theory ArchCNode_AC

lemma list_integ_lift[CNode_AC_assms]:
  assumes li:
    "\<lbrace>list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st and Q\<rbrace>
     f
     \<lbrace>\<lambda>_. list_integ (cdt_change_allowed aag {pasSubject aag}  (cdt st) (tcb_states_of_state st)) st\<rbrace>"
  assumes ekh: "\<And>P. f \<lbrace>\<lambda>s. P (ekheap s)\<rbrace>"
  assumes rq: "\<And>P. f \<lbrace>\<lambda>s. P (ready_queues s)\<rbrace>"
  shows "\<lbrace>integrity aag X st and Q\<rbrace> f \<lbrace>\<lambda>_. integrity aag X st\<rbrace>" apply (rule hoare_pre) apply (unfold integrity_def[abs_def] integrity_asids_def) apply (simp only: integrity_cdt_list_as_list_integ) apply (rule hoare_lift_Pf2[where f="ekheap"]) apply (simp add: tcb_states_of_state_def get_tcb_def) apply (wp li[simplified tcb_states_of_state_def get_tcb_def] ekh rq)+ apply (simp only: integrity_cdt_list_as_list_integ) apply (simp add: tcb_states_of_state_def get_tcb_def) done

(* Proof state trace *)
proof (prove)
goal (1 subgoal):
 1. \<lbrace>integrity aag X st and Q\<rbrace> f \<lbrace>\<lambda>_. integrity aag X st\<rbrace> proof (prove)
goal (2 subgoals):
 1. \<lbrace>?Q\<rbrace> f \<lbrace>\<lambda>_. integrity aag X st\<rbrace>
 2. \<And>s. (integrity aag X st and Q) s \<Longrightarrow> ?Q s proof (prove)
goal (2 subgoals):
 1. \<lbrace>?Q\<rbrace> f \<lbrace>\<lambda>_ s'. integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st s' \<and> (\<forall>x. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag x) (ekheap st x) (ekheap s' x)) \<and> integrity_cdt_state aag {pasSubject aag} st s' \<and> (\<forall>x. cdt_list_integrity aag (cdt st) (tcb_states_of_state st) x (cdt_list st x) (cdt_list s' x)) \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node s' x, interrupt_states s' x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues s' d p)) \<and> (\<forall>x. memory_integrity X aag x (tcb_states_of_state st) (tcb_states_of_state s') (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state s') x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (tcb_states_of_state st) (tcb_states_of_state s') (device_state (machine_state st) x) (device_state (machine_state s') x)) \<and> (\<forall>x a. asid_table st (asid_high_bits_of a) = asid_table s' (asid_high_bits_of a) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of a \<longrightarrow> pasASIDAbs aag asid' \<in> {pasSubject aag}))\<rbrace>
 2. \<And>s. ((\<lambda>s'. integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st s' \<and> (\<forall>x. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag x) (ekheap st x) (ekheap s' x)) \<and> integrity_cdt_state aag {pasSubject aag} st s' \<and> (\<forall>x. cdt_list_integrity aag (cdt st) (tcb_states_of_state st) x (cdt_list st x) (cdt_list s' x)) \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node s' x, interrupt_states s' x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues s' d p)) \<and> (\<forall>x. memory_integrity X aag x (tcb_states_of_state st) (tcb_states_of_state s') (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state s') x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (tcb_states_of_state st) (tcb_states_of_state s') (device_state (machine_state st) x) (device_state (machine_state s') x)) \<and> (\<forall>x a. asid_table st (asid_high_bits_of a) = asid_table s' (asid_high_bits_of a) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of a \<longrightarrow> pasASIDAbs aag asid' \<in> {pasSubject aag}))) and Q) s \<Longrightarrow> ?Q s proof (prove)
goal (2 subgoals):
 1. \<lbrace>?Q\<rbrace> f \<lbrace>\<lambda>_ s'. integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st s' \<and> (\<forall>x. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag x) (ekheap st x) (ekheap s' x)) \<and> integrity_cdt_state aag {pasSubject aag} st s' \<and> list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st s' \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node s' x, interrupt_states s' x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues s' d p)) \<and> (\<forall>x. memory_integrity X aag x (tcb_states_of_state st) (tcb_states_of_state s') (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state s') x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (tcb_states_of_state st) (tcb_states_of_state s') (device_state (machine_state st) x) (device_state (machine_state s') x)) \<and> (\<forall>x a. asid_table st (asid_high_bits_of a) = asid_table s' (asid_high_bits_of a) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of a \<longrightarrow> pasASIDAbs aag asid' \<in> {pasSubject aag}))\<rbrace>
 2. \<And>s. ((\<lambda>s'. integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st s' \<and> (\<forall>x. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag x) (ekheap st x) (ekheap s' x)) \<and> integrity_cdt_state aag {pasSubject aag} st s' \<and> (\<forall>x. cdt_list_integrity aag (cdt st) (tcb_states_of_state st) x (cdt_list st x) (cdt_list s' x)) \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node s' x, interrupt_states s' x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues s' d p)) \<and> (\<forall>x. memory_integrity X aag x (tcb_states_of_state st) (tcb_states_of_state s') (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state s') x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (tcb_states_of_state st) (tcb_states_of_state s') (device_state (machine_state st) x) (device_state (machine_state s') x)) \<and> (\<forall>x a. asid_table st (asid_high_bits_of a) = asid_table s' (asid_high_bits_of a) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of a \<longrightarrow> pasASIDAbs aag asid' \<in> {pasSubject aag}))) and Q) s \<Longrightarrow> ?Q s proof (prove)
goal (3 subgoals):
 1. \<And>x. \<lbrace>?Q3 x\<rbrace> f \<lbrace>\<lambda>_ a. integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st a \<and> (\<forall>xa. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag xa) (ekheap st xa) (x xa)) \<and> integrity_cdt_state aag {pasSubject aag} st a \<and> list_integ (\<lambda>a. cdt_change_allowed' aag a st) st a \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node a x, interrupt_states a x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues a d p)) \<and> (\<forall>x. memory_integrity X aag x (tcb_states_of_state st) (tcb_states_of_state a) (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state a) x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (tcb_states_of_state st) (tcb_states_of_state a) (device_state (machine_state st) x) (device_state (machine_state a) x)) \<and> (\<forall>x aa. asid_table st (asid_high_bits_of aa) = asid_table a (asid_high_bits_of aa) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of aa \<longrightarrow> pasASIDAbs aag asid' \<in> {pasSubject aag}))\<rbrace>
 2. \<And>P. \<lbrace>\<lambda>s'. P (ekheap s')\<rbrace> f \<lbrace>\<lambda>_ s'. P (ekheap s')\<rbrace>
 3. \<And>s. ((\<lambda>s'. integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st s' \<and> (\<forall>x. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag x) (ekheap st x) (ekheap s' x)) \<and> integrity_cdt_state aag {pasSubject aag} st s' \<and> (\<forall>x. cdt_list_integrity aag (cdt st) (tcb_states_of_state st) x (cdt_list st x) (cdt_list s' x)) \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node s' x, interrupt_states s' x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues s' d p)) \<and> (\<forall>x. memory_integrity X aag x (tcb_states_of_state st) (tcb_states_of_state s') (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state s') x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (tcb_states_of_state st) (tcb_states_of_state s') (device_state (machine_state st) x) (device_state (machine_state s') x)) \<and> (\<forall>x a. asid_table st (asid_high_bits_of a) = asid_table s' (asid_high_bits_of a) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of a \<longrightarrow> pasASIDAbs aag asid' \<in> {pasSubject aag}))) and Q) s \<Longrightarrow> ?Q3 (ekheap s) s proof (prove)
goal (3 subgoals):
 1. \<And>x. \<lbrace>?Q3 x\<rbrace> f \<lbrace>\<lambda>_ a. integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st a \<and> (\<forall>xa. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag xa) (ekheap st xa) (x xa)) \<and> (\<forall>aa b. cdt_integrity aag (cdt st) (\<lambda>a. map_option tcb_state (case kheap st a of None \<Rightarrow> None | Some (TCB x) \<Rightarrow> Some x | Some _ \<Rightarrow> None)) (aa, b) (cdt st (aa, b), is_original_cap st (aa, b)) (cdt a (aa, b), is_original_cap a (aa, b))) \<and> list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (\<lambda>a. map_option tcb_state (case kheap st a of None \<Rightarrow> None | Some (TCB x) \<Rightarrow> Some x | Some _ \<Rightarrow> None))) st a \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node a x, interrupt_states a x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues a d p)) \<and> (\<forall>x. memory_integrity X aag x (\<lambda>a. map_option tcb_state (case kheap st a of None \<Rightarrow> None | Some (TCB x) \<Rightarrow> Some x | Some _ \<Rightarrow> None)) (\<lambda>aa. map_option tcb_state (case kheap a aa of None \<Rightarrow> None | Some (TCB x) \<Rightarrow> Some x | Some _ \<Rightarrow> None)) (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state a) x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (\<lambda>a. map_option tcb_state (case kheap st a of None \<Rightarrow> None | Some (TCB x) \<Rightarrow> Some x | Some _ \<Rightarrow> None)) (\<lambda>aa. map_option tcb_state (case kheap a aa of None \<Rightarrow> None | Some (TCB x) \<Rightarrow> Some x | Some _ \<Rightarrow> None)) (device_state (machine_state st) x) (device_state (machine_state a) x)) \<and> (\<forall>aa. asid_table st (asid_high_bits_of aa) = asid_table a (asid_high_bits_of aa) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of aa \<longrightarrow> is_subject_asid aag asid'))\<rbrace>
 2. \<And>P. \<lbrace>\<lambda>s'. P (ekheap s')\<rbrace> f \<lbrace>\<lambda>_ s'. P (ekheap s')\<rbrace>
 3. \<And>s. ((\<lambda>s'. integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st s' \<and> (\<forall>x. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag x) (ekheap st x) (ekheap s' x)) \<and> integrity_cdt_state aag {pasSubject aag} st s' \<and> (\<forall>x. cdt_list_integrity aag (cdt st) (tcb_states_of_state st) x (cdt_list st x) (cdt_list s' x)) \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node s' x, interrupt_states s' x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues s' d p)) \<and> (\<forall>x. memory_integrity X aag x (tcb_states_of_state st) (tcb_states_of_state s') (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state s') x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (tcb_states_of_state st) (tcb_states_of_state s') (device_state (machine_state st) x) (device_state (machine_state s') x)) \<and> (\<forall>x a. asid_table st (asid_high_bits_of a) = asid_table s' (asid_high_bits_of a) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of a \<longrightarrow> pasASIDAbs aag asid' \<in> {pasSubject aag}))) and Q) s \<Longrightarrow> ?Q3 (ekheap s) s proof (prove)
goal (1 subgoal):
 1. \<And>s. ((\<lambda>s'. integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st s' \<and> (\<forall>x. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag x) (ekheap st x) (ekheap s' x)) \<and> integrity_cdt_state aag {pasSubject aag} st s' \<and> (\<forall>x. cdt_list_integrity aag (cdt st) (tcb_states_of_state st) x (cdt_list st x) (cdt_list s' x)) \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node s' x, interrupt_states s' x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues s' d p)) \<and> (\<forall>x. memory_integrity X aag x (tcb_states_of_state st) (tcb_states_of_state s') (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state s') x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (tcb_states_of_state st) (tcb_states_of_state s') (device_state (machine_state st) x) (device_state (machine_state s') x)) \<and> (\<forall>x a. asid_table st (asid_high_bits_of a) = asid_table s' (asid_high_bits_of a) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of a \<longrightarrow> pasASIDAbs aag asid' \<in> {pasSubject aag}))) and Q) s \<Longrightarrow> integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st s \<and> (\<forall>x. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag x) (ekheap st x) (ekheap s x)) \<and> (\<forall>a b. cdt_integrity aag (cdt st) (\<lambda>a. map_option tcb_state (case kheap st a of None \<Rightarrow> None | Some (TCB a) \<Rightarrow> Some a | Some _ \<Rightarrow> None)) (a, b) (cdt st (a, b), is_original_cap st (a, b)) (cdt s (a, b), is_original_cap s (a, b))) \<and> (list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (\<lambda>p. map_option tcb_state (case kheap st p of None \<Rightarrow> None | Some (TCB tcb) \<Rightarrow> Some tcb | Some _ \<Rightarrow> None))) st and Q) s \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node s x, interrupt_states s x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues s d p)) \<and> (\<forall>x. memory_integrity X aag x (\<lambda>a. map_option tcb_state (case kheap st a of None \<Rightarrow> None | Some (TCB a) \<Rightarrow> Some a | Some _ \<Rightarrow> None)) (\<lambda>a. map_option tcb_state (case kheap s a of None \<Rightarrow> None | Some (TCB a) \<Rightarrow> Some a | Some _ \<Rightarrow> None)) (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state s) x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (\<lambda>a. map_option tcb_state (case kheap st a of None \<Rightarrow> None | Some (TCB a) \<Rightarrow> Some a | Some _ \<Rightarrow> None)) (\<lambda>a. map_option tcb_state (case kheap s a of None \<Rightarrow> None | Some (TCB a) \<Rightarrow> Some a | Some _ \<Rightarrow> None)) (device_state (machine_state st) x) (device_state (machine_state s) x)) \<and> (\<forall>a. asid_table st (asid_high_bits_of a) = asid_table s (asid_high_bits_of a) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of a \<longrightarrow> is_subject_asid aag asid')) proof (prove)
goal (1 subgoal):
 1. \<And>s. ((\<lambda>s'. integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st s' \<and> (\<forall>x. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag x) (ekheap st x) (ekheap s' x)) \<and> integrity_cdt_state aag {pasSubject aag} st s' \<and> list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st s' \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node s' x, interrupt_states s' x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues s' d p)) \<and> (\<forall>x. memory_integrity X aag x (tcb_states_of_state st) (tcb_states_of_state s') (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state s') x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (tcb_states_of_state st) (tcb_states_of_state s') (device_state (machine_state st) x) (device_state (machine_state s') x)) \<and> (\<forall>x a. asid_table st (asid_high_bits_of a) = asid_table s' (asid_high_bits_of a) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of a \<longrightarrow> pasASIDAbs aag asid' \<in> {pasSubject aag}))) and Q) s \<Longrightarrow> integrity_obj_state aag (pasMayActivate aag) {pasSubject aag} st s \<and> (\<forall>x. integrity_eobj aag {pasSubject aag} (pasObjectAbs aag x) (ekheap st x) (ekheap s x)) \<and> (\<forall>a b. cdt_integrity aag (cdt st) (\<lambda>a. map_option tcb_state (case kheap st a of None \<Rightarrow> None | Some (TCB a) \<Rightarrow> Some a | Some _ \<Rightarrow> None)) (a, b) (cdt st (a, b), is_original_cap st (a, b)) (cdt s (a, b), is_original_cap s (a, b))) \<and> (list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (\<lambda>p. map_option tcb_state (case kheap st p of None \<Rightarrow> None | Some (TCB tcb) \<Rightarrow> Some tcb | Some _ \<Rightarrow> None))) st and Q) s \<and> (\<forall>x. integrity_interrupts aag {pasSubject aag} x (interrupt_irq_node st x, interrupt_states st x) (interrupt_irq_node s x, interrupt_states s x)) \<and> (\<forall>d p. integrity_ready_queues aag {pasSubject aag} (pasDomainAbs aag d) (ready_queues st d p) (ready_queues s d p)) \<and> (\<forall>x. memory_integrity X aag x (\<lambda>a. map_option tcb_state (case kheap st a of None \<Rightarrow> None | Some (TCB a) \<Rightarrow> Some a | Some _ \<Rightarrow> None)) (\<lambda>a. map_option tcb_state (case kheap s a of None \<Rightarrow> None | Some (TCB a) \<Rightarrow> Some a | Some _ \<Rightarrow> None)) (auth_ipc_buffers st) (underlying_memory (machine_state st) x) (underlying_memory (machine_state s) x)) \<and> (\<forall>x. integrity_device aag {pasSubject aag} x (\<lambda>a. map_option tcb_state (case kheap st a of None \<Rightarrow> None | Some (TCB a) \<Rightarrow> Some a | Some _ \<Rightarrow> None)) (\<lambda>a. map_option tcb_state (case kheap s a of None \<Rightarrow> None | Some (TCB a) \<Rightarrow> Some a | Some _ \<Rightarrow> None)) (device_state (machine_state st) x) (device_state (machine_state s) x)) \<and> (\<forall>a. asid_table st (asid_high_bits_of a) = asid_table s (asid_high_bits_of a) \<or> (\<forall>asid'. asid' \<noteq> 0 \<and> asid_high_bits_of asid' = asid_high_bits_of a \<longrightarrow> is_subject_asid aag asid')) proof (prove)
goal:
No subgoals!