src/HOL/IMP/Sem_Equiv.thy
changeset 52121 5b889b1b465b
parent 52046 bc01725d7918
child 54296 111ecbaa09f7
     1.1 --- a/src/HOL/IMP/Sem_Equiv.thy	Thu May 23 11:39:40 2013 +1000
     1.2 +++ b/src/HOL/IMP/Sem_Equiv.thy	Thu May 23 13:51:21 2013 +1000
     1.3 @@ -9,12 +9,12 @@
     1.4  definition
     1.5    equiv_up_to :: "assn \<Rightarrow> com \<Rightarrow> com \<Rightarrow> bool" ("_ \<Turnstile> _ \<sim> _" [50,0,10] 50)
     1.6  where
     1.7 -  "P \<Turnstile> c \<sim> c' \<equiv> \<forall>s s'. P s \<longrightarrow> (c,s) \<Rightarrow> s' \<longleftrightarrow> (c',s) \<Rightarrow> s'"
     1.8 +  "(P \<Turnstile> c \<sim> c') = (\<forall>s s'. P s \<longrightarrow> (c,s) \<Rightarrow> s' \<longleftrightarrow> (c',s) \<Rightarrow> s')"
     1.9  
    1.10  definition
    1.11    bequiv_up_to :: "assn \<Rightarrow> bexp \<Rightarrow> bexp \<Rightarrow> bool" ("_ \<Turnstile> _ <\<sim>> _" [50,0,10] 50)
    1.12  where
    1.13 -  "P \<Turnstile> b <\<sim>> b' \<equiv> \<forall>s. P s \<longrightarrow> bval b s = bval b' s"
    1.14 +  "(P \<Turnstile> b <\<sim>> b') = (\<forall>s. P s \<longrightarrow> bval b s = bval b' s)"
    1.15  
    1.16  lemma equiv_up_to_True:
    1.17    "((\<lambda>_. True) \<Turnstile> c \<sim> c') = (c \<sim> c')"