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Theorems · Theorem · combinatorics

Quiver.Path.length_comp

∀ {V : Type u} [inst : Quiver V] {a b : V} (p : Quiver.Path a b) {c : V} (q : Quiver.Path b c),
  (p.comp q).length = p.length + q.length
Defined in
Mathlib.Combinatorics.Quiver.Path
Cited by
5 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
Quiver
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Around this declaration

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

Quiver.Path.comp_inj' · cited by 1Path.comp_inj'Quiver.Path.nil_of_comp_eq_nil_left · cited by 1Path.nil_of_comp_eq_nil_l…Quiver.Path.nil_of_comp_eq_nil_right · cited by 1Path.nil_of_comp_eq_nil_r…Matrix.IsIrreducible.transpose · cited by 1IsIrreducible.transposeQuiver.IsStronglyConnected.isSStronglyConnected_of_hom · cited by 0IsStronglyConnected.isSSt…Quiver · cited by 405QuiverQuiver.Path · cited by 166Quiver.PathQuiver.Path.comp · cited by 45Path.compQuiver.Path.length · cited by 39Path.lengthQuiver.Path.brecOn · cited by 10Path.brecOnPath.length_compCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.