∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} D]
  {Z : D} (F : CategoryTheory.Functor C D) (M : (x : C) → Z ⟶ F.obj x)
  (hM : ∀ (x y : C) (f : x ⟶ y), CategoryTheory.CategoryStruct.comp (M x) (F.map f) = M y) (x : C),
  (CategoryTheory.WithInitial.inclLift F M hM).hom.app x =
    CategoryTheory.CategoryStruct.id
      (match CategoryTheory.WithInitial.incl.obj x with
      | CategoryTheory.WithInitial.of x => F.obj x
      | CategoryTheory.WithInitial.star => Z)