--- a/src/HOL/IMP/Sem_Equiv.thy Thu May 23 11:39:40 2013 +1000
+++ b/src/HOL/IMP/Sem_Equiv.thy Thu May 23 13:51:21 2013 +1000
@@ -9,12 +9,12 @@
definition
equiv_up_to :: "assn \<Rightarrow> com \<Rightarrow> com \<Rightarrow> bool" ("_ \<Turnstile> _ \<sim> _" [50,0,10] 50)
where
- "P \<Turnstile> c \<sim> c' \<equiv> \<forall>s s'. P s \<longrightarrow> (c,s) \<Rightarrow> s' \<longleftrightarrow> (c',s) \<Rightarrow> s'"
+ "(P \<Turnstile> c \<sim> c') = (\<forall>s s'. P s \<longrightarrow> (c,s) \<Rightarrow> s' \<longleftrightarrow> (c',s) \<Rightarrow> s')"
definition
bequiv_up_to :: "assn \<Rightarrow> bexp \<Rightarrow> bexp \<Rightarrow> bool" ("_ \<Turnstile> _ <\<sim>> _" [50,0,10] 50)
where
- "P \<Turnstile> b <\<sim>> b' \<equiv> \<forall>s. P s \<longrightarrow> bval b s = bval b' s"
+ "(P \<Turnstile> b <\<sim>> b') = (\<forall>s. P s \<longrightarrow> bval b s = bval b' s)"
lemma equiv_up_to_True:
"((\<lambda>_. True) \<Turnstile> c \<sim> c') = (c \<sim> c')"