Corollary no_co_in_erased_tm : forall B g,
 open_tm_wrt_co (erase B) g = erase B.Definition close_tm_rec_erase_tm := fun x => proj1 (close_tm_erase_all x).Definition close_co_rec_erase_tm := fun x => proj1 (close_co_erase_all x).

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