Proof with eauto using wf_typ_narrowing.
induction F; intros U X Wf_env Wf;
inversion Wf_env; subst; simpl_env in *...
Qed.

(* Specifications: *)
Lemma wf_env_strengthening : forall x T E F,
wf_env (F ++ x ~ bind_typ T ++ E) ->
wf_env (F ++ E).