syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / ynat / ynat.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat.ma b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat.ma
index 3dbc0c662b11c6465346474c53e3e2787ce82720..4f3f85bb9757709a2c0e314c09a5a3c663951689 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "arithmetics/nat.ma".
-include "ground_2/notation/constructors/infinity_0.ma".
+include "ground_2/lib/arith.ma".
+include "ground_2/notation/functions/infinity_0.ma".
 
 (* NATURAL NUMBERS WITH INFINITY ********************************************)
 
@@ -32,3 +32,11 @@ interpretation "ynat infinity" 'Infinity = Y.
 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-.