+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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/lib/arith.ma".
-include "ground_2/notation/functions/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-.
-
-(* Basic properties *********************************************************)
-
-lemma eq_ynat_dec: ∀n1,n2:ynat. Decidable (n1 = n2).
-* [ #n1 ] * [1,3: #n2 ] /2 width=1 by or_introl/
-[2,3: @or_intror #H destruct ]
-elim (eq_nat_dec n1 n2) /4 width=1 by yinj_inj, or_intror, or_introl/
-qed-.