Definition makeM2 (m m':Map) :=
    match m, m' with
    | M0, M0 => M0
    | M0, M1 a y => M1 (Ndouble_plus_one a) y
    | M1 a y, M0 => M1 (Ndouble a) y
    | _, _ => M2 m m'
    end.

Lemma makeM2_M2 : forall m m':Map, eqm (MapGet (makeM2 m m')) (MapGet (M2 m m')).