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

Lemma MapRemove_canon : forall m:Map A, mapcanon m -> forall a:ad, mapcanon (MapRemove A m a).