--- a/src/HOL/Parity.thy Sun Feb 22 11:30:57 2009 +0100
+++ b/src/HOL/Parity.thy Sun Feb 22 17:25:28 2009 +0100
@@ -228,20 +228,9 @@
lemma zero_le_odd_power: "odd n ==>
(0 <= (x::'a::{recpower,ordered_idom}) ^ n) = (0 <= x)"
- apply (simp add: odd_nat_equiv_def2)
- apply (erule exE)
- apply (erule ssubst)
- apply (subst power_Suc)
- apply (subst power_add)
- apply (subst zero_le_mult_iff)
- apply auto
- apply (subgoal_tac "x = 0 & y > 0")
- apply (erule conjE, assumption)
- apply (subst power_eq_0_iff [symmetric])
- apply (subgoal_tac "0 <= x^y * x^y")
- apply simp
- apply (rule zero_le_square)+
- done
+apply (auto simp: odd_nat_equiv_def2 power_Suc power_add zero_le_mult_iff)
+apply (metis field_power_not_zero no_zero_divirors_neq0 order_antisym_conv zero_le_square)
+done
lemma zero_le_power_eq[presburger]: "(0 <= (x::'a::{recpower,ordered_idom}) ^ n) =
(even n | (odd n & 0 <= x))"