| import OAI.Geometry.CylinderCovering.Beams.FullDefinitions |
| import OAI.Geometry.CylinderCovering.Beams.Main |
| import OAI.Geometry.CylinderCovering.Beams.ShapeCompact |
| import OAI.Geometry.CylinderCovering.Beams.Geometry |
|
|
| namespace OAI |
|
|
| noncomputable section |
| namespace ShortenedBeam |
|
|
| theorem finiteMixedFullStatement : FiniteMixedStatement := by |
| intro a ha ha' ε hε |
| obtain ⟨n,C,hC,hcover,hcost⟩ := finiteMixedStatement a ε ha ha' hε |
| exact ⟨n,C,fun i => ⟨hC i,(hC i).isCompact⟩,hcover,hcost⟩ |
|
|
| theorem primaryConstruction : |
| CoverageStatement ∧ FiniteBeamsStatement ∧ FiniteStripStatement ∧ |
| CylinderCovering.BeamCost.CostStatement ∧ FiniteMixedStatement ∧ |
| CanonicalCounterexampleStatement ∧ RegularCounterexampleStatement := |
| ⟨coverageStatement, finiteBeamsStatement, finiteStripStatement, |
| CylinderCovering.BeamCost.fullCost, finiteMixedFullStatement, |
| canonicalCounterexample, regularMixedCounterexample⟩ |
|
|
| theorem full_of_geometry_and_neighborhood |
| (hgeometry : GeometryStatement) (hneighborhood : NeighborhoodAlternativeStatement) : |
| FullStatement := |
| ⟨hgeometry, coverageStatement, finiteBeamsStatement, finiteStripStatement, |
| CylinderCovering.BeamCost.fullCost, finiteMixedFullStatement, |
| canonicalCounterexample, regularMixedCounterexample, hneighborhood⟩ |
|
|
| theorem primaryConstructionWithGeometry : |
| GeometryStatement ∧ CoverageStatement ∧ FiniteBeamsStatement ∧ FiniteStripStatement ∧ |
| CylinderCovering.BeamCost.CostStatement ∧ FiniteMixedStatement ∧ |
| CanonicalCounterexampleStatement ∧ RegularCounterexampleStatement := |
| ⟨geometryStatement, primaryConstruction⟩ |
|
|
| theorem full_of_neighborhood (h : NeighborhoodAlternativeStatement) : FullStatement := |
| full_of_geometry_and_neighborhood geometryStatement h |
|
|
| end ShortenedBeam |
|
|
| end |
|
|
| end OAI |
|
|
