openAI-math-dataset / lean /OAI /Geometry /CylinderCovering /Convexity /RegularAngularDefinitions.lean
| import OAI.Geometry.CylinderCovering.Convexity.GlobalDefinitions | |
| namespace OAI | |
| noncomputable section | |
| namespace CylinderCovering | |
| def RegularExplicitAngularStatement : Prop := | |
| ∀ K : Set Space, IsRegularTetrahedron K → | |
| ∀ ε : ℝ, 0 < ε → ε ≤ 1 / 2000 → | |
| ∃ C : Fin (2 * TriangularCovering.n ε) → TriangularCovering.TriCylinder, | |
| triangularCovers K C ∧ | |
| |TriangularCovering.totalArea C / minimumShadowArea K - | |
| (1 / 2 - (13 / 6000 : ℝ) * ε ^ 2)| ≤ 2 * ε ^ 4 ∧ | |
| TriangularCovering.totalArea C < minimumShadowArea K / 2 ∧ | |
| triangularRelativeCost K C < 1 / 2 | |
| end CylinderCovering | |
| end | |
| end OAI | |