+++ /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/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-.