--- /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 *)
+(* *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/test/".
+
+include "nat/div_and_mod.ma".
+include "nat/factorial.ma".
+include "nat/primes.ma".
+
+theorem prova : \forall n. (n+O)*(S O) = n.
+intro.
+applyS times_n_SO.
+qed.
+
+lemma foo: ∀n.(S n)! = (S n) * n!.
+intro; reflexivity.
+qed.
+
+theorem prova2 :
+ \forall n. S n \divides (S n)!.
+intros.
+applyS (witness ? ? ? (refl_eq ? ?)).
+qed.