(** 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_1_eq :
forall (m m':Map) (f:ad -> option A),
eqm (MapGet (M2 m m')) f -> eqm (MapGet m) (fun a:ad => f (Ndouble a)).