- natural numbers with infinity for lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / ynat / ynat.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat.ma b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat.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 "arithmetics/nat.ma".
+include "ground_2/notation/constructors/infinity_0.ma".
+
+(* NATURAL NUMBERS WITH INFINITY ********************************************)
+
+(* the type of natural numbers with infinity *)
+inductive ynat: Type[0] ≝
+| yinj: nat → ynat
+| Y   : ynat
+.
+
+coercion yinj.
+
+interpretation "ynat infinity" 'Infinity = Y.
+
+(* Inversion lemmas *********************************************************)
+
+lemma yinj_inj: ∀m,n. yinj m = yinj n → m = n.
+#m #n #H destruct //
+qed-.