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_exact i f : nb_digits f < nb_digits (unorm (app (abs i) f)) -> del_tail_int (nb_digits f) (norm (app_int i f)) = norm i.