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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 | import OAI.Geometry.CylinderCovering.Angular.CubicCoverDefinitions
namespace OAI
noncomputable section
open Set Filter Asymptotics
open scoped Topology
namespace CylinderCovering.Cubic
open TriangularCovering
def minimumShadow4 : ℝ :=
sInf {a : ℝ | ∃ u : Space, ‖u‖ = 1 ∧ a = area (projection u '' K4)}
def FullCubicStatement : Prop :=
minimumShadow4 = 4 * H ∧
FiniteCoverStatement ∧
(∀ eps : ℝ, 0 < eps → eps ≤ 1 / 2 →
|cubicCost eps / H - (2 - eps ^ 2 / 15)| ≤ 3208 * eps ^ 3) ∧
((fun eps : ℝ => cubicCost eps - (2 * H - H / 15 * eps ^ 2))
=O[𝓝[>] (0 : ℝ)] (fun eps => eps ^ 3)) ∧
∃ delta : ℝ, 0 < delta ∧
∀ eps : ℝ, 0 < eps → eps < delta →
∃ C : Fin (2 * n eps) → TriCylinder,
CoversK4 C ∧ PrescribedFamily eps C ∧
totalArea C = cubicCost eps ∧ totalArea C < minimumShadow4 / 2
end CylinderCovering.Cubic
end
end OAI
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