add lemma of_int_power
authorhuffman
Tue, 21 Aug 2007 20:51:10 +0200
changeset 24391 b57c48f7e2d4
parent 24390 9b5073c79a0b
child 24392 000327cea3eb
add lemma of_int_power
src/HOL/IntDiv.thy
--- a/src/HOL/IntDiv.thy	Tue Aug 21 20:50:12 2007 +0200
+++ b/src/HOL/IntDiv.thy	Tue Aug 21 20:51:10 2007 +0200
@@ -1357,6 +1357,9 @@
   show "z^(Suc n) = z * (z^n)" by simp
 qed
 
+lemma of_int_power:
+  "of_int (z ^ n) = (of_int z ^ n :: 'a::{recpower, ring_1})"
+  by (induct n) (simp_all add: power_Suc)
 
 lemma zpower_zmod: "((x::int) mod m)^y mod m = x^y mod m"
 apply (induct "y", auto)