Theorems · Definition · combinatorics
Quiver.Path.brecOn
{V : Type u} →
[inst : Quiver V] →
{a : V} →
{motive : (a_1 : V) → Quiver.Path a a_1 → Sort u_1} →
{a_1 : V} →
(t : Quiver.Path a a_1) →
((a_2 : V) → (t : Quiver.Path a a_2) → Quiver.Path.below t → motive a_2 t) → motive a_1 t- Defined in
- Mathlib.Combinatorics.Quiver.Path
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 6 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.
- Quiverstatement and proof · cited by 405
- Quiver.Pathstatement and proof · cited by 166
- Quiver.Path.brecOn.goproof · cited by 7
- Quiver.Path.belowstatement and proof · cited by 7
Cited by21
Results whose statement or proof uses this declaration.
- Quiver.Path.compproof · cited by 45
- Quiver.Path.lengthproof · cited by 39
- Quiver.Path.verticesproof · cited by 21
- CategoryTheory.composePathproof · cited by 16
- Prefunctor.mapPathproof · cited by 15
- Quiver.Path.reverseproof · cited by 7
- Quiver.Path.toListproof · cited by 6
- Quiver.Path.brecOn.eqstatement and proof · cited by 6
- Quiver.Path.length_compproof · cited by 5
- IsFreeGroupoid.SpanningTree.homOfPathproof · cited by 4
- Quiver.Path.comp_assocproof · cited by 3
- Quiver.SingleObj.pathToListproof · cited by 3