∀ {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.Over X)}
  (X_1 : CategoryTheory.Limits.Cone (CategoryTheory.WithTerminal.liftFromOver.obj K)),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.id X_1).hom
      { pt := CategoryTheory.Over.mk (X_1.π.app CategoryTheory.WithTerminal.star),
            π :=
              {
                app := fun a =>
                  { left := X_1.π.app (CategoryTheory.WithTerminal.of a),
                    right :=
                      CategoryTheory.CategoryStruct.id
                        (((CategoryTheory.Functor.const J).obj
                                (CategoryTheory.Over.mk (X_1.π.app CategoryTheory.WithTerminal.star))).obj
                            a).right,
                    w := ⋯ },
                naturality := ⋯ } }.pt.hom =
    X_1.π.app CategoryTheory.WithTerminal.star