X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2FZ%2Ftimes.ma;h=979cc87aa37f8ddbebe67e2273cc42a48a894f76;hb=2afec2cc82077163425701cc02ffb719a6345fb6;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..979cc87aa 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".
 
@@ -42,6 +40,8 @@ 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 +49,7 @@ 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 +68,23 @@ 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.
@@ -233,3 +249,13 @@ qed.
 variant distr_Ztimes_Zplus: \forall x,y,z.
 x * (y + z) = x*y + x*z \def
 distributive_Ztimes_Zplus.
+
+theorem eq_plus_Zplus: \forall n,m:nat. Z_of_nat (n+m) =
+Z_of_nat n + Z_of_nat m.
+intro.cases n;intro
+  [reflexivity
+  |cases m
+    [simplify.rewrite < plus_n_O.reflexivity
+    |simplify.reflexivity.
+    ]]
+qed.