∀ {B : Type u} [inst : Quiver B] {a b c : B} (f : CategoryTheory.FreeBicategory.Hom a b)
  (g : CategoryTheory.FreeBicategory.Hom b c),
  CategoryTheory.FreeBicategory.normalizeAux Quiver.Path.nil (f.comp g) =
    (CategoryTheory.FreeBicategory.normalizeAux Quiver.Path.nil f).comp
      (CategoryTheory.FreeBicategory.normalizeAux Quiver.Path.nil g)