update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / arith / nat_plus_pplus.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_plus_pplus.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_plus_pplus.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ground/arith/nat_rplus_pplus.ma".
+include "ground/arith/nat_plus_rplus.ma".
+
+(* ADDITION FOR NON-NEGATIVE INTEGERS ***************************************)
+
+lemma nplus_inj_bi (p) (q):
+      ninj (pplus p q) = nplus (ninj p) (ninj q).
+// qed.
+
+lemma nplus_pnpred_sn (p) (q):
+      pnpred (p + q) = nplus (pnpred p) (ninj q).
+#p #q
+<pplus_comm >nplus_comm >nrplus_pnpred_dx //
+qed.