Reorganization of results.

[helm.git] / matita / library / Z / times.ma

diff --git a/matita/library/Z/times.ma b/matita/library/Z/times.ma
index 58de9c82737871b27a4a67541268337975649132..90a71b520ff3fde852bb2026812af9beea519cbe 100644 (file)
--- a/matita/library/Z/times.ma
+++ b/matita/library/Z/times.ma
@@ -42,6 +42,8 @@ simplify.reflexivity.
 simplify.reflexivity.
 qed.
 
+definition Zone \def pos O.
+
 theorem Ztimes_neg_Zopp: \forall n:nat.\forall x:Z.
 neg n * x = - (pos n * x).
 intros.elim x.
@@ -68,6 +70,21 @@ qed.
 variant sym_Ztimes : \forall x,y:Z. x*y = y*x
 \def symmetric_Ztimes.
 
+theorem Ztimes_Zone_l: \forall z:Z. Ztimes Zone z = z.
+intro.unfold Zone.simplify.
+elim z;simplify
+  [reflexivity
+  |rewrite < plus_n_O.reflexivity
+  |rewrite < plus_n_O.reflexivity
+  ]
+qed.
+
+theorem Ztimes_Zone_r: \forall z:Z. Ztimes z Zone = z.
+intro.
+rewrite < sym_Ztimes.
+apply Ztimes_Zone_l.
+qed.
+
 theorem associative_Ztimes: associative Z Ztimes.
 unfold associative.
 intros.elim x.