theory ArchAcc_R

lemma dmo_clearMemory_invs'[wp]:
  "\<lbrace>invs'\<rbrace> doMachineOp (clearMemory w sz) \<lbrace>\<lambda>_. invs'\<rbrace>" apply (simp add: doMachineOp_def split_def) apply wp apply (clarsimp simp: invs'_def valid_state'_def) apply (rule conjI) apply (simp add: valid_irq_masks'_def, elim allEI, clarsimp) apply (drule use_valid) apply (rule no_irq_clearMemory[simplified no_irq_def, rule_format]) apply simp_all apply (drule clearMemory_vms') apply fastforce done

(* Proof state trace *)
proof (prove)
goal (1 subgoal):
 1. \<lbrace>invs'\<rbrace> doMachineOp (clearMemory w sz) \<lbrace>\<lambda>_. invs'\<rbrace> proof (prove)
goal (1 subgoal):
 1. \<lbrace>invs'\<rbrace> do ms <- gets ksMachineState;
p <- select_f (clearMemory w sz ms);
modify (ksMachineState_update (\<lambda>_. snd p))
od \<lbrace>\<lambda>_. invs'\<rbrace> proof (prove)
goal (1 subgoal):
 1. \<And>s. invs' s \<Longrightarrow> \<forall>x\<in>fst (clearMemory w sz (ksMachineState s)). invs' (s\<lparr>ksMachineState := snd x\<rparr>) proof (prove)
goal (1 subgoal):
 1. \<And>s b. \<lbrakk>((), b) \<in> fst (clearMemory w sz (ksMachineState s)); valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_irq_states' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s\<rbrakk> \<Longrightarrow> valid_irq_masks' (intStateIRQTable (ksInterruptState s)) (irq_masks b) \<and> valid_machine_state' (s\<lparr>ksMachineState := b\<rparr>) proof (prove)
goal (2 subgoals):
 1. \<And>s b. \<lbrakk>((), b) \<in> fst (clearMemory w sz (ksMachineState s)); valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_irq_states' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s\<rbrakk> \<Longrightarrow> valid_irq_masks' (intStateIRQTable (ksInterruptState s)) (irq_masks b)
 2. \<And>s b. \<lbrakk>((), b) \<in> fst (clearMemory w sz (ksMachineState s)); valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_irq_states' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s\<rbrakk> \<Longrightarrow> valid_machine_state' (s\<lparr>ksMachineState := b\<rparr>) proof (prove)
goal (2 subgoals):
 1. \<And>s b irq. \<lbrakk>((), b) \<in> fst (clearMemory w sz (ksMachineState s)); valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s; intStateIRQTable (ksInterruptState s) irq = irqstate.IRQInactive; irq_masks (ksMachineState s) irq\<rbrakk> \<Longrightarrow> irq_masks b irq
 2. \<And>s b. \<lbrakk>((), b) \<in> fst (clearMemory w sz (ksMachineState s)); valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_irq_states' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s\<rbrakk> \<Longrightarrow> valid_machine_state' (s\<lparr>ksMachineState := b\<rparr>) proof (prove)
goal (4 subgoals):
 1. \<And>s b irq. \<lbrakk>valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s; intStateIRQTable (ksInterruptState s) irq = irqstate.IRQInactive; irq_masks (ksMachineState s) irq\<rbrakk> \<Longrightarrow> \<lbrace>?P67 s b irq\<rbrace> clearMemory w sz \<lbrace>?Q67 s b irq\<rbrace>
 2. \<And>s b irq. \<lbrakk>valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s; intStateIRQTable (ksInterruptState s) irq = irqstate.IRQInactive; irq_masks (ksMachineState s) irq\<rbrakk> \<Longrightarrow> ?P67 s b irq (ksMachineState s)
 3. \<And>s b irq. \<lbrakk>valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s; intStateIRQTable (ksInterruptState s) irq = irqstate.IRQInactive; irq_masks (ksMachineState s) irq; ?Q67 s b irq () b\<rbrakk> \<Longrightarrow> irq_masks b irq
 4. \<And>s b. \<lbrakk>((), b) \<in> fst (clearMemory w sz (ksMachineState s)); valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_irq_states' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s\<rbrakk> \<Longrightarrow> valid_machine_state' (s\<lparr>ksMachineState := b\<rparr>) proof (prove)
goal (3 subgoals):
 1. \<And>s b irq. \<lbrakk>valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s; intStateIRQTable (ksInterruptState s) irq = irqstate.IRQInactive; irq_masks (ksMachineState s) irq\<rbrakk> \<Longrightarrow> ?P71 s b irq (irq_masks (ksMachineState s))
 2. \<And>s b irq. \<lbrakk>valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s; intStateIRQTable (ksInterruptState s) irq = irqstate.IRQInactive; irq_masks (ksMachineState s) irq; ?P71 s b irq (irq_masks b)\<rbrakk> \<Longrightarrow> irq_masks b irq
 3. \<And>s b. \<lbrakk>((), b) \<in> fst (clearMemory w sz (ksMachineState s)); valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_irq_states' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s\<rbrakk> \<Longrightarrow> valid_machine_state' (s\<lparr>ksMachineState := b\<rparr>) proof (prove)
goal (1 subgoal):
 1. \<And>s b. \<lbrakk>((), b) \<in> fst (clearMemory w sz (ksMachineState s)); valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_irq_states' s; valid_machine_state' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s\<rbrakk> \<Longrightarrow> valid_machine_state' (s\<lparr>ksMachineState := b\<rparr>) proof (prove)
goal (1 subgoal):
 1. \<And>s b. \<lbrakk>((), b) \<in> fst (clearMemory w sz (ksMachineState s)); valid_pspace' s; sch_act_wf (ksSchedulerAction s) s; Invariants_H.valid_queues s; sym_refs (state_refs_of' s); if_live_then_nonz_cap' s; if_unsafe_then_cap' s; valid_idle' s; valid_global_refs' s; valid_arch_state' s; valid_irq_node' (irq_node' s) s; valid_irq_handlers' s; valid_irq_states' s; irqs_masked' s; valid_queues' s; ct_not_inQ s; ct_idle_or_in_cur_domain' s; valid_pde_mappings' s; pspace_domain_valid s; ksCurDomain s \<le> maxDomain; ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> []; \<forall>x\<in>set (ksDomSchedule (KernelInit_H.newKernelState undefined)). dschDomain x \<le> maxDomain \<and> 0 < dschLength x; ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined); ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)); untyped_ranges_zero' s; cur_tcb' s; \<forall>x\<in>fst (clearMemory (?ptr74 s b) (?bits74 s b) (ksMachineState s)). valid_machine_state' (s\<lparr>ksMachineState := snd x\<rparr>)\<rbrakk> \<Longrightarrow> valid_machine_state' (s\<lparr>ksMachineState := b\<rparr>) proof (prove)
goal:
No subgoals!