# HG changeset patch
# User nipkow
# Date 1447758079 -3600
# Node ID f6b9f528c89c78214301057a14912cfc78e6bf7a
# Parent  cb595e12451d8bd5b66620e3d9978e07235a3414
converted lookup to cmp

diff -r cb595e12451d -r f6b9f528c89c src/HOL/Data_Structures/AList_Upd_Del.thy
--- a/src/HOL/Data_Structures/AList_Upd_Del.thy	Tue Nov 17 11:44:10 2015 +0100
+++ b/src/HOL/Data_Structures/AList_Upd_Del.thy	Tue Nov 17 12:01:19 2015 +0100
@@ -80,23 +80,6 @@
 
 lemmas upd_list_simps = sorted_lems upd_list_sorted1 upd_list_sorted2
 
-(*
-lemma set_ins_list[simp]: "set (ins_list x xs) = insert x (set xs)"
-by(induction xs) auto
-
-lemma distinct_if_sorted: "sorted xs \<Longrightarrow> distinct xs"
-apply(induction xs rule: sorted.induct)
-apply auto
-by (metis in_set_conv_decomp_first less_imp_not_less sorted_mid_iff2)
-
-lemma set_del_list_eq [simp]: "distinct xs ==> set(del_list x xs) = set xs - {x}"
-apply(induct xs)
- apply simp
-apply simp
-apply blast
-done
-*)
-
 
 subsection \<open>Lemmas for @{const del_list}\<close>
 
diff -r cb595e12451d -r f6b9f528c89c src/HOL/Data_Structures/Lookup2.thy
--- a/src/HOL/Data_Structures/Lookup2.thy	Tue Nov 17 11:44:10 2015 +0100
+++ b/src/HOL/Data_Structures/Lookup2.thy	Tue Nov 17 12:01:19 2015 +0100
@@ -5,17 +5,16 @@
 theory Lookup2
 imports
   Tree2
+  Cmp
   Map_by_Ordered
 begin
 
-fun lookup :: "('a::linorder * 'b, 'c) tree \<Rightarrow> 'a \<Rightarrow> 'b option" where
+fun lookup :: "('a::cmp * 'b, 'c) tree \<Rightarrow> 'a \<Rightarrow> 'b option" where
 "lookup Leaf x = None" |
 "lookup (Node _ l (a,b) r) x =
-  (if x < a then lookup l x else
-   if x > a then lookup r x else Some b)"
+  (case cmp x a of LT \<Rightarrow> lookup l x | GT \<Rightarrow> lookup r x | EQ \<Rightarrow> Some b)"
 
-lemma lookup_eq:
-  "sorted1(inorder t) \<Longrightarrow> lookup t x = map_of (inorder t) x"
+lemma lookup_eq: "sorted1(inorder t) \<Longrightarrow> lookup t x = map_of (inorder t) x"
 by(induction t) (auto simp: map_of_simps split: option.split)
 
 end
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