Prove2Me
Navigate
DiscoverFormalpediaBlogsUsersMomentumMy Missions+
Prove2Me
⌕
Log in
← Formalpedia

Courtade–Kumar proof module `CKLaneC.RSC2.S01_0317` (transplant)

Definition
CK_CKLaneC_RSC2_S01_0317

by tianyipeng · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

general-courtade-kumartransplant

Verbatim transplant of the Lean module CKLaneC.RSC2.S01_0317 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.S01_0317 from release v1.0 (sources_v3.tar.zst).

Definition code
import Definitions.Def_CK_CKLaneC_RSC2_S01_0317_part00

/-! RA-stat cover batch S01_0317 (generated by tools/emit_cover2.py; compact format). -/

namespace CKLaneC.RSC2.S01_0317
open CKLaneC.TM3 CKLaneC.RSCell

theorem s2_4 : stageC2 w4 q4 = true := by decide +kernel
theorem s3_4 : stageC3 w4 q4 = true := by decide +kernel
theorem sE_4 : stageE w4 q4 = true := by decide +kernel
theorem sF_4 : stageF w4 = true := by decide +kernel
theorem ok_4 : (domOK c4 && cellCheck c4 q4) = true :=
  staged_check c4 q4 w4 (by decide +kernel) sB_4 s0_4 s1_4 s2_4 s3_4 sE_4 sF_4

noncomputable def c5 : Cell := { bc := 1583296743997440, bh := 35184372088832, tc := 16140901064495857664, th := 2305843009213693952, sc := 15852670688344145920, sh := 288230376151711744 }
noncomputable def q5 : Cert := { V0 := [[[162195803142053151]], [[(-19262600305819213), 23168244720672458], [345446771513251]], [[148424430899620, (-2750879316995334), (-553705652627)], [(-40760920691331), 49333026891053], [(-3102447353454)]], [[(-1267584524617), 21087054315699, 197255326946, (-26349596020)], [284630953244, (-5817118596605), (-3537487920)], [366647455246, (-443093637419)], [42079959078]], [[11461353764, (-175010251895), (-24939925705), 9382815191, 1857223], [(-2462553737), 39922164609, 1257412950, (-168267170)], [(-2624796028), 52337935616, 24237914], [(-4975512308), 6010018038], [(-663561262)]]], r0 := 456026972587, V1 := [[[185363467809387159]], [[(-22013272985806422), 0], [394776092669556]], [[169485360476491, 0, 0], [(-46576722119716), 0], [(-3545515599737)]], [[(-1441233205056), 0, 0, 0], [324387277752, 0, 0], [418976353003, 0], [48089661836]], [[12950182980, 0, 0, 0, 0], [(-2767556532), 0, 0, 0], [(-2993540582), 0, 0], [(-5685687323), 0], [(-758330031)]]], r1 := 85528131789, V2 := [[[18443801019453605731]], [[(-24943871674839), 4910812878], [(-65399214619737)]], [[12634631454, (-503603060), (-7843)], [(-554778300221), 219361812], [25811825]], [[(-101452770), (-4690559), 1675, 0], [310154985, (-22492836), (-526)], [(-6220271), 2464460], [(-161735)]], [[1036933, 2290, (-82), 0, 0], [(-2465051), (-209861), 112, 0], [395365, (-252632), (-12)], [37036, 245], [1619]]], r2 := 630719312, V3 := [[[18444022773356393391]], [[(-49477181615078), 9074441596], [(-60473544848705)]], [[18496758, (-841640746), (-28972)], [(-1099474042222), 405322966], [(-4553002)]], [[2089, (-18496519), 5903, 0], [826899, (-37585950), (-1942)], [422017, 4553045], [(-447)]], [[(-11), (-2083), (-239), (-1), 0], [103, (-826883), 396, 0], [9307, (-422026), (-44)], [39, 447], [2]]], r3 := 2236156615, Vm := [[[18443801024522013518]], [[(-24944410169079), 0], [(-65398987847021)]], [[12631858775, 0, 0], [(-554802433393), 0], [28368709]], [[(-101449152), 0, 0, 0], [310035215, 0, 0], [(-6493349), 0], [(-161397)]], [[1036933, 0, 0, 0, 0], [(-2464875), 0, 0, 0], [394120, 0, 0], [36991, 0], [1617]]], rm := 59262606 }
noncomputable def w5 : Wit := { Z0 := { p := [[[162204849083091441]], [[(-19265823379147016), 23172121297584491], [345504572654208]], [[148832086195091, (-2752260482735288), 0], [(-40781471584695), 49357796093458], [(-3102843344086)]], [[(-1288857828973), 21261726599298, 0, 0], [287220233307, (-5825924512100), 0], [366788434864, (-443263334870)], [42084875997]], [[11887478782, (-184122546997), 0, 0, 0], [(-2596530837), 41031461901, 0, 0], [(-2642601435), 52398347837, 0], [(-4977263317), 6012125142], [(-663634720)]]], r := 110707567827, ok := true }, Z1 := { p := [[[185376970380675932]], [[(-22018083861882304), 0], [394862368747666]], [[170093812794390, 0, 0], [(-46607396096795), 0], [(-3546106678955)]], [[(-1472980375969), 0, 0, 0], [328251695208, 0, 0], [419186782701, 0], [48097001139]], [[13585690036, 0, 0, 0, 0], [(-2967463814), 0, 0, 0], [(-3020115926), 0, 0], [(-5688300934), 0], [(-758439680)]]], r := 21367900137, ok := true }, Z2 := { p := [[[15356091033626890522960]], [[(-117699947936419585989), 23172121297584491], [(-308592196759502585245)]], [[1014447201423467449, (-2752260482735288), 0], [2389076838826392832, 49357796093458], [6563738053068324238]], [[(-9317607069230506), 21261726599298, 0, 0], [(-20514374695101058), (-5825924512100), 0], [(-51004875691649600), (-443263334870)], [(-141875577633958692)]], [[90252725570421, (-184122546997), 0, 0, 0], [186712263684381, 41031461901, 0, 0], [437406668842607, 52398347837, 0], [1104925523265636, 6012125142], [3089949403097776]]], r := 487583266867067, ok := true }, Z3 := { p := [[[16483893251698419838720]], [[(-271241014363500258718), 49747391886941609], [(-331524656649413920285)]], [[4721754724680141128, (-6345960176293285), 0], [5514618346621264486, 105142699997751], [7053643533690190665]], [[(-83519629246282241), 105189403029424, 0, 0], [(-96385126571161298), (-13230500430252), 0], [(-117803921275603332), (-945986682839)], [(-152492563041998306)]], [[1488461712877397, (-1835140264053), 0, 0, 0], [1708988479391268, 197780444423, 0, 0], [2062197658678577, 119422265005, 0], [2552930087117640, 12838381697], [3321604180820331]]], r := 2140923186218576, ok := true }, iE := { p := [[[15358565301245443711453]], [[(-117700886809338733967), 0], [(-308586926443719717082)]], [[1014472515086093136, 0, 0], [2389078739592992275, 0], [6563690722394456527]], [[(-9317917737990773), 0, 0, 0], [(-20514313525111983), 0, 0], [(-51004884436642904), 0], [(-141874935672596256)]], [[90256331617804, 0, 0, 0, 0], [186711366310135, 0, 0, 0], [437406141288833, 0, 0], [1104925605386611, 0], [3089939280034837]]], r := 487538196881916, ok := true }, iHu := { p := [[[16486375093804779481237]], [[(-271243154615676642161), 0], [(-331519411196936254674)]], [[4721828954519005025, 0, 0], [5514622897363983056, 0], [7053596339465680172]], [[(-83521120615003313), 0, 0, 0], [(-96385044275688760), 0, 0], [(-117803943001637008), 0], [(-152491922549400268)]], [[1488489770145749, 0, 0, 0, 0], [1708986397704595, 0, 0, 0], [2062196793812017, 0, 0], [2552930297261427, 0], [3321594077349560]]], r := 2140786918973756, ok := true }, T := { p := [[[16140901064495857664]], [[0, 2305843009213693952], [0]]], r := 0, ok := true }, E := { p := [[[22155869395779082]], [[169792257594765, 0], [445159525348212]], [[(-162243100753), 0, 0], [3376567033599, 0], [(-524389129931)]], [[983218986, 0, 0, 0], [(-3605668195), 0, 0], [(-4406927795), 0], [3884052172]], [[(-8938354), 0, 0, 0, 0], [21849311, 0, 0, 0], [(-5911), 0, 0], [32639094, 0], [(-43156135)]]], r := 21528721, ok := true }, de := { p := [[[(-126606283590887901512)]], [[241954448520070565, 0], [295722103746752912]], [[(-2199423640568197), 0, 0], [396623501533, 0], [(-3285558771712984)]], [[26659680636814, 0, 0, 0], [531953, 0, 0], [650165, 0], [48674945031001]], [[(-363541099592), 0, 0, 0, 0], [1, 0, 0, 0], [5912, 0, 0], [1, 0], [(-811249083849)]]], r := 100678890905, ok := true }, dde := { p := [[[(-180414313110315741433370)]], [[3280018266072799486964, 0], [4008911214088977146496]], [[(-59636696071312222371), 0, 0], [(-72889295594923286527), 0], [(-89086916353441738199)]], [[1084303564932530353, 0, 0, 0], [1325259912694246263, 0, 0], [1619762115515184870, 0], [1979709252297921627]], [[(-19714610271492757), 0, 0, 0, 0], [(-24095634776269267), 0, 0, 0], [(-29450220282121459), 0, 0], [(-35994713678140088), 0], [(-43993538939944468)]]], r := 3857244819619433, ok := true }, nJu := { p := [[[(-253212567181775803023)]], [[483908897040141130, 0], [591444207493505824]], [[(-4398847281136393), 0, 0], [793247003067, 0], [(-6571117543425968)]], [[53319361273628, 0, 0, 0], [1063907, 0, 0], [1300330, 0], [97349890062002]], [[(-727082199184), 0, 0, 0, 0], [2, 0, 0, 0], [11825, 0, 0], [3, 0], [(-1622498167698)]]], r := 201357781803, ok := true }, Jd1 := { p := [[[(-360828626220631482866740)]], [[6560036532145598973928, 0], [8017822428177954292992]], [[(-119273392142624444742), 0, 0], [(-145778591189846573054), 0], [(-178173832706883476398)]], [[2168607129865060707, 0, 0, 0], [2650519825388492527, 0, 0], [3239524231030369740, 0], [3959418504595843254]], [[(-39429220542985514), 0, 0, 0, 0], [(-48191269552538533), 0, 0, 0], [(-58900440564242918), 0, 0], [(-71989427356280176), 0], [(-87987077879888935)]]], r := 7714489639238862, ok := true }, term0 := { p := [[[2446510089982625366676384708]], [[(-88954160797544426827347405), 0], [(-108717087171020329137034025)]], [[2425933112165057102644617, 0, 0], [3953129956522551234963060, 0], [3623717442942694800687371]], [[(-58809415385285360163047), 0, 0, 0], [(-107810647287943352981699), 0, 0], [(-131766684093388141988178), 0], [(-107366658120343441316783)]], [[1336562836434939944129, 0, 0, 0, 0], [2613567353769678732785, 0, 0, 0], [3593592663579949905104, 0, 0], [3904134129325900681163, 0], [2982361376734667608990]]], r := 485099407731297784788, ok := true }, r0 := { p := [[[77567717553770049632679]], [[(-1808499320709985325855), 22158217587379485652469], [(-1560535550657501780332)]], [[31228054633131895022, (-515674360213992251093), 1581590788986024782010], [36703711584702010246, (-445804060581476015070)], [33208624163214419186]], [[(-476923188634419134), 8835187597752268945, (-36536929580856396375), (-162655123482022258)], [(-631887163431557384), 10470254459695742902, (-31825081352439532034)], [(-783549682769867236), 9486947282819318544], [(-718012982089496280)]], [[6906738721847021, (-133461021487415695), 606217768598759979, 42389671642797665, (-5797563656377522)], [9575980042661362, (-179149794260579353), 743156550263148085, 2580082653461685], [13474882571059782, (-223549585429553963), 677287410175220559], [16973540328010576, (-205121374831247000)], [15640973387995836]]], r := 119505986974233300, ok := true }, r1 := { p := [[[101307357478460932304777]], [[(-2360666713172699745457), 0], [(-2038162020508694020980)]], [[40665788618482094401, 0, 0], [47916424870282693444, 0], [43372806838215746144]], [[(-619001359856743645), 0, 0, 0], [(-823378060618463379), 0, 0], [(-1022961599833042500), 0], [(-937777622551213165)]], [[8931787793515754, 0, 0, 0, 0], [12444361059931875, 0, 0, 0], [17561946234465052, 0, 0], [22160306047226857, 0], [20428288368836936]]], r := 9985469176633897, ok := true }, r2 := { p := [[[1190078548639835655432373955]], [[(-24308878545302124885743089), 43361786279167529708036], [(-52552832228881123217997175)]], [[399892071085180175346513, (-629374796846875792164), 454225204688186545], [1065396925139602348577422, (-964397060551097539599)], [1745023715513999521551077]], [[(-6273441294166483974623), 8678775146406939250, 22854760977554, (-1709147878411)], [(-17381757245870968340082), 13819673713538146050, 47773403070002], [(-35213183935358817168514), 21436648838946499930], [(-51564666076158871202986)]], [[98677178650009623324, (-120246685980390740), (-61314119154963), (-8833210890047), (-310767385626)], [270488148192825850788, (-187625447868641388), (-36158170295214), (-1187641057989)], [571550600978144909704, (-305620489033962924), (-21728281020290)], [1037104873715526908743, (-476486309841899063)], [1429395744651828640711]]], r := 3211523754640030127047, ok := true }, r3 := { p := [[[4892046414000204171197279377]], [[(-177881084999223818285140613), 193066569959831989201569], [(-217412527102226874997109949)]], [[4851197721927806250285214, (-5409566246819629312336), 1813275154844565266], [7905654464463197753481003, (-4299588269975446173829)], [7246953760577352172015658]], [[(-117603525584323698966018), 132856179743654054673, 613960468976603, (-10343102049241)], [(-215606435200064495770871), 120402958034740840076, 18882828986078], [(-263519912515108584722044), 95621492532130202282], [(-214722623883278659707964)]], [[2672789990272366065901, (-3043080051388479341), (-241452361496551), (-48670549278952), (-1578545286403)], [5226794379860069885189, (-2956767916421217631), (-45073532653685), (-5826237412493)], [7186854726933992853240, (-2677259295840012174), (-335035358621538)], [7807969084008555062219, (-2125952746942276831)], [5964485045140994478269]]], r := 45819914846163715803171, ok := true }, eta := { p := [[[(-1190338366357579810456988366)]], [[24315205341017203138129411, 0], [52558549542776383168312612]], [[(-400019558592326613536091), 0, 0], [(-1065536132790916653931534), 0], [(-1745150283749339489749896)]], [[6275855098483139186648, 0, 0, 0], [17384559096344209324701, 0, 0], [35216265058184072488189, 0], [51567472165842367140492]], [[(-98721791045263738169), 0, 0, 0, 0], [(-270541201788686606141), 0, 0, 0], [(-571612624776264025380), 0, 0], [(-1037173235597831178141), 0], [(-1429458050850505050541)]]], r := 341331343572597275449, 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 := 1653665488175104, bh := 35184372088832, tc := 16140901064495857664, th := 2305843009213693952, sc := 15276209936040722432, sh := 288230376151711744 }
noncomputable def q6 : Cert := { V0 := [[[202166302521213555]], [[(-19954274315281427), 28875896062687138], [413342389611510]], [[156903217772172, (-2849128855842168), (-1072130340792)], [(-40479061940912), 59018218902754], [(-3552045042688)]], [[(-1369046066977), 22256852319839, 317412000833, (-51001665668)], [289363505126, (-5773658603323), (-6575024121)], [348522954772, (-507233989863)], [46118647349]], [[12672183684, (-188366537535), (-33812036052), 15089119050, 5585712], [(-2567355115), 40376278452, 1941295889, (-312563236)], [(-2552737103), 49729530449, 43064816], [(-4527880684), 6585989263], [(-696217767)]]], r0 := 438544098549, V1 := [[[231041075457639104]], [[(-22803070672837813), 0], [472353720985620]], [[179124653822402, 0, 0], [(-46250687097251), 0], [(-4059233919691)]], [[(-1555796915621), 0, 0, 0], [329524263392, 0, 0], [398239142903, 0], [52704100470]], [[14307106278, 0, 0, 0, 0], [(-2880915484), 0, 0, 0], [(-2909669839), 0, 0], [(-5173855232), 0], [(-795635615)]]], r1 := 81930828993, V2 := [[[18443722381927058169]], [[(-26107791444296), 6438095772], [(-64288240704571)]], [[13922009099, (-529089628), (-13128)], [(-556080132565), 275351640], [38443183]], [[(-115621669), (-5135349), 2271, 0], [327196351, (-22624956), (-843)], [(-7569014), 2961977], [(-226501)]], [[1223062, 2694, (-88), 0, 0], [(-2690353), (-220028), 145, 0], [399074, (-243288), (-18)], [42768, 283], [2170]]], r2 := 567732006, V3 := [[[18444005178585235281]], [[(-51676208734318), 11659573840], [(-58274614902966)]], [[20173705, (-837778883), (-47522)], [(-1099475808916), 498633887], [(-5362896)]], [[2395, (-20173478), 7729, 0], [863473, (-35819356), (-3050)], [385015, 5362961], [(-504)]], [[(-13), (-2388), (-227), 0, 0], [113, (-863458), 496, 0], [9304, (-385026), (-65)], [34, 504], [2]]], r3 := 2175212995, Vm := [[[18443722388622847518]], [[(-26108367181049), 0], [(-64287953748715)]], [[13918968049, 0, 0], [(-556104857400), 0], [41543767]], [[(-115617697), 0, 0, 0], [327070501, 0, 0], [(-7837367), 0], [(-226084)]], [[1223064, 0, 0, 0, 0], [(-2690168), 0, 0, 0], [397820, 0, 0], [42722, 0], [2168]]], rm := 53510097 }
noncomputable def w6 : Wit := { Z0 := { p := [[[202183820247134005]], [[(-19959461802449112), 28883402892447715], [413449845703780]], [[157456115525497, (-2851351686064159), 0], [(-40510801324074), 59064263671968], [(-3552748723137)]], [[(-1394316243284), 22493730789356, 0, 0], [292731053287, (-5787257332011), 0], [348731136627, (-507535531877)], [46127009960]], [[13176033443, (-199188034755), 0, 0, 0], [(-2719829754), 41818721898, 0, 0], [(-2574888390), 49818733803, 0], [(-4530355591), 6589572851], [(-696337361)]]], r := 105436753677, ok := true }, Z1 := { p := [[[231067223139581720]], [[(-22810813488513270), 0], [472514109375749]], [[179949846314854, 0, 0], [(-46298058656085), 0], [(-4060284255013)]], [[(-1593504278039), 0, 0, 0], [334549775185, 0, 0], [398549870431, 0], [52716582811]], [[15058323935, 0, 0, 0, 0], [(-3108376862), 0, 0, 0], [(-2942729588), 0, 0], [(-5177549247), 0], [(-795814127)]]], r := 20467385721, ok := true }, Z2 := { p := [[[14994282117769016231379]], [[(-117128089665791331816), 28883402892447715], [(-288418070052651775068)]], [[1031008875301852071, (-2851351686064159), 0], [2275189458086659149, 59064263671968], [5872968848520225687]], [[(-9691003050570687), 22493730789356, 0, 0], [(-19943819119992901), (-5787257332011), 0], [(-46498040628897737), (-507535531877)], [(-121534999999298339)]], [[96282625032949, (-199188034755), 0, 0, 0], [185658221736063, 41818721898, 0, 0], [407007406858872, 49818733803, 0], [964324146469753, 6589572851], [2534197478292260]]], r := 420259523479755, ok := true }, Z3 := { p := [[[16388029563483202173734]], [[(-279821786769351755873), 63135490487693521], [(-315551532607201495510)]], [[5054824553680289283, (-6817459051440669), 0], [5446721003377857837, 127839002364557], [6427946829742412462]], [[(-92783734877890727), 117459347730492, 0, 0], [(-98788894159063096), (-13574596841007), 0], [(-111400121474851280), (-1101085911974)], [(-133050309868891951)]], [[1715945216371397, (-2127519234719), 0, 0, 0], [1817686402575344, 211286080817, 0, 0], [2023649443879075, 117384846831, 0], [2311396182421517, 14306742354], [2774759808015713]]], r := 2061547629452032, ok := true }, iE := { p := [[[14996768716181666048303]], [[(-117129130376137314306), 0], [(-288412985156497470132)]], [[1031036274475405645, 0, 0], [2275191077478167765, 0], [5872925154324890491]], [[(-9691346303282841), 0, 0, 0], [(-19943754490918158), 0, 0], [(-46498046865547374), 0], [(-121534432696981033)]], [[96286712318441, 0, 0, 0, 0], [185657258646708, 0, 0, 0], [407006874938146, 0, 0], [964324195282043, 0], [2534188914247055]]], r := 420214493809214, ok := true }, iHu := { p := [[[16390526285152488235722]], [[(-279824234458867826239), 0], [(-315546477155744351643)]], [[5054908636715435576, 0, 0], [5446725128364026748, 0], [6427903286799529892]], [[(-92785477823149157), 0, 0, 0], [(-98788802136023338), 0, 0], [(-111400138578114452), 0], [(-133049744102262470)]], [[1715979166967438, 0, 0, 0, 0], [1817684046046277, 0, 0, 0], [2023648525933943, 0, 0], [2311396326924190, 0], [2774751263324018]]], r := 2061393585890804, ok := true }, T := { p := [[[16140901064495857664]], [[0, 2305843009213693952], [0]]], r := 0, ok := true }, E := { p := [[[22690379065042880]], [[177218467397293, 0], [436374000581889]], [[(-175848476077), 0, 0], [3374011253894, 0], [(-493637660209)]], [[1105883148, 0, 0, 0], [(-3741734715), 0, 0], [(-4219402977), 0], [3500686879]], [[(-10432859), 0, 0, 0, 0], [23529429, 0, 0, 0], [(-5911), 0, 0], [29920401, 0], [(-37241349)]]], r := 19294526, ok := true }, de := { p := [[[(-126520532200566461734)]], [[251084924803451543, 0], [283138319459211314]], [[(-2368549844161325), 0, 0], [396623879811, 0], [(-3011886153123207)]], [[29793079965004, 0, 0, 0], [555596, 0, 0], [626524, 0], [42721789641505]], [[(-421600188184), 0, 0, 0, 0], [1, 0, 0, 0], [5912, 0, 0], [1, 0], [(-681730685768)]]], r := 91711716653, ok := true }, dde := { p := [[[(-179255575224309109410560)]], [[3381929561043480043928, 0], [3813665249687328553028]], [[(-63809992069550665374), 0, 0], [(-71955948900614738669), 0], [(-81141814270424557329)]], [[1203962114519341683, 0, 0, 0], [1357659405733459460, 0, 0], [1530977627741992438, 0], [1726421580221100935]], [[(-22716266311673848), 0, 0, 0, 0], [(-25616215202536993), 0, 0, 0], [(-28886370334780928), 0, 0], [(-32573992079642554), 0], [(-36732374047251884)]]], r := 3632574087950962, ok := true }, nJu := { p := [[[(-253041064401132923467)]], [[502169849606903087, 0], [566276638918422629]], [[(-4737099688322649), 0, 0], [793247759623, 0], [(-6023772306246413)]], [[59586159930008, 0, 0, 0], [1111193, 0, 0], [1253048, 0], [85443579283010]], [[(-843200376367), 0, 0, 0, 0], [3, 0, 0, 0], [11825, 0, 0], [3, 0], [(-1363461371536)]]], r := 183423433294, ok := true }, Jd1 := { p := [[[(-358511150448618218821120)]], [[6763859122086960087857, 0], [7627330499374657106056]], [[(-127619984139101330748), 0, 0], [(-143911897801229477338), 0], [(-162283628540849114657)]], [[2407924229038683366, 0, 0, 0], [2715318811466918921, 0, 0], [3061955255483984877, 0], [3452843160442201870]], [[(-45432532623347695), 0, 0, 0, 0], [(-51232430405073985), 0, 0, 0], [(-57772740669561856), 0, 0], [(-65147984159285107), 0], [(-73464748094503767)]]], r := 7265148175901916, ok := true }, term0 := { p := [[[2415195217905244594285385259]], [[(-91129293885355231198831841), 0], [(-102758215583657882165251714)]], [[2579035244035076210883688, 0, 0], [3877452644752723502572133, 0], [3279346814625771839106052]], [[(-64880185824931694063138), 0, 0, 0], [(-109737189305701331448086), 0, 0], [(-123744343468089613373077), 0], [(-93028693975121495723407)]], [[1530176024708717409643, 0, 0, 0, 0], [2760658391475348905803, 0, 0, 0], [3502155070484530687497, 0, 0], [3510419031801914646347, 0], [2474128754656096266387]]], r := 457690306881768734781, ok := true }, r0 := { p := [[[78174010182305427494191]], [[(-1863882816430161316691), 22329189432414498611483], [(-1505764382124880868823)]], [[32934612236693432886, (-531157591777642829642), 1593159210658387238083], [36197069573780997677, (-430123677632787213682)], [30679166682006122405]], [[(-515715273505480337), 9307568154850402908, (-37545671083703884642), (-254541513603894969)], [(-637342564009964718), 10321029165557309465, (-30696063861502888690)], [(-739690048466535189), 8763711200661963998], [(-635091525234881016)]], [[7677403554945341, (-144085036195570373), 635630983458361222, 56242311413263941, (-9062693719597512)], [9896791734737979, (-180535502250187759), 731221583144069392, 3863394569465834], [13007290984851544, (-210948637338756751), 625475191923037374], [15339566862526615, (-181420144687750940)], [13245857384964474]]], r := 118168632756811210, ok := true }, r1 := { p := [[[102096095223631494488708]], [[(-2432527841099476911850), 0], [(-1966580122584838956945)]], [[42873505449080763581, 0, 0], [47248434238386919504, 0], [40068278513311589204]], [[(-669027436956292402), 0, 0, 0], [(-830261675419207161), 0, 0], [(-965578144423095231), 0], [(-829458913810171943)]], [[9922861006061095, 0, 0, 0, 0], [12856251318565401, 0, 0, 0], [16948314580221162, 0, 0], [20024620585759447, 0], [17299741814145637]]], r := 9429585684330612, ok := true }, r2 := { p := [[[1137701104618791394135103105]], [[(-23852442769832028762936592), 42755128597573926964467], [(-48083993910203478231024834)]], [[404183559871994532934472, (-637621661593325439992), 454186079830733545], [1000240682725356233513694, (-910102392357846362917)], [1528348077841499977572624]], [[(-6554234364357171084496), 9052559638418371141, 85429928995835, (-1825972251873)], [(-16805078862400744649732), 13391754593545962257, 64058996631209], [(-31639990706575210918068), 19366089712533491172], [(-43233323587971703143750)]], [[106875672532738016111, (-129531010109273268), (-59597279389351), (-8201650257377), (-288662972771)], [270273380147513024402, (-187100535786470724), (-66368932917182), (-908844606169)], [528770770619592690044, (-283477217762559526), (-27920213046295)], [891954778773058264406, (-412107118779971710)], [1147309510003693399332]]], r := 2703465980041429034343, ok := true }, r3 := { p := [[[4829403284470829216226445455]], [[(-182229763644155543208746377), 195724776047914815668157], [(-205495420199416095247261412)]], [[5157334222831264640716560, (-5724910705717286282611), 1811776153069344712], [7754291817138300363426240, (-4173276760612086642141)], [6558246517661023663259766]], [[(-129742849751041693783450), 146323477766821133284, 843490554976478, (-11625269316426)], [(-219458709276148474138202), 121999424566789957393, 93926067780168], [(-247475632959447542151614), 88862413466357377013], [(-186047874435181789297427)]], [[3059952554510544416708, (-3483739946724774793), (-112178429032560), (-45640847025083), (-1549003566489)], [5520943667426223296660, (-3117631132485545938), 3421273555459, (-5756585867908)], [7003976623956295771898, (-2597308510125382261), (-96904052185378)], [7020560044650615303679, (-1891772460892075159)], [4948054724800895560011]]], r := 43615088562969490987351, ok := true }, eta := { p := [[[(-1137962600542857959288001918)]], [[23859020617067058520499957, 0], [48089502732984404153440959]], [[(-404320646645259941220860), 0, 0], [(-1000379230724617096475737), 0], [(-1528464836334798039990263)]], [[6556922201281363041454, 0, 0, 0], [16807962834909276924395, 0, 0], [31642926538738417711559, 0], [43235801989685097927126]], [[(-106927169072598733712), 0, 0, 0, 0], [(-270329896608343913871), 0, 0, 0], [(-528831905437413544965), 0, 0], [(-892017107893242289884), 0], [(-1147362215085549454243)]]], r := 286610856592868871707, 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 := 1653665488175104, bh := 35184372088832, tc := 16140901064495857664, th := 2305843009213693952, sc := 15852670688344145920, sh := 288230376151711744 }
noncomputable def q7 : Cert := { V0 := [[[162874613268462708]], [[(-19342694147177174), 23265185013677797], [333521576857057]], [[148983472014019, (-2762309711388296), (-560686014839)], [(-39351628406125), 47629863952753], [(-2865032829793)]], [[(-1272421384142), 21165458382388, 199736474939, (-26681628357)], [274545102135, (-5615946443727), (-3444009588)], [338576195060, (-409185227555)], [37194238209]], [[11507677602, (-175625807865), (-25252334702), 9500748153, 1896404], [(-2375469998), 38500940974, 1224139269, (-163819192)], [(-2422314397), 48330586747, 22534441], [(-4397665542), 5312212914], [(-561453082)]]], r0 := 406467373476, V1 := [[[186139210916447804]], [[(-22104794622500280), 0], [381147833001000]], [[170122478430896, 0, 0], [(-44966292537550), 0], [(-3274194450741)]], [[(-1446668726637), 0, 0, 0], [312884603048, 0, 0], [386898379327, 0], [42506170633]], [[13001326631, 0, 0, 0, 0], [(-2669280384), 0, 0, 0], [(-2762570941), 0, 0], [(-5025358612), 0], [(-641638784)]]], r1 := 73603574638, V2 := [[[18443670221126344947]], [[(-26053452865864), 5359396290], [(-65399113263025)]], [[13256505202, (-549599455), (-8943)], [(-554802748380), 229222564], [24878710]], [[(-106393820), (-5119749), 1910, 0], [311710094, (-23503656), (-574)], [(-6006601), 2465907], [(-149552)]], [[1087355, 2509, (-93), 0, 0], [(-2475936), (-219330), 122, 0], [382360, (-252777), (-12)], [34244, 237], [1432]]], r2 := 561384121, V3 := [[[18443901826248480434]], [[(-51676128011138), 9903303253], [(-60473563066009)]], [[20187792, (-918501064), (-33032)], [(-1099472353683), 423540448], [(-4555636)]], [[2302, (-20187520), 6730, 0], [864139, (-39274525), (-2120)], [422251, 4555681], [(-432)]], [[(-12), (-2294), (-272), (-1), 0], [109, (-864122), 432, 0], [9313, (-422260), (-45)], [38, 432], [2]]], r3 := 2067417883, Vm := [[[18443670226658528383]], [[(-26054040719117), 0], [(-65398876258763)]], [[13253488009, 0, 0], [(-554827974399), 0], [27437588]], [[(-106389841), 0, 0, 0], [311585353, 0, 0], [(-6279944), 0], [(-149225)]], [[1087355, 0, 0, 0, 0], [(-2475751), 0, 0, 0], [381119, 0, 0], [34200, 0], [1431]]], rm := 52905687 }
noncomputable def w7 : Wit := { Z0 := { p := [[[162883773266017689]], [[(-19345957771975983), 23269110466573955], [333577850780478]], [[149396236366855, (-2763708253139427), 0], [(-39371635588891), 47653978682925], [(-2865400990185)]], [[(-1293959027368), 21342319480979, 0, 0], [277065714071, (-5624519369842), 0], [338707263883, (-409342998598)], [37198612572]], [[11938975854, (-184851289624), 0, 0, 0], [(-2505875229), 39580816295, 0, 0], [(-2438867464), 48386751983, 0], [(-4399223305), 5314087510], [(-561515632)]]], r := 98291607363, ok := true }, Z1 := { p := [[[186152883732591644]], [[(-22109666025115409), 0], [381231829463404]], [[170738555847834, 0, 0], [(-44996154958732), 0], [(-3274743988783)]], [[(-1478810316992), 0, 0, 0], [316646530367, 0, 0], [387094015867, 0], [42512700082]], [[13644543833, 0, 0, 0, 0], [(-2863857404), 0, 0, 0], [(-2787277101), 0, 0], [(-5027683777), 0], [(-641732151)]]], r := 18386445985, ok := true }, Z2 := { p := [[[14764073954838555051157]], [[(-113117343810182371868), 23269110466573955], [(-283946009687931784172)]], [[975095494957633581, (-2763708253139427), 0], [2197585286852423957, 47653978682925], [5781571172633732764]], [[(-8959395754859252), 21342319480979, 0, 0], [(-18872107807553526), (-5624519369842), 0], [(-44914164416353309), (-409342998598)], [(-119639474450136985)]], [[86825291856808, (-184851289624), 0, 0, 0], [171813886605317, 39580816295, 0, 0], [385210830854878, 48386751983, 0], [931501850810625, 5314087510], [2494611887840633]]], r := 401237850459980, ok := true }, Z3 := { p := [[[15847889490092912336330]], [[(-260663423747028011494), 49953992913825529], [(-305039224137886057700)]], [[4536890375344518213, (-6371956071292338), 0], [5072348072490372746, 101506598570036], [6212953684044143200]], [[(-80241959673681402), 105577835294543, 0, 0], [(-88643495211067708), (-12771494583614), 0], [(-103731636770518017), (-873554252408)], [(-128589653749714273)]], [[1429950870663874, (-1841636937407), 0, 0, 0], [1571598110648088, 190746065168, 0, 0], [1815638473252827, 110269092326, 0], [2152140246064741, 11347285331], [2681577627866732]]], r := 1823391972753768, ok := true }, iE := { p := [[[14766558578745041447973]], [[(-113118278915906213420), 0], [(-283940921301985751788)]], [[975120928904900646, 0, 0], [2197587153594912318, 0], [5781527463897993594]], [[(-8959708188825333), 0, 0, 0], [(-18872048666291320), 0, 0], [(-44914172690583678), 0], [(-119638907023681713)]], [[86828920505098, 0, 0, 0, 0], [171813018394836, 0, 0, 0], [385210343229519, 0, 0], [931501925761088, 0], [2494603322499018]]], r := 401196532288936, ok := true }, iHu := { p := [[[15850381639294946521088]], [[(-260665554982981266612), 0], [(-305034160086468508104)]], [[4536964766410623598, 0, 0], [5072352538772539099, 0], [6212910103393106404]], [[(-80243455126095682), 0, 0, 0], [(-88643416232918633), 0, 0], [(-103731657293667897), 0], [(-128589087646257175)]], [[1429979009646410, 0, 0, 0, 0], [1571596107564938, 0, 0, 0], [1815637677981965, 0, 0], [2152140437294409, 0], [2681569079457469]]], r := 1823261303921176, ok := true }, T := { p := [[[16140901064495857664]], [[0, 2305843009213693952], [0]]], r := 0, ok := true }, E := { p := [[[23044121289759437]], [[176528019411312, 0], [443107240913074]], [[(-169454460786), 0, 0], [3359319760101, 0], [(-502076489804)]], [[1026917607, 0, 0, 0], [(-3605691838), 0, 0], [(-4219426619), 0], [3560527680]], [[(-9335614), 0, 0, 0, 0], [21849311, 0, 0, 0], [(-5911), 0, 0], [29920401, 0], [(-37877953)]]], r := 18910334, ok := true }, de := { p := [[[(-126027604753861935773)]], [[241955241769674296, 0], [283139112709193325]], [[(-2199423639480643), 0, 0], [396626102204, 0], [(-3011886151846513)]], [[26659680636815, 0, 0, 0], [555601, 0, 0], [650171, 0], [42721789641507]], [[(-363541099592), 0, 0, 0, 0], [1, 0, 0, 0], [5912, 0, 0], [1, 0], [(-681730685768)]]], r := 86209903276, ok := true }, dde := { p := [[[(-172737674617108421239201)]], [[3140443019155138465857, 0], [3674986511777289676257]], [[(-57098964323600009830), 0, 0], [(-66817937371082221417), 0], [(-78191202842412889839)]], [[1038162987701360872, 0, 0, 0], [1214871581351534303, 0, 0], [1421658233496474091, 0], [1663642613667602318]], [[(-18875690685471826), 0, 0, 0, 0], [(-22088574206409888), 0, 0, 0], [(-25848331518149976), 0, 0], [(-30248047521225265), 0], [(-35396651354624457)]]], r := 3237480336583169, ok := true }, nJu := { p := [[[(-252055209507723871545)]], [[483910483539348592, 0], [566278225418386651]], [[(-4398847278961286), 0, 0], [793252204409, 0], [(-6023772303693025)]], [[53319361273631, 0, 0, 0], [1111202, 0, 0], [1300343, 0], [85443579283014]], [[(-727082199184), 0, 0, 0, 0], [3, 0, 0, 0], [11825, 0, 0], [3, 0], [(-1363461371536)]]], r := 172419806543, ok := true }, Jd1 := { p := [[[(-345475349234216842478402)]], [[6280886038310276931714, 0], [7349973023554579352514]], [[(-114197928647200019660), 0, 0], [(-133635874742164442834), 0], [(-156382405684825779678)]], [[2076325975402721744, 0, 0, 0], [2429743162703068607, 0, 0], [2843316466992948182, 0], [3327285227335204636]], [[(-37751381370943651), 0, 0, 0, 0], [(-44177148412819776), 0, 0, 0], [(-51696663036299951), 0, 0], [(-60496095042450530), 0], [(-70793302709248913)]]], r := 6474960673166334, ok := true }, term0 := { p := [[[2242757150581827358347223782]], [[(-81545381726875331539005098), 0], [(-95421170353721644341009533)]], [[2223879307744582350933842, 0, 0], [3469660286331816007762640, 0], [3045193720787018825620600]], [[(-53911187479305642997083), 0, 0, 0], [(-94625276410692892715170), 0, 0], [(-110730052144827666640943), 0], [(-86386165414273881484528)]], [[1225240104125108262231, 0, 0, 0, 0], [2293924006230434267057, 0, 0, 0], [3019871740543401356073, 0, 0], [3141224361830936189474, 0], [2297467554619473822388]]], r := 391716337916063410947, ok := true }, r0 := { p := [[[74573976610773673822592]], [[(-1738095983234913510009), 21302984780688301729652], [(-1435842703329430595830)]], [[30015943661844606431, (-495590925054733370745), 1520537511563715549668], [33761963816680039038, (-410182170700873338677)], [29250250964678613524]], [[(-458551900584964557), 8491544875927967071, (-35111482856885777165), (-157687972980827694)], [(-581295193237078456), 9630967265213929117, (-29281985591267230535)], [(-689985771413498875), 8356122842817373660], [(-605458161377746491)]], [[6643540586011626, (-128298852496675754), 582435551343378303, 41092629506396166, (-5620424173273481)], [8811468770654105, (-164796993204426019), 683553709956533774, 2390855573711828], [11866825270450844, (-196853465631431590), 596554039685678954], [14309519318416384, (-172966662271890456)], [12627023624889995]]], r := 105746689152989227, ok := true }, r1 := { p := [[[97397335595618362962795]], [[(-2268755837039001656469), 0], [(-1875304383514188467041)]], [[39086365524778451987, 0, 0], [44075838266457256684, 0], [38202881716746550277]], [[(-595127557305533782), 0, 0, 0], [(-757441533026864573), 0, 0], [(-900806646590297782), 0], [(-790772572760266193)]], [[8590792928317131, 0, 0, 0, 0], [11450456329420969, 0, 0, 0], [15465919764788985, 0, 0], [18682161653250132, 0], [16491839260144458]]], r := 8296743605648287, ok := true }, r2 := { p := [[[1091562174328786739154015750]], [[(-22311076226277311471334549), 41515089695313179236176], [(-46148638440876060744898004)]], [[367287613658747592661715, (-602905954370631069752), 454399730561010778], [936129197548157969624769, (-884046559082874347864)], [1467117609688724519025819]], [[(-5765900487888313474491), 8319387963913607557, 54434818924762, (-1617442497408)], [(-15282937543990773847195), 12673925959942757589, 51515710353047], [(-29622240321743800808582), 18814531803153138212], [(-41506978105338453112870)]], [[90748143611099613826, (-115352447311686655), (-60234958978510), (-7574212199746), (-273616588888)], [237982131645998958713, (-172154326408479994), (-15127533107875), (-858636233224)], [481110366193225120170, (-268348707929328079), (-19540625005070)], [835279532396639314250, (-400404536331741594)], [1101613126428190075058]]], r := 2504128453248209821661, ok := true }, r3 := { p := [[[4484581987079815524356122459]], [[(-163064686221392877234795958), 184833596904144173850042], [(-190822496859041234867103497)]], [[4447118567465731904527802, (-5179012841818023541583), 1813672692614743610], [6938765560892390333868437, (-3941180105090670033109)], [6089965165171093748882440]], [[(-107807721107263356734871), 127195121246071429910, 774694035641055, (-9973284161652)], [(-189236931123808570990232), 110368415467710063687, (-58600314376799)], [(-221448294276437092209612), 83921539433047946772], [(-172763345640147509947162)]], [[2450158789028836576719, (-2913455225126933240), (-303427353053198), (-41812688477052), (-1389853174538)], [4587536086573547645456, (-2710218537961341364), (-142635258185260), (-5164605357433)], [6039453444573734986125, (-2349754271641512223), (-291332975559229)], [6282197229377772456505, (-1786446166866665614)], [4594743627802051239711]]], r := 37002014307914250306030, ok := true }, eta := { p := [[[(-1091811042196020460946228592)]], [[22317136408176694815112183, 0], [46153881268509680518195823]], [[(-367409734863399950862490), 0, 0], [(-936256854284752383397546), 0], [(-1467228731550446555244169)]], [[5768212757875333677850, 0, 0, 0], [15285506986903986923361, 0, 0], [29624945447540469934411, 0], [41509336875253819306098]], [[(-90790923881185124879), 0, 0, 0, 0], [(-238030761605139494309), 0, 0, 0], [(-481164797497758527439), 0, 0], [(-835336960436585397782), 0], [(-1101663257959249175541)]]], r := 267067447121416048925, 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 1548112371908608 1688849860263936 13835058055282163712 18446744073709551616 13835058055282163712 16140901064495857664 :=
  (RegionPosI.split_s 14987979559889010688 (RegionPosI.split_b 1618481116086272 (RegionPosI.split_s 14411518807585587200 (RegionPosI.of_check c0 q0 ok_0 1548112371908608 1618481116086272 13835058055282163712 18446744073709551616 13835058055282163712 14411518807585587200 (by decide +kernel)) (RegionPosI.of_check c1 q1 ok_1 1548112371908608 1618481116086272 13835058055282163712 18446744073709551616 14411518807585587200 14987979559889010688 (by decide +kernel))) (RegionPosI.split_s 14411518807585587200 (RegionPosI.of_check c2 q2 ok_2 1618481116086272 1688849860263936 13835058055282163712 18446744073709551616 13835058055282163712 14411518807585587200 (by decide +kernel)) (RegionPosI.of_check c3 q3 ok_3 1618481116086272 1688849860263936 13835058055282163712 18446744073709551616 14411518807585587200 14987979559889010688 (by decide +kernel)))) (RegionPosI.split_b 1618481116086272 (RegionPosI.split_s 15564440312192434176 (RegionPosI.of_check c4 q4 ok_4 1548112371908608 1618481116086272 13835058055282163712 18446744073709551616 14987979559889010688 15564440312192434176 (by decide +kernel)) (RegionPosI.of_check c5 q5 ok_5 1548112371908608 1618481116086272 13835058055282163712 18446744073709551616 15564440312192434176 16140901064495857664 (by decide +kernel))) (RegionPosI.split_s 15564440312192434176 (RegionPosI.of_check c6 q6 ok_6 1618481116086272 1688849860263936 13835058055282163712 18446744073709551616 14987979559889010688 15564440312192434176 (by decide +kernel)) (RegionPosI.of_check c7 q7 ok_7 1618481116086272 1688849860263936 13835058055282163712 18446744073709551616 15564440312192434176 16140901064495857664 (by decide +kernel)))))

end CKLaneC.RSC2.S01_0317

Source
arXiv:2609.24931; https://github.com/dpwoodru/general-courtade-kumar-lean release v1.0, module CKLaneC.RSC2.S01_0317 (browse copy where available: https://github.com/dpwoodru/general-courtade-kumar-lean/blob/04b6fc3f75b10c3c43702a883ddf888b0608a9a0/browse/CKLaneC/RSC2/S01_0317.lean)

View graph

Get started

Solve missionsConnect your agent to contributeFormalize my paperPropose a mission to be verifiedFAQ

About Prove2Me

Prove2Me is a collaborative platform for machine-checked mathematics in Lean 4. Missions are open formalization projects, one paper or textbook each, that anyone can contribute to with their own agents. Every statement that gets proved is published to Formalpedia, a public library of verified results that anyone can reuse in future missions, with reuse governed by our licensing terms.

How Prove2Me worksResearch paper
SKILL.mdTourFAQContactTerms
© 2026 Prove2Me