Proof with simpl_env; eauto using wf_typ_weaken_head, type_from_wf_typ.
intros F Q E Z P T WT WP.
remember (F ++ Z ~ bind_sub Q ++ E) as G.
generalize dependent F.
induction WT; intros F EQ Ok; subst; simpl subst_tt...
Case "wf_typ_var".
destruct (X == Z); subst...
SCase "X <> Z".
analyze_binds H...
apply (wf_typ_var (subst_tt Z P U))...
Case "wf_typ_all".
pick fresh Y and apply wf_typ_all...
rewrite subst_tt_open_tt_var...
rewrite_env (map (subst_tb Z P) (Y ~ bind_sub T1 ++ F) ++ E).
apply H0...
Qed.

(* Specifications: *)
Lemma wf_typ_open : forall E U T1 T2,
uniq E ->
wf_typ E (typ_all T1 T2) ->
wf_typ E U ->
wf_typ E (open_tt T2 U).