Courtade–Kumar proof module `CKLaneC.RSC2.S00_0091` (transplant)
DefinitionCK_CKLaneC_RSC2_S00_0091Verbatim transplant of the Lean module CKLaneC.RSC2.S00_0091 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.S00_0091 from release v1.0 (sources_v3.tar.zst).
import Definitions.Def_CK_CKLaneC_RSC2_S00_0091_part00
/-! RA-stat cover batch S00_0091 (generated by tools/emit_cover2.py; compact format). -/
namespace CKLaneC.RSC2.S00_0091
open CKLaneC.TM3 CKLaneC.RSCell
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 := 1073123348709376, bh := 17592186044416, tc := 6917529027641081856, th := 2305843009213693952, sc := 8935141660703064064, sh := 288230376151711744 }
noncomputable def q6 : Cert := { V0 := [[[303089022165714636]], [[(-12221612678415444), 100990330013819039], [452001345841224]], [[127051610590445, (-4069111755816868), (-19662986697182)], [(-17990522482419), 150491104439583], [(-3030894106610)]], [[(-1507309118868), 42109190941562, 2377747269703, (-2179759884323)], [184303047820, (-5975642986468), (-87938064662)], [120997675574, (-1009380237068)], [30446705324]], [[19813173461, (-495282983985), (-120507178775), 263183049768, 1252657677], [(-2435705356), 60364222222, 10585377526, (-9733502104)], [(-1244100036), 40221741945, 458648440], [(-1216679286), 10140434961], [(-355014541)]]], r0 := 487661984320, V1 := [[[807277668414387208]], [[(-32475039339087069), 0], [1201049474709520]], [[332941687430230, 0, 0], [(-47459576890418), 0], [(-8060005288300)]], [[(-3846675815998), 0, 0, 0], [465589673113, 0, 0], [319962920372, 0], [80984726829]], [[49098918759, 0, 0, 0, 0], [(-5736001962), 0, 0, 0], [(-3181513588), 0, 0], [(-3219570369), 0], [(-944419805)]]], r1 := 111829396804, V2 := [[[18445160884826447723]], [[(-17468180414497), 6526550596], [(-25938550965349)]], [[17319996802, (-125120080), (-25809)], [(-287478525725), 214884975], [147333343]], [[(-234940187), (-2269444), 1275, 0], [310982410, (-4112263), (-1275)], [(-10854388), 1777581], [(-671144)]], [[4097721, 3011, (-6), 0, 0], [(-4196005), (-75042), 63, 0], [264759, (-33886), (-21)], [47541, 107], [4986]]], r2 := 208161010, V3 := [[[18445704442764075396]], [[(-33535199528824), 8540619771], [(-17043836123355)]], [[41868610, 18966924, (-67397)], [(-549758971099), 281195212], [(-11628870)]], [[8490, (-8374078), 1881, 0], [1378801, 630978, (-3330)], [(-26733), 2326049], [(-692)]], [[(-85), (-1688), 71, (-1), 0], [305, (-275778), 93, 0], [11411, 5339, (-55)], [(-6), 140], [2]]], r3 := 2273463614, Vm := [[[18445160918379678725]], [[(-17468861901091), 0], [(-25937444742938)]], [[17309536420, 0, 0], [(-287501015010), 0], [156511180]], [[(-234928301), 0, 0, 0], [310637642, 0, 0], [(-11041346), 0], [(-670413)]], [[4097602, 0, 0, 0, 0], [(-4195592), 0, 0, 0], [261900, 0, 0], [47524, 0], [4984]]], rm := 26670893 }
noncomputable def w6 : Wit := { Z0 := { p := [[[303148058562746490]], [[(-12228755484016871), 101049352854248830], [452265513740330]], [[127414002793794, (-4076251828005624), 0], [(-18022349740258), 150755171246776], [(-3032271368793)]], [[(-1518059921287), 42471334264598, 0, 0], [185911007934, (-6007449913420), 0], [121164014321, (-1010757122931)], [30459410367]], [[20048129812, (-506019973763), 0, 0, 0], [(-2483372823), 61970335978, 0, 0], [(-1252524255), 40388004773, 0], [(-1218214615), 10153136789], [(-355155156)]]], r := 100021062056, ok := true }, Z1 := { p := [[[808394822833990640]], [[(-32610014624044989), 0], [1206041369974214]], [[339770674116784, 0, 0], [(-48059599307353), 0], [(-8086056983447)]], [[(-4048159790097), 0, 0, 0], [495762687824, 0, 0], [323104038191, 0], [81225094313]], [[53461679498, 0, 0, 0, 0], [(-6622327528), 0, 0, 0], [(-3340064678), 0, 0], [(-3248572305), 0], [(-947080415)]]], r := 27930750144, ok := true }, Z2 := { p := [[[26947221318497551668528]], [[(-270456545224477268497), 101049352854248830], [(-401601696098546334293)]], [[3130712474340359507, (-4076251828005624), 0], [4050242176914923179, 150755171246776], [6314022581366596587]], [[(-40076087404974425), 42471334264598, 0, 0], [(-46430535436646415), (-6007449913420), 0], [(-63794413718581597), (-1010757122931)], [(-100800526238367867)]], [[567723187647060, (-506019973763), 0, 0, 0], [584659633218088, 61970335978, 0, 0], [728673387963935, 40388004773, 0], [1019565258063129, 10153136789], [1620892778628053]]], r := 566337086618137, ok := true }, Z3 := { p := [[[39533588114454961549091]], [[(-1164186067806692423209), 296490573739342588], [(-591682674788802364778)]], [[36074435806598435144, (-17715422348442877), 0], [17582190411187499791, 423507032717705], [9317430088525606872]], [[(-1134345446867776454), 535113471024768, 0, 0], [(-546686530856841536), (-24114150166308), 0], [(-277823405948410885), (-2866382912579)], [(-148892666491355204)]], [[35917202254205501, (-16705322638808), 0, 0, 0], [17225889058989060, 677367133440, 0, 0], [8650146708594545, 164911703144, 0], [4448807346697668, 28885152793], [2395863720695474]]], r := 13455084737789965, ok := true }, iE := { p := [[[26950053762479072279676]], [[(-270475785857835506199), 0], [(-401597470385412901914)]], [[3130949340866192799, 0, 0], [4050215543202112879, 0], [6313994249538150801]], [[(-40079232494280569), 0, 0, 0], [(-46430151603366742), 0, 0], [(-63794232057836103), 0], [(-100800241642866958)]], [[567769198479321, 0, 0, 0, 0], [584653694965581, 0, 0, 0], [728670861593677, 0, 0], [1019563422873389, 0], [1620889460259178]]], r := 566295125139314, ok := true }, iHu := { p := [[[39537298738908123624516]], [[(-1164268382147768993055), 0], [(-591677374534120170464)]], [[36077027965853323966, 0, 0], [17582087733362095621, 0], [9317394215309155510]], [[(-1134427319552075372), 0, 0, 0], [(-546683357149259486), 0, 0], [(-277822689700889383), 0], [(-148892304989291454)]], [[35919800000912796, 0, 0, 0, 0], [17225790856222601, 0, 0, 0], [8650124532208957, 0, 0], [4448800055335161, 0], [2395859497581081]]], r := 13454515458722456, ok := true }, T := { p := [[[6917529027641081856]], [[0, 2305843009213693952], [0]]], r := 0, ok := true }, E := { p := [[[12626407721482656]], [[126720992140808, 0], [188152997604107]], [[(-195089889076), 0, 0], [1879105229805, 0], [(-154407775925)]], [[2097681632, 0, 0, 0], [(-3198285024), 0, 0], [(-1625357963), 0], [843717511]], [[(-33833574), 0, 0, 0, 0], [34388224, 0, 0, 0], [(-1477), 0, 0], [8881237, 0], [(-6915717)]]], r := 23683545, ok := true }, de := { p := [[[(-139411505369220806718)]], [[429254453568100904, 0], [218145705911657837]], [[(-6923263833131264), 0, 0], [198293671519, 0], [(-1788029170556072)]], [[148887394379115, 0, 0, 0], [180249, 0, 0], [91602, 0], [19541302425966]], [[(-3602114380139), 0, 0, 0, 0], [1, 0, 0, 0], [1478, 0, 0], [1, 0], [(-240261915074)]]], r := 496299382525, ok := true }, dde := { p := [[[(-472242274522885217644124)]], [[15233192492253266912868, 0], [7741458479669693014882]], [[(-491393306591920005405), 0, 0], [(-249724467482717663921), 0], [(-126909155505196173340)]], [[15851396986835823613, 0, 0, 0], [8055627976916190595, 0, 0], [4093843725973800778, 0], [2080477959101555631]], [[(-511335386672101741), 0, 0, 0, 0], [(-259858966997291460), 0, 0, 0], [(-132059475031395339), 0, 0], [(-67112192229078024), 0], [(-34106196050840138)]]], r := 34072639451646948, ok := true }, nJu := { p := [[[(-278823010738441613435)]], [[858508907136201808, 0], [436291411823315675]], [[(-13846527666262527), 0, 0], [396587343038, 0], [(-3576058341112144)]], [[297774788758230, 0, 0, 0], [360498, 0, 0], [183204, 0], [39082604851932]], [[(-7204228760278), 0, 0, 0, 0], [2, 0, 0, 0], [2957, 0, 0], [2, 0], [(-480523830148)]]], r := 992598765046, ok := true }, Jd1 := { p := [[[(-944484549045770435288247)]], [[30466384984506533825737, 0], [15482916959339386029764]], [[(-982786613183840010810), 0, 0], [(-499448934965435327842), 0], [(-253818311010392346680)]], [[31702793973671647227, 0, 0, 0], [16111255953832381190, 0, 0], [8187687451947601557, 0], [4160955918203111262]], [[(-1022670773344203482), 0, 0, 0, 0], [(-519717933994582920), 0, 0, 0], [(-264118950062790678), 0, 0], [(-134224384458156047), 0], [(-68212392101680275)]]], r := 68145278903293890, ok := true }, term0 := { p := [[[16761116990219706910534605686]], [[(-1081316682595646850226954052), 0], [(-549505610428615542953979346)]], [[52321037874349698446561531, 0, 0], [35451225692963786494669519, 0], [13512111676594864763821271]], [[(-2250351369005154136350219), 0, 0, 0], [(-1715369804927183502009267), 0, 0], [(-871736858894297630088301), 0], [(-295343191108824071888835)]], [[90739591055117986100094, 0, 0, 0, 0], [73779086589512901971329, 0, 0, 0], [42180617663735476222246, 0, 0], [19054198089798752574601, 0], [6052071389056797029653]]], r := 10138766939022019536191, ok := true }, r0 := { p := [[[39099578142624870610836]], [[(-1265070620846842773023), 26050086008470653757445], [(-583572399117263856478)]], [[30993079688910683962, (-841545236193277203027), 4330822250925830298751], [18837940691616624298, (-388853473033680110145)], [9180462467153453031]], [[(-703597713763227560), 20567413917907495147, (-139035541419128546968), (-3614567275984691324)], [(-455295887490158434), 12536677209686516288, (-64679117693426727897)], [(-296089466486960088), 6117494095266231150], [(-146614253162992134)]], [[16061480435076583, (-465787311713319834), 3364939901003439581, 406364350387553966, (-299126135186018612)], [10141691999289851, (-302400132008022025), 2074825988104457482, 43219812975283214], [7119274159317881, (-197075790487041214), 1017707103260297331], [4726117966217400, (-97700201431641417)], [2358179212263784]]], r := 366363751903449268, ok := true }, r1 := { p := [[[276983444232722566244650]], [[(-8877294956019355767431), 0], [(-4137190802109543470002)]], [[214303409499575233486, 0, 0], [132535655918684064003, 0], [65100378729890545030]], [[(-4794081565613727186), 0, 0, 0], [(-3164667132728281321), 0, 0], [(-2084952636290977295), 0], [(-1039818848761650861)]], [[108317675051568230, 0, 0, 0, 0], [69620848224281179, 0, 0, 0], [49570800566843567, 0, 0], [33296168783731566, 0], [16726357466289710]]], r := 36420312194810948, ok := true }, r2 := { p := [[[4625790764795494134949805389]], [[(-138529200736703981188412266), 97172752019000368608159], [(-149984788513984927874022150)]], [[3603071577263693588576669, (-2079253206230432373308), 450032350136061138], [4442293896200949918789223, (-1583743411592113056783)], [3663246143291466890669282]], [[(-95800391105258043532063), 44636654168592846210, (-626134781001640), (-9581396860822)], [(-114299674567207817745527), 33194860459222973140, (-823595180512106)], [(-107758271480890762151947), 25899104937087229367], [(-79687535786537952185210)]], [[2682730629968226410251, (-1033436661390746340), (-795513993816410), (-95274043519279), (-2012580971743)], [3013343469620830717633, (-696009241967378569), (-424942877891557), (-7847379719139)], [2753822182954117290307, (-538624142499369668), (-223449502731827)], [2332593423787974204579, (-424247663813972189)], [1626933693529294685274]]], r := 10612435166385556572558, ok := true }, r3 := { p := [[[33515752405765977127484383074]], [[(-2162283162822471662435152389), 717434096297736979934604], [(-1098904875284528357452331673)]], [[104626227100244156266306966, (-38787882372757543489018), 1765712298180611038], [70896706585381693902176200, (-11779594474470290424784)], [27022479425388895624590023]], [[(-4500044651237593482674334), 1755783027555258663174, (-4181331714180628), (-16654618686181434)], [(-3430479652760941243280875), 636614658418268774614, (-6803551840585478)], [(-1743379532182992733015550), 193208704673693179533], [(-590657789030344632142762)]], [[181453214173015660723003, (-72930739866806422120), (-5851721669771163), 1922728711849214, (-1673338066478937)], [147547367806309002642863, (-28819365328399341392), (-15358248871451940), 924011339932944], [84356966954963199694439, (-10446503361221351181), (-7501783141816632)], [38106838587528479311125, (-3172851656992408763)], [12103658560923099450438]]], r := 879110237225384307530564, ok := true }, eta := { p := [[[(-4626980180748103163855732213)]], [[138569631798335173986910559, 0], [150004125427211778774639301]], [[(-3604344541775430541759645), 0, 0], [(-4442947586564862472299670), 0], [(-3663562077011566476326332)]], [[95840332779824401941247, 0, 0, 0], [114320191011993365732230, 0, 0], [107768926644789534681910, 0], [79692704143609586739078]], [[(-2683994552847943833046), 0, 0, 0, 0], [(-3013987139035229761606), 0, 0, 0], [(-2754156698584085777044), 0, 0], [(-2332768115644029232206), 0], [(-1627018549683060768365)]]], r := 980226516406163027411, 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 := 1108307720798208, bh := 17592186044416, tc := 6917529027641081856, th := 2305843009213693952, sc := 8935141660703064064, sh := 288230376151711744 }
noncomputable def q7 : Cert := { V0 := [[[303981139314050919]], [[(-12257119244578642), 101287353979839352], [440232116787618]], [[127415338200715, (-4080905317449241), (-19837061351289)], [(-17520691585757), 146571600590826], [(-2856389526740)]], [[(-1512117489721), 42228315255635, 2398700593727, (-2199027272378)], [179472406806, (-5819464030766), (-86152791603)], [114024492501, (-951260683356)], [27776734216]], [[19886280679, (-496823074884), (-121563849299), 265496274188, 1271187669], [(-2373279037), 58775841592, 10369903238, (-9535681629)], [(-1172319801), 37903223810, 434340986], [(-1109924921), 9251150945], [(-313559401)]]], r0 := 459938619066, V1 := [[[809648160481338018]], [[(-32568703811301584), 0], [1169751973019268]], [[333860391984691, 0, 0], [(-46217194363982), 0], [(-7595845951271)]], [[(-3857995444757), 0, 0, 0], [453237650825, 0, 0], [301510850456, 0], [73882032098]], [[49261272479, 0, 0, 0, 0], [(-5585121075), 0, 0, 0], [(-2997324102), 0, 0], [(-2936971076), 0], [(-834130449)]]], r1 := 102604885369, V2 := [[[18445109008308559579]], [[(-18043180508724), 6963431722], [(-25937969529750)]], [[17943011682, (-133480156), (-28445)], [(-287521383845), 221996575], [143422565]], [[(-243345376), (-2422035), 1405, 0], [312028045, (-4247818), (-1361)], [(-10577377), 1778217], [(-633027)]], [[4244337, 3222, (-7), 0, 0], [(-4209127), (-77550), 67, 0], [258123, (-33892), (-22)], [44837, 105], [4552]]], r2 := 196636090, V3 := [[[18445670355045307707]], [[(-34634717577998), 9112315504], [(-17043882647068)]], [[44671862, 20250244, (-74278)], [(-549759078100), 290501073], [(-11632969)]], [[9113, (-8934764), 2073, 0], [1424453, 652347, (-3553)], [(-26768), 2326878], [(-675)]], [[(-91), (-1812), 78, (-1), 0], [317, (-284910), 99, 0], [11415, 5345, (-57)], [(-6), 136], [2]]], r3 := 2224880855, Vm := [[[18445109044110952568]], [[(-18043907721856), 0], [(-25936826587284)]], [[17931850326, 0, 0], [(-287544621166), 0], [152604738]], [[(-243332647), 0, 0, 0], [311671838, 0, 0], [(-10764437), 0], [(-632313)]], [[4244210, 0, 0, 0, 0], [(-4208698), 0, 0, 0], [255262, 0, 0], [44820, 0], [4550]]], rm := 26095809 }
noncomputable def w7 : Wit := { Z0 := { p := [[[304040698637276050]], [[(-12264325051357880), 101346899545758683], [440490923731428]], [[127780913236361, (-4088108350452627), 0], [(-17551871384664), 146830307910476], [(-2857693801795)]], [[(-1522962645751), 42593637745453, 0, 0], [181047576897, (-5850623794888), 0], [114182011310, (-952564600599)], [27788379344]], [[20123320638, (-507654215251), 0, 0, 0], [(-2419974014), 60349192299, 0, 0], [(-1180297084), 38060670436, 0], [(-1111332124), 9262793114], [(-313684164)]]], r := 92964980333, ok := true }, Z1 := { p := [[[810775196366069467]], [[(-32704866803621012), 0], [1174642463283809]], [[340749101963630, 0, 0], [(-46804990359104), 0], [(-7620516804786)]], [[(-4061233722001), 0, 0, 0], [482793538393, 0, 0], [304485363494, 0], [74102344917]], [[53662188369, 0, 0, 0, 0], [(-6453264036), 0, 0, 0], [(-3147458889), 0, 0], [(-2963552330), 0], [(-836491102)]]], r := 25616306126, ok := true }, Z2 := { p := [[[26168492735417422315671]], [[(-262603336306354537919), 101346899545758683], [(-377505359004285756054)]], [[3040676028252868162, (-4088108350452627), 0], [3806794678896461729, 146830307910476], [5746124249132573835]], [[(-38942115627781197), 42593637745453, 0, 0], [(-43649543256966729), (-5850623794888), 0], [(-58050579835755659), (-952564600599)], [(-88816178307475311)]], [[551977040790416, (-507654215251), 0, 0, 0], [549856085377843, 60349192299, 0, 0], [663202572827400, 38060670436, 0], [898259263397499, 9262793114], [1382777990283750]]], r := 504243476213044, ok := true }, Z3 := { p := [[[38386338477936287454951]], [[(-1130098501270125580727), 297326348088236337], [(-556125979427971002009)]], [[35014588933579982450, (-17763004039126943), 0], [16522077639685138916, 412377655420909], [8478622122565430463]], [[(-1100950925131742079), 536449762625772, 0, 0], [(-513680762301257083), (-23473910513921), 0], [(-252762704868137365), (-2700842505541)], [(-131179163530059269)]], [[34858293464349766, (-16745665642000), 0, 0, 0], [16185052452896251, 659107109280, 0, 0], [7869253576414815, 155354881742, 0], [3918813293293068, 26347559522], [2043731934354197]]], r := 12335476087019556, ok := true }, iE := { p := [[[26171333519722871612100]], [[(-262622629494841874494), 0], [(-377501243306260992706)]], [[3040913652536984840, 0, 0], [3806768750470347290, 0], [5746097548458163127]], [[(-38945272444500993), 0, 0, 0], [(-43649169235591648), 0, 0], [(-58050408691757429), 0], [(-88815918668577399)]], [[552023250219648, 0, 0, 0, 0], [549850294780809, 0, 0, 0], [663200191041812, 0, 0], [898257589656260, 0], [1382775059396368]]], r := 504204097034450, ok := true }, iHu := { p := [[[38390059562232058412749]], [[(-1130181018158856603766), 0], [(-556120818459131946388)]], [[35017187353310771550, 0, 0], [16521977742011292524, 0], [8478588321112255061]], [[(-1101032991522392967), 0, 0, 0], [(-513677674670022401), 0, 0], [(-252762030395850463), 0], [(-131178833786359792)]], [[34860897257681561, 0, 0, 0, 0], [16184956922483960, 0, 0, 0], [7869232694655160, 0, 0], [3918806646171725, 0], [2043728204987730]]], r := 12334903625079067, ok := true }, T := { p := [[[6917529027641081856]], [[0, 2305843009213693952], [0]]], r := 0, ok := true }, E := { p := [[[13002102726806017]], [[130472771076130, 0], [187545275110497]], [[(-201486465035), 0, 0], [1872708099110, 0], [(-149506178962)]], [[2166458079, 0, 0, 0], [(-3198290934), 0, 0], [(-1573762205), 0], [790998453]], [[(-34942871), 0, 0, 0, 0], [34388224, 0, 0, 0], [(-1477), 0, 0], [8326300, 0], [(-6277765)]]], r := 23987027, ok := true }, de := { p := [[[(-138982213489699406216)]], [[429254850155810346, 0], [211220640552859060]], [[(-6923263832764857), 0, 0], [198294037925, 0], [(-1676305503473678)]], [[148887394379115, 0, 0, 0], [186159, 0, 0], [91602, 0], [17738682591465]], [[(-3602114380139), 0, 0, 0, 0], [1, 0, 0, 0], [1478, 0, 0], [1, 0], [(-211174792756)]]], r := 493906101695, ok := true }, dde := { p := [[[(-457250878737248496760530)]], [[14749599079020174554088, 0], [7257739229359133502371]], [[(-475793519081066510274), 0, 0], [(-234120620698507142489), 0], [(-115202210087403581735)]], [[15348178034872767769, 0, 0, 0], [7552278080651305315, 0, 0], [3716200325399871835, 0], [1828606509323854969]], [[(-495102517253939335), 0, 0, 0, 0], [(-243621873569391461), 0, 0, 0], [(-119877429851591266), 0, 0], [(-58987306752378549), 0], [(-29025500147981172)]]], r := 32040321108619339, ok := true }, nJu := { p := [[[(-277964426979398812431)]], [[858509700311620693, 0], [422441281105718121]], [[(-13846527665529713), 0, 0], [396588075850, 0], [(-3352611006947355)]], [[297774788758231, 0, 0, 0], [372318, 0, 0], [183205, 0], [35477365182931]], [[(-7204228760278), 0, 0, 0, 0], [2, 0, 0, 0], [2957, 0, 0], [2, 0], [(-422349585511)]]], r := 987812203380, ok := true }, Jd1 := { p := [[[(-914501757474496993521059)]], [[29499198158040349108176, 0], [14515478458718267004742]], [[(-951587038162133020547), 0, 0], [(-468241241397014284978), 0], [(-230404420174807163470)]], [[30696356069745535539, 0, 0, 0], [15104556161302610631, 0, 0], [7432400650799743670, 0], [3657213018647709938]], [[(-990205034507878670), 0, 0, 0, 0], [(-487243747138782922), 0, 0, 0], [(-239754859703182531), 0, 0], [(-117974613504757098), 0], [(-58051000295962343)]]], r := 64080642217238672, ok := true }, term0 := { p := [[[15713884634335483433597936527]], [[(-1013754755576896508810562737), 0], [(-498816721405440229297026441)]], [[49051935773123826514643919, 0, 0], [32181021599783149505525396, 0], [11876296883166610397496031]], [[(-2109745330235895371164030), 0, 0, 0], [(-1557134878023932941369811), 0, 0], [(-766201553538807243812586), 0], [(-251347111583152311303010)]], [[85070004892300005422553, 0, 0, 0, 0], [66973299518939604716814, 0, 0, 0], [37074088903473165418598, 0, 0], [16215765720863530837453, 0], [4987009114715563846246]]], r := 9154379547679607735316, ok := true }, r0 := { p := [[[37968018830572920500610]], [[(-1228542466156844915162), 25296091793824404557071], [(-548537391356579783817)]], [[30110086939827172755, (-817235801446454846549), 4205408856912033514900], [17707959117609446239, (-365507566776850727758)], [8354467927089325711]], [[(-683924634355228352), 19980949607242912073, (-135012389093116125751), (-3530552166410333255)], [(-428122252471684906), 11784569530145160222, (-60795306929660667898)], [(-269462867240986944), 5567071819453975297], [(-129178913201547328)]], [[15621655388471541, (-452747598510112893), 3268658579275653801, 396907931958254251, (-292161390771870993)], [9540752006021568, (-284346841673967287), 1950282955198956263, 40830903451414839], [6480974850042590, (-179351862540873110), 926130484688631780], [4164286986241450, (-86081533432156077)], [2011692834473824]]], r := 347091643895077996, ok := true }, r1 := { p := [[[268961404840360440237357]], [[(-8620305385723650342918), 0], [(-3888752673569732717131)]], [[208166238457302592342, 0, 0], [124578928541995475952, 0], [59242289539993478194]], [[(-4659039802406994399), 0, 0, 0], [(-2975468734154663972), 0, 0], [(-1897368506683099443), 0], [(-916152238254553057)]], [[105325625573056777, 0, 0, 0, 0], [65485452485403492, 0, 0, 0], [45122077342464393, 0, 0], [29336709950261385, 0], [14268590109910895]]], r := 32962493011931474, ok := true }, r2 := { p := [[[4339861719434663868322131464]], [[(-130057715751516533694436502), 94105579884486915143981], [(-136238433298586813153267105)]], [[3385031483999444220845278, (-2014946637243268575434), 450108451769256120], [4037804761003772617669786, (-1485019154710839507168)], [3221753349800423145416794]], [[(-90050629194194176258323), 43288315159571311415, (-657099421881238), (-8908476067391)], [(-103959531779389448503002), 31142911357124979706, 37938991258020], [(-94831129830448176435669), 23513614724666705464], [(-67857083132793933317133)]], [[2522575568648282862330, (-1002954451528841038), (-699968316242455), (-84121812139785), (-1831399735678)], [2742141840906116863017, (-653990939396669730), (-377809904317677), (-7132435896486)], [2424986452574304668231, (-489219309603708941), (-252982143891242)], [1987512918923859831199, (-373395209105796322)], [1341392421300545142398]]], r := 9239165419713645594051, ok := true }, r3 := { p := [[[31421493630945784284241982996]], [[(-2027170433537916655180555404), 694623248190294911532305], [(-997533744214633434497143860)]], [[98088526322800903359307986, (-37555076512261435638823), 1769674853644245293], [64356657447059706411484134, (-11043143600388458260982)], [23751010742363251670287674]], [[(-4218853479534171547477147), 1699976626886217819914, (-2159778530255356), (-14776152911038402)], [(-3114026046115912043556425), 596813450831234837736, (-5297067551522046)], [(-1532317597861557423060909), 175374880143029466091], [(-502669095490125043917753)]], [[170114855956632838281273, (-70611823503576793027), (-4480596836796390), 1713530974980827, (-1489693934701866)], [133936476754781386122751, (-27020714535468237353), (-13668935033116415), 783687921105001], [74144302593453577511228, (-9488342026025365424), (-7028459755000164)], [32430166946224880668604, (-2797269662725527801)], [9973609597957750741232]]], r := 780571775722884767310489, ok := true }, eta := { p := [[[(-4341013685253964651987358103)]], [[130096880707681709624476277, 0], [136256565902080474807830728]], [[(-3386264708450163369363283), 0, 0], [(-4038417829064724289524689), 0], [(-3222040196502068843956518)]], [[90089325338232632156756, 0, 0, 0], [103978775123049949035620, 0, 0], [94840805498445462230355, 0], [67861626597225210921636]], [[(-2523800023414709511295), 0, 0, 0, 0], [(-2742745223238337436616), 0, 0, 0], [(-2425289927673545383242), 0, 0], [(-1987666274176560280452), 0], [(-1341464779576206649204)]]], r := 855491415064606062289, 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 985162418487296 1125899906842624 4611686018427387904 9223372036854775808 8070450532247928832 9223372036854775808 :=
(RegionPosI.split_b 1055531162664960 (RegionPosI.split_s 8646911284551352320 (RegionPosI.split_b 1020346790576128 (RegionPosI.of_check c0 q0 ok_0 985162418487296 1020346790576128 4611686018427387904 9223372036854775808 8070450532247928832 8646911284551352320 (by decide +kernel)) (RegionPosI.of_check c1 q1 ok_1 1020346790576128 1055531162664960 4611686018427387904 9223372036854775808 8070450532247928832 8646911284551352320 (by decide +kernel))) (RegionPosI.split_b 1020346790576128 (RegionPosI.of_check c2 q2 ok_2 985162418487296 1020346790576128 4611686018427387904 9223372036854775808 8646911284551352320 9223372036854775808 (by decide +kernel)) (RegionPosI.of_check c3 q3 ok_3 1020346790576128 1055531162664960 4611686018427387904 9223372036854775808 8646911284551352320 9223372036854775808 (by decide +kernel)))) (RegionPosI.split_s 8646911284551352320 (RegionPosI.split_s 8358680908399640576 (RegionPosI.of_check c4 q4 ok_4 1055531162664960 1125899906842624 4611686018427387904 9223372036854775808 8070450532247928832 8358680908399640576 (by decide +kernel)) (RegionPosI.of_check c5 q5 ok_5 1055531162664960 1125899906842624 4611686018427387904 9223372036854775808 8358680908399640576 8646911284551352320 (by decide +kernel))) (RegionPosI.split_b 1090715534753792 (RegionPosI.of_check c6 q6 ok_6 1055531162664960 1090715534753792 4611686018427387904 9223372036854775808 8646911284551352320 9223372036854775808 (by decide +kernel)) (RegionPosI.of_check c7 q7 ok_7 1090715534753792 1125899906842624 4611686018427387904 9223372036854775808 8646911284551352320 9223372036854775808 (by decide +kernel)))))
end CKLaneC.RSC2.S00_0091