1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "ground_2/lib/arith.ma".
16 include "ground_2/notation/constructors/infinity_0.ma".
18 (* NATURAL NUMBERS WITH INFINITY ********************************************)
20 (* the type of natural numbers with infinity *)
21 inductive ynat: Type[0] ≝
28 interpretation "ynat infinity" 'Infinity = Y.
30 (* Inversion lemmas *********************************************************)
32 lemma yinj_inj: ∀m,n. yinj m = yinj n → m = n.
36 (* Basic properties *********************************************************)
38 lemma eq_ynat_dec: ∀n1,n2:ynat. Decidable (n1 = n2).
39 * [ #n1 ] * [1,3: #n2 ] /2 width=1 by or_introl/
40 [2,3: @or_intror #H destruct ]
41 elim (eq_nat_dec n1 n2) /4 width=1 by yinj_inj, or_intror, or_introl/