branch for universe

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

diff --git a/matita/tests/demodulation_matita.ma b/matita/tests/demodulation_matita.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/minus.ma".
+
+theorem p2: \forall x,y:nat. x+x = (S(S O))*x.
+intros.
+demodulate by times_n_Sm times_n_O sym_times plus_n_O.
+qed.
+
+theorem p4: \forall x:nat. (x+(S O))*(x-(S O))=x*x - (S O).
+intro.
+apply (nat_case x)
+[simplify.reflexivity
+|intro.demodulate.reflexivity]
+qed.
+
+theorem p5: \forall x,y:nat. (x+y)*(x+y) = x*x + (S(S O))*(x*y) + (y*y).
+intros.demodulate.reflexivity.
+qed.
+