OAI/Geometry/HyperbolicGroups/PictureFaceCorners.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

  1. lemma OAI.HyperbolicObstruction.PictureSwitch.PictureMap.faceCorners_card_le_fiber line 19
  2. theorem OAI.HyperbolicObstruction.PictureSwitch.PictureMap.faceCorners_card_le line 30

    Source 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
    …