Section MapAxioms.
Variables A B C : Type.
Definition eqmap (m m':Map A) := eqm A (MapGet A m) (MapGet A m').
End MapAxioms.

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).