src/HOL/Power.thy
changeset 25231 1aa9c8f022d0
parent 25162 ad4d5365d9d8
child 25836 f7771e4f7064
equal deleted inserted replaced
25230:022029099a83 25231:1aa9c8f022d0
   192 proof (induct "n")
   192 proof (induct "n")
   193   case 0
   193   case 0
   194     show ?case by (simp add: zero_less_one)
   194     show ?case by (simp add: zero_less_one)
   195 next
   195 next
   196   case (Suc n)
   196   case (Suc n)
   197     show ?case by (force simp add: prems power_Suc zero_less_mult_iff)
   197     show ?case by (auto simp add: prems power_Suc zero_less_mult_iff
       
   198       abs_zero)
   198 qed
   199 qed
   199 
   200 
   200 lemma zero_le_power_abs [simp]:
   201 lemma zero_le_power_abs [simp]:
   201      "(0::'a::{ordered_idom,recpower}) \<le> (abs a)^n"
   202      "(0::'a::{ordered_idom,recpower}) \<le> (abs a)^n"
   202 by (rule zero_le_power [OF abs_ge_zero])
   203 by (rule zero_le_power [OF abs_ge_zero])