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

Lemma MapMerge_DomRestrBy : forall (m m':Map A) (m'':Map B), eqmap (MapDomRestrBy A B (MapMerge A m m') m'') (MapMerge A (MapDomRestrBy A B m m'') (MapDomRestrBy A B m' m'')).