propagating the arithmetics library, partial commit

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

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/ynat_lminus_plus.ma b/matita/matita/contribs/lambdadelta/ground/arith/ynat_lminus_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/nat_minus_plus.ma".
+include "ground/arith/ynat_plus.ma".
+include "ground/arith/ynat_lminus_succ.ma".
+
+(* LEFT SUBTRACTION FOR NON-NEGATIVE INTEGERS WITH INFINITY *****************)
+
+(* Constructions with yplus *************************************************)
+
+(*** yplus_minus *)
+lemma ylminus_plus_sn_refl_sn (x) (n):
+      x = x + yinj_nat n - n.
+#x @(ynat_split_nat_inf … x) -x //
+#n <yplus_inf_sn //
+qed.
+
+(*** yminus_plus2 *)
+lemma yminus_plus_dx (x:ynat) (n) (o):
+      x - n - o = x - (n + o).
+#x @(ynat_split_nat_inf … x) -x //
+qed.