| import Mathlib |
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| namespace OAI |
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| section |
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| namespace PlanarL1.Parameters |
| noncomputable section |
| /-- Universal ordered parameter choices. The |
| strictly / |
| def R : ℝ := 1/ |
| def ℝ /10^3 |
| def g : ℝ := 1/ |
| def ℝ /10^20 |
| def epsilon : ℝ := 1/ |
| def ℝ /1000 |
| def EB : ℝ := R/ |
| def ℝ /100 |
| def zetaB : ℝ := 1/ |
| def ₁ ℝ /10^100 |
| def a₂ : ℝ := 1/ |
| def ℝ ₁/10^6 |
| def kappaB : ℝ := a₂/ |
| def ℝ /(10^12*100) |
|
|
| lemma positive : 0<R ∧ 0<D ∧ 0<g ∧ 0<j ∧ 0<epsilon ∧ 0<EA ∧ 0<EB ∧ |
| 0<zetaA ∧ 0<zetaB ∧ 0<a₁ ∧ 0<a₂ ∧ 0<kappaA ∧ 0<kappaB ∧ 0<lambda := by |
| norm_num [R,D,g,j,epsilon,EA,EB,zetaA,zetaB,a₁,a₂,kappaA,kappaB,lambda] |
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| lemma interpolationA : 0<EA ∧ 0<a₁ ∧ 0<zetaA ∧ zetaA<1 ∧ |
| a₁ ≤ zetaA*(EA//1000000 := by |
| norm_num [EA,epsilon,a₁,zetaA] |
| lemma interpolationB : 0<EB ∧ 0<a₂ ∧ 0<zetaB ∧ zetaB<1 ∧ |
| a₂ ≤ zetaB*(EB//1000000 := by |
| norm_num [EB,R,a₂,zetaB] |
| lemma thinA : a₁≤(1/ℝ/1000 := by norm_num [a₁] |
| lemma widthA : a₁≤EA/ ∧ ₁≤/10^6 := by norm_num [a₁,EA,epsilon,g] |
| lemma widthB : a₂ ≤ min a₁ (kappaA*j)/ |
| norm_num ₁₂ |
| lemma ≤ ∧ /(9*a₁/≤ ∧ |
| kappaA*(3/(9*a₁/100))<1 := by |
| norm_num ₁ |
| lemma ≤ ∧ /(9*a₂/≤ ∧ |
| kappaB*(3/(9*a₂/100))<1 ∧ kappaB*5≤1 := by |
| norm_num ₂ |
|
|
| /-- Numeric input to the literal interpolation hierarchy. -/ |
| structure |
| error ℝ |
| width ℝ |
| zeta ℝ |
| error_pos |
| width_pos |
| zeta_pos |
| zeta_lt |
| width_bound ≤ /8)/ |
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|
| def ⟨₁ |
| interpolationA.2.1,interpolationA.2.2.1,interpolationA.2.2.2.1, |
| interpolationA.2.2.2.2⟩ |
| def ⟨₂ |
| interpolationB.2.1,interpolationB.2.2.1,interpolationB.2.2.2.1, |
| interpolationB.2.2.2.2⟩ |
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|
| end |
| end |
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| end |
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| end |
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|
