src/HOL/Orderings.thy

 
 text {* Dual order *}
 
 lemma dual_preorder:
   "preorder (op \<ge>) (op >)"
-by unfold_locales (auto simp add: less_le_not_le intro: order_trans)
+proof qed (auto simp add: less_le_not_le intro: order_trans)
 
 end
 
 
 subsection {* Partial orders *}