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785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | 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
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