∀ {V : Type u} [inst : Quiver V] (X Z : Quiver.Symmetrify V) (f : X ⟶ Z),
  Quiver.FreeGroupoid.redStep (CategoryTheory.CategoryStruct.id ((CategoryTheory.Paths.of (Quiver.Symmetrify V)).obj X))
    (CategoryTheory.CategoryStruct.comp f.toPath (Quiver.reverse f).toPath)