Section MapSubsetExtra.
Variables A B : Type.
Variables C D : Type.

Lemma MapSubset_DomRestrBy_mono :
forall (m:Map A) (m':Map B) (m'':Map C) (m''':Map D),
MapSubset _ _ m m'' ->
MapSubset _ _ m''' m' ->
MapSubset _ _ (MapDomRestrBy _ _ m m') (MapDomRestrBy _ _ m'' m''').