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 nztail_spec d : let (r, n) := nztail d in let (r', n') := lnztail (to_list d) in to_list r = r' /\ n = n'.