Definition map2 (elt elt' elt'':Type)(f:option elt->option elt'->option elt'') :=
   _map2 (fun o1 o2 => match o1,o2 with None,None => None | _, _ => f o1 o2 end).

(* Specifications: *)
Lemma map2_1 : forall (elt elt' elt'':Type)(m: t elt)(m': t elt') (x:key)(f:option elt->option elt'->option elt''), In x m \/ In x m' -> find x (map2 f m m') = f (find x m) (find x m').
Lemma map2_2 : forall (elt elt' elt'':Type)(m: t elt)(m': t elt') (x:key)(f:option elt->option elt'->option elt''), In x (map2 f m m') -> In x m \/ In x m'.