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465b10d | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | 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
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