X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2FZ%2Ftimes.ma;h=eefe4af7ead7d2f818216c44c6c9174fe298ccad;hb=647b419e96770d90a82d7a9e5e8843566a9f93ee;hp=e5e1cdb452fa38ce33a8ba73f95b6ca4a5d5f27d;hpb=55b82bd235d82ff7f0a40d980effe1efde1f5073;p=helm.git

diff --git a/helm/software/matita/library/Z/times.ma b/helm/software/matita/library/Z/times.ma
index e5e1cdb45..eefe4af7e 100644
--- a/helm/software/matita/library/Z/times.ma
+++ b/helm/software/matita/library/Z/times.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/Z/times".
-
 include "nat/lt_arith.ma".
 include "Z/plus.ma".
 
@@ -32,8 +30,7 @@ definition Ztimes :Z \to Z \to Z \def
          | (pos n) \Rightarrow (neg (pred ((S m) * (S n))))
          | (neg n) \Rightarrow (pos (pred ((S m) * (S n))))]].
          
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "integer times" 'times x y = (cic:/matita/Z/times/Ztimes.con x y).
+interpretation "integer times" 'times x y = (Ztimes x y).
 
 theorem Ztimes_z_OZ:  \forall z:Z. z*OZ = OZ.
 intro.elim z.
@@ -42,6 +39,8 @@ 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.
@@ -49,6 +48,7 @@ simplify.reflexivity.
 simplify.reflexivity.
 simplify.reflexivity.
 qed.
+
 theorem symmetric_Ztimes : symmetric Z Ztimes.
 change with (\forall x,y:Z. x*y = y*x).
 intros.elim x.rewrite > Ztimes_z_OZ.reflexivity.
@@ -67,8 +67,23 @@ 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.
-change with (\forall x,y,z:Z. (x*y)*z = x*(y*z)).
+unfold associative.
 intros.elim x.
   simplify.reflexivity. 
   elim y.