theory CSpaceAcc_C

lemma ccorres_pre_getDomainTime:
  assumes cc: "\<And>rv. ccorres r xf (P rv) (P' rv) hs (f rv) c"
  shows   "ccorres r xf
                  (\<lambda>s. (\<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s))
                  {s. \<forall>rv. ksDomainTime_' (globals s) = rv
                                 \<longrightarrow> s \<in> P' rv }
                          hs (getDomainTime >>= (\<lambda>rv. f rv)) c" apply (rule ccorres_guard_imp) apply (rule ccorres_symb_exec_l) defer apply wp[1] apply (simp add: getDomainTime_def) apply (rule gets_sp) apply (clarsimp simp: empty_fail_def getDomainTime_def simpler_gets_def) apply assumption apply clarsimp defer apply (rule ccorres_guard_imp) apply (rule cc) apply clarsimp apply assumption apply (clarsimp simp: rf_sr_ksDomainTime) done

(* Proof state trace *)
proof (prove)
goal (1 subgoal):
 1. ccorres r xf (\<lambda>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s) {s. \<forall>rv. ksDomainTime_' (globals s) = rv \<longrightarrow> s \<in> P' rv} hs (getDomainTime >>= f) c proof (prove)
goal (3 subgoals):
 1. ccorres r xf ?Q ?Q' hs (getDomainTime >>= f) c
 2. \<And>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s \<Longrightarrow> ?Q s
 3. \<And>s. s \<in> {s. \<forall>rv. ksDomainTime_' (globals s) = rv \<longrightarrow> s \<in> P' rv} \<Longrightarrow> s \<in> ?Q' proof (prove)
goal (6 subgoals):
 1. \<And>rv. ccorres r xf (?Q4 rv) (?Q'4 rv) hs (f rv) c
 2. \<And>s. \<lbrace>(=) s\<rbrace> getDomainTime \<lbrace>\<lambda>r. (=) s\<rbrace>
 3. \<lbrace>?Q\<rbrace> getDomainTime \<lbrace>?Q4\<rbrace>
 4. empty_fail getDomainTime
 5. \<And>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s \<Longrightarrow> ?Q s
 6. \<And>s. s \<in> {s. \<forall>rv. ksDomainTime_' (globals s) = rv \<longrightarrow> s \<in> P' rv} \<Longrightarrow> s \<in> {s'. \<forall>rv s. (s, s') \<in> rf_sr \<and> ?Q4 rv s \<longrightarrow> s' \<in> ?Q'4 rv} proof (prove)
goal (6 subgoals):
 1. \<And>s. \<lbrace>(=) s\<rbrace> getDomainTime \<lbrace>\<lambda>r. (=) s\<rbrace>
 2. \<lbrace>?Q\<rbrace> getDomainTime \<lbrace>?Q4\<rbrace>
 3. empty_fail getDomainTime
 4. \<And>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s \<Longrightarrow> ?Q s
 5. \<And>s. s \<in> {s. \<forall>rv. ksDomainTime_' (globals s) = rv \<longrightarrow> s \<in> P' rv} \<Longrightarrow> s \<in> {s'. \<forall>rv s. (s, s') \<in> rf_sr \<and> ?Q4 rv s \<longrightarrow> s' \<in> ?Q'4 rv}
 6. \<And>rv. ccorres r xf (?Q4 rv) (?Q'4 rv) hs (f rv) c proof (prove)
goal (5 subgoals):
 1. \<lbrace>?Q\<rbrace> getDomainTime \<lbrace>?Q4\<rbrace>
 2. empty_fail getDomainTime
 3. \<And>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s \<Longrightarrow> ?Q s
 4. \<And>s. s \<in> {s. \<forall>rv. ksDomainTime_' (globals s) = rv \<longrightarrow> s \<in> P' rv} \<Longrightarrow> s \<in> {s'. \<forall>rv s. (s, s') \<in> rf_sr \<and> ?Q4 rv s \<longrightarrow> s' \<in> ?Q'4 rv}
 5. \<And>rv. ccorres r xf (?Q4 rv) (?Q'4 rv) hs (f rv) c proof (prove)
goal (5 subgoals):
 1. \<lbrace>?Q\<rbrace> gets ksDomainTime \<lbrace>?Q4\<rbrace>
 2. empty_fail getDomainTime
 3. \<And>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s \<Longrightarrow> ?Q s
 4. \<And>s. s \<in> {s. \<forall>rv. ksDomainTime_' (globals s) = rv \<longrightarrow> s \<in> P' rv} \<Longrightarrow> s \<in> {s'. \<forall>rv s. (s, s') \<in> rf_sr \<and> ?Q4 rv s \<longrightarrow> s' \<in> ?Q'4 rv}
 5. \<And>rv. ccorres r xf (?Q4 rv) (?Q'4 rv) hs (f rv) c proof (prove)
goal (4 subgoals):
 1. empty_fail getDomainTime
 2. \<And>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s \<Longrightarrow> ?Q s
 3. \<And>s. s \<in> {s. \<forall>rv. ksDomainTime_' (globals s) = rv \<longrightarrow> s \<in> P' rv} \<Longrightarrow> s \<in> {s'. \<forall>rv s. (s, s') \<in> rf_sr \<and> (?Q and (\<lambda>s. ksDomainTime s = rv)) s \<longrightarrow> s' \<in> ?Q'4 rv}
 4. \<And>rv. ccorres r xf (?Q and (\<lambda>s. ksDomainTime s = rv)) (?Q'4 rv) hs (f rv) c proof (prove)
goal (3 subgoals):
 1. \<And>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s \<Longrightarrow> ?Q s
 2. \<And>s. s \<in> {s. \<forall>rv. ksDomainTime_' (globals s) = rv \<longrightarrow> s \<in> P' rv} \<Longrightarrow> s \<in> {s'. \<forall>rv s. (s, s') \<in> rf_sr \<and> (?Q and (\<lambda>s. ksDomainTime s = rv)) s \<longrightarrow> s' \<in> ?Q'4 rv}
 3. \<And>rv. ccorres r xf (?Q and (\<lambda>s. ksDomainTime s = rv)) (?Q'4 rv) hs (f rv) c proof (prove)
goal (2 subgoals):
 1. \<And>s. s \<in> {s. \<forall>rv. ksDomainTime_' (globals s) = rv \<longrightarrow> s \<in> P' rv} \<Longrightarrow> s \<in> {s'. \<forall>rv s. (s, s') \<in> rf_sr \<and> ((\<lambda>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s) and (\<lambda>s. ksDomainTime s = rv)) s \<longrightarrow> s' \<in> ?Q'4 rv}
 2. \<And>rv. ccorres r xf ((\<lambda>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s) and (\<lambda>s. ksDomainTime s = rv)) (?Q'4 rv) hs (f rv) c proof (prove)
goal (2 subgoals):
 1. \<And>s sa. \<lbrakk>s \<in> P' (ksDomainTime_' (globals s)); (sa, s) \<in> rf_sr; P (ksDomainTime sa) sa\<rbrakk> \<Longrightarrow> s \<in> ?Q'4 (ksDomainTime sa)
 2. \<And>rv. ccorres r xf ((\<lambda>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s) and (\<lambda>s. ksDomainTime s = rv)) (?Q'4 rv) hs (f rv) c proof (prove)
goal (2 subgoals):
 1. \<And>rv. ccorres r xf ((\<lambda>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s) and (\<lambda>s. ksDomainTime s = rv)) (?Q'4 rv) hs (f rv) c
 2. \<And>s sa. \<lbrakk>s \<in> P' (ksDomainTime_' (globals s)); (sa, s) \<in> rf_sr; P (ksDomainTime sa) sa\<rbrakk> \<Longrightarrow> s \<in> ?Q'4 (ksDomainTime sa) proof (prove)
goal (4 subgoals):
 1. \<And>rv. ccorres r xf (?Q22 rv) (?Q'22 rv) hs (f rv) c
 2. \<And>rv s. ((\<lambda>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s) and (\<lambda>s. ksDomainTime s = rv)) s \<Longrightarrow> ?Q22 rv s
 3. \<And>rv s. s \<in> ?Q'4 rv \<Longrightarrow> s \<in> ?Q'22 rv
 4. \<And>s sa. \<lbrakk>s \<in> P' (ksDomainTime_' (globals s)); (sa, s) \<in> rf_sr; P (ksDomainTime sa) sa\<rbrakk> \<Longrightarrow> s \<in> ?Q'4 (ksDomainTime sa) proof (prove)
goal (3 subgoals):
 1. \<And>rv s. ((\<lambda>s. \<forall>rv. ksDomainTime s = rv \<longrightarrow> P rv s) and (\<lambda>s. ksDomainTime s = rv)) s \<Longrightarrow> P rv s
 2. \<And>rv s. s \<in> ?Q'4 rv \<Longrightarrow> s \<in> P' rv
 3. \<And>s sa. \<lbrakk>s \<in> P' (ksDomainTime_' (globals s)); (sa, s) \<in> rf_sr; P (ksDomainTime sa) sa\<rbrakk> \<Longrightarrow> s \<in> ?Q'4 (ksDomainTime sa) proof (prove)
goal (2 subgoals):
 1. \<And>rv s. s \<in> ?Q'4 rv \<Longrightarrow> s \<in> P' rv
 2. \<And>s sa. \<lbrakk>s \<in> P' (ksDomainTime_' (globals s)); (sa, s) \<in> rf_sr; P (ksDomainTime sa) sa\<rbrakk> \<Longrightarrow> s \<in> ?Q'4 (ksDomainTime sa) proof (prove)
goal (1 subgoal):
 1. \<And>s sa. \<lbrakk>s \<in> P' (ksDomainTime_' (globals s)); (sa, s) \<in> rf_sr; P (ksDomainTime sa) sa\<rbrakk> \<Longrightarrow> s \<in> P' (ksDomainTime sa) proof (prove)
goal:
No subgoals!