no_shm_selinux/Enrich2.thy
changeset 82 0a68c605ae79
child 83 e79e3a8a4ceb
equal deleted inserted replaced
81:1ac0c3031ed2 82:0a68c605ae79
       
     1 theory Enrich
       
     2 imports Main Flask Static Init_prop Valid_prop Tainted_prop Delete_prop Co2sobj_prop S2ss_prop S2ss_prop2
       
     3  Temp Enrich
       
     4 begin
       
     5 
       
     6 context tainting_s begin
       
     7 
       
     8 lemma get_parentfs_ctxts_prop:
       
     9   "\<lbrakk>get_parentfs_ctxts s (a # f) = Some ctxts; sectxt_of_obj s (O_dir f) = Some ctxt; valid s\<rbrakk>
       
    10    \<Longrightarrow> ctxt \<in> set (ctxts)"
       
    11 apply (induct f)
       
    12 apply (auto split:option.splits)
       
    13 done
       
    14 
       
    15 lemma search_check_allp_intro:
       
    16   "\<lbrakk>search_check s sp pf; get_parentfs_ctxts s pf = Some ctxts; valid s; is_dir s pf\<rbrakk>
       
    17    \<Longrightarrow> search_check_allp sp (set ctxts)"
       
    18 apply (case_tac pf)
       
    19 apply (simp split:option.splits if_splits add:search_check_allp_def)
       
    20 apply (rule ballI)
       
    21 apply (auto simp:search_check_ctxt_def search_check_dir_def split:if_splits option.splits)
       
    22 apply (auto simp:search_check_allp_def search_check_file_def)
       
    23 apply (frule is_dir_not_file, simp)
       
    24 done
       
    25 
       
    26 lemma search_check_leveling_f:
       
    27   "\<lbrakk>search_check s sp pf; parent f = Some pf; is_file s f; valid s;
       
    28     sectxt_of_obj s (O_file f) = Some fctxt; search_check_file sp fctxt\<rbrakk>
       
    29    \<Longrightarrow> search_check s sp f"
       
    30 apply (case_tac f, simp+)
       
    31 apply (auto split:option.splits simp:search_check_ctxt_def)
       
    32 apply (frule parentf_is_dir_prop2, simp)
       
    33 apply (erule get_pfs_secs_prop, simp)
       
    34 apply (erule_tac search_check_allp_intro, simp_all)
       
    35 apply (simp add:parentf_is_dir_prop2)
       
    36 done
       
    37 
       
    38 lemma enrich_proc_prop:
       
    39   "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk>
       
    40    \<Longrightarrow> valid (enrich_proc s p p') \<and> 
       
    41        (\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and> 
       
    42        (\<forall> obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive (enrich_proc s p p') obj) \<and>
       
    43        (files_hung_by_del (enrich_proc s p p') = files_hung_by_del s) \<and> 
       
    44        (\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp) \<and>
       
    45        (\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and> 
       
    46        (\<forall> q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and> 
       
    47        (\<forall> tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f) \<and>
       
    48        (\<forall> tp fd flags. flags_of_proc_fd s tp fd = Some flags \<longrightarrow> 
       
    49                       flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and>
       
    50        (\<forall> q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q) \<and>
       
    51        (\<forall> tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and>
       
    52        (cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and>
       
    53        (\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)"
       
    54 proof (induct s)
       
    55   case Nil
       
    56   thus ?case by (auto simp:is_created_proc_def)
       
    57 next
       
    58   case (Cons e s)
       
    59   hence vd_cons: "valid (e # s)" and created_cons: "is_created_proc (e # s) p"
       
    60     and all_procs_cons: "p' \<notin> all_procs (e # s)" and vd: "valid s" 
       
    61     and os: "os_grant s e" and grant: "grant s e"
       
    62     by (auto dest:vd_cons vt_grant_os vt_grant)
       
    63   from all_procs_cons have all_procs: "p' \<notin> all_procs s" by (case_tac e, auto)
       
    64   from Cons have pre: "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p') \<and>
       
    65      (\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and>
       
    66      (\<forall>obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive (enrich_proc s p p') obj) \<and>
       
    67      files_hung_by_del (enrich_proc s p p') = files_hung_by_del s \<and>
       
    68      (\<forall>tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp) \<and>
       
    69      (\<forall>f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and>
       
    70      (\<forall>q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and>
       
    71      (\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f) \<and>
       
    72      (\<forall>tp fd flags.
       
    73          flags_of_proc_fd s tp fd = Some flags \<longrightarrow> flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and>
       
    74      (\<forall>q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q) \<and>
       
    75      (\<forall>tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and>     
       
    76      (cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and>
       
    77      (\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)"
       
    78     using vd all_procs by auto
       
    79   have alive_pre: "is_created_proc s p \<Longrightarrow> (\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj)"
       
    80     using pre by simp
       
    81   hence curf_pre: "is_created_proc s p \<Longrightarrow> (\<forall>f. f \<in> current_files s \<longrightarrow> f \<in> current_files (enrich_proc s p p'))"
       
    82     using vd apply auto
       
    83     apply (drule is_file_or_dir, simp)
       
    84     apply (erule disjE)
       
    85     apply (erule_tac x = "O_file f" in allE, simp add:is_file_in_current)
       
    86     apply (erule_tac x = "O_dir f" in allE, simp add:is_dir_in_current)
       
    87     done
       
    88   have vd_enrich_cons: "valid (enrich_proc (e # s) p p')"
       
    89   proof-
       
    90     from pre have pre': "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p')" by simp
       
    91     have "is_created_proc s p \<Longrightarrow> valid (e # enrich_proc s p p')" 
       
    92       apply (frule pre')
       
    93       apply (erule_tac s = s in enrich_valid_intro_cons)
       
    94       apply (simp_all add:os grant vd pre)
       
    95       done  
       
    96     moreover have "\<And>f fds. \<lbrakk>valid (Execve p f fds # enrich_proc s p p'); is_created_proc s p; 
       
    97       valid (Execve p f fds # s); p' \<notin> all_procs s\<rbrakk>
       
    98       \<Longrightarrow> valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')"
       
    99     proof-
       
   100       fix f fds
       
   101       assume a1: "valid (Execve p f fds # enrich_proc s p p')" and a2: "is_created_proc s p"
       
   102         and a3: "valid (Execve p f fds # s)" and a0: "p' \<notin> all_procs s"
       
   103       have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
       
   104         and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
       
   105         and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
       
   106         and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> 
       
   107                                    file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
       
   108         and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
       
   109         and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
       
   110         using pre a2 by auto
       
   111       show "valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')"
       
   112       proof-
       
   113         from a0 a3 have a0': "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3)
       
   114         from a3 have grant: "grant s (Execve p f fds)" and os: "os_grant s (Execve p f fds)"
       
   115           by (auto dest:vt_grant_os vt_grant simp del:os_grant.simps)
       
   116         have f_in: "is_file (enrich_proc s p p') f" 
       
   117         proof-
       
   118           from pre a2
       
   119           have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj"
       
   120             by (auto)
       
   121           show ?thesis using a3 a4
       
   122             apply (erule_tac x = "O_file f" in allE)
       
   123             by (auto dest:vt_grant_os)
       
   124         qed
       
   125         moreover have a5: "proc_file_fds s p \<subseteq> proc_file_fds (Execve p f fds # enrich_proc s p p') p'" 
       
   126           using a3 a0'
       
   127           apply (frule_tac vt_grant_os)
       
   128           apply (auto simp:proc_file_fds_def)
       
   129           apply (rule_tac x = fa in exI)
       
   130           apply (erule enrich_proc_dup_ffd)
       
   131           apply (simp_all add:vd all_procs a2)
       
   132           done
       
   133         ultimately have "os_grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))"
       
   134           apply (auto simp:is_file_simps enrich_proc_dup_in a2 vd all_procs a1 enrich_proc_dup_ffds)
       
   135           done
       
   136         moreover have "grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))"
       
   137         proof-
       
   138           from grant obtain up rp tp uf rf tf 
       
   139             where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
       
   140             and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)" 
       
   141             by (simp split:option.splits, blast)
       
   142           with grant obtain pu nr nt where p3: "npctxt_execve (up, rp, tp) (uf, rf, tf) = Some (pu, nr, nt)"
       
   143             by (simp split:option.splits del:npctxt_execve.simps, blast)
       
   144           have p1': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)"
       
   145             using p1 dup_sp a1 a0'
       
   146             apply (simp add:sectxt_of_obj_simps)
       
   147             by (simp add:cp2sproc_def split:option.splits)
       
   148           from os have f_in': "is_file s f"  by simp 
       
   149           from vd os have "\<exists> sf. cf2sfile s f = Some sf"
       
   150             by (auto dest!:is_file_in_current current_file_has_sfile)
       
   151           hence p2': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)" 
       
   152             using f_in p2 cf2sf os a1
       
   153             apply (erule_tac x = f in allE)
       
   154             apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits)
       
   155             apply (case_tac f, simp)
       
   156             apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
       
   157             done 
       
   158           from dup_sfd a5 have "\<forall>fd. fd \<in> proc_file_fds s p \<longrightarrow> 
       
   159             cfd2sfd (Execve p f fds # enrich_proc s p p') p' fd = cfd2sfd s p fd"
       
   160             apply (rule_tac allI)
       
   161             apply (erule_tac x = fd in allE, clarsimp)
       
   162             apply (drule set_mp, simp)
       
   163             apply (auto simp:cfd2sfd_execve proc_file_fds_def a1)
       
   164             done
       
   165           hence "inherit_fds_check (Execve p f fds # enrich_proc s p p') (up, nr, nt) p' (fds \<inter> proc_file_fds s p)"
       
   166             using grant os p1 p2 p3 vd
       
   167             apply (clarsimp)
       
   168             apply (rule_tac s = s and p = p and fds = fds in enrich_inherit_fds_check_dup)
       
   169             apply simp_all
       
   170             done
       
   171           moreover have "search_check (Execve p f fds # enrich_proc s p p') (up, rp, tp) f"
       
   172             using p1 p2 p2' vd cf2sf f_in f_in' grant p3 f_in a1
       
   173             apply (rule_tac s = s in enrich_search_check)
       
   174             apply (simp_all add:is_file_simps)
       
   175             apply (rule allI, rule impI, erule_tac x = fa in allE, simp)
       
   176             apply (drule_tac ff = fa in cf2sfile_other')
       
   177             by (auto simp:a2 curf_pre)
       
   178           ultimately show ?thesis 
       
   179             using p1' p2' p3
       
   180             apply (simp split:option.splits)
       
   181             using grant p1 p2
       
   182             apply simp
       
   183             done
       
   184         qed
       
   185         ultimately show ?thesis using a1
       
   186           by (erule_tac valid.intros(2), auto)
       
   187       qed
       
   188     qed
       
   189     moreover have "\<And>tp fds. \<lbrakk>valid (Clone tp p fds # s); p' \<noteq> p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> 
       
   190       valid (Clone tp p' (fds \<inter> proc_file_fds s tp) # Clone tp p fds # s)"
       
   191       apply (frule vt_grant_os, frule vt_grant, drule not_all_procs_prop3)
       
   192       apply (rule valid.intros(2))
       
   193       apply (simp_all split:option.splits add:sectxt_of_obj_simps)
       
   194       apply (auto simp add:proc_file_fds_def)[1]
       
   195       apply (auto simp:inherit_fds_check_def sectxt_of_obj_simps sectxts_of_fds_def inherit_fds_check_ctxt_def)
       
   196       done
       
   197     moreover have "\<And>f flags fd opt. \<lbrakk>valid (Open p f flags fd opt # enrich_proc s p p'); 
       
   198       is_created_proc s p; valid (Open p f flags fd opt # s); p' \<notin> all_procs s\<rbrakk>
       
   199        \<Longrightarrow> valid (Open p' f (remove_create_flag flags) fd None # Open p f flags fd opt # enrich_proc s p p')"
       
   200     proof-
       
   201       fix f flags fd opt
       
   202       assume a1: "valid (Open p f flags fd opt # enrich_proc s p p')" and a2: "is_created_proc s p"
       
   203         and a3: "valid (Open p f flags fd opt # s)" and a4: "p' \<notin> all_procs s"
       
   204       have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
       
   205         and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
       
   206         and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
       
   207         and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> 
       
   208                                    file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
       
   209         and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
       
   210         and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
       
   211         using pre a2 by auto
       
   212       from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3 split:option.splits)
       
   213       have a5: "p' \<in> current_procs (enrich_proc s p p')" 
       
   214         using a2 a3 vd
       
   215         apply (erule_tac enrich_proc_dup_in)
       
   216         by (simp_all add:vd a4)
       
   217       have a6: "is_file (Open p f flags fd opt # enrich_proc s p p') f"
       
   218         using a1 a3
       
   219         by (auto simp:is_file_open dest:vt_grant_os)
       
   220       have a7: "fd \<notin> current_proc_fds (enrich_proc s p p') p'"
       
   221         using a2 a4 vd
       
   222         apply (simp add:enrich_proc_dup_ffds_eq_fds)
       
   223         apply (rule notI)
       
   224         apply (drule_tac p = p in file_fds_subset_pfds)
       
   225         apply (drule set_mp, simp)
       
   226         using a3
       
   227         apply (drule_tac vt_grant_os)
       
   228         apply (auto split:option.splits)
       
   229         done
       
   230       from a1 have a8: "valid (enrich_proc s p p')" by (erule_tac valid.cases, auto)
       
   231       from a3 have grant: "grant s (Open p f flags fd opt)" and os: "os_grant s (Open p f flags fd opt)"
       
   232         by (auto dest:vt_grant_os vt_grant)
       
   233       show "valid (Open p' f (remove_create_flag flags) fd None # Open p f flags fd opt # enrich_proc s p p')"
       
   234       proof (cases opt)
       
   235         case None
       
   236         have f_in: "is_file (enrich_proc s p p') f" 
       
   237         proof-
       
   238           from pre a2
       
   239           have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj"
       
   240             by (auto)
       
   241           show ?thesis using a3 a4 None
       
   242             apply (erule_tac x = "O_file f" in allE)
       
   243             by (auto dest:vt_grant_os)
       
   244         qed
       
   245         from grant None obtain up rp tp uf rf tf 
       
   246           where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
       
   247           and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)" 
       
   248           apply (simp split:option.splits)
       
   249           by (case_tac a, case_tac aa, blast)
       
   250         have p1': "sectxt_of_obj (Open p f flags fd opt # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)"
       
   251           using p1 dup_sp a1
       
   252           apply (simp add:sectxt_of_obj_simps)
       
   253           by (simp add:cp2sproc_def split:option.splits)
       
   254         from os None have f_in': "is_file s f" by simp 
       
   255         from vd os None have "\<exists> sf. cf2sfile s f = Some sf"
       
   256           by (auto dest!:is_file_in_current current_file_has_sfile)
       
   257         hence p2': "sectxt_of_obj (Open p f flags fd opt # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)" 
       
   258           using p2 cf2sf os a1 None f_in' vd f_in
       
   259           apply (erule_tac x = f in allE)
       
   260           apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits)
       
   261           apply (case_tac f, simp)
       
   262           apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
       
   263           done 
       
   264         have "search_check (Open p f flags fd opt # enrich_proc s p p') (up, rp, tp) f"
       
   265           using p1 p2 p2' vd cf2sf f_in f_in' grant f_in a1 None
       
   266           apply (rule_tac s = s in enrich_search_check)
       
   267           apply (simp_all add:is_file_simps)
       
   268           apply (rule allI, rule impI, erule_tac x = fa in allE, simp)
       
   269           apply (simp add:cf2sfile_open_none)
       
   270           done
       
   271         thus ?thesis using a0 a5 a6 a7 None a1
       
   272           apply (rule_tac valid.intros(2))
       
   273           apply (simp_all add:a1)
       
   274           apply (case_tac flags, simp add:is_creat_excl_flag_def)
       
   275           using p1' p2'
       
   276           apply simp
       
   277           using grant p1 p2
       
   278           apply (simp add:oflags_check_remove_create)
       
   279           done
       
   280       next
       
   281         case (Some inum)
       
   282         with os obtain pf where parent: "parent f = Some pf" by auto
       
   283         with grant Some obtain pu rp pt pfu pfr pft where
       
   284           p1: "sectxt_of_obj s (O_proc p) = Some (pu, rp, pt)" 
       
   285           and p2: "sectxt_of_obj s (O_dir pf) = Some (pfu, pfr, pft)"
       
   286           apply (simp split:option.splits)
       
   287           apply (case_tac a, case_tac aa, blast)
       
   288           done
       
   289         from p1 have p1': "sectxt_of_obj (enrich_proc s p p') (O_proc p) = Some (pu, rp, pt)"
       
   290           using cp2sp os
       
   291           apply (erule_tac x = p in allE)
       
   292           apply (auto split:option.splits simp:cp2sproc_def)
       
   293           done
       
   294         from os parent Some
       
   295         have pf_in: "is_dir s pf" by auto
       
   296         hence "\<exists> sf. cf2sfile s pf = Some sf" using vd
       
   297           by (auto dest!:is_dir_in_current current_file_has_sfile)
       
   298         from a1 parent Some have pf_in': "is_dir (enrich_proc s p p') pf" 
       
   299           apply (frule_tac vt_grant_os)
       
   300           by (clarsimp)
       
   301         have p2': "sectxt_of_obj (enrich_proc s p p') (O_dir pf) = Some (pfu, pfr, pft)"
       
   302         proof-
       
   303           have "cf2sfile (enrich_proc s p p') pf = cf2sfile s pf"
       
   304             using cf2sf pf_in
       
   305             apply (drule_tac is_dir_in_current)
       
   306             apply (erule_tac x = pf in allE)
       
   307             by simp
       
   308           with pf_in pf_in' p2 vd Some a8
       
   309           show ?thesis            
       
   310             apply (frule_tac is_dir_not_file)
       
   311             apply (frule_tac s = "enrich_proc s p p'" in is_dir_not_file)
       
   312             apply (simp add:cf2sfile_def)
       
   313             apply (case_tac pf, simp) 
       
   314             apply (simp add:sroot_def root_sec_remains)            
       
   315             by (auto split:option.splits dest!:current_has_sec' get_pfs_secs_prop' dest:parentf_is_dir_prop1)        
       
   316         qed
       
   317         from p1 have dup: "sectxt_of_obj (Open p f flags fd (Some inum) # enrich_proc s p p') (O_proc p') 
       
   318           = Some (pu, rp, pt)"
       
   319           using a1 Some
       
   320           apply (simp add:sec_open)
       
   321           using dup_sp
       
   322           apply (auto split:option.splits if_splits simp:cp2sproc_def)
       
   323           done        
       
   324         have nsf: "sectxt_of_obj (Open p f flags fd (Some inum) # enrich_proc s p p') (O_file f) 
       
   325           = Some (pu, R_object, type_transition pt pft C_file True)"
       
   326           using a1 Some p1 p2 parent p2' p1'
       
   327           by (simp add:sec_open)
       
   328         have "search_check (Open p f flags fd (Some inum) # enrich_proc s p p') (pu, rp, pt) f"
       
   329         proof-
       
   330           have "search_check (Open p f flags fd (Some inum) # enrich_proc s p p') (pu, rp, pt) pf"
       
   331             using grant Some parent p1 p2 vd a1 pf_in pf_in' p2'
       
   332             apply simp 
       
   333             apply (rule_tac s = s in enrich_search_check') 
       
   334             apply (simp_all add:is_dir_simps sectxt_of_obj_simps)
       
   335             apply (rule allI, rule impI)
       
   336             apply (case_tac "fa = f")
       
   337             using os Some
       
   338             apply simp
       
   339             apply (drule_tac f' = fa in cf2sfile_open)
       
   340             apply (simp add:current_files_simps)
       
   341             using curf_pre a2
       
   342             apply simp
       
   343             apply simp
       
   344             using cf2sf
       
   345             apply simp
       
   346             done
       
   347           moreover have "is_file (Open p f flags fd (Some inum) # enrich_proc s p p') f"
       
   348             using a1 Some
       
   349             by (simp add:is_file_open)
       
   350           ultimately 
       
   351           show ?thesis
       
   352             using parent a1 Some nsf
       
   353             apply (erule_tac search_check_leveling_f)
       
   354             apply (simp_all)
       
   355             apply (simp add:search_check_file_def)
       
   356             apply (simp add:permission_check.simps)
       
   357             sorry
       
   358         qed
       
   359         thus ?thesis using a0 a5 a6 a7 a1 Some
       
   360           apply (rule_tac valid.intros(2))
       
   361           apply (simp add:a1)
       
   362           apply simp
       
   363           apply (case_tac flags, simp add:is_creat_excl_flag_def)
       
   364           using grant p1 p2 parent dup nsf
       
   365           apply (simp add:oflags_check_remove_create)
       
   366           done
       
   367       qed
       
   368     qed
       
   369     moreover have "\<And>fd. \<lbrakk>valid (CloseFd p fd # enrich_proc s p p'); is_created_proc s p; 
       
   370       valid (CloseFd p fd # s); p' \<notin> all_procs s; fd \<in> proc_file_fds s p\<rbrakk>
       
   371       \<Longrightarrow> valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')"
       
   372     proof-
       
   373       fix fd
       
   374       assume a1: "valid (CloseFd p fd # enrich_proc s p p')" and a2: "is_created_proc s p" 
       
   375         and a3: "p' \<notin> all_procs s" and a4: "valid (CloseFd p fd # s)"
       
   376         and a5: "fd \<in> proc_file_fds s p"
       
   377       from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3)
       
   378       have "p' \<in> current_procs (enrich_proc s p p')" 
       
   379         using a2 a3 vd
       
   380         by (auto intro:enrich_proc_dup_in)
       
   381       moreover have "fd \<in> current_proc_fds (enrich_proc s p p') p'"      
       
   382         using a5 a2 a3 vd pre'
       
   383         apply (simp)
       
   384         apply (drule_tac s = "enrich_proc s p p'" and p = p' in file_fds_subset_pfds)
       
   385         apply (erule set_mp)
       
   386         apply (simp add:enrich_proc_dup_ffds)
       
   387         done
       
   388       ultimately show "valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')"
       
   389         apply (rule_tac valid.intros(2))
       
   390         apply (simp_all add:a1 a0 a2 pre')
       
   391         done
       
   392     qed
       
   393     moreover have "\<And> fd. \<lbrakk>valid (ReadFile p fd # enrich_proc s p p');
       
   394             is_created_proc s p; valid (ReadFile p fd # s); p' \<notin> all_procs s\<rbrakk>
       
   395            \<Longrightarrow> valid (ReadFile p' fd # ReadFile p fd # enrich_proc s p p')"
       
   396     proof-
       
   397       fix fd
       
   398       assume a1: "valid (ReadFile p fd # enrich_proc s p p')" and a2: "is_created_proc s p"
       
   399         and a3: "valid (ReadFile p fd # s)" and a4: "p' \<notin> all_procs s"
       
   400       from a3 have os: "os_grant s (ReadFile p fd)" and grant: "grant s (ReadFile p fd)"
       
   401         by (auto dest:vt_grant_os vt_grant)
       
   402       have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
       
   403         and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
       
   404         and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
       
   405         and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> 
       
   406                                    file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
       
   407         and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
       
   408         and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
       
   409         using pre a2 by auto
       
   410       have vd_enrich: "valid (enrich_proc s p p')" using a1 by (auto dest:valid.cases)
       
   411       show "valid (ReadFile p' fd # ReadFile p fd # enrich_proc s p p')"
       
   412       proof-
       
   413         have "os_grant (ReadFile p fd # enrich_proc s p p') (ReadFile p' fd)"
       
   414           using a1 a2 a4 vd os
       
   415           apply (clarsimp simp:current_files_simps enrich_proc_dup_in enrich_proc_dup_ffds_eq_fds)
       
   416           apply (simp add:proc_file_fds_def)
       
   417           apply (rule conjI)
       
   418           apply (rule_tac x = f in exI, simp add:enrich_proc_dup_ffd)
       
   419           using curf_pre
       
   420           apply (simp)
       
   421           apply (drule enrich_proc_dup_fflags)
       
   422           apply simp_all
       
   423           apply (erule disjE)
       
   424           apply auto
       
   425           apply (simp add:is_read_flag_def)
       
   426           done
       
   427         moreover have "grant (ReadFile p fd # enrich_proc s p p') (ReadFile p' fd)"
       
   428         proof-
       
   429           from grant obtain f sp sfd sf where p1: "file_of_proc_fd s p fd = Some f"
       
   430             and p2: "sectxt_of_obj s (O_proc p) = Some sp" 
       
   431             and p3: "sectxt_of_obj s (O_fd p fd) = Some sfd"
       
   432             and p4: "sectxt_of_obj s (O_file f) = Some sf"
       
   433             by (auto split:option.splits) 
       
   434           from os obtain flag where p0: "flags_of_proc_fd s p fd = Some flag"
       
   435             by auto
       
   436           from os have f_in_s: "f \<in> current_files s" using p1 by simp
       
   437           from p1 vd have isfile_s: "is_file s f" by (erule_tac file_of_pfd_is_file, simp)
       
   438           with alive_pre a2 have isfile_s': "is_file (enrich_proc s p p') f"
       
   439             apply simp
       
   440             apply (erule_tac x = "O_file f" in allE, simp)
       
   441             done          
       
   442           from p0 obtain flag' where p0': "flags_of_proc_fd (enrich_proc s p p') p' fd = Some flag'"
       
   443             and p0'': "(flag' = flag) \<or> (flag' = remove_create_flag flag)"
       
   444             using a2 a4 vd
       
   445             apply (drule_tac enrich_proc_dup_fflags)
       
   446             apply auto
       
   447             apply (case_tac flag, auto)
       
   448             apply (case_tac flag, auto)
       
   449             done            
       
   450           from p1 have p1': "file_of_proc_fd (enrich_proc s p p') p' fd = Some f"
       
   451             using a2 a4 vd
       
   452             by (simp add:enrich_proc_dup_ffd)
       
   453           from p2 have p2': "sectxt_of_obj (enrich_proc s p p') (O_proc p') = Some sp"
       
   454             using dup_sp
       
   455             by (auto simp:cp2sproc_def split:option.splits)
       
   456           from p3 p1 p1' p0 p0' os have p3': "sectxt_of_obj (enrich_proc s p p') (O_fd p' fd) = Some sfd"
       
   457             using dup_sfd
       
   458             apply (erule_tac x = fd in allE)
       
   459             apply (auto simp:proc_file_fds_def cfd2sfd_def split:option.splits)
       
   460             apply (drule current_file_has_sfile')
       
   461             apply (simp add:vd, simp)
       
   462             apply (drule current_file_has_sfile')
       
   463             apply (simp add:vd, simp)
       
   464             done
       
   465           from p4 have p4': "sectxt_of_obj (enrich_proc s p p') (O_file f) = Some sf" 
       
   466             using f_in_s cf2sf isfile_s isfile_s' a1 vd_enrich vd
       
   467             apply (erule_tac x = f in allE)
       
   468             apply (simp)
       
   469             apply (auto simp:cf2sfile_def split:option.splits 
       
   470               dest!:current_has_sec' get_pfs_secs_prop' dest:parentf_is_dir is_file_in_current)
       
   471             apply (case_tac f, simp, drule root_is_dir', simp, simp, simp)
       
   472             done
       
   473           show ?thesis using p1' p2' p3' p4' a1
       
   474             apply (simp add:sectxt_of_obj_simps)
       
   475             using grant p1 p2 p3 p4 
       
   476             apply simp
       
   477             done
       
   478         qed
       
   479         ultimately show ?thesis
       
   480           using a1
       
   481           by (erule_tac valid.intros(2), simp+)
       
   482       qed
       
   483     qed
       
   484     ultimately show ?thesis 
       
   485       using created_cons vd_cons all_procs_cons
       
   486       apply (case_tac e)
       
   487       apply (auto simp:is_created_proc_simps split:if_splits)
       
   488       done
       
   489   qed
       
   490   moreover have "\<forall>obj. alive (e # s) obj \<longrightarrow> alive (enrich_proc (e # s) p p') obj"
       
   491     sorry
       
   492   moreover have "\<forall>obj. enrich_not_alive (e # s) obj \<longrightarrow> enrich_not_alive (enrich_proc (e # s) p p') obj"
       
   493     sorry
       
   494   moreover have "files_hung_by_del (enrich_proc (e # s) p p') = files_hung_by_del (e # s)"
       
   495     sorry
       
   496   moreover have "\<forall>tp. tp \<in> current_procs (e # s) \<longrightarrow> cp2sproc (enrich_proc (e # s) p p') tp = cp2sproc (e # s) tp"
       
   497     sorry
       
   498   moreover have "\<forall>f. f \<in> current_files (e # s) \<longrightarrow> cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
       
   499     sorry
       
   500   moreover have "\<forall>q. q \<in> current_msgqs (e # s) \<longrightarrow> cq2smsgq (enrich_proc (e # s) p p') q = cq2smsgq (e # s) q"
       
   501     sorry
       
   502   moreover have "\<forall>tp fd f. file_of_proc_fd (e # s) tp fd = Some f \<longrightarrow> 
       
   503     file_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some f"
       
   504     sorry
       
   505   moreover have "\<forall>tp fd flags. flags_of_proc_fd (e # s) tp fd = Some flags \<longrightarrow>
       
   506         flags_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some flags"
       
   507     sorry
       
   508   moreover have "\<forall>q. msgs_of_queue (enrich_proc (e # s) p p') q = msgs_of_queue (e # s) q"
       
   509     sorry 
       
   510   moreover have "\<forall>tp fd. fd \<in> proc_file_fds (e # s) tp \<longrightarrow> 
       
   511     cfd2sfd (enrich_proc (e # s) p p') tp fd = cfd2sfd (e # s) tp fd"
       
   512     sorry 
       
   513   moreover have "cp2sproc (enrich_proc (e # s) p p') p' = cp2sproc (e # s) p"
       
   514   proof-
       
   515     from pre have b0: "is_created_proc s p \<Longrightarrow> cp2sproc (enrich_proc s p p') p' = cp2sproc s p" by simp
       
   516     have b1: "\<And> tp f fds. \<lbrakk>valid (enrich_proc (Execve tp f fds # s) p p'); valid (Execve tp f fds # s);
       
   517       is_created_proc (Execve tp f fds # s) p; p' \<notin> all_procs (Execve tp f fds # s)\<rbrakk>
       
   518       \<Longrightarrow> cp2sproc (enrich_proc (Execve tp f fds # s) p p') p' = cp2sproc (Execve tp f fds # s) p"
       
   519     proof-
       
   520       fix tp f fds
       
   521       assume a1: "valid (enrich_proc (Execve tp f fds # s) p p')"
       
   522       and a2: "valid (Execve tp f fds # s)" and a3: "is_created_proc (Execve tp f fds # s) p"
       
   523       and a4: "p' \<notin> all_procs (Execve tp f fds # s)"
       
   524       show "cp2sproc (enrich_proc (Execve tp f fds # s) p p') p' = cp2sproc (Execve tp f fds # s) p"
       
   525       proof (cases "tp = p")
       
   526         case True
       
   527         show ?thesis using True a1 a2 a3 a4
       
   528           thm not_all_procs_prop3
       
   529           apply (auto simp add:cp2sproc_execve is_created_proc_def split:option.splits dest!:current_has_sec' 
       
   530             dest:vt_grant_os not_all_procs_prop2 not_all_procs_prop3)
       
   531           
       
   532           sorry
       
   533       next
       
   534         case False
       
   535         show ?thesis sorry
       
   536       qed
       
   537     qed
       
   538     have b2: "\<And> tp fd. cp2sproc (enrich_proc (ReadFile tp fd # s) p p') p' = cp2sproc (ReadFile tp fd # s) p"
       
   539       sorry
       
   540     have b3: "\<And> tp. cp2sproc (enrich_proc (Exit tp # s) p p') p' = cp2sproc (Exit tp # s) p"
       
   541       sorry
       
   542     have b4: "\<And> tp tp'. cp2sproc (enrich_proc (Kill tp tp' # s) p p') p' = cp2sproc (Kill tp tp' # s) p"
       
   543       sorry
       
   544     have b5: "\<And> tp tp' fds. cp2sproc (enrich_proc (Clone tp tp' fds # s) p p') p' = 
       
   545       cp2sproc (Clone tp tp' fds # s) p"
       
   546       sorry
       
   547     have b6: "\<And> tp f flags fd opt. cp2sproc (enrich_proc (Open tp f flags fd opt # s) p p') p' =
       
   548       cp2sproc (Open tp f flags fd opt # s) p"
       
   549       sorry
       
   550     have b7: "\<And> tp fd. cp2sproc (enrich_proc (CloseFd tp fd # s) p p') p' = cp2sproc (CloseFd tp fd # s) p"
       
   551       sorry
       
   552     show ?thesis using vd_enrich_cons
       
   553       apply (case_tac e)
       
   554       apply (simp_all only:b1 b2 b3 b4 b5 b6 b7)
       
   555       using created_cons vd_enrich_cons vd_cons b0
       
   556       apply (auto simp:cp2sproc_other is_created_proc_def)
       
   557       done
       
   558   qed
       
   559   moreover have "\<forall> fd. fd \<in> proc_file_fds (e # s) p \<longrightarrow> 
       
   560     cfd2sfd (enrich_proc (e # s) p p') p' fd = cfd2sfd (e # s) p fd"
       
   561     sorry
       
   562   ultimately show ?case
       
   563     by simp
       
   564 qed
       
   565   
       
   566 
       
   567 lemma enrich_proc_valid:
       
   568   "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (enrich_proc s p p')"
       
   569 by (auto dest:enrich_proc_prop)
       
   570 
       
   571 lemma enrich_proc_valid:
       
   572   "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> " 
       
   573 
       
   574  
       
   575 
       
   576 lemma enrich_proc_tainted: 
       
   577   "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
       
   578    \<Longrightarrow> tainted (enrich_proc s p p') = (if (O_proc p \<in> tainted s) 
       
   579          then tainted s \<union> {O_proc p'} else tainted s)"
       
   580 apply (induct s)
       
   581 apply (simp add:is_created_proc_def)
       
   582 apply (frule vt_grant_os, frule vd_cons, simp)
       
   583 apply (frule enrich_proc_dup_in, simp+)
       
   584 apply (frule not_all_procs_prop3)
       
   585 apply (case_tac a)
       
   586 prefer 3
       
   587 apply (simp split:if_splits)
       
   588 apply (rule impI|rule conjI)+
       
   589 apply (simp add:is_created_proc_def)
       
   590 apply (auto simp:is_created_proc_def split:if_splits dest:tainted_in_current)[1]
       
   591 apply (simp add:is_created_proc_def)
       
   592 
       
   593 prefer 4
       
   594 apply (simp split:if_splits)
       
   595 apply (rule impI|rule conjI)+
       
   596 apply (simp add:is_created_proc_def)
       
   597 apply (auto simp:is_created_proc_def split:if_splits dest:tainted_in_current)[1]
       
   598 apply (simp add:is_created_proc_def)
       
   599 
       
   600 prefer 4
       
   601 apply (auto simp:is_created_proc_def split:if_splits option.splits dest:tainted_in_current)[1]
       
   602 
       
   603 prefer 4
       
   604 apply (auto simp:is_created_proc_def split:if_splits option.splits dest:tainted_in_current enrich_proc_dup_ffd enrich_proc_dup_ffd')[1]
       
   605 
       
   606 
       
   607 
       
   608 lemma enrich_proc_dup_tainted:
       
   609   "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
       
   610    \<Longrightarrow> (O_proc p' \<in> tainted (enrich_proc s p p')) = (O_proc p \<in> tainted s)"
       
   611 apply (induct s)
       
   612 apply (simp add:is_created_proc_def)
       
   613 apply (frule vt_grant_os, frule vd_cons)
       
   614 apply (case_tac a)
       
   615 apply (auto simp:is_created_proc_def)[1]
       
   616 
       
   617 
       
   618 lemma enrich_proc_tainted:
       
   619   ""
       
   620 
       
   621 
       
   622 end
       
   623 
       
   624 end