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openAI-math-dataset / lean /OAI /MathematicalPhysics /DefocusingNLS /Profile /ProfileCertificateValues.lean
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import OAI.MathematicalPhysics.DefocusingNLS.Profile.ProfileCertificateRecipe
namespace OAI
/-! Exact intermediate rational values for Appendix `cert:profile`.
Every recurrence transition is proved by kernel reduction. -/
namespace DefocusingNLS.ProfileCertificate
namespace Computed
def stage0 : State := initial
def stage4 : State :=
⟨⟨⟨(473389420852990707572186868228319438689556581787110448672331 / 1391280000000000000000000000000000000000000000000000000000000), (-198945475349241026349725618423338174880102869 / 347820000000000000000000000000000000000000000)⟩, ⟨(-441582866941409870531620824937178850545486283864520617543779 / 6956400000000000000000000000000000000000000000000000000000000), (-5426960103024316165938611734703791888798785749 / 23188000000000000000000000000000000000000000000)⟩, ⟨(3169782311878258141059438968639710402297456373369641752718669 / 1159400000000000000000000000000000000000000000000000000000000), (-800608655957435165075463877997182759885899849 / 1054000000000000000000000000000000000000000000)⟩, ⟨(972842845388836007879461141977205173998878198800012143484239 / 1159400000000000000000000000000000000000000000000000000000000), (-2521074013990028302536379271597301784152012991 / 5797000000000000000000000000000000000000000000)⟩⟩,
⟨⟨(-8480554333646519489248190005101608001801416791 / 139128000000000000000000000000000000000000000000), (-888109323670835572732184546177 / 14880000000000000000000000000000)⟩, ⟨(-1698890840959916742338477076003840540220564043 / 69564000000000000000000000000000000000000000000), (3046487860483509309306891580669 / 695640000000000000000000000000000)⟩, ⟨(-3563405351001194225766137576057663933387802767 / 46376000000000000000000000000000000000000000000), (-1033600914412567082966625349760339 / 2782560000000000000000000000000000)⟩, ⟨(-109324909410330167355840651874435034933823431 / 2529600000000000000000000000000000000000000000), (-304135182570127222288273134192733 / 2782560000000000000000000000000000)⟩⟩,
⟨⟨(-4677278459610142289136650683318649950491206273 / 69564000000000000000000000000000000000000000000), (-92672902469844071045916831500589 / 463760000000000000000000000000000)⟩, ⟨(-190618357901348654040067231783614693781841987 / 4347750000000000000000000000000000000000000000), (-310756104777524771758736594949 / 3710080000000000000000000000000)⟩, ⟨(-782498052664642686452446660130663612801820423 / 23188000000000000000000000000000000000000000000), (-108364622927518301865524842322771 / 463760000000000000000000000000000)⟩, ⟨(-19918634007967368381672849191191557526685317 / 748000000000000000000000000000000000000000000), (-6165876735406141363227127646669 / 42160000000000000000000000000000)⟩⟩,
⟨(62896937679620465573448570917263 / 1391280000000000000000000000000000), (124065067854642798027976046219 / 5610000000000000000000000000000), (146308627690004873387965277270821 / 2782560000000000000000000000000000), (2255526301392935884909707274057 / 81840000000000000000000000000000)⟩⟩
theorem transition4 : step 30 (step 31 (step 32 (step 33 (stage0)))) = stage4 := by
decide +kernel
def stage8 : State :=
⟨⟨⟨(-19183182109167059028153871103976209245897701785040553712618576418784797308325928042083077948467753760162710101687144321881 / 28596021300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-141140608647260434668577809928917967347467790238711645042885124510409542448039116086793243996380049420848177 / 142980106500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-9620061580367327930488936173686715316909442375047654763422119772296265869162013669787350610814879074691556598647166389331 / 28596021300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-140873859225544709302290692288343668102881174887352537030061446016972346884421942371003301769295043948409 / 706074600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(418850044548804336415501124027308674694714815693054471165460546299030547571422575934677275955850985498710639426952698099 / 185688450000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-131840797987759622391185858488994612650044958022946337223469354097647618937820817272414238178072299258588833 / 35745026625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(21664448810679976317235747345658271275317334971748361583410119569400526671477740510748573739814168763525643313066813783 / 190640142000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-186858159417180029080806613432467772127667362295851754108798468357068156644272237368737707894205187182487123 / 142980106500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩,
⟨⟨(-31861017031315643610688542078351262352452847068283523663272448784322590378892381063491246229612851600042787 / 114384085200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (308687211900335695252224095930946457502135288790473195807037512143292837951422760916123303421 / 2287681704000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-1139079464362801452147793966874326878209775181347632228922786108183898488179931942371003301769295043948409 / 19064014200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (536027232394205861173053572784865314417172308427882185387430261949500281713903321518406141 / 7060746000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-78125292492416664691454742549145214430038200112552382006044356569662090407366957656796203946227206454047819 / 81702918000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-242522208908998223527785759840708553996984886525228522536478656654757324350586343963965729641 / 326811672000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-38321590398979937665364971999108384253046283119452950578389941058841349673614349409265226418997081336352333 / 114384085200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-151556340006502770948494852907428553589977126746235624873104819928785580553172509178530696333 / 2287681704000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩,
⟨⟨(-161480006239858270570763608118163724754062259203493349408545349332400757135692914728757414692913675794637167 / 285960213000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-1203516872447373928029126443531668828367614538053529065270769320857107131819264844410544312749 / 5719204260000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-32444798450018820830905114775575655882605294126775857460865299931991137241842735462568816293473070105592061 / 142980106500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (233918706278213991533733776598711126334933656208122223292673520324153553585553447501729829 / 42364476000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-7408957354066064543488415886119370782607403824964421564519882519427157071575806093162724357811092921857409 / 8665461000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-6348322884931932448708662311208771853978691210283829769473667700270208945957007100132837290279 / 5719204260000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-2733884644335666217055492173226883358273478927247102177609575146514747718891049306747106269021500790743401 / 6354671400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-2171121187196341565561547351917425734301659978697049784325342667324174679171488988081281224331 / 5719204260000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩,
⟨(566377511226608322590788655581111570939234590556101389296058267590569060364922035583195729779 / 1143840852000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (62751803148721883837745463911114657466688108951100501583656818847142411930966332911603854607 / 317733570000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (3665126292590030638454098321814836766532331612765827065586676277803626657385116117897938963729 / 3812802840000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (154605938264545326722169208504872674322375535688897628790295031710117514454139625726382938437 / 381280284000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩
theorem transition8 : step 26 (step 27 (step 28 (step 29 (stage4)))) = stage8 := by
decide +kernel
def stage12 : State :=
⟨⟨⟨(-42484418223416255090294860159839434217681137411147716312471732235809512494183990402665627678913946927278841115836317485658922521472085323038060657729070753982479414746019975803198563 / 21375525921750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (6966997465219026101914172225404643101494298088816653869307271511738149247743713279089664768368400551956928660781257094744236196245764784438273584421680313987872372141 / 160316444413125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-7075253213814904339133152906026649939148685813472099912875620199188920014208595210165079558882757728771582220780871264010984956495700688717486285388169235874300369414096547286479271 / 12825315553050000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (677541494117065040402758303939425264248802606881536520035026646869145249128849950310550440261464894561861124564384505346259300116212482879382447464874124518738226423 / 2331875555100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-40848842254399201394886159914550133814115754309853422240584998770949126287241600031935816435609894674823676393529068836371157802722904422343935580187465751854179895292369067807833 / 14947920225000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-24143893048040500409616694051930849689933723983800037947917757598433170800231613395017235226191435115256354946113647309278166803852026314787794353323936135077563760491 / 4164063491250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-4652591904293269723259190407655048462683336631215670981447554968182239763847309125684412167278066491631471595126946971242613569489333191821476289658231236707997108962162599589872697 / 2914844443875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-9027730972903265681630548049301994620757044022036650826206827204110763273671567943025452016110742521584584392675038413227087062029073159294801014487775616489493455653 / 7287111109687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩,
⟨⟨(-43731757336431408185744825002197502401620881745305894821601963537355667398314552098845004729256452267867284125500737971916641463234094121094789625125295316699612297901 / 427510518435000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (21556879454232536650722244932181267255211950724814519304035382660168802456633257254270626402167081451947867968733833598048081412617728322361904828617826781 / 25650631106100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(55398841126128541594939071126371123569210940742593729498994090440709799276998920476778483382793594974081836443891969113861764676146160767923206922113615369706120490653 / 641265777652500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (6831862255240670062659496718458134309844747873686343796705698584083994387691752425998001243647460578448163509403958274222353957452587136782556105534397 / 28500701229000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-3467256881291405367491312508451969548979772785840223154388754864186296411604482984207319935738104124232400181702925224895033450969371801666381010010560069533580629476461 / 1282531555305000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (3281579810811850298428779094995859688389116441335818247338379921864921872765614651559845114707396077730514244619936680794647722846013589480586972333114267 / 3664375872300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-771965697931090163972418670416464053721221830842597777095489225647108348138820522929497212687661414738387680672330858275801152502745661547130782719603116689511077875009 / 1282531555305000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (15854573535930956870659860391596157482350327154837544983877101194975703922044426615476320754061154777869393402172544080075700842859641142370335978856625019 / 25650631106100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩,
⟨⟨(-3249879480001982534452540793570599828198532088347963940624108756616652008428062949234249987841104542760667244189723946128997058814325200500063800559834050096404915173 / 2955141832500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (9211214684455638121411547624571102167298792399370900782032601416915478568406673864261854831836507500508269722069430808113728738822559603970963965825683 / 9327502220400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-12390161460726012745507222936898840098345282389106488797450066677185989635524621361553213158766242561320345380825553525603405606623971958060329675650744311474775848491 / 53438814804375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (4516029613107629550359930073087442117657060966883449057382694308820249652616997969456959012809037285379870209450064186899714000009425611283567439268103 / 9327502220400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-73715092799361505290563519831538740436514800581821587699385042513583643489025775996400975207321538572508688718751960734399375973310210064744549328501066801393656467981 / 19432296292500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-1362317944572998663384497311834564156280204427857950700694941930937397250243941615622238826514413492470930526144513718009277052913960587133091518549891 / 3587500854000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-4620902872114092473137672543285862579516353010541102921769866867946630527010585263250475932018729047583647919985500148930310001173437899532967318789706187878195488827 / 3429228757500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (14056998408111109022335559726602202298961626174761240800113555768752867165055600348366617696601523610041008537518196527214904665003389285047367765348573 / 46637511102000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩,
⟨(515690778751742816774697244736674736127071069669067327621965312905780892043383361242957743183579824371754721175918761818537639212233825942912833821179693 / 213755259217500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (12236893499581549749540093062357068182149223065373156438633936004771674651590697999757182163712976475989800594582169143642624484818362083651412742507897 / 13940560383750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (13546558837111894241263046248883614419817204444360313570499723978081330889118963015579157735739699383319303885063302655883464041354514078730211548654055589 / 2331875555100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (898215070246969769292802072238376068751588569140560658864015170398213972485310928084069535688021473730479052357926190283841680791533844261028108087434513 / 413719856550000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩
theorem transition12 : step 22 (step 23 (step 24 (step 25 (stage8)))) = stage12 := by
decide +kernel
def stage16 : State :=
⟨⟨⟨(-2707619760753738454307902183909268677156195658964499964710960735334808143359959856326587173753169270089487622007267941934579009261781892127920633774803571612382216891124950406155012786815395731168756218309912234150084297683369919796704348979 / 2010368212940587500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (1040020918002184614014192814072990027710003086092421349284075397411041969596452943542388920039660777793041131705300389439223125241000199965518521904604528861750493271267562177518441221169193371843791839617903425370612746466456301 / 351814437264602812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(165801568608801284577758256068806210283168045235807469771315721118793243384878860459457994971415977856123913707946770788140221897689622986350580256946863936809257563243886212843515037619727733136001779742356188949082481939804627313352110333 / 4138993379583562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (2085320544774925786622606194471052847078514233851275664386170854484842792730824414850335057177693424397781161468322343958190691656621533963522917723164921089416357866445658549699177393655215819848561689814373160505757330394399 / 2039503984142625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-5379570885566818917498352445778788943919163797509479920681273321568691847094278560399292033787222061626216773106741759813546156146409835404392286804245874902631955892189999287549738746085157038558664082096838218691266325275819378174787588151 / 558435614705718750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-8072387735802273469179792924466376054077677536324568976838834758889519153505196545146569673305272862498070506370761949098881058998846757523037565961347467096887032785615533656361038018749586874846345305851135865823657659746893 / 19545246514700156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-984464652511578340957437775249117925618109792946661470728851829644424138009373065108385409592436628264081079709406417254757326990908516023360415662211317068278428049712466374314138222240153360721953073843097052773042184908558716450563828737 / 355368118449093750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (1250530996393692989968027919055355105616079287223796187221176026630293134887785431017191647581065054889101536531148663796462564257645198591347944137132759879403661247449800388330843137447815855126892722878366300035833695718261 / 1002320334087187500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩,
⟨⟨(265627265201626917920765880734316261663795466852007827558191914731399074388067134459802226708459278173900498083617492713748559872738961936326072510911361043187236281533536782154039115524929129410964025621654003544641869692334297 / 156361972117601250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (108885705064951501930333955616649199373978108097789681033743550802721026396525480960601498018181133090565671519216792606115485107031980459422478699728006327278145143511901833628723514380327552029062180248549921117 / 98754929758485000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(357294473756576956593056303531900999273169179426038025663661526281183597025750138124291949271087448129685742401414547082414099671456399623117675890360852214907835303119267881016960805631656819511697428269313248895132806548079 / 579118415250375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (3968840893684899367218595569441309660510055651639586124461051659165732790829196842958770481352880336534803302457629492477167715296987043128484183070910511090777079639497877084932203922136421727088240377480710571 / 61185119524278750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-490084360120248810464344772410312791418262061632202168734457198694947086850565224364379193877656088496070134124406390402819193057120779430480183379404363991751736062837079092623203283568844369274351682713507924849242310028248559 / 469085916352803750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (4933176489328475289493597644381727946300279422642456437958903240327713703654526089790013575654007650849225871413655910148019021398880551419994613075560107470713278984323116089434720247933359152639618002253787898247 / 804147285176235000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(114154324414697151884190946167172449088472269868531499890237132654265956838154820502666220399406217239681324545540134349535591074553537297448753992474740697567939963593397016183031984241668461401848239985779262440943443902739529 / 201036821294058750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (2052452000525635597418401262290246618923530889495891132764626031329052217012268885429551277412136590317520973738324676332768881613767453421305167555110813074056779714348574052648660948239537772218087465435278797039 / 1125806199246729000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩,
⟨⟨(733915627174850832515290104963903546304589125892782306822084673294059795157154331747589681803195318045240853431151670849250745407436707427739837675815568390391637368623441685609234683515281384228214083113590564338512474286565749 / 703628874529205625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (1496005112810105512283356304032613101219439792495790606853157888517859755542570609901748137980537433785644654432478492659236260612543683899553572331242450557689328413614057327032430005391060487509571420173104119 / 465593961640500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(272626141085609069441063559227066726967387726484788497653028397301774677077899436373921214798237071496280288988165378841637768958284724126986206252170813958167484813472647213417260425718308363374982473272519233089261205551836377 / 351814437264602812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (632965700892176319101315366287332060341404061799065255958966627551701924532538537360902586112029208236973046188340146336173846537309619263809996424568770510332873786617653816138241999503580679176381157180190847 / 715615433032500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-4704394415982362091023585528140628884733900885659502255762279790286752394767094712620727373486322348129539447737265536776306187063459561114935621568398464557382913218748359362689064563909888407610186184421882058102040925900013 / 919776306574125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (421316563904520898581084499847608766711035784168587436581419455603598094387632057244041251527445637974459405365566518954365465117185593867671934864831249611004077396267783609155571788656353972496233922010745026413 / 62544788847040500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(-12604418761955453392422966683492617183103796806830461669800369612567138609640301810065031693679037446583894881156404569656132347426273086454838935380099125473947690026080502995635941565664257651932831965143286707555776373713489 / 15636197211760125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (295480970636049706736504545410113261173345774051233396336694343563580118782171117808213681484550946525161183586077729808059022821358086263700881169847753852402661493165217456481227911960075881810032178475400940559 / 104241314745067500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩,
⟨(1575895865659289765883939253258524114307628688832425409914465656903982218503851203940436711695496169864077543957743297389068578361379091358336941480098358706040227753630187364934869174048781218676745127614211957761 / 161753764259587500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (786645301185692209022066502308792271167588035798591414166564577817085151812594840592010817579735760208810191178193366095088118345694979084918317879652626623529564733494984555676180514797663524815838404472202736481 / 226977056299743750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (17763730459860019262276333196128080492374185779647234328156536705061972482076521420919793252874203348499986211185990718265279315079554541789750786838832607189390841542334656343840287088109518346391358828279098038457 / 721670640542775000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (850014007685852101222383936413398641255998673717517290310667288889343307722267735198696213469911262310981686638760909220826991758320878736139931892419325465294591414442610162921661307091131445298543642135066767527 / 95731819663837500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩
theorem transition16 : step 18 (step 19 (step 20 (step 21 (stage12)))) = stage16 := by
decide +kernel
def stage20 : State :=
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⟨⟨(102157420214497203427209735647481359759931659433093843056095462406084432934354713492154294238686542272663694839096597199947864052050478346044302907922669295131611020905943938348974358012766458174362017643141222284071085914156656748663128298748951307883616285011386313330642278955960018769 / 14041984930821973125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-221073131608605657604035877485299020021539744506128921805802544467924816651858631911089974106251346814059449564093864861744467090207794190541826130846145832834569338730053128997135802441991748361410195647913027770232911720031335114072581069866187632232442603840351611426153 / 922759009739729662500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(12832401997028899871784559261619821555832690069874568699339128241673372269344174395230819285480842647656234407415782562138449278926613621103867026941019066225614064136547468083857049163674298450124664973081416901774409835281009759452719464607673334673113449058075525610953493066976465459 / 5767243810873310390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (-331450261342439692781386201586667371808737027102993939675625974069956879601267957406882643441283970819847520758717230360596051311170823869214475322119178364697740301999231439779384758063423491192856489592585859316181247316038920732164192266948424633175013705175895249288783 / 307586336579909887500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(312627941165736201402115483450050665384066537541631793260040058310820357047152666377654351566250741195662612142521490442129914846314198111374306180576416527773342875271393672616768539325632385668659435043132250919820205147314806001744704958268726869026736441818977492295300177948102603683 / 35885072600989486875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (62082145476651974429126945258902538817024405834504342381956280370816940817739752802875899246336292385627044042042760431311473554220591237414575054802003125657608105703287984173292448173896864846381106633354932100387974132417086099745376716555142528480270277572035502727169 / 4252345667003362500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩, ⟨(166951004377909504714544092498282176448451981866404532222521047316147137622826374291443286918682051912526349805396564921567734635551245857004895644110105311027675443519017142643999826286310661738737734615930031652294166724869080624396531294436560234815741318632739530265708533804044262887 / 35885072600989486875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (287461490229771178155971124694012527343829254703678790293869459856209410074599793804872452956244904697352454652777137179164760026111737075830135351338166714719316907630437006238220045338352980277495021804868744058822991541750918245121194995157232343205702401792883716915943 / 83887182703611787500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩,
⟨(239714755608071352485759976940805846623513802257221579566646898574118813731971144979326153460248916227942519705186769256945536282067215086377239298084371673281910768099987898450021062997536482270610609366344938295409957571425679177458713939928266241008507788969515285514578143 / 6459313068178107637500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (41962757033530163451228245166131687635033011514081880626697593962398330019820009229714566579467184050796615040813363955735273304189603803654253124022200478711472179858663505362487554920899299665838197519884839467626188308139667180392124684628630534044158482920744884825392491 / 3229656534089053818750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (1188215970751998323933417973015504442375057626238968322654400697265012337693057019382962401749504566245105794883339677119532529027301372491534028912546806337542127975676745480916676403409548403644971213341816957161921221077485899938559542482098800719091662606960292721156227641 / 12918626136356215275000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), (13085323214808388771534763344753364933332929613382372121932531508005536388998153442232207660702039179344874896476271443330122015149173682070460145764568048650902929937895534191027047555726363834365153301635514004565344265481008100971834367626062014874298086269763352764559439 / 403707066761131727343750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)⟩⟩
theorem transition20 : step 14 (step 15 (step 16 (step 17 (stage16)))) = stage20 := by
decide +kernel
def stage24 : State :=
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theorem transition24 : step 10 (step 11 (step 12 (step 13 (stage20)))) = stage24 := by
decide +kernel
def stage28 : State :=
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theorem transition28 : step 6 (step 7 (step 8 (step 9 (stage24)))) = stage28 := by
decide +kernel
def stage32 : State :=
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theorem transition32 : step 2 (step 3 (step 4 (step 5 (stage28)))) = stage32 := by
decide +kernel
def stage34 : State :=
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theorem transition34 : step 0 (step 1 (stage32)) = stage34 := by
decide +kernel
end Computed
theorem result_eq_computed : result = Computed.stage34 := by
have h : List.range 34 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33] := by decide
unfold result
rw [h]
simp only [List.foldr_cons, List.foldr_nil]
change step 0 (step 1 (step 2 (step 3 (step 4 (step 5 (step 6 (step 7 (step 8 (step 9 (step 10 (step 11 (step 12 (step 13 (step 14 (step 15 (step 16 (step 17 (step 18 (step 19 (step 20 (step 21 (step 22 (step 23 (step 24 (step 25 (step 26 (step 27 (step 28 (step 29 (step 30 (step 31 (step 32 (step 33 (Computed.stage0)))))))))))))))))))))))))))))))))) = Computed.stage34
rw [Computed.transition4, Computed.transition8, Computed.transition12, Computed.transition16, Computed.transition20, Computed.transition24, Computed.transition28, Computed.transition32, Computed.transition34]
end DefocusingNLS.ProfileCertificate
end OAI