milestone update in ground, partial commit

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

diff --git a/matita/matita/contribs/lambdadelta/ground/ynat/ynat_pred.ma b/matita/matita/contribs/lambdadelta/ground/ynat/ynat_pred.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/ynat/ynat.ma".
-
-(* NATURAL NUMBERS WITH INFINITY ********************************************)
-
-(* the predecessor function *)
-definition ypred: ynat → ynat ≝ λm. match m with
-[ yinj m ⇒ ↓m
-| Y      ⇒ Y
-].
-
-interpretation "ynat predecessor" 'DownArrow m = (ypred m).
-
-lemma ypred_O: ↓(yinj 0) = yinj 0.
-// qed.
-
-lemma ypred_S: ∀m:nat. ↓(↑m) = yinj m.
-// qed.
-
-lemma ypred_Y: (↓∞) = ∞.
-// qed.
-
-(* Inversion lemmas *********************************************************)
-
-lemma ypred_inv_refl: ∀m:ynat. ↓m = m → m = 0 ∨ m = ∞.
-* // #m #H lapply (yinj_inj … H) -H (**) (* destruct lemma needed *)
-/4 width=1 by pred_inv_fix_sn, or_introl, eq_f/
-qed-.