164814458059, ok := true }, Jd1 := { p := [[[(-57802568470939035287136)]], [[2751234805264711047964, 0], [2511996996111257918982]], [[(-131011209038846897645), 0, 0], [(-119618955407254735750), 0], [(-109217283905730591246)]], [[6238629001239011850, 0, 0, 0], [5696139521754943864, 0, 0], [5200823041602340255, 0], [4748577560653778722]], [[(-297077571487583221), 0, 0, 0, 0], [(-271244739184349340), 0, 0, 0], [(-247658240149115247), 0, 0], [(-226122740983550817), 0], [(-206459893941472311)]]], r := 72392940348448789, ok := true }, term0 := { p := [[[62977579079306738775798794]], [[(-5993731482129387187054226), 0], [(-5464881830312182160973565)]], [[428025419034236047269730, 0, 0], [520285507937024130154993, 0], [356156997474861396263551]], [[(-27173097767034524375155), 0, 0, 0], [(-37158978455933241429235), 0, 0], [(-33911912810661120351925), 0], [(-20639584221723835268217)]], [[1617334891567504797202, 0, 0, 0, 0], [2359164597055050338127, 0, 0, 0], [2422093742795913645547, 0, 0], [1965335503671740154297, 0], [1121481808552762590118]]], r := 745733050800338416811, ok := true }, r0 := { p := [[[8279648424392098340951]], [[(-253641585623758386119), 3256538767498134797150], [(-304290837958516606577)]], [[7612924697221308194, (-98074562741115965067), 303945490916236385136], [8871319989114172513, (-120332935114856522466)], [12387646625294510781]], [[(-265460927333150013), 2921266777378950281, (-8493668915740069951), (-4176900159095564450)], [(-250679506323365481), 3466361950446438315, (-11485431418051293865)], [(-355491796636460008), 4904590812017628415], [(-517090642950820193)]], [[10549313229572737, (-102165240190690298), 244524258846839054, 247537232783477852, (-168893214044270777)], [8397911032513592, (-97417696639564714), 314264585200547795, 107376846587485790], [9845488293484206, (-139212362565758810), 470465716208668503], [14699092143462099, (-204868845917119316)], [21834104961447560]]], r := 418180328997072326, ok := true }, r1 := { p := [[[20659460151084139398543]], [[(-617017979014919008172), 0], [(-765386065930733694721)]], [[18324556691214958144, 0, 0], [21909426493544833608, 0], [31215976210448597753]], [[(-642191866416783015), 0, 0, 0], [(-614150315446544620), 0, 0], [(-880936360837137131), 0], [(-1304386799218313088)]], [[25740290994736609, 0, 0, 0, 0], [20668891096424903, 0, 0, 0], [24209445544684531, 0, 0], [36496599537890444, 0], [55116349937655500]]], r := 114538153204434852, ok := true }, r2 := { p := [[[6109238440219041069052138]], [[(-242860940331920833907333), 4241350057520027811672], [(-507215972610526020143782)]], [[9937242108352140984705, (-119565108673549546568), 454464481567016789], [19693974231078968723669, (-174881075515499879884)], [32183397490545861968592]], [[(-436260179607646737864), 4180367547095989367, 515711909566506, (-137857789373575)], [(-797165255094991554179), 4601788114486954092, 118333864259990], [(-1231429425932099917345), 7460289374797931153], [(-1830258194346430260814)]], [[19894103650707133393, (-170625589069036268), (-12981046465354), 1189647434486, 40950360652], [34879608626884604084, (-154930386912609132), 7602602107587, (-6096021403191)], [49509265133351241151, (-191045139018484486), (-2476433153664)], [69295608146399930947, (-320672819450731053)], [98029600339102923629]]], r := 370580459633167695303, ok := true }, r3 := { p := [[[125241878911995203918924673]], [[(-11924268175773675986071046), 101093022146115243972117], [(-10898714775972817728972064)]], [[851649264675083700791002, (-8968324391843673474200), 1438169624888557113], [1037820606558833760181759, (-4408545282268640887616)], [710963433497031443728973]], [[(-54070285450078938035504), 624982064695277158268, 32019231593718587, (-975429185512870)], [(-74126411487506981370229), 390858751696532919085, (-2795309503754738)], [(-67704199858505888690755), 191879483037207651662], [(-41220433244378938476355)]], [[3218373099864228285522, (-39189588419234831677), (-1955851629105782), (-291154996751), 322938165175], [4706323138544653632179, (-27230389511813962760), 253535509323999, (-41829104514873)], [4835856744711411743280, (-17008129638295528091), 37241157291017], [3925468810166918266673, (-8347633527114522598)], [2240409463987268136315]]], r := 97566840098357948934668, ok := true }, eta := { p := [[[(-6180487888824807273646987)]], [[246417111335056029985248, 0], [510219161683739264381795]], [[(-10105350814351664727142), 0, 0], [(-19843027534475250006460), 0], [(-32312579899914122311381)]], [[444206606632738716158, 0, 0, 0], [804201927410211154020, 0, 0], [1237827730454771611045, 0], [1835839454793089616979]], [[(-20270805946356690318), 0, 0, 0, 0], [(-35212275348807493124), 0, 0, 0], [(-49811222178915133542), 0, 0], [(-69571710781777506055), 0], [(-98271200436406470500)]]], r := 37442091599918722365, 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
noncomputable def c7 : Cell := { bc := 51791395714760704, bh := 2251799813685248, tc := 11529215046068469760, th := 2305843009213693952, sc := 3314649325744685056, sh := 144115188075855872 }
noncomputable def q7 : Cert := { V0 := [[[1549584166930883472]], [[(-25414929374332372), 306770371785412847], [9357422821501960]], [[203622973407668, (-4928451455043512), (-932652236102840)], [(-154336002731324), 1814587144462608], [(-146953584540640)]], [[(-2302222511044), 36963483515615, 45437321656906, (-58463114434593)], [1409588563929, (-28070907277209), (-16729388634450)], [2427074113121, (-28839190769007)], [3783802916888]], [[36155454329, (-392476317043), (-1090806619288), 2727022774177, 540349370089], [(-20304048157), 212861838962, 811094773782, (-1004051782558)], [(-21329054536), 458269589477, 164205547834], [(-62468428318), 743819918693], [(-114659231354)]]], r0 := 16182971848238, V1 := [[[2459970899466337926]], [[(-39721541100696877), 0], [14624917886896668]], [[303211620277527, 0, 0], [(-230143626542202), 0], [(-231715100732385)]], [[(-3284016529400), 0, 0, 0], [1850851415379, 0, 0], [3716479941181, 0], [5974147858843]], [[51162297943, 0, 0, 0, 0], [(-25121882299), 0, 0, 0], [(-30105586810), 0, 0], [(-96045097138), 0], [(-181180218267)]]], r1 := 5781413051564, V2 := [[[18388116989801848399]], [[(-476397928883932), 19509776826450], [(-2534737747614666)]], [[1068250034979, (-24269809093), (-6122315092)], [(-21168995182778), 1709861062564], [361506950229]], [[(-17621813341), (-1885028741), 65314436, 1877970], [53106153459, (-1905512009), (-806664936)], [(-12706276696), 37858987411], [(-4686975169)]], [[397316837, 9171839, 528693, (-37779), (-569)], [(-871777614), (-169528404), 8530272, 330043], [187792954, (-31259278), (-35666973)], [127387493, 14041826], [87833654]]], r2 := 179938812721, V3 := [[[18428095091726438985]], [[(-810501676631930), 12172303428161], [(-812437148481377)]], [[14685421142, 420948707774, (-7542852051)], [(-35295199013895), 1068504711575], [(-70871808956)]], [[12917890, (-4911602303), (-192171838), 4582488], [1283707568, 37018379233, (-993931321)], [(-2468410858), 23755348544], [(-27630943)]], [[(-198002), (-4234150), 5500643, 74577, (-2754)], [1261057, (-430068228), (-25396402), 804973], [28255571, 826181254, (-43963410)], [(-1169463), 11187446], [163925]]], r3 := 753247530746, Vm := [[[18388184770357998353]], [[(-476656997858099), 0], [(-2528737147462227)]], [[1064144411553, 0, 0], [(-21192066835080), 0], [497369949589]], [[(-17619120915), 0, 0, 0], [52737551355, 0, 0], [(-13234398944), 0], [(-4580043963)]], [[397459676, 0, 0, 0, 0], [(-871416285), 0, 0, 0], [179152643, 0, 0], [126897877, 0], [87153563]]], rm := 29141658095 }
noncomputable def w7 : Wit := { Z0 := { p := [[[1557521624883794849]], [[(-25807122027486035), 311504324976758969], [9501822690924848]], [[213265318991722, (-5161424405497207), 0], [(-161504159345256), 1900364538184969], [(-148340148668738)]], [[(-2478937687057), 42653063798344, 0, 0], [1589538844566, (-32300831869052), 0], [2495570705213, (-29668029733748)], [3816364849308]], [[39217071144, (-495787537412), 0, 0, 0], [(-23762134650), 317907768913, 0, 0], [(-23006459192), 499114141042, 0], [(-64076500550), 763272969861], [(-115585397233)]]], r := 3682103782230, ok := true }, Z1 := { p := [[[2492034599814071759]], [[(-41291395243977656), 0], [15202916305479757]], [[341224510386755, 0, 0], [(-258406654952409), 0], [(-237344237869980)]], [[(-3966300299291), 0, 0, 0], [2543262151307, 0, 0], [3992913128340, 0], [6106183758894]], [[62747313831, 0, 0, 0, 0], [(-38019415439), 0, 0, 0], [(-36810334708), 0, 0], [(-102522400880), 0], [(-184936635572)]]], r := 1499378645150, ok := true }, Z2 := { p := [[[1077505584900633217328]], [[(-7606443506628039540), 311504324976758969], [(-40471081657548418598)]], [[75342070884346741, (-5161424405497207), 0], [282237892344482695, 1900364538184969], [1655790926996157371]], [[(-999435955684284), 42653063798344, 0, 0], [(-2652447478965699), (-32300831869052), 0], [(-11515683419431039), (-29668029733748)], [(-69332009057145771)]], [[17635846367213, (-495787537412), 0, 0, 0], [33160265060938, 317907768913, 0, 0], [106445895079076, 499114141042, 0], [481386446693511, 763272969861], [2933990946940851]]], r := 405546396597047, ok := true }, Z3 := { p := [[[2941847612998575993170]], [[(-113096340565105725032), 1698507250094627634], [(-113366413767605243463)]], [[4668562615071276014, (-81426946232759972), 0], [4430268296130094680, 8597454600412839], [4678937879541624215]], [[(-196488239441518172), 3315085813871287, 0, 0], [(-183931058989059240), (-368551872493461), 0], [(-183908267726252622), (-143335676244780)], [(-196916546633944079)]], [[8344520149048118, (-139024349687260), 0, 0, 0], [7767206418553207, 13964346721162, 0, 0], [7651415196245559, 6367259118956, 0], [7766015552838419, 3744714454709], [8362546768035328]]], r := 17044952523438442, ok := true }, iE := { p := [[[1082023880966724683150]], [[(-7623443808328963210), 0], [(-40443517322389792799)]], [[75553053669455968, 0, 0], [282122387496034943, 0], [1655360599288685968]], [[(-1002586777735488), 0, 0, 0], [(-2650474483496536), 0, 0], [(-11513955010091346), 0], [(-69320937964449585)]], [[17695996463712, 0, 0, 0, 0], [33125261138078, 0, 0, 0], [106419382817886, 0, 0], [481342349126635, 0], [2933655639207548]]], r := 403657910716621, ok := true }, iHu := { p := [[[2949919566501406652118]], [[(-113325555388123281493), 0], [(-113325555388123281493)]], [[4678256693804041883, 0, 0], [4429315327254949817, 0], [4678256693804041883]], [[(-196898750324297411), 0, 0, 0], [(-183891321076904497), 0, 0], [(-183891321076904497), 0], [(-196898750324297411)]], [[8362002751475456, 0, 0, 0, 0], [7765565311521788, 0, 0, 0], [7650710552640258, 0, 0], [7765565311521788, 0], [8362002751475456]]], r := 17020980171470304, ok := true }, T := { p := [[[11529215046068469760]], [[0, 2305843009213693952], [0]]], r := 0, ok := true }, E := { p := [[[314486928529632994]], [[2215730604723458, 0], [11754784497260571]], [[(-6348242539620), 0, 0], [83639628169605, 0], [(-41759189273147)]], [[91957076444, 0, 0, 0], [(-276149861070), 0, 0], [(-276149861070), 0], [603714271091]], [[(-1999067388), 0, 0, 0, 0], [3998131721, 0, 0, 0], [(-6060269), 0, 0], [3998131721, 0], [(-13124312232)]]], r := 11918826783, ok := true }, de := { p := [[[(-101015736286021915514)]], [[578836066889184414, 0], [578836066889184414]], [[(-12577041311655926), 0, 0], [12702893609210, 0], [(-12577041311655926)]], [[364552015001109, 0, 0, 0], [278772377, 0, 0], [278772377, 0], [364552015001109]], [[(-11887565705028), 0, 0, 0, 0], [6118, 0, 0, 0], [6069446, 0, 0], [6118, 0], [(-11887565705028)]]], r := 4322751169021, ok := true }, dde := { p := [[[(-26389287290191018907761)]], [[1146781188731384714293, 0], [1146781188731384714062]], [[(-49860064393278621265), 0, 0], [(-49860077102583994695), 0], [(-49860064393278621473)]], [[2167828886385377907, 0, 0, 0], [2167828885827549327, 0, 0], [2167828885827549337, 0], [2167828886385377842]], [[(-94253429842847018), 0, 0, 0, 0], [(-94253429842864989), 0, 0, 0], [(-94253429855004486), 0, 0], [(-94253429842864987), 0], [(-94253429842847050)]]], r := 25943910533198799, ok := true }, nJu := { p := [[[(-202031472572043831028)]], [[1157672133778368828, 0], [1157672133778368828]], [[(-25154082623311851), 0, 0], [25405787218421, 0], [(-25154082623311851)]], [[729104030002218, 0, 0, 0], [557544754, 0, 0], [557544754, 0], [729104030002218]], [[(-23775131410056), 0, 0, 0, 0], [12237, 0, 0, 0], [12138893, 0, 0], [12237, 0], [(-23775131410056)]]], r := 8645502338035, ok := true }, Jd1 := { p := [[[(-52778574580382037815522)]], [[2293562377462769428587, 0], [2293562377462769428124]], [[(-99720128786557242530), 0, 0], [(-99720154205167989390), 0], [(-99720128786557242945)]], [[4335657772770755814, 0, 0, 0], [4335657771655098655, 0, 0], [4335657771655098674, 0], [4335657772770755684]], [[(-188506859685694036), 0, 0, 0, 0], [(-188506859685729978), 0, 0, 0], [(-188506859710008971), 0, 0], [(-188506859685729973), 0], [(-188506859685694100)]]], r := 51887821066397592, ok := true }, term0 := { p := [[[52508049368450230712911299]], [[(-4562471203622774094877636), 0], [(-4556089117007225518163935)]], [[297477679838274438869370, 0, 0], [396032082280572644385296, 0], [296922715643288381945591]], [[(-17242915060285611713152), 0, 0, 0], [(-25824927530034154791610), 0, 0], [(-25812863091017375463704), 0], [(-17206721743225960014155)]], [[937044258856177763858, 0, 0, 0, 0], [1497002994688363254024, 0, 0, 0], [1683306212747902140424, 0, 0], [1495953913034460021872, 0], [934946095548371859904]]], r := 488964511064193680587, ok := true }, r0 := { p := [[[7800848761375944360287]], [[(-226070527682300337460), 3071317556712579055630], [(-287488568317429785456)]], [[6241446260683423143, (-87497511394594928545), 287872024655475015179], [7959894345384197449, (-113765592142339581065)], [11713628216912835827]], [[(-196380565900095322), 2393882727199880594, (-7609498750869243274), (-3714793869590101217)], [(-207175815524517814), 3112253390932111992, (-10889220772204391295)], [(-319649097051603817), 4640563893538479851], [(-489202982561516343)]], [[7019656513956825, (-75448523091258802), 199875536169398416, 215545481830734992, (-152421171204306974)], [6248056117197338, (-80475104393388703), 282953970923442165, 95632404940458167], [8158427882013614, (-125252637552540942), 446263288519602026], [13234049441016235, (-193930749475285110)], [20663855277264755]]], r := 354466477786722137, ok := true }, r1 := { p := [[[19493964102988131912034]], [[(-550682594805585319426), 0], [(-723870448574769851309)]], [[15010892583296918934, 0, 0], [19677350912995345085, 0], [29544977281104578138]], [[(-473847583579719544), 0, 0, 0], [(-507194423694528592), 0, 0], [(-792831163186246619), 0], [(-1235115067942060577)]], [[17081925367897452, 0, 0, 0, 0], [15343564785185864, 0, 0, 0], [20048233590629022, 0, 0], [32887527411861418, 0], [52205671655792047]]], r := 98644883468467084, ok := true }, r2 := { p := [[[5660066725348742664187390]], [[(-207776893126813273908648), 4017686410441041843928], [(-470760919023402262741214)]], [[7732414537457799825455, (-104675516978358749183), 455447605892672649], [16878314190499947458009, (-166251299612909359096)], [29902723374079195039801]], [[(-308121214951481961874), 3312802757366446886, 469079738697697, (-135466293022522)], [(-620861676954000786290), 4049107764506442067, 132781173985685], [(-1056511210564340481813), 7101667653128283908], [(-1701870082420228827279)]], [[12775091109349677627, (-122065810357826560), (-10472772922243), 1199879115529, 38620109337], [24642277227167438778, (-123173993326263500), 6871743975744, (-5993238344024)], [38581527828949634150, (-168435752091554890), (-2620077408625)], [59498818702960096451, (-305504620576637456)], [91207301613598631825]]], r := 312288456574335705162, ok := true }, r3 := { p := [[[104413575993612717565198710]], [[(-9076499105324220741515412), 85376037629745928820498], [(-9085949850240050210340211)]], [[591881569862828980542409, (-6873872048651802968142), 1495209215038804815], [789955710909346752205755, (-3723540161046005375914)], [592704532738936432725423]], [[(-34310112109633538762983), 436396553988110820688, 25389671186704920, (-973357051765392)], [(-51516087931377458382196), 299601064144022698739, (-2340140764232751)], [(-51534020621826865472884), 162071311035709828865], [(-34363825977128548892940)]], [[1864619010339416641820, (-24955836680017026964), (-1399078457592240), 1675189873143, 494665714829], [2986359553641351680271, (-19014913571702770337), 203969243467133, (-41945485820084)], [3360794545085868380991, (-13037371723853445134), 30354386357681], [2987919780613872760112, (-7050988565438250542)], [1867734516624266541755]]], r := 62345428527273293480310, ok := true }, eta := { p := [[[(-5724818199846802306552919)]], [[210745216133402077465904, 0], [473491717362796910094959]], [[(-7860634407018072616838), 0, 0], [(-17002761769087099209417), 0], [(-30020212680776041420074)]], [[313653155567440328961, 0, 0, 0], [626228561696179349849, 0, 0], [1061853651555835074651, 0], [1706946747719911972042]], [[(-13014437757445057078), 0, 0, 0, 0], [(-24873834094389173583), 0, 0, 0], [(-38811824626837253143), 0, 0], [(-59729366877820185998), 0], [(-91427076875946129321)]]], r := 32294163813419486470, ok := true } }
theorem sB_7 : stageB c7 w7 = true := by decide +kernel
theorem s0_7 : stageC0 w7 q7 = true := by decide +kernel
theorem s1_7 : stageC1 w7 q7 = true := by decide +kernel
theorem s2_7 : stageC2 w7 q7 = true := by decide +kernel
theorem s3_7 : stageC3 w7 q7 = true := by decide +kernel
theorem sE_7 : stageE w7 q7 = true := by decide +kernel
theorem sF_7 : stageF w7 = true := by decide +kernel
theorem ok_7 : (domOK c7 && cellCheck c7 q7) = true :=
staged_check c7 q7 w7 (by decide +kernel) sB_7 s0_7 s1_7 s2_7 s3_7 sE_7 sF_7
theorem region : RegionPosI 45035996273704960 54043195528445952 9223372036854775808 13835058055282163712 2305843009213693952 3458764513820540928 :=
(RegionPosI.split_s 2882303761517117440 (RegionPosI.split_s 2594073385365405696 (RegionPosI.split_b 49539595901075456 (RegionPosI.of_check c0 q0 ok_0 45035996273704960 49539595901075456 9223372036854775808 13835058055282163712 2305843009213693952 2594073385365405696 (by decide +kernel)) (RegionPosI.of_check c1 q1 ok_1 49539595901075456 54043195528445952 9223372036854775808 13835058055282163712 2305843009213693952 2594073385365405696 (by decide +kernel))) (RegionPosI.split_b 49539595901075456 (RegionPosI.of_check c2 q2 ok_2 45035996273704960 49539595901075456 9223372036854775808 13835058055282163712 2594073385365405696 2882303761517117440 (by decide +kernel)) (RegionPosI.of_check c3 q3 ok_3 49539595901075456 54043195528445952 9223372036854775808 13835058055282163712 2594073385365405696 2882303761517117440 (by decide +kernel)))) (RegionPosI.split_b 49539595901075456 (RegionPosI.split_s 3170534137668829184 (RegionPosI.of_check c4 q4 ok_4 45035996273704960 49539595901075456 9223372036854775808 13835058055282163712 2882303761517117440 3170534137668829184 (by decide +kernel)) (RegionPosI.of_check c5 q5 ok_5 45035996273704960 49539595901075456 9223372036854775808 13835058055282163712 3170534137668829184 3458764513820540928 (by decide +kernel))) (RegionPosI.split_s 3170534137668829184 (RegionPosI.of_check c6 q6 ok_6 49539595901075456 54043195528445952 9223372036854775808 13835058055282163712 2882303761517117440 3170534137668829184 (by decide +kernel)) (RegionPosI.of_check c7 q7 ok_7 49539595901075456 54043195528445952 9223372036854775808 13835058055282163712 3170534137668829184 3458764513820540928 (by decide +kernel)))))
end CKLaneC.RSC2.S06_0011