(** 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 MapSingleton_semantics :
forall (a:ad) (y:A),
eqm (MapGet (MapSingleton a y))
(fun a':ad => if Neqb a a' then Some y else None).