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).

Lemma MapFold_ext_f :
forall (f g:ad -> A -> M) (m:Map A),
(forall (a:ad) (y:A), MapGet _ m a = Some y -> f a y = g a y) ->
MapFold _ _ neutral op f m = MapFold _ _ neutral op g m.