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 (**************************************************************************)
15 set "baseuri" "cic:/matita/RELATIONAL/NLE/inv".
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; subst;
23 | destruct H2. clear H2. subst. auto
27 theorem nle_inv_succ_succ: \forall x,y. x < succ y \to x <= y.
28 intros. inversion H; clear H; intros; subst;
30 | destruct H2. destruct H3. clear H2 H3. subst. auto
34 theorem nle_inv_succ_zero: \forall x. x < zero \to False.
35 intros. inversion H; clear H; intros; subst;
41 theorem nle_inv_zero_2: \forall x. x <= zero \to x = zero.
42 intros. inversion H; clear H; intros; subst;
48 theorem nle_inv_succ_2: \forall y,x. x <= succ y \to
49 x = zero \lor \exists z. x = succ z \land z <= y.
50 intros. inversion H; clear H; intros; subst;
52 | destruct H3. clear H3. subst. auto depth = 4