Theorems · Theorem · combinatorics
Quiver.Path.brecOn.eq
∀ {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) (F_1 : (a_2 : V) → (t : Quiver.Path a a_2) → Quiver.Path.below t → motive a_2 t),
Quiver.Path.brecOn t F_1 = F_1 a_1 t (Quiver.Path.brecOn.go t F_1).2- Defined in
- Mathlib.Combinatorics.Quiver.Path
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Quiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- Quiverstatement and proof · cited by 405
- Quiver.Pathstatement and proof · cited by 166
- Quiver.Path.casesOnproof · cited by 12
- Quiver.Path.brecOnstatement and proof · cited by 10
- Quiver.Path.brecOn.gostatement · cited by 7
- Quiver.Path.belowstatement and proof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- Quiver.Path.reverse.eq_defproof · cited by 0
- CategoryTheory.composePath.eq_defproof · cited by 0
- Quiver.Path.length.eq_defproof · cited by 0
- Quiver.Path.toList.eq_defproof · cited by 0
- IsFreeGroupoid.SpanningTree.homOfPath.eq_defproof · cited by 0
- CategoryTheory.FreeBicategory.inclusionPathAux.eq_defproof · cited by 0