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 include "ground/arith/nat_lt_minus.ma".
16 include "ground/arith/ynat_lminus.ma".
17 include "ground/arith/ynat_le.ma".
18 include "ground/arith/ynat_lt.ma".
20 (* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
22 (* Constructions with yle and ylminus ***************************************)
24 (*** monotonic_ylt_minus_dx *)
25 lemma ylt_lminus_bi_dx (o) (x) (y):
26 x < y → yinj_nat o ≤ x → x - o < y - o.
28 /4 width=1 by ylt_inj, yle_inv_inj_bi, nlt_minus_bi_dx/