Definition F_pathlen (a: elt) (rec: forall b, order uf.(m) b a -> nat) : nat :=
  match getlink uf.(m) a with
  | inleft (exist a' P) => S (rec a' P)
  | inright _ => O
  end.Definition pathlen (a: elt) : nat := Fix uf.(mwf) (fun _ => nat) F_pathlen a.

Lemma pathlen_some: forall a a', M.get a uf.(m) = Some a' -> pathlen a = S (pathlen a').