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[helm.git] / matita / contribs / RELATIONAL / NLE / defs.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 "NPlus/defs.ma".
+
+inductive NLE: Nat \to Nat \to Prop \def
+   | nle_zero_1: \forall q. NLE zero q
+   | nle_succ_succ: \forall p,q. NLE p q \to NLE (succ p) (succ q)
+.
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "natural 'greater or equal to'" 'geq y x=
+   (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1) x y).
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "natural 'greater than'" 'gt y x = 
+   (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1) 
+      (cic:/matita/RELATIONAL/datatypes/Nat/Nat.ind#xpointer(1/1/2) x) y).
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "natural 'less or equal to'" 'leq x y =
+   (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1) x y).
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "natural 'less than'" 'lt x y = 
+   (cic:/matita/RELATIONAL/NLE/defs/NLE.ind#xpointer(1/1) 
+      (cic:/matita/RELATIONAL/datatypes/Nat/Nat.ind#xpointer(1/1/2) x) y).