milestone update in ground, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / arith / ynat_lt_minus1_plus.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_minus1_plus.ma b/matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_minus1_plus.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_minus1_plus.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_plus.ma".
+include "ground/arith/ynat_minus1.ma".
+include "ground/arith/ynat_lt_pred_succ.ma".
+
+(* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
+
+(* Constructions with yminus1 and yplus *************************************)
+
+(*** ylt_plus1_to_minus_inj2 *)
+lemma ylt_plus_sn_dx_minus1_dx (n) (x) (z):
+      x + yinj_nat n < z → x < z - n.
+#n @(nat_ind_succ … n) -n //
+#n #IH #x #z >ysucc_inj <yplus_succ_shift
+/3 width=1 by ylt_des_succ_sn/
+qed.
+
+(*** ylt_plus1_to_minus_inj1 *)
+lemma ylt_plus_sn_sn_minus1_dx (n) (x) (z):
+      yinj_nat n + x < z → x < z - n.
+/2 width=1 by ylt_plus_sn_dx_minus1_dx/ qed.