arithmetics for λδ

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

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_tri.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_lt_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_succ_tri.ma".
+include "ground/arith/nat_lt.ma".
+
+(* STRICT ORDER FOR NON-NEGATIVE INTEGERS ***********************************)
+
+(* Destructions with ntri ***************************************************)
+
+(*** tri_lt *)
+lemma ntri_lt (A) (a1) (a2) (a3) (n1) (n2):
+      n1 < n2 → a1 = ntri A n1 n2 a1 a2 a3.
+#A #a1 #a2 #a3 #n1 #n2 #H @(nlt_ind_alt … H) -H //
+qed-.
+
+(*** tri_gt *)
+lemma ntri_gt (A) (a1) (a2) (a3) (n1) (n2):
+      n2 < n1 → a3 = ntri A n1 n2 a1 a2 a3.
+#A #a1 #a2 #a3 #n1 #n2 #H @(nlt_ind_alt … H) -H //
+qed-.