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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 40 41 42 43 44 45 | 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
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