(* ----- substitution ---------- *)

Lemma subst_co_erase : forall a x,
(forall b, (erase b) =
erase (co_subst_co_tm a x b)) /\
(forall b, (erase b) =
erase (co_subst_co_brs a x b)) /\
(forall g:co, True) /\
(forall p, (erase p) =
erase (co_subst_co_constraint a x p)).