src/HOL/IMP/Abs_State.thy
changeset 49497 860b7c6bd913
parent 49399 a9d9f3483b71
child 49577 b199aa1d33fd
--- a/src/HOL/IMP/Abs_State.thy	Fri Sep 21 13:39:30 2012 +0200
+++ b/src/HOL/IMP/Abs_State.thy	Fri Sep 21 13:56:57 2012 +0200
@@ -184,16 +184,16 @@
 locale Gamma = Val_abs where \<gamma>=\<gamma> for \<gamma> :: "'av::semilattice \<Rightarrow> val set"
 begin
 
-abbreviation \<gamma>\<^isub>f :: "'av st \<Rightarrow> state set"
-where "\<gamma>\<^isub>f == \<gamma>_st \<gamma>"
+abbreviation \<gamma>\<^isub>s :: "'av st \<Rightarrow> state set"
+where "\<gamma>\<^isub>s == \<gamma>_st \<gamma>"
 
 abbreviation \<gamma>\<^isub>o :: "'av st option \<Rightarrow> state set"
-where "\<gamma>\<^isub>o == \<gamma>_option \<gamma>\<^isub>f"
+where "\<gamma>\<^isub>o == \<gamma>_option \<gamma>\<^isub>s"
 
 abbreviation \<gamma>\<^isub>c :: "'av st option acom \<Rightarrow> state set acom"
 where "\<gamma>\<^isub>c == map_acom \<gamma>\<^isub>o"
 
-lemma gamma_f_Top[simp]: "\<gamma>\<^isub>f (top c) = UNIV"
+lemma gamma_s_Top[simp]: "\<gamma>\<^isub>s (top c) = UNIV"
 by(auto simp: top_st_def \<gamma>_st_def)
 
 lemma gamma_o_Top[simp]: "\<gamma>\<^isub>o (top c) = UNIV"
@@ -201,13 +201,13 @@
 
 (* FIXME (maybe also le \<rightarrow> sqle?) *)
 
-lemma mono_gamma_f: "f \<sqsubseteq> g \<Longrightarrow> \<gamma>\<^isub>f f \<subseteq> \<gamma>\<^isub>f g"
+lemma mono_gamma_s: "f \<sqsubseteq> g \<Longrightarrow> \<gamma>\<^isub>s f \<subseteq> \<gamma>\<^isub>s g"
 apply(simp add:\<gamma>_st_def subset_iff le_st_def split: if_splits)
 by (metis mono_gamma subsetD)
 
 lemma mono_gamma_o:
   "S1 \<sqsubseteq> S2 \<Longrightarrow> \<gamma>\<^isub>o S1 \<subseteq> \<gamma>\<^isub>o S2"
-by(induction S1 S2 rule: le_option.induct)(simp_all add: mono_gamma_f)
+by(induction S1 S2 rule: le_option.induct)(simp_all add: mono_gamma_s)
 
 lemma mono_gamma_c: "C1 \<sqsubseteq> C2 \<Longrightarrow> \<gamma>\<^isub>c C1 \<le> \<gamma>\<^isub>c C2"
 by (induction C1 C2 rule: le_acom.induct) (simp_all add:mono_gamma_o)