diff -r 044308b4948a -r 0a35bee25c20 src/HOL/Power.thy
--- a/src/HOL/Power.thy	Sun Feb 22 11:30:57 2009 +0100
+++ b/src/HOL/Power.thy	Sun Feb 22 17:25:28 2009 +0100
@@ -143,11 +143,13 @@
 done
 
 lemma power_eq_0_iff [simp]:
-  "(a^n = 0) = (a = (0::'a::{ring_1_no_zero_divisors,recpower}) & n>0)"
+  "(a^n = 0) \<longleftrightarrow>
+   (a = (0::'a::{mult_zero,zero_neq_one,no_zero_divisors,recpower}) & n\<noteq>0)"
 apply (induct "n")
-apply (auto simp add: power_Suc zero_neq_one [THEN not_sym])
+apply (auto simp add: power_Suc zero_neq_one [THEN not_sym] no_zero_divisors)
 done
 
+
 lemma field_power_not_zero:
   "a \<noteq> (0::'a::{ring_1_no_zero_divisors,recpower}) ==> a^n \<noteq> 0"
 by force
@@ -370,6 +372,13 @@
 lemma nat_zero_less_power_iff [simp]: "(x^n > 0) = (x > (0::nat) | n=0)"
 by (induct "n", auto)
 
+lemma nat_power_eq_Suc_0_iff [simp]: 
+  "((x::nat)^m = Suc 0) = (m = 0 | x = Suc 0)"
+by (induct_tac m, auto)
+
+lemma power_Suc_0[simp]: "(Suc 0)^n = Suc 0"
+by simp
+
 text{*Valid for the naturals, but what if @{text"0<i<1"}?
 Premises cannot be weakened: consider the case where @{term "i=0"},
 @{term "m=1"} and @{term "n=0"}.*}