matita/matita/contribs/lambdadelta/ground/arith/nat_succ_tri.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 include "ground/arith/nat_tri.ma".
  16 include "ground/arith/nat_succ.ma".
  17
  18 (* SUCCESSOR FOR NON-NEGATIVE INTEGERS **************************************)
  19
  20 (* Constructions with ntri **************************************************)
  21
  22 lemma ntri_zero_succ (A) (a1) (a2) (a3) (n):
  23       a1 = ntri A (𝟎) (↑n) a1 a2 a3.
  24 #A #a1 #a2 #a3 * //
  25 qed.
  26
  27 lemma ntri_succ_zero (A) (a1) (a2) (a3) (n):
  28       a3 = ntri A (↑n) (𝟎) a1 a2 a3.
  29 #A #a1 #a2 #a3 * //
  30 qed.
  31
  32 lemma ntri_succ_bi (A) (a1) (a2) (a3) (n1) (n2):
  33       ntri A (n1) (n2) a1 a2 a3 = ntri A (↑n1) (↑n2) a1 a2 a3.
  34 #A #a1 #a2 #a3 * [| #p1 ] * //
  35 qed.