--- 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
\ No newline at end of file