OAI/GroupTheory/Hyperbolic/Model.lean
4 declarations, 0 contain sorry, 0 declared as axioms
- def
OAI.Release075.TorsionFreeline 10Source 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 := …
- def
OAI.Release075.Geodesicline 14Source 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 := … - def
OAI.Release075.SideThinline 18Source documentation
Each vertex of
pis withinδof a vertex ofqorr.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 := … - def
OAI.Release075.WordHyperbolicline 24Source documentation
A finitely generated group with a unit-edge Cayley graph whose geodesic triangles are uniformly thin. Connectedness of this Cayley graph asserts that
Sgenerates.Also declared: ComparatorChallenges/TorsionFreeHyperbolic.lean:24 (same declaration text).
def WordHyperbolic (G : Type u) [Group G] : Prop := …