Fixpoint xmap2_r (m : t B) : t C :=
match m with
| Leaf => Leaf
| Node l o r => Node (xmap2_r l) (f None o) (xmap2_r r)
end.

(* Specifications: *)
Lemma xgmap2_r : forall (i : key) (m : t B),
f None None = None -> find i (xmap2_r m) = f None (find i m).