Lemma open_co_erase2_rec : forall a, (forall b k g, (open_tm_wrt_co_rec k g (erase b)) = erase (open_tm_wrt_co_rec k a b)) /\ (forall b k g, (open_brs_wrt_co_rec k g (erase b)) = erase (open_brs_wrt_co_rec k a b)) /\ (forall g:co, True) /\ (forall b k g, (open_constraint_wrt_co_rec k g (erase b)) = erase (open_constraint_wrt_co_rec k a b)).