- Procedural convertible rewrites in the conclusion are now detected and replaced...

[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 00da44a00335ba1725c676d36bdfd52cf4617459..242be1b536a4cb036663be64e3168c94547f6eb7 100644 (file)
--- a/helm/software/matita/library/Z/plus.ma
+++ b/helm/software/matita/library/Z/plus.ma
@@ -39,7 +39,17 @@ definition Zplus :Z \to Z \to Z \def
          | (neg n) \Rightarrow (neg (pred ((S m)+(S n))))] ].
 
 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.