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785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | 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
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