(* *)
(**************************************************************************)
-include "ground_2/lib/arith.ma".
+include "ground/arith/nat_le.ma".
include "static_2/notation/functions/one_0.ma".
include "static_2/notation/functions/two_0.ma".
include "static_2/notation/functions/omega_0.ma".
definition ac_eq (k): ac ≝ mk_ac (eq … k).
interpretation "one (applicability domain)"
- 'Two = (ac_eq (S O)).
+ 'Two = (ac_eq (nsucc nzero)).
interpretation "zero (applicability domain)"
- 'One = (ac_eq O).
+ 'One = (ac_eq nzero).
lemma ac_eq_props (k): ac_props (ac_eq k) ≝ mk_ac_props ….
-#m elim (le_dec m k) #Hm
+#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/
]
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 (le_dec m k) #Hm
+#m elim (nle_dec m k) #Hm
[ /3 width=3 by or_introl, ex2_intro/
| @or_intror * #n #Hn #Hmn
- /3 width=3 by transitive_le/
+ /3 width=3 by nle_trans/
]
qed.