updating the structures for sorts

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

diff --git a/helm/software/matita/library/Z/plus.ma b/helm/software/matita/library/Z/plus.ma
index cd565124589d1e20dbac077a384e1aac6fa06125..242be1b536a4cb036663be64e3168c94547f6eb7 100644 (file)
--- a/helm/software/matita/library/Z/plus.ma
+++ b/helm/software/matita/library/Z/plus.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/Z/plus".
-
 include "Z/z.ma".
 include "nat/minus.ma".
 
@@ -40,9 +38,18 @@ definition Zplus :Z \to Z \to Z \def
                 | GT \Rightarrow (neg (pred (m-n)))]     
          | (neg n) \Rightarrow (neg (pred ((S m)+(S n))))] ].
 
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "integer plus" 'plus x y = (cic:/matita/Z/plus/Zplus.con x y).
-         
+interpretation "integer plus" 'plus x y = (Zplus x y).
+
+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.
+
 theorem Zplus_z_OZ:  \forall z:Z. z+OZ = z.
 intro.elim z.
 simplify.reflexivity.
@@ -258,8 +265,7 @@ definition Zopp : Z \to Z \def
 | (pos n) \Rightarrow (neg n)
 | (neg n) \Rightarrow (pos n) ].
 
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "integer unary minus" 'uminus x = (cic:/matita/Z/plus/Zopp.con x).
+interpretation "integer unary minus" 'uminus x = (Zopp x).
 
 theorem eq_OZ_Zopp_OZ : OZ = (- OZ).
 reflexivity.
@@ -308,7 +314,6 @@ intro.simplify.intros (z y).
 rewrite < Zplus_z_OZ.
 rewrite < (Zplus_z_OZ y).
 rewrite < (Zplus_Zopp x).
-rewrite < (Zplus_Zopp x).
 rewrite < assoc_Zplus.
 rewrite < assoc_Zplus.
 apply eq_f2
@@ -326,4 +331,4 @@ qed.
 (* minus *)
 definition Zminus : Z \to Z \to Z \def \lambda x,y:Z. x + (-y).
 
-interpretation "integer minus" 'minus x y = (cic:/matita/Z/plus/Zminus.con x y).
+interpretation "integer minus" 'minus x y = (Zminus x y).