milestone update in ground, partial commit

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

diff --git a/matita/matita/contribs/lambdadelta/ground/ynat/ynat.ma b/matita/matita/contribs/lambdadelta/ground/ynat/ynat.ma
deleted file mode 100644 (file)
index d2729ca..0000000
--- a/matita/matita/contribs/lambdadelta/ground/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 "ground/lib/arith.ma".
-include "ground/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-.