(* 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_cons_inversion: forall o1 o2 e1 e2, subsume (o1 :: e1) (o2 :: e2) -> osub o1 o2 /\ subsume e1 e2.