milestone update in ground, partial commit

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

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/ynat_pred_succ.ma b/matita/matita/contribs/lambdadelta/ground/arith/ynat_pred_succ.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_pred_succ.ma".
+include "ground/arith/ynat_succ.ma".
+include "ground/arith/ynat_pred.ma".
+
+(* PREDECESSOR FOR NON-NEGATIVE INTEGERS WITH INFINITY **********************)
+
+(* Constructions with ysucc *************************************************)
+
+(*** ypred_succ ypred_S *)
+lemma ypred_succ (x): x = ↓↑x.
+#x @(ynat_split_nat_inf … x) -x //
+qed.
+
+(* Inversion with ysucc *****************************************************)
+
+(*** ynat_cases *)
+lemma ynat_split_zero_pos (x): ∨∨ 𝟎 = x | x = ↑↓x.
+#x @(ynat_split_nat_inf … x) -x //
+#n elim (nat_split_zero_pos n)
+/2 width=1 by or_introl, or_intror/
+qed-.