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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 28 29 30 31 32 33 34 35 36 37 38 39 | import OAI.Geometry.CylinderCovering.Cubic.RescalingDefinitions
import OAI.Geometry.CylinderCovering.Angular.ConstructionDefinitions
namespace OAI
noncomputable section
open Set Filter Asymptotics
open scoped Topology
namespace CylinderCovering.Cubic
open TriangularCovering
def FullCubicRescaledStatement : Prop :=
contraction '' K4 = K ∧
(∀ a b : ℝ, a ≤ b →
IsGreatest (TriangularCovering.d '' Icc a b)
(max (TriangularCovering.d a) (TriangularCovering.d b))) ∧
(∀ τ a b : ℝ, cap (τ / 2) a b / 2 =
1 / 2 + τ ^ 2 *
(max (TriangularCovering.d a) (TriangularCovering.d b) + 25 / 4 * τ)) ∧
Tendsto (fun τ : ℝ => 25 / 4 * τ) (𝓝[>] (0 : ℝ)) (𝓝 0) ∧
RescaledFiniteCoverStatement ∧
(∀ τ : ℝ, 0 < τ → τ ≤ 1 →
|cubicCost (τ / 2) / (4 * H) - (1 / 2 - τ ^ 2 / 240)| ≤
(401 / 4 : ℝ) * τ ^ 3) ∧
((fun τ : ℝ => cubicCost (τ / 2) / (4 * H) - (1 / 2 - τ ^ 2 / 240))
=O[𝓝[>] (0 : ℝ)] (fun τ => τ ^ 3)) ∧
∃ delta : ℝ, 0 < delta ∧
∀ τ : ℝ, 0 < τ → τ < delta →
∃ C : Fin (2 * n (τ / 2)) → TriCylinder,
Covers C ∧ ContractedFamily (τ / 2) C ∧
totalArea C = cubicCost (τ / 2) / 4 ∧ totalArea C < A_min / 2
end CylinderCovering.Cubic
end
end OAI
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