theory Interrupt_R

lemma tcbSchedAppend_invs_but_ct_not_inQ':
  "\<lbrace>invs' and st_tcb_at' runnable' t \<rbrace>
   tcbSchedAppend t \<lbrace>\<lambda>_. all_invs_but_ct_not_inQ'\<rbrace>" apply (simp add: invs'_def valid_state'_def) apply (rule hoare_pre) apply (wp sch_act_wf_lift valid_irq_node_lift irqs_masked_lift
             valid_irq_handlers_lift' cur_tcb_lift ct_idle_or_in_cur_domain'_lift2
             untyped_ranges_zero_lift
        | simp add: cteCaps_of_def o_def
        | fastforce elim!: st_tcb_ex_cap'' split: thread_state.split_asm)+ done

(* Proof state trace *)
proof (prove)
goal (1 subgoal):
 1. \<lbrace>invs' and st_tcb_at' runnable' t\<rbrace> tcbSchedAppend t \<lbrace>\<lambda>_ s. valid_pspace' s \<and> sch_act_wf (ksSchedulerAction s) s \<and> Invariants_H.valid_queues s \<and> sym_refs (state_refs_of' s) \<and> if_live_then_nonz_cap' s \<and> if_unsafe_then_cap' s \<and> valid_idle' s \<and> valid_global_refs' s \<and> valid_arch_state' s \<and> valid_irq_node' (irq_node' s) s \<and> valid_irq_handlers' s \<and> valid_irq_states' s \<and> irqs_masked' s \<and> valid_machine_state' s \<and> cur_tcb' s \<and> valid_queues' s \<and> ct_idle_or_in_cur_domain' s \<and> valid_pde_mappings' s \<and> pspace_domain_valid s \<and> ksCurDomain s \<le> maxDomain \<and> valid_dom_schedule' s \<and> untyped_ranges_zero' s\<rbrace> proof (prove)
goal (1 subgoal):
 1. \<lbrace>(\<lambda>s. valid_pspace' s \<and> sch_act_wf (ksSchedulerAction s) s \<and> Invariants_H.valid_queues s \<and> sym_refs (state_refs_of' s) \<and> if_live_then_nonz_cap' s \<and> if_unsafe_then_cap' s \<and> valid_idle' s \<and> valid_global_refs' s \<and> valid_arch_state' s \<and> valid_irq_node' (irq_node' s) s \<and> valid_irq_handlers' s \<and> valid_irq_states' s \<and> valid_machine_state' s \<and> irqs_masked' s \<and> valid_queues' s \<and> ct_not_inQ s \<and> ct_idle_or_in_cur_domain' s \<and> valid_pde_mappings' s \<and> pspace_domain_valid s \<and> ksCurDomain s \<le> maxDomain \<and> ksDomSchedule s \<noteq> [] \<and> (\<forall>x\<in>set (ksDomSchedule s). dschDomain x \<le> maxDomain \<and> 0 < dschLength x) \<and> ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined) \<and> ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)) \<and> untyped_ranges_zero' s) and cur_tcb' and st_tcb_at' runnable' t\<rbrace> tcbSchedAppend t \<lbrace>\<lambda>_ s. valid_pspace' s \<and> sch_act_wf (ksSchedulerAction s) s \<and> Invariants_H.valid_queues s \<and> sym_refs (state_refs_of' s) \<and> if_live_then_nonz_cap' s \<and> if_unsafe_then_cap' s \<and> valid_idle' s \<and> valid_global_refs' s \<and> valid_arch_state' s \<and> valid_irq_node' (irq_node' s) s \<and> valid_irq_handlers' s \<and> valid_irq_states' s \<and> irqs_masked' s \<and> valid_machine_state' s \<and> cur_tcb' s \<and> valid_queues' s \<and> ct_idle_or_in_cur_domain' s \<and> valid_pde_mappings' s \<and> pspace_domain_valid s \<and> ksCurDomain s \<le> maxDomain \<and> ksDomSchedule s \<noteq> [] \<and> (\<forall>x\<in>set (ksDomSchedule s). dschDomain x \<le> maxDomain \<and> 0 < dschLength x) \<and> ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined) \<and> ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)) \<and> untyped_ranges_zero' s\<rbrace> proof (prove)
goal (2 subgoals):
 1. \<lbrace>?Q\<rbrace> tcbSchedAppend t \<lbrace>\<lambda>_ s. valid_pspace' s \<and> sch_act_wf (ksSchedulerAction s) s \<and> Invariants_H.valid_queues s \<and> sym_refs (state_refs_of' s) \<and> if_live_then_nonz_cap' s \<and> if_unsafe_then_cap' s \<and> valid_idle' s \<and> valid_global_refs' s \<and> valid_arch_state' s \<and> valid_irq_node' (irq_node' s) s \<and> valid_irq_handlers' s \<and> valid_irq_states' s \<and> irqs_masked' s \<and> valid_machine_state' s \<and> cur_tcb' s \<and> valid_queues' s \<and> ct_idle_or_in_cur_domain' s \<and> valid_pde_mappings' s \<and> pspace_domain_valid s \<and> ksCurDomain s \<le> maxDomain \<and> ksDomSchedule s \<noteq> [] \<and> (\<forall>x\<in>set (ksDomSchedule s). dschDomain x \<le> maxDomain \<and> 0 < dschLength x) \<and> ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined) \<and> ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)) \<and> untyped_ranges_zero' s\<rbrace>
 2. \<And>s. ((\<lambda>s. valid_pspace' s \<and> sch_act_wf (ksSchedulerAction s) s \<and> Invariants_H.valid_queues s \<and> sym_refs (state_refs_of' s) \<and> if_live_then_nonz_cap' s \<and> if_unsafe_then_cap' s \<and> valid_idle' s \<and> valid_global_refs' s \<and> valid_arch_state' s \<and> valid_irq_node' (irq_node' s) s \<and> valid_irq_handlers' s \<and> valid_irq_states' s \<and> valid_machine_state' s \<and> irqs_masked' s \<and> valid_queues' s \<and> ct_not_inQ s \<and> ct_idle_or_in_cur_domain' s \<and> valid_pde_mappings' s \<and> pspace_domain_valid s \<and> ksCurDomain s \<le> maxDomain \<and> ksDomSchedule s \<noteq> [] \<and> (\<forall>x\<in>set (ksDomSchedule s). dschDomain x \<le> maxDomain \<and> 0 < dschLength x) \<and> ksDomSchedule s = ksDomSchedule (KernelInit_H.newKernelState undefined) \<and> ksDomScheduleIdx s < length (ksDomSchedule (KernelInit_H.newKernelState undefined)) \<and> untyped_ranges_zero' s) and cur_tcb' and st_tcb_at' runnable' t) s \<Longrightarrow> ?Q s proof (prove)
goal:
No subgoals!