Proof with auto.
intros.
unfold open_tt.
apply subst_tt_intro_rec...
Qed.
(* ********************************************************************** *)
(** ** Properties of type substitution in expressions *)
(** This section follows the structure of the previous section.  The one notable difference is that we require two auxiliary lemmas to show that substituting a type in a locally-closed expression is the identity. *)

Lemma open_te_rec_expr_aux : forall e j u i P ,
open_ee_rec j u e = open_te_rec i P (open_ee_rec j u e) ->
e = open_te_rec i P e.