src/HOL/Library/Sublist_Order.thy

 
 instantiation list :: (type) ord
 begin
 
 definition
-  "(xs :: 'a list) \<le> ys \<longleftrightarrow> sub xs ys"
+  "(xs :: 'a list) \<le> ys \<longleftrightarrow> sublisteq xs ys"
 
 definition
   "(xs :: 'a list) < ys \<longleftrightarrow> xs \<le> ys \<and> \<not> ys \<le> xs"
 
 instance ..

   fix xs :: "'a list"
   show "xs \<le> xs" by (simp add: less_eq_list_def)
 next
   fix xs ys :: "'a list"
   assume "xs <= ys" and "ys <= xs"
-  thus "xs = ys" by (unfold less_eq_list_def) (rule sub_antisym)
+  thus "xs = ys" by (unfold less_eq_list_def) (rule sublisteq_antisym)
 next
   fix xs ys zs :: "'a list"
   assume "xs <= ys" and "ys <= zs"
-  thus "xs <= zs" by (unfold less_eq_list_def) (rule sub_trans)
+  thus "xs <= zs" by (unfold less_eq_list_def) (rule sublisteq_trans)
 qed
 
 lemmas less_eq_list_induct [consumes 1, case_names empty drop take] =
-  emb.induct [of "op =", folded less_eq_list_def]
-lemmas less_eq_list_drop = emb.emb_Cons [of "op =", folded less_eq_list_def]
-lemmas le_list_Cons2_iff [simp, code] = sub_Cons2_iff [folded less_eq_list_def]
-lemmas le_list_map = sub_map [folded less_eq_list_def]
-lemmas le_list_filter = sub_filter [folded less_eq_list_def]
-lemmas le_list_length = emb_length [of "op =", folded less_eq_list_def]
+  list_hembeq.induct [of "op =", folded less_eq_list_def]
+lemmas less_eq_list_drop = list_hembeq.list_hembeq_Cons [of "op =", folded less_eq_list_def]
+lemmas le_list_Cons2_iff [simp, code] = sublisteq_Cons2_iff [folded less_eq_list_def]
+lemmas le_list_map = sublisteq_map [folded less_eq_list_def]
+lemmas le_list_filter = sublisteq_filter [folded less_eq_list_def]
+lemmas le_list_length = list_hembeq_length [of "op =", folded less_eq_list_def]
 
 lemma less_list_length: "xs < ys \<Longrightarrow> length xs < length ys"
-  by (metis emb_length sub_same_length le_neq_implies_less less_list_def less_eq_list_def)
+  by (metis list_hembeq_length sublisteq_same_length le_neq_implies_less less_list_def less_eq_list_def)
 
 lemma less_list_empty [simp]: "[] < xs \<longleftrightarrow> xs \<noteq> []"
-  by (metis less_eq_list_def emb_Nil order_less_le)
+  by (metis less_eq_list_def list_hembeq_Nil order_less_le)
 
 lemma less_list_below_empty [simp]: "xs < [] \<longleftrightarrow> False"
-  by (metis emb_Nil less_eq_list_def less_list_def)
+  by (metis list_hembeq_Nil less_eq_list_def less_list_def)
 
 lemma less_list_drop: "xs < ys \<Longrightarrow> xs < x # ys"
   by (unfold less_le less_eq_list_def) (auto)
 
 lemma less_list_take_iff: "x # xs < x # ys \<longleftrightarrow> xs < ys"
-  by (metis sub_Cons2_iff less_list_def less_eq_list_def)
+  by (metis sublisteq_Cons2_iff less_list_def less_eq_list_def)
 
 lemma less_list_drop_many: "xs < ys \<Longrightarrow> xs < zs @ ys"
-  by (metis sub_append_le_same_iff sub_drop_many order_less_le self_append_conv2 less_eq_list_def)
+  by (metis sublisteq_append_le_same_iff sublisteq_drop_many order_less_le self_append_conv2 less_eq_list_def)
 
 lemma less_list_take_many_iff: "zs @ xs < zs @ ys \<longleftrightarrow> xs < ys"
-  by (metis less_list_def less_eq_list_def sub_append')
+  by (metis less_list_def less_eq_list_def sublisteq_append')
 
 lemma less_list_rev_take: "xs @ zs < ys @ zs \<longleftrightarrow> xs < ys"
   by (unfold less_le less_eq_list_def) auto
 
 end