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 toplevel_erased2 : forall F a A, binds F (Ax a A) toplevel -> erased_tm A.
Hint Resolve toplevel_erased1 toplevel_erased2 : erased.