Qed.
(* FIXME: find a good place for this tactic. *)
(* cannot move this to ett_ind.v because need Toplevel_lc ??? *)
Ltac lc_toplevel_inversion :=
match goal with
| [ b : binds ?F _ toplevel |- _ ] =>
apply Toplevel_lc in b; inversion b; auto
end.

Lemma Typing_erased_type : forall G b A, Typing G b A -> erased_tm A.