OAI/GroupTheory/Hyperbolic/Model.lean

GitHub source file

4 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.Release075.TorsionFree line 10

    Source documentation

    No nonidentity element has finite order. This does not assert unique roots.

    Also declared: ComparatorChallenges/TorsionFreeHyperbolic.lean:10 (same declaration text).

    def TorsionFree (G : Type u) [Group G] : Prop :=
    …
  2. def OAI.Release075.Geodesic line 14

    Source documentation

    A shortest edge path in the unit-edge graph.

    Also declared: ComparatorChallenges/TorsionFreeHyperbolic.lean:14 (same declaration text).

    def Geodesic {V : Type u} (X : SimpleGraph V) {x y : V} (p : X.Walk x y) : Prop :=
    …
  3. def OAI.Release075.SideThin line 18

    Source documentation

    Each vertex of p is within δ of a vertex of q or r.

    Also declared: ComparatorChallenges/TorsionFreeHyperbolic.lean:18 (same declaration text).

    def SideThin {V : Type u} (X : SimpleGraph V) (δ : ℕ) {x y z : V}
        (p : X.Walk x y) (q : X.Walk y z) (r : X.Walk z x) : Prop :=
    …
  4. def OAI.Release075.WordHyperbolic line 24

    Source documentation

    A finitely generated group with a unit-edge Cayley graph whose geodesic triangles are uniformly thin. Connectedness of this Cayley graph asserts that S generates.

    Also declared: ComparatorChallenges/TorsionFreeHyperbolic.lean:24 (same declaration text).

    def WordHyperbolic (G : Type u) [Group G] : Prop :=
    …