--- /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_iter.ma".
+include "ground/arith/nat_succ.ma".
+
+(* NON-NEGATIVE INTEGERS ****************************************************)
+
+(* Rewrites with niter ******************************************************)
+
+lemma niter_succ (A) (f) (n) (a): f (f^n a) = f^{A}(↑n) a.
+#A #f * //
+qed.