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 *)

(* ----- fv  ---------- *)
Lemma fv_tm_erase_tm : ∀ x (a : tm),
x `notin` fv_tm a -> x `notin` fv_tm (erase a).