matita/matita/tests/demodulation_matita.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15
  16
  17 include "nat/minus.ma".
  18
  19 theorem p2: \forall x,y:nat. x+x = (S(S O))*x.
  20 intros.
  21 demodulate by times_n_Sm times_n_O sym_times plus_n_O.
  22 qed.
  23
  24 theorem p4: \forall x:nat. (x+(S O))*(x-(S O))=x*x - (S O).
  25 intro.
  26 apply (nat_case x)
  27 [simplify.reflexivity
  28 |intro.demodulate.reflexivity]
  29 qed.
  30
  31 theorem p5: \forall x,y:nat. (x+y)*(x+y) = x*x + (S(S O))*(x*y) + (y*y).
  32 intros.demodulate.reflexivity.
  33 qed.
  34