Proof with eauto 6 using wf_typ_subst_tb.
induction F; intros Wf_env WP; simpl_env;
inversion Wf_env; simpl_env in *; simpl subst_tb...
Qed.
(* ********************************************************************** *)
(** * #<a name="subst"></a># Environment is unchanged by substitution for a fresh name *)

(* Specifications: *)
Lemma notin_fv_tt_open : forall (Y X : atom) T,
X `notin` fv_tt (open_tt T Y) ->
X `notin` fv_tt T.
Lemma notin_fv_wf : forall E (X : atom) T,
wf_typ E T ->
X `notin` dom E ->
X `notin` fv_tt T.