diff -r d76b830366bc -r 33df3c4eb629 src/HOL/Divides.thy
--- a/src/HOL/Divides.thy	Wed Feb 18 09:47:58 2009 -0800
+++ b/src/HOL/Divides.thy	Wed Feb 18 10:24:48 2009 -0800
@@ -889,21 +889,9 @@
   apply (simp only: dvd_eq_mod_eq_0)
   done
 
-lemma le_imp_power_dvd: "!!i::nat. m \<le> n ==> i^m dvd i^n"
-  apply (unfold dvd_def)
-  apply (erule linorder_not_less [THEN iffD2, THEN add_diff_inverse, THEN subst])
-  apply (simp add: power_add)
-  done
-
 lemma nat_zero_less_power_iff [simp]: "(x^n > 0) = (x > (0::nat) | n=0)"
   by (induct n) auto
 
-lemma power_le_dvd [rule_format]: "k^j dvd n --> i\<le>j --> k^i dvd (n::nat)"
-  apply (induct j)
-   apply (simp_all add: le_Suc_eq)
-  apply (blast dest!: dvd_mult_right)
-  done
-
 lemma power_dvd_imp_le: "[|i^m dvd i^n;  (1::nat) < i|] ==> m \<le> n"
   apply (rule power_le_imp_le_exp, assumption)
   apply (erule dvd_imp_le, simp)