theory CSpace_R

lemma setupReplyMaster_invs'[wp]:
  "\<lbrace>invs' and tcb_at' t and ex_nonz_cap_to' t\<rbrace>
     setupReplyMaster t
   \<lbrace>\<lambda>rv. invs'\<rbrace>" apply (simp add: invs'_def valid_state'_def) apply (rule hoare_pre) apply (wp setupReplyMaster_valid_pspace' sch_act_wf_lift tcb_in_cur_domain'_lift ct_idle_or_in_cur_domain'_lift
             valid_queues_lift cur_tcb_lift valid_queues_lift' hoare_vcg_disj_lift
             valid_irq_node_lift | simp)+ apply (clarsimp simp: ex_nonz_tcb_cte_caps' valid_pspace'_def
                        objBits_simps' tcbReplySlot_def
                        ex_nonz_cap_not_global' dom_def) done

(* Proof state trace *)
proof (prove)
goal (1 subgoal):
 1. \<lbrace>invs' and tcb_at' t and ex_nonz_cap_to' t\<rbrace> setupReplyMaster t \<lbrace>\<lambda>rv. invs'\<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 tcb_at' t and ex_nonz_cap_to' t\<rbrace> setupReplyMaster t \<lbrace>\<lambda>rv. (\<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'\<rbrace> proof (prove)
goal (2 subgoals):
 1. \<lbrace>?Q\<rbrace> setupReplyMaster t \<lbrace>\<lambda>rv. (\<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'\<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 tcb_at' t and ex_nonz_cap_to' t) s \<Longrightarrow> ?Q s proof (prove)
goal (1 subgoal):
 1. \<And>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' s \<and> tcb_at' t s \<and> ex_nonz_cap_to' t s \<Longrightarrow> ex_cte_cap_wp_to' (\<lambda>_. True) (t + 2 ^ objBits undefined * tcbReplySlot) s \<and> t \<notin> global_refs' s \<and> valid_objs' s \<and> ksDomSchedule (KernelInit_H.newKernelState undefined) \<noteq> [] \<and> valid_mdb' s \<and> valid_objs' s proof (prove)
goal:
No subgoals!