| import OAI.Geometry.CylinderCovering.Cartesian.StatementDefinitions | |
| import OAI.Geometry.CylinderCovering.Cartesian.CoverDefinitions | |
| namespace OAI | |
| noncomputable section | |
| namespace CylinderCovering | |
| def CartesianCaps.untruncated (τ η q : ℝ) : Set ℝ := | |
| {s | 0 ≤ s ∧ s ≤ CartesianCaps.height τ η (q*s)} | |
| def CartesianCutoffStatement : Prop := | |
| ∀ τ η q : ℝ, τ ∈ Set.Ioc (0 : ℝ) (1/4) → | |
| η ∈ Set.Ioc (0 : ℝ) 1 → q ≠ 0 → |q| ≤ 1 → | |
| ¬ BddAbove (CartesianCaps.untruncated τ η q) ∧ | |
| ¬ IsPreconnected (CartesianCaps.untruncated τ η q) ∧ | |
| ∃ B : ℝ, 1 ≤ B ∧ Set.Ici B ⊆ CartesianCaps.untruncated τ η q | |
| def CartesianFullStatement : Prop := | |
| CartesianApertureStatement ∧ CartesianCoverStatement ∧ CartesianCutoffStatement | |
| end CylinderCovering | |
| end | |
| end OAI | |