(** The semantics of maps is given by the function [MapGet]. The semantics of a map [m] is a partial, finite function from [ad] to [A]: *)
Definition newMap := M0.
Definition MapSingleton := M1.
Definition eqm (g g':ad -> option A) := forall a:ad, g a = g' a.

Lemma MapGet_M2_bit_0_if :
forall (m m':Map) (a:ad),
MapGet (M2 m m') a =
(if Nbit0 a then MapGet m' (Ndiv2 a) else MapGet m (Ndiv2 a)).