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

Lemma MapDomRestrTo_By :
forall (m:Map A) (m':Map B) (m'':Map C),
eqmap (MapDomRestrTo A C (MapDomRestrBy A B m m') m'')
(MapDomRestrTo A C m (MapDomRestrBy C B m'' m')).