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[helm.git] / matita / tests / applys.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "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.
+(* se non trova subito sym_times poi si perde! *)
+(* alternativamente si puo' abilitare la are_convertible nella
+   is_identity, ma poi va peggio nel resto (conv lunghe) *)
+letin www \def sym_times.
+clearbody www.
+applyS (witness ? ? ? (refl_eq ? ?)).
+qed.