Proof with eauto using wf_typ_strengthening.
induction F; intros Wf_env; inversion Wf_env; subst; simpl_env in *...
Qed.

(* Specifications: *)
Lemma wf_env_subst_tb : forall Q Z P E F,
wf_env (F ++ Z ~ bind_sub Q ++ E) ->
wf_typ E P ->
wf_env (map (subst_tb Z P) F ++ E).