propagating the arithmetics library, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / arith / ynat_lt_le_lminus.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_le_lminus.ma b/matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_le_lminus.ma
new file mode 100644 (file)
index 0000000..04e0c4c
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_le_lminus.ma
@@ -0,0 +1,29 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/nat_lt_minus.ma".
+include "ground/arith/ynat_lminus.ma".
+include "ground/arith/ynat_le.ma".
+include "ground/arith/ynat_lt.ma".
+
+(* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
+
+(* Cobstructions with yle and ylminus  **************************************)
+
+(*** monotonic_ylt_minus_dx *)
+lemma ylt_lminus_bi_dx (o) (x) (y):
+      x < y → yinj_nat o ≤ x → x - o < y - o.
+#o #x #y * -x -y
+/4 width=1 by ylt_inj, yle_inv_inj_bi, nlt_minus_bi_dx/
+qed.