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Theorems · Theorem · combinatorics

Quiver.Path.nil_of_comp_eq_nil_right

∀ {V : Type u_1} [inst : Quiver V] {a b : V} {p : Quiver.Path a b} {q : Quiver.Path b a},
  p.comp q = Quiver.Path.nil → q.length = 0

If a composition is nil, the right component must be nil

Defined in
Mathlib.Combinatorics.Quiver.Path.Vertices
Cited by
1 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext
Assumes
Quiver
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Quiver.Path.comp_eq_nil_iff · cited by 0Path.comp_eq_nil_iffQuiver · cited by 405QuiverQuiver.Path · cited by 166Quiver.PathQuiver.Path.comp · cited by 45Path.compQuiver.Path.length · cited by 39Path.lengthQuiver.Path.length_comp · cited by 5Path.length_compPath.nil_of_comp_eq_nil_rightCITED BYCITES

Cites5

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Cited by1

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