+#m elim (nle_dec m k) #Hm
+[ /3 width=3 by or_introl, ex2_intro/
+| @or_intror * #n #Hn #Hmn destruct /2 width=1 by/
+]
+qed.
+
+definition ac_le (k): ac ≝ mk_ac (λn. n ≤ k).
+
+lemma ac_le_props (k): ac_props (ac_le k) ≝ mk_ac_props ….
+#m elim (nle_dec m k) #Hm