Theorems · Theorem · combinatorics
Quiver.Path.cast_cons
∀ {U : Type u_1} [inst : Quiver U] {u v w u' w' : U} (p : Quiver.Path u v) (e : v ⟶ w) (hu : u = u') (hw : w = w'),
Quiver.Path.cast hu hw (p.cons e) = (Quiver.Path.cast hu ⋯ p).cons (Quiver.Hom.cast ⋯ hw e)- Defined in
- Mathlib.Combinatorics.Quiver.Cast
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Quiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.caststatement and proof · cited by 12
- Quiver.Hom.caststatement · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Prefunctor.pathStar_injectiveproof · cited by 1