erase_tm lc_tm_open_tm_wrt_co_erase_tm : lc.

(* ----- automation ---------- *)

(* TODO *)
Hint Rewrite open_co_erase_tm open_co_erase_tm2 open_tm_erase_tm : TODO.
Hint Resolve lc_erase binds_map_2.

(* Specifications: *)
destruct a. simpl. rewrite IHG. eauto.
Lemma path_erase : forall T p, Path T p -> Path T (erase p). Proof. intros. induction H; simpl; eauto.
rewrite open_tm_erase_tm; eauto].
Lemma Value_erase : (forall v, Value v -> Value (erase v)).