diff -r 3869b2400e22 -r 0d25e02759b7 src/HOL/HOLCF/One.thy
--- a/src/HOL/HOLCF/One.thy	Mon Jan 01 21:17:28 2018 +0100
+++ b/src/HOL/HOLCF/One.thy	Mon Jan 01 23:07:24 2018 +0100
@@ -5,69 +5,67 @@
 section \<open>The unit domain\<close>
 
 theory One
-imports Lift
+  imports Lift
 begin
 
-type_synonym
-  one = "unit lift"
+type_synonym one = "unit lift"
 
 translations
-  (type) "one" <= (type) "unit lift"
+  (type) "one" \<leftharpoondown> (type) "unit lift"
 
 definition ONE :: "one"
-  where "ONE == Def ()"
+  where "ONE \<equiv> Def ()"
 
 text \<open>Exhaustion and Elimination for type @{typ one}\<close>
 
 lemma Exh_one: "t = \<bottom> \<or> t = ONE"
-unfolding ONE_def by (induct t) simp_all
+  by (induct t) (simp_all add: ONE_def)
 
 lemma oneE [case_names bottom ONE]: "\<lbrakk>p = \<bottom> \<Longrightarrow> Q; p = ONE \<Longrightarrow> Q\<rbrakk> \<Longrightarrow> Q"
-unfolding ONE_def by (induct p) simp_all
+  by (induct p) (simp_all add: ONE_def)
 
-lemma one_induct [case_names bottom ONE]: "\<lbrakk>P \<bottom>; P ONE\<rbrakk> \<Longrightarrow> P x"
-by (cases x rule: oneE) simp_all
+lemma one_induct [case_names bottom ONE]: "P \<bottom> \<Longrightarrow> P ONE \<Longrightarrow> P x"
+  by (cases x rule: oneE) simp_all
 
 lemma dist_below_one [simp]: "ONE \<notsqsubseteq> \<bottom>"
-unfolding ONE_def by simp
+  by (simp add: ONE_def)
 
 lemma below_ONE [simp]: "x \<sqsubseteq> ONE"
-by (induct x rule: one_induct) simp_all
+  by (induct x rule: one_induct) simp_all
 
 lemma ONE_below_iff [simp]: "ONE \<sqsubseteq> x \<longleftrightarrow> x = ONE"
-by (induct x rule: one_induct) simp_all
+  by (induct x rule: one_induct) simp_all
 
 lemma ONE_defined [simp]: "ONE \<noteq> \<bottom>"
-unfolding ONE_def by simp
+  by (simp add: ONE_def)
 
 lemma one_neq_iffs [simp]:
   "x \<noteq> ONE \<longleftrightarrow> x = \<bottom>"
   "ONE \<noteq> x \<longleftrightarrow> x = \<bottom>"
   "x \<noteq> \<bottom> \<longleftrightarrow> x = ONE"
   "\<bottom> \<noteq> x \<longleftrightarrow> x = ONE"
-by (induct x rule: one_induct) simp_all
+  by (induct x rule: one_induct) simp_all
 
 lemma compact_ONE: "compact ONE"
-by (rule compact_chfin)
+  by (rule compact_chfin)
 
 text \<open>Case analysis function for type @{typ one}\<close>
 
-definition
-  one_case :: "'a::pcpo \<rightarrow> one \<rightarrow> 'a" where
-  "one_case = (\<Lambda> a x. seq\<cdot>x\<cdot>a)"
+definition one_case :: "'a::pcpo \<rightarrow> one \<rightarrow> 'a"
+  where "one_case = (\<Lambda> a x. seq\<cdot>x\<cdot>a)"
 
 translations
-  "case x of XCONST ONE \<Rightarrow> t" == "CONST one_case\<cdot>t\<cdot>x"
-  "case x of XCONST ONE :: 'a \<Rightarrow> t" => "CONST one_case\<cdot>t\<cdot>x"
-  "\<Lambda> (XCONST ONE). t" == "CONST one_case\<cdot>t"
+  "case x of XCONST ONE \<Rightarrow> t" \<rightleftharpoons> "CONST one_case\<cdot>t\<cdot>x"
+  "case x of XCONST ONE :: 'a \<Rightarrow> t" \<rightharpoonup> "CONST one_case\<cdot>t\<cdot>x"
+  "\<Lambda> (XCONST ONE). t" \<rightleftharpoons> "CONST one_case\<cdot>t"
 
 lemma one_case1 [simp]: "(case \<bottom> of ONE \<Rightarrow> t) = \<bottom>"
-by (simp add: one_case_def)
+  by (simp add: one_case_def)
 
 lemma one_case2 [simp]: "(case ONE of ONE \<Rightarrow> t) = t"
-by (simp add: one_case_def)
+  by (simp add: one_case_def)
 
 lemma one_case3 [simp]: "(case x of ONE \<Rightarrow> ONE) = x"
-by (induct x rule: one_induct) simp_all
+  by (induct x rule: one_induct) simp_all
 
 end