(* Then, it is extended pointwise to environments. *)

  Definition subsume (e1 e2 : env A) :=
    forall x,
    osub (lookup x e1) (lookup x e2).

Lemma subsume_cons: forall o e1 e2, osub o (lookup 0 e2) -> subsume e1 (tl e2) -> subsume (o :: e1) e2.