--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "ground/arith/ynat_lminus_plus.ma".
+include "ground/arith/ynat_lt_le_lminus.ma".
+
+(* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
+
+(* Constructions with yle and ylminus and yplus ****************************)
+
+(*** ylt_plus2_to_minus_inj2 *)
+lemma ylt_plus_dx_dx_lminus_sn (o) (x) (y):
+ yinj_nat o ≤ x → x < y + yinj_nat o → x - o < y.
+/2 width=1 by ylt_lminus_bi_dx/ qed.
+
+(*** ylt_plus2_to_minus_inj1 *)
+lemma ylt_plus_dx_sn_lminus_sn (o) (x) (y):
+ yinj_nat o ≤ x → x < yinj_nat o + y → x - o < y.
+/2 width=1 by ylt_plus_dx_dx_lminus_sn/ qed.