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

Lemma MapPut_behind_as_Merge :
forall (m:Map A) (a:ad) (y:A),
eqmap (MapPut_behind A m a y) (MapMerge A (M1 A a y) m).