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

Lemma mapcanon_exists :
forall m:Map A, {m' : Map A | eqmap A m m' /\ mapcanon m'}.