theory PolicySystemSAC

lemma c_affects : "subjectAffects SACAuthGraph (partition_label NicC) = {partition_label NicC}" apply (rule subset_antisym) defer 
    (* backward *)
     apply (rule subsetI) apply (rule c_affects_self_only, assumption) 
    (* forward *)
     apply (rule subsetI) apply (erule subjectAffects.induct) by (simp, blast?)+

(* Proof state trace *)
proof (prove)
goal (1 subgoal):
 1. subjectAffects SACAuthGraph (partition_label NicC) = {partition_label NicC} proof (prove)
goal (2 subgoals):
 1. subjectAffects SACAuthGraph (partition_label NicC) \<subseteq> {partition_label NicC}
 2. {partition_label NicC} \<subseteq> subjectAffects SACAuthGraph (partition_label NicC) proof (prove)
goal (2 subgoals):
 1. {partition_label NicC} \<subseteq> subjectAffects SACAuthGraph (partition_label NicC)
 2. subjectAffects SACAuthGraph (partition_label NicC) \<subseteq> {partition_label NicC} proof (prove)
goal (2 subgoals):
 1. {partition_label NicC} \<subseteq> subjectAffects SACAuthGraph (partition_label NicC)
 2. subjectAffects SACAuthGraph (partition_label NicC) \<subseteq> {partition_label NicC} proof (prove)
goal (2 subgoals):
 1. \<And>x. x \<in> {partition_label NicC} \<Longrightarrow> x \<in> subjectAffects SACAuthGraph (partition_label NicC)
 2. subjectAffects SACAuthGraph (partition_label NicC) \<subseteq> {partition_label NicC} proof (prove)
goal (1 subgoal):
 1. subjectAffects SACAuthGraph (partition_label NicC) \<subseteq> {partition_label NicC} proof (prove)
goal (1 subgoal):
 1. subjectAffects SACAuthGraph (partition_label NicC) \<subseteq> {partition_label NicC} proof (prove)
goal (1 subgoal):
 1. \<And>x. x \<in> subjectAffects SACAuthGraph (partition_label NicC) \<Longrightarrow> x \<in> {partition_label NicC} proof (prove)
goal (12 subgoals):
 1. \<And>x. partition_label NicC \<in> {partition_label NicC}
 2. \<And>x auth l'. \<lbrakk>(partition_label NicC, auth, l') \<in> SACAuthGraph; auth \<in> {Control, Write}\<rbrakk> \<Longrightarrow> l' \<in> {partition_label NicC}
 3. \<And>x auth l'. \<lbrakk>(partition_label NicC, auth, l') \<in> SACAuthGraph; auth \<in> {Receive, Notify, SyncSend, Call, Reset}\<rbrakk> \<Longrightarrow> l' \<in> {partition_label NicC}
 4. \<And>x auth ep l' l''. \<lbrakk>(partition_label NicC, auth, ep) \<in> SACAuthGraph; auth \<in> {SyncSend, Notify, Call}; (l', Receive, ep) \<in> SACAuthGraph; (l', Write, l'') \<in> SACAuthGraph\<rbrakk> \<Longrightarrow> l'' \<in> {partition_label NicC}
 5. \<And>x ep l'. \<lbrakk>(partition_label NicC, Receive, ep) \<in> SACAuthGraph; (l', SyncSend, ep) \<in> SACAuthGraph\<rbrakk> \<Longrightarrow> l' \<in> {partition_label NicC}
 6. \<And>x l'. (l', Reply, partition_label NicC) \<in> SACAuthGraph \<Longrightarrow> l' \<in> {partition_label NicC}
 7. \<And>x l' l''. \<lbrakk>(partition_label NicC, Reply, l') \<in> SACAuthGraph; (l', Write, l'') \<in> SACAuthGraph\<rbrakk> \<Longrightarrow> l'' \<in> {partition_label NicC}
 8. \<And>x l'. (partition_label NicC, DeleteDerived, l') \<in> SACAuthGraph \<Longrightarrow> l' \<in> {partition_label NicC}
 9. \<And>x l' l''. \<lbrakk>(partition_label NicC, DeleteDerived, l') \<in> SACAuthGraph; (l'', DeleteDerived, l') \<in> SACAuthGraph\<rbrakk> \<Longrightarrow> l'' \<in> {partition_label NicC}
 10. \<And>x ep l' auth l''. \<lbrakk>(partition_label NicC, Reset, ep) \<in> SACAuthGraph; (l', auth, ep) \<in> SACAuthGraph; auth \<in> {SyncSend, Receive}; (l', Write, l'') \<in> SACAuthGraph\<rbrakk> \<Longrightarrow> l'' \<in> {partition_label NicC}
A total of 12 subgoals...