File size: 4,944 Bytes
fcab081 | 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 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 | import OAI.Combinatorics.HadwigerCounterexample.PredictionClassBounds
namespace OAI
/-! # Compatible Pair Tests -/
noncomputable section
namespace HadwigerCounterexample
open Filter Finset Function Module LinearMap Matrix
open scoped BigOperators Topology
open Template
namespace StatusAnalysis
open PreparationParameters Station PredictionClass Club Guild DualAnalysis
variable {p:Shape} {n N M r s0:ℕ}
{w:rhythms p M} {b:PreparationParameters}
set_option maxHeartbeats 1800000 in
theorem foretold (w:rhythms p M) (m:cycleM p) (x:Sketch p M)
(v:Station p n (M*n) b.pins (w n)) (hv:v.bank)
(U:Wgt (UnitType p n (M*n))) (h:Lead U (w n) (m n) b)
(hE:AnalyticParameters p M b s0)
(hm:(w n).within (engrave x b m w n))
(hn:2*p.r≤n) (Y:Silhouette p (M*n) r) (f:Bool→Pulsar p r)
{τ ε δ η a d0:ℝ} (hh: hue x.c Y f (fun i=>x.g i n) x.α τ)
(hε:0<ε) (hp:Jubilee p b.pins ε η)
(hB:supportBudget p b.pins η a)
(hz:x.ε n ≤scanPrice p*ε) (ht:10*ε≤τ) (hT:2*τ<1)
(hF:Beams b (m n) Y (w n) U v a ε δ d0) (i : ViewPair p n (M*n) (w n))
(hx:cirque (w n) U i ≠0)
(hg1:gauze p δ δ Y (m n) b.pins i.1.2) (hg2:gauze p δ δ Y (m n) b.pins i.2.2)
(hC:matchProg x n (i.1.2,i.2.2))
(hS:secureAt p (w n).rooting (i.1.2,i.2.2)) :
eligiblePair v (m n) i.1 i.2 Y a := by
classical
let s:=w n; let μ:= U; let K:=b.pins
let X:=i.1.2; let Z:=i.2.2
let j:=i.1.1; let k:=i.2.1
let L:=troupe s μ
have hs : L i.1≠0:=left_ne_zero_of_mul hx
have hl : L i.2 ≠0:=right_ne_zero_of_mul hx
have hX := troupe_home h i.1 hs
have hZ:= troupe_home h i.2 hl
have hL i:= (h.strength.leaf _ (Subtype.prop (show s.T from i))).bound
obtain ⟨g,hg⟩:= ready_loupe s v hv hE hL
let d:= g.r j; let e:=g.r k
let t:=v.cAxes j (toRates d); let u:=v.cAxes k (toRates e)
let A:=g.H j; let B:=g.H k
let m':=x.m n
let F:=x.L n X; let H:=x.L n Z
let P:= A⊔F; let Q:=B⊔ H
obtain ⟨⟨h1,h2⟩,h3,h4⟩:=hm _ j.property X hX.1
obtain ⟨⟨h1',h2'⟩,h3',h4'⟩:=hm _ k.property Z hZ.1
let M0:=s.pin j.val; let M1:=s.pin k.val
have he (i):m' X i∈ effective M0.sp i:= (hX.2.1 ▸ (h1 i).2)
have he' i:m' Z i∈effective M1.sp i:= (hZ.2.1 ▸ (h1' i).2)
choose T hP using fun i=> show m' X i∈LinearMap.range (t i) from
(hg.charts j i).1.symm ▸ he i
choose S hQ using fun i=> show m' Z i∈ LinearMap.range (u i) from
(hg.charts k i).1.symm ▸ he' i
let Γ:PredictionData p (toRates d) (toRates e) r := ⟨x.α,f,T,S⟩
have ht0:= hE.enter.first
let M' := m n
let D:=wisp p Y; let X0:=wake p Y M' X t; let X1:=wake p Y M' Z u
let β:=trimBeta p K
let C:=stellar D X0 X1 η P Q
have hk0 i t:=Nat.lt_succ_iff.mp (g.r i t).isLt
have hA: reports p r D X0 β δ:=routeLive s g v hg M' hE hn i.1 Y δ hF.haze.1 (hL _) hg1
have hB1: reports p r D X1 β δ:=routeLive s g v hg M' hE hn i.2 Y δ hF.haze.1 (hL _) hg2
have hR := boothseek b _ (g.H j) F (hg.baseline j) hE (fun i=>(h1 i).1)
have hR' := boothseek b _ (g.H k) H (hg.baseline k) hE (fun i=>(h1' i).1)
have hG: rich C:= plenitude hF.soft hA hB1 ht0.hG P Q hR hR' (trimBeta_pos ..) hp.pos
hp.sturdyR (hk0 _) (hk0 _)
obtain ⟨E,hE0,hr⟩:=stable C hG
obtain ⟨y,hy⟩:= issueTicket X Z s v j k h.strength.part hX.1 hZ.1 hv hS
let U0:=v.mails j k y
have hQ': x.c.compatible x.α (glint p (m' X)) (cardTone m' X U0,cardTone m' Z
(reciprocal p U0)) := by
change glint p _=_ at h3
have he1 l: cardTone m' X U0 l=(quench p (delta m') (X,Z)).1 l:=
(fitsTone m' X hy.2.2 he l).trans (actualTone m' X Z l)
have he2 l:cardTone m' Z (reciprocal p U0) l=(quench p (delta m') (X,Z)).2 l:= by
have hg := fits_recip hy.2.2; rw [reciprocal_actual] at hg
exact (fitsTone m' Z hg he' l).trans (actualTone m' Z X l)
rw [funext he1,funext he2,h3]; exact hC
have hc: countStory p K η δ ε β D:=⟨hF.soft,(trimBeta_pos ..).le,hε.le,hp.pos.le,
hp.book,hp.low⟩
have hv : Γ.colored D X0 X1 P Q (2*ε):= by
constructor
· exact crew_praise p x.c Y f (fun i=>x.g i n) x.α τ hh (m n) t T m' X F P le_sup_right
hP hε.le hF.haze.2 hE hn (fun i j hj k f=>(h2 i j hj k f).trans hz) h4 hg1
exact crew_praise p x.c Y f (fun i=>x.g i n) x.α τ hh (m n) u S m' Z H Q le_sup_right
hQ hε.le hF.haze.2 hE hn (fun i j hj k f=>(h2' i j hj k f).trans hz) h4' hg2
have hZ0 := laysScore p K Y (m n) D X Z m' (toRates d) (toRates e) t u x.c Γ P Q
E η ε β δ τ hP hQ (paintChorus _ _ f _ x.α τ hh T S) (by linarith only [hε,ht]) hT hc
hA hB1 hv (hk0 _) (hk0 _) ht0.hG ht hR hR' hE0 U0 (h3.trans h3'.symm) hQ' hG
exact inform (w n) v _ Y i.1 i.2 hX.2.2.1 hZ.2.2.1 hX.2.2.2 hZ.2.2.2 d e (hg.charts _)
(hg.charts _) hB A B (hg.baseline _) (hg.baseline _) P Q le_sup_left le_sup_left ht0.hG
hE.jump hp.pos y hy E hr hZ0
end StatusAnalysis
end HadwigerCounterexample
end
end OAI
|