| import Mathlib | |
| namespace OAI | |
| namespace BorsukNine | |
| abbrev Vector4 := EuclideanSpace ℝ (Fin 4) | |
| abbrev Matrix4 := EuclideanSpace ℝ (Fin 4 × Fin 4) | |
| def projector (u : Vector4) : Matrix4 := | |
| WithLp.toLp 2 (fun ij => u ij.1 * u ij.2) | |
| def projectorSet : Set Matrix4 := | |
| projector '' {u : Vector4 | ‖u‖ = 1} | |
| def traceOneSymmetric : Set Matrix4 := | |
| {A | (∀ i j : Fin 4, A (i, j) = A (j, i)) ∧ ∑ i : Fin 4, A (i, i) = 1} | |
| def HasTenSmallCover : Prop := | |
| ∃ C : Fin 10 → Set Matrix4, | |
| (∀ i, C i ⊆ projectorSet) ∧ | |
| projectorSet ⊆ ⋃ i, C i ∧ | |
| ∀ i, Metric.diam (C i) < Real.sqrt 2 | |
| end BorsukNine | |
| end OAI | |