propagating the arithmetics library, 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
deleted file mode 100644 (file)
index f0f1627..0000000
--- a/matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_minus1_plus.ma
+++ /dev/null
@@ -1,34 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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.