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

Lemma MapDomRestrBy_ext : forall (A B:Type) (m1:Map A) (m2:Map B) (m'1:Map A) (m'2:Map B), eqmap A m1 m'1 -> eqmap B m2 m'2 -> eqmap A (MapDomRestrBy A B m1 m2) (MapDomRestrBy A B m'1 m'2).