matita/matita/contribs/lambdadelta/ground/arith/nat_plus_rplus.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_rplus_succ.ma".
  16 include "ground/arith/nat_plus.ma".
  17
  18 (* ADDITION FOR NON-NEGATIVE INTEGERS ***************************************)
  19
  20 (* Constructions with nrplus ************************************************)
  21
  22 lemma nrplus_inj_sn (p) (n):
  23       ninj (p + n) = ninj p + n.
  24 #p #n @(nat_ind_succ … n) -n //
  25 #n #IH <nplus_succ_dx <IH //
  26 qed.
  27
  28 (* Constructions with nrplus and npsucc *************************************)
  29
  30 lemma nrplus_npsucc_sn (m) (n):
  31       npsucc (m + n) = npsucc m + n.
  32 #m @(nat_ind_succ … m) -m //
  33 #m #IH #n <npsucc_succ <nrplus_succ_sn //
  34 qed.