changeset 23305 | 8ae6f7b0903b |
parent 23183 | af27d3ad9baf |
child 23431 | 25ca91279a9b |
--- 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 \<le> i ==> Suc 0 \<le> i^n" by (insert one_le_power [of i n], simp)