
diff -r d9dc04c3ea90 -r dfde07c7cd6b no_shm_selinux/Enrich.thy
--- a/no_shm_selinux/Enrich.thy	Thu Jan 09 14:39:00 2014 +0800
+++ b/no_shm_selinux/Enrich.thy	Thu Jan 09 19:09:09 2014 +0800
@@ -6,16 +6,8 @@
 (* enriched objects, closely related to static objects, so are only 3 kinds *)
 datatype t_enrich_obj = 
   E_proc "t_process" "t_msgq" "t_msgq"
-| E_file_link "t_file"
 | E_file "t_file" "nat" 
- (*
-| E_fd   "t_process" "t_fd" 
-| E_inum "nat" *)
 | E_msgq "t_msgq"
-(*
-| E_msg  "t_msgq"    "t_msg"
-*)
-
 
 (* objects that need dynamic indexing, all nature-numbers *)
 datatype t_index_obj = 
@@ -45,6 +37,7 @@
 *)
 | "no_del_event (_ # \<tau>) = no_del_event \<tau>"
 
+(*
 fun all_inums :: "t_state \<Rightarrow> t_inode_num set"
 where
   "all_inums [] = current_inode_nums []"
@@ -71,6 +64,7 @@
   "all_msgqs [] = {}"
 | "all_msgqs (CreateMsgq p q # s) = all_msgqs s \<union> {q}"
 | "all_msgqs (e # s) = all_msgqs s"
+*)
 
 fun all_msgs:: "t_state \<Rightarrow> t_msgq \<Rightarrow> t_msg set"
 where
@@ -128,6 +122,7 @@
     (f \<notin> current_files s \<and> (\<exists> pf. parent f = Some pf \<and> is_dir s pf))"
 | "notin_cur s (E_msgq q)  = (q \<notin> current_msgqs s)"
 
+(*
 lemma not_all_procs_cons:
   "p \<notin> all_procs (e # s) \<Longrightarrow> p \<notin> all_procs s"
 by (case_tac e, auto)
@@ -148,10 +143,11 @@
   "p' \<notin> all_procs s \<Longrightarrow> p' \<notin> current_procs s"
 apply (induct s, simp)
 by (case_tac a, auto)
-
+*)
+(*
 lemma not_all_msgqs_cons:
   "p \<notin> all_msgqs (e # s) \<Longrightarrow> p \<notin> all_msgqs s"
-by (case_tac e, auto)
+apply (case_tac e, auto)
 
 lemma not_all_msgqs_prop:
   "\<lbrakk>p' \<notin> all_msgqs s; p \<in> current_msgqs s; valid s\<rbrakk> \<Longrightarrow> p' \<noteq> p"
@@ -164,7 +160,8 @@
   "p' \<notin> all_msgqs s \<Longrightarrow> p' \<notin> current_msgqs s"
 apply (induct s, simp)
 by (case_tac a, auto)
-  
+  *)
+
 fun enrich_not_alive :: "t_state \<Rightarrow> t_enrich_obj \<Rightarrow> t_index_obj \<Rightarrow> bool"
 where
   "enrich_not_alive s obj (I_file f)  = 
@@ -427,7 +424,7 @@
       by (auto simp:Clone)
     have p'_not_in: "p' \<notin> current_procs s'" using  alive' notin_cur os Clone
       apply (erule_tac x = "I_proc p'" in allE)
-      apply (auto dest:not_all_procs_prop3 simp del:nums_of_recvmsg.simps)
+      apply (auto simp del:nums_of_recvmsg.simps)
       done
     have fd_in: "fds \<subseteq> proc_file_fds s' p" using os alive ffd_remain
       by (auto simp:Clone proc_file_fds_def)
@@ -537,8 +534,7 @@
       have fd_not_in: "fd \<notin> current_proc_fds s' p"
         using os alive' p_in notin_cur Open None
         apply (erule_tac x = "I_fd p fd" in allE)
-        apply (case_tac obj')
-        apply (auto dest:not_all_procs_prop3)
+        apply (case_tac obj', auto)
         done
       have "os_grant s' e" using p_in f_in fd_not_in os
         by (simp add:Open None)
@@ -589,7 +585,7 @@
       have fd_not_in: "fd \<notin> current_proc_fds s' p"
         using os alive' p_in Open Some notin_cur
         apply (erule_tac x = "I_fd p fd" in allE)
-        apply (case_tac obj', auto dest:not_all_procs_prop3)
+        apply (case_tac obj', auto)
         done
       have inum_not_in: "inum \<notin> current_inode_nums s'"
         using os alive' Open Some notin_cur nodel
@@ -1137,7 +1133,7 @@
     have m_not_in: "m \<notin> set (msgs_of_queue s' q)" 
       using os alive' notin_cur SendMsg q_in nodel vd
       apply (erule_tac x = "I_msg q m" in allE)
-      apply (case_tac obj', auto dest:not_all_msgqs_prop3)
+      apply (case_tac obj', auto)
       apply (drule nums_of_recv_0, simp+)
       apply (drule new_msgq_1, simp+)
       done
@@ -1305,6 +1301,1034 @@
 apply (auto simp:oflags_check_def perms_of_flags_def perm_of_oflag_def split:bool.splits)
 done
 
+fun enrich_msgq :: "t_state \<Rightarrow> t_msgq \<Rightarrow> t_msgq \<Rightarrow> t_state"
+where
+  "enrich_msgq [] tq dq = []"
+| "enrich_msgq (CreateMsgq p q # s) tq dq = 
+    (if (tq = q) 
+     then (CreateMsgq p dq # CreateMsgq p q # s)
+     else CreateMsgq p q # (enrich_msgq s tq dq))"
+| "enrich_msgq (SendMsg p q m # s) tq dq = 
+    (if (tq = q) 
+     then (SendMsg p dq m # SendMsg p q m # (enrich_msgq s tq dq))
+     else SendMsg p q m # (enrich_msgq s tq dq))"
+| "enrich_msgq (RecvMsg p q m # s) tq dq = 
+    (if (tq = q) 
+     then (RecvMsg p dq m # RecvMsg p q m # (enrich_msgq s tq dq))
+     else RecvMsg p q m # (enrich_msgq s tq dq))"
+| "enrich_msgq (e # s) tq dq = e # (enrich_msgq s tq dq)"
+
+lemma enrich_msgq_duq_in:
+  "\<lbrakk>q' \<notin> current_msgqs s; q \<in> current_msgqs s; no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> q' \<in> current_msgqs (enrich_msgq s q q')"
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons, case_tac a)
+apply auto
+done
+
+lemma enrich_msgq_duq_sms:
+  "\<lbrakk>q' \<notin> current_msgqs s; q \<in> current_msgqs s; no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> msgs_of_queue (enrich_msgq s q q') q' = msgs_of_queue s q"
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons, case_tac a)
+apply auto
+done
+
+lemma enrich_msgq_cur_inof:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> inum_of_file (enrich_msgq s q q') f = inum_of_file s f"
+apply (induct s arbitrary:f, simp)
+apply (frule vt_grant_os, frule vd_cons, case_tac a)
+apply (auto split:option.splits)
+done
+
+lemma enrich_msgq_cur_inos:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> inum_of_socket (enrich_msgq s q q') = inum_of_socket s"
+apply (rule ext)
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons, case_tac a)
+apply (auto split:option.splits)
+done
+
+lemma enrich_msgq_cur_inos':
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> inum_of_socket (enrich_msgq s q q') sock = inum_of_socket s sock"
+apply (simp add:enrich_msgq_cur_inos)
+done
+
+lemma enrich_msgq_cur_inums:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> current_inode_nums (enrich_msgq s q q') = current_inode_nums s"
+apply (auto simp:current_inode_nums_def current_file_inums_def 
+  current_sock_inums_def enrich_msgq_cur_inof enrich_msgq_cur_inos)
+done
+
+lemma enrich_msgq_cur_itag:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> itag_of_inum (enrich_msgq s q q') = itag_of_inum s"
+apply (rule ext)
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons, case_tac a)
+apply (auto split:option.splits t_socket_type.splits)
+done
+
+lemma enrich_msgq_cur_tcps:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> is_tcp_sock (enrich_msgq s q q') = is_tcp_sock s"
+apply (rule ext)
+apply (auto simp:is_tcp_sock_def enrich_msgq_cur_itag enrich_msgq_cur_inos
+  split:option.splits t_inode_tag.splits)
+done
+
+lemma enrich_msgq_cur_udps:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> is_udp_sock (enrich_msgq s q q') = is_udp_sock s"
+apply (rule ext)
+apply (auto simp:is_udp_sock_def enrich_msgq_cur_itag enrich_msgq_cur_inos
+  split:option.splits t_inode_tag.splits)
+done
+
+lemma enrich_msgq_cur_msgqs:
+  "\<lbrakk>q \<in> current_msgqs s; no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> current_msgqs (enrich_msgq s q q') = current_msgqs s \<union> {q'}"
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons)
+apply (case_tac a, auto)
+done
+
+lemma enrich_msgq_cur_msgs:
+  "\<lbrakk>q' \<notin> current_msgqs s; q \<in> current_msgqs s; no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> msgs_of_queue (enrich_msgq s q q') =  (msgs_of_queue s) (q' := msgs_of_queue s q)" 
+apply (rule ext, simp, rule conjI, rule impI)
+apply (simp add:enrich_msgq_duq_sms)
+apply (rule impI) 
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons)
+apply (case_tac a, auto)
+done
+
+lemma enrich_msgq_cur_procs:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> current_procs (enrich_msgq s q q') = current_procs s"
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons)
+apply (case_tac a, auto)
+done
+  
+lemma enrich_msgq_cur_files:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> current_files (enrich_msgq s q q') = current_files s"
+apply (auto simp:current_files_def)
+apply (simp add:enrich_msgq_cur_inof)+
+done
+
+lemma enrich_msgq_cur_fds:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> current_proc_fds (enrich_msgq s q q') = current_proc_fds s"
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons, case_tac a)
+apply auto
+done
+
+lemma enrich_msgq_filefd:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> file_of_proc_fd (enrich_msgq s q q') = file_of_proc_fd s"
+apply (rule ext, rule ext)
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons, case_tac a)
+apply auto
+done
+
+lemma enrich_msgq_flagfd:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> flags_of_proc_fd (enrich_msgq s q q') = flags_of_proc_fd s"
+apply (rule ext, rule ext)
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons, case_tac a)
+apply auto
+done
+
+lemma enrich_msgq_proc_fds:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> proc_file_fds (enrich_msgq s q q') = proc_file_fds s"
+apply (auto simp:proc_file_fds_def enrich_msgq_filefd)
+done
+
+lemma enrich_msgq_hungs:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> files_hung_by_del (enrich_msgq s q q') = files_hung_by_del s"
+apply (induct s, simp)
+apply (frule vt_grant_os, frule vd_cons, case_tac a)
+apply (auto simp:files_hung_by_del.simps)
+done
+  
+lemma enrich_msgq_is_file:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> is_file (enrich_msgq s q q') = is_file s"
+apply (rule ext)
+apply (auto simp add:is_file_def enrich_msgq_cur_itag enrich_msgq_cur_inof
+  split:option.splits t_inode_tag.splits)
+done
+
+lemma enrich_msgq_is_dir:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> is_dir (enrich_msgq s q q') = is_dir s"
+apply (rule ext)
+apply (auto simp add:is_dir_def enrich_msgq_cur_itag enrich_msgq_cur_inof
+  split:option.splits t_inode_tag.splits)
+done
+
+lemma enrich_msgq_sameinode:
+  "\<lbrakk>no_del_event s; valid s\<rbrakk>
+  \<Longrightarrow> (f \<in> same_inode_files (enrich_msgq s q q') f') = (f \<in> same_inode_files s f')"
+apply (induct s, simp)
+apply (simp add:same_inode_files_def)
+apply (auto simp:enrich_msgq_is_file enrich_msgq_cur_inof)
+done
+
+lemma enrich_msgq_tainted_aux1:
+  "\<lbrakk>no_del_event s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; valid s\<rbrakk>
+   \<Longrightarrow> (tainted s \<union> {O_msg q' m| m. O_msg q m \<in> tainted s}) \<subseteq> tainted (enrich_msgq s q q')"
+apply (induct s, simp) 
+apply (frule vt_grant_os, frule vd_cons)
+apply (case_tac a)
+apply (auto split:option.splits if_splits dest:tainted_in_current
+  simp:enrich_msgq_filefd enrich_msgq_sameinode)
+done
+
+lemma enrich_msgq_tainted_aux2:
+  "\<lbrakk>no_del_event s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; valid s; valid (enrich_msgq s q q')\<rbrakk>
+   \<Longrightarrow> tainted (enrich_msgq s q q') \<subseteq> (tainted s \<union> {O_msg q' m| m. O_msg q m \<in> tainted s})"
+apply (induct s, simp) 
+apply (frule vt_grant_os, frule vd_cons)
+apply (case_tac a)
+apply (auto split:option.splits if_splits simp:enrich_msgq_filefd enrich_msgq_sameinode 
+  dest:tainted_in_current vd_cons)
+apply (drule_tac vd_cons)+
+apply (simp)
+apply (drule set_mp)
+apply simp
+apply simp
+apply (drule_tac s = s in tainted_in_current)
+apply simp+
+done
+
+lemma enrich_msgq_alive:
+  "\<lbrakk>alive s obj; valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> alive (enrich_msgq s q q') obj"
+apply (case_tac obj)
+apply (simp_all add:enrich_msgq_is_file enrich_msgq_is_dir enrich_msgq_cur_msgqs 
+  enrich_msgq_cur_msgs enrich_msgq_cur_procs enrich_msgq_cur_fds
+  enrich_msgq_cur_tcps enrich_msgq_cur_udps)
+apply (rule impI, simp)
+done
+
+lemma enrich_msgq_alive':
+  "\<lbrakk>alive (enrich_msgq s q q') obj; valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> alive s obj \<or> obj = O_msgq q' \<or> (\<exists> m. obj = O_msg q' m \<and> alive s (O_msg q m))"
+apply (case_tac obj)
+apply (simp_all add:enrich_msgq_is_file enrich_msgq_is_dir enrich_msgq_cur_msgqs 
+  enrich_msgq_cur_msgs enrich_msgq_cur_procs enrich_msgq_cur_fds
+  enrich_msgq_cur_tcps enrich_msgq_cur_udps)
+apply (auto split:if_splits)
+done
+
+lemma enrich_msgq_not_alive:
+  "\<lbrakk>enrich_not_alive s (E_msgq q') obj; q' \<notin> current_msgqs s; q \<in> current_msgqs s; no_del_event s; valid s\<rbrakk>
+   \<Longrightarrow> enrich_not_alive (enrich_msgq s q q') (E_msgq q') obj"
+apply (case_tac obj)
+apply (auto simp:enrich_msgq_cur_fds enrich_msgq_cur_files 
+  enrich_msgq_cur_procs enrich_msgq_cur_inums enrich_msgq_cur_msgqs enrich_msgq_cur_msgs)
+done
+
+lemma enrich_msgq_nodel:
+  "no_del_event (enrich_msgq s q q') = no_del_event s"
+apply (induct s, simp)
+by (case_tac a, auto)
+
+lemma enrich_msgq_died_proc:
+  "died (O_proc p) (enrich_msgq s q q') = died (O_proc p) s"
+apply (induct s, simp)
+by (case_tac a, auto)
+
+lemma cf2sfile_execve:
+  "\<lbrakk>ff \<in> current_files (Execve p f fds # s); valid (Execve p f fds # s)\<rbrakk>
+   \<Longrightarrow> cf2sfile (Execve p f fds # s) ff= cf2sfile s ff"
+by (auto dest:cf2sfile_other' simp:current_files_simps)
+lemma cf2sfile_clone:
+  "\<lbrakk>ff \<in> current_files (Clone p p' fds # s); valid (Clone p p' fds # s)\<rbrakk>
+   \<Longrightarrow> cf2sfile (Clone p p' fds # s) ff= cf2sfile s ff"
+by (auto dest:cf2sfile_other' simp:current_files_simps)
+lemma cf2sfile_ptrace:
+  "\<lbrakk>ff \<in> current_files (Ptrace p p' # s); valid (Ptrace p p' # s)\<rbrakk>
+   \<Longrightarrow> cf2sfile (Ptrace p p' # s) ff= cf2sfile s ff"
+by (auto dest:cf2sfile_other' simp:current_files_simps)
+lemma cf2sfile_readfile:
+  "\<lbrakk>ff \<in> current_files (ReadFile p fd # s); valid (ReadFile p fd # s)\<rbrakk>
+   \<Longrightarrow> cf2sfile (ReadFile p fd # s) ff= cf2sfile s ff"
+by (auto dest:cf2sfile_other' simp:current_files_simps)
+lemma cf2sfile_writefile:
+  "\<lbrakk>ff \<in> current_files (WriteFile p fd # s); valid (WriteFile p fd # s)\<rbrakk>
+   \<Longrightarrow> cf2sfile (WriteFile p fd # s) ff= cf2sfile s ff"
+by (auto dest:cf2sfile_other' simp:current_files_simps)
+lemma cf2sfile_truncate:
+  "\<lbrakk>ff \<in> current_files (Truncate p f len # s); valid (Truncate p f len # s)\<rbrakk>
+   \<Longrightarrow> cf2sfile (Truncate p f len # s) ff= cf2sfile s ff"
+by (auto dest:cf2sfile_other' simp:current_files_simps)
+lemma cf2sfile_createmsgq:
+  "\<lbrakk>ff \<in> current_files (CreateMsgq p q # s); valid (CreateMsgq p q # s)\<rbrakk>
+   \<Longrightarrow> cf2sfile (CreateMsgq p q # s) ff= cf2sfile s ff"
+by (auto dest:cf2sfile_other' simp:current_files_simps)
+lemma cf2sfile_sendmsg:
+  "\<lbrakk>ff \<in> current_files (SendMsg p q m # s); valid (SendMsg p q m # s)\<rbrakk>
+   \<Longrightarrow> cf2sfile (SendMsg p q m # s) ff = cf2sfile s ff"
+by (auto dest:cf2sfile_other' simp:current_files_simps)
+lemma cf2sfile_recvmsg:
+  "\<lbrakk>ff \<in> current_files (RecvMsg p q m # s); valid (RecvMsg p q m # s)\<rbrakk>
+   \<Longrightarrow> cf2sfile (RecvMsg p q m # s) ff = cf2sfile s ff"
+by (auto dest:cf2sfile_other' simp:current_files_simps)
+lemmas cf2sfile_other'' = cf2sfile_recvmsg cf2sfile_sendmsg cf2sfile_createmsgq cf2sfile_truncate
+  cf2sfile_writefile cf2sfile_readfile cf2sfile_ptrace cf2sfile_clone cf2sfile_execve
+
+lemma enrich_msgq_prop:
+  "\<lbrakk>valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> valid (enrich_msgq s q q') \<and>
+       (\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_msgq s q q') tp = cp2sproc s tp) \<and>
+       (\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_msgq s q q') f = cf2sfile s f) \<and> 
+       (\<forall> tq. tq \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_msgq s q q') tq = cq2smsgq s tq) \<and> 
+       (\<forall> tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_msgq s q q') tp fd = cfd2sfd s tp fd) \<and>
+       (cq2smsgq (enrich_msgq s q q') q' = cq2smsgq s q) \<and>
+       (tainted (enrich_msgq s q q') = (tainted s \<union> {O_msg q' m| m. O_msg q m \<in> tainted s}))"
+proof (induct s)
+  case Nil
+  thus ?case by (auto)
+next
+  case (Cons e s)
+  hence vd_cons': "valid (e # s)" and curq_cons: "q \<in> current_msgqs (e # s)"
+    and curq'_cons: "q' \<notin> current_msgqs (e # s)" and nodel_cons: "no_del_event (e # s)"
+    and os: "os_grant s e" and grant: "grant s e"  and vd: "valid s"
+    by (auto dest:vd_cons vt_grant_os vt_grant)
+  from curq'_cons nodel_cons have curq': "q' \<notin> current_msgqs s" by (case_tac e, auto)
+  from nodel_cons have nodel: "no_del_event s" by (case_tac e, auto)
+  from nodel curq' vd Cons
+  have pre: "q \<in> current_msgqs s \<Longrightarrow> valid (enrich_msgq s q q') \<and>
+     (\<forall>tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_msgq s q q') tp = cp2sproc s tp) \<and>
+     (\<forall>f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_msgq s q q') f = cf2sfile s f) \<and>
+     (\<forall>tq. tq \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_msgq s q q') tq = cq2smsgq s tq) \<and>
+     (\<forall>tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_msgq s q q') tp fd = cfd2sfd s tp fd) \<and>
+     (cq2smsgq (enrich_msgq s q q') q' = cq2smsgq s q) \<and>
+     (tainted (enrich_msgq s q q') = (tainted s \<union> {O_msg q' m| m. O_msg q m \<in> tainted s}))"
+    by auto
+  
+  from pre have pre_vd: "q \<in> current_msgqs s \<Longrightarrow> valid (enrich_msgq s q q')" by simp
+  from pre have pre_sp: "\<And> tp. \<lbrakk>tp \<in> current_procs s; q \<in> current_msgqs s\<rbrakk>
+    \<Longrightarrow> cp2sproc (enrich_msgq s q q') tp = cp2sproc s tp" by auto
+  from pre have pre_sf: "\<And> f. \<lbrakk>f \<in> current_files s; q \<in> current_msgqs s\<rbrakk>
+    \<Longrightarrow> cf2sfile (enrich_msgq s q q') f = cf2sfile s f" by auto
+  from pre have pre_sq: "\<And> tq. \<lbrakk>tq \<in> current_msgqs s; q \<in> current_msgqs s\<rbrakk>
+    \<Longrightarrow> cq2smsgq (enrich_msgq s q q') tq = cq2smsgq s tq" by auto
+  from pre have pre_sfd: "\<And> tp fd. \<lbrakk>fd \<in> proc_file_fds s tp; q \<in> current_msgqs s\<rbrakk>
+    \<Longrightarrow> cfd2sfd (enrich_msgq s q q') tp fd = cfd2sfd s tp fd" by auto
+  hence pre_sfd': "\<And> tp fd f. \<lbrakk>file_of_proc_fd s tp fd = Some f; q \<in> current_msgqs s\<rbrakk>
+    \<Longrightarrow> cfd2sfd (enrich_msgq s q q') tp fd = cfd2sfd s tp fd" by (auto simp:proc_file_fds_def)
+  from pre have pre_duq: "q \<in> current_msgqs s \<Longrightarrow> cq2smsgq (enrich_msgq s q q') q' = cq2smsgq s q"
+    by auto
+  have vd_enrich:"q \<in> current_msgqs s \<Longrightarrow> valid (e # enrich_msgq s q q')" 
+    apply (frule pre_vd)
+    apply (erule_tac s = s and obj' = "E_msgq q'" in enrich_valid_intro_cons)
+    apply (simp_all add:pre nodel nodel_cons curq_cons vd_cons' vd enrich_msgq_hungs)
+    apply (clarsimp simp:nodel vd curq' enrich_msgq_alive)
+    apply (rule allI, rule impI, erule enrich_msgq_not_alive)
+    apply (simp_all add:curq' curq'_cons nodel vd enrich_msgq_cur_msgs enrich_msgq_filefd enrich_msgq_flagfd)
+    done
+  
+  have q_neq_q': "q' \<noteq> q" using curq'_cons curq_cons by auto
+
+  have vd_enrich_cons: "valid (enrich_msgq (e # s) q q')"
+  proof-
+    have "\<And> p q''. e = CreateMsgq p q'' \<Longrightarrow> valid (enrich_msgq (e # s) q q')"
+    proof-
+      fix p q'' assume ev: "e = CreateMsgq p q''" 
+      show "valid (enrich_msgq (e # s) q q')"
+      proof (cases "q'' = q")
+        case False with ev vd_enrich curq_cons
+        show ?thesis by simp
+      next
+        case True 
+        have "os_grant (CreateMsgq p q # s) (CreateMsgq p q')"
+          using os ev
+          by (simp add:q_neq_q' curq')
+        moreover have "grant (CreateMsgq p q # s) (CreateMsgq p q')"
+          using grant ev
+          by (auto simp add:sectxt_of_obj_def split:option.splits)
+        ultimately 
+        show ?thesis using  ev vd_cons' True 
+          by (auto intro: valid.intros(2))
+      qed
+    qed
+    moreover have "\<And> p q'' m. \<lbrakk>e = SendMsg p q'' m; q \<in> current_msgqs s\<rbrakk>
+      \<Longrightarrow> valid (enrich_msgq (e # s) q q')" 
+    proof-
+      fix p q'' m assume ev: "e = SendMsg p q'' m" and q_in: "q \<in> current_msgqs s"
+      show "valid (enrich_msgq (e # s) q q')"
+      proof (cases "q'' = q")
+        case False with ev vd_enrich q_in
+        show ?thesis by simp
+      next
+        case True
+        from grant os ev True obtain psec qsec 
+          where psec: "sectxt_of_obj s (O_proc p) = Some psec"
+          and qsec: "sectxt_of_obj s (O_msgq q) = Some qsec"
+          by (auto split:option.splits)
+        from psec q_in os ev 
+        have psec':"sectxt_of_obj (enrich_msgq s q q') (O_proc p) = Some psec"  
+          by (auto dest!:pre_sp simp:cp2sproc_def split:option.splits)
+        from qsec q_in pre_duq vd
+        have qsec': "sectxt_of_obj (enrich_msgq s q q') (O_msgq q') = Some qsec"
+          by (auto simp:cq2smsgq_def split:option.splits dest!:current_has_sms')
+        show ?thesis using ev True vd_cons' q_in vd_enrich nodel vd 
+          curq' psec psec' qsec qsec' grant os q_neq_q'
+          apply (simp, erule_tac valid.intros(2))    
+          apply (auto simp:q_neq_q' enrich_msgq_cur_msgqs enrich_msgq_cur_procs
+            enrich_msgq_cur_msgs sectxt_of_obj_simps)
+          done        
+      qed
+    qed
+    moreover have "\<And> p q'' m. \<lbrakk>e = RecvMsg p q'' m; q \<in> current_msgqs s\<rbrakk>
+           \<Longrightarrow> valid (enrich_msgq (e # s) q q')"
+    proof-
+      fix p q'' m assume ev: "e = RecvMsg p q'' m" and q_in: "q \<in> current_msgqs s"
+      show "valid (enrich_msgq (e # s) q q')"
+      proof (cases "q'' = q")
+        case False with ev vd_enrich q_in
+        show ?thesis by simp
+      next
+        case True
+        from grant os ev True obtain psec qsec msec
+          where psec: "sectxt_of_obj s (O_proc p) = Some psec"
+          and qsec: "sectxt_of_obj s (O_msgq q) = Some qsec"
+          and msec: "sectxt_of_obj s (O_msg q (hd (msgs_of_queue s q))) = Some msec"
+          by (auto split:option.splits)
+        from psec q_in os ev 
+        have psec':"sectxt_of_obj (enrich_msgq s q q') (O_proc p) = Some psec"  
+          by (auto dest!:pre_sp simp:cp2sproc_def split:option.splits)
+        from qsec q_in pre_duq vd
+        have qsec': "sectxt_of_obj (enrich_msgq s q q') (O_msgq q') = Some qsec"
+          by (auto simp:cq2smsgq_def split:option.splits dest!:current_has_sms')
+        from qsec q_in vd
+        have qsec'': "sectxt_of_obj (enrich_msgq s q q') (O_msgq q) = Some qsec"
+          apply (frule_tac pre_sq, simp_all)          
+          by (auto simp:cq2smsgq_def split:option.splits dest!:current_has_sms')
+        from msec q_in pre_duq vd qsec qsec' qsec'' curq' nodel
+        have msec': "sectxt_of_obj (enrich_msgq s q q') (O_msg q' (hd (msgs_of_queue s q))) = Some msec"
+          apply (auto simp:cq2smsgq_def  enrich_msgq_cur_msgs
+            split:option.splits dest!:current_has_sms')
+          apply (case_tac "msgs_of_queue s q")
+          using os ev True apply simp
+          apply (simp add:cqm2sms.simps split:option.splits)
+          apply (auto simp:cm2smsg_def split:option.splits)
+          done          
+        show ?thesis using ev True vd_cons' q_in vd_enrich nodel vd 
+          curq'  grant os q_neq_q' psec psec' msec msec' qsec qsec'
+          apply (simp, erule_tac valid.intros(2))
+          apply (auto simp:enrich_msgq_cur_msgqs enrich_msgq_cur_procs
+            enrich_msgq_cur_msgs sectxt_of_obj_simps)
+          done
+      qed
+    qed
+    ultimately
+    show ?thesis using vd_enrich curq_cons vd_cons'
+      apply (case_tac e)
+      apply (auto simp del:enrich_msgq.simps)
+      apply (auto split:if_splits )
+      done
+  qed
+
+  have curpsec: "\<And> tp. \<lbrakk>tp \<in> current_procs s; q \<in> current_msgqs s\<rbrakk> \<Longrightarrow> 
+    sectxt_of_obj (enrich_msgq s q q') (O_proc tp) = sectxt_of_obj s (O_proc tp)"
+    using pre_vd vd
+    apply (frule_tac pre_sp, simp)
+    by (auto simp:cp2sproc_def split:option.splits if_splits dest!:current_has_sec')    
+  have curfsec: "\<And> f. \<lbrakk>is_file s f; q \<in> current_msgqs s\<rbrakk> \<Longrightarrow> 
+    sectxt_of_obj (enrich_msgq s q q') (O_file f) = sectxt_of_obj s (O_file f)"
+  proof-
+    fix f 
+    assume a1: "is_file s f" and a2: "q \<in> current_msgqs s"
+    from a2 pre_sf pre_vd
+    have pre': "\<And>f. f \<in> current_files s \<Longrightarrow> cf2sfile (enrich_msgq s q q') f = cf2sfile s f"
+      and vd_enrich: "valid (enrich_msgq s q q')"
+      by auto
+    hence csf: "cf2sfile (enrich_msgq s q q') f = cf2sfile s f"
+      using a1 by (auto simp:is_file_in_current)
+    from a1 obtain sf where csf_some: "cf2sfile s f = Some sf"
+      apply (case_tac "cf2sfile s f")
+      apply (drule current_file_has_sfile')
+      apply (simp add:vd, simp add:is_file_in_current, simp)
+      done
+    from a1 have a1': "is_file (enrich_msgq s q q') f"
+      using vd nodel by (simp add:enrich_msgq_is_file)
+    show "sectxt_of_obj (enrich_msgq s q q') (O_file f) = sectxt_of_obj s (O_file f)"
+      using csf csf_some vd_enrich vd a1 a1'
+      apply (auto simp:cf2sfile_def split:option.splits if_splits)
+      apply (case_tac f, simp_all)
+      apply (drule root_is_dir', simp+)
+      done
+  qed
+  have curdsec: "\<And> tf. \<lbrakk>is_dir s tf; q \<in> current_msgqs s\<rbrakk>
+    \<Longrightarrow> sectxt_of_obj (enrich_msgq s q q') (O_dir tf) = sectxt_of_obj s (O_dir tf)"
+  proof-  
+    fix tf 
+    assume a1: "is_dir s tf" and a2: "q \<in> current_msgqs s"
+    from a2 pre_sf pre_vd
+    have pre': "\<And>f. f \<in> current_files s \<Longrightarrow> cf2sfile (enrich_msgq s q q') f = cf2sfile s f"
+      and vd_enrich: "valid (enrich_msgq s q q')"
+      by auto
+    hence csf: "cf2sfile (enrich_msgq s q q') tf = cf2sfile s tf"
+      using a1 by (auto simp:is_dir_in_current)
+    from a1 obtain sf where csf_some: "cf2sfile s tf = Some sf"
+      apply (case_tac "cf2sfile s tf")
+      apply (drule current_file_has_sfile')
+      apply (simp add:vd, simp add:is_dir_in_current, simp)
+      done      
+    from a1 have a1': "is_dir (enrich_msgq s q q') tf"
+      using enrich_msgq_is_dir vd nodel by simp
+    from a1 have a3: "\<not> is_file s tf" using vd by (simp add:is_dir_not_file)
+    from a1' vd have a3': "\<not> is_file (enrich_msgq s q q') tf" by (simp add:is_dir_not_file)  
+    show "sectxt_of_obj (enrich_msgq s q q') (O_dir tf) = sectxt_of_obj s (O_dir tf)"
+      using csf csf_some a3 a3' vd_enrich vd
+      apply (auto simp:cf2sfile_def split:option.splits)
+      apply (case_tac tf)
+      apply (simp add:root_sec_remains, simp)
+      done
+  qed
+  have curpsecs: "\<And> tf ctxts'. \<lbrakk>is_dir s tf; q \<in> current_msgqs s; get_parentfs_ctxts s tf = Some ctxts'\<rbrakk>
+    \<Longrightarrow> \<exists> ctxts. get_parentfs_ctxts (enrich_msgq s q q') tf = Some ctxts \<and> set ctxts = set ctxts'"
+  proof-
+    fix tf ctxts'
+    assume a1: "is_dir s tf" and a2: "q \<in> current_msgqs s" 
+      and a4: "get_parentfs_ctxts s tf = Some ctxts'"
+    from a2 pre
+    have pre': "\<And>f. f \<in> current_files s \<Longrightarrow> cf2sfile (enrich_msgq s q q') f = cf2sfile s f"
+      and vd_enrich': "valid (enrich_msgq s q q')"
+      by auto
+    hence csf: "cf2sfile (enrich_msgq s q q') tf = cf2sfile s tf"
+      using a1 by (auto simp:is_dir_in_current)
+    from a1 obtain sf where csf_some: "cf2sfile s tf = Some sf"
+      apply (case_tac "cf2sfile s tf")
+      apply (drule current_file_has_sfile')
+      apply (simp add:vd, simp add:is_dir_in_current, simp)
+      done      
+    from a1 have a1': "is_dir (enrich_msgq s q q') tf"
+      using enrich_msgq_is_dir vd nodel by simp
+    from a1 have a5: "\<not> is_file s tf" using vd by (simp add:is_dir_not_file)
+    from a1' vd have a5': "\<not> is_file (enrich_msgq s q q') tf" by (simp add:is_dir_not_file) 
+    
+    from a1' pre_vd a2 obtain ctxts 
+      where a3: "get_parentfs_ctxts (enrich_msgq s q q') tf = Some ctxts"
+      apply (case_tac "get_parentfs_ctxts (enrich_msgq s q q') tf")
+      apply (drule get_pfs_secs_prop', simp+)
+      done
+    moreover have "set ctxts = set ctxts'"
+    proof (cases tf)
+      case Nil          
+      with a3 a4 vd vd_enrich'
+      show ?thesis
+        by (simp add:get_parentfs_ctxts.simps root_sec_remains split:option.splits)
+    next
+      case (Cons a ff)
+      with csf csf_some a5 a5' vd_enrich' vd a3 a4
+      show ?thesis
+        apply (auto simp:cf2sfile_def split:option.splits if_splits)
+        done
+    qed
+    ultimately 
+    show "\<exists> ctxts. get_parentfs_ctxts (enrich_msgq s q q') tf = Some ctxts \<and> set ctxts = set ctxts'"
+      by auto        
+  qed
+    
+  have psec_cons: "\<And> tp. tp \<in> current_procs (e # s) \<Longrightarrow> 
+    sectxt_of_obj (enrich_msgq (e # s) q q') (O_proc tp) = sectxt_of_obj (e # s) (O_proc tp)"
+    using curq_cons vd_enrich_cons vd_cons' os pre_vd nodel_cons vd
+    apply (case_tac e)
+    apply (auto intro:curpsec simp:sectxt_of_obj_simps)
+    apply (frule curpsec, simp, frule curfsec, simp)    
+    apply (auto split:option.splits)[1]
+    apply (frule vd_cons) defer apply (frule vd_cons)
+    apply (auto intro:curpsec simp:sectxt_of_obj_simps)
+    done
+  
+
+  have sf_cons: "\<And> f. f \<in> current_files (e # s) \<Longrightarrow> cf2sfile (enrich_msgq (e # s) q q') f = cf2sfile (e # s) f"
+  proof-
+    fix f
+    assume a1: "f \<in> current_files (e # s)"
+    hence a1': "f \<in> current_files (enrich_msgq (e # s) q q')"
+      using nodel_cons os vd vd_cons' vd_enrich_cons
+      apply (case_tac e)
+      apply (auto simp:current_files_simps enrich_msgq_cur_files dest:is_file_in_current split:option.splits)
+      done
+    have b1: "\<And> p f' flags fd opt. e = Open p f' flags fd opt \<Longrightarrow> 
+      cf2sfile (enrich_msgq (e # s) q q') f = cf2sfile (e # s) f"
+    proof-
+      fix p f' flags fd opt 
+      assume ev: "e = Open p f' flags fd opt"
+      show "cf2sfile (enrich_msgq (e # s) q q') f = cf2sfile (e # s) f"
+      proof (cases opt)
+        case None
+        with a1 a1' ev vd_cons' vd_enrich_cons curq_cons
+        show ?thesis
+          apply (simp add:cf2sfile_open_none)
+          apply (simp add:pre_sf current_files_simps)
+          done
+      next
+        case (Some inum)
+        show ?thesis
+        proof (cases "f = f'")
+          case False
+          with a1 a1' ev vd_cons' vd_enrich_cons curq_cons Some
+          show ?thesis
+            apply (simp add:cf2sfile_open)
+            apply (simp add:pre_sf current_files_simps)
+            done
+        next
+          case True
+          with vd_cons' ev os Some
+          obtain pf where pf: "parent f = Some pf" by auto
+          then obtain ctxts where psecs: "get_parentfs_ctxts s pf = Some ctxts"
+            using os vd ev Some True
+            apply (case_tac "get_parentfs_ctxts s pf")
+            apply (drule get_pfs_secs_prop', simp, simp)
+            apply auto
+            done
+            
+          have "sectxt_of_obj (Open p f' flags fd (Some inum) # enrich_msgq s q q') (O_file f') = 
+                sectxt_of_obj (Open p f' flags fd (Some inum) # s) (O_file f')"
+            using Some vd_enrich_cons vd_cons' ev pf True os curq_cons
+            by (simp add:sectxt_of_obj_simps curpsec curdsec)
+          moreover 
+          have "sectxt_of_obj (enrich_msgq s q q') (O_dir pf) = sectxt_of_obj s (O_dir pf)"
+            using curq_cons ev pf Some True os 
+            by (simp add:curdsec)
+          moreover
+          have "\<exists> ctxts'. get_parentfs_ctxts (enrich_msgq s q q') pf = Some ctxts' \<and> set ctxts' = set ctxts"
+            using curq_cons ev pf Some True os vd psecs
+            apply (case_tac "get_parentfs_ctxts s pf")
+            apply (drule get_pfs_secs_prop', simp+)
+            apply (rule curpsecs, simp+)
+            done
+          then obtain ctxts' where psecs': "get_parentfs_ctxts (enrich_msgq s q q') pf = Some ctxts'"
+            and psecs_eq: "set ctxts' = set ctxts" by auto
+          ultimately show ?thesis
+            using a1 a1' ev vd_cons' vd_enrich_cons Some True pf psecs
+            by (simp add:cf2sfile_open split:option.splits)
+        qed
+      qed
+    qed
+    have b2: "\<And> p f' inum. e = Mkdir p f' inum \<Longrightarrow> 
+      cf2sfile (enrich_msgq (e # s) q q') f = cf2sfile (e # s) f"
+    proof-
+      fix p f' inum
+      assume ev: "e = Mkdir p f' inum"
+      show "cf2sfile (enrich_msgq (e # s) q q') f = cf2sfile (e # s) f"
+      proof (cases "f' = f")
+        case False
+        with a1 a1' ev vd_cons' vd_enrich_cons curq_cons
+        show ?thesis
+          apply (simp add:cf2sfile_mkdir)
+          apply (simp add:pre_sf current_files_simps)
+          done
+      next
+        case True
+        with vd_cons' ev os
+        obtain pf where pf: "parent f = Some pf" by auto
+        then obtain ctxts where psecs: "get_parentfs_ctxts s pf = Some ctxts"
+          using os vd ev True
+          apply (case_tac "get_parentfs_ctxts s pf")
+          apply (drule get_pfs_secs_prop', simp, simp)
+          apply auto
+          done
+
+        have "sectxt_of_obj (Mkdir p f' inum # enrich_msgq s q q') (O_dir f') = 
+          sectxt_of_obj (Mkdir p f' inum # s) (O_dir f')"
+          using vd_enrich_cons vd_cons' ev pf True os curq_cons
+          by (simp add:sectxt_of_obj_simps curpsec curdsec)
+        moreover 
+        have "sectxt_of_obj (enrich_msgq s q q') (O_dir pf) = sectxt_of_obj s (O_dir pf)"
+          using curq_cons ev pf True os 
+          by (simp add:curdsec)
+        moreover
+        have "\<exists> ctxts'. get_parentfs_ctxts (enrich_msgq s q q') pf = Some ctxts' \<and> set ctxts' = set ctxts"
+          using curq_cons ev pf True os vd psecs
+          apply (case_tac "get_parentfs_ctxts s pf")
+          apply (drule get_pfs_secs_prop', simp+)
+          apply (rule curpsecs, simp+)
+          done
+        then obtain ctxts' where psecs': "get_parentfs_ctxts (enrich_msgq s q q') pf = Some ctxts'"
+          and psecs_eq: "set ctxts' = set ctxts" by auto
+        ultimately show ?thesis
+          using a1 a1' ev vd_cons' vd_enrich_cons True pf psecs
+          apply (simp add:cf2sfile_mkdir split:option.splits)
+          done
+      qed
+    qed
+    have b3: "\<And> p f' f''. e = LinkHard p f' f'' \<Longrightarrow> 
+      cf2sfile (enrich_msgq (e # s) q q') f = cf2sfile (e # s) f"
+    proof-
+      fix p f' f''
+      assume ev: "e = LinkHard p f' f''"
+      show "cf2sfile (enrich_msgq (e # s) q q') f = cf2sfile (e # s) f"
+      proof (cases "f'' = f")
+        case False
+        with a1 a1' ev vd_cons' vd_enrich_cons curq_cons
+        show ?thesis
+          apply (simp add:cf2sfile_linkhard)
+          apply (simp add:pre_sf current_files_simps)
+          done
+      next
+        case True
+        with vd_cons' ev os
+        obtain pf where pf: "parent f = Some pf" by auto
+        then obtain ctxts where psecs: "get_parentfs_ctxts s pf = Some ctxts"
+          using os vd ev True
+          apply (case_tac "get_parentfs_ctxts s pf")
+          apply (drule get_pfs_secs_prop', simp, simp)
+          apply auto
+          done
+
+        have "sectxt_of_obj (LinkHard p f' f'' # enrich_msgq s q q') (O_file f) = 
+          sectxt_of_obj (LinkHard p f' f'' # s) (O_file f)"
+          using vd_enrich_cons vd_cons' ev pf True os curq_cons
+          by (simp add:sectxt_of_obj_simps curpsec curdsec)
+        moreover 
+        have "sectxt_of_obj (enrich_msgq s q q') (O_dir pf) = sectxt_of_obj s (O_dir pf)"
+          using curq_cons ev pf True os 
+          by (simp add:curdsec)
+        moreover
+        have "\<exists> ctxts'. get_parentfs_ctxts (enrich_msgq s q q') pf = Some ctxts' \<and> set ctxts' = set ctxts"
+          using curq_cons ev pf True os vd psecs
+          apply (case_tac "get_parentfs_ctxts s pf")
+          apply (drule get_pfs_secs_prop', simp+)
+          apply (rule curpsecs, simp+)
+          done
+        then obtain ctxts' where psecs': "get_parentfs_ctxts (enrich_msgq s q q') pf = Some ctxts'"
+          and psecs_eq: "set ctxts' = set ctxts" by auto
+        ultimately show ?thesis
+          using a1 a1' ev vd_cons' vd_enrich_cons True pf psecs
+          apply (simp add:cf2sfile_linkhard split:option.splits)
+          done
+      qed
+    qed
+    show "cf2sfile (enrich_msgq (e # s) q q') f = cf2sfile (e # s) f"
+      apply (case_tac e)
+      prefer 6 apply (erule b1)
+      prefer 11 apply (erule b2)
+      prefer 11 apply (erule b3)
+      apply (simp_all only:b1 b2 b3)
+      using a1' a1 vd_enrich_cons vd_cons' curq_cons nodel_cons 
+      apply (simp_all add:cf2sfile_other'' cf2sfile_simps enrich_msgq.simps no_del_event.simps split:if_splits)
+      apply (simp_all add:pre_sf cf2sfile_other' current_files_simps split:if_splits)
+      apply (drule vd_cons, simp add:cf2sfile_other', drule pre_sf, simp+)+
+      done
+  qed
+  
+  have sfd_cons:"\<And> tp fd f. file_of_proc_fd (e # s) tp fd = Some f \<Longrightarrow> 
+    cfd2sfd (enrich_msgq (e # s) q q') tp fd = cfd2sfd (e # s) tp fd"
+  proof-
+    fix tp fd f
+    assume a1: "file_of_proc_fd (e # s) tp fd = Some f"
+    hence a1': "file_of_proc_fd (enrich_msgq (e # s) q q') tp fd = Some f"
+      using nodel_cons vd_enrich os vd_cons'
+      apply (case_tac e, auto simp:enrich_msgq_filefd simp del:enrich_msgq.simps)
+      done
+    have b1: "\<And> p f' flags fd' opt. e = Open p f' flags fd' opt \<Longrightarrow> 
+      cfd2sfd (enrich_msgq (e # s) q q') tp fd = cfd2sfd (e # s) tp fd"
+    proof-
+      fix p f' flags fd' opt
+      assume ev: "e = Open p f' flags fd' opt"
+      have c1': "file_of_proc_fd (Open p f' flags fd' opt # s) tp fd = Some f"
+        using a1' ev a1 by (simp split:if_splits)
+      show "cfd2sfd (enrich_msgq (e # s) q q') tp fd = cfd2sfd (e # s) tp fd"        thm cfd2sfd_open
+      proof (cases "tp = p \<and> fd = fd'")
+        case False
+        show ?thesis using ev vd_enrich_cons vd_cons' a1' a1 False curq_cons
+          apply (simp add:cfd2sfd_open split:if_splits del:file_of_proc_fd.simps)
+          apply (rule conjI, rule impI, simp)
+          apply (rule conjI, rule impI, simp)
+          apply (auto simp: False  intro!:pre_sfd' split:if_splits)
+          done
+      next
+        case True
+        have "f' \<in> current_files (Open p f' flags fd' opt # s)" using ev vd_cons' os
+          by (auto simp:current_files_simps is_file_in_current split:option.splits) 
+        hence "cf2sfile (Open p f' flags fd' opt # enrich_msgq s q q') f' 
+          = cf2sfile (Open p f' flags fd' opt # s) f'"
+          using sf_cons ev by auto
+        moreover have "sectxt_of_obj (enrich_msgq s q q') (O_proc p) = sectxt_of_obj s (O_proc p)"
+          apply (rule curpsec)
+          using os ev curq_cons   
+          by (auto split:option.splits)
+        ultimately show ?thesis
+          using ev True a1 a1' vd_enrich_cons vd_cons'
+          apply (simp add:cfd2sfd_open sectxt_of_obj_simps del:file_of_proc_fd.simps)
+          done
+      qed
+    qed
+    show "cfd2sfd (enrich_msgq (e # s) q q') tp fd = cfd2sfd (e # s) tp fd"
+      apply (case_tac e)
+      prefer 6 apply (erule b1)
+      using a1' a1 vd_enrich_cons vd_cons' curq_cons
+      apply (simp_all only:cfd2sfd_simps enrich_msgq.simps)
+      apply (auto simp:cfd2sfd_simps pre_sfd' dest:vd_cons cfd2sfd_other split:if_splits)
+      done
+  qed
+
+  have pfds_cons: "\<And> tp. tp \<in> current_procs (e # s) \<Longrightarrow> 
+    cpfd2sfds (enrich_msgq (e # s) q q') tp = cpfd2sfds (e # s) tp"
+    apply (auto simp add:cpfd2sfds_def proc_file_fds_def)
+    apply (rule_tac x = fd in exI, rule conjI, rule_tac x = f in exI)
+    prefer 3
+    apply (rule_tac x = fd in exI, rule conjI, rule_tac x = f in exI)
+    apply (auto simp:sfd_cons enrich_msgq_filefd nodel_cons vd_cons')
+    done  
+  
+  have tainted_cons: "tainted (enrich_msgq (e # s) q q') = 
+    (tainted (e # s) \<union> {O_msg q' m | m. O_msg q m \<in> tainted (e # s)})"
+    apply (rule equalityI)
+    using nodel_cons curq_cons curq'_cons vd_cons' vd_enrich_cons
+    apply (rule enrich_msgq_tainted_aux2)
+    using nodel_cons curq_cons curq'_cons vd_cons' 
+    apply (rule enrich_msgq_tainted_aux1)
+    done
+  have pre_tainted: "q \<in> current_msgqs s \<Longrightarrow> tainted (enrich_msgq s q q') = 
+    (tainted s \<union> {O_msg q' m| m. O_msg q m \<in> tainted s})" by (simp add:pre)
+
+  have "\<forall>tp fd. fd \<in> proc_file_fds (e # s) tp \<longrightarrow> cfd2sfd (enrich_msgq (e # s) q q') tp fd = cfd2sfd (e # s) tp fd"
+    by (auto simp:proc_file_fds_def elim!:sfd_cons)
+  moreover 
+  have "\<forall>tp. tp \<in> current_procs (e # s) \<longrightarrow> cp2sproc (enrich_msgq (e # s) q q') tp = cp2sproc (e # s) tp"
+    by (auto simp:cp2sproc_def pfds_cons psec_cons enrich_msgq_died_proc split:option.splits)    
+  moreover 
+  have "\<forall>tq. tq \<in> current_msgqs (e # s) \<longrightarrow> cq2smsgq (enrich_msgq (e # s) q q') tq = cq2smsgq (e # s) tq"
+  proof clarify
+    fix tq assume a1: "tq \<in> current_msgqs (e # s)"
+    
+    have curqsec: "\<And> tq. \<lbrakk>tq \<in> current_msgqs s; q \<in> current_msgqs s\<rbrakk> \<Longrightarrow> 
+      sectxt_of_obj (enrich_msgq s q q') (O_msgq tq) = sectxt_of_obj s (O_msgq tq)"
+      using pre_vd vd
+      apply (frule_tac pre_sq, simp)
+      by (auto simp:cq2smsgq_def split:option.splits if_splits dest!:current_has_sec' current_has_sms')
+    have cursms: "\<And> q''. \<lbrakk>q'' \<in> current_msgqs s; q \<in> current_msgqs s\<rbrakk> \<Longrightarrow> 
+      cqm2sms (enrich_msgq s q q') q'' (msgs_of_queue (enrich_msgq s q q') q'') =
+      cqm2sms s q'' (msgs_of_queue s q'')"
+      using pre_vd vd
+      apply (frule_tac pre_sq, simp)
+      by (auto simp:cq2smsgq_def split:option.splits if_splits dest!:current_has_sec' current_has_sms')
+    have qsec_cons: "sectxt_of_obj (enrich_msgq (e # s) q q') (O_msgq tq) = sectxt_of_obj (e # s) (O_msgq tq)"
+      using curq_cons vd_enrich_cons vd_cons' os pre_vd nodel_cons vd curq'_cons curq_cons a1
+      apply (case_tac e)
+      apply (auto intro:curqsec simp:sectxt_of_obj_simps curpsec split:option.splits dest!:current_has_sec')      
+      apply (frule vd_cons) defer apply (frule vd_cons)
+      apply (auto intro:curqsec simp:sectxt_of_obj_simps)
+      done
+    have sms_cons: "cqm2sms (enrich_msgq (e # s) q q') tq (msgs_of_queue (enrich_msgq (e # s) q q') tq) =
+      cqm2sms (e # s) tq (msgs_of_queue (e # s) tq)"
+    proof-      
+      have b1: "\<And> p q'' m. e = SendMsg p q'' m \<Longrightarrow> 
+        cqm2sms (enrich_msgq (e # s) q q') tq (msgs_of_queue (enrich_msgq (e # s) q q') tq) =
+        cqm2sms (e # s) tq (msgs_of_queue (e # s) tq)"
+        apply (case_tac e)
+        using a1 curq_cons vd_enrich_cons vd_cons' os pre_vd nodel_cons vd curq'_cons
+        apply (auto simp:sectxt_of_obj_simps cqm2sms_simps curpsec qsec_cons curqsec cursms pre_tainted       
+            split:option.splits dest!:current_has_sec' current_has_sms' simp del:cqm2sms.simps)
+        apply (tactic {*ALLGOALS (ftac @{thm vd_cons})*})
+        apply (auto simp:sectxt_of_obj_simps cqm2sms_simps curpsec qsec_cons curqsec cursms pre_tainted       
+            split:option.splits dest!:current_has_sec' current_has_sms' simp del:cqm2sms.simps)
+        done
+      have b2: "\<And> p q''. e = CreateMsgq p q'' \<Longrightarrow> 
+        cqm2sms (enrich_msgq (e # s) q q') tq (msgs_of_queue (enrich_msgq (e # s) q q') tq) =
+        cqm2sms (e # s) tq (msgs_of_queue (e # s) tq)"
+        using a1 curq_cons curq'_cons vd_enrich_cons vd_cons'
+        apply (auto simp:cqm2sms_simps intro:cursms)
+        apply (auto simp:cqm2sms.simps)
+        done
+      have b3: "\<And> p q'' m. e = RecvMsg p q'' m \<Longrightarrow>
+        cqm2sms (enrich_msgq (e # s) q q') tq (msgs_of_queue (enrich_msgq (e # s) q q') tq) =
+        cqm2sms (e # s) tq (msgs_of_queue (e # s) tq)"
+        using a1 curq_cons vd_enrich_cons vd_cons' os pre_vd nodel_cons vd curq'_cons
+        apply (auto  simp:sectxt_of_obj_simps cqm2sms_simps curpsec qsec_cons curqsec cursms        
+            split:option.splits dest!:current_has_sec' current_has_sms' simp del:cqm2sms.simps)
+        apply (frule vd_cons) defer apply (frule vd_cons) 
+        apply (auto simp:sectxt_of_obj_simps cqm2sms_simps curpsec qsec_cons curqsec cursms        
+            split:option.splits dest!:current_has_sec' current_has_sms' simp del:cqm2sms.simps)
+        done      
+      show "cqm2sms (enrich_msgq (e # s) q q') tq (msgs_of_queue (enrich_msgq (e # s) q q') tq) =
+        cqm2sms (e # s) tq (msgs_of_queue (e # s) tq)"
+        apply (case_tac e)
+        prefer 15 apply (erule b2)
+        prefer 15 apply (erule b1)
+        prefer 15 apply (erule b3)
+        using curq_cons vd_enrich_cons vd_cons' os pre_vd nodel_cons vd curq'_cons a1
+        apply (auto intro:cursms simp:sectxt_of_obj_simps cqm2sms_simps curpsec qsec_cons curqsec 
+          split:option.splits dest!:current_has_sec' current_has_sms' simp del:cqm2sms.simps)
+        done
+    qed
+    
+    show "cq2smsgq (enrich_msgq (e # s) q q') tq = cq2smsgq (e # s) tq"
+      using a1 curq_cons
+      apply (simp add:cq2smsgq_def qsec_cons sms_cons)
+      done
+  qed
+  moreover 
+  have "cq2smsgq (enrich_msgq (e # s) q q') q' = cq2smsgq (e # s) q"
+  proof-
+    have duqsec: "q \<in> current_msgqs s \<Longrightarrow> 
+      sectxt_of_obj (enrich_msgq s q q') (O_msgq q') = sectxt_of_obj s (O_msgq q)"
+      apply (frule pre_duq) using vd
+      by (auto simp:cq2smsgq_def split:option.splits if_splits dest!:current_has_sec' current_has_sms')
+    have duqsms: "q \<in> current_msgqs s \<Longrightarrow> 
+      cqm2sms (enrich_msgq s q q') q' (msgs_of_queue (enrich_msgq s q q') q') =
+      cqm2sms s q (msgs_of_queue s q)"
+      apply (frule pre_duq) using vd
+      by (auto simp:cq2smsgq_def split:option.splits if_splits dest!:current_has_sec' current_has_sms')
+    have qsec_cons: "sectxt_of_obj (enrich_msgq (e # s) q q') (O_msgq q') = sectxt_of_obj (e # s) (O_msgq q)"
+      using curq_cons vd_enrich_cons vd_cons' os pre_vd nodel_cons vd curq'_cons curq_cons
+      apply (case_tac e)
+      apply (auto simp:duqsec sectxt_of_obj_simps curpsec split:option.splits dest!:current_has_sec')      
+      apply (frule vd_cons) defer apply (frule vd_cons)
+      apply (auto intro:duqsec simp:sectxt_of_obj_simps)
+      done
+    have sms_cons: "cqm2sms (enrich_msgq (e # s) q q') q' (msgs_of_queue (enrich_msgq (e # s) q q') q') = 
+      cqm2sms (e # s) q (msgs_of_queue (e # s) q)"
+    proof-
+      have b1: "\<And> p q'' m. e = SendMsg p q'' m \<Longrightarrow> 
+        cqm2sms (enrich_msgq (e # s) q q') q' (msgs_of_queue (enrich_msgq (e # s) q q') q') =
+        cqm2sms (e # s) q (msgs_of_queue (e # s) q)"
+        apply (case_tac e)
+        using curq_cons vd_enrich_cons vd_cons' os pre_vd nodel_cons vd curq'_cons
+        apply (auto simp:sectxt_of_obj_simps cqm2sms_simps curpsec qsec_cons duqsec duqsms pre_tainted
+          enrich_msgq_cur_procs enrich_msgq_cur_msgqs
+            split:option.splits dest!:current_has_sec' current_has_sms' simp del:cqm2sms.simps)
+        apply (tactic {*ALLGOALS (ftac @{thm vd_cons})*})
+        apply (auto simp:sectxt_of_obj_simps cqm2sms_simps curpsec qsec_cons duqsec duqsms pre_tainted
+          enrich_msgq_cur_procs enrich_msgq_cur_msgqs    dest:tainted_in_current      
+            split:option.splits dest!:current_has_sec' current_has_sms' simp del:cqm2sms.simps)
+        done
+      have b2: "\<And> p q''. e = CreateMsgq p q'' \<Longrightarrow> 
+        cqm2sms (enrich_msgq (e # s) q q') q' (msgs_of_queue (enrich_msgq (e # s) q q') q') =
+        cqm2sms (e # s) q (msgs_of_queue (e # s) q)"
+        using curq_cons curq'_cons vd_enrich_cons vd_cons'
+        apply (auto simp:cqm2sms_simps intro:duqsms)
+        apply (auto simp:cqm2sms.simps)
+        done
+      have b3: "\<And> p q'' m. e = RecvMsg p q'' m \<Longrightarrow>
+        cqm2sms (enrich_msgq (e # s) q q') q' (msgs_of_queue (enrich_msgq (e # s) q q') q') =
+        cqm2sms (e # s) q (msgs_of_queue (e # s) q)"
+        using curq_cons vd_enrich_cons vd_cons' os pre_vd nodel_cons vd curq'_cons
+        apply (auto simp:sectxt_of_obj_simps cqm2sms_simps curpsec qsec_cons duqsec duqsms pre_tainted
+          enrich_msgq_cur_procs enrich_msgq_cur_msgqs
+            split:option.splits dest!:current_has_sec' current_has_sms' simp del:cqm2sms.simps)
+        apply (tactic {*ALLGOALS (ftac @{thm vd_cons})*})
+        apply (auto simp:sectxt_of_obj_simps cqm2sms_simps curpsec qsec_cons duqsec duqsms pre_tainted
+          enrich_msgq_cur_procs enrich_msgq_cur_msgqs    dest:tainted_in_current      
+            split:option.splits dest!:current_has_sec' current_has_sms' simp del:cqm2sms.simps)
+        done
+      show ?thesis
+      apply (case_tac e)      
+        prefer 15 apply (erule b2)
+        prefer 15 apply (erule b1)
+        prefer 15 apply (erule b3)
+        using curq_cons vd_enrich_cons vd_cons' os pre_vd nodel_cons vd curq'_cons
+        apply (auto intro:duqsms simp:sectxt_of_obj_simps cqm2sms_simps curpsec qsec_cons duqsms 
+          split:option.splits dest!:current_has_sec' current_has_sms' simp del:cqm2sms.simps)
+        done
+    qed
+    show ?thesis
+      using curq_cons
+      apply (simp add:cq2smsgq_def qsec_cons sms_cons)
+      done
+  qed
+  ultimately show ?case using vd_enrich_cons sf_cons tainted_cons
+    by auto
+qed
+
+lemma enrich_msgq_vd:
+  "\<lbrakk>q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s; valid s\<rbrakk> \<Longrightarrow> 
+   valid (enrich_msgq s q q')"
+by (auto dest:enrich_msgq_prop)
+
+lemma enrich_msgq_sp:
+  "\<lbrakk>tp \<in> current_procs s; valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> cp2sproc (enrich_msgq s q q') tp = cp2sproc s tp"
+by (auto dest:enrich_msgq_prop)
+
+lemma enrich_msgq_sf: 
+  "\<lbrakk>f \<in> current_files s; valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> cf2sfile (enrich_msgq s q q') f = cf2sfile s f"
+by (auto dest:enrich_msgq_prop)
+
+lemma enrich_msgq_sfs: 
+  "\<lbrakk>is_file s f; valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> cf2sfiles (enrich_msgq s q q') f = cf2sfiles s f"
+apply (auto simp add:cf2sfiles_def)
+apply (rule_tac x = f' in bexI) defer
+apply (simp add:enrich_msgq_sameinode)
+apply (rule_tac x = f' in bexI) defer
+apply (simp add:enrich_msgq_sameinode)+
+apply (drule same_inode_files_prop11, drule_tac f = f' in is_file_in_current)
+apply (simp add:enrich_msgq_sf)
+apply (drule same_inode_files_prop11, drule_tac f = f' in is_file_in_current)
+apply (simp add:enrich_msgq_sf)
+done
+
+lemma enrich_msgq_sq:
+  "\<lbrakk>tq \<in> current_msgqs s; valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> cq2smsgq (enrich_msgq s q q') tq = cq2smsgq s tq"
+by (auto dest:enrich_msgq_prop)
+
+lemma enrich_msgq_sfd':
+  "\<lbrakk>fd \<in> proc_file_fds s tp; valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> cfd2sfd (enrich_msgq s q q') tp fd = cfd2sfd s tp fd"
+by (auto dest:enrich_msgq_prop)
+
+lemma enrich_msgq_sfd:
+  "\<lbrakk>file_of_proc_fd s tp fd = Some f; valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> cfd2sfd (enrich_msgq s q q') tp fd = cfd2sfd s tp fd"
+by (auto intro:enrich_msgq_sfd' simp:proc_file_fds_def)
+
+lemma enrich_msgq_duq:
+  "\<lbrakk>valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> cq2smsgq (enrich_msgq s q q') q' = cq2smsgq s q"
+by (auto dest:enrich_msgq_prop)
+  
+lemma enrich_msgq_tainted:
+  "\<lbrakk>valid s; q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s\<rbrakk>
+   \<Longrightarrow> tainted (enrich_msgq s q q') = (tainted s \<union> {O_msg q' m| m. O_msg q m \<in> tainted s})"
+by (auto dest:enrich_msgq_prop)
+
+lemma enrich_msgq_dalive:
+  "\<lbrakk>q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s; valid s\<rbrakk> 
+   \<Longrightarrow> dalive (enrich_msgq s q q') obj = (dalive s obj \<or> obj = D_msgq q')"
+apply (case_tac obj)
+apply (auto simp:enrich_msgq_is_file enrich_msgq_is_dir enrich_msgq_cur_msgqs enrich_msgq_cur_procs)
+done
+
+lemma enrich_msgq_s2ss:
+  "\<lbrakk>q \<in> current_msgqs s; q' \<notin> current_msgqs s; no_del_event s; valid s\<rbrakk> \<Longrightarrow> 
+   s2ss (enrich_msgq s q q') = s2ss s"
+apply (auto simp add:s2ss_def)
+apply (simp add:enrich_msgq_dalive)
+apply (erule disjE)
+apply (rule_tac x = obj in exI) defer 
+apply (rule_tac x = "D_msgq q" in exI) defer 
+apply (rule_tac x = obj in exI) 
+apply (case_tac[!] obj)
+apply (auto simp:enrich_msgq_duq enrich_msgq_tainted enrich_msgq_sq enrich_msgq_sf
+  enrich_msgq_sp co2sobj.simps enrich_msgq_is_file enrich_msgq_is_dir 
+  enrich_msgq_cur_procs enrich_msgq_cur_msgqs enrich_msgq_sfs
+  split:option.splits dest:is_dir_in_current)
+done
+
 end
 
 end
\ No newline at end of file




