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/props".
19 theorem nle_refl: \forall x. x <= x.
20 intros 1; elim x; clear x; intros; auto new.
23 theorem nle_trans_succ: \forall x,y. x <= y \to x <= succ y.
24 intros. elim H; clear H x y; intros; auto new.
27 theorem nle_lt_or_eq: \forall y,x. x <= y \to x < y \lor x = y.
28 intros 1. elim y; clear y; intros;
29 [ lapply linear nle_gen_zero_2 to H. auto new
30 | lapply linear nle_gen_succ_2 to H1. decompose;
32 | lapply linear H to H3 as H0. decompose;