--- a/Attic/Quot/Quotient_Product.thy	Tue Feb 19 05:38:46 2013 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,104 +0,0 @@
-(*  Title:      Quotient_Product.thy
-    Author:     Cezary Kaliszyk and Christian Urban
-*)
-theory Quotient_Product
-imports Quotient Quotient_Syntax
-begin
-
-section {* Quotient infrastructure for the product type. *}
-
-fun
-  prod_rel
-where
-  "prod_rel R1 R2 = (\<lambda>(a, b) (c, d). R1 a c \<and> R2 b d)"
-
-declare [[map * = (prod_fun, prod_rel)]]
-
-
-lemma prod_equivp[quot_equiv]:
-  assumes a: "equivp R1"
-  assumes b: "equivp R2"
-  shows "equivp (prod_rel R1 R2)"
-  apply(rule equivpI)
-  unfolding reflp_def symp_def transp_def
-  apply(simp_all add: split_paired_all)
-  apply(blast intro: equivp_reflp[OF a] equivp_reflp[OF b])
-  apply(blast intro: equivp_symp[OF a] equivp_symp[OF b])
-  apply(blast intro: equivp_transp[OF a] equivp_transp[OF b])
-  done
-
-lemma prod_quotient[quot_thm]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  assumes q2: "Quotient R2 Abs2 Rep2"
-  shows "Quotient (prod_rel R1 R2) (prod_fun Abs1 Abs2) (prod_fun Rep1 Rep2)"
-  unfolding Quotient_def
-  apply(simp add: split_paired_all)
-  apply(simp add: Quotient_abs_rep[OF q1] Quotient_rel_rep[OF q1])
-  apply(simp add: Quotient_abs_rep[OF q2] Quotient_rel_rep[OF q2])
-  using q1 q2
-  unfolding Quotient_def
-  apply(blast)
-  done
-
-lemma Pair_rsp[quot_respect]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  assumes q2: "Quotient R2 Abs2 Rep2"
-  shows "(R1 ===> R2 ===> prod_rel R1 R2) Pair Pair"
-  by simp
-
-lemma Pair_prs[quot_preserve]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  assumes q2: "Quotient R2 Abs2 Rep2"
-  shows "(Rep1 ---> Rep2 ---> (prod_fun Abs1 Abs2)) Pair = Pair"
-  apply(simp add: expand_fun_eq)
-  apply(simp add: Quotient_abs_rep[OF q1] Quotient_abs_rep[OF q2])
-  done
-
-lemma fst_rsp[quot_respect]:
-  assumes "Quotient R1 Abs1 Rep1"
-  assumes "Quotient R2 Abs2 Rep2"
-  shows "(prod_rel R1 R2 ===> R1) fst fst"
-  by simp
-
-lemma fst_prs[quot_preserve]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  assumes q2: "Quotient R2 Abs2 Rep2"
-  shows "(prod_fun Rep1 Rep2 ---> Abs1) fst = fst"
-  apply(simp add: expand_fun_eq)
-  apply(simp add: Quotient_abs_rep[OF q1])
-  done
-
-lemma snd_rsp[quot_respect]:
-  assumes "Quotient R1 Abs1 Rep1"
-  assumes "Quotient R2 Abs2 Rep2"
-  shows "(prod_rel R1 R2 ===> R2) snd snd"
-  by simp
-
-lemma snd_prs[quot_preserve]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  assumes q2: "Quotient R2 Abs2 Rep2"
-  shows "(prod_fun Rep1 Rep2 ---> Abs2) snd = snd"
-  apply(simp add: expand_fun_eq)
-  apply(simp add: Quotient_abs_rep[OF q2])
-  done
-
-lemma split_rsp[quot_respect]:
-  shows "((R1 ===> R2 ===> (op =)) ===> (prod_rel R1 R2) ===> (op =)) split split"
-  by auto
-
-lemma split_prs[quot_preserve]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  and     q2: "Quotient R2 Abs2 Rep2"
-  shows "(((Abs1 ---> Abs2 ---> id) ---> prod_fun Rep1 Rep2 ---> id) split) = split"
-  by (simp add: expand_fun_eq Quotient_abs_rep[OF q1] Quotient_abs_rep[OF q2])
-
-lemma prod_fun_id[id_simps]:
-  shows "prod_fun id id = id"
-  by (simp add: prod_fun_def)
-
-lemma prod_rel_eq[id_simps]:
-  shows "prod_rel (op =) (op =) = (op =)"
-  by (simp add: expand_fun_eq)
-
-
-end