src/HOL/Lifting_Product.thy
changeset 56525 b5b6ad5dc2ae
parent 56520 3373f5d1e074
child 56526 58ac520db7ae
--- a/src/HOL/Lifting_Product.thy	Thu Apr 10 17:48:18 2014 +0200
+++ b/src/HOL/Lifting_Product.thy	Thu Apr 10 17:48:32 2014 +0200
@@ -8,69 +8,6 @@
 imports Lifting Basic_BNFs
 begin
 
-subsection {* Relator and predicator properties *}
-
-definition pred_prod :: "('a \<Rightarrow> bool) \<Rightarrow> ('b \<Rightarrow> bool) \<Rightarrow> 'a \<times> 'b \<Rightarrow> bool"
-where "pred_prod R1 R2 = (\<lambda>(a, b). R1 a \<and> R2 b)"
-
-lemma pred_prod_apply [simp]:
-  "pred_prod P1 P2 (a, b) \<longleftrightarrow> P1 a \<and> P2 b"
-  by (simp add: pred_prod_def)
-
-lemmas rel_prod_eq[relator_eq] = prod.rel_eq
-lemmas rel_prod_mono[relator_mono] = prod.rel_mono
-
-lemma rel_prod_OO[relator_distr]:
-  "(rel_prod A B) OO (rel_prod C D) = rel_prod (A OO C) (B OO D)"
-by (rule ext)+ (auto simp: rel_prod_def OO_def)
-
-lemma Domainp_prod[relator_domain]: 
-  "Domainp (rel_prod T1 T2) = (pred_prod (Domainp T1) (Domainp T2))"
-unfolding rel_prod_def pred_prod_def by blast
-
-lemma left_total_rel_prod [transfer_rule]:
-  assumes "left_total R1"
-  assumes "left_total R2"
-  shows "left_total (rel_prod R1 R2)"
-  using assms unfolding left_total_def rel_prod_def by auto
-
-lemma left_unique_rel_prod [transfer_rule]:
-  assumes "left_unique R1" and "left_unique R2"
-  shows "left_unique (rel_prod R1 R2)"
-  using assms unfolding left_unique_def rel_prod_def by auto
-
-lemma right_total_rel_prod [transfer_rule]:
-  assumes "right_total R1" and "right_total R2"
-  shows "right_total (rel_prod R1 R2)"
-  using assms unfolding right_total_def rel_prod_def by auto
-
-lemma right_unique_rel_prod [transfer_rule]:
-  assumes "right_unique R1" and "right_unique R2"
-  shows "right_unique (rel_prod R1 R2)"
-  using assms unfolding right_unique_def rel_prod_def by auto
-
-lemma bi_total_rel_prod [transfer_rule]:
-  assumes "bi_total R1" and "bi_total R2"
-  shows "bi_total (rel_prod R1 R2)"
-  using assms unfolding bi_total_def rel_prod_def by auto
-
-lemma bi_unique_rel_prod [transfer_rule]:
-  assumes "bi_unique R1" and "bi_unique R2"
-  shows "bi_unique (rel_prod R1 R2)"
-  using assms unfolding bi_unique_def rel_prod_def by auto
-
-lemma prod_relator_eq_onp [relator_eq_onp]: 
-  "rel_prod (eq_onp P1) (eq_onp P2) = eq_onp (pred_prod P1 P2)"
-  by (simp add: fun_eq_iff rel_prod_def pred_prod_def eq_onp_def) blast
-
-subsection {* Quotient theorem for the Lifting package *}
-
-lemma Quotient_prod[quot_map]:
-  assumes "Quotient R1 Abs1 Rep1 T1"
-  assumes "Quotient R2 Abs2 Rep2 T2"
-  shows "Quotient (rel_prod R1 R2) (map_prod Abs1 Abs2) (map_prod Rep1 Rep2) (rel_prod T1 T2)"
-  using assms unfolding Quotient_alt_def by auto
-
 subsection {* Transfer rules for the Transfer package *}
 
 context