Fixpoint merge s1 :=
  if s1 is x1 :: s1' then
    let fix merge_s1 s2 :=
      if s2 is x2 :: s2' then
        if leT x2 x1 then x2 :: merge_s1 s2' else x1 :: merge s1' s2
      else s1 in
    merge_s1
  else id.

Lemma merge_uniq s1 s2 : uniq (merge s1 s2) = uniq (s1 ++ s2).