Proof with auto.
intros e1 e2 x u k WP. revert k.
induction e1; intros k; simpl; f_equal...
Case "exp_bvar".
destruct (k === n); subst...
Case "exp_fvar".
destruct (a == x); subst... apply open_ee_rec_expr...
Qed.

(* Specifications: *)
Lemma subst_ee_open_ee : forall e1 e2 x u,
expr u ->
subst_ee x u (open_ee e1 e2) =
open_ee (subst_ee x u e1) (subst_ee x u e2).