diff -r bb18eed53ed6 -r a1119cf551e8 src/HOL/IMP/Abs_State.thy --- a/src/HOL/IMP/Abs_State.thy Tue Aug 13 14:20:22 2013 +0200 +++ b/src/HOL/IMP/Abs_State.thy Tue Aug 13 16:25:47 2013 +0200 @@ -132,29 +132,29 @@ for \ :: "'av::semilattice_sup_top \ val set" begin -abbreviation \\<^isub>s :: "'av st \ state set" -where "\\<^isub>s == \_st \" +abbreviation \\<^sub>s :: "'av st \ state set" +where "\\<^sub>s == \_st \" -abbreviation \\<^isub>o :: "'av st option \ state set" -where "\\<^isub>o == \_option \\<^isub>s" +abbreviation \\<^sub>o :: "'av st option \ state set" +where "\\<^sub>o == \_option \\<^sub>s" -abbreviation \\<^isub>c :: "'av st option acom \ state set acom" -where "\\<^isub>c == map_acom \\<^isub>o" +abbreviation \\<^sub>c :: "'av st option acom \ state set acom" +where "\\<^sub>c == map_acom \\<^sub>o" -lemma gamma_s_top[simp]: "\\<^isub>s \ = UNIV" +lemma gamma_s_top[simp]: "\\<^sub>s \ = UNIV" by(auto simp: \_st_def fun_top) -lemma gamma_o_Top[simp]: "\\<^isub>o \ = UNIV" +lemma gamma_o_Top[simp]: "\\<^sub>o \ = UNIV" by (simp add: top_option_def) -lemma mono_gamma_s: "f \ g \ \\<^isub>s f \ \\<^isub>s g" +lemma mono_gamma_s: "f \ g \ \\<^sub>s f \ \\<^sub>s g" by(simp add:\_st_def le_st_iff subset_iff) (metis mono_gamma subsetD) lemma mono_gamma_o: - "S1 \ S2 \ \\<^isub>o S1 \ \\<^isub>o S2" + "S1 \ S2 \ \\<^sub>o S1 \ \\<^sub>o S2" by(induction S1 S2 rule: less_eq_option.induct)(simp_all add: mono_gamma_s) -lemma mono_gamma_c: "C1 \ C2 \ \\<^isub>c C1 \ \\<^isub>c C2" +lemma mono_gamma_c: "C1 \ C2 \ \\<^sub>c C1 \ \\<^sub>c C2" by (simp add: less_eq_acom_def mono_gamma_o size_annos anno_map_acom size_annos_same[of C1 C2]) lemma in_gamma_option_iff: