src/HOL/MetisExamples/set.thy

 by (metis Set.subsetI Union_upper insertCI set_eq_subset)
   --{*found by SPASS*}
 
 lemma (*singleton_example_2:*)
      "\<forall>x \<in> S. \<Union>S \<subseteq> x \<Longrightarrow> \<exists>z. S \<subseteq> {z}"
-by (metis Un_absorb2 Union_insert insertI1 insert_Diff insert_Diff_single subset_eq)
+by (metis Set.subsetI Union_upper insert_code mem_def set_eq_subset)
 
 lemma singleton_example_2:
      "\<forall>x \<in> S. \<Union>S \<subseteq> x \<Longrightarrow> \<exists>z. S \<subseteq> {z}"
 proof (neg_clausify)
 assume 0: "\<And>x. \<not> S \<subseteq> {x}"

       "(\<forall>C. (0, 0) \<in> C \<and> (\<forall>x y. (x, y) \<in> C \<longrightarrow> (Suc x, Suc y) \<in> C) \<longrightarrow> (n, m) \<in> C) \<and> Q n \<longrightarrow> Q m" 
 apply (metis atMost_iff)
 apply (metis emptyE)
 apply (metis insert_iff singletonE)
 apply (metis insertCI singletonE zless_le)
-apply (metis insert_iff singletonE)
-apply (metis insert_iff singletonE)
+apply (metis Collect_def Collect_mem_eq)
+apply (metis Collect_def Collect_mem_eq)
 apply (metis DiffE)
 apply (metis pair_in_Id_conv) 
 done
 
 end