Proof with simpl_env; eauto.
intros V U T E F X Hwf_typ.
remember (F ++ X ~ bind_sub V ++ E) as G.
generalize dependent F.
induction Hwf_typ; intros F Heq; subst...
Case "wf_typ_var".
analyze_binds H...
Case "typ_all".
pick fresh Y and apply wf_typ_all...
rewrite <- app_assoc.
apply H0...
Qed.

(* Specifications: *)
Lemma wf_typ_strengthening : forall E F x U T,
wf_typ (F ++ x ~ bind_typ U ++ E) T ->
wf_typ (F ++ E) T.