| 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 | |