arithmetics for λδ

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

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_le_pred.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_pred_succ.ma".
+include "ground/arith/nat_le.ma".
+
+(* NON-NEGATIVE INTEGERS ****************************************************)
+
+(* Basic constructions with pred ********************************************)
+
+(*** le_pred_n *)
+lemma nle_pred_sn_refl (m): ↓m ≤ m.
+#m elim m -m //
+qed.
+
+(*** monotonic_pred *)
+lemma nle_pred_bi (m) (n): m ≤ n → ↓m ≤ ↓n.
+#m #n #H elim H -n
+/2 width=3 by nle_trans/
+qed.