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

Lemma MapMerge_DomRestrTo : forall (m m':Map A) (m'':Map B), eqmap (MapDomRestrTo A B (MapMerge A m m') m'') (MapMerge A (MapDomRestrTo A B m m'') (MapDomRestrTo A B m' m'')).