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 del_tail_app_int n d d' : n <= nb_digits d' -> del_tail_int n (app_int d d') = app_int d (del_tail n d').