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_mutual:
(forall G b A, Typing G b A -> erased_tm b) /\
(forall G0 phi (H : PropWff G0 phi),
forall A B T, phi = Eq A B T -> erased_tm A /\ erased_tm B /\ erased_tm T) /\
(forall G0 D p1 p2 (H : Iso G0 D p1 p2), True ) /\
(forall G0 D A B T (H : DefEq G0 D A B T), True) /\
(forall G0 (H : Ctx G0), True).