| import OAI.Computability.Logspace.EstimatorMachine |
| import OAI.Computability.Logspace.TransitionEvaluation |
|
|
| namespace OAI |
|
|
| /-! |
| Evaluation of terminal estimator requests and their approximation guarantees. |
|
|
| From OpenAI, *Exact Derandomization of Logarithmic Space: L = RL = BPL*. |
| -/ |
|
|
| set_option autoImplicit true |
|
|
| section |
|
|
| namespace ExactDerandomization.Gyre |
| open Analysis Relay Counter Rill Fret At Hie |
| open Arena Amber Song Fret.Lyric Reed Lu Est Net |
| open Grain Terrain Bank Helix Helix.Age Helix.Mold Helix.Foil Helix.Moon Helix.Orbit Chime Dome Scheme Finset Stage |
| open SiteX |
| open Line Line.Fabric Fret.Seats |
| open Cambria.Wear.Paper |
| open Glass Glass.Rod Tiber.Sky |
| noncomputable section |
| open scoped Classical |
| variable {q w h:ℕ} {u:Line (q:=q) (w:=w) (h:=h)} |
|
|
| namespace Term |
| variable (r:Rock q w h) |
| abbrev selfC:Sight:=⟨_,VK.left⟩ |
| abbrev header:Cub ℕ Crt:=⟨_,(Kn.unpack (α:=Crt)).comp VK.left⟩ |
| abbrev spirit:Cub ℕ Scout:=⟨_,header.runs.right.right.left⟩ |
| def ahead(i:ℕ):Sight:= ⟨_,Tiber.Sky.pK i⟩ |
| def stomp (x:Word)(p:ℕ):Bool:= |
| let q:= spirit.f x p |
| decide (Foil.delta0 q) |
| def ebit : Cub ℕ Bool:= |
| let p:= spirit.runs.right.left |
| ⟨_, GK.decideK (GK.orG (GK.eqG p (Kn.fix 2)) (GK.eqG p (Kn.fix 3)))⟩ |
| def avail (r:Rock q w h):Cub ℕ Bool := |
| let p:= header.runs |
| ⟨_, GK.decideK (Foil.onRK r.w p.right.right.left p.right.left.left)⟩ |
| def fire (r:Rock q w h) :Cub ℕ Bool:=⟨_,leftQ.runs.lt (Kn.fix r.w.p.K)⟩ |
| abbrev te(k:ℕ):Kiwi := |
| Flash.clan (⟨_, Kn.wash.comp ((ahead 12).runs.tuple leftQ.runs)⟩) k |
|
|
| def rally (p:Scheme) :ℕ → Cog |
| | 0=> Cargo.knock |
| | k_tube+1=>.seq (Pier.walk p (te (k_tube+1)) true true) |
| (.bif Cargo.flag0 (rally p k_tube) |
| (.seq (Pier.walk p (te (k_tube+1)) false false) (Flash.plumb (k_tube+1)))) |
|
|
| def ent (r:Rock q w h)(v:Tags) :Cog := |
| let p:=Song.pleas ebit |
| (Song.pleas (fire r) (rally (schedule r v) (clim r.w.p)) Cargo.knock) |
| (Flash.chose (tag 9 0 true) 1) |
| Song.pleas (avail r) p Cargo.knock |
|
|
| end Term |
| namespace OrbitR |
| open Term |
| structure Prism(u:Line (q:=q) (w:=w) (h:=h))where |
| s:Fabric u |
| p:MintV |
| namespace Prism |
| variable (e:Prism u) |
| abbrev v :=e.s |
| abbrev origin := e.v.leaveE |
| abbrev src :=e.origin.dataN |
| abbrev target(x):=Studio.dockA u e.src x |
| abbrev screen (x j):=Studio.stk u e.src x j |
| abbrev fare(r:Rock q w h)(v:Tags) :=Cambria.Era.tariff r+v.e+50 |
| structure Ready (e:Prism u) :Prop where |
| season : Stone.Rector e.v e.p |
| spend : fare u.r u.v ≤ u.v.slope |
|
|
| namespace Ready |
| variable {e:Prism u}(he:e.Ready) |
| include he |
| lemma motto : u.D.Suite e.src := he.season.endUnits _ (Or.inl rfl) |
| omit he in |
| lemma crown :u.D.D e.src=1:= e.v.ageEnd _ (by decide) |
| lemma includes0 : e.origin.Front u:=he.season.frontE |
| omit he in |
| lemma price0: Cambria.Era.tariff u.r ≤ fare u.r u.v:=by unfold fare;omega |
| omit he in |
| lemma price2:4 ≤ fare u.r u.v∧ clim u.w0.p+2 ≤ fare u.r u.v ∧ u.v.e+20 ≤ fare u.r u.v:=by |
| unfold fare Cambria.Era.tariff Cambria.Era.budget bootC |
| change _∧clim u.r.w.p+2 ≤_∧_; omega |
| omit he in |
| lemma playsC (x j):(Term.spirit.f u.x (e.screen x j).info)=bitR e.s.t:=by |
| change Age.styx (Term.header.f _ _)=_ |
| change ((dec (dec _ :Stool).1:Crt).2.2.1)=_ |
| change ((dec (dec (enc ((_,_,_):Stool)):Stool).1:Crt).2.2.1)=_ |
| rw [dec_round];change (Age.styx (dec (enc _)))=_ |
| rw [dec_round] |
| omit he in |
| lemma toneC (x j) : |
| Term.ebit.f u.x (e.screen x j).info=e.v.govern∧ |
| (Term.avail u.r).f u.x (e.screen x j).info=decide e.v.activeR∧ |
| (Term.fire u.r).f u.x (e.screen x j).info=decide (j<e.origin.m):=by |
| let s:=e.screen x j |
| have hp: Term.spirit.f u.x s.info=bitR e.s.t:=Ready.playsC (e := e) x j |
| refine ⟨?_,?_,?_⟩ |
| · change decide ((Term.spirit.f u.x s.info).2.1=2∨ (Term.spirit.f u.x s.info).2.1=3)=_ |
| have hQ:=congrArg (fun a:Scout=> decide (a.2.1=2∨ a.2.1=3)) hp |
| apply hQ.trans |
| change _= e.s.t.tag.narrow |
| unfold bitR |
| cases e.s.t.tag |
| · rfl |
| · rfl |
| · next b h=> cases b <;> rfl |
| · rfl |
| · have hh: Age.MV (Term.header.f u.x s.info)=e.s.m:=by |
| change Age.MV (dec (dec (enc ((_,_,_):Stool)):Stool).1)=_ |
| rw [dec_round];change Age.MV (dec (enc _))=_ |
| rw [dec_round] |
| change decide (operateR u.r.w (Age.MV _) (Term.spirit.f u.x s.info))=_ |
| rw [hh,hp] |
| simp only [decide_eq_decide] |
| exact e.v.workR.symm |
| change decide (leftQ.f _ _ < _)=_ |
| rw [show leftQ.f u.x s.info=j by simp [s,leftQ,film,info,panelx]] |
| omit he in |
| lemma gem (b a:ℕ)(x j): (Tiber.Sky.seek a b ⟨_,Tiber.Sky.whoK true⟩).f |
| u.x (e.screen x j).info=hole (e.v.c a 0) (hole b j):=by |
| have h: Reed.V u.x (e.screen x j).info=(e.src,j,0):=dec_round .. |
| change hole (pointer (Reed.V u.x _).1 _) (hole _ _)=_ |
| unfold Tiber.Sky.whichSide;rw [h] |
| have hs:pointer e.src a=e.v.c a 0:=Stone.pointing .. |
| rw [hs]; change hole _ (hole _ (Reed.V u.x (e.screen x j).info).2.1)=_ |
| rw [h] |
| omit he in |
| lemma spinC (i x j): (Term.te i).f u.x (e.screen x j).info= |
| (e.v.slotWord j,i):=by |
| have h: Reed.V u.x (e.screen x j).info=(e.src,j,0):=dec_round .. |
| have hs:pointer e.src 12=e.v.c 12 0:=Stone.pointing .. |
| change (hole (pointer (Reed.V u.x _).1 12) (leftQ.f u.x _),i)=_ |
| have hb:leftQ.f u.x (e.screen x j).info=j:=by change (Reed.V u.x (e.screen x j).info).2.1=j;rw [h] |
| rw [h,hb,hs];rfl |
| end Ready |
| |
| def lifted (e:Prism u)(f:Producer) (tb:ℕ→ℕ→ℕ) :Producer := |
| { tag:= fun x i=> if e.v.govern then tb x i else if f.awake x i then 1 else 0 |
| locate:= f.locate } |
| structure Enabled (e:Prism u)(f:Bool→Producer)(tb:ℕ→ℕ→ℕ) :Prop where |
| ready:e.Ready |
| onR : e.v.activeR |
| report : e.v.Tgood e.p f |
| allocate : e.v.govern = true → e.v.Profession (f false) tb |
|
|
| end Prism |
| end OrbitR |
| end |
| end ExactDerandomization.Gyre |
|
|
| end |
|
|
| section |
|
|
| namespace ExactDerandomization.Gyre.OrbitR.Prism |
| open Analysis Relay Counter Rill Fret At Hie |
| open Arena Amber Song Fret.Lyric Reed Lu Est Net |
| open Grain Terrain Bank Helix Helix.Age Helix.Mold Helix.Foil Helix.Moon Helix.Orbit Chime Dome Scheme Finset Stage |
| open SiteX |
| open Line Line.Fabric Fret.Seats |
| open Cambria.Wear.Paper |
| open Glass Glass.Rod Tiber.Sky Term Producer |
| noncomputable section |
| open scoped Classical |
| variable {q w h:ℕ} {u:Line (q:=q) (w:=w) (h:=h)} |
| variable {e:Prism u}{f:Bool→Producer}{tb:ℕ→ℕ→ℕ} |
| abbrev rankF (u:Line (q:=q) (w:=w) (h:=h)):= fare u.r u.v |
| lemma chooses {a:Cub ℕ Bool}{v:Seats}{p f:Cog}{c:ℕ}{i:ℕ}(h:a.f v.l.x v.info=true) |
| (he:v.rite c p i):v.rite c (pleas a p f) i := |
| fun _ hx=>Song.park a h (he _ hx) |
| lemma doesno {a:Cub ℕ Bool}{v:Seats}{p f:Cog}{c:ℕ}{i:ℕ}(h:a.f v.l.x v.info=false) |
| (he:v.rite c f i):v.rite c (pleas a p f) i := |
| fun _ hx=>Song.parks a h (he _ hx) |
| namespace Enabled |
| variable (he:Enabled e f tb) |
| include he |
| abbrev core12(e:Prism u):=e.v.c 12 0 |
| abbrev frame(e:Prism u):=e.v.terminal false |
| lemma capR (h:e.v.govern=true){i:ℕ}(hi:i<e.v.Rslots){t x:ℕ}(ht:0<t)(hs:t ≤ clim u.w0.p) |
| (hx:x∈u.D.P): |
| Pier.Liaison u.D x e.src (e.v.slotWord i) t ∧ |
| u.D.curve (e.v.slotWord i) t true x = if tb x i=t then some ((f false).locate x i) else none:=by |
| obtain ⟨hd,hp,hv⟩:= (he.allocate h).guide x hx i hi t ht hs |
| refine ⟨⟨?_,hx,hd,hp⟩,hv⟩ |
| rw [show cell (e.v.slotWord i)=e.v.c 12 0 by simp [Fabric.slotWord,hole,cell],(Ready.crown (e := e))] |
| exact Fabric.parentL e.v (by decide) (by decide) (by decide) |
|
|
| lemma roves (h:e.s.govern=true){i:ℕ}(hi:i< e.v.Rslots) |
| {x:ℕ}(hx:x∈u.D.P)(a:ℕ) (ha:a ≤ clim u.w0.p): |
| let c:=rankF u |
| (e.screen x i).rite c (rally u.D.s a) (if tb x i ≤ a then tb x i else 0):=by |
| intro c |
| let S:=e.screen x i |
| let b:=tb x i |
| let p:= e.v.slotWord i |
| have hp:= he.ready |
| have hs:=hp.motto |
| have hm:4 ≤ c∧ clim u.w0.p+2 ≤ c:=⟨(Ready.price2 (u := u)).1,(Ready.price2 (u := u)).2.1⟩ |
| have hW:2≤c:=by omega |
| induction a with |
| | zero=> |
| have ht:(if tb x i ≤ 0 then tb x i else 0)=0:=by split<;>omega |
| rw [ht]; exact Fret.Seats.blankD (hs.pit hx S.info) hW |
| | succ a ih=> |
| let d:=a+1 |
| have hj:=he.capR h hi (show 0<d by unfold d;omega) ha hx |
| have hz := (Ready.spinC (e := e)) d x i |
| rintro _ ⟨f',hf,rfl⟩ |
| have hQ := Pier.shares hs hW hj.1 true f' hf hz |
| have hc':u.D.s=u.D.s:=rfl |
| by_cases hc:b=d |
| · rw [ite_eq_left (show tb x i ≤ a+1 from hc.le)] |
| rw [hj.2,ite_eq_left hc] at hQ |
| let y:= (f false).locate x i; let r:=u.D |
| have hF:r.curve p d true x=some y:=hj.2.trans (ite_eq_left hc) |
| have hv := (hj.1.ready.swaps d hj.1.holds x hx true y hF) |
| have hR:= Pier.stroll hs hW (Pier.street hj.1 hF) (Pier.seal1 r (q:=S.info) hs hW) |
| (j:=0) false f' hf hz hv.2 |
| apply Lot.Mane.seq hQ |
|
|
| refine Lot.Mane.no ?_ (Lot.Mane.seq hR ?_) |
| · exact (show decide (1= (0:ℕ))=false from rfl) |
| have hL:= hs.pit hx S.info (glove f' x) ⟨f',hf,rfl⟩ |
| have hl : Punct S.head c (tb x i):=by |
| unfold Punct;change lb b+1 ≤ c*u.D.D e.src |
| have h1:=lb_le_inc d; have h2:d≤ clim u.w0.p:=ha |
| rw [(Ready.crown (e := e)),hc]; omega |
| exact etches _ _ (i:=1) hc.symm hR.spots.2 (plight hl hL (by omega)) |
| rw [hj.2,ite_eq_right hc] at hQ |
| have hq:(if tb x i ≤ d then tb x i else 0)=if tb x i ≤ a then tb x i else 0:=by |
| unfold b d at *; split <;> split <;> omega |
| rw [hq] |
| exact Lot.Mane.seq hQ (Lot.Mane.yes (show decide (0 =(0:ℕ))=true from rfl) |
| (ih (by omega) (glove f' x) ⟨_,hf,rfl⟩)) |
|
|
| lemma mounted (x:ℕ) (hx:x∈u.D.P)(i:ℕ)(ht:u.smallQ e.src i) : |
| let g:= e.lifted (f false) tb |
| let c:=rankF u |
| (e.screen x i).rite c (Term.ent u.r u.v) (g.tag x i):=by |
| intro g c; let s:=e.screen x i |
| let t:= clim u.w0.p |
| have h0:= he.ready; have hC:= (he.report.secure false) |
| have h2:e.v.activeR:=he.onR |
| have hp:=h0.motto |
| have h3:4 ≤ c ∧t+2 ≤ c∧u.eye.e+20 ≤ c:=(Ready.price2 (u := u)) |
| have hk:=(Ready.toneC (e := e)) x i |
| apply chooses (hk.2.1.trans (decide_eq_true h2)) |
| by_cases hz:e.v.govern=true |
| · have hm:g.tag x i=tb x i:=ite_eq_left hz |
| rw [hm] |
| apply chooses (hk.1.trans hz) |
| by_cases hu:i< e.v.Rslots |
| · apply chooses (hk.2.2.trans (decide_eq_true hu)) |
| have he0:tb x i ≤ t:=by |
| by_cases hb:tb x i=0; rw [hb];omega |
| exact ((he.allocate hz).bound x i hb).2 |
| have he1:= he.roves hz hu hx t le_rfl |
| change s.rite c _ (if tb x i ≤ t then _ else 0) at he1 |
| rwa [ite_eq_left he0] at he1 |
| apply doesno (hk.2.2.trans (decide_eq_false hu)) |
| have hh:tb x i=0:=by by_contra hp; apply hu (hC.suit.lacks hx ((he.allocate hz).bound x i hp).1) |
| rw [hh]; exact Fret.Seats.blankD (hp.pit hx s.info) (by omega) |
| apply doesno (hk.1.trans (by cases h:e.v.govern; rfl; contradiction)) |
| let w:= e.v.terminal false |
| have hg:g.tag x i=Flash.win ((f false).tag x i) 1:=by |
| unfold g lifted |
| dsimp only; rw [ite_eq_right hz]; unfold Flash.win Producer.awake; split <;> simp_all |
| rw [hg]; apply Flash.picks u.D hp hx (by omega) _ _ _ (Pier.seal1 _ hp (by omega) (q:=s.info)) |
| have hv := hC.suit |
| have hd:u.D.D w.dataN=1:=e.v.ageEnd _ (by decide) |
| have heD:u.D.D w.visN=1:=by rw [← hv.coil.grain]; exact hd |
| have hm:u.smallQ w.dataN i:=by |
| change lb i ≤ u.eye.e*u.D.D w.dataN;rw [hd,←(Ready.crown (e := e))]; exact ht |
| let z:=(f false).tag x i |
| have hP : Punct s.head c z:=by |
| have hf:= (hv.trace _ hx).fits i hm |
| change lb z ≤ u.eye.e*u.D.D w.visN at hf;rw [heD] at hf |
| unfold Punct;change lb z+1 ≤ c*u.D.D e.src; rw [(Ready.crown (e := e))];omega |
| apply Bullet.copy u.D hp (by omega) hx _ ((Ready.gem (e := e)) 0 9 x i) |
| hP ((hv.trace _ hx).next i hm) |
| rw [(Ready.crown (e := e))];exact e.v.parentL (by decide) (by decide) (by decide) |
| |
| lemma ancestor {y x:ℕ}(h:e.v.govern=true)(he1 : e.v.finalE x y≠0): |
| ∃ i,(f false).awake x i∧ (f false).locate x i=y ∧tb x i≠0:=by |
| have hu:= he.report.secure false |
| have hv : e.v.aimE false x y ≠0 := by |
| intro hk |
| apply he1 |
| unfold Fabric.finalE forecast current; dsimp only |
| rw [ite_eq_left (show Net.onQ u.plotM.gap e.v.m (e.v.t.key u.plotM)=true from he.onR)] |
| change e.v.grid.pre e.v.grains (e.v.trio false) e.v.t.two x y*_*_=_ |
| rw [show e.v.grid.pre e.v.grains (e.v.trio false) e.v.t.two x y=0 from ?_];ring |
| change e.v.grid.pre e.v.grains (e.v.trio false) false x y=0 at hk |
| unfold At.Grid.pre at hk ⊢ |
| split at hk <;> split <;> grind |
| obtain ⟨i,hi,hq⟩:=hu.light.defend x y hv |
| refine ⟨i,hi,hq,?_⟩ |
| apply ((he.allocate h).quota _ _ hi).2 |
| rw [hq] |
| by_contra! h0 |
| let d:=e.v.grid |
| have hk : 1 ≤ d.rankin e.v.grains y:=by |
| apply (Analysis.rank_ge (show (0:ℝ)<1 by norm_num)).mpr |
| apply lt_of_lt_of_le h0 (card_le_card _) |
| intro x hx; obtain ⟨hx,i,hi,hj⟩:=mem_filter.1 hx |
| refine mem_filter.2 ⟨(hu.light.insured _ _ hi).1, Eq.ge ?_⟩ |
| exact hj ▸ he.report.seat x i hi |
| apply he1 |
| unfold Fabric.finalE forecast current; dsimp only; rw [ite_eq_left (show Net.onQ u.plotM.gap e.v.m (e.v.t.key u.plotM)=true from he.onR)] |
| have hz :d.incG e.v.grains y=0:=by unfold At.Grid.incG;rw [ite_eq_left (show d.sp=true from h), shutoff_zero (by linarith)] |
| change _ * d.incG e.v.grains y * _=0 |
| rw [hz];ring |
| end Enabled |
| end |
| end ExactDerandomization.Gyre.OrbitR.Prism |
| |
| end |
| |
| section |
| |
| namespace ExactDerandomization.Gyre.Term |
| open Analysis Relay Counter Rill Fret At Hie |
| open Arena Amber Song Fret.Lyric Reed Lu Est Net |
| open Grain Terrain Bank Helix Helix.Age Helix.Mold Helix.Foil Helix.Moon Helix.Orbit Chime Dome Scheme Finset Stage |
| open SiteX |
| open Line Line.Fabric Fret.Seats |
| open Cambria.Wear.Paper |
| open Glass Glass.Rod Tiber.Sky |
| noncomputable section |
| open scoped Classical |
| variable {q w h:ℕ} |
|
|
| abbrev need :Cub ℕ Bool:= |
| let h:=spirit.runs |
| ⟨_, (h.right.left.eq (Kn.fix 4)).cond (Kn.fix false) h.right.right.right⟩ |
| def noteQ: Cub ℕ (ℕ×ℕ×NoteM):= |
| let h:=header.runs.right.right |
| let k:= h.left.left.right.right.right |
| let g:=Kn.wash.comp ((Kn.fix ((4,false):ℕ×Bool)).tuple (((Kn.fix 0).tuple k).tuple ((Kn.fix ((0,0):ℕ×ℕ)).tuple h.right))) |
| ⟨_, (ahead 10).runs.tuple (leftQ.runs.tuple ((Kn.fix ((1,0):Arch)).tuple g))⟩ |
| abbrev sees:Cog:= Bullet.snap (Flash.garnish noteQ) |
|
|
| variable (r:Rock q w h) |
| def portals (x:Word)(a:ℕ):ℕ:= |
| let q:= Term.spirit.f x a |
| if q.2.2.2 then (if q.2.1=2 then q.2.2.1+1 else r.w.p.T) else 0 |
| lemma portalsK: Kn (portals r):= |
| let h:=spirit.runs.right |
| h.right.right.cond (h.left.cond_eq (Kn.fix 2) h.right.left.succ (Kn.fix r.w.p.T)) (Kn.fix 0) |
| def candle(j:ℕ): Cub ℕ Bool:= ⟨_,(Kn.fix j).lt (portalsK r)⟩ |
| def changeP (i j:ℕ): Scout:=bitV (detector i j) |
| lemma changeK {α}[Wire α]{p:PT α ℕ}(h:Kn p)(j): Kn (fun x a => changeP (p x a) j) := |
| (h.tuple (h.tuple (Kn.fix _))).tuple (Kn.fix ((6,j,false):ChoiceX)) |
| def atlas (j:ℕ)(x:Word)(a:ℕ):ℕ:=by |
| let v:= Term.header.f x a |
| let z:Issue:=dec (Age.env v) |
| exact hole (enc (kit 17 (MV v-1,0) (changeP (Age.styx v).1.1 j) |
| (enc ((z.2.1,z.1,z.2.2):Issue)))) (hole 1 0) |
| lemma atlasK(j):Kn (atlas j) := |
| let h:= Term.header.runs; let p:= (Kn.unpack (α:=Issue)).comp h.right.right.right |
| let w:=Kn.wash.comp (p.right.left.tuple (p.left.tuple p.right.right)) |
| let g:= (Kn.fix 17).tuple ((h.right.left.left.pred.tuple (Kn.fix 0)).tuple |
| ((changeK h.right.right.left.left.left j).tuple w)) |
| Kn.wash.comp ((Kn.wash.comp g).tuple (Kn.fix _)) |
|
|
| variable (v:Tags)(p:MintV) |
| abbrev b0:=campk (knob r v) |
| abbrev bright(k j:ℕ): Lyric:= |
| let f:= Pier.escort (schedule r v) (te k) (Bullet.snap ⟨_,atlasK j⟩) |
| Lyric.use 0 (pleas (candle r j) f (snow (b0 r v) 0)) |
| def tuneE(k:ℕ) : ℕ → Lyric |
| | 0=>zeroE |
| | i+1=> Lu.sup (tuneE k i) (bright r v k i) |
|
|
| abbrev originC := tag 9 1 true |
| def summit(k:ℕ): Cog := |
| Pier.escort (schedule r v) (te k) |
| (Bullet.snap (seek 13 1 ⟨_,Kn.fix 0⟩)) |
| def double(k:ℕ):Lyric:= |
| let h:=Lu.diff Song.ein (Song.boostR (.use 0 (summit r v k))) |
| times (Lu.times (.use p.coin originC) h) (Song.gammaR (tuneE r v k r.w.p.T)) |
|
|
| def melody(k:ℕ):Cog:= |
| let K:=b0 r v |
| let g:=snow K p.coin |
| let f:= Song.pleas Term.ebit (roost K (double r v p k) p.coin) originC |
| if k=0 then g else |
| Song.pleas need (Cargo.choose sees g f) f |
| def costamp:Cog:= |
| let g:= clim r.w.p+1 |
| Arena.Iris.dial (Term.ent r v) (melody r v p) g |
| def endC(i:ℕ):Cog:= if i=0 then Term.ent r v else costamp r v p |
| abbrev fullD:= Studio.arrange (endC r v p) 1 |
| namespace Budget0 |
| open Cambria.Wear |
| abbrev H (r:Rock q w h)(v:Tags)(p:MintV)(k:ℕ): Lyric:= reset (double r v p k) p.coin |
| abbrev wallet (r:Rock q w h)(u:Tags):ℕ:= OrbitR.Prism.fare r u |
| def cost (r:Rock q w h)(u:Tags)(p:MintV):ℕ:= |
| let c:=wallet r u |
| let v:=H r noneT p 0 |
| c+v.cost c + v.tail |
| lemma mantis (r:Rock q w h)(p:MintV)(u v:Tags)(i j:ℕ):Paper.same (H r u p i) (H r v p j):=by |
| let a:= tuneE r u i |
| let b:= tuneE r v j |
| have h0(x):Paper.same (a x) (b x):=by |
| induction x with |
| | zero=>exact oneself _ |
| | succ x ih=>exact same.plies ih (Paper.use ..) _ |
| have h:= h0 r.w.p.T |
| have hg : Paper.same (Song.gammaR (a r.w.p.T)) (Song.gammaR (b r.w.p.T)):= by |
| apply Paper.same.plies (oneself _) |
| apply Paper.same.rosebud |
| apply Paper.same.plies _ (Paper.oneself _) Doop.prod |
| exact ((oneself _).plies h _).plies (oneself _) _ |
| apply Paper.same.stow |
| exact (((oneself _).plies ((oneself _).plies (Paper.same.red (Paper.use ..)) _) _).plies hg _) |
| lemma fareE (r:Rock q w h)(v:Tags)(p:MintV)(k:ℕ): |
| let h:= H r v p k; let c:=wallet r v |
| c ≤ Budget0.cost r v p∧ h.cost c ≤ Budget0.cost r v p∧h.tail ≤ Budget0.cost r v p:=by |
| intro h c |
| have he:= mantis r p v noneT k 0 |
| change same h _ at he |
| obtain ⟨h1,h2,h3⟩:=he |
| rw [h2,h3]; unfold Budget0.cost; dsimp only; unfold c; omega |
| |
| end Budget0 |
| end |
| end ExactDerandomization.Gyre.Term |
| |
| end |
| |
| section |
| |
| namespace ExactDerandomization.Gyre.OrbitR.Prism |
| open Analysis Relay Counter Rill Fret At Hie |
| open Arena Amber Song Fret.Lyric Reed Lu Est Net |
| open Grain Terrain Bank Helix Helix.Age Helix.Mold Helix.Foil Helix.Moon Helix.Orbit Chime Dome Scheme Finset Stage |
| open SiteX |
| open Line Line.Fabric Fret.Seats |
| open Cambria.Wear.Paper |
| open Glass Glass.Rod Tiber.Sky Term Producer |
| open Helix.Torch |
| noncomputable section |
| open scoped Classical |
| variable {q w h:ℕ} {u:Line (q:=q) (w:=w) (h:=h)} |
| variable {e:Prism u}{f:Bool → Producer}{tb:ℕ→ℕ→ℕ} |
| abbrev LampT (e:Prism u):= e.s.t |
| abbrev Hx (e:Prism u):=u.D.high e.src |
| abbrev Tc (e:Prism u):= e.Hx + Budget0.cost u.r u.v e.p |
|
|
| abbrev across (e:Prism u):=crossP e.s.dye |
| abbrev heightR(e:Prism u) := if e.s.t.main then e.s.t.steps u.plotM else 0 |
| abbrev vale (e:Prism u):=e.s.m-1 |
| abbrev euro(e:Prism u)(j:ℕ):Peek:=detector e.s.t.i j |
| abbrev stationE(e:Prism u)(j:ℕ):ℕ:=u.vecL (e.euro j) e.vale 17 0 e.across |
| abbrev paintE (e:Prism u)(j y:ℕ):ℝ:= if j<e.heightR then (e.s.roll e.vale).outV (e.euro j) e.across y else 0 |
| abbrev outV (r:Fabric u)(x:ℕ):ℝ:=rank r.S0 (fun i=>r.aimE true i x) (clim u.w0.p) |
| structure Court (e:Prism u)(f:Bool → Producer)(tb:ℕ→ℕ→ℕ):Prop where |
| step0:e.Enabled f tb |
| stake: Budget0.cost u.r u.v e.p ≤ u.v.slope |
| may : u.wick0.Veil u.torch (e.s.c 10 0) |
| rank0: e.s.govern=true → ∀ x∈u.D.P, |
| let p:=e.v.c 13 0 |
| u.D.Voice p x (hole 1 0) (u.D.high p) 0 (outV e.v x) |
| tower0:e.s.govern=true→∀ j<e.heightR, |
| ∀ y∈u.D.P, u.D.Voice (e.stationE j) y (hole 1 0) (u.D.high (e.stationE j)) 0 (e.paintE j y) |
|
|
| namespace Court |
| variable (h0:Court e f tb) |
| include h0 |
|
|
| omit h0 in |
| lemma skewed(x j): Term.header.f u.x (e.screen x j).info=kit 14 (e.v.m,0) (bitR e.v.t) (enc (Print.issued e.v.dye)):=by |
| change (dec (Reed.V _ _).1:Crt)=_ |
| have hp: Reed.V u.x (e.screen x j).info=(e.src,j,0):=dec_round .. |
| rw [hp]; exact Wire.eq _ |
| |
| lemma readyK : 4 ≤ rankF u∧powder 100 ≤ rankF u∧Bullet.roomS ≤ rankF u:= by |
| have h:=h0.step0.ready |
| have hp:= (Ready.price0 (u := u)) |
| exact ⟨(Ready.price2 (u := u)).1,le_trans (Cambria.Era.billed ..).2.2 hp,le_trans (Cambria.Era.billed ..).2.1 hp⟩ |
| lemma stake0{x:ℕ}(hx:x∈u.D.P)(j): Lu.Standard (e.screen x j) (b0 u.r u.v) e.Tc:=by |
| let W:= Budget0.cost u.r u.v e.p; let p:= e.target x |
| have hs:=h0.step0.ready |
| have ht:e.Tc ≤ u.D.H := by |
| have hk:=Studio.stayedC hs.motto le_rfl h0.stake |
| rw [(Ready.crown (e := e)),mul_one] at hk; exact hk |
| exact ⟨Studio.positioned hs.motto hx j 0,spanFilm (Studio.vital (u:=u) _ ht) ..⟩ |
| omit h0 in |
| lemma invoice(x j:ℕ)(a:ℕ)(hb:e.v.govern=true): |
| Term.portals u.r u.x (e.screen x j).info=e.heightR ∧ |
| Term.atlas a u.x (e.screen x j).info=hole (e.stationE a) (hole 1 0) :=by |
| let k:=e.screen x j |
| have hp:=(Court.skewed (e := e)) x j |
| have hh:= (Ready.playsC (e := e)) x j |
| refine ⟨?_,?_⟩ |
| · unfold portals heightR; rw [hh] |
| unfold Fabric.govern at hb |
| unfold bitR Quest.steps |
| cases he:e.s.t.tag <;> rw [he] at hb <;> first|contradiction|skip |
| next b i=> cases b <;> rfl |
| unfold Term.atlas; rw [hp] |
| dsimp only [kit,Age.env,Age.styx,Age.MV] |
| rw [dec_round]; rfl |
| |
| omit h0 in |
| lemma seeks(x j):need.f u.x (e.screen x j).info=e.v.t.two:=by |
| let s:= Term.spirit.f u.x (e.screen x j).info |
| change (if decide (s.2.1=4) then false else s.2.2.2)=_ |
| have hq:s=bitR e.v.t:=Ready.playsC (e := e) x j |
| rw [hq] |
| unfold bitR Quest.two |
| cases h:e.v.t.tag |
| · simp [shaped,Kind.paired] |
| · simp [shaped,Kind.paired] |
| · next b u=> cases b <;> simp [shaped,Kind.paired] |
| simp [shaped,Kind.paired] |
| |
| lemma realm {a}(h:u.D.W a+1 ≤ u.D.W e.src):e.Tc ≤ u.D.high a:=by |
| have hs:=h0.step0.ready |
| have ht:= Studio.soonerC hs.motto ((Ready.crown (e := e)).symm ▸ h) h0.stake le_rfl |
| rw [(Ready.crown (e := e)),mul_one] at ht; exact ht |
| |
| abbrev lampC(e:Prism u)(y:ℕ):Bool:=Print.shoot u.n e.s.t.t y (Print.badge e.s.dye.2.1) |
| lemma seesR {x j y:ℕ}(hx:x∈u.D.P)(hi:(f false).awake x j)(hq:(f false).locate x j=y): |
| let v:=e.screen x j |
| v.rite (rankF u) sees (enc (lampC e y)):=by |
| subst y |
| let y:=(f false).locate x j |
| let s:=e.screen x j; let h:=(h0.step0.report.secure false) |
| let v:=e.v.terminal false |
| let p0:= enc (Print.issued e.s.dye); let p:=trail e.s.t.t p0 |
| let hP:NoteM:=Helix.Torch.waxy p |
| have hv : Term.noteQ.f u.x s.info=(v.visN,j,hP):=by |
| change (pointer (Reed.V u.x _).1 10,(leftQ.f _ _),_)=_ |
| have hu:= (Court.skewed (e := e)) x j |
| have he: Reed.V u.x s.info=(e.src,j,0):=dec_round .. |
| rw [show pointer (Reed.V u.x s.info).1 10 = v.visN from ?_,show leftQ.f u.x s.info=j from |
| congrArg (fun x:Stool=>x.2.1) he] |
| · let v0:Crt:=Term.header.f u.x s.info |
| change (v.visN,j,( (1,0),enc (trail (Age.styx v0).1.2.2.2 (Age.env v0))))=_ |
| rw [show v0=_ from hu]; rfl |
| rw [he]; exact Stone.pointing .. |
| have hs:=h0.step0.ready |
| have hr:u.wick0.Ok hP:=by |
| have hk:= hs.season.good.2.2.2.2.2.1 |
| refine ⟨Helix.Torch.housed u.r u.v u.x (by decide:(4:ℕ) ≤16) (Nat.zero_le _) ?_ (Nat.zero_le _) (Nat.zero_le _) (Print.boxbound _).le, |
| NeZero.pos u.n,Nat.zero_le _⟩ |
| change e.s.t.t≤ roof u.r u.x |
| exact le_trans (Nat.le_add_right ..) hk |
| have ht :u.D.W v.visN+u.D.D e.src ≤ u.D.W e.src:=by |
| rw [(Ready.crown (e := e))];exact Fabric.parentL e.v (by decide) (by decide) (by decide) |
| have hk:u.eye.Flora u.torch.p v.visN j x (some ((f false).tag x j,y)):=by |
| have hf:=h.suit.orbit (h.suit.lacks hx hi) hx |
| unfold Producer.coversF at hf; rw [ite_eq_left hi] at hf; exact hf |
| refine Arena.Flash.maskB hs.motto hx (by have:= h0.readyK;omega) ht h0.may hv hr hk _ ?_ |
| intro z hp |
| have hh:y ≤ u.n:=Nat.le_of_lt_succ (mem_range.1 (Fabric.Good.n1 hs.season.chart hs.season.good |
| (h.light.insured _ _ hi).2)) |
| change u.torch.lit u.D.x hP y z = (lampC e y,z) |
| rw [show u.torch.lit u.D.x hP y z=_ from Helix.Torch.litwax u.r u.v u.x _ p z y hh] |
| unfold Helix.Torch.ray |
| dsimp only [p,Helix.Torch.trail] |
| simp only [ite_eq_right (by decide: ¬ (4:ℕ)<4), ite_true,p0,dec_round]; rfl |
| |
| end Court |
| end |
| end ExactDerandomization.Gyre.OrbitR.Prism |
| |
| end |
| |
| section |
| |
| namespace ExactDerandomization.Gyre.OrbitR.Prism.Court |
| open Analysis Relay Counter Rill Fret At Hie |
| open Arena Amber Song Fret.Lyric Reed Lu Est Net |
| open Grain Terrain Bank Helix Helix.Age Helix.Mold Helix.Foil Helix.Moon Helix.Orbit Chime Dome Scheme Finset Stage |
| open SiteX |
| open Line Line.Fabric Fret.Seats |
| open Cambria.Wear.Paper |
| open Glass Glass.Rod Tiber.Sky Term Producer |
| open Helix.Torch |
| noncomputable section |
| open scoped Classical |
| variable {q w h:ℕ} {u:Line (q:=q) (w:=w) (h:=h)} |
| variable {e:Prism u}{f:Bool → Producer}{tb:ℕ→ℕ→ℕ} |
| variable (hp:Court e f tb) |
| include hp |
|
|
| abbrev okY(e:Prism u)(y:ℕ):Bool:= if e.v.t.two then lampC e y else true |
| lemma awakeY {x j:ℕ}(h:(f false).awake x j): |
| let y:=(f false).locate x j |
| e.v.grid.pre e.v.grains (e.v.trio false) e.v.t.two x y= |
| if okY e y then (f false).scoreF (e.v.aimE false) x j else 0 :=by |
| intro y; let s:=e.v |
| have hv:=hp.step0; have ht:= (hv.report.secure false).light.insured _ _ h |
| unfold scoreF; rw [ite_eq_left h] |
| have hj : y ∈ (s.world.S).filter (fun _=>True):= mem_filter.2 ⟨(mem_filter.1 ht.2).1,trivial⟩ |
| have he: e.v.aimE false x y= (s.grains x).val s.S1 s.Rslots (s.trio false) y:=ite_eq_left |
| ⟨ht.1,ht.2,Or.inl (rfl : (false:Bool)=false)⟩ |
| have hh : lampC e y=true ↔ y∈s.S2:=by |
| unfold lampC |
| rw [Print.shoots] |
| unfold Fabric.S2 Spray.dst1 |
| simp only [dst,retain,mem_filter]; apply (iff_and_self.mpr ?_) |
| exact fun _=>(mem_filter.1 ht.2).1 |
| unfold okY; cases hC:e.v.t.two |
| · simp only [Bool.false_eq_true,ite_false,ite_true];rfl |
| simp only [ite_true]; rw [show (f false).locate x j=y from rfl,he] |
| by_cases hY:y∈s.S2 |
| · rw [ite_eq_left (hh.2 hY)]; exact ite_eq_left ⟨ht.1,ht.2,Or.inr hY⟩ |
| rw [ite_eq_right (mt hh.mp hY)] |
| exact ite_eq_right fun h=>hY (h.2.2.resolve_left (by decide)) |
| |
| lemma tinted {x i y:ℕ}(he:(e.lifted (f false) tb).awake x i)(hq:(f false).locate x i=y): |
| let q:=e.v |
| (e.lifted (f false) tb).scoreF q.finalE x i= |
| ((if okY e y then (f false).scoreF (q.aimE false) x i else 0)* |
| q.grid.incG q.grains y)*q.t.tower u.plotM q.roll q.m e.across y :=by |
| intro v; unfold scoreF; rw [ite_eq_left he] |
| have ht:v.activeR:=hp.step0.onR |
| have hm:(f false).awake x i:=by |
| change (if v.govern then _ else _) ≠ 0 at he |
| split at he |
| · next hc=> exact ((hp.step0.allocate hc).bound x i he).1 |
| split at he |
| · assumption |
| contradiction |
| change v.finalE x ((f false).locate x i)=_ |
| unfold Fabric.finalE forecast current; dsimp only; rw [ite_eq_left (show Net.onQ u.plotM.gap v.m (v.t.key u.plotM)=true from ht)] |
| change e.v.grid.pre e.v.grains (e.v.trio false) e.v.t.two x _ * v.grid.incG _ _ * _ = _ |
| subst y; rw [hp.awakeY hm];rfl |
| |
| abbrev bill(e:Prism u):= Budget0.cost u.r u.v e.p |
| omit hp in |
| lemma sharp(k:ℕ) : rankF u ≤ bill e ∧ |
| (Budget0.H u.r u.v e.p k).cost (rankF u) ≤ bill e ∧ |
| (Budget0.H u.r u.v e.p k).tail ≤ bill e:=Budget0.fareE .. |
|
|
| lemma frail{x i:ℕ}(h:x∈u.D.P)(hi:(f false).awake x i): |
| let s:= e.screen x i |
| s.band (rankF u) e.Tc e.p.coin originC ((f false).scoreF (e.v.aimE false) x i):=by |
| intro s |
| let k:=Enabled.frame e |
| have he:= hp.step0; have h0:=he.ready |
| have hs := (he.report.secure false).suit |
| have hs' :=hs.coil |
| have hf:u.D.W k.dataN+1 ≤ u.D.W e.src:=e.v.parentL (by decide) (by decide) (by decide) |
| have hj:=(hs.voices x h).ready i (hs'.awake (hs'.size0 i (hs.lacks h hi))) |
| have hn:u.D.D k.dataN=u.D.D e.src:=(e.v.ageEnd _ (by decide:¬Brole 9)).trans (Ready.crown (e := e)).symm |
| rw [show (e.v.terminal false).dataN=k.dataN from rfl,hn] at hj |
| apply Bullet.clef u.D h0.motto hp.readyK.2.2 h (by rw [(Ready.crown (e := e))];exact hf) |
| ((Ready.gem (e := e)) 1 9 x i) (hp.realm hf) hj |
|
|
| lemma summitR {x i:ℕ}(hx:x∈u.D.P)(he:e.v.govern=true)(hz:tb x i≠0): |
| let b:=f false; let y:=b.locate x i |
| let j:=tb x i; let s:=e.screen x i |
| s.band (rankF u) e.Tc 0 (summit u.r u.v j) (outV e.v y):=by |
| intro b y j s |
| have hv:= hp.step0; have hs:=hv.allocate he |
| have hm:=hs.bound x i hz |
| have hb:= hv.ready |
| have ht:= hv.capR he ((hv.report.secure false).suit.lacks hx hm.1) (Nat.pos_of_ne_zero hz) hm.2 hx |
| obtain ⟨hR,hq⟩:=ht |
| have hP:= hR.ready |
| have hg:u.D.curve (e.v.slotWord i) (tb x i) true x= some y:= hq.trans (ite_eq_left rfl) |
| have hf: y∈u.D.P := (hP.swaps _ hR.holds x hx true y hg).1 |
| have hw:u.D.W (e.v.c 13 0)+1 ≤ u.D.W e.src := e.v.parentL (by decide) (by decide) (by decide) |
| have hL: (seek 13 1 ⟨_,Kn.fix 0⟩).f s.l.x s.info=hole (e.v.c 13 0) (hole 1 0):=by |
| have h1: Reed.V u.x s.info=(e.src,i,0):=dec_round .. |
| change hole (pointer (Reed.V u.x s.info).1 13) (hole 1 0)=_ |
| rw [h1,show pointer e.src 13=e.v.c 13 0 from Stone.pointing ..] |
| apply Pier.bowls hb.motto ((by omega: 2 ≤ 4).trans hp.readyK.1) hR hp.readyK.2.2 ((Ready.spinC (e := e)) j x i) hg |
| apply Bullet.clef u.D hb.motto hp.readyK.2.2 hf (by rw [(Ready.crown (e := e))]; exact hw) hL (hp.realm hw) |
| simpa only [Nat.zero_mul] using hp.rank0 he y hf |
| |
| lemma prompter {x i:ℕ}(hx:x∈u.D.P)(he:e.v.govern=true)(hz:tb x i≠0)(k:ℕ): |
| let b:=f false; let y:=b.locate x i |
| let j:=tb x i; let s:=e.screen x i |
| Chor (b0 u.r u.v) (rankF u) e.Tc s (bright u.r u.v j k) (paintE e k y):=by |
| intro b y j s; have hr:= hp.step0 |
| have hm:2 ≤ rankF u:= (by omega: 2 ≤ 4).trans hp.readyK.1 |
| obtain ⟨hH,hA⟩:= Court.invoice (e := e) x i k he |
| have ha:(Term.candle u.r k).f s.l.x s.info=decide (k<e.heightR):= |
| congrArg (fun j=> decide (k<j)) hH |
| apply Chor.byear |
| by_cases hW:k<e.heightR |
| · apply Song.pinTrue _ (ha.trans (decide_eq_true hW)) |
| have hh:=(hr.allocate he).bound x i hz |
| let p:=hr.report.secure false |
| obtain ⟨ht,hk⟩:=hr.capR he (p.suit.lacks hx hh.1) (Nat.pos_of_ne_zero hz) hh.2 hx |
| have hg: u.D.curve (e.v.slotWord i) (tb x i) true x=some y:= hk.trans (ite_eq_left rfl) |
| have hy: y∈u.D.P := (ht.ready.swaps _ ht.holds x hx true y hg).1 |
| apply Pier.bowls hr.ready.motto hm ht hp.readyK.2.2 ((Ready.spinC (e := e)) j x i) hg |
| have hpv: u.D.W (e.stationE k)+1 ≤ u.D.W e.src:=by |
| let K:=e.v; have he2:0<K.m:=by |
| have hm:K.activeR:=hp.step0.onR; unfold Fabric.activeR Net.onQ at hm; by_contra hn; simp [Nat.eq_zero_of_not_pos hn] at hm |
| change Age.W _+1 ≤ Age.W _ |
| unfold stationE vecL; rw [Line.rolfe]; change Age.weight e.vale 17 0+1 ≤ u.D.W (e.v.c 14 0) |
| rw [Stone.W]; exact Age.renewal (a:=14) (i:=0) (n:=K.m) (m:=K.m-1) (by change K.m-1+1 ≤ K.m;omega) |
| apply Bullet.clef u.D hr.ready.motto hp.readyK.2.2 hy (by rw [(Ready.crown (e := e))];exact hpv) hA (hp.realm hpv) |
| simpa only [Nat.zero_mul] using hp.tower0 he k hW y hy |
| apply Song.pinFalse _ (ha.trans (decide_eq_false hW)) |
| unfold paintE; rw [ite_eq_right hW] |
| exact Amber.steam _ _ (hp.stake0 hx i) hp.readyK.2.1 |
| |
| end |
| end ExactDerandomization.Gyre.OrbitR.Prism.Court |
| |
| end |
| |
| section |
| |
| namespace ExactDerandomization.Gyre.OrbitR.Prism.Court |
| open Analysis Relay Counter Rill Fret At Hie |
| open Arena Amber Song Fret.Lyric Reed Lu Est Net |
| open Grain Terrain Bank Helix Helix.Age Helix.Mold Helix.Foil Helix.Moon Helix.Orbit Chime Dome Scheme Finset Stage |
| open SiteX |
| open Line Line.Fabric Fret.Seats |
| open Cambria.Wear.Paper |
| open Glass Glass.Rod Tiber.Sky Term Producer |
| open Helix.Torch |
| noncomputable section |
| open scoped Classical |
| variable {q w h:ℕ} {u:Line (q:=q) (w:=w) (h:=h)} |
| variable {e:Prism u}{f:Bool → Producer}{tb:ℕ→ℕ→ℕ} |
| variable (hp:Court e f tb) |
| include hp |
| def sumR (v:ℕ→ℝ):ℕ→ℝ |
| | 0=>0 |
| | k_stack+1=>max (sumR v k_stack) (v k_stack) |
| omit hp in |
| lemma pg(x:ℕ){v:ℕ→ℝ}:0 ≤ sumR v x:=by induction x with |
| | zero=>rfl |
| | succ x ih=>exact le_trans ih (le_max_left ..) |
| lemma towerQ (he:e.s.govern=true) (x): |
| e.v.t.tower u.plotM e.v.roll e.v.m e.across x=gamma (sumR (fun k=>paintE e k x) u.w0.p.T):=by |
| have hG:=hp.step0 |
| let m:= e.heightR |
| let H(n):= sumR (fun k=> e.paintE k x) n |
| have hh(d):m ≤ d→ H d=H m :=by |
| induction d with |
| | zero=> intro h; exact (show m=0 by omega) ▸ rfl |
| | succ n ih=> |
| intro hn; by_cases hs:m=n+1; rw [hs] |
| have ht :m ≤ n:=by omega |
| unfold H; rw [sumR,paintE,ite_eq_right (show ¬ n < m by omega)] |
| change max (H n) 0=_ |
| rw [ih ht,max_eq_left (show 0 ≤ H m from by exact pg _)] |
| unfold Quest.tower |
| let v:=e.s.t |
| cases he0:v.main |
| · simp only [Bool.false_and,Bool.false_eq_true,ite_false] |
| have hz:m=0:=by unfold m heightR; rw [show e.s.t.main=false from he0];rfl |
| change 1=gamma (H _) |
| rw [hh u.w0.p.T (by omega),hz]; exact (gamma_full (x:=0) (by norm_num)).symm |
| have hm:m=v.steps u.plotM:= ite_eq_left he0 |
| have hT:m ≤ u.w0.p.T:=by |
| rw [hm] |
| have hs:= hG.ready.season.good.2.2.2.2.2.2 |
| unfold Quest.steps |
| cases h:v.tag <;> first| exact Nat.zero_le _|skip |
| next b i=>rw [show _=v.tag from rfl,h] at hs; cases b<;> dsimp only <;> first|exact le_rfl| exact hs.2 |
| let s:= fun j=> (e.v.roll e.vale).outV (e.euro j) |
| have hb(d): d ≤ m→ H d= Maxer s d e.across x:=by |
| induction d with |
| | zero=>exact fun _=>rfl |
| | succ d ih=> intro h;exact congrArg₂ max (ih (by omega)) |
| (show paintE e d x=_ from ite_eq_left (by change d < m; omega)) |
| rw [ite_eq_left (show (true && e.v.t.tag.narrow) = true from by rw [show e.v.t.tag.narrow=true from he];rfl)] |
| rw [show sumR (fun k=>e.paintE k x) u.w0.p.T=_ from hh u.w0.p.T hT,hb m le_rfl,hm] |
| rfl |
| |
| lemma warmV {j x i:ℕ}(hx:x∈u.D.P)(he:e.v.govern=true)(hz:tb x i≠0): |
| let b:=f false; let y:=b.locate x i; let s:=e.screen x i |
| Chor (b0 u.r u.v) (rankF u) e.Tc s (tuneE u.r u.v (tb x i) j) (sumR (fun k=>paintE e k y) j):=by |
| intro b y s |
| induction j with |
| | zero=> exact (hp.stake0 hx i).sil |
| | succ j ih=> exact (hp.stake0 hx i).up0 ih (hp.prompter hx he hz j) |
|
|
| abbrev showR (e:Prism u)(y:ℕ) :ℝ:= e.v.grid.incG e.v.grains y* e.v.t.tower u.plotM e.v.roll e.v.m e.across y |
|
|
| attribute [local irreducible] tuneE |
| set_option maxHeartbeats 900000 in |
| lemma earnsR {i x:ℕ}(hx:x∈u.D.P)(he:e.v.govern=true)(hz:tb x i≠0): |
| let b:=f false; let y:=b.locate x i; let s:=e.screen x i |
| let X:= b.scoreF (e.v.aimE false) x i |
| s.band (bill e) (Hx e) e.p.coin (roost (b0 u.r u.v) (double u.r u.v e.p (tb x i)) e.p.coin) (X*showR e y):=by |
| intro b y s X |
| let k:=b0 u.r u.v |
| have hp0:=hp.step0 |
| have ht:= hp.stake0 hx i |
| have h1:= hp0.allocate he |
| have hc:= hp.readyK.1 |
| have he0:=hp0.report.secure false |
| let r:=outV e.v y |
| have hv:e.v.grid.incG e.v.grains y=shutoff r:=ite_eq_left he |
| let A:=sumR (fun k=> e.paintE k y) u.w0.p.T |
| have ha:e.v.t.tower u.plotM e.v.roll e.v.m e.across y=gamma A:=hp.towerQ he y |
| have hh0 :=hp.frail hx (h1.bound x i hz).1 |
| have hU :Chor k (rankF u) e.Tc s (double u.r u.v e.p (tb x i)) (X*showR e y):=by |
| have hjp := Song.Paint.boosted ht (Chor.byear (hp.summitR hx he hz)) |
| have hw:= Song.Paint.gammed ht (hp.warmV (j:=u.w0.p.T) hx he hz) |
| have hP: Chor k (rankF u) e.Tc s Song.ein 1 :=by simpa using ht.rove (rankF u) 1 |
| unfold showR; rw [hv,ha,←mul_assoc] |
| exact ht.mult0 (ht.mult0 (Chor.byear hh0) (ht.dubs hP hjp)) hw |
| have hu:= (Court.sharp (e := e)) (tb x i) |
| let h:=Budget0.H u.r u.v e.p (tb x i) |
| have he0:e.Hx+h.tail*s.d ≤ e.Tc:=by |
| rw [show s.d=1 from (Ready.crown (e := e)),mul_one]; exact Nat.add_le_add_left hu.2.2 _ |
| have he1: |showR e y| ≤ 1:=by |
| have hr:{x y:ℝ}→in01 x→in01 y→|x*y| ≤ 1:=by |
| rintro x y ⟨h1,h2⟩ ⟨h3,h4⟩; rw [abs_le]; constructor <;> nlinarith only [h1,h2,h3,h4] |
| unfold showR; rw [ha] |
| exact hr (e.v.grid.incG_bounds e.v.grains y) (gamma_mem A) |
| have hs:|X*showR e y| ≤ massB e.p.coin s.d:=by |
| rw [abs_mul]; refine le_trans (mul_le_mul_of_nonneg_left he1 (abs_nonneg _)) ?_ |
| rw [mul_one]; exact Seats.maxv hh0 |
| exact Amber.onQ _ _ _ ht hU (show 1 ≤ rankF u by omega) he0 hu.2.1 hs |
| |
| lemma plain {i x:ℕ}(hx:x∈u.D.P)(hi:(f false).awake x i)(he:e.s.govern=false): |
| let y:=(f false).locate x i; let s:=e.screen x i;let X:=(f false).scoreF (e.v.aimE false) x i |
| s.band (bill e) (Hx e) e.p.coin originC (X*showR e y):=by |
| intro y s X |
| have ha:e.v.grid.incG e.v.grains y=1:=ite_eq_right (by rw [show e.v.grid.sp=e.s.govern from rfl,he];decide) |
| have hz:e.v.t.tower u.plotM e.v.roll e.v.m e.across y=1:=by |
| unfold Quest.tower; rw [show e.v.t.tag.narrow=false from he]; simp |
| unfold showR; rw [ha,hz,mul_one,mul_one] |
| apply flex (hp.frail hx hi) (by have :=hp.readyK;omega) ((Court.sharp (e := e)) 0).1; unfold Tc; omega |
| lemma salmon (x:ℕ)(hx:x∈u.D.P)(i:ℕ): |
| (e.screen x i).band (bill e) (Hx e) e.p.coin (snow (b0 u.r u.v) e.p.coin) 0:=by |
| apply flex (steam _ _ (hp.stake0 hx i) hp.readyK.2.1) (by have:=hp.readyK;omega) |
| ((Court.sharp (e := e)) 0).1 |
| unfold Tc; omega |
| |
| lemma choirR(x:ℕ)(hx:x∈u.D.P)(i:ℕ)(hk:u.smallQ e.src i): |
| let g:=e.lifted (f false) tb |
| (e.screen x i).band (bill e) (Hx e) e.p.coin |
| (costamp u.r u.v e.p) (g.scoreF e.v.finalE x i):=by |
| intro g; let s:=e.screen x i |
| let r:=g.tag x i |
| have he:=hp.step0; have hs:= he.ready |
| have hm:= he.mounted x hx i hk |
| have hw:= higher hm (by have hp:=hp.readyK;omega) ((Court.sharp (e := e)) r).1 |
| let X:=g.scoreF e.v.finalE x i |
| let f0:=f false |
| have hc : ebit.f s.l.x s.info=e.v.govern:= ((Ready.toneC (e := e)) x i).1 |
| have hr : r=(if e.v.govern then tb x i else if f0.awake x i then 1 else 0):=rfl |
| have hR:r ≤ clim u.w0.p+1:=by |
| rw [hr]; split |
| · next ht=> |
| by_cases h:tb x i=0; rw [h]; omega |
| exact ((he.allocate ht).bound x i h).2.trans (by omega) |
| split <;> omega |
| apply Iris.parcel hR hw |
| unfold Term.melody; dsimp only |
| by_cases hz:r=0 |
| · rw [ite_eq_left hz]; unfold Producer.scoreF; rw [ite_eq_right (not_not_intro hz)] |
| exact hp.salmon x hx i |
| rw [ite_eq_right hz] |
| let q:= f0.scoreF (e.v.aimE false) x i; let y:=f0.locate x i |
| have hh:f0.awake x i:=by |
| rw [hr] at hz; split at hz |
| · next hc=> exact ((he.allocate hc).bound x i hz).1 |
| split at hz; assumption; contradiction |
| let Q:=Song.pleas Term.ebit (roost (b0 u.r u.v) (double u.r u.v e.p r) e.p.coin) originC |
| have hN: s.band (bill e) e.Hx e.p.coin Q (q*showR e y):=by |
| cases hV:e.v.govern |
| · exact Song.pinFalse ebit (hc.trans hV) (hp.plain hx hh hV) |
| · have hW:r=tb x i:=hr.trans (ite_eq_left hV) |
| apply Song.pinTrue _ (hc.trans hV) |
| rw [hW]; exact hp.earnsR hx hV (hW ▸hz) |
| let a:=lampC e y |
| have hY: need.f s.l.x s.info=e.v.t.two:=Court.seeks (e := e) x i |
| rw [show g.scoreF _ x i = _ from hp.tinted hz rfl] |
| cases ht:e.v.t.two |
| · apply Song.pinFalse need (hY.trans ht) |
| have hb:okY e y=true:=ite_eq_right (by rw [ht];decide) |
| rw [ite_eq_left hb,mul_assoc];exact hN |
| apply Song.pinTrue need (hY.trans ht) |
| have hO:okY e y=a:=ite_eq_left ht |
| have hk:= hp.seesR hx hh rfl |
| apply Seats.avis (higher hk (by have :=hp.readyK;omega) ((Court.sharp (e := e)) r).1) |
| · intro hj; have hv:a=false:=by |
| change enc a=0 at hj; cases ht:a; rfl; rw [ht] at hj; change 1=0 at hj; contradiction |
| rw [ite_eq_right (by rw [hO,hv];decide),zero_mul,zero_mul];exact hp.salmon x hx i |
| intro hj; have hv:a=true:=by |
| change enc a≠0 at hj |
| cases he:a |
| · rw [he] at hj; exact False.elim (hj rfl) |
| rfl |
| rw [ite_eq_left (hO.trans hv),mul_assoc];exact hN |
| end |
| end ExactDerandomization.Gyre.OrbitR.Prism.Court |
| |
| end |
| |
| section |
| |
| namespace ExactDerandomization.Gyre.OrbitR.Prism |
| open Analysis Relay Counter Rill Fret At Hie |
| open Arena Amber Song Fret.Lyric Reed Lu Est Net |
| open Grain Terrain Bank Helix Helix.Age Helix.Mold Helix.Foil Helix.Moon Helix.Orbit Chime Dome Scheme Finset Stage |
| open SiteX |
| open Line Line.Fabric Fret.Seats |
| open Cambria.Wear.Paper |
| open Glass Glass.Rod Tiber.Sky Term Producer |
| open Helix.Torch |
| noncomputable section |
| open scoped Classical |
| variable {q w h:ℕ} {u:Line (q:=q) (w:=w) (h:=h)} |
| variable {e:Prism u}{f:Bool → Producer}{tb:ℕ→ℕ→ℕ} |
|
|
| structure Ace (e:Prism u):Prop where |
| he:e.Ready |
| hC : Court.bill e ≤ u.v.slope |
| hd: Studio.Parcel u e.src (fullD u.r u.v e.p) |
|
|
| namespace Ace |
| variable (hA:e.Ace) |
| include hA |
| omit hA in |
| lemma price : rankF u ≤ Court.bill e∧4 ≤ rankF u∧powder 100 ≤ rankF u:= |
| ⟨(Budget0.fareE u.r u.v e.p 0).1,(Ready.price2 (u := u)).1, |
| le_trans (Cambria.Era.billed _).2.2 (Ready.price0 (u := u))⟩ |
| lemma emits {x i}(hp:u.smallQ e.src i){h:ℕ}(hv:(e.screen x i).rite (rankF u) (ent u.r u.v) h): |
| u.D.swears (post e.src 0 i 0) x h:= |
| Studio.echoTicket hA.he.motto (by omega:(0:ℕ) ≤ 1) (by omega) hp (by have :=(Ace.price (e := e));omega) |
| (le_trans (Ace.price (e := e)).1 hA.hC) hv hA.hd |
| lemma songT {x i}(hv:u.smallQ e.src i){X:ℝ} |
| (hp:(e.screen x i).band (Court.bill e) e.Hx e.p.coin (Term.costamp u.r u.v e.p) X): |
| u.D.Voice e.src x (hole 1 i) e.Hx (e.p.coin*u.D.D e.src) X:= |
| Studio.scoreTicket hA.he.motto (show (1:ℕ) ≤ 1 from by omega) (by omega) hv (by have :=(Ace.price (e := e));omega) |
| hA.hC le_rfl hp hA.hd |
| lemma kingdom {i:ℕ}(h:i≤clim u.w0.p+1): u.smallQ e.origin.visN i:=by |
| have ht:=lb_le_inc i; have hf:=hA.he.season.book.cost0 |
| change lb i ≤ u.eye.e*u.D.D _ |
| rw [show u.D.D e.origin.visN=1 from hA.he.includes0.grain ▸ (Ready.crown (e := e)),mul_one] |
| apply ht.trans |
| apply le_trans _ hf |
| unfold Bank.hx Bank.hu Bank.hi bootC; change i≤clim u.r.w.p+1 at h;omega |
| lemma deadgate (x i:ℕ)(hx:x∈u.D.P)(hi:u.smallQ e.src i)(ht:u.D.swears (post e.src 0 i 0) x 0): |
| u.eye.Flora u.torch.p e.origin.visN i x none:=by |
| have hf:=hA.he.includes0 |
| refine Cone.ConeX.Flora.abs ⟨hf.point0 hA.he.season.chart i (hf.back0 hi),hx,?_⟩ |
| rw [show u.eye.ear u.torch.p _ _ = post e.src 0 i 0 from hf.ear0 i] |
| exact u.D.identity ht |
| end Ace |
|
|
| namespace Court |
| variable (hp:Court e f tb) |
| include hp |
| abbrev tribe(e:Prism u)(f:Bool→Producer)(tb):=e.lifted (f false) tb |
|
|
| lemma matter : (tribe e f tb).Light e.v.finalE e.v.S0 e.v.S1:=by |
| let g:=tribe e f tb; have hr:=hp.step0; let h:=f false |
| have ht:= (hr.report.secure false).light |
| have he(k j:ℕ)(hh:g.awake k j):h.awake k j:=by |
| change (if _ then _ else _)≠0 at hh |
| change (if e.v.govern then tb k j else _)≠0 at hh |
| split at hh |
| · next hi=> exact ((hr.allocate hi).bound k j hh).1 |
| split at hh; assumption;contradiction |
| refine ⟨fun i j hh=> ht.insured _ _ (he _ _ hh),fun x i j hm hn hQ=> ht.fair _ _ _ (he _ _ hm) (he _ _ hn) hQ,?_⟩ |
| intro x y ho |
| cases hG:e.v.govern |
| · have hu: e.v.aimE false x y≠0 := by |
| intro hn |
| apply ho |
| unfold finalE forecast current; dsimp only |
| rw [ite_eq_left (show Net.onQ u.plotM.gap e.v.m (e.v.t.key u.plotM)=true from hr.onR)] |
| change e.v.grid.pre e.v.grains (e.v.trio false) e.v.t.two x y * e.v.grid.incG e.v.grains y * _=0 |
| have he: e.v.grid.pre e.v.grains (e.v.trio false) e.v.t.two x y=0:=by |
| change e.v.grid.pre e.v.grains (e.v.trio false) false x y=0 at hn |
| unfold At.Grid.pre at *; grind |
| rw [he];ring |
| obtain ⟨i,hi,hx⟩:=ht.defend x y hu |
| refine ⟨i,?_,hx⟩ |
| show (if e.v.govern then _ else if h.awake x i then 1 else 0)≠0 |
| rw [hG,ite_eq_left hi]; exact Nat.ne_of_gt Nat.one_pos |
| obtain ⟨i,ha,hb,hC⟩:= hr.ancestor hG ho |
| exact ⟨i,(show (if e.v.govern then _ else _)≠0 from (by rw [ite_eq_left hG];exact hC)),hb⟩ |
| lemma roy {x i:ℕ}: let g:=tribe e f tb |
| g.tag x i ≤ clim u.w0.p +1 ∧ (g.awake x i→(f false).awake x i):=by |
| intro g; have hr:= hp.step0 |
| unfold Producer.awake g tribe lifted; dsimp only |
| split |
| · next he=> |
| have hf:= (hr.allocate he).bound x i |
| by_cases hh:tb x i=0; simp [hh] |
| exact ⟨(hf hh).2.trans (Nat.le_add_right ..),fun _=>(hf hh).1⟩ |
| split <;> grind |
| set_option maxHeartbeats 700000 in |
| lemma plants(hA:e.Ace): e.v.Efine e.p (tribe e f tb):=by |
| let g:=tribe e f tb |
| have hp0:=hp.step0;have hs:=hp0.ready; have hc:= hs.season; let f0:= f false |
| have ht:=hp0.report.secure false |
| let N:= e.origin |
| refine ⟨⟨hp.matter, hs.includes0,?_,?_⟩,?_,?_,?_⟩ |
| · intro x hx |
| have he(i:ℕ)(hi:u.smallQ e.src i): u.D.swears (post e.src 0 i 0) x (g.tag x i):= |
| hA.emits hi (hp0.mounted x hx _ hi) |
| refine ⟨fun i hh=> he _ hh,fun i _=>hA.kingdom hp.roy.1,fun i hA=>?_,fun i hB=>?_⟩ |
| · by_contra hk |
| have hv:= ht.suit.lacks hx (hp.roy.2 (show g.awake x i from hk)) |
| exact not_lt_of_ge hA hv |
| change u.eye.Flora u.torch.p e.origin.visN i x (if g.tag x i=0 then _ else _) |
| by_cases hf:g.tag x i=0 |
| · have he0:= he i hB |
| rw [hf] at he0; rw [ite_eq_left hf]; exact hA.deadgate x i hx hB he0 |
| rw [ite_eq_right hf] |
| let p:=e.v.terminal false; let F:=p.visN; let y:=g.locate x i |
| have hg:f0.awake x i:= hp.roy.2 (show g.awake x i from hf) |
| have hl:= ht.suit.coil |
| apply hs.season.chart.Rope hs.includes0 i x (g.tag x i) i F y (f0.tag x i) hB (hA.kingdom hp.roy.1) hf |
| hx _ _ _ _ (Fabric.Good.n1 hc.chart hc.good (ht.light.insured x i hg).2) |
| (he _ hB) ((ht.suit.trace x hx).caseM i hg (hl.awake (hl.size0 i (ht.suit.lacks hx hg)))) |
| · unfold Mold.offer; dsimp only |
| rw [Stone.roleR,ite_eq_right (by decide:(15:ℕ)≠ 2),ite_eq_right (by decide:(15:ℕ)≠4),ite_eq_left rfl] |
| exact congrArg (fun v=>rope v i) (Stone.pointing ..) |
| · exact Stone.zeroR .. |
| · rw [show u.D.D e.origin.visN=1 from e.v.ageEnd _ (by decide)] |
| exact e.v.parentL (by decide) (by decide) (by decide) |
| rw [show u.D.D e.origin.visN=1 from e.v.ageEnd _ (by decide),show u.D.D F=1 from e.v.ageEnd _ (by decide)];omega |
| · intro x hx; exact ⟨fun i hi=>hA.songT hi (hp.choirR x hx i hi)⟩ |
| · cases hV:e.v.govern |
| · exact Or.inr rfl |
| exact Or.inl (hp0.allocate hV).t1 |
| · intro he x i hi |
| have hu:g.tag x i=tb x i:=ite_eq_left he |
| exact hu.symm ▸ ((hp0.allocate he).bound x i (fun h=>hi (hu.trans h))).2 |
| intro h i hi t he hr |
| have hv:= hp0.allocate h |
| have hc:=hv.guide |
| have hm : 0∈u.D.P:=mem_range.2 (Nat.zero_lt_succ ..) |
| refine ⟨(hc 0 hm i hi t he hr).1,(hc 0 hm i hi t he hr).2.1,fun x hx=>?_⟩ |
| have hw:= (hc x hx i hi t he hr).2.2 |
| rw [hw] |
| change _=(if g.tag x i=t then _ else _) |
| rw [show g.tag x i=tb x i from ite_eq_left h]; rfl |
| end Court |
| |
| end |
| end ExactDerandomization.Gyre.OrbitR.Prism |
| |
| end |
| |
| section |
| |
| namespace ExactDerandomization.Gyre.OrbitR.Prism |
| open Analysis Relay Counter Rill Fret At Hie |
| open Arena Amber Song Fret.Lyric Reed Lu Est Net |
| open Grain Terrain Bank Helix Helix.Age Helix.Mold Helix.Foil Helix.Moon Helix.Orbit Chime Dome Scheme Finset Stage |
| open SiteX |
| open Line Line.Fabric Fret.Seats |
| open Cambria.Wear.Paper |
| open Glass Glass.Rod Tiber.Sky Term Producer |
| open Helix.Torch |
| noncomputable section |
| open scoped Classical |
| variable {q w h:ℕ} {u:Line (q:=q) (w:=w) (h:=h)} |
| variable {e:Prism u} |
|
|
| namespace Ace |
| variable (hb:e.Ace)(hc:¬e.v.activeR) |
| include hb hc |
| def flat:Producer:=⟨fun _ _=>0,fun _ _=>0⟩ |
| omit hb in |
| lemma past : e.v.finalE=fun _ _=>0:=by |
| unfold finalE forecast current; dsimp only |
| rw [ite_eq_right (show ¬ (Net.onQ u.plotM.gap e.v.m (e.v.t.key u.plotM))=true from hc)] |
| lemma mark0(x i:ℕ)(hx:x∈u.D.P): (e.screen x i).rite (rankF u) (ent u.r u.v) 0:=by |
| let v:= e.screen x i |
| have ht: (avail u.r).f v.l.x v.info=false:= ((Ready.toneC (e := e)) x i).2.1.trans (decide_eq_false hc) |
| exact doesno ht (blankD (hb.he.motto.pit hx _) (by have :=(Ace.price (e := e));omega)) |
| lemma seed0(x i:ℕ)(hx:x∈u.D.P)(_:u.smallQ e.src i): |
| (e.screen x i).band (Court.bill e) e.Hx e.p.coin (Term.costamp u.r u.v e.p) 0:=by |
| have hs:=hb.he.motto |
| have ht:=(Ace.price (e := e)) |
| have hm := higher (hb.mark0 hc x i hx) (by omega) ht.1 |
| have hd:e.Hx≤u.D.H:=by unfold Hx high;omega |
| have hp: Standard (e.screen x i) (b0 u.r u.v) e.Hx:=⟨Studio.positioned hs hx i 0, |
| spanFilm (Studio.vital (u:=u) _ hd) ..⟩ |
| apply Iris.parcel (Nat.zero_le _) hm |
| unfold melody; dsimp only; rw [ite_eq_left rfl] |
| exact steam _ _ hp (le_trans ht.2.2 ht.1) |
| omit hb hc in |
| lemma deltaP (e:Prism u)(hp:e.v.govern=true): Foil.delta0 (bitR e.v.t):=by |
| unfold delta0 bitR |
| unfold govern at hp |
| cases h:e.v.t.tag <;> rw [h] at hp <;> first| contradiction| skip |
| next b i=> cases b <;> simp [shaped] |
| lemma water (hd:u.s.scripted 12=Line.Fabric.capprog u.r u.v u.s.pave):e.v.Efine e.p flat:=by |
| let f:=e.origin |
| have hx:=hb.he;have he:=hx.season |
| have hp(h:e.v.govern=true):= he.endUnits 12 (Or.inr (Or.inr (Or.inl ⟨rfl,Ace.deltaP e h⟩))) |
| constructor |
| · refine ⟨?_,hx.includes0,fun x hm=>?_,fun x hm=>?_⟩ |
| · exact ⟨fun _ _ h=> (h rfl).elim,fun _ _ _ h _ _=> (h rfl).elim, |
| fun x y h=>(h ((Ace.past (e := e)) hc ▸ rfl)).elim⟩ |
| · have he0(i)(hz:u.smallQ e.src i):= hb.emits hz (hb.mark0 hc x i hm) |
| exact ⟨he0,fun i h=>hb.kingdom (show 0 ≤ _ from Nat.zero_le _),fun _ _=>rfl,fun i hi=>by |
| have hs:=hb.deadgate x i hm hi (he0 i hi) |
| exact hs⟩ |
| exact ⟨fun i hi=>by |
| have hr :flat.scoreF e.v.finalE x i=0:=ite_eq_right (fun h=>h rfl) |
| rw [hr] |
| exact hb.songT hi (hb.seed0 hc x i hm hi)⟩ |
| · cases h:e.v.govern; exact Or.inr rfl |
| exact Or.inl (hp h).stage |
| · intro h x i hd; exact (hd rfl).elim |
| intro h i hi t ht hj |
| have hl :=hp h |
| have he0:u.D.dual (e.v.slotWord i) t:= (Line.Fabric.cap_dual hl).2 |
| ⟨hi,Nat.one_le_iff_ne_zero.2 (by omega),hj⟩ |
| have hq:= Line.Fabric.desert12 (v:=e.v) i he.good hc hl he.chart hd |
| exact ⟨he0,hq.canonicalS,fun x h=>by rw [hq.lines he0 h];exact (ite_eq_right (Nat.ne_of_lt ht)).symm⟩ |
| |
| end Ace |
| end |
| end ExactDerandomization.Gyre.OrbitR.Prism |
| |
| end |
| |
| end OAI |
| |
