Theorems · Definition · combinatorics
Quiver.Path.length
{V : Type u} → [inst : Quiver V] → {a b : V} → Quiver.Path a b → ℕThe length of a path is the number of arrows it uses.
- Defined in
- Mathlib.Combinatorics.Quiver.Path
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- Quiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiverstatement and proof · cited by 405
- Quiver.Pathstatement and proof · cited by 166
- Quiver.Path.brecOnproof · cited by 10
Cited by42
Results whose statement or proof uses this declaration.
- Quiver.IsSStronglyConnectedproof · cited by 8
- Quiver.Path.eq_of_length_zerostatement and proof · cited by 5
- Quiver.Path.length_compstatement · cited by 5
- Quiver.Path.vertices_lengthstatement and proof · cited by 5
- Quiver.Path.vertices_ne_nilproof · cited by 4
- Quiver.Path.comp_injstatement and proof · cited by 2
- Quiver.Path.eq_toPath_comp_of_length_eq_succstatement and proof · cited by 2
- Quiver.Path.exists_eq_comp_of_le_lengthstatement and proof · cited by 2
- Quiver.Path.getElem_vertices_zeroproof · cited by 2
- Quiver.Path.length_consstatement · cited by 2
- Quiver.Path.length_ne_zero_iff_eq_consstatement and proof · cited by 2
- Quiver.Path.comp_inj'statement and proof · cited by 1