Proof with auto.
intros.
unfold open_ee.
apply subst_ee_intro_rec...
Qed.
(* *********************************************************************** *)
(** * #<a name="lc"></a># Local closure is preserved under substitution *)
(** While these lemmas may be considered properties of substitution, we separate them out due to the lemmas that they depend on. *)
(** The following lemma depends on [subst_tt_open_tt_var]. *)

Lemma subst_tt_type : forall Z P T,
type T ->
type P ->
type (subst_tt Z P T).