(* Then, it is extended pointwise to environments. *)
Definition subsume (e1 e2 : env A) :=
forall x,
osub (lookup x e1) (lookup x e2).
(* Subsumption of environments is reflexive and transitive. *)

Lemma osub_transitive:
forall o1 o2 o3,
osub o1 o2 ->
osub o2 o3 ->
osub o1 o3.