Section MapFoldResults.
Variable A : Type.
Variable M : Type.
Variable neutral : M.
Variable op : M -> M -> M.
Variable nleft : forall a:M, op neutral a = a.
Variable nright : forall a:M, op a neutral = a.
Variable assoc : forall a b c:M, op (op a b) c = op a (op b c).
Variable comm : forall a b:M, op a b = op b a.

Lemma MapFold_Put_behind_disjoint :
forall (f:ad -> A -> M) (m:Map A) (a:ad) (y:A),
MapGet A m a = None ->
MapFold A M neutral op f (MapPut_behind A m a y) =
op (f a y) (MapFold A M neutral op f m).