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

Lemma MapMerge_canon :
forall m m':Map A, mapcanon m -> mapcanon m' -> mapcanon (MapMerge A m m').