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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                  *)
(*                                                                        *)
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include "ground_2/notation.ma".
include "ground_2/xoa_props.ma".
include "ground_2/ynat/ynat.ma".

(* INFINITARY NATURAL NUMBERS ***********************************************)

(* "is_zero" predicate *)
definition yzero: predicate ynat ≝ λx. match x with
[ YO   ⇒ ⊤
| YS _ ⇒ ⊥
].

(* Inversion lemmas *********************************************************)

lemma discr_YS_YO: ∀n. ⫯n = 0 → ⊥.
#n #H change with (yzero (⫯n))
>H -H //
qed-.

lemma discr_YO_YS: ∀n. ynat_of_nat 0 = ⫯n → ⊥. (**) (* explicit coercion *)
/2 width=2 by discr_YS_YO/ qed-.