--- /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 "NLE/defs.ma".
+
+theorem nle_inv_succ_1: \forall x,y. x < y \to
+ \exists z. y = succ z \land x <= z.
+ intros. inversion H; clear H; intros; destruct. autobatch.
+qed.
+
+theorem nle_inv_succ_succ: \forall x,y. x < succ y \to x <= y.
+ intros. inversion H; clear H; intros; destruct. autobatch.
+qed.
+
+theorem nle_inv_succ_zero: \forall x. x < zero \to False.
+ intros. inversion H; clear H; intros; destruct.
+qed.
+
+theorem nle_inv_zero_2: \forall x. x <= zero \to x = zero.
+ intros. inversion H; clear H; intros; destruct. autobatch.
+qed.
+
+theorem nle_inv_succ_2: \forall y,x. x <= succ y \to
+ x = zero \lor \exists z. x = succ z \land z <= y.
+ intros. inversion H; clear H; intros; destruct;
+ autobatch depth = 4.
+qed.