(** 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 Map2_semantics_2 :
forall m m':Map,
eqm (MapGet m') (fun a:ad => MapGet (M2 m m') (Ndouble_plus_one a)).