Courtade–Kumar proof module `CKLaneC.RSC2.S03_0151` (transplant)
DefinitionCK_CKLaneC_RSC2_S03_0151Verbatim transplant of the Lean module CKLaneC.RSC2.S03_0151 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.S03_0151 from release v1.0 (sources_v3.tar.zst).
import Definitions.Def_CK_CKLaneC_RSC2_S03_0151_part00
/-! RA-stat cover batch S03_0151 (generated by tools/emit_cover2.py; compact format). -/
namespace CKLaneC.RSC2.S03_0151
open CKLaneC.TM3 CKLaneC.RSCell
noncomputable def c3 : Cell := { bc := 8725724278030336, bh := 281474976710656, tc := 6917529027641081856, th := 2305843009213693952, sc := 13258597302978740224, sh := 576460752303423488 }
noncomputable def q3 : Cert := { V0 := [[[178425800323233643]], [[(-22768062132005863), 59467239445940637], [654528689930999]], [[383363614054318, (-7586281131508212), (-4013025395013)], [(-82403776987481), 218087890909003], [(-8153830625989)]], [[(-7434571354509), 127344034400382, 1536048664933, (-445536860088)], [1273370878719, (-27434260273720), (-44157816969)], [1030715679185, (-2717167091946)], [158357551000]], [[156297495131, (-2447309196210), (-221807600209), 170445693771, 88677159], [(-26616608898), 419629311874, 16825239001, (-4899916209)], [(-16354424692), 343274873016, 388165018], [(-20040247608), 52772154801], [(-3595726789)]]], r0 := 4987105482453, V1 := [[[475606053633244090]], [[(-60639807930426526), 0], [1743253062656361]], [[1011478422903402, 0, 0], [(-218922141279043), 0], [(-21724581887083)]], [[(-19074426288972), 0, 0, 0], [3278098206173, 0, 0], [2741323255665, 0], [421952248881]], [[387082758975, 0, 0, 0, 0], [(-62929968891), 0, 0, 0], [(-42566693250), 0, 0], [(-53312676203), 0], [(-9581446664)]]], r1 := 1816427094904, V2 := [[[18431771148440442974]], [[(-278725709862972), 280881307854], [(-482937284564135)]], [[429338869229, (-25907470212), (-5008077)], [(-9012090939077), 18251929668], [650889855]], [[(-7923382584), (-596397745), 1017546, 87], [15641322159, (-1682582927), (-488521)], [(-369845229), 299145267], [(-17033689)]], [[190848764, 959189, (-40515), (-27), 0], [(-283725761), (-38884400), 99236, 11], [37181883, (-27545386), (-15963)], [3993418, 65289], [240371]]], r2 := 41173636360, V3 := [[[18434198497710863126]], [[(-545200378142813), 469553380228], [(-404772784288168)]], [[11455661480, (-31492705597), (-16718170)], [(-17581969685253), 30509204026], [(-2498456807)]], [[4437207, (-2290923621), 2972599, 584], [745027468, (-2044720382), (-1630521)], [167044415, 499957599], [(-529032)]], [[(-53181), (-842093), (-41800), (-168), 0], [318520, (-148985248), 289819, 76], [12233294, (-33456171), (-53266)], [31106, 108751], [2977]]], r3 := 248512234561, Vm := [[[18431772576378515643]], [[(-278860433767136), 0], [(-482844401961193)]], [[426638904976, 0, 0], [(-9020861296782), 0], [2176604233]], [[(-7918328061), 0, 0, 0], [15466286159, 0, 0], [(-514166804), 0], [(-16655458)]], [[190775490, 0, 0, 0, 0], [(-283373145), 0, 0, 0], [34328061, 0, 0], [3954036, 0], [238244]]], rm := 5195967830 }
noncomputable def w3 : Wit := { Z0 := { p := [[[178437842753535343]], [[(-22772672417989140), 59479280917845114], [654661224901581]], [[384029619023634, (-7590890805996380), 0], [(-82454291849959), 218220408300527], [(-8154995436088)]], [[(-7480931294704), 128009873007878, 0, 0], [1280616899180, (-27484763949987), 0], [1031161295669, (-2718331812030)], [158378096567]], [[158146416776, (-2493643764902), 0, 0, 0], [(-27115333583), 426872299726, 0, 0], [(-16418723923), 343720431889, 0], [(-20048111490), 52792698855], [(-3596166365)]]], r := 1191737726736, ok := true }, Z1 := { p := [[[475834247342760916]], [[(-60727126447971039), 0], [1745763266404216]], [[1024078984063024, 0, 0], [(-219878111599891), 0], [(-21746654496235)]], [[(-19949150119210), 0, 0, 0], [3414978397815, 0, 0], [2749763455117, 0], [422341590846]], [[421723778070, 0, 0, 0, 0], [(-72307556219), 0, 0, 0], [(-43783263794), 0, 0], [(-53461630640), 0], [(-9589776971)]]], r := 452669919097, ok := true }, Z2 := { p := [[[3573485564497368958233]], [[(-59022812598760303785), 59479280917845114], [(-102266550358043506884)]], [[1135209402969371830, (-7590890805996380), 0], [1710416051667025139, 218220408300527], [3135225614598828660]], [[(-23725166892237490), 128009873007878, 0, 0], [(-32610196791549162), (-27484763949987), 0], [(-52666195066667674), (-2718331812030)], [(-97959825687318840)]], [[531820869942333, (-2493643764902), 0, 0, 0], [670614515477789, 426872299726, 0, 0], [1001295185990123, 343720431889, 0], [1649772844411472, 52792698855], [3087883976918722]]], r := 1430518725739903, ok := true }, Z3 := { p := [[[4181481984490519479292]], [[(-161615643089949726646), 139191340565625466], [(-119988203348064851360)]], [[6684655363397010038, (-20843950790559251), 0], [4708842480437800132, 499731485499104], [3681978972303765520]], [[(-281668136905062503), 820039123593697, 0, 0], [(-195798241825818201), (-72413050221518), 0], [(-145264821045057421), (-6264654532932)], [(-115106854376476713)]], [[11971679339153778, (-34090933127117), 0, 0, 0], [8276023544071378, 2540620989705, 0, 0], [6052186674319374, 916527853409, 0], [4555499880176815, 121883037267], [3629797528640322]]], r := 12188744828443775, ok := true }, iE := { p := [[[3576690836857941722738]], [[(-59055909469602742044), 0], [(-102254790702707311814)]], [[1135899985763637771, 0, 0], [1710314296783175504, 0], [3135079126717847083]], [[(-23740145204758323), 0, 0, 0], [(-32607660803808279), 0, 0], [(-52664854896328913), 0], [(-97956980747436057)]], [[532166176634556, 0, 0, 0, 0], [670551510927155, 0, 0, 0], [1001263738353119, 0, 0], [1649746422925011, 0], [3087819379115517]]], r := 1430451713001733, ok := true }, iHu := { p := [[[4185023630822689282819]], [[(-161706092465190992032), 0], [(-119975487958044929712)]], [[6688522889140344874, 0, 0], [4708579368879543629, 0], [3681819571649538715]], [[(-281832490301950698), 0, 0, 0], [(-195786969437182469), 0, 0], [(-145261299904990181), 0], [(-115103753130306227)]], [[11978691982107520, 0, 0, 0, 0], [8275554563052564, 0, 0, 0], [6052037022796642, 0, 0], [4555430139232191, 0], [3629727036941152]]], r := 12189802902472354, ok := true }, T := { p := [[[6917529027641081856]], [[0, 2305843009213693952], [0]]], r := 0, ok := true }, E := { p := [[[95138881844165870]], [[1570869121627536, 0], [2719946144188132]], [[(-4277459415633), 0, 0], [44325999629303, 0], [(-5631014765039)]], [[61971081876, 0, 0, 0], [(-138029489736), 0, 0], [(-102408976256), 0], [60523262516]], [[(-1347197587), 0, 0, 0, 0], [1999066695, 0, 0, 0], [(-1514319), 0, 0], [1100422770, 0], [(-976181826)]]], r := 1907940849, ok := true }, de := { p := [[[(-106269397424497666510)]], [[578740810865480996, 0], [429388343545356868]], [[(-12577043061154726), 0, 0], [6349356527858, 0], [(-6923263037826067)]], [[364552014968570, 0, 0, 0], [93887804, 0, 0], [69658693, 0], [148887394384968]], [[(-11887565705029), 0, 0, 0, 0], [1389, 0, 0, 0], [1515865, 0, 0], [765, 0], [(-3602114380139)]]], r := 2641657503369, ok := true }, dde := { p := [[[(-39151853193166619374316)]], [[1701675549018500390917, 0], [1262533471852435772803]], [[(-73985901996325855171), 0, 0], [(-54892772348789968093), 0], [(-40726890901203304376)]], [[3216778347539758975, 0, 0, 0], [2386641999599721873, 0, 0], [1770734386799793770, 0], [1313770674180668779]], [[(-139859928153899578), 0, 0, 0, 0], [(-103767043469027008), 0, 0, 0], [(-76988451609085286), 0, 0], [(-57120464094813180), 0], [(-42379699167116909)]]], r := 20595750326177121, ok := true }, nJu := { p := [[[(-212538794848995333020)]], [[1157481621730961993, 0], [858776687090713737]], [[(-25154086122309451), 0, 0], [12698713055717, 0], [(-13846526075652134)]], [[729104029937141, 0, 0, 0], [187775608, 0, 0], [139317386, 0], [297774788769937]], [[(-23775131410058), 0, 0, 0, 0], [2778, 0, 0, 0], [3031730, 0, 0], [1530, 0], [(-7204228760278)]]], r := 5283315006732, ok := true }, Jd1 := { p := [[[(-78303706386333238748632)]], [[3403351098037000781834, 0], [2525066943704871545606]], [[(-147971803992651710341), 0, 0], [(-109785544697579936186), 0], [(-81453781802406608752)]], [[6433556695079517951, 0, 0, 0], [4773283999199443747, 0, 0], [3541468773599587541, 0], [2627541348361337558]], [[(-279719856307799156), 0, 0, 0, 0], [(-207534086938054016), 0, 0, 0], [(-153976903218170571), 0, 0], [(-114240928189626359), 0], [(-84759398334233818)]]], r := 41191500652354235, ok := true }, term0 := { p := [[[115290409800466158051077858]], [[(-10020142209864326646881062), 0], [(-7432542490622932924665521)]], [[653376556662832910110251, 0, 0], [646143364480587830023461, 0], [359549730725182108763917]], [[(-37873685057177514863922), 0, 0, 0], [(-42136204674136040398667), 0, 0], [(-31259881772940056286527), 0], [(-15462581491694729396072)]], [[2058247553813504486700, 0, 0, 0, 0], [2442574764790586257475, 0, 0, 0], [2038572459036164367418, 0, 0], [1344400942233335313606, 0], [623444663641924809844]]], r := 557310420662797162099, ok := true }, r0 := { p := [[[3839019100611691051256]], [[(-197977274021528999201), 2558789458665296761886], [(-110090014710260439561)]], [[7791591972240170307, (-131814300735569461246), 426093926728603649305], [5719518829343075200, (-73381461761321951012)], [3378778946378620209]], [[(-276881335124931213), 5174563849181120167, (-21855401145165918945), (-123601547868943000)], [(-222708024640934390), 3809358079951139583, (-12222323957835333899)], [(-175977580832451745), 2252189792277157259], [(-105635787877870997)]], [[9501231731517519, (-183329539350618253), 849218759924796221, 37849605786092374, (-10275359872314233)], [7779490291548964, (-148044854223461733), 632457403386458385, 2639056322877806], [6827938852639961, (-117216954332969631), 375145327071359909], [5509978886844991, (-70414178613556558)], [3331289415130863]]], r := 172328968962238020, ok := true }, r1 := { p := [[[27263461996731995634422]], [[(-1396751021888814528708), 0], [(-782088583454617968636)]], [[54121340002600935834, 0, 0], [40434337449456551102, 0], [24005412689141944411]], [[(-1887898666354641585), 0, 0, 0], [(-1555958142395444432), 0, 0], [(-1244794952894794656), 0], [(-750557364056884024)]], [[63656732354904186, 0, 0, 0, 0], [53561182596450914, 0, 0, 0], [47783084345772961, 0, 0], [38988034661636580, 0], [23670154702914616]]], r := 53014307100947448, ok := true }, r2 := { p := [[[49174426432792986520821929]], [[(-2346999951660736472071803), 9057004492045103557502], [(-3137223734305349812877168)]], [[91977973764826063825049, (-307802983525771172167), 460124285454568734], [148049686320293739095943, (-291859299565049362746)], [150795694422078443068048]], [[(-3487962002709739908112), 10086937821639533181, 321436318462170, (-7875384599375)], [(-5736205360136133306782), 9704216966856656743, 155387677666590], [(-7067346728091135995709), 9410016344202578978], [(-6455823038042406040486)]], [[133769777653849245002, (-337443505165015517), (-6363070689674), 809977459071, (-24068584631)], [215343741155787241585, (-310482241010823148), 2245980297063, (-302312326162)], [271903087572793974943, (-310254063369668662), (-2005267513114)], [301088299563951127098, (-303442595176128134)], [259399710969679889057]]], r := 1961728043225040699555, ok := true }, r3 := { p := [[[230163008045936825196597701]], [[(-20011504141780403800274650), 46105658107736180847013], [(-14851584791098804595477022)]], [[1305040453392129745407583, (-3181363196406949716275), 1827960944415676751], [1291357092295919343330485, (-1492399891718147570008)], [718663685603021366743146]], [[(-75652848477536971144232), 189413983538416158690, 3320625264066968, (-62593815556007)], [(-84217099236453569980594), 102872064583187650536, 535121267892428], [(-62489761350489876210871), 48199044657787890444], [(-30911100486717475173486)]], [[4111513315015308454366, (-10456818554593930292), (-130272086324448), 6310055508136, (-184209305854)], [4882097287097274215434, (-6122707905293261570), 21828985420515, (-2181902995785)], [4075359995420258026786, (-3321240735795922625), (-6807405794729)], [2687833811547423620648, (-1555850904236754392)], [1246435583630394488700]]], r := 62928853868646041330995, ok := true }, eta := { p := [[[(-49271635734464719627491065)]], [[2351704316841109461215175, 0], [3140329008862589714931311]], [[(-92183416782936819136136), 0, 0], [(-148198898592528639709274), 0], [(-150895509374295730351400)]], [[3496728186514969489608, 0, 0, 0], [5742685326638563459306, 0, 0], [7072128658923520743477, 0], [6459036012569784620857]], [[(-134143120471280851297), 0, 0, 0, 0], [(-215619282282503018045), 0, 0, 0], [(-272110306060444765511), 0, 0], [(-301241948536079775089), 0], [(-259503200097791821511)]]], r := 214771643033046382063, ok := true } }
theorem sB_3 : stageB c3 w3 = true := by decide +kernel
theorem s0_3 : stageC0 w3 q3 = true := by decide +kernel
theorem s1_3 : stageC1 w3 q3 = true := by decide +kernel
theorem s2_3 : stageC2 w3 q3 = true := by decide +kernel
theorem s3_3 : stageC3 w3 q3 = true := by decide +kernel
theorem sE_3 : stageE w3 q3 = true := by decide +kernel
theorem sF_3 : stageF w3 = true := by decide +kernel
theorem ok_3 : (domOK c3 && cellCheck c3 q3) = true :=
staged_check c3 q3 w3 (by decide +kernel) sB_3 s0_3 s1_3 s2_3 s3_3 sE_3 sF_3
theorem region : RegionPosI 7881299347898368 9007199254740992 4611686018427387904 9223372036854775808 11529215046068469760 13835058055282163712 :=
(RegionPosI.split_s 12682136550675316736 (RegionPosI.split_b 8444249301319680 (RegionPosI.of_check c0 q0 ok_0 7881299347898368 8444249301319680 4611686018427387904 9223372036854775808 11529215046068469760 12682136550675316736 (by decide +kernel)) (RegionPosI.of_check c1 q1 ok_1 8444249301319680 9007199254740992 4611686018427387904 9223372036854775808 11529215046068469760 12682136550675316736 (by decide +kernel))) (RegionPosI.split_b 8444249301319680 (RegionPosI.of_check c2 q2 ok_2 7881299347898368 8444249301319680 4611686018427387904 9223372036854775808 12682136550675316736 13835058055282163712 (by decide +kernel)) (RegionPosI.of_check c3 q3 ok_3 8444249301319680 9007199254740992 4611686018427387904 9223372036854775808 12682136550675316736 13835058055282163712 (by decide +kernel))))
end CKLaneC.RSC2.S03_0151