Fixpoint MapCanonicalize (m:Map A) : Map A :=
    match m with
    | M2 m0 m1 => makeM2 A (MapCanonicalize m0) (MapCanonicalize m1)
    | _ => m
    end.

Lemma MapFold_canon : forall m0:Map B, mapcanon B m0 -> forall op:Map B -> Map B -> Map B, (forall m1:Map B, mapcanon B m1 -> forall m2:Map B, mapcanon B m2 -> mapcanon B (op m1 m2)) -> forall f:ad -> A -> Map B, (forall (a:ad) (y:A), mapcanon B (f a y)) -> forall m:Map A, mapcanon B (MapFold A (Map B) m0 op f m).