--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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.
+*)