--- a/src/HOL/Library/Quotient_Option.thy Fri Feb 14 07:53:45 2014 +0100
+++ b/src/HOL/Library/Quotient_Option.thy Fri Feb 14 07:53:46 2014 +0100
@@ -11,20 +11,16 @@
subsection {* Rules for the Quotient package *}
lemma option_rel_map1:
- "option_rel R (Option.map f x) y \<longleftrightarrow> option_rel (\<lambda>x. R (f x)) x y"
+ "option_rel R (map_option f x) y \<longleftrightarrow> option_rel (\<lambda>x. R (f x)) x y"
by (simp add: option_rel_def split: option.split)
lemma option_rel_map2:
- "option_rel R x (Option.map f y) \<longleftrightarrow> option_rel (\<lambda>x y. R x (f y)) x y"
+ "option_rel R x (map_option f y) \<longleftrightarrow> option_rel (\<lambda>x y. R x (f y)) x y"
by (simp add: option_rel_def split: option.split)
-lemma option_map_id [id_simps]:
- "Option.map id = id"
- by (simp add: id_def Option.map.identity fun_eq_iff)
-
-lemma option_rel_eq [id_simps]:
- "option_rel (op =) = (op =)"
- by (simp add: option_rel_def fun_eq_iff split: option.split)
+declare
+ map_option.id [id_simps]
+ option_rel_eq [id_simps]
lemma option_symp:
"symp R \<Longrightarrow> symp (option_rel R)"
@@ -40,9 +36,9 @@
lemma option_quotient [quot_thm]:
assumes "Quotient3 R Abs Rep"
- shows "Quotient3 (option_rel R) (Option.map Abs) (Option.map Rep)"
+ shows "Quotient3 (option_rel R) (map_option Abs) (map_option Rep)"
apply (rule Quotient3I)
- apply (simp_all add: Option.map.compositionality comp_def Option.map.identity option_rel_eq option_rel_map1 option_rel_map2 Quotient3_abs_rep [OF assms] Quotient3_rel_rep [OF assms])
+ apply (simp_all add: option.map_comp comp_def option.map_id[unfolded id_def] option_rel_eq option_rel_map1 option_rel_map2 Quotient3_abs_rep [OF assms] Quotient3_rel_rep [OF assms])
using Quotient3_rel [OF assms]
apply (simp add: option_rel_def split: option.split)
done
@@ -61,12 +57,12 @@
lemma option_None_prs [quot_preserve]:
assumes q: "Quotient3 R Abs Rep"
- shows "Option.map Abs None = None"
+ shows "map_option Abs None = None"
by simp
lemma option_Some_prs [quot_preserve]:
assumes q: "Quotient3 R Abs Rep"
- shows "(Rep ---> Option.map Abs) Some = Some"
+ shows "(Rep ---> map_option Abs) Some = Some"
apply(simp add: fun_eq_iff)
apply(simp add: Quotient3_abs_rep[OF q])
done