proposition: Lemma subst_ee_open_ee_rec : forall e1 e2 x u k, expr u -> subst_ee x u (open_ee_rec k e2 e1) = open_ee_rec k (subst_ee x u e2) (subst_ee x u e1).
proof: Proof. 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.
imports: Fsub.Fsub_LetSum_Definitions