| import OAI.Geometry.CylinderCovering.Angular.EndpointDefinitions | |
| import OAI.Geometry.CylinderCovering.Angular.FamilyDefinitions | |
| namespace OAI | |
| noncomputable section | |
| namespace CylinderCovering | |
| def AngularEndpointStatement : Prop := | |
| ∀ k : ℕ, 14000 ≤ k → | |
| ∃ C : Fin (2*(k^2+1)) → TriangularCovering.TriCylinder, | |
| TriangularCovering.AngularFamily.PrescribedFamily C (1/(k:ℝ)) | |
| (fun j => AngularEndpoint.boundary (k^2) j) | |
| (fun j => AngularEndpoint.boundary (k^2) (j+1)) | |
| (fun j => AngularEndpoint.alpha (k^2) j) | |
| (fun j => AngularEndpoint.beta (k^2) j) | |
| (fun j => AngularEndpoint.radius (1/(k:ℝ)) (1/1000) (k^2) j) ∧ | |
| TriangularCovering.Covers C ∧ | |
| |TriangularCovering.totalArea C/TriangularCovering.H - | |
| (1/2-(13/6000:ℝ)*(1/(k:ℝ))^2)| ≤ 14*(1/(k:ℝ))^4 ∧ | |
| TriangularCovering.totalArea C < TriangularCovering.A_min/2 ∧ | |
| TriangularCovering.relativeCost C < 1/2 | |
| end CylinderCovering | |
| end | |
| end OAI | |