File size: 901 Bytes
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 | import OAI.Geometry.CylinderCovering.Barycentric.CoreDefinitions
import OAI.Geometry.CylinderCovering.Barycentric.Coverage
import OAI.Geometry.CylinderCovering.Barycentric.SweepCompact
import OAI.Geometry.CylinderCovering.Barycentric.Cost
namespace OAI
namespace RadialCoordinates
theorem barycentricCore : CylinderCovering.BarycentricCoreStatement := by
refine ⟨?_, ?_, ?_, ?_, ?_, ?_⟩
· intro k
exact ⟨firstSweep_isCompact k, secondSweep_isCompact k⟩
· intro k hk hkbound
exact barycentric_simplex_covered hk hkbound
· intro k hk
exact J_expansion hk
· intro k hk hkbound
exact J_strict_half_target hk hkbound
· intro a b z ha hb
exact CylinderCovering.BarycentricRadial.existsUnique_parameter ha hb z
· intro a b z ha hb
exact CylinderCovering.BarycentricRadial.exists_nonnegative_radial_representation ha hb z
end RadialCoordinates
end OAI
|