--- a/src/HOL/Library/Product_ord.thy Fri Dec 07 15:07:56 2007 +0100
+++ b/src/HOL/Library/Product_ord.thy Fri Dec 07 15:07:59 2007 +0100
@@ -9,9 +9,18 @@
imports Main
begin
-instance "*" :: (ord, ord) ord
+instantiation "*" :: (ord, ord) ord
+begin
+
+definition
prod_le_def [code func del]: "x \<le> y \<longleftrightarrow> fst x < fst y \<or> fst x = fst y \<and> snd x \<le> snd y"
- prod_less_def [code func del]: "x < y \<longleftrightarrow> fst x < fst y \<or> fst x = fst y \<and> snd x < snd y" ..
+
+definition
+ prod_less_def [code func del]: "x < y \<longleftrightarrow> fst x < fst y \<or> fst x = fst y \<and> snd x < snd y"
+
+instance ..
+
+end
lemma [code func]:
"(x1\<Colon>'a\<Colon>{ord, eq}, y1) \<le> (x2, y2) \<longleftrightarrow> x1 < x2 \<or> x1 = x2 \<and> y1 \<le> y2"
@@ -29,10 +38,19 @@
instance * :: (linorder, linorder) linorder
by default (auto simp: prod_le_def)
-instance * :: (linorder, linorder) distrib_lattice
+instantiation * :: (linorder, linorder) distrib_lattice
+begin
+
+definition
inf_prod_def: "(inf \<Colon> 'a \<times> 'b \<Rightarrow> _ \<Rightarrow> _) = min"
+
+definition
sup_prod_def: "(sup \<Colon> 'a \<times> 'b \<Rightarrow> _ \<Rightarrow> _) = max"
+
+instance
by intro_classes
(auto simp add: inf_prod_def sup_prod_def min_max.sup_inf_distrib1)
end
+
+end