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 *)
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15 include "ground/arith/ynat_lminus_plus.ma".
16 include "ground/arith/ynat_lt_le_lminus.ma".
18 (* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
20 (* Constructions with yle and ylminus and yplus *****************************)
22 (*** ylt_plus2_to_minus_inj2 *)
23 lemma ylt_plus_dx_dx_lminus_sn (o) (x) (y):
24 yinj_nat o ≤ x → x < y + yinj_nat o → x - o < y.
25 /2 width=1 by ylt_lminus_bi_dx/ qed.
27 (*** ylt_plus2_to_minus_inj1 *)
28 lemma ylt_plus_dx_sn_lminus_sn (o) (x) (y):
29 yinj_nat o ≤ x → x < yinj_nat o + y → x - o < y.
30 /2 width=1 by ylt_plus_dx_dx_lminus_sn/ qed.