propagating the arithmetics library, partial commit

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

diff --git a/matita/matita/contribs/lambdadelta/ground/etc/ynat_old/ynat.etc b/matita/matita/contribs/lambdadelta/ground/etc/ynat_old/ynat.etc
deleted file mode 100644 (file)
index 09df4db..0000000
--- a/matita/matita/contribs/lambdadelta/ground/etc/ynat_old/ynat.etc
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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".
-
-(* INFINITARY NATURAL NUMBERS ***********************************************)
-
-(* the type of infinitary natural numbers *)
-coinductive ynat: Type[0] ≝
-| YO: ynat
-| YS: ynat → ynat
-.
-
-interpretation "ynat successor" 'Successor m = (YS m).
-
-(* the coercion of nat to ynat *)
-let rec ynat_of_nat n ≝ match n with
-[ O   ⇒ YO
-| S m ⇒ YS (ynat_of_nat m)
-].
-
-coercion ynat_of_nat.
-
-(* the infinity *)
-let corec Y : ynat ≝ ⫯Y.
-
-interpretation "ynat infinity" 'Infinity = Y.
-
-(* destructing identity on ynat *)
-definition yid: ynat → ynat ≝ λm. match m with
-[ YO   ⇒ 0
-| YS n ⇒ ⫯n
-].
-
-(* Properties ***************************************************************)
-
-fact yid_rew: ∀n. yid n = n.
-* // qed-.
-
-lemma Y_rew: ⫯∞ = ∞.
-<(yid_rew ∞) in ⊢ (???%); //
-qed.