∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{u_1, u_2} D] (F : CategoryTheory.Functor (CategoryTheory.WithInitial C) D)
  (x y : C) (f : x ⟶ y),
  CategoryTheory.CategoryStruct.comp
      ((fun x => F.map (CategoryTheory.WithInitial.starInitial.to (CategoryTheory.WithInitial.of x))) x)
      ((CategoryTheory.WithInitial.incl.comp F).map f) =
    (fun x => F.map (CategoryTheory.WithInitial.starInitial.to (CategoryTheory.WithInitial.of x))) y