Theorems · Theorem · combinatorics
Quiver.Path.exists_eq_comp_of_le_length
∀ {V : Type u_1} [inst : Quiver V] {a b : V} (p : Quiver.Path a b) {n : ℕ},
n ≤ p.length → ∃ v p₁ p₂, p = p₁.comp p₂ ∧ p₁.length = nGiven a path p : Path a b and an index n ≤ p.length,
we can split p = p₁.comp p₂ with p₁.length = n.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
- Assumes
- Quiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.compstatement and proof · cited by 45
- Quiver.Path.lengthstatement and proof · cited by 39
- Quiver.Path.length_consproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Quiver.Path.exists_eq_comp_and_length_eq_of_lt_lengthproof · cited by 1
- Matrix.IsIrreducible.exists_posproof · cited by 0