Theorems · Theorem · combinatorics
Quiver.Path.length_cons
∀ {V : Type u} [inst : Quiver V] (a b c : V) (p : Quiver.Path a b) (e : b ⟶ c), (p.cons e).length = p.length + 1- Defined in
- Mathlib.Combinatorics.Quiver.Path
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Quiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- Quiverstatement and proof · cited by 405
- Quiver.Pathstatement and proof · cited by 166
- Quiver.Path.lengthstatement · cited by 39
Cited by2
Results whose statement or proof uses this declaration.
- Quiver.Path.exists_eq_comp_of_le_lengthproof · cited by 2
- Quiver.Path.eq_toPath_comp_of_length_eq_succproof · cited by 2