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

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   3 (*      ||M||                                                             *)
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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/pnat_plus.ma".
  16 include "ground/arith/nat_rplus_succ.ma".
  17
  18 (* RIGHT ADDITION FOR NON-NEGATIVE INTEGERS *********************************)
  19
  20 (* Constructions with pplus *************************************************)
  21
  22 lemma nrplus_inj_dx (p) (q):
  23       p + q = p + ninj q.
  24 // qed.
  25
  26 lemma nrplus_pplus_assoc (p,q:pnat) (n:nat):
  27       (p+q)+n = p+(q+n).
  28 #p #q #n
  29 @(nat_ind_succ … n) -n // #n #IH
  30 <nrplus_succ_dx <nrplus_succ_dx <pplus_succ_dx //
  31 qed.