Lemma open_tm_erase_rec : forall a, (forall b k, open_tm_wrt_tm_rec k (erase a) (erase b) = erase (open_tm_wrt_tm_rec k a b)) /\ (forall b k, open_brs_wrt_tm_rec k (erase a) (erase b) = erase (open_brs_wrt_tm_rec k a b)) /\ (forall g:co, True) /\ (forall b k, open_constraint_wrt_tm_rec k (erase a) (erase b) = erase (open_constraint_wrt_tm_rec k a b)).