Definition eqmap (m m':Map A) := eqm A (MapGet A m) (MapGet A m').

Lemma MapDom_Split_3 :
forall (m:Map A) (m':Map B),
eqmap
(MapDomRestrTo A A (MapDomRestrTo A B m m') (MapDomRestrBy A B m m'))
(M0 A).