+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/RELATIONAL-ARITHMETICS/nat_gen".
+
+include "library/logic/equality.ma".
+include "nat_defs.ma".
+
+theorem eq_gen_O_S: \forall (P:Prop). \forall m2. O = S m2 \to P.
+ intros. discriminate H.
+qed.
+
+theorem eq_gen_S_O: \forall (P:Prop). \forall m1. S m1 = O \to P.
+ intros. discriminate H.
+qed.
+
+theorem eq_gen_S_S: \forall m1,m2. S m1 = S m2 \to m1 = m2.
+ intros. injection H. assumption.
+qed.