(* *)
(**************************************************************************)
-include "arithmetics/nat.ma".
+include "ground_2/lib/arith.ma".
include "ground_2/notation/constructors/infinity_0.ma".
(* NATURAL NUMBERS WITH INFINITY ********************************************)
lemma yinj_inj: ∀m,n. yinj m = yinj n → m = n.
#m #n #H destruct //
qed-.
+
+(* Basic properties *********************************************************)
+
+lemma eq_ynat_dec: ∀n1,n2:ynat. Decidable (n1 = n2).
+* [ #n1 ] * [1,3: #n2 ] /2 width=1 by or_introl/
+[2,3: @or_intror #H destruct ]
+elim (eq_nat_dec n1 n2) /4 width=1 by yinj_inj, or_intror, or_introl/
+qed-.