apply diff_true_false.
rewrite H0 in H.
rewrite (Dle_refl d') in H; trivial.
Qed.
Hint Immediate Dnotle_not_eq.

(* Specifications: *)
Lemma Dnotle_not_eq_sym : forall d d' : D, Dle d d' = false -> d' <> d.
Hint Immediate Dnotle_not_eq_sym.