(**  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'.