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

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

Lemma subsume_insert: forall e1 e2, subsume e1 e2 -> forall x o1 o2, osub o1 o2 -> subsume (raw_insert x o1 e1) (raw_insert x o2 e2).