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

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_minus_pminus.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_minus_pminus.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/pnat_minus.ma".
+include "ground/arith/pnat_lt.ma".
+include "ground/arith/nat_minus.ma".
+
+(* SUBTRACTION FOR NON-NEGATIVE INTEGERS ************************************)
+
+(* Constructions with pminus ************************************************)
+
+lemma nminus_inj_bi (p1) (p2):
+      p2 < p1 →
+      ninj (p1 - p2) = ninj p1 - ninj p2.
+#p2 #p1 #H0 @(plt_ind_alt … H0) -p1 -p2 //
+qed-.