--- a/src/HOL/Library/List_lexord.thy Wed Jan 02 15:14:15 2008 +0100
+++ b/src/HOL/Library/List_lexord.thy Wed Jan 02 15:14:17 2008 +0100
@@ -9,9 +9,18 @@
imports List
begin
-instance list :: (ord) ord
+instantiation list :: (ord) ord
+begin
+
+definition
list_less_def [code func del]: "(xs::('a::ord) list) < ys \<longleftrightarrow> (xs, ys) \<in> lexord {(u,v). u < v}"
- list_le_def [code func del]: "(xs::('a::ord) list) \<le> ys \<longleftrightarrow> (xs < ys \<or> xs = ys)" ..
+
+definition
+ list_le_def [code func del]: "(xs::('a::ord) list) \<le> ys \<longleftrightarrow> (xs < ys \<or> xs = ys)"
+
+instance ..
+
+end
instance list :: (order) order
apply (intro_classes, unfold list_less_def list_le_def)
@@ -32,12 +41,21 @@
apply simp
done
-instance list :: (linorder) distrib_lattice
+instantiation list :: (linorder) distrib_lattice
+begin
+
+definition
[code func del]: "(inf \<Colon> 'a list \<Rightarrow> _) = min"
+
+definition
[code func del]: "(sup \<Colon> 'a list \<Rightarrow> _) = max"
+
+instance
by intro_classes
(auto simp add: inf_list_def sup_list_def min_max.sup_inf_distrib1)
+end
+
lemma not_less_Nil [simp]: "\<not> (x < [])"
by (unfold list_less_def) simp