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[helm.git] / matitaB / matita / contribs / RELATIONAL / NLE / nplus.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 "NLE/defs.ma".
+
+theorem nle_nplus: ∀p, q, r. p ⊕ q ≍ r → q ≤ r.
+ intros; elim H; clear H q r; autobatch.
+qed.
+
+axiom nle_nplus_comp: ∀x1,x2,x3. x1 ⊕ x2 ≍ x3 → ∀y1,y2,y3. y1 ⊕ y2 ≍ y3 →
+                      x1 ≤ y1 → x2 ≤ y2 → x3 ≤ y3.
+
+axiom nle_nplus_comp_lt_2: ∀x1,x2,x3. x1 ⊕ x2 ≍ x3 → ∀y1,y2,y3. y1 ⊕ y2 ≍ y3 →
+                           x1 ≤ y1 → x2 < y2 → x3 < y3.