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[helm.git] / matita / contribs / RELATIONAL / ZEq / setoid.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/fun.ma".
+include "ZEq/defs.ma".
+
+theorem zeq_refl: \forall z. z = z.
+ intros. elim z. clear z.
+ lapply (nplus_total t t1). decompose.
+ autobatch.
+qed.
+
+theorem zeq_sym: \forall z1,z2. z1 = z2 \to z2 = z1.
+ intros. elim H. clear H z1 z2. autobatch.
+qed.
+(*
+theorem zeq_trans: \forall z1,z2. z1 = z2 \to 
+                   \forall z3. z2 = z3 \to z1 = z3.
+ intros 3. elim H. clear H z1 z2. 
+ inversion H3. clear H3. intros. destruct.
+ lapply (nplus_total n5 n6). decompose.
+ lapply (nplus_total n4 n9). decompose.
+ apply zeq.
+*)