OAI/Geometry/HyperbolicGroups/PictureFaceCorners.lean
2 declarations, 0 contain sorry, 0 declared as axioms
- lemma
OAI.HyperbolicObstruction.PictureSwitch.PictureMap.faceCorners_card_le_fiberline 19 - theorem
OAI.HyperbolicObstruction.PictureSwitch.PictureMap.faceCorners_card_leline 30Source documentation
A bound on the literal side-degree of each face bounds the number of its distinct corner vertices, even for faces touching the same vertex repeatedly or traversing both sides of a loop.
theorem faceCorners_card_le (k : ℕ) (hdegree : ∀ x : D, Fintype.card {y : D // M.face.SameCycle x y} ≤ k) (f : M.dual.GraphVertex) : (M.faceCorners f).card ≤ k := by …