Proof with try solve [eauto | congruence].
induction e; intros j v i u Neq H; simpl in *;
try solve [inversion H; f_equal; eauto].
Case "bvar".
destruct (j == n)...
destruct (i == n)...
Qed.
(** With the help of this lemma, we can complete the proof. *)

(* Specifications: *)
Lemma open_rec_lc : forall k u e,
lc e -> e = {k ~> u} e.