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[helm.git] / 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: \forall p, q, r. (p + q == r) \to q <= r.
+ intros. elim H; clear H q r; autobatch.
+qed.
+
+axiom nle_nplus_comp: \forall x1, x2, x3. (x1 + x2 == x3) \to
+                      \forall y1, y2, y3. (y1 + y2 == y3) \to
+                      x1 <= y1 \to x2 <= y2 \to x3 <= y3.
+
+axiom nle_nplus_comp_lt_2: \forall x1, x2, x3. (x1 + x2 == x3) \to
+                           \forall y1, y2, y3. (y1 + y2 == y3) \to
+                           x1 <= y1 \to x2 < y2 \to x3 < y3.