Definition close_tm_erase_all := fun x => close_tmco_erase_all (inl x).
Definition close_co_erase_all := fun x => close_tmco_erase_all (inr x).
Definition close_tm_erase_tm := fun x => proj1 (close_tm_erase_all x).
Definition close_co_erase_tm := fun x => proj1 (close_co_erase_all x).
*)
(* Pointless to close erased terms wrt co variables *)

Lemma close_co_erase_tm2 : forall x a, close_tm_wrt_co x (erase a) = erase a.