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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 | import OAI.Geometry.CylinderCovering.Angular.CubicTheoremDefinitions
import OAI.Geometry.CylinderCovering.Angular.CubicFamily
import OAI.Geometry.CylinderCovering.Angular.CubicCost
import OAI.Geometry.CylinderCovering.Cubic.Similarity
namespace OAI
noncomputable section
namespace CylinderCovering.Cubic
open TriangularCovering
lemma minimumShadow4_eq : minimumShadow4 = 4 * H := K4_projection_minimum
theorem fullCubic_proof : FullCubicStatement := by
refine ⟨minimumShadow4_eq, finiteCover_proof, ?_, cubicCost_bigO,
(1 / 100000 : ℝ), by norm_num, ?_⟩
· intro eps he0 he1
exact cubicCost_expansion he0 he1
· intro eps he0 he1
obtain ⟨C, hcover, harea, hprescribed⟩ := finiteCover_proof eps he0 (by linarith)
refine ⟨C, hcover, hprescribed, harea, ?_⟩
rw [harea, minimumShadow4_eq]
have h := cubicCost_strict he0 he1.le
linarith
end CylinderCovering.Cubic
end
end OAI
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