(* 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 subsume_transitive:
forall e1 e2 e3,
subsume e1 e2 ->
subsume e2 e3 ->
subsume e1 e3.