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

Lemma MapRemove_as_RestrBy :
forall (m:Map A) (a:ad) (y:B),
eqmap (MapRemove A m a) (MapDomRestrBy A B m (M1 B a y)).