From 1a4e36e57d838a43ab9765a9e9c7a602ae9c0124 Mon Sep 17 00:00:00 2001
From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Thu, 15 Jun 2006 09:39:55 +0000
Subject: [PATCH] some examples of the new ApplyS tactic

---
 matita/tests/applys.ma | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)
 create mode 100644 matita/tests/applys.ma

diff --git a/matita/tests/applys.ma b/matita/tests/applys.ma
new file mode 100644
index 000000000..74573177f
--- /dev/null
+++ b/matita/tests/applys.ma
@@ -0,0 +1,34 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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.
-- 
2.39.2