Fixpoint xmap2_l (m : t A) : t C :=
      match m with
      | Leaf => Leaf
      | Node l o r => Node (xmap2_l l) (f o None) (xmap2_l r)
      end.

(* Specifications: *)
Lemma xgmap2_l : forall (i : key) (m : t A), f None None = None -> find i (xmap2_l m) = f (find i m) None.