--- a/src/HOL/Lifting_Product.thy Mon Jan 20 20:00:33 2014 +0100
+++ b/src/HOL/Lifting_Product.thy Mon Jan 20 20:21:12 2014 +0100
@@ -5,23 +5,14 @@
header {* Setup for Lifting/Transfer for the product type *}
theory Lifting_Product
-imports Lifting
+imports Lifting Basic_BNFs
begin
subsection {* Relator and predicator properties *}
-definition
- prod_rel :: "('a \<Rightarrow> 'b \<Rightarrow> bool) \<Rightarrow> ('c \<Rightarrow> 'd \<Rightarrow> bool) \<Rightarrow> 'a \<times> 'c \<Rightarrow> 'b \<times> 'd \<Rightarrow> bool"
-where
- "prod_rel R1 R2 = (\<lambda>(a, b) (c, d). R1 a c \<and> R2 b d)"
-
definition prod_pred :: "('a \<Rightarrow> bool) \<Rightarrow> ('b \<Rightarrow> bool) \<Rightarrow> 'a \<times> 'b \<Rightarrow> bool"
where "prod_pred R1 R2 = (\<lambda>(a, b). R1 a \<and> R2 b)"
-lemma prod_rel_apply [simp]:
- "prod_rel R1 R2 (a, b) (c, d) \<longleftrightarrow> R1 a c \<and> R2 b d"
- by (simp add: prod_rel_def)
-
lemma prod_pred_apply [simp]:
"prod_pred P1 P2 (a, b) \<longleftrightarrow> P1 a \<and> P2 b"
by (simp add: prod_pred_def)