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

Lemma MapPut_behind_ext :
forall m m':Map A,
eqmap m m' ->
forall (a:ad) (y:A),
eqmap (MapPut_behind A m a y) (MapPut_behind A m' a y).