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).