| import Mathlib | |
| namespace OAI | |
| noncomputable section | |
| namespace CylinderCovering.CartesianCaps | |
| def D (y : ℝ) : ℝ := y ^ 2 / 4 + y ^ 4 | |
| def d (q : ℝ) : ℝ := (q ^ 2 + q ^ 4) / 16 | |
| def residual (τ η q s : ℝ) : ℝ := s - 1 / 2 - τ ^ 2 * (D (q * s) + η) | |
| def aperture (τ η b q : ℝ) : Set ℝ := | |
| {s | 0 ≤ s ∧ s ≤ b ∧ s ≤ 1 / 2 + τ ^ 2 * (D (q * s) + η)} | |
| def cap (τ η q : ℝ) : ℝ := by | |
| classical | |
| exact if h : ∃ s : ℝ, s ∈ Set.Icc (1 / 2 : ℝ) (3 / 4) ∧ residual τ η q s = 0 then | |
| Classical.choose h | |
| else 1 / 2 | |
| end CylinderCovering.CartesianCaps | |
| end | |
| end OAI | |