ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / etc / ynat_old / ynat_pred.etc

diff --git a/matita/matita/contribs/lambdadelta/ground/etc/ynat_old/ynat_pred.etc b/matita/matita/contribs/lambdadelta/ground/etc/ynat_old/ynat_pred.etc
new file mode 100644 (file)
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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_2/ynat/ynat.ma".
+
+(* INFINITARY NATURAL NUMBERS ***********************************************)
+
+(* the predecessor on ynat *)
+definition ypred: ynat → ynat ≝ λm. match m with
+[ YO   ⇒ 0
+| YS n ⇒ n
+].
+
+notation "hvbox( ⫰ term 55 T )" 
+   non associative with precedence 55
+   for @{ 'Predecessor $T }.
+
+interpretation "ynat predecessor" 'Predecessor m = (ypred m).
+
+(* Properties ***************************************************************)
+
+lemma ypred_S: ∀m. ⫰⫯m = m.
+// qed.
+
+(* Inversion lemmas *********************************************************)
+
+lemma YS_inj: ∀m,n. ⫯m = ⫯n → m = n.
+#m #n #H <(ypred_S m) <(ypred_S n) //
+qed-.