Definition lnztail l :=
  let fix aux l_rev :=
    match l_rev with
    | cons d0 l_rev => let (r, n) := aux l_rev in pair r (S n)
    | _ => pair l_rev O
    end in
  let (r, n) := aux (List.rev l) in pair (List.rev r) n.

Lemma nzhead_app_nil d d' : nb_digits (nzhead (app d d')) <= nb_digits d' -> nzhead d = Nil.