Definition partition'  (f: key -> bool) (s: tree) : (tree*tree) :=
  match partition_aux f s (1%positive, nil) (1%positive,  nil)
   with ((n1,l1),(n2,l2)) => (fst (treeify_g n1 l1), fst (treeify_g n2 l2))
  end.

Lemma fold'_spec: forall s (A : Type) (i : A) (f : key -> A -> A), fold' _ f s i = List.fold_left (fun a e => f e a) (List.rev (fold' _ (@cons _) s nil)) i.