∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {J : Type u_4}
  [inst_1 : CategoryTheory.Category.{u_3, u_4} J] {X : C} {K : CategoryTheory.Functor J (CategoryTheory.Under X)}
  (t : CategoryTheory.Limits.Cocone (CategoryTheory.WithInitial.liftFromUnder.obj K)) (a : J),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Functor.fromPUnit X).map (CategoryTheory.CategoryStruct.id (K.obj a).left))
      (((CategoryTheory.Functor.const J).obj (CategoryTheory.Under.mk (t.ι.app CategoryTheory.WithInitial.star))).obj
          a).hom =
    CategoryTheory.CategoryStruct.comp (K.obj a).hom
      ((CategoryTheory.Functor.id C).map (t.ι.app (CategoryTheory.WithInitial.of a)))