OAI/Geometry/HyperbolicGroups/BipartiteLink.lean

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  1. lemma OAI.HyperbolicObstruction.PictureSwitch.four_le_link line 18

    Source documentation

    A cyclic link whose steps alternate bipartition, with no two-step backtrack, has at least four actual corners. This is a cardinality result about the permutation orbit, not a simple-cycle field supplied by a user.

    lemma four_le_link (p : Perm D) (a : D) (c : D → Bool)
        (hc : ∀ x, p.SameCycle a x → c (p x) ≠ c x)
        (h₂ : p (p a) ≠ a) : 4 ≤ Fintype.card {x // p.SameCycle a x} := by
    …