
diff -r a6f3e1b08494 -r b6873d123f9b Attic/Quot/Quotient_Sum.thy
--- a/Attic/Quot/Quotient_Sum.thy	Sat May 12 21:05:59 2012 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,96 +0,0 @@
-(*  Title:      Quotient_Sum.thy
-    Author:     Cezary Kaliszyk and Christian Urban
-*)
-theory Quotient_Sum
-imports Quotient Quotient_Syntax
-begin
-
-section {* Quotient infrastructure for the sum type. *}
-
-fun
-  sum_rel
-where
-  "sum_rel R1 R2 (Inl a1) (Inl b1) = R1 a1 b1"
-| "sum_rel R1 R2 (Inl a1) (Inr b2) = False"
-| "sum_rel R1 R2 (Inr a2) (Inl b1) = False"
-| "sum_rel R1 R2 (Inr a2) (Inr b2) = R2 a2 b2"
-
-fun
-  sum_map
-where
-  "sum_map f1 f2 (Inl a) = Inl (f1 a)"
-| "sum_map f1 f2 (Inr a) = Inr (f2 a)"
-
-declare [[map "+" = (sum_map, sum_rel)]]
-
-
-text {* should probably be in Sum_Type.thy *}
-lemma split_sum_all:
-  shows "(\<forall>x. P x) \<longleftrightarrow> (\<forall>x. P (Inl x)) \<and> (\<forall>x. P (Inr x))"
-  apply(auto)
-  apply(case_tac x)
-  apply(simp_all)
-  done
-
-lemma sum_equivp[quot_equiv]:
-  assumes a: "equivp R1"
-  assumes b: "equivp R2"
-  shows "equivp (sum_rel R1 R2)"
-  apply(rule equivpI)
-  unfolding reflp_def symp_def transp_def
-  apply(simp_all add: split_sum_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 sum_quotient[quot_thm]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  assumes q2: "Quotient R2 Abs2 Rep2"
-  shows "Quotient (sum_rel R1 R2) (sum_map Abs1 Abs2) (sum_map Rep1 Rep2)"
-  unfolding Quotient_def
-  apply(simp add: split_sum_all)
-  apply(simp_all add: Quotient_abs_rep[OF q1] Quotient_rel_rep[OF q1])
-  apply(simp_all add: Quotient_abs_rep[OF q2] Quotient_rel_rep[OF q2])
-  using q1 q2
-  unfolding Quotient_def
-  apply(blast)+
-  done
-
-lemma sum_Inl_rsp[quot_respect]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  assumes q2: "Quotient R2 Abs2 Rep2"
-  shows "(R1 ===> sum_rel R1 R2) Inl Inl"
-  by simp
-
-lemma sum_Inr_rsp[quot_respect]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  assumes q2: "Quotient R2 Abs2 Rep2"
-  shows "(R2 ===> sum_rel R1 R2) Inr Inr"
-  by simp
-
-lemma sum_Inl_prs[quot_preserve]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  assumes q2: "Quotient R2 Abs2 Rep2"
-  shows "(Rep1 ---> sum_map Abs1 Abs2) Inl = Inl"
-  apply(simp add: expand_fun_eq)
-  apply(simp add: Quotient_abs_rep[OF q1])
-  done
-
-lemma sum_Inr_prs[quot_preserve]:
-  assumes q1: "Quotient R1 Abs1 Rep1"
-  assumes q2: "Quotient R2 Abs2 Rep2"
-  shows "(Rep2 ---> sum_map Abs1 Abs2) Inr = Inr"
-  apply(simp add: expand_fun_eq)
-  apply(simp add: Quotient_abs_rep[OF q2])
-  done
-
-lemma sum_map_id[id_simps]:
-  shows "sum_map id id = id"
-  by (simp add: expand_fun_eq split_sum_all)
-
-lemma sum_rel_eq[id_simps]:
-  shows "sum_rel (op =) (op =) = (op =)"
-  by (simp add: expand_fun_eq split_sum_all)
-
-end




