| import OAI.Geometry.ProjectionBodies.AffineCovariance | |
| namespace OAI | |
| noncomputable section | |
| open Set MeasureTheory | |
| namespace PettyProjection | |
| /-- The exact unrestricted inequality and its global equality characterization. | |
| -/ | |
| theorem petty_projection_volume (n : ℕ) (hn : 4 ≤ n) | |
| (K : Set (Space n)) (hK : IsConvexBody K) : | |
| pettyConstant n ≤ projectionRatio K ∧ | |
| (projectionRatio K = pettyConstant n ↔ IsEllipsoid K) := by | |
| obtain ⟨hbound,hrigid⟩ := projection_lower_bound hn hK | |
| exact ⟨hbound,hrigid,ellipsoid_projectionRatio (by omega)⟩ | |
| theorem mainClaim_proved : MainClaim := petty_projection_volume | |
| theorem MainClaim_proved : MainClaim := mainClaim_proved | |
| end PettyProjection | |
| end | |
| end OAI | |