Proof with auto.
intros G Z P H.
induction H; simpl; intros Fr; simpl_env...
rewrite <- IHwf_env...
rewrite <- subst_tt_fresh... eapply notin_fv_wf; eauto.
rewrite <- IHwf_env...
rewrite <- subst_tt_fresh... eapply notin_fv_wf; eauto.
Qed.
(* ********************************************************************** *)
(** * #<a name="regularity"></a># Regularity of relations *)

Lemma sub_regular : forall E S T,
sub E S T ->
wf_env E /\ wf_typ E S /\ wf_typ E T.