(* The type [ad] of addresses is now [N] in [BinNat]. *)

Definition ad := N.Inductive Map :=
    | M0 : Map
    | M1 : ad -> A -> Map
    | M2 : Map -> Map -> Map.Inductive Map :=
    | M0 : Map
    | M1 : ad -> A -> Map
    | M2 : Map -> Map -> Map.Inductive Map :=
    | M0 : Map
    | M1 : ad -> A -> Map
    | M2 : Map -> Map -> Map.Inductive Map :=
    | M0 : Map
    | M1 : ad -> A -> Map
    | M2 : Map -> Map -> Map.

Lemma option_sum : forall o:option A, {y : A | o = Some y} + {o = None}.