matita/matita/contribs/lambdadelta/ground/arith/nat_plus_pplus.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "ground/arith/nat_rplus_pplus.ma".
  16 include "ground/arith/nat_plus_rplus.ma".
  17
  18 (* ADDITION FOR NON-NEGATIVE INTEGERS ***************************************)
  19
  20 lemma nplus_inj_bi (p) (q):
  21       ninj (pplus p q) = nplus (ninj p) (ninj q).
  22 // qed.
  23
  24 lemma nplus_pnpred_sn (p) (q):
  25       pnpred (p + q) = nplus (pnpred p) (ninj q).
  26 #p #q
  27 <pplus_comm >nplus_comm >nrplus_pnpred_dx //
  28 qed.