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 map_dom_empty_1 : forall m:Map A, eqmap A m (M0 A) -> forall a:ad, in_dom _ a m = false.