Hint Resolve lc_tm_open_tm_wrt_tm_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.
Ltac auto_rew_erase :=
multimatch goal with
| [ e: erase _ = erase _ |- _ ] => rewrite e in *; clear e
end.
(* ----- useful property for pi types -------------- *)

Lemma asymmetric_erase : forall B x g,
erase (open_tm_wrt_tm B (a_Var_f x)) =
erase (open_tm_wrt_tm B (a_Conv (a_Var_f x) g)).