| import OAI.Geometry.CylinderCovering.Cartesian.StatementDefinitions | |
| import OAI.Geometry.CylinderCovering.Cartesian.Domain | |
| namespace OAI | |
| namespace CylinderCovering.CartesianCaps | |
| theorem cartesianAperture_proved : CylinderCovering.CartesianApertureStatement := by | |
| intro τ η hτ hη | |
| have hcap := cap_properties τ η hτ hη | |
| refine ⟨hcap.1, hcap.2, ?_⟩ | |
| intro b hb | |
| have harea := domain_area_bounds τ η b hτ hη hb | |
| exact ⟨domain_isCompact τ η b hb.2, domain_radial τ η b hτ hη hb, harea⟩ | |
| end CylinderCovering.CartesianCaps | |
| end OAI | |