(** [MapInter], [MapRngRestrTo], [MapRngRestrBy], [MapInverse] 
      not implemented: need a decidable equality on [A]. *)

  Fixpoint MapDelta (m:Map) : Map -> Map :=
    match m with
    | M0 => fun m':Map => m'
    | M1 a y =>
        fun m':Map =>
          match MapGet m' a with
          | None => MapPut m' a y
          | _ => MapRemove m' a
          end
    | M2 m1 m2 =>
        fun m':Map =>
          match m' with
          | M0 => m
          | M1 a' y' =>
              match MapGet m a' with
              | None => MapPut m a' y'
              | _ => MapRemove m a'
              end
          | M2 m'1 m'2 => makeM2 (MapDelta m1 m'1) (MapDelta m2 m'2)
          end
    end.

Lemma MapDelta_semantics_2_2 : forall (a:ad) (y:A) (m':Map) (a0:ad) (y0:A), MapGet (M1 a y) a0 = Some y0 -> MapGet m' a0 = None -> MapGet (MapDelta (M1 a y) m') a0 = Some y0.