End MapSubsetDef.
Section MapSubsetOrder.
Variables A B C : Type.

(* Specifications: *)
Lemma MapSubset_refl : forall m:Map A, MapSubset A A m m.
Lemma MapSubset_antisym :
forall (m:Map A) (m':Map B),
MapSubset A B m m' ->
MapSubset B A m' m -> eqmap unit (MapDom A m) (MapDom B m').
Lemma MapSubset_trans :
forall (m:Map A) (m':Map B) (m'':Map C),
MapSubset A B m m' -> MapSubset B C m' m'' -> MapSubset A C m m''.