intros; split; unfold ordre_total in |- *; intro.
apply (first_n N k H H0 H1 H2).
apply (last_n N k H H0 H1 H2).
Qed.

(* Specifications: *)
(**********)
Lemma le_first_last :
forall N : nat, N >= 2 -> ordre_total (first N) (last N).