| import Mathlib | |
| namespace OAI | |
| namespace PlanarFalconer | |
| open MeasureTheory Set | |
| abbrev Plane := EuclideanSpace ℝ (Fin 2) | |
| def distanceSet (E : Set Plane) : Set ℝ := | |
| {r | ∃ x ∈ E, ∃ y ∈ E, dist x y = r} | |
| def MainTarget : Prop := | |
| ∀ E : Set Plane, IsCompact E → 1 < dimH E → 0 < volume (distanceSet E) | |
| end PlanarFalconer | |
| namespace PlanarFalconer | |
| theorem mainTarget_proved : MainTarget := by | |
| sorry | |
| end PlanarFalconer | |
| end OAI | |