Definition MapSubset (m:Map A) (m':Map B) :=
    forall a:ad, in_dom A a m = true -> in_dom B a m' = true.Definition MapSubset_1 (m:Map A) (m':Map B) :=
    match MapSweep A (fun (a:ad) (_:A) => negb (in_dom B a m')) m with
    | None => true
    | _ => false
    end.Definition MapSubset_2 (m:Map A) (m':Map B) :=
    eqmap A (MapDomRestrBy A B m m') (M0 A).

Lemma MapSubset_Merge_mono : forall (m m':Map A) (m'' m''':Map B), MapSubset A B m m'' -> MapSubset A B m' m''' -> MapSubset A B (MapMerge A m m') (MapMerge B m'' m''').