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 MapFold1_as_Fold :
forall (f:ad -> A -> M) (pf:ad -> ad) (m:Map A),
MapFold1 _ _ neutral op f pf m =
MapFold _ _ neutral op (fun (a:ad) (y:A) => f (pf a) y) m.