| 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 |
|
|
