(**  An alternative tail-recursive definition for reverse *)

  Fixpoint rev_append (l l': list A) : list A :=
    match l with
      | [] => l'
      | a :: l => rev_append l (a::l')
    end.Definition rev' l : list A := rev_append l [].

Lemma rev_append_rev : forall l l', rev_append l l' = rev l ++ l'.