∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} D]
  {F G : CategoryTheory.Functor C D} (η : F ⟶ G) (X : CategoryTheory.WithInitial C),
  (CategoryTheory.WithInitial.map₂ η).app X =
    match X with
    | CategoryTheory.WithInitial.of x => η.app x
    | CategoryTheory.WithInitial.star => CategoryTheory.CategoryStruct.id CategoryTheory.WithInitial.star