--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "ground/arith/nat_pred_succ.ma".
+include "ground/arith/nat_lt.ma".
+
+(* NON-NEGATIVE INTEGERS ****************************************************)
+
+(* Basic constructions with pred ********************************************)
+
+lemma nlt_zero_sn (m): m = ↑↓m → 𝟎 < m.
+// qed.
+
+(* Basic inversions with pred ***********************************************)
+
+(*** S_pred *)
+lemma nlt_inv_zero_sn (m): 𝟎 < m → m = ↑↓m.
+#m @(nat_ind … m) -m //
+#H elim (nlt_inv_refl … H)
+qed-.