# HG changeset patch # User huffman # Date 1181521479 -7200 # Node ID 8ae6f7b0903b4ed96b5c1b6844ed504594cc3937 # Parent 83f3b6dc58b543cc58a3091812b6054f208bf607 add lemma of_nat_power diff -r 83f3b6dc58b5 -r 8ae6f7b0903b src/HOL/Power.thy --- a/src/HOL/Power.thy Mon Jun 11 01:22:29 2007 +0200 +++ b/src/HOL/Power.thy Mon Jun 11 02:24:39 2007 +0200 @@ -331,6 +331,10 @@ show "z^(Suc n) = z * (z^n)" by simp qed +lemma of_nat_power: + "of_nat (m ^ n) = (of_nat m::'a::{semiring_1,recpower}) ^ n" +by (induct n, simp_all add: power_Suc) + lemma nat_one_le_power [simp]: "1 \ i ==> Suc 0 \ i^n" by (insert one_le_power [of i n], simp)