Proof with auto.
intros.
unfold open_te.
apply subst_te_intro_rec...
Qed.
(* ********************************************************************** *)
(** ** Properties of expression substitution in expressions *)
(** This section follows the structure of the previous two sections. *)

Lemma open_ee_rec_expr_aux : forall e j v u i,
i <> j ->
open_ee_rec j v e = open_ee_rec i u (open_ee_rec j v e) ->
e = open_ee_rec i u e.