--- a/src/HOL/Library/Option_ord.thy Tue Mar 11 23:09:30 2008 +0100
+++ b/src/HOL/Library/Option_ord.thy Wed Mar 12 08:45:51 2008 +0100
@@ -18,34 +18,34 @@
definition less_option where
[code func del]: "x < y \<longleftrightarrow> (case y of None \<Rightarrow> False | Some y \<Rightarrow> (case x of None \<Rightarrow> True | Some x \<Rightarrow> x < y))"
-lemma less_eq_option_None [simp]: "None \<le> (x\<Colon>'a option)"
+lemma less_eq_option_None [simp]: "None \<le> x"
by (simp add: less_eq_option_def)
-lemma less_eq_option_None_code [code]: "None \<le> (x\<Colon>'a option) \<longleftrightarrow> True"
+lemma less_eq_option_None_code [code]: "None \<le> x \<longleftrightarrow> True"
by simp
-lemma less_eq_option_None_is_None: "(x\<Colon>'a option) \<le> None \<Longrightarrow> x = None"
+lemma less_eq_option_None_is_None: "x \<le> None \<Longrightarrow> x = None"
by (cases x) (simp_all add: less_eq_option_def)
-lemma less_eq_option_Some_None [simp, code]: "Some (x\<Colon>'a) \<le> None \<longleftrightarrow> False"
+lemma less_eq_option_Some_None [simp, code]: "Some x \<le> None \<longleftrightarrow> False"
by (simp add: less_eq_option_def)
-lemma less_eq_option_Some [simp, code]: "Some (x\<Colon>'a) \<le> Some y \<longleftrightarrow> x \<le> y"
+lemma less_eq_option_Some [simp, code]: "Some x \<le> Some y \<longleftrightarrow> x \<le> y"
by (simp add: less_eq_option_def)
-lemma less_option_None [simp, code]: "(x\<Colon>'a option) < None \<longleftrightarrow> False"
+lemma less_option_None [simp, code]: "x < None \<longleftrightarrow> False"
by (simp add: less_option_def)
-lemma less_option_None_is_Some: "None < (x\<Colon>'a option) \<Longrightarrow> \<exists>z. x = Some z"
+lemma less_option_None_is_Some: "None < x \<Longrightarrow> \<exists>z. x = Some z"
by (cases x) (simp_all add: less_option_def)
-lemma less_option_None_Some [simp]: "None < Some (x\<Colon>'a)"
+lemma less_option_None_Some [simp]: "None < Some x"
by (simp add: less_option_def)
-lemma less_option_None_Some_code [code]: "None < Some (x\<Colon>'a) \<longleftrightarrow> True"
+lemma less_option_None_Some_code [code]: "None < Some x \<longleftrightarrow> True"
by simp
-lemma less_option_Some [simp, code]: "Some (x\<Colon>'a) < Some y \<longleftrightarrow> x < y"
+lemma less_option_Some [simp, code]: "Some x < Some y \<longleftrightarrow> x < y"
by (simp add: less_option_def)
instance by default