arithmetics for λδ

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

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_succ_tri.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_succ_tri.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_tri.ma".
+include "ground/arith/nat_succ.ma".
+
+(* SUCCESSOR FOR NON-NEGATIVE INTEGERS **************************************)
+
+(* Rewrites with ntri *******************************************************)
+
+lemma ntri_succ_bi (A) (a1) (a2) (a3) (n1) (n2):
+      ntri A (n1) (n2) a1 a2 a3 = ntri A (↑n1) (↑n2) a1 a2 a3.
+#A #a1 #a2 #a3 * [| #p1 ] * //
+qed.