--- a/src/HOL/Library/Sublist_Order.thy Thu Dec 13 09:21:45 2012 +0100
+++ b/src/HOL/Library/Sublist_Order.thy Thu Dec 13 13:11:38 2012 +0100
@@ -21,7 +21,7 @@
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"
@@ -40,41 +40,41 @@
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