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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 = n

Given a path p : Path a b and an index n ≤ p.length, we can split p = p₁.comp p₂ with p₁.length = n.

Defined in
Mathlib.Combinatorics.Quiver.Path.Vertices
Cited by
2 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext
Assumes
Quiver

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