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

diff --git a/helm/software/matita/library/Z/times.ma b/helm/software/matita/library/Z/times.ma
index 90a71b520ff3fde852bb2026812af9beea519cbe..742ef5462022e3be9a3cdc0f42f262a947c891fa 100644 (file)
--- 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.
@@ -251,3 +248,13 @@ 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.