∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} D]
  (F : CategoryTheory.Functor C D) (X : CategoryTheory.WithInitial C),
  (CategoryTheory.WithInitial.map F).obj X =
    match X with
    | CategoryTheory.WithInitial.of x => CategoryTheory.WithInitial.of (F.obj x)
    | CategoryTheory.WithInitial.star => CategoryTheory.WithInitial.star