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_1 :
forall (m:Map A) (f f':ad -> A -> M) (pf pf':ad -> ad),
(forall (a:ad) (y:A), f (pf a) y = f' (pf' a) y) ->
MapFold1 _ _ neutral op f pf m = MapFold1 _ _ neutral op f' pf' m.