add lemma norm_power
authorhuffman
Fri, 22 Sep 2006 23:17:39 +0200
changeset 20684 74e8b46abb97
parent 20683 3d07617c8bf3
child 20685 fee8c75e3b5d
add lemma norm_power
src/HOL/Real/RealVector.thy
--- a/src/HOL/Real/RealVector.thy	Fri Sep 22 21:42:12 2006 +0200
+++ b/src/HOL/Real/RealVector.thy	Fri Sep 22 23:17:39 2006 +0200
@@ -6,7 +6,7 @@
 header {* Vector Spaces and Algebras over the Reals *}
 
 theory RealVector
-imports RealDef
+imports RealPow
 begin
 
 subsection {* Locale for additive functions *}
@@ -489,4 +489,9 @@
   shows "norm (a / b) = norm a / norm b"
 by (simp add: divide_inverse norm_mult norm_inverse)
 
+lemma norm_power:
+  fixes x :: "'a::{real_normed_div_algebra,recpower}"
+  shows "norm (x ^ n) = norm x ^ n"
+by (induct n, simp, simp add: power_Suc norm_mult)
+
 end