1.1 --- a/src/HOL/Power.thy Mon Feb 23 13:55:36 2009 -0800
1.2 +++ b/src/HOL/Power.thy Mon Feb 23 16:25:52 2009 -0800
1.3 @@ -31,7 +31,7 @@
1.4 by (induct n) (simp_all add: power_Suc)
1.5
1.6 lemma power_one_right [simp]: "(a::'a::recpower) ^ 1 = a"
1.7 - by (simp add: power_Suc)
1.8 + unfolding One_nat_def by (simp add: power_Suc)
1.9
1.10 lemma power_commutes: "(a::'a::recpower) ^ n * a = a * a ^ n"
1.11 by (induct n) (simp_all add: power_Suc mult_assoc)
1.12 @@ -366,8 +366,8 @@
1.13 "of_nat (m ^ n) = (of_nat m::'a::{semiring_1,recpower}) ^ n"
1.14 by (induct n, simp_all add: power_Suc of_nat_mult)
1.15
1.16 -lemma nat_one_le_power [simp]: "1 \<le> i ==> Suc 0 \<le> i^n"
1.17 -by (insert one_le_power [of i n], simp)
1.18 +lemma nat_one_le_power [simp]: "Suc 0 \<le> i ==> Suc 0 \<le> i^n"
1.19 +by (rule one_le_power [of i n, unfolded One_nat_def])
1.20
1.21 lemma nat_zero_less_power_iff [simp]: "(x^n > 0) = (x > (0::nat) | n=0)"
1.22 by (induct "n", auto)
1.23 @@ -452,4 +452,3 @@
1.24 *}
1.25
1.26 end
1.27 -