1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
17 include "NLE/defs.ma".
19 theorem nle_inv_succ_1: \forall x,y. x < y \to
20 \exists z. y = succ z \land x <= z.
21 intros. inversion H; clear H; intros; destruct. autobatch.
24 theorem nle_inv_succ_succ: \forall x,y. x < succ y \to x <= y.
25 intros. inversion H; clear H; intros; destruct. autobatch.
28 theorem nle_inv_succ_zero: \forall x. x < zero \to False.
29 intros. inversion H; clear H; intros; destruct.
32 theorem nle_inv_zero_2: \forall x. x <= zero \to x = zero.
33 intros. inversion H; clear H; intros; destruct. autobatch.
36 theorem nle_inv_succ_2: \forall y,x. x <= succ y \to
37 x = zero \lor \exists z. x = succ z \land z <= y.
38 intros. inversion H; clear H; intros; destruct;