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_disjoint_1 :
forall (p:positive) (f:ad -> A -> M) (pf:ad -> ad)
(a1 a2:ad) (y1 y2:A),
Nxor a1 a2 = Npos p ->
MapFold1 A M neutral op f pf (MapPut1 A a1 y1 a2 y2 p) =
op (f (pf a1) y1) (f (pf a2) y2).