| import OAI.MathematicalPhysics.Transonic.Profile.Equations | |
| namespace OAI | |
| section | |
| noncomputable section | |
| open scoped ContDiff | |
| namespace SepticProfile | |
| def RelativisticProfileExists : Prop := | |
| ∃ (beta : ℝ) (g : ℝ → ℝ), | |
| 1 < beta ∧ beta*(ell + Real.sqrt ell) < 3 ∧ | |
| ContDiffOn ℝ ∞ g (Set.Ici 0) ∧ | |
| let v : ℝ → ℝ := fun y => y*g (y^2) | |
| (∀ y : ℝ, 0 ≤ y → |v y| < 1) ∧ | |
| (∀ y : ℝ, 0 ≤ y → | |
| profileDenom ell y (v y) * deriv v y = profileNumer ell beta y (v y)) ∧ | |
| (∀ y : ℝ, 0 < y → v y < y ∧ y*v y < 1) ∧ | |
| 0 < sonicRadius beta ∧ sonicRadius beta < 1 ∧ | |
| (∀ y : ℝ, 0 ≤ y → | |
| (velocityToU y (v y) = sonicSpeed ↔ y = sonicRadius beta)) ∧ | |
| 0 < deriv (fun y => velocityToU y (v y)) (sonicRadius beta) | |
| end SepticProfile | |
| end | |
| end | |
| end OAI | |