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

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