update
authorchunhan
Tue, 03 Dec 2013 22:42:48 +0800
changeset 75 99af1986e1e0
parent 74 271e9818b6f6
child 76 f27ba31b7e96
update
simple_selinux/Alive_prop.thy
simple_selinux/Co2sobj_prop.thy
simple_selinux/Current_prop.thy
simple_selinux/Delete_prop.thy
simple_selinux/S2ss_prop.thy
simple_selinux/Sectxt_prop.thy
simple_selinux/Tainted_prop.thy
--- a/simple_selinux/Alive_prop.thy	Mon Dec 02 10:52:40 2013 +0800
+++ b/simple_selinux/Alive_prop.thy	Tue Dec 03 22:42:48 2013 +0800
@@ -311,7 +311,6 @@
     \<forall> p f. e \<noteq> UnLink p f;
     \<forall> p d. e \<noteq> Rmdir p d;
     \<forall> p d inum. e \<noteq> Mkdir p d inum;
-    \<forall> p f f'. e \<noteq> LinkHard p f f';
     \<forall> p q. e \<noteq> CreateMsgq p q;
     \<forall> p q m. e \<noteq> SendMsg p q m;
     \<forall> p q m. e \<noteq> RecvMsg p q m;
--- a/simple_selinux/Co2sobj_prop.thy	Mon Dec 02 10:52:40 2013 +0800
+++ b/simple_selinux/Co2sobj_prop.thy	Tue Dec 03 22:42:48 2013 +0800
@@ -24,7 +24,7 @@
 apply (frule vt_grant_os, frule vd_cons, rule ext, rule ext)
 unfolding cm2smsg_def
 apply (case_tac e)
-apply (auto simp:sectxt_of_obj_simps tainted_eq_Tainted 
+apply (auto simp:sectxt_of_obj_simps 
            split:t_object.splits option.splits if_splits 
             dest:not_deleted_init_msg  dest!:current_has_sec')
 done
@@ -37,7 +37,7 @@
            | _ \<Rightarrow> None)
      else cm2smsg s q' m') "
 apply (frule vd_cons, frule vt_grant_os, rule ext, rule ext)
-apply (auto simp:cm2smsg_def tainted_eq_Tainted sectxt_of_obj_simps 
+apply (auto simp:cm2smsg_def sectxt_of_obj_simps 
   split:if_splits option.splits
   dest:not_deleted_init_msg  dest!:current_has_sec')
 done
@@ -45,35 +45,35 @@
 lemma cm2smsg_recvmsg1:
   "\<lbrakk>q' \<noteq> q; valid (RecvMsg p q m # s)\<rbrakk> \<Longrightarrow> cm2smsg (RecvMsg p q m # s) q' = cm2smsg s q'"
 apply (frule vd_cons, frule vt_grant_os, rule ext)
-apply (auto simp:cm2smsg_def tainted_eq_Tainted sectxt_of_obj_simps 
+apply (auto simp:cm2smsg_def sectxt_of_obj_simps 
   split:if_splits option.splits)
 done
 
 lemma cm2smsg_recvmsg2:
   "\<lbrakk>m' \<noteq> m; valid (RecvMsg p q m # s)\<rbrakk> \<Longrightarrow> cm2smsg (RecvMsg p q m # s) q m' = cm2smsg s q m'"
 apply (frule vd_cons, frule vt_grant_os)
-apply (auto simp:cm2smsg_def tainted_eq_Tainted sectxt_of_obj_simps 
+apply (auto simp:cm2smsg_def sectxt_of_obj_simps 
   split:if_splits option.splits)
 done
 
 lemma cm2smsg_recvmsg1':
   "\<lbrakk>valid (RecvMsg p q m # s); q' \<noteq> q\<rbrakk> \<Longrightarrow> cm2smsg (RecvMsg p q m # s) q' = cm2smsg s q'"
 apply (frule vd_cons, frule vt_grant_os, rule ext)
-apply (auto simp:cm2smsg_def tainted_eq_Tainted sectxt_of_obj_simps 
+apply (auto simp:cm2smsg_def sectxt_of_obj_simps 
   split:if_splits option.splits)
 done
 
 lemma cm2smsg_recvmsg2':
   "\<lbrakk>valid (RecvMsg p q m # s); m' \<noteq> m\<rbrakk> \<Longrightarrow> cm2smsg (RecvMsg p q m # s) q m' = cm2smsg s q m'"
 apply (frule vd_cons, frule vt_grant_os)
-apply (auto simp:cm2smsg_def tainted_eq_Tainted sectxt_of_obj_simps 
+apply (auto simp:cm2smsg_def sectxt_of_obj_simps 
   split:if_splits option.splits)
 done
 
 lemma cm2smsg_removemsgq:
   "\<lbrakk>q' \<noteq> q; valid (RemoveMsgq p q # s)\<rbrakk> \<Longrightarrow> cm2smsg (RemoveMsgq p q # s) q' = cm2smsg s q'"
 apply (frule vd_cons, frule vt_grant_os, rule ext)
-apply (auto simp:cm2smsg_def tainted_eq_Tainted sectxt_of_obj_simps 
+apply (auto simp:cm2smsg_def sectxt_of_obj_simps 
   split:if_splits option.splits)
 done
 
@@ -358,6 +358,7 @@
     apply (drule cq2smsg_createmsgq, simp, simp)
 
     apply (drule_tac m = m and q = q and qi = qi and qsec = "(aa,ab,b)" in p1, simp+)
+    apply (drule_tac m = m and q = q and qi = qi and qsec = "(aa,ab,b)" in p1, simp+)
 
     apply (simp add:cq2smsgq_def split:option.splits)
     apply (rule_tac m = m and sm = sm in cqm2sms_prop0, simp+)
@@ -670,62 +671,6 @@
 apply (simp add:cf2sfile_mkdir1 current_files_simps)
 done
 
-lemma cf2sfile_linkhard1:
-  "\<lbrakk>valid (LinkHard p oldf f # s); f' \<in> current_files s\<rbrakk>
-   \<Longrightarrow> cf2sfile (LinkHard p oldf f# s) f' = cf2sfile s f'"
-apply (frule vd_cons, frule vt_grant_os, frule noroot_events)
-apply (case_tac "f = f'", simp)
-apply (induct f', simp add:sroot_only, simp)
-apply (frule parentf_in_current', simp+)
-apply (simp add:cf2sfile_def is_file_simps is_dir_simps current_files_simps sectxt_of_obj_simps 
-               get_parentfs_ctxts_simps split:if_splits option.splits)
-done
-
-lemma cf2sfile_linkhard2:
-  "\<lbrakk>valid (LinkHard p oldf f # s); is_file s f'\<rbrakk>
-   \<Longrightarrow> cf2sfile (LinkHard p oldf f # s) f' = cf2sfile s f'"
-apply (frule vd_cons, drule is_file_in_current)
-by (simp add:cf2sfile_linkhard1)
-
-lemma cf2sfile_linkhard3:
-  "\<lbrakk>valid (LinkHard p oldf f # s); is_dir s f'\<rbrakk>
-   \<Longrightarrow> cf2sfile (LinkHard p oldf f # s) f' = cf2sfile s f'"
-apply (frule vd_cons, drule is_dir_in_current)
-by (simp add:cf2sfile_linkhard1)
-
-lemma cf2sfile_linkhard4:
-  "valid (LinkHard p oldf f # s)
-  \<Longrightarrow> cf2sfile (LinkHard p oldf f # s) f = (case (parent f) of
-         Some pf \<Rightarrow> (case (sectxt_of_obj (LinkHard p oldf f # s) (O_file f), sectxt_of_obj s (O_dir pf), 
-                           get_parentfs_ctxts s pf) of
-                      (Some sec, Some psec, Some asecs) \<Rightarrow> Some (Created, sec, Some psec, set asecs)
-                    | _ \<Rightarrow> None)
-       | None \<Rightarrow> None)"
-apply (frule vd_cons, frule vt_grant_os, frule noroot_events)
-apply (case_tac f, simp)
-apply (simp add:cf2sfile_def is_file_simps is_dir_simps current_files_simps sectxt_of_obj_simps 
-               get_parentfs_ctxts_simps)
-apply (rule impI, (erule conjE)+)
-apply (drule not_deleted_init_file, simp+)
-apply (simp add:is_file_in_current)
-done
-
-lemma cf2sfile_linkhard:
-  "\<lbrakk>valid (LinkHard p oldf f # s); f' \<in> current_files (LinkHard p oldf f # s)\<rbrakk>
-  \<Longrightarrow> cf2sfile (LinkHard p oldf f # s) f' = (
-    if (f' = f) 
-    then (case (parent f) of
-             Some pf \<Rightarrow> (case (sectxt_of_obj (LinkHard p oldf f # s) (O_file f), sectxt_of_obj s (O_dir pf), 
-                 get_parentfs_ctxts s pf) of
-                          (Some sec, Some psec, Some asecs) \<Rightarrow> Some (Created, sec, Some psec, set asecs)
-                        | _ \<Rightarrow> None)
-           | None \<Rightarrow> None)
-     else cf2sfile s f')"
-apply (case_tac "f = f'")
-apply (simp add:cf2sfile_linkhard4 split:option.splits)
-apply (simp add:cf2sfile_linkhard1 current_files_simps)
-done
-
 lemma cf2sfile_other:
   "\<lbrakk>ff \<in> current_files s;
     \<forall> p f flag fd opt. e \<noteq> Open p f flag fd opt;
@@ -733,7 +678,6 @@
     \<forall> p f. e \<noteq> UnLink p f;
     \<forall> p f. e \<noteq> Rmdir p f;
     \<forall> p f i. e \<noteq> Mkdir p f i;
-    \<forall> p f f'. e \<noteq> LinkHard p f f'; 
     valid (e # s)\<rbrakk> \<Longrightarrow> cf2sfile (e # s) ff = cf2sfile s ff"
 apply (frule vd_cons, frule vt_grant_os)
 apply (induct ff, simp add:sroot_only)
@@ -749,7 +693,6 @@
     \<forall> p f. e \<noteq> UnLink p f;
     \<forall> p f. e \<noteq> Rmdir p f;
     \<forall> p f i. e \<noteq> Mkdir p f i;
-    \<forall> p f f'. e \<noteq> LinkHard p f f'; 
     ff \<in> current_files s\<rbrakk> \<Longrightarrow> cf2sfile (e # s) ff = cf2sfile s ff"
 by (auto intro!:cf2sfile_other)
   
@@ -785,15 +728,17 @@
 apply (frule vd_cons, frule vt_grant_os)
 apply (simp add:current_files_simps split:if_splits option.splits) 
 (* costs too much time, but solved *)
-
+(*
 apply (auto simp:cf2sfile_def sectxt_of_obj_simps get_parentfs_ctxts_simps is_file_simps is_dir_simps 
            split:if_splits option.splits  
             dest:init_file_dir_conflict pfdof_simp5 pfdof_simp6 file_of_pfd_is_file
                  not_deleted_init_file not_deleted_init_dir is_file_not_dir is_dir_not_file
             dest!:current_has_sec')
 done
+*)
+sorry
 
-lemmas cf2sfile_simps = cf2sfile_open cf2sfile_mkdir cf2sfile_linkhard cf2sfile_other
+lemmas cf2sfile_simps = cf2sfile_open cf2sfile_mkdir cf2sfile_other
   cf2sfile_unlink cf2sfile_rmdir cf2sfile_closefd
   
 (*********** cfd2sfd simpset *********)
@@ -871,8 +816,8 @@
 done
 
 lemma cfd2sfd_clone:
-  "\<lbrakk>valid (Clone p p' fds shms # s); file_of_proc_fd (Clone p p' fds shms # s) p'' fd' = Some f\<rbrakk>
-   \<Longrightarrow> cfd2sfd (Clone p p' fds shms # s) p'' fd' = (
+  "\<lbrakk>valid (Clone p p' fds # s); file_of_proc_fd (Clone p p' fds # s) p'' fd' = Some f\<rbrakk>
+   \<Longrightarrow> cfd2sfd (Clone p p' fds # s) p'' fd' = (
      if (p'' = p') then cfd2sfd s p fd'
      else cfd2sfd s p'' fd')"
 apply (frule vd_cons, frule vt_grant_os)
@@ -927,7 +872,7 @@
 lemma cfd2sfd_other:
   "\<lbrakk>valid (e # s); file_of_proc_fd (e # s) p' fd' = Some f';
     \<forall> p f flags fd opt. e \<noteq> Open p f flags fd opt;
-    \<forall> p p'' fds shms. e \<noteq> Clone p p'' fds shms\<rbrakk>
+    \<forall> p p'' fds. e \<noteq> Clone p p'' fds\<rbrakk>
    \<Longrightarrow> cfd2sfd (e # s) p' fd' = cfd2sfd s p' fd'"
 apply (frule vd_cons, frule vt_grant_os)
 apply (frule proc_fd_in_fds, simp)
@@ -1057,8 +1002,8 @@
 done
 
 lemma cpfd2sfds_clone:
-  "valid (Clone p p' fds shms # s) 
-   \<Longrightarrow> cpfd2sfds (Clone p p' fds shms # s) = (cpfd2sfds s) (p' := {sfd. \<exists> fd \<in> fds. \<exists> f. file_of_proc_fd s p fd = Some f \<and> cfd2sfd s p fd = Some sfd})"
+  "valid (Clone p p' fds # s) 
+   \<Longrightarrow> cpfd2sfds (Clone p p' fds # s) = (cpfd2sfds s) (p' := {sfd. \<exists> fd \<in> fds. \<exists> f. file_of_proc_fd s p fd = Some f \<and> cfd2sfd s p fd = Some sfd})"
 apply (frule vd_cons, frule vt_grant_os)
 apply (rule ext)
 apply (rule set_eqI, rule iffI)
@@ -1087,7 +1032,7 @@
     \<forall> p p'. e \<noteq> Kill p p';
     \<forall> p. e \<noteq> Exit p;
     \<forall> p fd. e \<noteq> CloseFd p fd;
-    \<forall> p p' fds shms. e \<noteq> Clone p p' fds shms\<rbrakk> \<Longrightarrow> cpfd2sfds (e # s) = cpfd2sfds s"
+    \<forall> p p' fds. e \<noteq> Clone p p' fds\<rbrakk> \<Longrightarrow> cpfd2sfds (e # s) = cpfd2sfds s"
 apply (frule vd_cons, frule vt_grant_os)
 apply (rule ext)
 unfolding cpfd2sfds_def proc_file_fds_def
@@ -1185,265 +1130,13 @@
 lemmas cpfd2sfds_simps = cpfd2sfds_open cpfd2sfds_execve cpfd2sfds_clone cpfd2sfds_kill cpfd2sfds_exit
   cpfd2sfds_closefd cpfd2sfds_other
 
-(********* ch2sshm simpset ********)
-
-lemma ch2sshm_createshm:
-  "valid (CreateShM p h # s) 
-   \<Longrightarrow> ch2sshm (CreateShM p h # s) = (ch2sshm s) (h := 
-     (case (sectxt_of_obj (CreateShM p h # s) (O_shm h)) of
-                    Some sec \<Rightarrow> 
- Some (if (\<not> deleted (O_shm h) s \<and> h \<in> init_shms) then Init h else Created, sec)
-                  | _ \<Rightarrow> None))"
-apply (frule vd_cons, frule vt_grant_os)
-apply (auto simp:ch2sshm_def sectxt_of_obj_simps dest!:current_has_sec' split:option.splits if_splits)
-done
-
-lemma ch2sshm_other:
-  "\<lbrakk>valid (e # s); 
-    \<forall> p h. e \<noteq> CreateShM p h; 
-    h' \<in> current_shms (e # s)\<rbrakk> \<Longrightarrow> ch2sshm (e # s) h' = ch2sshm s h'"
-apply (frule vd_cons, frule vt_grant_os)
-apply (case_tac e)
-apply (auto simp:ch2sshm_def sectxt_of_obj_simps dest!:current_has_sec' split:option.splits if_splits)
-done
-
-lemmas ch2sshm_simps = ch2sshm_createshm ch2sshm_other
-
-lemma current_shm_has_sh:
-  "\<lbrakk>h \<in> current_shms s; valid s\<rbrakk> \<Longrightarrow> \<exists> sh. ch2sshm s h = Some sh"
-by (auto simp:ch2sshm_def split:option.splits dest!:current_has_sec')
-
-lemma current_shm_has_sh':
-  "\<lbrakk>ch2sshm s h = None; valid s\<rbrakk> \<Longrightarrow> h \<notin> current_shms s"
-by (auto dest:current_shm_has_sh)
-
-(********** cph2spshs simpset **********)
-
-lemma cph2spshs_attach:
-  "valid (Attach p h flag # s) \<Longrightarrow> 
-   cph2spshs (Attach p h flag # s) = (cph2spshs s) (p := 
-     (case (ch2sshm s h) of 
-        Some sh \<Rightarrow> cph2spshs s p \<union> {(sh, flag)}
-      | _       \<Rightarrow> cph2spshs s p) )"
-apply (frule vd_cons, frule vt_grant_os, rule ext)
-using ch2sshm_other[where e = "Attach p h flag" and s = s]
-apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
-dest!:current_shm_has_sh' dest: procs_of_shm_prop1 simp:cph2spshs_def)
-apply (erule_tac x = ha in allE, frule procs_of_shm_prop1, simp, simp)
-apply (erule_tac x = ha in allE, frule procs_of_shm_prop1, simp, simp)
-apply (erule_tac x = ha in allE, frule procs_of_shm_prop1, simp, simp)
-apply (erule_tac x = ha in allE, frule procs_of_shm_prop1, simp, simp)
-apply (erule_tac x = ha in allE, frule procs_of_shm_prop1, simp, simp)
-apply (case_tac "ha = h", simp, frule procs_of_shm_prop1, simp)
-apply (rule_tac x = ha in exI, simp)
-apply (rule_tac x = ha in exI, simp, drule procs_of_shm_prop1, simp, simp)
-apply (rule_tac x = ha in exI, simp)
-apply (frule procs_of_shm_prop1, simp, simp)
-apply (rule impI, simp)
-done
-
-lemma cph2spshs_detach: "valid (Detach p h # s) \<Longrightarrow> 
-  cph2spshs (Detach p h # s) = (cph2spshs s) (p := 
-    (case (ch2sshm s h, flag_of_proc_shm s p h) of 
-       (Some sh, Some flag) \<Rightarrow> if (\<exists> h'. h' \<noteq> h \<and> (p,flag) \<in> procs_of_shm s h' \<and> ch2sshm s h' = Some sh)
-                  then cph2spshs s p else cph2spshs s p - {(sh, flag)}
-     | _       \<Rightarrow> cph2spshs s p)             )"
-apply (frule vd_cons, frule vt_grant_os, rule ext)
-apply (case_tac "x = p")  defer
-using ch2sshm_other[where e = "Detach p h" and s = s] 
-apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
-dest!:current_shm_has_sh' procs_of_shm_prop4' dest:procs_of_shm_prop1 procs_of_shm_prop3 simp:cph2spshs_def) [1]
-apply (rule_tac x = ha in exI, frule_tac h = ha in procs_of_shm_prop1, simp, simp)
-apply (rule_tac x = ha in exI, frule_tac h = ha in procs_of_shm_prop1, simp, simp)
-apply (rule impI, simp)
-
-apply (clarsimp)
-apply (frule current_shm_has_sh, simp, erule exE)
-apply (frule procs_of_shm_prop4, simp, simp)
-apply (rule allI | rule conjI| erule conjE | erule exE | rule impI)+
-
-apply (simp only:cph2spshs_def, rule set_eqI, rule iffI)
-apply (erule CollectE | erule exE| erule conjE| rule CollectI)+
-apply (case_tac "ha = h", simp)
-apply (rule_tac x = sha in exI, rule_tac x = flaga in exI, rule_tac x = ha in exI, simp)
-using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
-
-apply (erule CollectE | erule exE| erule conjE| rule CollectI)+
-apply (case_tac "ha = h", simp)
-apply (rule_tac x = h' in exI, simp)
-apply (frule_tac flag = flag and flag' = flaga in procs_of_shm_prop3, simp+)
-apply (frule_tac flag = flaga in procs_of_shm_prop4, simp+)
-using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
-apply (frule_tac h = h' in procs_of_shm_prop1, simp, simp)
-apply (rule_tac x = ha in exI, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
-using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
-
-apply (rule allI | rule conjI| erule conjE | erule exE | rule impI)+
-apply (simp only:cph2spshs_def, rule set_eqI, rule iffI)
-apply (erule CollectE | erule exE| erule conjE| rule DiffI |rule CollectI)+
-apply (simp split:if_splits)
-apply (rule_tac x = ha in exI, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
-using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
-apply (rule notI, simp split:if_splits)
-apply (erule_tac x = ha in allE, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
-using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
-apply (erule CollectE | erule exE| erule conjE| erule DiffE |rule CollectI)+
-apply (simp split:if_splits)
-apply (erule_tac x = ha in allE, simp, rule_tac x = ha in exI, simp)
-apply (case_tac "ha = h", simp add:procs_of_shm_prop3, frule_tac h = ha in procs_of_shm_prop1, simp+)
-using ch2sshm_other[where e = "Detach p h" and s = s] apply (simp add:procs_of_shm_prop1)
-done
-
-lemma cph2spshs_deleteshm:
-  "valid (DeleteShM p h # s) \<Longrightarrow>     
-   cph2spshs (DeleteShM p h # s) = (\<lambda> p'. 
-    (case (ch2sshm s h, flag_of_proc_shm s p' h) of 
-       (Some sh, Some flag) \<Rightarrow> if (\<exists> h'. h' \<noteq> h \<and> (p', flag) \<in> procs_of_shm s h' \<and> ch2sshm s h' = Some sh)
-                  then cph2spshs s p' else cph2spshs s p' - {(sh, flag)}
-     | _       \<Rightarrow> cph2spshs s p')   )"
-apply (frule vd_cons, frule vt_grant_os, rule ext)
-
-apply (clarsimp)
-apply (frule current_shm_has_sh, simp, erule exE, simp, simp split:option.splits)
-apply (rule conjI, rule impI)
-using ch2sshm_other[where e = "DeleteShM p h" and s = s] 
-apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
-dest!:current_shm_has_sh' procs_of_shm_prop4' dest:procs_of_shm_prop1 procs_of_shm_prop3 simp:cph2spshs_def) [1]
-apply (rule_tac x = ha in exI, frule_tac h = ha in procs_of_shm_prop1, simp+)
-apply (rule_tac x = ha in exI, simp)
-apply (case_tac "ha = h", simp+, frule_tac h = ha in procs_of_shm_prop1, simp+)
-
-apply (rule allI | rule conjI| erule conjE | erule exE | rule impI)+
-
-apply (simp only:cph2spshs_def, rule set_eqI, rule iffI)
-apply (erule CollectE | erule exE| erule conjE| rule CollectI)+
-apply (case_tac "ha = h", simp)
-apply (rule_tac x = sha in exI, rule_tac x = flag in exI, rule_tac x = ha in exI, simp)
-using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
-
-apply (erule CollectE | erule exE| erule conjE| rule CollectI)+
-apply (case_tac "ha = h", simp)
-apply (rule_tac x = h' in exI, simp)
-apply (frule_tac flag = flag in procs_of_shm_prop4, simp+)
-using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
-apply (frule_tac h = h' in procs_of_shm_prop1, simp, simp)
-apply (rule_tac x = ha in exI, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
-using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
-
-apply (rule allI | rule conjI| erule conjE | erule exE | rule impI)+
-apply (simp only:cph2spshs_def, rule set_eqI, rule iffI)
-apply (erule CollectE | erule exE| erule conjE| rule DiffI |rule CollectI)+
-apply (simp split:if_splits)
-apply (rule_tac x = ha in exI, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
-using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
-apply (rule notI, simp split:if_splits)
-apply (erule_tac x = ha in allE, simp, frule_tac h = ha in procs_of_shm_prop1, simp+)
-using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
-apply (erule CollectE | erule exE| erule conjE| erule DiffE |rule CollectI)+
-apply (simp split:if_splits)
-apply (erule_tac x = ha in allE, simp, rule_tac x = ha in exI, simp)
-apply (case_tac "ha = h", simp add:procs_of_shm_prop4)
-apply (frule_tac h = ha in procs_of_shm_prop1, simp+)
-using ch2sshm_other[where e = "DeleteShM p h" and s = s] apply (simp add:procs_of_shm_prop1)
-done
-
-lemma flag_of_proc_shm_prop1:
-  "\<lbrakk>flag_of_proc_shm s p h = Some flag; valid s\<rbrakk> \<Longrightarrow> (p, flag) \<in> procs_of_shm s h"
-apply (induct s arbitrary:p)
-apply (simp add:init_shmflag_has_proc)
-apply (frule vt_grant_os, frule vd_cons, case_tac a, auto split:if_splits option.splits)
-done
-
-lemma cph2spshs_clone:
-  "valid (Clone p p' fds shms # s) \<Longrightarrow> 
-   cph2spshs (Clone p p' fds shms # s) = (cph2spshs s) (p' := 
-     {(sh, flag) | h sh flag. h \<in> shms \<and> ch2sshm s h = Some sh \<and> flag_of_proc_shm s p h = Some flag} )"
-apply (frule vd_cons, frule vt_grant_os, rule ext)
-using ch2sshm_other[where e = "Clone p p' fds shms" and s = s]
-apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
-dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 simp:cph2spshs_def)
-apply (erule_tac x = h in allE, frule procs_of_shm_prop1, simp, simp add:procs_of_shm_prop4)
-apply (rule_tac x = h in exI, simp, frule flag_of_proc_shm_prop1, simp+, simp add:procs_of_shm_prop1)
-apply (rule_tac x = h in exI, simp, frule procs_of_shm_prop1, simp+)+
-done
-
-lemma cph2spshs_execve:
-  "valid (Execve p f fds # s) \<Longrightarrow>
-  cph2spshs (Execve p f fds # s) = (cph2spshs s) (p := {})"
-apply (frule vd_cons, frule vt_grant_os, rule ext)
-using ch2sshm_other[where e = "Execve p f fds" and s = s]
-apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
-dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 simp:cph2spshs_def)
-apply (rule_tac x = h in exI, simp add:procs_of_shm_prop1)+
-done
-
-lemma cph2spshs_kill:
-  "valid (Kill p p' # s) \<Longrightarrow> cph2spshs (Kill p p' # s) = (cph2spshs s) (p' := {})"
-apply (frule vd_cons, frule vt_grant_os, rule ext)
-using ch2sshm_other[where e = "Kill p p'" and s = s]
-apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
-dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 simp:cph2spshs_def)
-apply (rule_tac x = h in exI, simp add:procs_of_shm_prop1)+
-done
-
-lemma cph2spshs_exit:
-  "valid (Exit p # s) \<Longrightarrow> cph2spshs (Exit p # s) = (cph2spshs s) (p := {})"
-apply (frule vd_cons, frule vt_grant_os, rule ext)
-using ch2sshm_other[where e = "Exit p" and s = s]
-apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
-dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 simp:cph2spshs_def)
-apply (rule_tac x = h in exI, simp add:procs_of_shm_prop1)+
-done
-
-lemma cph2spshs_createshm:
-  "valid (CreateShM p h # s) \<Longrightarrow> cph2spshs (CreateShM p h # s) = cph2spshs s"
-apply (frule vt_grant_os, frule vd_cons, rule ext)
-apply (auto simp:cph2spshs_def)
-using ch2sshm_createshm
-apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
-dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 simp:cph2spshs_def)
-apply (rule_tac x = ha in exI, auto simp:procs_of_shm_prop1)
-done
-
-lemma cph2spshs_other:
-  "\<lbrakk>valid (e # s); 
-    \<forall> p h flag. e \<noteq> Attach p h flag;
-    \<forall> p h. e \<noteq> Detach p h;
-    \<forall> p h. e \<noteq> DeleteShM p h;
-    \<forall> p p' fds shms. e \<noteq> Clone p p' fds shms;
-    \<forall> p f fds. e \<noteq> Execve p f fds;
-    \<forall> p p'. e \<noteq> Kill p p';
-    \<forall> p. e \<noteq> Exit p\<rbrakk> \<Longrightarrow> cph2spshs (e # s) = cph2spshs s"
-apply (frule vt_grant_os, frule vd_cons, rule ext)
-unfolding cph2spshs_def 
-apply (rule set_eqI, rule iffI)
-apply (erule CollectE | erule conjE| erule exE| rule conjI| rule impI| rule CollectI)+
-apply (frule procs_of_shm_prop1, simp, rule_tac x= sh in exI, rule_tac x = flag in exI, rule_tac x = h in exI)
-apply (case_tac e)
-using ch2sshm_other[where e = e and s = s] 
-apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
-dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3
- simp:ch2sshm_createshm)
-apply (rule_tac x = h in exI, case_tac e)
-using ch2sshm_other[where e = e and s = s] 
-apply (auto split del:t_open_must_flag.splits t_open_option_flag.splits split add:if_splits option.splits
-dest!:current_shm_has_sh' dest: procs_of_shm_prop1 procs_of_shm_prop2 procs_of_shm_prop3 
- simp:ch2sshm_createshm)
-done
-
-lemmas cph2spshs_simps = cph2spshs_attach cph2spshs_detach cph2spshs_deleteshm cph2spshs_clone cph2spshs_execve
-  cph2spshs_exit cph2spshs_kill cph2spshs_other
-
-(******** cp2sproc simpset *********)
-
 lemma cp2sproc_clone:
-  "valid (Clone p p' fds shms # s) \<Longrightarrow> cp2sproc (Clone p p' fds shms # s) = (cp2sproc s) (p' := 
+  "valid (Clone p p' fds # s) \<Longrightarrow> cp2sproc (Clone p p' fds # s) = (cp2sproc s) (p' := 
      case (sectxt_of_obj s (O_proc p)) of 
        Some sec \<Rightarrow> Some (Created, sec, 
-  {sfd. \<exists> fd \<in> fds. \<exists> f. file_of_proc_fd s p fd = Some f \<and> cfd2sfd s p fd = Some sfd},
-  {(sh, flag) | h sh flag. h \<in> shms \<and> ch2sshm s h = Some sh \<and> flag_of_proc_shm s p h = Some flag})
+  {sfd. \<exists> fd \<in> fds. \<exists> f. file_of_proc_fd s p fd = Some f \<and> cfd2sfd s p fd = Some sfd})
      | _        \<Rightarrow> None)"
-apply (frule cph2spshs_clone, frule cpfd2sfds_clone)
+apply (frule cpfd2sfds_clone)
 apply (frule vd_cons, frule vt_grant_os, simp only:os_grant.simps)
 apply ((erule exE| erule conjE)+, frule not_init_intro_proc, simp, rule ext, case_tac "x = p'", simp)
 apply (auto simp:cp2sproc_def sectxt_of_obj_simps dest!:current_has_sec' 
@@ -1454,14 +1147,11 @@
   "\<lbrakk>valid (e # s); 
     \<forall> p f flags fd opt. e \<noteq> Open p f flags fd opt;
     \<forall> p fd. e \<noteq> CloseFd p fd;
-    \<forall> p h flag. e \<noteq> Attach p h flag;
-    \<forall> p h. e \<noteq> Detach p h;
-    \<forall> p h. e \<noteq> DeleteShM p h;
-    \<forall> p p' fds shms. e \<noteq> Clone p p' fds shms;
+    \<forall> p p' fds. e \<noteq> Clone p p' fds;
     \<forall> p f fds. e \<noteq> Execve p f fds;
     \<forall> p p'. e \<noteq> Kill p p';
     \<forall> p. e \<noteq> Exit p\<rbrakk> \<Longrightarrow> cp2sproc (e # s) = cp2sproc s"
-apply (frule cph2spshs_other, simp+, frule cpfd2sfds_other, simp+)
+apply (frule cpfd2sfds_other, simp+)
 apply (frule vt_grant_os, frule vd_cons, rule ext, case_tac e, simp_all) 
 apply (auto simp:cp2sproc_def sectxt_of_obj_simps dest!:current_has_sec' 
             dest:current_proc_has_sec not_deleted_init_proc split:option.splits if_splits)
@@ -1474,9 +1164,8 @@
            cf2sfile (Open p f flags fd opt # s) f) of 
        (Some sec, Some fdsec, Some sf) \<Rightarrow> Some (if (\<not> deleted (O_proc p) s \<and> p \<in> init_procs) 
                                                then Init p else Created, sec, 
-                                                (cpfd2sfds s p) \<union> {(fdsec, flags, sf)}, cph2spshs s p)
+                                                (cpfd2sfds s p) \<union> {(fdsec, flags, sf)})
      | _        \<Rightarrow> None)"
-apply (frule cph2spshs_other, simp, simp, simp, simp, simp, simp, simp)
 apply (frule cpfd2sfds_open, frule vt_grant_os, frule vd_cons, rule ext)
 apply (case_tac "x = p") 
 apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps 
@@ -1494,29 +1183,11 @@
                           else (case (sectxt_of_obj s (O_proc p)) of
                                   Some sec \<Rightarrow> Some (if (\<not> deleted (O_proc p) s \<and> p \<in> init_procs) 
                                                     then Init p else Created, 
-                                                    sec, cpfd2sfds s p - {sfd}, cph2spshs s p)
+                                                    sec, cpfd2sfds s p - {sfd})
                                 | _        \<Rightarrow> None))
            | _        \<Rightarrow> cp2sproc s p)
      else cp2sproc s p)"
-apply (frule cpfd2sfds_closefd, frule cph2spshs_other, simp, simp, simp, simp, simp, simp, simp)
-apply (frule vt_grant_os, frule vd_cons, rule ext)
-apply (case_tac "x = p") 
-apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps 
-           dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
-            dest:current_proc_has_sec not_deleted_init_proc split:option.splits if_splits)
-done
-
-lemma cp2sproc_attach:
-  "valid (Attach p h flag # s) \<Longrightarrow> 
-   cp2sproc (Attach p h flag # s) = (cp2sproc s) (p := 
-     (case (ch2sshm s h) of 
-        Some sh \<Rightarrow> (case (sectxt_of_obj s (O_proc p)) of
-                      Some sec \<Rightarrow> Some (if (\<not> deleted (O_proc p) s \<and> p \<in> init_procs) 
-                                        then Init p else Created, 
-                                        sec, cpfd2sfds s p, cph2spshs s p \<union> {(sh, flag)})
-                    | _        \<Rightarrow> None)
-      | _       \<Rightarrow> cp2sproc s p) )"
-apply (frule cph2spshs_attach, frule cpfd2sfds_other, simp, simp, simp, simp, simp, simp)
+apply (frule cpfd2sfds_closefd)
 apply (frule vt_grant_os, frule vd_cons, rule ext)
 apply (case_tac "x = p") 
 apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps 
@@ -1524,53 +1195,14 @@
             dest:current_proc_has_sec not_deleted_init_proc split:option.splits if_splits)
 done
 
-lemma cp2sproc_detach:
-  "valid (Detach p h # s) \<Longrightarrow> 
-   cp2sproc (Detach p h # s) = (cp2sproc s) (p := 
-    (case (ch2sshm s h, flag_of_proc_shm s p h) of 
-       (Some sh, Some flag) \<Rightarrow> if (\<exists> h'. h' \<noteq> h \<and> (p,flag) \<in> procs_of_shm s h' \<and> ch2sshm s h' = Some sh)
-                              then cp2sproc s p 
-                              else (case (sectxt_of_obj s (O_proc p)) of
-                                      Some sec \<Rightarrow> Some (if (\<not> deleted (O_proc p) s \<and> p \<in> init_procs) 
-                                                       then Init p else Created, sec,
-                                                       cpfd2sfds s p, cph2spshs s p - {(sh, flag)})
-                                    | None     \<Rightarrow> None)                   
-     | _       \<Rightarrow> cp2sproc s p)             )"
-apply (frule cph2spshs_detach, frule cpfd2sfds_other, simp, simp, simp, simp, simp, simp)
-apply (frule vt_grant_os, frule vd_cons, rule ext)
-apply (case_tac "x = p") 
-apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps 
-           dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
-            dest:current_proc_has_sec not_deleted_init_proc split:option.splits if_splits)
-done
-
-lemma cp2sproc_deleteshm:
-  "valid (DeleteShM p h # s) \<Longrightarrow> 
-   cp2sproc (DeleteShM p h # s) = (\<lambda> p'. 
-    (case (ch2sshm s h, flag_of_proc_shm s p' h) of 
-       (Some sh, Some flag) \<Rightarrow> if (\<exists> h'. h' \<noteq> h \<and> (p', flag) \<in> procs_of_shm s h' \<and> ch2sshm s h' = Some sh)
-                              then cp2sproc s p' 
-                              else (case (sectxt_of_obj s (O_proc p')) of
-                                      Some sec \<Rightarrow> Some (if (\<not> deleted (O_proc p') s \<and> p' \<in> init_procs) 
-                                                       then Init p' else Created, sec,
-                                                       cpfd2sfds s p', cph2spshs s p' - {(sh, flag)})
-                                    | None     \<Rightarrow> None)                   
-     | _       \<Rightarrow> cp2sproc s p')             )"
-apply (frule cph2spshs_deleteshm, frule cpfd2sfds_other, simp, simp, simp, simp, simp, simp)
-apply (frule vt_grant_os, frule vd_cons, rule ext)
-apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps 
-           dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
-            dest:current_proc_has_sec not_deleted_init_proc split:option.splits if_splits)
-done
-
 lemma cp2sproc_execve:
   "valid (Execve p f fds # s) \<Longrightarrow> 
    cp2sproc (Execve p f fds # s) = (cp2sproc s) (p := 
      (case (sectxt_of_obj (Execve p f fds # s) (O_proc p)) of
         Some sec \<Rightarrow> Some (if (\<not> deleted (O_proc p) s \<and> p \<in> init_procs) then Init p else Created, sec, 
-                         {sfd. \<exists> fd \<in> fds. \<exists> f. file_of_proc_fd s p fd = Some f \<and> cfd2sfd s p fd = Some sfd}, {})
+                         {sfd. \<exists> fd \<in> fds. \<exists> f. file_of_proc_fd s p fd = Some f \<and> cfd2sfd s p fd = Some sfd})
       | _        \<Rightarrow> None)                        )"
-apply (frule cph2spshs_execve, frule cpfd2sfds_execve)
+apply (frule cpfd2sfds_execve)
 apply (frule vt_grant_os, frule vd_cons, rule ext)
 apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps 
            dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
@@ -1580,7 +1212,7 @@
 lemma cp2sproc_kill:
   "\<lbrakk>valid (Kill p p' # s); p'' \<noteq> p'\<rbrakk> \<Longrightarrow> 
    cp2sproc (Kill p p' # s) p'' = (cp2sproc s) p''"
-apply (frule cph2spshs_kill, frule cpfd2sfds_kill)
+apply (frule cpfd2sfds_kill)
 apply (frule vt_grant_os, frule vd_cons)
 apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps 
            dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
@@ -1595,7 +1227,7 @@
 lemma cp2sproc_exit:
   "\<lbrakk>valid (Exit p # s); p' \<noteq> p\<rbrakk> \<Longrightarrow> 
    cp2sproc (Exit p # s) p' = (cp2sproc s) p'"
-apply (frule cph2spshs_exit, frule cpfd2sfds_exit)
+apply (frule cpfd2sfds_exit)
 apply (frule vt_grant_os, frule vd_cons)
 apply (auto simp:cp2sproc_def sectxt_of_obj_simps current_files_simps 
            dest!:current_has_sec' dest!:current_file_has_sfile' dest:is_file_in_current is_dir_in_current
@@ -1607,8 +1239,8 @@
    cp2sproc (Exit p # s) p' = (cp2sproc s) p'"
 by (drule_tac p'= p' in cp2sproc_exit, simp+)
 
-lemmas cp2sproc_simps = cp2sproc_open cp2sproc_closefd cp2sproc_attach cp2sproc_detach cp2sproc_deleteshm
-  cp2sproc_clone cp2sproc_execve cp2sproc_kill cp2sproc_exit cp2sproc_other 
+lemmas cp2sproc_simps = cp2sproc_open cp2sproc_closefd cp2sproc_clone cp2sproc_execve 
+  cp2sproc_kill cp2sproc_exit cp2sproc_other 
 
 lemma current_proc_has_sp:
   "\<lbrakk>p \<in> current_procs s; valid s\<rbrakk> \<Longrightarrow> \<exists> sp. cp2sproc s p = Some sp"
@@ -1618,230 +1250,23 @@
   "\<lbrakk>cp2sproc s p = None; valid s\<rbrakk> \<Longrightarrow> p \<notin> current_procs s"
 by (auto dest:current_proc_has_sp)
 
-
-
-(* simpset for cf2sfiles *)
-
-lemma cf2sfiles_open:
-  "\<lbrakk>valid (Open p f flag fd opt # s); f' \<in> current_files (Open p f flag fd opt # s)\<rbrakk>
-   \<Longrightarrow> cf2sfiles (Open p f flag fd opt # s) f' = (
-     if (f' = f \<and> opt \<noteq> None) 
-     then (case cf2sfile (Open p f flag fd opt # s) f of 
-             Some sf \<Rightarrow> {sf}  
-           | _       \<Rightarrow> {} )
-     else cf2sfiles s f')"
-apply (frule vt_grant_os, frule vd_cons)
-apply (auto simp:cf2sfiles_def cf2sfile_open_none cf2sfile_simps same_inode_files_open
-  split:if_splits option.splits dest!:current_file_has_sfile' dest:cf2sfile_open)
-apply (rule_tac x = "f'a" in bexI, drule same_inode_files_prop1, simp add:cf2sfile_open_some1, simp)+
-done
-
-lemma cf2sfiles_other:
-  "\<lbrakk>valid (e # s);
-    \<forall> p f flag fd opt. e \<noteq> Open p f flag fd opt;
-    \<forall> p fd. e \<noteq> CloseFd p fd;
-    \<forall> p f. e \<noteq> UnLink p f;
-    \<forall> p f f'. e \<noteq> LinkHard p f f'\<rbrakk> \<Longrightarrow> cf2sfiles (e # s) = cf2sfiles s"
-apply (frule vt_grant_os, frule vd_cons, rule ext)
-apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI)
-apply (drule Set.CollectD, erule bexE, rule CollectI)
-apply (rule_tac x = f' in bexI, case_tac e)
-apply (auto simp:cf2sfiles_def cf2sfile_simps same_inode_files_simps current_files_simps
-  split:if_splits option.splits dest!:current_file_has_sfile' dest:same_inode_files_prop1 cf2sfile_other')
-apply (drule_tac f' = f' in cf2sfile_rmdir)
-apply (simp add:current_files_simps same_inode_files_prop1 same_inode_files_prop3 dir_is_empty_def)+
-
-apply (rule_tac x = f' in bexI, case_tac e)
-apply (auto simp:cf2sfiles_def cf2sfile_simps same_inode_files_simps current_files_simps
-  split:if_splits option.splits dest!:current_file_has_sfile' dest:same_inode_files_prop1 cf2sfile_other')
-apply (drule_tac f' = f' in cf2sfile_rmdir)
-apply (simp add:current_files_simps same_inode_files_prop1 same_inode_files_prop3 dir_is_empty_def)+
-done
-
-lemma cf2sfile_linkhard1':
-  "\<lbrakk>valid (LinkHard p oldf f # s); f' \<in> same_inode_files s f''\<rbrakk>
-   \<Longrightarrow> cf2sfile (LinkHard p oldf f# s) f' = cf2sfile s f'"
-apply (drule same_inode_files_prop1)
-by (simp add:cf2sfile_linkhard1)
-
-lemma cf2sfiles_linkhard:
-  "valid (LinkHard p oldf f # s) \<Longrightarrow> cf2sfiles (LinkHard p oldf f # s) = (\<lambda> f'. 
-     if (f' = f \<or> f' \<in> same_inode_files s oldf)
-     then (case (cf2sfile (LinkHard p oldf f # s) f) of
-             Some sf \<Rightarrow> cf2sfiles s oldf \<union> {sf}
-           | _       \<Rightarrow> {})
-     else cf2sfiles s f')"
-apply (frule vt_grant_os, frule vd_cons, rule ext)
-apply (auto simp:cf2sfiles_def cf2sfile_linkhard1' same_inode_files_linkhard current_files_linkhard 
-  split:if_splits option.splits dest!:current_file_has_sfile' current_has_sec' dest:same_inode_files_prop1)
-done
-
-lemma cf2sfile_unlink':
-  "\<lbrakk>valid (UnLink p f # s); f' \<in> same_inode_files (UnLink p f # s) f''\<rbrakk>
-   \<Longrightarrow> cf2sfile (UnLink p f # s) f' = cf2sfile s f'"
-apply (drule same_inode_files_prop1)
-by (simp add:cf2sfile_unlink)
-
-lemma cf2sfiles_unlink:
-  "\<lbrakk>valid (UnLink p f # s); f' \<in> current_files (UnLink p f # s)\<rbrakk> \<Longrightarrow> cf2sfiles (UnLink p f # s) f' = ( 
-     if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {} \<and> 
-         (\<forall> f'' \<in> same_inode_files s f. f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f)) then 
-        (case (cf2sfile s f) of 
-           Some sf \<Rightarrow> cf2sfiles s f' - {sf}
-         | _       \<Rightarrow> {})
-     else cf2sfiles s f')"
-apply (frule vt_grant_os, frule vd_cons, simp add:current_files_simps split:if_splits)
-apply (rule conjI, clarify, frule is_file_has_sfile', simp, erule exE, simp)
-apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
-apply (erule bexE, frule_tac f' = f' in same_inode_files_unlink)
-apply (simp add:current_files_unlink, simp, erule conjE)
-apply (erule_tac x = f'a in ballE, frule_tac f' = "f'a" in cf2sfile_unlink)
-apply (simp add:current_files_unlink same_inode_files_prop1, simp)
-apply (rule_tac x = f'a in bexI, simp, simp)
-apply (drule_tac f = f and f' = f' and f'' = f'a in same_inode_files_prop4, simp+)
-apply (erule conjE|erule exE|erule bexE)+
-apply (case_tac "f'a = f", simp)
-apply (frule_tac f' = f' in same_inode_files_unlink, simp add:current_files_unlink)
-apply (frule_tac f' = f'a in cf2sfile_unlink, simp add:current_files_unlink same_inode_files_prop1)
-apply (rule_tac x = f'a in bexI, simp, simp)
-
-apply (rule impI)+
-apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
-apply (erule bexE, frule_tac f' = f' in same_inode_files_unlink)
-apply (simp add:current_files_unlink, simp, (erule conjE)+)
-apply (rule_tac x = f'a in bexI, frule_tac f' = "f'a" in cf2sfile_unlink)
-apply (simp add:current_files_unlink same_inode_files_prop1, simp, simp)
-apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_unlink)
-apply (simp add:current_files_unlink, simp)
-apply (case_tac "f'a = f", simp)
-apply (frule_tac f = f' and f' = f in same_inode_files_prop5, simp)
-apply (erule bexE, erule conjE)
-apply (rule_tac x = f'' in bexI)
-apply (drule_tac f' = f'' in cf2sfile_unlink, simp add:current_files_unlink same_inode_files_prop1)
-apply (simp, simp, erule same_inode_files_prop4, simp)
-apply (rule_tac x = f'a in bexI)
-apply (drule_tac f' = f'a in cf2sfile_unlink, simp add:current_files_unlink same_inode_files_prop1)
-apply (simp, simp)
-
-
-apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
-apply (erule bexE, frule_tac f' = f' in same_inode_files_unlink)
-apply (simp add:current_files_unlink, simp)
-apply (rule_tac x = f'a in bexI)
-apply (frule_tac f' = f'a in cf2sfile_unlink)
-apply (simp add:same_inode_files_prop1 current_files_unlink, simp, simp)
-apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_unlink)
-apply (simp add:current_files_unlink, simp)
-apply (rule_tac x = f'a in bexI)
-apply (frule_tac f' = f'a in cf2sfile_unlink)
-apply (simp add:same_inode_files_prop1 current_files_unlink, simp, simp)
-done
-
-lemma cf2sfiles_closefd:
-  "\<lbrakk>valid (CloseFd p fd # s); f' \<in> current_files (CloseFd p fd # s)\<rbrakk> \<Longrightarrow> cf2sfiles (CloseFd p fd # s) f' = (
-     case (file_of_proc_fd s p fd) of
-       Some f \<Rightarrow> if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {(p, fd)} \<and> f \<in> files_hung_by_del s \<and> 
-                    (\<forall> f'' \<in> same_inode_files s f. f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f)) 
-                 then (case (cf2sfile s f) of 
-                         Some sf \<Rightarrow> cf2sfiles s f' - {sf}
-                       | _       \<Rightarrow> {})
-                 else cf2sfiles s f'
-     | _       \<Rightarrow> cf2sfiles s f')"
-
-apply (frule vt_grant_os, frule vd_cons, case_tac "file_of_proc_fd s p fd")
-apply (simp_all add:current_files_simps split:if_splits)
-
-apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
-apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
-apply (simp add:current_files_closefd, simp)
-apply (rule_tac x = f'a in bexI)
-apply (frule_tac f = f'a in cf2sfile_closefd)
-apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
-apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
-apply (simp add:current_files_closefd, simp)
-apply (rule_tac x = f'a in bexI)
-apply (frule_tac f = f'a in cf2sfile_closefd)
-apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
-
-apply (rule conjI, clarify, frule file_of_pfd_is_file, simp)
-apply (frule is_file_has_sfile', simp, erule exE, simp)
-apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
-apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
-apply (simp add:current_files_closefd, simp, erule conjE)
-apply (erule_tac x = f'a in ballE, frule_tac f = "f'a" in cf2sfile_closefd)
-apply (simp add:current_files_closefd same_inode_files_prop1, simp)
-apply (rule_tac x = f'a in bexI, simp, simp)
-apply (drule_tac f = a and f' = f' and f'' = f'a in same_inode_files_prop4, simp+)
-apply (erule conjE|erule exE|erule bexE)+
-apply (case_tac "f'a = a", simp)
-apply (frule_tac f' = f' in same_inode_files_closefd, simp add:current_files_closefd, simp)
-apply (frule_tac f = f'a in cf2sfile_closefd, simp add:current_files_closefd same_inode_files_prop1)
-apply (rule_tac x = f'a in bexI, simp, simp)
-
-apply (rule impI)+
-apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
-apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
-apply (simp add:current_files_closefd, simp, (erule conjE)+)
-apply (rule_tac x = f'a in bexI, frule_tac f = f'a in cf2sfile_closefd)
-apply (simp add:current_files_closefd same_inode_files_prop1, simp, simp)
-apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
-apply (simp add:current_files_closefd, simp)
-apply (case_tac "f'a = a", simp)
-apply (frule_tac f = f' and f' = a in same_inode_files_prop5, simp)
-apply (erule bexE, erule conjE)
-apply (rule_tac x = f'' in bexI)
-apply (drule_tac f = f'' in cf2sfile_closefd, simp add:current_files_closefd same_inode_files_prop1)
-apply (simp, simp, erule same_inode_files_prop4, simp)
-apply (rule_tac x = f'a in bexI)
-apply (drule_tac f = f'a in cf2sfile_closefd, simp add:current_files_closefd same_inode_files_prop1)
-apply (simp, simp)
-
-apply (rule conjI, clarify)
-
-apply (rule impI)
-apply (case_tac "a \<in> files_hung_by_del s", simp_all)
-apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
-apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
-apply (simp add:current_files_closefd, simp)
-apply (rule_tac x = f'a in bexI)
-apply (frule_tac f = f'a in cf2sfile_closefd)
-apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
-apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
-apply (simp add:current_files_closefd, simp)
-apply (rule_tac x = f'a in bexI)
-apply (frule_tac f = f'a in cf2sfile_closefd)
-apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
-apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
-apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
-apply (simp add:current_files_closefd, simp)
-apply (rule_tac x = f'a in bexI)
-apply (frule_tac f = f'a in cf2sfile_closefd)
-apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
-apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
-apply (simp add:current_files_closefd, simp)
-apply (rule_tac x = f'a in bexI)
-apply (frule_tac f = f'a in cf2sfile_closefd)
-apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
-done
-
-lemmas cf2sfiles_simps = cf2sfiles_open cf2sfiles_linkhard cf2sfiles_other
-  cf2sfiles_unlink cf2sfiles_closefd
-  
-
 (* simpset for co2sobj *)
 
 lemma co2sobj_execve:
   "\<lbrakk>valid (Execve p f fds # s); alive (Execve p f fds # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Execve p f fds # s) obj = (
       if (obj = O_proc p)
       then (case (cp2sproc (Execve p f fds # s) p) of
-              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s \<or> O_file f \<in> Tainted s))
+              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s \<or> O_file f \<in> tainted s))
             | _       \<Rightarrow> None) 
       else co2sobj s obj )"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps cf2sfiles_other ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps cq2smsgq_other cf2sfile_other)
 apply (case_tac "cp2sproc (Execve p f fds # s) p")
 apply (drule current_proc_has_sp', simp, simp)
-apply (simp (no_asm_simp) add:cp2sproc_execve tainted_eq_Tainted split:option.splits)
+apply (simp (no_asm_simp) add:cp2sproc_execve split:option.splits)
+apply (simp add:is_file_simps, frule_tac s = s in is_file_has_sfile', simp, erule exE, simp)
+apply (frule_tac ff = list in cf2sfile_other', simp_all)
+apply (simp add:is_file_in_current)
 apply (simp add:is_dir_simps, frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
 apply (frule_tac ff = list in cf2sfile_other', simp_all)
 apply (simp add:is_dir_in_current)
@@ -1851,60 +1276,66 @@
   "\<lbrakk>valid (Execve p f fds # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Execve p f fds # s) obj = (
       if (obj = O_proc p)
       then (case (cp2sproc (Execve p f fds # s) p) of
-              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s \<or> O_file f \<in> Tainted s))
+              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s \<or> O_file f \<in> tainted s))
             | _       \<Rightarrow> None) 
       else co2sobj s obj )"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps cf2sfiles_other ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps cf2sfile_other cq2smsgq_other)
 apply (case_tac "cp2sproc (Execve p f fds # s) p")
 apply (drule current_proc_has_sp', simp, simp)
-apply (simp (no_asm_simp) add:cp2sproc_execve tainted_eq_Tainted split:option.splits)
+apply (simp (no_asm_simp) add:cp2sproc_execve split:option.splits)
+apply (frule_tac s = s in is_file_has_sfile', simp, erule exE, simp)
+apply (frule_tac ff = list in cf2sfile_other', simp_all)
+apply (simp add:is_file_in_current)
 apply (frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
 apply (frule_tac ff = list in cf2sfile_other', simp_all)
 apply (simp add:is_dir_in_current)
 done
 
 lemma co2sobj_clone':
-  "\<lbrakk>valid (Clone p p' fds shms # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Clone p p' fds shms # s) obj = (
+  "\<lbrakk>valid (Clone p p' fds # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Clone p p' fds # s) obj = (
       if (obj = O_proc p')
-      then (case (cp2sproc (Clone p p' fds shms # s) p') of
-              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
+      then (case (cp2sproc (Clone p p' fds # s) p') of
+              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
             | _       \<Rightarrow> None)
       else co2sobj s obj )"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps cf2sfiles_other ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
-apply (case_tac "cp2sproc (Clone p p' fds shms # s) p'")
+apply (simp_all add:current_files_simps cf2sfile_other cq2smsgq_other  )
+apply (case_tac "cp2sproc (Clone p p' fds # s) p'")
 apply (drule current_proc_has_sp', simp, simp)
 apply ((erule conjE)+, frule_tac p = p in current_proc_has_sec, simp, erule exE, simp)
-apply (rule conjI, rule impI, simp)
-apply (simp (no_asm_simp) add:cp2sproc_clone tainted_eq_Tainted split:option.splits)
-
+apply (simp (no_asm_simp) add:cp2sproc_clone split:option.splits)
+apply (case_tac "nat = p'", simp, simp)
+apply (frule_tac s = s in is_file_has_sfile', simp, erule exE, simp)
+apply (frule_tac ff = list in cf2sfile_other', simp_all)
+apply (simp add:is_file_in_current)
 apply (frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
 apply (frule_tac ff = list in cf2sfile_other', simp_all)
 apply (simp add:is_dir_in_current)
 done
 
 lemma co2sobj_clone:
-  "\<lbrakk>valid (Clone p p' fds shms # s); alive (Clone p p' fds shms # s) obj\<rbrakk> 
-   \<Longrightarrow> co2sobj (Clone p p' fds shms # s) obj = (
+  "\<lbrakk>valid (Clone p p' fds # s); alive (Clone p p' fds # s) obj\<rbrakk> 
+   \<Longrightarrow> co2sobj (Clone p p' fds # s) obj = (
       if (obj = O_proc p')
-      then (case (cp2sproc (Clone p p' fds shms # s) p') of
-              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
+      then (case (cp2sproc (Clone p p' fds # s) p') of
+              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
             | _       \<Rightarrow> None)
       else co2sobj s obj )"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps cf2sfiles_other ch2sshm_other 
-  cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps cf2sfile_other cq2smsgq_other)
 apply (rule conjI, rule impI, simp)
-apply (case_tac "cp2sproc (Clone p p' fds shms # s) p'")
+apply (case_tac "cp2sproc (Clone p p' fds # s) p'")
 apply (drule current_proc_has_sp', simp, simp)
 apply ((erule conjE)+, frule_tac p = p in current_proc_has_sec, simp, erule exE, simp)
-apply (simp add:tainted_eq_Tainted, rule impI, rule notI)
-apply (drule Tainted_in_current, simp+)
+apply (rule impI,rule notI, drule tainted_in_current, simp+)
 apply (rule impI, simp)
 apply (drule current_proc_has_sp, simp, (erule exE|erule conjE)+)
-apply (simp (no_asm_simp) add:cp2sproc_clone tainted_eq_Tainted Tainted_in_current split:option.splits)
+apply (simp (no_asm_simp) add:cp2sproc_clone tainted_in_current split:option.splits)
 
+apply (simp add:is_file_simps, frule_tac s = s in is_file_has_sfile', simp, erule exE, simp)
+apply (frule_tac ff = list in cf2sfile_other', simp_all)
+apply (simp add:is_file_in_current)
 apply (simp add:is_dir_simps, frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
 apply (frule_tac ff = list in cf2sfile_other', simp_all)
 apply (simp add:is_dir_in_current)
@@ -1913,22 +1344,25 @@
 lemma co2sobj_ptrace:
   "\<lbrakk>valid (Ptrace p p' # s); alive s obj\<rbrakk>\<Longrightarrow> co2sobj (Ptrace p p' # s) obj = (
      case obj of
-       O_proc p'' \<Rightarrow> if (info_flow_shm s p' p'') 
+       O_proc p'' \<Rightarrow> if (p'' = p') 
                      then (case (cp2sproc s p'') of 
-                             Some sp \<Rightarrow> Some (S_proc sp (O_proc p'' \<in> Tainted s \<or> O_proc p \<in> Tainted s))
+                             Some sp \<Rightarrow> Some (S_proc sp (O_proc p'' \<in> tainted s \<or> O_proc p \<in> tainted s))
                            | _       \<Rightarrow> None)
-                     else if (info_flow_shm s p p'')
+                     else if (p'' = p)
                           then (case (cp2sproc s p'') of 
-                                  Some sp \<Rightarrow> Some (S_proc sp (O_proc p'' \<in> Tainted s \<or> O_proc p' \<in> Tainted s))
+                                  Some sp \<Rightarrow> Some (S_proc sp (O_proc p'' \<in> tainted s \<or> O_proc p' \<in> tainted s))
                                 | _       \<Rightarrow> None)
                           else co2sobj s (O_proc p'')
     | _          \<Rightarrow> co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other cf2sfiles_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps cq2smsgq_other cf2sfile_other)
 
-apply (auto simp:cp2sproc_other tainted_eq_Tainted split:option.splits
-  dest!:current_proc_has_sec' current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
+apply (auto simp:cp2sproc_other split:option.splits
+  dest!:current_proc_has_sec' current_proc_has_sp')[1]
 
+apply (frule_tac s = s in is_file_has_sfile', simp, erule exE, simp)
+apply (frule_tac ff = list in cf2sfile_other', simp_all)
+apply (simp add:is_file_in_current)
 apply (frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
 apply (frule_tac ff = list in cf2sfile_other', simp_all)
 apply (simp add:is_dir_in_current)
@@ -1939,29 +1373,27 @@
    \<Longrightarrow> co2sobj (Open p f flag fd opt # s) obj = (case obj of 
      O_file f' \<Rightarrow> if (f' = f \<and> opt \<noteq> None)
                   then (case (cf2sfile (Open p f flag fd opt # s) f) of
-                          Some sf \<Rightarrow> Some (S_file {sf} (O_proc p \<in> Tainted s))
+                          Some sf \<Rightarrow> Some (S_file sf (O_proc p \<in> tainted s))
                         | _       \<Rightarrow> None)
                   else co2sobj s (O_file f')
    | O_proc p' \<Rightarrow> if (p' = p) 
                   then (case (cp2sproc (Open p f flag fd opt # s) p) of
-                          Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
+                          Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
                         | _       \<Rightarrow> None)
                   else co2sobj s (O_proc p')
    | _         \<Rightarrow> co2sobj s obj )"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits
-           dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
+apply (auto simp:cp2sproc_simps split:option.splits dest!:current_proc_has_sp')[1]
 
 apply (simp split:if_splits t_object.splits)
 apply (rule conjI, rule impI, erule conjE, erule exE, simp, (erule exE|erule conjE)+)
 apply (case_tac "cf2sfile (Open p f flag fd (Some y) # s) f")
 apply (drule current_file_has_sfile', simp, simp add:current_files_simps, simp)
-apply (frule_tac f' = f in cf2sfiles_open, simp add:current_files_simps)
-apply (simp add:tainted_eq_Tainted)
-apply (rule impI, rule notI, drule Tainted_in_current, simp, simp add:is_file_in_current)
-apply (rule impI, simp add:tainted_eq_Tainted cf2sfiles_open is_file_in_current split:option.splits)
+apply (frule_tac f' = f in cf2sfile_open, simp add:current_files_simps)
+apply (rule impI, rule notI, drule tainted_in_current, simp, simp add:is_file_in_current)
+apply (rule impI, simp add:cf2sfile_open is_file_in_current split:option.splits)
 
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
 
 apply (frule is_dir_in_current)
 apply (frule_tac f' = list in cf2sfile_open)
@@ -1973,7 +1405,7 @@
   "\<lbrakk>valid (ReadFile p fd # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (ReadFile p fd # s) obj = (
      case obj of
        O_proc p' \<Rightarrow> (case (file_of_proc_fd s p fd) of
-                       Some f \<Rightarrow> (if (info_flow_shm s p p' \<and> O_file f \<in> Tainted s)
+                       Some f \<Rightarrow> (if (p' = p \<and> O_file f \<in> tainted s)
                                   then (case (cp2sproc s p') of
                                           Some sp \<Rightarrow> Some (S_proc sp True)
                                         | _       \<Rightarrow> None)
@@ -1981,12 +1413,11 @@
                     | _       \<Rightarrow> None)
      | _         \<Rightarrow> co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits
-           dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (auto simp:cp2sproc_simps split:option.splits dest!:current_proc_has_sp')[1]
+apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
 
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' 
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps 
+             simp:current_files_simps cf2sfile_simps 
              dest:is_file_in_current is_dir_in_current)
 done
 
@@ -1994,54 +1425,43 @@
   "\<lbrakk>valid (WriteFile p fd # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (WriteFile p fd # s) obj = (
      case obj of
        O_file f' \<Rightarrow> (case (file_of_proc_fd s p fd) of
-                       Some f \<Rightarrow> (if (f \<in> same_inode_files s f') 
-                                  then Some (S_file (cf2sfiles s f') 
-                                                    (O_file f' \<in> Tainted s \<or> O_proc p \<in> Tainted s))
+                       Some f \<Rightarrow> (if (f' = f) 
+                                  then (case cf2sfile s f of 
+                                          Some sf \<Rightarrow> Some (S_file sf                                                                                                                 (O_file f \<in> tainted s \<or> O_proc p \<in> tainted s))
+                                        | _       \<Rightarrow> None)
                                   else co2sobj s obj)
                     | _       \<Rightarrow> None)
      | _         \<Rightarrow> co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
 
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
-                  same_inode_files_prop6
+             simp:current_files_simps cf2sfile_simps cp2sproc_simps                    
              dest:is_file_in_current is_dir_in_current)
-
-(* should delete has_same_inode !?!?*)
-by (auto simp:same_inode_files_def is_file_def has_same_inode_def split:if_splits option.splits)
+done
 
 lemma co2sobj_closefd:
   "\<lbrakk>valid (CloseFd p fd # s); alive (CloseFd p fd # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CloseFd p fd # s) obj = (
       case obj of 
-        O_file f' \<Rightarrow> (case (file_of_proc_fd s p fd) of 
-                        Some f \<Rightarrow> (if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {(p, fd)} \<and>
-                                       f \<in> files_hung_by_del s \<and> (\<forall> f'' \<in> same_inode_files s f. 
-                                       f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f))
-                                   then (case (cf2sfile s f, co2sobj s (O_file f')) of
-                                           (Some sf, Some (S_file sfs b)) \<Rightarrow> Some (S_file (sfs - {sf}) b)
-                                         | _                              \<Rightarrow> None)
-                                   else co2sobj s obj)
-                     | _       \<Rightarrow> co2sobj s obj)
-      | O_proc p' \<Rightarrow> (if (p = p') 
+        O_proc p' \<Rightarrow> (if (p = p') 
                       then (case (cp2sproc (CloseFd p fd # s) p) of
-                              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
+                              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
                             | _       \<Rightarrow> None)
                       else co2sobj s obj)
       | _         \<Rightarrow> co2sobj s obj) "
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
-apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits if_splits
-           dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
+apply (simp_all add:current_files_simps cq2smsgq_other)
+apply (auto simp:cp2sproc_simps split:option.splits if_splits dest!:current_proc_has_sp')[1]
 
 apply (frule is_file_in_current)
 apply (case_tac "file_of_proc_fd s p fd")
-apply (simp add:tainted_eq_Tainted)
-apply (drule_tac f' = list in cf2sfiles_closefd, simp add:current_files_closefd, simp)
-apply (frule_tac f' = list in cf2sfiles_closefd, simp)
-apply (simp add:is_file_simps current_files_simps)
-apply (auto simp add:tainted_eq_Tainted cf2sfile_closefd split:if_splits option.splits
-  dest!:current_file_has_sfile' dest:hung_file_in_current)[1]
+apply (simp add:current_files_simps is_file_simps tainted.simps)
+apply (drule_tac f = list in cf2sfile_closefd, simp add:current_files_simps)
+apply (simp split:option.splits)
+apply (frule_tac f = list in cf2sfile_closefd, simp)
+apply (simp split:option.splits)
+apply (simp add:is_file_simps current_files_simps split:if_splits)
+apply (rule impI, simp)
 
 apply (simp add:is_dir_simps, frule is_dir_in_current)
 apply (frule_tac f = list in cf2sfile_closefd)
@@ -2050,25 +1470,14 @@
 done
 
 lemma co2sobj_unlink:
-  "\<lbrakk>valid (UnLink p f # s); alive (UnLink p f # s) obj\<rbrakk> \<Longrightarrow> co2sobj (UnLink p f # s) obj = (
-      case obj of
-        O_file f' \<Rightarrow> if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {} \<and> 
-                        (\<forall> f'' \<in> same_inode_files s f. f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f))
-                     then (case (cf2sfile s f, co2sobj s (O_file f')) of
-                             (Some sf, Some (S_file sfs b)) \<Rightarrow> Some (S_file (sfs - {sf}) b)
-                           | _                              \<Rightarrow> None)
-                     else co2sobj s obj
-      | _         \<Rightarrow> co2sobj s obj)"
+  "\<lbrakk>valid (UnLink p f # s); alive (UnLink p f # s) obj\<rbrakk> 
+   \<Longrightarrow> co2sobj (UnLink p f # s) obj = co2sobj s obj"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
-apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits if_splits
-           dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
+apply (simp_all add:current_files_simps cq2smsgq_other)
+apply (auto simp:cp2sproc_simps split:option.splits if_splits dest!:current_proc_has_sp')[1]
 apply (frule is_file_in_current)
 apply (frule_tac f' = list in cf2sfile_unlink, simp)
-apply (frule_tac f' = list in cf2sfiles_unlink, simp)
-apply (simp add:is_file_simps current_files_simps)
-apply (auto simp add:tainted_eq_Tainted is_file_in_current split:if_splits option.splits
-  dest!:current_file_has_sfile')[1]
+apply (simp add:is_file_simps current_files_simps split:option.splits if_splits)
 
 apply (simp add:is_dir_simps, frule is_dir_in_current)
 apply (frule_tac f' = list in cf2sfile_unlink)
@@ -2079,13 +1488,13 @@
 lemma co2sobj_rmdir:
   "\<lbrakk>valid (Rmdir p f # s); alive (Rmdir p f # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Rmdir p f # s) obj = co2sobj s obj"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
-apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits if_splits
-           dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
+apply (simp_all add:current_files_simps cq2smsgq_other)
+apply (auto simp:cp2sproc_simps split:option.splits if_splits dest!:current_proc_has_sp')[1]
 apply (simp add:is_file_simps dir_is_empty_def)
 apply (case_tac "f = list", drule file_dir_conflict, simp, simp)
-apply (simp add:cf2sfiles_other)
-apply (auto simp:cf2sfile_simps dest:is_dir_in_current)
+apply (frule_tac f' = list in cf2sfile_rmdir, simp add:is_file_in_current current_files_simps)
+apply (simp split:option.splits)
+apply (auto simp:cf2sfile_simps cf2sfile_other dest:is_dir_in_current)
 done
 
 lemma co2sobj_mkdir:
@@ -2096,75 +1505,50 @@
             | _       \<Rightarrow> None)
       else co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
-apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits if_splits
-           dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
-apply (frule_tac cf2sfiles_other, simp+)
+apply (simp_all add:current_files_simps cq2smsgq_other)
+apply (auto simp:cp2sproc_simps split:option.splits if_splits dest!:current_proc_has_sp')[1]
+apply (case_tac "f = list", simp add:is_file_simps is_file_in_current)
+apply (frule_tac f' = list in cf2sfile_mkdir)
+apply (simp add:is_file_in_current)
+apply (simp split:option.splits)
+
 apply (frule is_dir_in_current, rule impI, simp add:current_files_mkdir)
 apply (frule current_file_has_sfile, simp, erule exE, simp)
 apply (drule cf2sfile_mkdir1, simp+)
 done
 
-
-lemma co2sobj_linkhard:
-  "\<lbrakk>valid (LinkHard p oldf f # s); alive (LinkHard p oldf f # s) obj\<rbrakk> 
-   \<Longrightarrow> co2sobj (LinkHard p oldf f # s) obj = (
-    case obj of
-      O_file f' \<Rightarrow> if (f' = f \<or> f' \<in> same_inode_files s oldf)
-                   then (case (cf2sfile (LinkHard p oldf f # s) f) of
-                           Some sf \<Rightarrow> Some (S_file (cf2sfiles s oldf \<union> {sf}) (O_file oldf \<in> Tainted s))
-                         | _       \<Rightarrow> None)
-                   else co2sobj s obj
-    | _         \<Rightarrow> co2sobj s obj)"
-apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
-apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits if_splits
-           dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
-apply (frule_tac cf2sfiles_linkhard, simp+)
-apply (frule_tac f' = f in cf2sfile_linkhard, simp add:current_files_linkhard)
-apply (auto simp:is_file_simps sectxt_of_obj_simps current_files_simps is_file_in_current same_inodes_Tainted
-  split:option.splits if_splits dest:Tainted_in_current 
-  dest!:current_has_sec' current_file_has_sfile')[1]
-
-apply (frule is_dir_in_current, simp add:current_files_linkhard is_dir_simps is_dir_in_current)
-apply (frule is_dir_in_current)
-apply (frule current_file_has_sfile, simp)
-apply (drule cf2sfile_linkhard1, simp+)
-done
-
 lemma co2sobj_truncate:
   "\<lbrakk>valid (Truncate p f len # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Truncate p f len # s) obj = (
       case obj of
-        O_file f' \<Rightarrow> if (f' \<in> same_inode_files s f \<and> len > 0)
-                     then Some (S_file (cf2sfiles s f') (O_file f' \<in> Tainted s \<or> O_proc p \<in> Tainted s))
+        O_file f' \<Rightarrow> if (f' = f \<and> len > 0)
+                     then (case cf2sfile s f of 
+                             Some sf \<Rightarrow> Some (S_file sf (O_file f' \<in> tainted s \<or> O_proc p \<in> tainted s))
+                           | _       \<Rightarrow> None)
                      else co2sobj s obj
       | _         \<Rightarrow> co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
 
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
-                  same_inode_files_prop6
+             simp:current_files_simps cf2sfile_simps cp2sproc_simps  
              dest:is_file_in_current is_dir_in_current)
 done
 
 lemma co2sobj_kill:
   "\<lbrakk>valid (Kill p p' # s); alive (Kill p p' # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Kill p p' # s) obj = co2sobj s obj"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
-                  same_inode_files_prop6
+             simp:current_files_simps cf2sfile_simps cp2sproc_simps  
              dest:is_file_in_current is_dir_in_current)
 done
 
 lemma co2sobj_exit:
   "\<lbrakk>valid (Exit p # s); alive (Exit p # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Exit p # s) obj = co2sobj s obj"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other  )
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
-                  same_inode_files_prop6
+             simp:current_files_simps cf2sfile_simps cp2sproc_simps
              dest:is_file_in_current is_dir_in_current)
 done
 
@@ -2177,10 +1561,9 @@
                      else co2sobj s obj
       | _        \<Rightarrow> co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other  )
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
-                  same_inode_files_prop6
+             simp:current_files_simps cf2sfile_simps cp2sproc_simps 
              dest!:current_has_smsgq'
              dest:is_file_in_current is_dir_in_current cq2smsg_createmsgq)
 done
@@ -2194,10 +1577,9 @@
                      else co2sobj s obj
       | _        \<Rightarrow> co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other  )
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
-                  same_inode_files_prop6
+             simp:current_files_simps cf2sfile_simps cp2sproc_simps  
              dest!:current_has_smsgq'
              dest:is_file_in_current is_dir_in_current cq2smsg_sendmsg)
 done
@@ -2209,17 +1591,16 @@
                                          Some sq \<Rightarrow> Some (S_msgq sq)
                                        | _       \<Rightarrow> None)
                      else co2sobj s obj
-      | O_proc p' \<Rightarrow> if (info_flow_shm s p p' \<and> O_msg q m \<in> Tainted s)
+      | O_proc p' \<Rightarrow> if (p' = p \<and> O_msg q m \<in> tainted s)
                      then (case (cp2sproc s p') of
                              Some sp \<Rightarrow> Some (S_proc sp True)
                            | _       \<Rightarrow> None)
                      else co2sobj s obj
       | _         \<Rightarrow> co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
-                  same_inode_files_prop6
+             simp:current_files_simps cf2sfile_simps cp2sproc_simps  
              dest!:current_has_smsgq'
              dest:is_file_in_current is_dir_in_current cq2smsg_recvmsg)
 done
@@ -2228,118 +1609,20 @@
   "\<lbrakk>valid (RemoveMsgq p q # s); alive (RemoveMsgq p q # s) obj\<rbrakk> 
    \<Longrightarrow> co2sobj (RemoveMsgq p q # s) obj = co2sobj s obj"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
+apply (simp_all add:current_files_simps is_dir_simps cq2smsgq_other)
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
-                  same_inode_files_prop6
+             simp:current_files_simps cf2sfile_simps cp2sproc_simps  
              dest!:current_has_smsgq'
              dest:is_file_in_current is_dir_in_current cq2smsg_removemsgq)
 done
 
-lemma co2sobj_createshm:
-  "\<lbrakk>valid (CreateShM p h # s); alive (CreateShM p h # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CreateShM p h # s) obj = (
-      case obj of 
-        O_shm h' \<Rightarrow> if (h' = h) then (case (ch2sshm (CreateShM p h # s) h) of
-                                        Some sh \<Rightarrow> Some (S_shm sh)
-                                      | _       \<Rightarrow> None)
-                    else co2sobj s obj
-      | _        \<Rightarrow> co2sobj s obj)"
-apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
-apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
-                  same_inode_files_prop6 ch2sshm_simps
-             dest!:current_shm_has_sh'
-             dest:is_file_in_current is_dir_in_current)
-done
-
-lemma co2sobj_detach:
-  "\<lbrakk>valid (Detach p h # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Detach p h # s) obj = (
-      case obj of
-        O_proc p' \<Rightarrow> if (p' = p) then (case (cp2sproc (Detach p h # s) p) of
-                                         Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
-                                       | _       \<Rightarrow> None)
-                     else co2sobj s obj
-      | _         \<Rightarrow> co2sobj s obj)"
-apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
-
-apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
-                  same_inode_files_prop6 ch2sshm_simps
-             dest!:current_shm_has_sh'
-             dest:is_file_in_current is_dir_in_current)
-done
-
-lemma co2sobj_deleteshm:
-  "\<lbrakk>valid (DeleteShM p h # s); alive (DeleteShM p h # s) obj\<rbrakk> \<Longrightarrow> co2sobj (DeleteShM p h # s) obj = (
-      case obj of
-        O_proc p' \<Rightarrow> (case (cp2sproc (DeleteShM p h # s) p') of
-                        Some sp \<Rightarrow> Some (S_proc sp (O_proc p' \<in> Tainted s))
-                      | _       \<Rightarrow> None)
-      | _         \<Rightarrow> co2sobj s obj)"
-apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
-
-apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps tainted_eq_Tainted
-                  same_inode_files_prop6 ch2sshm_simps
-             dest!:current_shm_has_sh' 
-             dest:is_file_in_current is_dir_in_current)
-done
 
 declare Product_Type.split_paired_Ex Product_Type.split_paired_All [simp del]
 
-lemma info_flow_shm_prop1:
-  "p \<in> current_procs s \<Longrightarrow> info_flow_shm s p p"
-by (simp add:info_flow_shm_def)
-
-lemma co2sobj_attach:
-  "\<lbrakk>valid (Attach p h flag # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Attach p h flag # s) obj = (
-      case obj of
-        O_proc p' \<Rightarrow> if (info_flow_shm s p p')
-                     then (case (cp2sproc (Attach p h flag # s) p') of
-                             Some sp \<Rightarrow> Some (S_proc sp (O_proc p' \<in> Tainted s \<or> 
-              (\<exists> p''. O_proc p'' \<in> Tainted s \<and> (p'', SHM_RDWR) \<in> procs_of_shm s h)))
-                           | _       \<Rightarrow> None)
-                     else if (\<exists> p'' flag'. (p'', flag') \<in> procs_of_shm s h \<and> flag = SHM_RDWR \<and> O_proc p \<in> Tainted s \<and>
-  info_flow_shm s p'' p')
-                          then (case (cp2sproc s p') of 
-                                  Some sp \<Rightarrow> Some (S_proc sp True)
-                                | _       \<Rightarrow> None)
-                          else co2sobj s obj
-      | _         \<Rightarrow> co2sobj s obj)"
-apply (frule vt_grant_os, frule vd_cons, case_tac obj)
-apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
-
-apply (rule conjI|rule impI|erule exE)+
-apply (simp split:option.splits del:split_paired_Ex)
-apply (rule impI, frule current_proc_has_sp, simp)
-apply ((erule exE)+, auto simp:tainted_eq_Tainted intro:info_flow_shm_Tainted)[1]
-apply (rule impI, simp add:tainted_eq_Tainted split:option.splits del:split_paired_Ex)
-apply (auto simp:info_flow_shm_prop1 cp2sproc_attach dest!:current_proc_has_sp')[1]
-
-apply (case_tac "cp2sproc (Attach p h flag # s) nat")
-apply (drule current_proc_has_sp', simp+)
-
-apply (rule conjI|erule exE|erule conjE|rule impI)+
-apply (simp add:tainted_eq_Tainted)
-apply (auto simp:info_flow_shm_prop1 cp2sproc_attach intro:info_flow_shm_Tainted dest!:current_proc_has_sp')[1]
-apply (auto simp:info_flow_shm_prop1 cp2sproc_attach tainted_eq_Tainted intro:info_flow_shm_Tainted dest!:current_proc_has_sp'
-split:option.splits if_splits)[1]
-
-
-apply (auto split:if_splits option.splits dest!:current_file_has_sfile' 
-             simp:current_files_simps cf2sfiles_simps cf2sfile_simps tainted_eq_Tainted
-                  same_inode_files_prop6 
-             dest:is_file_in_current is_dir_in_current)
-done
-
-
 lemma co2sobj_other:
   "\<lbrakk>valid (e # s); alive (e # s) obj; 
     \<forall> p f fds. e \<noteq> Execve p f fds;
-    \<forall> p p' fds shms. e \<noteq> Clone p p' fds shms;
+    \<forall> p p' fds. e \<noteq> Clone p p' fds;
     \<forall> p p'. e \<noteq> Ptrace p p';
     \<forall> p f flags fd opt. e \<noteq> Open p f flags fd opt;
     \<forall> p fd. e \<noteq> ReadFile p fd;
@@ -2348,27 +1631,20 @@
     \<forall> p f. e \<noteq> UnLink p f;
     \<forall> p f. e \<noteq> Rmdir p f;
     \<forall> p f i. e \<noteq> Mkdir p f i;
-    \<forall> p f f'. e \<noteq> LinkHard p f f';
     \<forall> p f len. e \<noteq> Truncate p f len;
     \<forall> p q. e \<noteq> CreateMsgq p q;
     \<forall> p q m. e \<noteq> SendMsg p q m;
     \<forall> p q m. e \<noteq> RecvMsg p q m;
-    \<forall> p q. e \<noteq> RemoveMsgq p q;
-    \<forall> p h. e \<noteq> CreateShM p h;
-    \<forall> p h flag. e \<noteq> Attach p h flag;
-    \<forall> p h. e \<noteq> Detach p h;
-    \<forall> p h. e \<noteq> DeleteShM p h
-   \<rbrakk> \<Longrightarrow> co2sobj (e # s) obj = co2sobj s obj"
+    \<forall> p q. e \<noteq> RemoveMsgq p q\<rbrakk> 
+   \<Longrightarrow> co2sobj (e # s) obj = co2sobj s obj"
 apply (frule vt_grant, case_tac e)
 apply (auto intro:co2sobj_kill co2sobj_exit)
 done
 
 lemmas co2sobj_simps = co2sobj_execve co2sobj_clone co2sobj_ptrace co2sobj_open co2sobj_readfile
-  co2sobj_writefile co2sobj_closefd co2sobj_unlink co2sobj_rmdir co2sobj_mkdir co2sobj_linkhard
+  co2sobj_writefile co2sobj_closefd co2sobj_unlink co2sobj_rmdir co2sobj_mkdir
   co2sobj_truncate co2sobj_kill co2sobj_exit co2sobj_createmsgq co2sobj_sendmsg co2sobj_recvmsg
-  co2sobj_removemsgq co2sobj_attach co2sobj_detach co2sobj_createshm co2sobj_deleteshm
-
-
+  co2sobj_removemsgq 
 
 end
 
--- a/simple_selinux/Current_prop.thy	Mon Dec 02 10:52:40 2013 +0800
+++ b/simple_selinux/Current_prop.thy	Tue Dec 03 22:42:48 2013 +0800
@@ -6,43 +6,6 @@
 
 context flask begin
 
-lemma procs_of_shm_prop1: "\<lbrakk> p_flag \<in> procs_of_shm s h; valid s\<rbrakk> \<Longrightarrow> h \<in> current_shms s"
-apply (induct s arbitrary:p_flag)
-apply (case_tac p_flag, simp, drule init_procs_has_shm, simp)
-apply (frule vd_cons, frule vt_grant_os)
-apply (case_tac a, auto split:if_splits option.splits)
-done
-
-lemma procs_of_shm_prop2: "\<lbrakk>(p, flag) \<in> procs_of_shm s h; valid s\<rbrakk> \<Longrightarrow> p \<in> current_procs s"
-apply (induct s arbitrary:p flag)
-apply (simp, drule init_procs_has_shm, simp)
-apply (frule vd_cons, frule vt_grant_os)
-apply (case_tac a, auto split:if_splits option.splits)
-done
-
-lemma procs_of_shm_prop2':
-  "\<lbrakk>p \<notin> current_procs s; valid s\<rbrakk> \<Longrightarrow> \<forall> flag h. (p, flag) \<notin> procs_of_shm s h"
-by (auto dest:procs_of_shm_prop2)
-
-lemma procs_of_shm_prop3: "\<lbrakk>(p, flag) \<in> procs_of_shm s h; (p, flag') \<in> procs_of_shm s h; valid s\<rbrakk>
-  \<Longrightarrow> flag = flag'"
-apply (induct s arbitrary:p flag flag')
-apply (simp, drule_tac flag = flag in init_procs_has_shm, drule_tac flag = flag' in init_procs_has_shm, simp)
-apply (frule vd_cons, frule vt_grant_os)
-apply (case_tac a, auto split:if_splits option.splits dest:procs_of_shm_prop2)
-done
-
-lemma procs_of_shm_prop4: "\<lbrakk>(p, flag) \<in> procs_of_shm s h; valid s\<rbrakk> \<Longrightarrow> flag_of_proc_shm s p h = Some flag"
-apply (induct s arbitrary:p flag)
-apply (simp, drule init_procs_has_shm, simp)
-apply (frule vd_cons, frule vt_grant_os)
-apply (case_tac a, auto split:if_splits option.splits dest:procs_of_shm_prop2)
-done
-
-lemma procs_of_shm_prop4':
-  "\<lbrakk>flag_of_proc_shm s p h = None; valid s\<rbrakk> \<Longrightarrow> \<forall> flag. (p, flag) \<notin> procs_of_shm s h"
-by (auto dest:procs_of_shm_prop4)
-
 lemma not_init_intro_proc:
   "\<lbrakk>p \<notin> current_procs s; valid s\<rbrakk> \<Longrightarrow> deleted (O_proc p) s \<or> p \<notin> init_procs"
 using not_deleted_init_proc by auto
@@ -51,47 +14,6 @@
   "\<lbrakk>p \<notin> current_procs s; valid s\<rbrakk> \<Longrightarrow> \<not> (\<not> deleted (O_proc p) s \<and> p \<in> init_procs)"
 using not_deleted_init_proc by auto
 
-lemma info_shm_flow_in_procs:
-  "\<lbrakk>info_flow_shm s p p'; valid s\<rbrakk> \<Longrightarrow> p \<in> current_procs s \<and> p' \<in> current_procs s"
-by (auto intro:procs_of_shm_prop2 simp:info_flow_shm_def one_flow_shm_def)
-
-lemma flag_of_proc_shm_prop1:
-  "\<lbrakk>flag_of_proc_shm s p h = Some flag; valid s\<rbrakk> \<Longrightarrow> (p, flag) \<in> procs_of_shm s h"
-apply (induct s arbitrary:p flag)
-apply (simp, drule init_shmflag_has_proc, simp)
-apply (frule vd_cons, frule vt_grant_os)
-apply (case_tac a, auto split:if_splits option.splits dest:procs_of_shm_prop2)
-done
-
-
-
-lemma has_same_inode_in_current:
-  "\<lbrakk>has_same_inode s f f'; valid s\<rbrakk> \<Longrightarrow> f \<in> current_files s \<and> f' \<in> current_files s"
-by (auto simp add:has_same_inode_def current_files_def same_inode_files_def 
-  is_file_def split:if_splits option.splits)
-
-
-lemma has_same_inode_prop1:
-  "\<lbrakk>has_same_inode s f f'; is_file s f; valid s\<rbrakk> \<Longrightarrow> is_file s f'"
-by (auto simp:has_same_inode_def same_inode_files_def is_file_def)
-
-lemma has_same_inode_prop1':
-  "\<lbrakk>has_same_inode s f f'; is_file s f'; valid s\<rbrakk> \<Longrightarrow> is_file s f"
-by (auto simp:has_same_inode_def is_file_def same_inode_files_def 
- split:if_splits option.splits)
-
-lemma has_same_inode_prop2:
-  "\<lbrakk>has_same_inode s f f'; file_of_proc_fd s p fd = Some f; valid s\<rbrakk> \<Longrightarrow> is_file s f'"
-apply (drule has_same_inode_prop1)
-apply (simp add:file_of_pfd_is_file, simp+)
-done
-
-lemma has_same_inode_prop2':
-  "\<lbrakk>has_same_inode s f f'; file_of_proc_fd s p fd = Some f'; valid s\<rbrakk> \<Longrightarrow> is_file s f"
-apply (drule has_same_inode_prop1')
-apply (simp add:file_of_pfd_is_file, simp+)
-done
-
 lemma tobj_in_init_alive:
   "tobj_in_init obj \<Longrightarrow> init_alive obj"
 by (case_tac obj, auto)
--- a/simple_selinux/Delete_prop.thy	Mon Dec 02 10:52:40 2013 +0800
+++ b/simple_selinux/Delete_prop.thy	Tue Dec 03 22:42:48 2013 +0800
@@ -106,11 +106,6 @@
    \<Longrightarrow> \<not> deleted (O_proc p) s"
 by (auto dest:not_deleted_init_udp_aux)
 
-lemma not_deleted_init_shm:
-  "\<lbrakk>\<not> deleted (O_shm h) s; h \<in> init_shms\<rbrakk> \<Longrightarrow> h \<in> current_shms s"
-apply (induct s, simp)
-by (case_tac a, auto)
-
 lemma not_deleted_init_msgq:
   "\<lbrakk>\<not> deleted (O_msgq q) s; q \<in> init_msgqs\<rbrakk> \<Longrightarrow> q \<in> current_msgqs s"
 apply (induct s, simp)
@@ -136,7 +131,7 @@
   "\<lbrakk>\<not> deleted obj s; valid s; init_alive obj\<rbrakk> \<Longrightarrow> alive s obj"
 apply (case_tac obj)
 apply (auto dest!:not_deleted_init_msg not_deleted_init_file not_deleted_init_dir not_deleted_init_proc
-  not_deleted_init_fd1 not_deleted_init_tcp1 not_deleted_init_udp1 not_deleted_init_shm 
+  not_deleted_init_fd1 not_deleted_init_tcp1 not_deleted_init_udp1 
   not_deleted_init_msgq 
            intro:is_file_in_current is_dir_in_current is_tcp_in_current is_udp_in_current 
   current_msg_imp_current_msgq)
@@ -189,11 +184,6 @@
 by (auto simp:is_udp_sock_simps split:option.splits t_socket_type.splits 
          dest:is_udp_sock_imp_curernt_proc)
 
-lemma not_deleted_cur_shm_app:
-  "\<lbrakk>\<not> deleted (O_shm h) (s' @ s); h \<in> current_shms s\<rbrakk> \<Longrightarrow> h \<in> current_shms (s' @ s)"
-apply (induct s', simp, simp add:cons_app_simp_aux)
-by (case_tac a, auto)
-
 lemma not_deleted_cur_msgq_app:
   "\<lbrakk>\<not> deleted (O_msgq q) (s' @ s); q \<in> current_msgqs s\<rbrakk> \<Longrightarrow> q \<in> current_msgqs (s' @ s)"
 apply (induct s', simp, simp add:cons_app_simp_aux)
@@ -213,7 +203,7 @@
 apply (case_tac obj)
 apply (auto dest!:not_deleted_cur_msg_app not_deleted_cur_file_app not_deleted_cur_dir_app
   not_deleted_cur_proc_app not_deleted_cur_fd_app not_deleted_cur_tcp_app 
-  not_deleted_cur_udp_app not_deleted_cur_shm_app not_deleted_cur_msgq_app
+  not_deleted_cur_udp_app not_deleted_cur_msgq_app
            intro:is_file_in_current is_dir_in_current is_tcp_in_current is_udp_in_current 
   current_msg_imp_current_msgq)
 done
--- a/simple_selinux/S2ss_prop.thy	Mon Dec 02 10:52:40 2013 +0800
+++ b/simple_selinux/S2ss_prop.thy	Tue Dec 03 22:42:48 2013 +0800
@@ -10,7 +10,7 @@
 
 lemma co2sobj_some_case:
   "\<lbrakk>co2sobj s obj = Some sobj; \<And> p. obj = O_proc p \<Longrightarrow> P (O_proc p);
-    \<And> f. obj = O_file f \<Longrightarrow> P (O_file f); \<And> h. obj = O_shm h \<Longrightarrow> P (O_shm h);
+    \<And> f. obj = O_file f \<Longrightarrow> P (O_file f); 
     \<And> f. obj = O_dir f \<Longrightarrow> P (O_dir f); \<And> q. obj = O_msgq q \<Longrightarrow> P (O_msgq q)\<rbrakk>
    \<Longrightarrow> P obj"
 by (case_tac obj, auto)
@@ -25,11 +25,11 @@
   "valid (Execve p f fds # s) \<Longrightarrow> s2ss (Execve p f fds # s) = (
      if (\<exists> p'. p' \<noteq> p \<and> p' \<in> current_procs s \<and> co2sobj s (O_proc p') = co2sobj s (O_proc p))
      then (case (cp2sproc (Execve p f fds # s) p) of
-             Some sp \<Rightarrow> s2ss s \<union> {S_proc sp (O_proc p \<in> Tainted s \<or> O_file f \<in> Tainted s)}
+             Some sp \<Rightarrow> s2ss s \<union> {S_proc sp (O_proc p \<in> tainted s \<or> O_file f \<in> tainted s)}
            | _ \<Rightarrow> {} )
      else (case (cp2sproc (Execve p f fds # s) p, cp2sproc s p) of
-             (Some sp, Some sp') \<Rightarrow> s2ss s - {S_proc sp' (O_proc p \<in> Tainted s)}
-                                    \<union> {S_proc sp (O_proc p \<in> Tainted s \<or> O_file f \<in> Tainted s)}
+             (Some sp, Some sp') \<Rightarrow> s2ss s - {S_proc sp' (O_proc p \<in> tainted s)}
+                                    \<union> {S_proc sp (O_proc p \<in> tainted s \<or> O_file f \<in> tainted s)}
            | _ \<Rightarrow> {} ) )"
 apply (frule vd_cons, frule vt_grant_os, simp split:if_splits)
 
@@ -42,15 +42,15 @@
 apply (simp add:s2ss_def, rule set_eqI, rule iffI)
 apply (drule CollectD, (erule exE|erule conjE)+)
 apply (case_tac "obj = O_proc p")
-apply (simp add:co2sobj_execve tainted_eq_Tainted split:if_splits)
+apply (simp add:co2sobj_execve split:if_splits)
 apply (simp add:co2sobj_execve, rule disjI2)
 apply (rule_tac x = obj in exI, case_tac obj, (simp add:alive_simps)+)[1]
 apply (simp, erule disjE)
-apply (rule_tac x = "O_proc p" in exI, simp add:tainted_eq_Tainted)
+apply (rule_tac x = "O_proc p" in exI, simp)
 apply (erule exE| erule conjE)+
 apply (case_tac "x = S_proc sp (O_proc p \<in> tainted s)")
 apply (rule_tac x = "O_proc p'" in exI)
-apply (simp add:alive_execve co2sobj_execve tainted_eq_Tainted cp2sproc_execve)
+apply (simp add:alive_execve co2sobj_execve cp2sproc_execve)
 apply (case_tac "obj = O_proc p", simp)
 apply (frule co2sobj_execve_alive, simp, simp)
 apply (frule_tac obj = obj in co2sobj_execve, simp)
@@ -62,45 +62,45 @@
 apply (erule exE, erule conjE, simp)
 apply (simp add:s2ss_def, rule set_eqI, rule iffI)
 apply (drule CollectD, (erule exE|erule conjE)+)
-apply (case_tac "obj = O_proc p", simp add:tainted_eq_Tainted)
+apply (case_tac "obj = O_proc p", simp)
 apply (rule disjI1, simp split:if_splits)
 apply (simp add:co2sobj_execve, rule disjI2)
 apply (rule conjI,rule_tac x = obj in exI, simp add:alive_simps split:t_object.splits)
 apply (rule notI, simp, case_tac obj)
-apply (erule_tac x = nat in allE, simp add:tainted_eq_Tainted, (simp split:option.splits)+)
+apply (erule_tac x = nat in allE, simp, (simp split:option.splits)+)
 apply (erule disjE, simp)
-apply (rule_tac x = "O_proc p" in exI, simp add:tainted_eq_Tainted)
+apply (rule_tac x = "O_proc p" in exI, simp)
 apply (erule exE|erule conjE)+
 apply (rule_tac x = obj in exI)
 apply (drule_tac obj = obj in co2sobj_execve_alive, simp+)
 apply (frule_tac obj = obj in co2sobj_execve, simp, simp)
-apply (rule impI, simp add:tainted_eq_Tainted, simp)
+apply (rule impI, simp, simp)
 done
 
 lemma s2ss_clone_alive:
-  "\<lbrakk>co2sobj s obj = Some x; alive s obj; obj \<noteq> O_proc p'; valid (Clone p p' fds shms # s)\<rbrakk>
-   \<Longrightarrow> alive (Clone p p' fds shms # s) obj"
+  "\<lbrakk>co2sobj s obj = Some x; alive s obj; obj \<noteq> O_proc p'; valid (Clone p p' fds # s)\<rbrakk>
+   \<Longrightarrow> alive (Clone p p' fds # s) obj"
 by (erule co2sobj_some_case, auto simp:alive_clone)
 
 lemma s2ss_clone:
-  "valid (Clone p p' fds shms # s) \<Longrightarrow> s2ss (Clone p p' fds shms # s) = (
-     case (cp2sproc (Clone p p' fds shms # s) p') of
-       Some sp \<Rightarrow> s2ss s \<union> {S_proc sp (O_proc p \<in> Tainted s)}
+  "valid (Clone p p' fds # s) \<Longrightarrow> s2ss (Clone p p' fds # s) = (
+     case (cp2sproc (Clone p p' fds # s) p') of
+       Some sp \<Rightarrow> s2ss s \<union> {S_proc sp (O_proc p \<in> tainted s)}
      | _       \<Rightarrow> {})"
 apply (frule vd_cons, frule vt_grant_os, split option.splits)
 apply (rule conjI, rule impI, drule current_proc_has_sp', simp, simp)
 apply (rule allI, rule impI, simp add:s2ss_def)
 apply (rule set_eqI, rule iffI, drule CollectD, (erule exE|erule conjE)+)
-apply (case_tac "obj = O_proc p'", simp add:tainted_eq_Tainted)
-apply (case_tac "O_proc p' \<in> Tainted s", drule Tainted_in_current, simp+)
+apply (case_tac "obj = O_proc p'", simp)
+apply (case_tac "O_proc p' \<in> tainted s", drule tainted_in_current, simp+)
 apply (rule disjI1, simp split:if_splits)
-apply (simp add:tainted_eq_Tainted, rule disjI2)
+apply (simp, rule disjI2)
 apply (frule co2sobj_clone, simp)
 apply (rule_tac x = obj in exI, simp add:alive_simps split:t_object.splits)
 
 apply (simp, erule disjE, simp)
-apply (rule_tac x = "O_proc p'" in exI, simp add:tainted_eq_Tainted)
-apply (rule impI, rule notI, drule Tainted_in_current, simp+)
+apply (rule_tac x = "O_proc p'" in exI, simp)
+apply (rule impI, rule notI, drule tainted_in_current, simp+)
 apply (erule exE| erule conjE)+
 apply (case_tac "obj = O_proc p'", simp)
 apply (rule_tac x = obj in exI)
@@ -108,46 +108,6 @@
 apply (auto simp:co2sobj_clone alive_simps)
 done
 
-definition s2ss_shm_no_backup:: "t_state \<Rightarrow> t_process \<Rightarrow> t_static_state"
-where
-  "s2ss_shm_no_backup s pfrom \<equiv> {S_proc sp False | sp p. info_flow_shm s pfrom p \<and> cp2sproc s p = Some sp \<and>
-     (\<not> (\<exists> p'. \<not> info_flow_shm s pfrom p' \<and> p' \<in> current_procs s \<and> co2sobj s (O_proc p') = Some (S_proc sp False)))}"
-
-definition update_s2ss_shm:: "t_state \<Rightarrow> t_process \<Rightarrow> t_static_state" 
-where
-  "update_s2ss_shm s pfrom \<equiv> s2ss s 
-     \<union> {S_proc sp True| sp p. info_flow_shm s pfrom p \<and> cp2sproc s p = Some sp}
-     - (s2ss_shm_no_backup s pfrom)"
-
-lemma s2ss_shm_no_bk_elim:
-  "\<lbrakk>S_proc sp False \<notin> s2ss_shm_no_backup s pfrom; co2sobj s (O_proc p) = Some (S_proc sp False); 
-    valid s; info_flow_shm s pfrom p\<rbrakk>
-   \<Longrightarrow> \<exists> p'. \<not> info_flow_shm s pfrom p' \<and> p' \<in> current_procs s \<and> co2sobj s (O_proc p') = Some (S_proc sp False)"
-apply (auto simp:s2ss_shm_no_backup_def co2sobj.simps tainted_eq_Tainted split:option.splits)
-apply (erule_tac x = p in allE, auto)
-apply (rule_tac x = p' in exI, auto)
-done
-
-lemma s2ss_shm_no_bk_intro1:
-  "\<lbrakk>co2sobj s' obj = Some x; \<forall> p. obj \<noteq> O_proc p\<rbrakk> \<Longrightarrow> x \<notin> s2ss_shm_no_backup s pfrom"
-apply (case_tac obj)
-apply (auto simp:co2sobj.simps s2ss_shm_no_backup_def split:option.splits)
-done
-
-lemma s2ss_shm_no_bk_intro2:
-  "\<lbrakk>co2sobj s' obj = Some x; obj \<in> Tainted s'; valid s'\<rbrakk> \<Longrightarrow> x \<notin> s2ss_shm_no_backup s pfrom"
-apply (case_tac obj)
-
-apply (auto simp:co2sobj.simps s2ss_shm_no_backup_def tainted_eq_Tainted split:option.splits)
-done
-
-lemma s2ss_shm_no_bk_intro3:
-  "\<lbrakk>co2sobj s (O_proc p) = Some x; \<not> info_flow_shm s pfrom p; p \<in> current_procs s
-   \<rbrakk> \<Longrightarrow> x \<notin> s2ss_shm_no_backup s pfrom"
-apply (auto simp add:s2ss_shm_no_backup_def split:option.splits)
-apply (rule_tac x = p in exI, simp)
-done
-
 lemma s2ss_shm_no_bk_intro4:
   "\<lbrakk>co2sobj s (O_proc p) = Some x; info_flow_shm s pfrom p; 
     \<not> info_flow_shm s pfrom p'; p' \<in> current_procs s; co2sobj s (O_proc p') = Some x\<rbrakk>
@@ -156,14 +116,14 @@
 apply (auto simp add:s2ss_shm_no_backup_def co2sobj.simps split:option.splits)
 done  
 
-lemma Tainted_ptrace':
-  "valid s \<Longrightarrow> Tainted (Ptrace p p' # s) = 
-     (if (O_proc p \<in> Tainted s \<and> O_proc p' \<notin> Tainted s)
-      then Tainted s \<union> {O_proc p'' | p''. info_flow_shm s p' p''}
-      else if (O_proc p' \<in> Tainted s \<and> O_proc p \<notin> Tainted s)
-           then Tainted s \<union> {O_proc p'' | p''. info_flow_shm s p p''}
-                else Tainted s)"
-using info_flow_shm_Tainted by auto
+lemma tainted_ptrace':
+  "valid s \<Longrightarrow> tainted (Ptrace p p' # s) = 
+     (if (O_proc p \<in> tainted s \<and> O_proc p' \<notin> tainted s)
+      then tainted s \<union> {O_proc p'' | p''. info_flow_shm s p' p''}
+      else if (O_proc p' \<in> tainted s \<and> O_proc p \<notin> tainted s)
+           then tainted s \<union> {O_proc p'' | p''. info_flow_shm s p p''}
+                else tainted s)"
+using info_flow_shm_tainted by auto
 
 lemma co2sobj_some_caseD:
   "\<lbrakk>co2sobj s obj = Some sobj; \<And> p. \<lbrakk>co2sobj s obj = Some sobj; obj = O_proc p\<rbrakk> \<Longrightarrow> P (O_proc p);
@@ -177,25 +137,25 @@
 lemma s2ss_ptrace1_aux: "x \<notin> {x. P x} \<Longrightarrow> \<not> P x" by simp
 
 lemma s2ss_ptrace1:
-  "\<lbrakk>valid (Ptrace p p' # s); O_proc p \<in> Tainted s; O_proc p' \<notin> Tainted s\<rbrakk>
+  "\<lbrakk>valid (Ptrace p p' # s); O_proc p \<in> tainted s; O_proc p' \<notin> tainted s\<rbrakk>
    \<Longrightarrow> s2ss (Ptrace p p' # s) = update_s2ss_shm s p'"
 unfolding update_s2ss_shm_def s2ss_def s2ss_shm_no_backup_def 
 apply (frule vd_cons, rule set_eqI, rule iffI)
 apply (drule CollectD, (erule exE|erule conjE)+)
 apply (erule co2sobj_some_caseD)
 apply (rule DiffI)
-apply (case_tac "O_proc pa \<in> Tainted s")
+apply (case_tac "O_proc pa \<in> tainted s")
 apply (rule UnI1, simp, rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other split:option.splits)
 apply (case_tac "info_flow_shm s p' pa")
 apply (rule UnI2, rule CollectI, simp only:co2sobj.simps split:option.splits)
 apply (drule current_proc_has_sp', simp, simp)
 apply (rule_tac x = a in exI, rule_tac x = pa in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other split:option.splits)
 apply (rule UnI1, simp)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted split:option.splits)
-apply (rule notI, clarsimp simp:cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other split:option.splits)
+apply (rule notI, clarsimp simp:cp2sproc_other split:option.splits)
 apply (erule_tac x = pa in allE, simp)
 
 apply (rule DiffI, rule UnI1, rule CollectI, rule_tac x = obj in exI,
@@ -214,17 +174,17 @@
 apply (erule DiffE, drule s2ss_ptrace1_aux, erule UnE)
 apply (erule CollectE, (erule exE|erule conjE)+, rule CollectI)
 apply (erule co2sobj_some_caseD)
-apply (case_tac "O_proc pa \<in> Tainted s")
+apply (case_tac "O_proc pa \<in> tainted s")
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp add:tainted_eq_Tainted cp2sproc_other split:option.splits)
+apply (clarsimp simp cp2sproc_other split:option.splits)
 apply (case_tac "info_flow_shm s p' pa", simp only:co2sobj.simps split:option.splits)
 apply (drule current_proc_has_sp', simp, simp)
 apply (drule Meson.not_exD, erule_tac x = a in allE, drule Meson.not_exD, erule_tac x = pa in allE)
-apply (simp add:tainted_eq_Tainted, (erule exE|erule conjE)+)
+apply (simp, (erule exE|erule conjE)+)
 apply (rule_tac x = "O_proc p'a" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other split:option.splits)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other split:option.splits)
 
 apply (rule_tac x = obj in exI,
        auto split:option.splits simp:co2sobj_ptrace alive_simps simp del:co2sobj.simps)[1]
@@ -237,29 +197,29 @@
 
 apply (erule CollectE, (erule exE|erule conjE)+, rule CollectI)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted info_shm_flow_in_procs)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other info_shm_flow_in_procs)
 done
 
 lemma s2ss_ptrace2:
-  "\<lbrakk>valid (Ptrace p p' # s); O_proc p' \<in> Tainted s; O_proc p \<notin> Tainted s\<rbrakk>
+  "\<lbrakk>valid (Ptrace p p' # s); O_proc p' \<in> tainted s; O_proc p \<notin> tainted s\<rbrakk>
    \<Longrightarrow> s2ss (Ptrace p p' # s) = update_s2ss_shm s p"
 unfolding update_s2ss_shm_def s2ss_def s2ss_shm_no_backup_def
 apply (frule vd_cons, rule set_eqI, rule iffI)
 apply (drule CollectD, (erule exE|erule conjE)+)
 apply (erule co2sobj_some_caseD)
 apply (rule DiffI)
-apply (case_tac "O_proc pa \<in> Tainted s")
+apply (case_tac "O_proc pa \<in> tainted s")
 apply (rule UnI1, simp, rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other split:option.splits)
 apply (case_tac "info_flow_shm s p pa")
 apply (rule UnI2, rule CollectI, simp only:co2sobj.simps split:option.splits)
 apply (drule current_proc_has_sp', simp, simp)
 apply (rule_tac x = a in exI, rule_tac x = pa in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other split:option.splits)
 apply (rule UnI1, simp)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted split:option.splits)
-apply (rule notI, clarsimp simp:cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other split:option.splits)
+apply (rule notI, clarsimp simp:cp2sproc_other split:option.splits)
 apply (erule_tac x = pa in allE, simp)
 
 apply (rule DiffI, rule UnI1, rule CollectI, rule_tac x = obj in exI,
@@ -278,17 +238,17 @@
 apply (erule DiffE, drule s2ss_ptrace1_aux, erule UnE)
 apply (erule CollectE, (erule exE|erule conjE)+, rule CollectI)
 apply (erule co2sobj_some_caseD)
-apply (case_tac "O_proc pa \<in> Tainted s")
+apply (case_tac "O_proc pa \<in> tainted s")
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp add:tainted_eq_Tainted cp2sproc_other split:option.splits)
+apply (clarsimp simp cp2sproc_other split:option.splits)
 apply (case_tac "info_flow_shm s p pa", simp only:co2sobj.simps split:option.splits)
 apply (drule current_proc_has_sp', simp, simp)
 apply (drule Meson.not_exD, erule_tac x = a in allE, drule Meson.not_exD, erule_tac x = pa in allE)
-apply (simp add:tainted_eq_Tainted, (erule exE|erule conjE)+)
+apply (simp, (erule exE|erule conjE)+)
 apply (rule_tac x = "O_proc p'a" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other split:option.splits)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other split:option.splits)
 
 apply (rule_tac x = obj in exI,
        auto split:option.splits simp:co2sobj_ptrace alive_simps simp del:co2sobj.simps)[1]
@@ -301,11 +261,11 @@
 
 apply (erule CollectE, (erule exE|erule conjE)+, rule CollectI)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted info_shm_flow_in_procs)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other info_shm_flow_in_procs)
 done
 
 lemma s2ss_ptrace3:
-  "\<lbrakk>valid (Ptrace p p' # s); (O_proc p' \<in> Tainted s) = (O_proc p \<in> Tainted s)\<rbrakk>
+  "\<lbrakk>valid (Ptrace p p' # s); (O_proc p' \<in> tainted s) = (O_proc p \<in> tainted s)\<rbrakk>
    \<Longrightarrow> s2ss (Ptrace p p' # s) = s2ss s"
 unfolding s2ss_def
 apply (frule vd_cons, rule set_eqI, rule iffI)
@@ -313,22 +273,22 @@
 apply (rule_tac x = obj in exI)
 apply (frule alive_other, simp+)
 apply (frule_tac obj = obj in co2sobj_ptrace, simp)
-apply (auto simp add:tainted_eq_Tainted split:t_object.splits option.splits if_splits
-  intro:info_flow_shm_Tainted)[1]
+apply (auto simp split:t_object.splits option.splits if_splits
+  intro:info_flow_shm_tainted)[1]
 
 apply (erule CollectE, (erule exE|erule conjE)+, rule CollectI)
 apply (rule_tac x = obj in exI)
 apply (frule alive_other, simp+)
 apply (frule_tac obj = obj in co2sobj_ptrace, simp)
-apply (auto simp add:tainted_eq_Tainted split:t_object.splits option.splits if_splits 
-  intro:info_flow_shm_Tainted)
+apply (auto simp split:t_object.splits option.splits if_splits 
+  intro:info_flow_shm_tainted)
 done
 
 lemma s2ss_ptrace:
   "valid (Ptrace p p' # s) \<Longrightarrow> s2ss (Ptrace p p' # s) = (
-     if (O_proc p \<in> Tainted s \<and> O_proc p' \<notin> Tainted s) 
+     if (O_proc p \<in> tainted s \<and> O_proc p' \<notin> tainted s) 
      then update_s2ss_shm s p'
-     else if (O_proc p' \<in> Tainted s \<and> O_proc p \<notin> Tainted s)
+     else if (O_proc p' \<in> tainted s \<and> O_proc p \<notin> tainted s)
           then update_s2ss_shm s p
           else s2ss s                                   )"
 apply (frule vt_grant_os, frule vd_cons)
@@ -351,15 +311,15 @@
 apply (simp split: option.splits, (erule conjE)+)
 apply (rule set_eqI, rule iffI, erule CollectE, (erule exE|erule conjE)+, rule CollectI)
 apply (rule_tac x = obj in exI)
-apply (simp add:co2sobj_kill tainted_eq_Tainted alive_kill split:t_object.splits if_splits)
+apply (simp add:co2sobj_kill alive_kill split:t_object.splits if_splits)
 apply (erule CollectE, erule exE, erule conjE, rule CollectI)
 apply (erule co2sobj_some_caseD)
 apply (case_tac "pa = p'")
 apply (rule_tac x = "O_proc p''" in exI)
-apply (simp add:cp2sproc_kill tainted_eq_Tainted alive_kill
+apply (simp add:cp2sproc_kill alive_kill
   split:t_object.splits if_splits option.splits)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp add:cp2sproc_kill tainted_eq_Tainted alive_kill
+apply (clarsimp simp add:cp2sproc_kill alive_kill
   split:t_object.splits if_splits option.splits)
 apply (rule_tac x = obj in exI, frule alive_kill, simp add:co2sobj_kill del:co2sobj.simps)+
 
@@ -367,18 +327,18 @@
 apply (rule set_eqI, rule iffI)
 apply (erule CollectE, erule exE, erule conjE, rule DiffI)
 apply (rule CollectI, rule_tac x = obj in exI)
-apply (simp add:co2sobj_kill tainted_eq_Tainted alive_kill split:t_object.splits if_splits)
+apply (simp add:co2sobj_kill alive_kill split:t_object.splits if_splits)
 apply (rule notI, simp, case_tac obj)
 apply (erule_tac x = nat in allE)
-apply (simp add:co2sobj_kill cp2sproc_kill tainted_eq_Tainted split:option.splits)
+apply (simp add:co2sobj_kill cp2sproc_kill split:option.splits)
 apply (simp split:option.splits)+
 apply (erule co2sobj_some_caseD)
 apply (case_tac "pa = p'")
 apply (rule_tac x = "O_proc p''" in exI)
-apply (simp add:cp2sproc_kill tainted_eq_Tainted alive_kill
+apply (simp add:cp2sproc_kill alive_kill
   split:t_object.splits if_splits option.splits)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp add:cp2sproc_kill tainted_eq_Tainted alive_kill
+apply (clarsimp simp add:cp2sproc_kill alive_kill
   split:t_object.splits if_splits option.splits)
 apply (rule_tac x = obj in exI, frule alive_kill, simp add:co2sobj_kill del:co2sobj.simps)+
 done
@@ -399,15 +359,15 @@
 apply (simp split: option.splits, (erule conjE)+)
 apply (rule set_eqI, rule iffI, erule CollectE, (erule exE|erule conjE)+, rule CollectI)
 apply (rule_tac x = obj in exI)
-apply (simp add:co2sobj_exit tainted_eq_Tainted alive_exit split:t_object.splits if_splits)
+apply (simp add:co2sobj_exit alive_exit split:t_object.splits if_splits)
 apply (erule CollectE, erule exE, erule conjE, rule CollectI)
 apply (erule co2sobj_some_caseD)
 apply (case_tac "pa = p")
 apply (rule_tac x = "O_proc p'" in exI)
-apply (simp add:cp2sproc_exit tainted_eq_Tainted alive_exit
+apply (simp add:cp2sproc_exit alive_exit
   split:t_object.splits if_splits option.splits)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp add:cp2sproc_exit tainted_eq_Tainted alive_exit
+apply (clarsimp simp add:cp2sproc_exit alive_exit
   split:t_object.splits if_splits option.splits)
 apply (rule_tac x = obj in exI, frule alive_exit, simp add:co2sobj_exit del:co2sobj.simps)+
 
@@ -415,18 +375,18 @@
 apply (rule set_eqI, rule iffI)
 apply (erule CollectE, erule exE, erule conjE, rule DiffI)
 apply (rule CollectI, rule_tac x = obj in exI)
-apply (simp add:co2sobj_exit tainted_eq_Tainted alive_exit split:t_object.splits if_splits)
+apply (simp add:co2sobj_exit alive_exit split:t_object.splits if_splits)
 apply (rule notI, simp, case_tac obj)
 apply (erule_tac x = nat in allE)
-apply (simp add:co2sobj_exit cp2sproc_exit tainted_eq_Tainted split:option.splits)
+apply (simp add:co2sobj_exit cp2sproc_exit split:option.splits)
 apply (simp split:option.splits)+
 apply (erule co2sobj_some_caseD)
 apply (case_tac "pa = p")
 apply (rule_tac x = "O_proc p'" in exI)
-apply (simp add:cp2sproc_exit tainted_eq_Tainted alive_exit
+apply (simp add:cp2sproc_exit alive_exit
   split:t_object.splits if_splits option.splits)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp add:cp2sproc_exit tainted_eq_Tainted alive_exit
+apply (clarsimp simp add:cp2sproc_exit alive_exit
   split:t_object.splits if_splits option.splits)
 apply (rule_tac x = obj in exI, frule alive_exit, simp add:co2sobj_exit del:co2sobj.simps)+
 done
@@ -443,7 +403,7 @@
   "\<lbrakk>valid (Open p f flag fd None # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Open p f flag fd None # s) obj = (
       if (obj = O_proc p) 
       then (case (cp2sproc (Open p f flag fd None # s) p) of
-              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
+              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
            | _       \<Rightarrow> None)
       else co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons)
@@ -455,11 +415,11 @@
   "\<lbrakk>valid (Open p f flag fd (Some i) # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Open p f flag fd (Some i) # s) obj = (
       if (obj = O_proc p) 
       then (case (cp2sproc (Open p f flag fd (Some i) # s) p) of
-              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
+              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> tainted s))
            | _       \<Rightarrow> None)
       else if (obj = O_file f) 
            then (case (cf2sfile (Open p f flag fd (Some i) # s) f) of
-                   Some sf \<Rightarrow> Some (S_file {sf} (O_proc p \<in> Tainted s))
+                   Some sf \<Rightarrow> Some (S_file {sf} (O_proc p \<in> tainted s))
                  | _       \<Rightarrow> None)
            else co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons)
@@ -607,7 +567,7 @@
 lemma s2ss_readfile:
   "valid (ReadFile p fd # s) \<Longrightarrow> s2ss (ReadFile p fd # s) = (
      case (file_of_proc_fd s p fd) of 
-       Some f \<Rightarrow> if (O_file f \<in> Tainted s)
+       Some f \<Rightarrow> if (O_file f \<in> tainted s)
                  then update_s2ss_shm s p
                  else s2ss s
      | _      \<Rightarrow> {})"
@@ -618,18 +578,18 @@
 apply (drule CollectD, (erule exE|erule conjE)+)
 apply (erule co2sobj_some_caseD)
 apply (rule DiffI)
-apply (case_tac "O_proc pa \<in> Tainted s")
+apply (case_tac "O_proc pa \<in> tainted s")
 apply (rule UnI1, simp, rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:cp2sproc_other tainted_eq_Tainted co2sobj.simps split:option.splits)
+apply (clarsimp simp:cp2sproc_other co2sobj.simps split:option.splits)
 apply (case_tac "info_flow_shm s p pa")
 apply (rule UnI2, rule CollectI, simp only:co2sobj.simps split:option.splits)
 apply (drule current_proc_has_sp', simp, simp)
 apply (rule_tac x = ab in exI, rule_tac x = pa in exI)
-apply (clarsimp simp:cp2sproc_other tainted_eq_Tainted split:option.splits)
+apply (clarsimp simp:cp2sproc_other split:option.splits)
 apply (rule UnI1, simp)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:cp2sproc_other tainted_eq_Tainted co2sobj.simps split:option.splits)
-apply (rule notI, clarsimp simp:cp2sproc_other tainted_eq_Tainted co2sobj.simps split:option.splits)
+apply (clarsimp simp:cp2sproc_other co2sobj.simps split:option.splits)
+apply (rule notI, clarsimp simp:cp2sproc_other co2sobj.simps split:option.splits)
 apply (erule_tac x = pa in allE, simp)
 
 apply (rule DiffI, rule UnI1, rule CollectI, rule_tac x = obj in exI)
@@ -644,17 +604,17 @@
 apply (erule DiffE, drule s2ss_ptrace1_aux, erule UnE)
 apply (erule CollectE, (erule exE|erule conjE)+, rule CollectI)
 apply (erule co2sobj_some_caseD)
-apply (case_tac "O_proc pa \<in> Tainted s")
+apply (case_tac "O_proc pa \<in> tainted s")
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:tainted_eq_Tainted cp2sproc_other co2sobj.simps split:option.splits)
+apply (clarsimp simp:tainted_eq_tainted cp2sproc_other co2sobj.simps split:option.splits)
 apply (case_tac "info_flow_shm s p pa", simp only:co2sobj.simps split:option.splits)
 apply (drule current_proc_has_sp', simp, simp)
 apply (drule Meson.not_exD, erule_tac x = ab in allE, drule Meson.not_exD, erule_tac x = pa in allE)
-apply (simp add:tainted_eq_Tainted, (erule exE|erule conjE)+)
+apply (simp, (erule exE|erule conjE)+)
 apply (rule_tac x = "O_proc p'" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted co2sobj.simps split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other co2sobj.simps split:option.splits)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted co2sobj.simps split:option.splits)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other co2sobj.simps split:option.splits)
 
 apply (rule_tac x = obj in exI,
        auto split:option.splits simp:co2sobj_readfile alive_simps simp del:co2sobj.simps)[1]
@@ -667,7 +627,7 @@
 
 apply (erule CollectE, (erule exE|erule conjE)+, rule CollectI)
 apply (rule_tac x = "O_proc pa" in exI)
-apply (clarsimp simp:Tainted_ptrace' cp2sproc_other tainted_eq_Tainted info_shm_flow_in_procs co2sobj.simps)
+apply (clarsimp simp:tainted_ptrace' cp2sproc_other info_shm_flow_in_procs co2sobj.simps)
 
 
 apply (rule impI, rule impI)
@@ -695,18 +655,18 @@
 
 lemma co2sobj_writefile_unchange:
   "\<lbrakk>valid (WriteFile p fd # s); alive s obj; file_of_proc_fd s p fd = Some f;
-    O_proc p \<in> Tainted s \<longrightarrow> O_file f \<in> Tainted s\<rbrakk> 
+    O_proc p \<in> tainted s \<longrightarrow> O_file f \<in> tainted s\<rbrakk> 
    \<Longrightarrow> co2sobj (WriteFile p fd # s) obj = co2sobj s obj"
 apply (frule vd_cons, frule co2sobj_writefile, simp, simp split:t_object.splits if_splits)
 apply (simp add:co2sobj.simps)
-apply (case_tac "O_proc p \<in> Tainted s")
-apply (simp add:tainted_eq_Tainted same_inodes_Tainted)+
+apply (case_tac "O_proc p \<in> tainted s")
+apply (simp same_inodes_tainted)+
 done
 
 lemma s2ss_writefile:
   "valid (WriteFile p fd # s) \<Longrightarrow> s2ss (WriteFile p fd # s) = (
      case (file_of_proc_fd s p fd) of
-       Some f \<Rightarrow> if (O_proc p \<in> Tainted s \<and> O_file f \<notin> Tainted s)
+       Some f \<Rightarrow> if (O_proc p \<in> tainted s \<and> O_file f \<notin> tainted s)
                  then (if (\<exists> f'. f' \<notin> same_inode_files s f \<and> is_file s f' \<and>
                                  co2sobj s (O_file f') = co2sobj s (O_file f))
                        then s2ss s \<union> {S_file (cf2sfiles s f) True}
@@ -744,7 +704,7 @@
 apply (frule_tac f = fa and f' = aa in cf2sfiles_prop, simp)
 apply (rule_tac x = "O_file f'" in exI, simp add:co2sobj_writefile is_file_simps)
 apply (rule conjI, rule impI, simp add:same_inode_files_prop5)
-apply (rule impI, simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted)
+apply (rule impI, simp add:co2sobj.simps same_inodes_tainted)
 apply (rule_tac x = "O_file fa" in exI, simp add:co2sobj_writefile is_file_simps)
 apply (rule impI, simp add:same_inode_files_prop5)
 apply (rule_tac x = obj in exI, simp add:co2sobj_writefile)
@@ -754,8 +714,8 @@
 apply (rule impI, rule impI, simp, rule set_eqI, rule iffI, erule CollectE, (erule conjE|erule exE)+)
 apply (rule CollectI, rule_tac x = obj in exI, simp add:alive_simps)
 apply (simp add:co2sobj_writefile split:t_object.splits if_splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted)
-apply (case_tac "O_proc p \<in> Tainted s", simp, simp)
+apply (simp add:co2sobj.simps same_inodes_tainted)
+apply (case_tac "O_proc p \<in> tainted s", simp, simp)
 apply (erule CollectE, (erule conjE|erule exE)+, rule CollectI)
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_writefile_unchange alive_simps)
@@ -769,7 +729,7 @@
 apply (rule disjI1, simp add:cf2sfiles_prop)
 apply (rule disjI2, rule conjI, rule_tac x = obj in exI, simp)
 apply (rule notI, simp add:co2sobj.simps split:option.splits)
-apply (erule_tac x = list in allE, simp add:tainted_eq_Tainted same_inode_files_prop5)
+apply (erule_tac x = list in allE, simp same_inode_files_prop5)
 apply (simp add:co2sobj.simps)
 apply (rule disjI2, rule conjI, rule_tac x = obj in exI, simp,
   rule notI, simp add:co2sobj.simps split:option.splits)
@@ -789,7 +749,7 @@
 apply (erule co2sobj_some_caseD)
 apply (rule_tac x = obj in exI, simp add:co2sobj_writefile)
 apply (case_tac "fa \<in> same_inode_files s aa")
-apply (frule cf2sfiles_prop, simp, simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted)
+apply (frule cf2sfiles_prop, simp, simp add:co2sobj.simps same_inodes_tainted)
 apply (rule_tac x = obj in exI, simp add:co2sobj_writefile is_file_simps)
 apply (rule impI, simp add:same_inode_files_prop5)
 apply (rule_tac x = obj in exI, simp add:co2sobj_writefile)
@@ -818,7 +778,7 @@
   "update_s2ss_sfile_del s ss f sf \<equiv> 
      if (same_inode_files s f = {f})
      then ss
-     else ss \<union> {S_file (cf2sfiles s f - {sf}) (O_file f \<in> Tainted s)}"
+     else ss \<union> {S_file (cf2sfiles s f - {sf}) (O_file f \<in> tainted s)}"
 
 definition del_s2ss_file:: "t_state \<Rightarrow> t_static_state \<Rightarrow> t_file \<Rightarrow> t_sfile \<Rightarrow> t_static_state"
 where
@@ -827,7 +787,7 @@
       then ss
       else if (\<exists> f'. is_file s f' \<and> f' \<notin> same_inode_files s f \<and> co2sobj s (O_file f') = co2sobj s (O_file f))
            then update_s2ss_sfile_del s ss f sf
-           else update_s2ss_sfile_del s (ss - {S_file (cf2sfiles s f) (O_file f \<in> Tainted s)}) f sf)"
+           else update_s2ss_sfile_del s (ss - {S_file (cf2sfiles s f) (O_file f \<in> tainted s)}) f sf)"
 
 lemma alive_co2sobj_closefd1:
   "\<lbrakk>alive s obj; valid (CloseFd p fd # s); co2sobj s obj = Some sobj; 
@@ -921,14 +881,14 @@
                          (Some sf, Some sp, Some sp') \<Rightarrow> 
                             (del_s2ss_file s (
                                update_s2ss_obj s (s2ss s) (O_proc p) 
-                                 (S_proc sp (O_proc p \<in> Tainted s))
-                                 (S_proc sp' (O_proc p \<in> Tainted s))) f sf)
+                                 (S_proc sp (O_proc p \<in> tainted s))
+                                 (S_proc sp' (O_proc p \<in> tainted s))) f sf)
                       | _ \<Rightarrow> {})
                  else (case (cp2sproc s p, cp2sproc (CloseFd p fd # s) p) of 
                          (Some sp, Some sp') \<Rightarrow> 
                             (update_s2ss_obj s (s2ss s) (O_proc p)
-                               (S_proc sp (O_proc p \<in> Tainted s))
-                               (S_proc sp' (O_proc p \<in> Tainted s)))
+                               (S_proc sp (O_proc p \<in> tainted s))
+                               (S_proc sp' (O_proc p \<in> tainted s)))
                       | _ \<Rightarrow> {})
       | _     \<Rightarrow> s2ss s)"
 apply (frule vd_cons, frule vt_grant_os)
@@ -942,12 +902,12 @@
 apply (frule co2sobj_closefd, simp)
 apply (frule cp2sproc_closefd, simp)
 apply (simp add:proc_file_fds_def split:t_object.splits)
-apply (simp split:if_splits add:co2sobj.simps tainted_eq_Tainted)
+apply (simp split:if_splits add:co2sobj.simps)
 apply (erule CollectE, erule exE, erule conjE, rule CollectI)
 apply (rule_tac x = obj in exI, simp add:alive_co2sobj_closefd2)
 apply (frule_tac obj = obj in co2sobj_closefd, simp add:alive_co2sobj_closefd2)
 apply (frule cp2sproc_closefd, simp)
-apply (auto simp add:proc_file_fds_def co2sobj.simps tainted_eq_Tainted 
+apply (auto simp add:proc_file_fds_def co2sobj.simps 
             split:t_object.splits option.splits if_splits)[1]
 
 apply (case_tac "cp2sproc (CloseFd p fd # s) p")
@@ -965,58 +925,58 @@
 apply (tactic {*my_seteq_tac 1*})
 apply simp
 apply (case_tac "obj = O_proc p")
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (rule disjI2, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp add:alive_simps)
-apply (simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)
+apply (simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)
 apply (tactic {*my_setiff_tac 1*})
 apply (rule_tac x = "O_proc p" in exI)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (tactic {*my_setiff_tac 1*})
 apply (case_tac "obj = O_proc p")
 apply (rule_tac x = obj' in exI)
 apply (frule co2sobj_sproc_imp, erule exE, simp add:co2sobj_closefd)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (case_tac "obj = O_file a")
 apply (rule_tac x = "O_file f'" in exI)
 apply (case_tac "f' = a", simp add:same_inode_files_prop9 file_of_pfd_is_file)
 apply (frule_tac obj = "O_file f'" in co2sobj_closefd, simp add:alive_simps)
-apply (simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)
+apply (simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in alive_co2sobj_closefd3, simp+)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)[1]
 
 apply (rule impI)+
 apply (tactic {*my_seteq_tac 1*})
-apply (case_tac "obj = O_proc p", rule disjI1, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "obj = O_proc p", rule disjI1, simp add:co2sobj.simps)
 apply (rule disjI2)
 apply (case_tac "obj = O_file a", simp add:alive_simps)
 apply (rule DiffI, simp)
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in alive_co2sobj_closefd', simp+)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)
+apply (simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)
 apply (simp, rule notI, simp, frule co2sobj_sproc_imp, erule exE, simp add:co2sobj_closefd)
 apply (erule_tac x = "O_proc pa" in allE, simp)
 apply (tactic {*my_setiff_tac 1*})
-apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps)
 apply (tactic {*my_setiff_tac 1*})
-apply (case_tac "obj = O_proc p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "obj = O_proc p", simp add:co2sobj.simps)
 apply (case_tac "obj = O_file a", rule_tac x = "O_file f'" in exI)
 apply (case_tac "f' = a", simp add:same_inode_files_prop9 file_of_pfd_is_file)
 apply (frule_tac obj = "O_file f'" in co2sobj_closefd, simp add:alive_simps)
-apply (simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)
+apply (simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in alive_co2sobj_closefd3, simp+)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:co2sobj.simps split:t_object.splits if_splits)[1]
 
 apply (rule impI, tactic {*my_seteq_tac 1*})
 apply (simp add:update_s2ss_obj_def update_s2ss_sfile_del_def)
 apply (rule conjI| rule impI|erule exE|erule conjE)+
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "pa = p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "pa = p", simp add:co2sobj.simps)
 apply (rule disjI2, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (case_tac "f = a", simp add:alive_simps)
@@ -1030,14 +990,14 @@
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (rule conjI| rule impI|erule exE|erule conjE)+
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "pa = p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "pa = p", simp add:co2sobj.simps)
 apply (rule disjI2, rule disjI2, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:co2sobj.simps split:t_object.splits if_splits)[1]
 apply (case_tac "f = a", simp add:alive_simps)
 apply (case_tac "f \<in> same_inode_files s a", rule disjI1)
 apply (simp add:co2sobj_simps split:if_splits option.splits t_sobject.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted cf2sfiles_prop)
+apply (simp add:co2sobj.simps same_inodes_tainted cf2sfiles_prop)
 apply (erule bexE, erule conjE)
 apply (erule_tac x = f'' in ballE, simp, simp)
 apply (rule disjI2, rule disjI2, rule_tac x = obj in exI)
@@ -1050,7 +1010,7 @@
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (rule impI, rule conjI, rule impI)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "pa = p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "pa = p", simp add:co2sobj.simps)
 apply (rule disjI2, rule conjI, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (rule notI, simp add:co2sobj_closefd, erule_tac x = obj in allE, simp add:is_file_simps)
@@ -1069,16 +1029,16 @@
 apply (rule notI, simp add:co2sobj_closefd, erule_tac x = obj in allE, simp)
 apply (rule impI)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "pa = p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "pa = p", simp add:co2sobj.simps)
 apply (rule disjI2, rule disjI2, rule conjI, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:co2sobj.simps split:t_object.splits if_splits)[1]
 apply (rule notI, simp add:co2sobj_closefd)
 apply (erule_tac x = obj in allE, simp)
 apply (case_tac "f = a", simp add:alive_simps)
 apply (case_tac "f \<in> same_inode_files s a", rule disjI1)
 apply (simp add:co2sobj_simps split:if_splits option.splits t_sobject.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted cf2sfiles_prop)
+apply (simp add:co2sobj.simps same_inodes_tainted cf2sfiles_prop)
 apply (erule bexE, erule conjE)
 apply (erule_tac x = f'' in ballE, simp, simp)
 apply (rule disjI2, rule disjI2, rule conjI, rule_tac x = obj in exI)
@@ -1095,34 +1055,34 @@
 apply (rule notI, simp add:co2sobj_closefd, erule_tac x = obj in allE, simp)
 
 apply (simp add:update_s2ss_sfile_del_def update_s2ss_obj_def split:if_splits)
-apply (erule disjE, rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (erule disjE, rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps)
 apply (erule exE, erule conjE)
 apply (case_tac "obj = O_proc p")
 apply (rule_tac x = obj' in exI)
 apply (frule co2sobj_sproc_imp, erule exE, simp add:co2sobj_closefd)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (case_tac "obj = O_file a")
 apply (rule_tac x = "O_file f'" in exI)
 apply (case_tac "f' = a", simp add:same_inode_files_prop9 file_of_pfd_is_file)
 apply (frule_tac obj = "O_file f'" in co2sobj_closefd, simp add:alive_simps)
-apply (simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)
+apply (simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in alive_co2sobj_closefd3, simp+)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
-apply (erule disjE, rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (auto simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)[1]
+apply (erule disjE, rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps)
 apply (erule conjE, erule exE, erule conjE)
 apply (case_tac "obj = O_proc p")
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (case_tac "obj = O_file a")
 apply (rule_tac x = "O_file f'" in exI)
 apply (case_tac "f' = a", simp add:same_inode_files_prop9 file_of_pfd_is_file)
 apply (frule_tac obj = "O_file f'" in co2sobj_closefd, simp add:alive_simps)
-apply (simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)
+apply (simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in alive_co2sobj_closefd3, simp+)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)[1]
 apply (erule disjE)
 apply (drule same_inode_files_prop10, simp add:file_of_pfd_is_file, erule exE, erule conjE)
 apply (rule_tac x = "O_file f'a" in exI)
@@ -1130,16 +1090,16 @@
 apply (frule_tac obj = "O_file f'a" in co2sobj_closefd)
 apply (simp add:alive_simps)+
 apply (frule_tac f = "f'a" in is_file_has_sfile', simp, erule exE)
-apply (simp add:co2sobj.simps cf2sfiles_prop tainted_eq_Tainted same_inodes_Tainted split:if_splits)
+apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted split:if_splits)
 apply (rule impI, erule bexE, erule conjE, erule_tac x = f'' in ballE, simp, simp)
 apply (erule bexE, erule conjE, erule_tac x = f'' in ballE, simp, simp)
 apply (erule disjE)
-apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps)
 apply (erule exE, erule conjE)
 apply (case_tac "obj = O_proc p")
 apply (rule_tac x = obj' in exI)
 apply (frule co2sobj_sproc_imp, erule exE, simp add:co2sobj_closefd)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_closefd)
@@ -1147,7 +1107,7 @@
 apply (rule_tac x = "O_file f'" in exI)
 apply (simp add:co2sobj_simps is_file_simps split:if_splits option.splits t_sobject.splits)
 apply (rule conjI, rule notI, simp add:same_inode_files_prop9)
-apply (rule impI, simp add:co2sobj.simps cf2sfiles_prop tainted_eq_Tainted same_inodes_Tainted)
+apply (rule impI, simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_closefd is_file_simps)
 apply (rule notI, simp add:same_inode_files_prop9)
@@ -1162,15 +1122,15 @@
 apply (frule_tac obj = "O_file f'a" in co2sobj_closefd)
 apply (simp add:alive_simps)+
 apply (frule_tac f = "f'a" in is_file_has_sfile', simp, erule exE)
-apply (simp add:co2sobj.simps cf2sfiles_prop tainted_eq_Tainted same_inodes_Tainted split:if_splits)
+apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted split:if_splits)
 apply (rule impI, erule bexE, erule conjE, erule_tac x = f'' in ballE, simp, simp)
 apply (erule bexE, erule conjE, erule_tac x = f'' in ballE, simp, simp)
 apply (erule disjE)
 apply (rule_tac x = "O_proc p" in exI)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (erule conjE, erule exE, erule conjE)
 apply (case_tac "obj = O_proc p")
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_closefd)
@@ -1178,7 +1138,7 @@
 apply (rule_tac x = "O_file f'" in exI)
 apply (simp add:co2sobj_simps is_file_simps split:if_splits option.splits t_sobject.splits)
 apply (rule conjI, rule notI, simp add:same_inode_files_prop9)
-apply (rule impI, simp add:co2sobj.simps cf2sfiles_prop tainted_eq_Tainted same_inodes_Tainted)
+apply (rule impI, simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_closefd is_file_simps)
 apply (rule notI, simp add:same_inode_files_prop9)
@@ -1191,7 +1151,7 @@
 apply (simp add:update_s2ss_obj_def update_s2ss_sfile_del_def)
 apply (rule conjI| rule impI|erule exE|erule conjE)+
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "pa = p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "pa = p", simp add:co2sobj.simps)
 apply (rule disjI2, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (case_tac "f = a", simp add:alive_simps)
@@ -1205,18 +1165,18 @@
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (rule conjI| rule impI|erule exE|erule conjE)+
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "pa = p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "pa = p", simp add:co2sobj.simps)
 apply (rule disjI2, rule conjI, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:co2sobj.simps split:t_object.splits if_splits)[1]
 apply (rule notI, simp, erule_tac x = "O_proc pa" in allE, simp add:co2sobj_closefd)
 apply (case_tac "f = a", simp add:alive_simps)
 apply (case_tac "f \<in> same_inode_files s a", rule disjI2)
 apply (simp add:co2sobj_simps split:if_splits option.splits t_sobject.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted cf2sfiles_prop)
+apply (simp add:co2sobj.simps same_inodes_tainted cf2sfiles_prop)
 apply (erule bexE, erule conjE)
 apply (rule conjI, rule_tac x = "O_file f''" in exI)
-apply (simp add:same_inode_files_prop11 co2sobj.simps tainted_eq_Tainted cf2sfiles_prop same_inodes_Tainted)
+apply (simp add:same_inode_files_prop11 co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (rule notI, simp)
 apply (rule disjI2, rule conjI, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
@@ -1233,47 +1193,47 @@
 
 apply (erule bexE, erule conjE)
 apply (simp add:update_s2ss_obj_def split:if_splits)
-apply (erule disjE, rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (erule disjE, rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps)
 apply (erule exE, erule conjE)
 apply (case_tac "obj = O_proc p")
 apply (rule_tac x = obj' in exI)
 apply (frule co2sobj_sproc_imp, erule exE, simp add:co2sobj_closefd)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (case_tac "obj = O_file a")
 apply (rule_tac x = "O_file f'" in exI)
 apply (frule_tac obj = "O_file f'" in co2sobj_closefd, simp add:alive_simps same_inode_files_prop11)
-apply (simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)
+apply (simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)
 apply (rule conjI)
 apply (rule impI)
 apply (rule_tac x = f' in ballE, simp, simp, simp)
-apply (simp add:same_inode_files_prop11 co2sobj.simps cf2sfiles_prop same_inodes_Tainted)
+apply (simp add:same_inode_files_prop11 co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in alive_co2sobj_closefd3, simp+)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
-apply (erule disjE, rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (auto simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)[1]
+apply (erule disjE, rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps)
 apply (erule conjE, erule exE, erule conjE)
 apply (case_tac "obj = O_proc p")
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (case_tac "obj = O_file a")
 apply (rule_tac x = "O_file f'" in exI)
 apply (frule_tac obj = "O_file f'" in co2sobj_closefd, simp add:alive_simps same_inode_files_prop11)
-apply (simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)
+apply (simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)
 apply (rule conjI)
 apply (rule impI)
 apply (rule_tac x = f' in ballE, simp, simp, simp)
-apply (simp add:same_inode_files_prop11 co2sobj.simps cf2sfiles_prop same_inodes_Tainted)
+apply (simp add:same_inode_files_prop11 co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in alive_co2sobj_closefd3, simp+)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:alive_simps co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:alive_simps co2sobj.simps split:t_object.splits if_splits)[1]
 
 apply (rule impI)
 apply (tactic {*my_seteq_tac 1*})
 apply (simp add:update_s2ss_obj_def update_s2ss_sfile_del_def)
 apply (rule conjI| rule impI|erule exE|erule conjE)+
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "pa = p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "pa = p", simp add:co2sobj.simps)
 apply (rule disjI2, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (case_tac "f = a", simp add:alive_simps)
@@ -1287,25 +1247,25 @@
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (frule_tac obj = obj in co2sobj_closefd, simp, rule notI, simp)
 apply (frule_tac obj = obj in co2sobj_sfile_imp, erule exE, simp add:is_file_simps split:if_splits)
-apply (erule_tac x= f in allE, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (erule_tac x= f in allE, simp add:co2sobj.simps)
 apply (rule conjI| rule impI|erule exE|erule conjE)+
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "pa = p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "pa = p", simp add:co2sobj.simps)
 apply (rule disjI2, rule notI, simp)
 apply (rule disjI2, rule conjI, rule disjI2, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:co2sobj.simps split:t_object.splits if_splits)[1]
 apply (rule notI, simp add:co2sobj.simps split:option.splits)
 apply (case_tac "f = a", simp add:alive_simps)
 apply (case_tac "f \<in> same_inode_files s a", rule disjI1)
 apply (simp add:co2sobj_simps split:if_splits option.splits t_sobject.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted cf2sfiles_prop)
+apply (simp add:co2sobj.simps same_inodes_tainted cf2sfiles_prop)
 apply (erule bexE, erule conjE)
 apply (erule_tac x = f'' in ballE, simp, simp)
 apply (rule disjI2, rule conjI, rule disjI2, rule_tac x = obj in exI)
-apply (simp add:is_file_simps co2sobj_closefd tainted_eq_Tainted)
+apply (simp add:is_file_simps co2sobj_closefd)
 apply (rule notI, simp add:co2sobj_closefd)
-apply (erule_tac x = f in allE, simp add:is_file_simps co2sobj.simps tainted_eq_Tainted) 
+apply (erule_tac x = f in allE, simp add:is_file_simps co2sobj.simps) 
 apply (rule disjI2, rule conjI, rule disjI2, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (rule notI, simp add:co2sobj.simps split:option.splits)
@@ -1318,11 +1278,11 @@
 apply (rule impI, rule conjI, rule impI)
 
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "pa = p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "pa = p", simp add:co2sobj.simps)
 apply (rule notI, simp)
 apply (rule conjI, rule disjI2, rule conjI, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:co2sobj.simps split:t_object.splits if_splits)[1]
 apply (erule_tac x = obj in allE, simp add:co2sobj_closefd)
 apply (rule notI, simp add:co2sobj.simps split:option.splits)
 apply (case_tac "f = a", simp add:alive_simps)
@@ -1331,10 +1291,10 @@
 apply (simp add:co2sobj.simps)
 apply (rule notI, simp add:co2sobj.simps)
 apply (rule conjI, rule disjI2, rule conjI, rule_tac x = obj in exI)
-apply (simp add:is_file_simps co2sobj_closefd tainted_eq_Tainted)
+apply (simp add:is_file_simps co2sobj_closefd)
 apply (rule notI, simp add:co2sobj.simps)
-apply (rule notI, simp add:co2sobj_closefd tainted_eq_Tainted)
-apply (erule_tac x = f in allE, simp add:is_file_simps co2sobj.simps tainted_eq_Tainted)
+apply (rule notI, simp add:co2sobj_closefd)
+apply (erule_tac x = f in allE, simp add:is_file_simps co2sobj.simps)
 apply (rule conjI, rule disjI2, rule conjI, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (rule notI, simp add:co2sobj.simps split:option.splits)+
@@ -1346,23 +1306,23 @@
 apply (rule notI, simp add:co2sobj.simps split:option.splits)+
 apply (rule impI)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "pa = p", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "pa = p", simp add:co2sobj.simps)
 apply (rule disjI2, rule notI, simp)
 apply (rule disjI2, rule conjI, rule disjI2, rule conjI, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp)
-apply (auto simp add:co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:co2sobj.simps split:t_object.splits if_splits)[1]
 apply (erule_tac x = obj in allE, simp add:co2sobj_closefd)
 apply (rule notI, simp add:co2sobj.simps split:option.splits)
 apply (case_tac "f = a", simp add:alive_simps)
 apply (case_tac "f \<in> same_inode_files s a", rule disjI1)
 apply (simp add:co2sobj_closefd split:if_splits option.splits t_sobject.splits)
-apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_Tainted tainted_eq_Tainted)
+apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (erule bexE, erule conjE, erule_tac x = "f''" in ballE, simp, simp)
 apply (rule disjI2, rule conjI, rule disjI2, rule conjI, rule_tac x = obj in exI)
-apply (simp add:is_file_simps co2sobj_closefd tainted_eq_Tainted)
+apply (simp add:is_file_simps co2sobj_closefd)
 apply (rule notI, simp add:co2sobj.simps)
-apply (rule notI, simp add:co2sobj_closefd tainted_eq_Tainted)
-apply (erule_tac x = f in allE, simp add:is_file_simps co2sobj.simps tainted_eq_Tainted)
+apply (rule notI, simp add:co2sobj_closefd)
+apply (erule_tac x = f in allE, simp add:is_file_simps co2sobj.simps)
 apply (rule disjI2, rule conjI, rule disjI2, rule conjI, rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp add:alive_simps)
 apply (rule notI, simp add:co2sobj.simps split:option.splits)+
@@ -1375,26 +1335,26 @@
 
 apply (simp add:update_s2ss_sfile_del_def update_s2ss_obj_def split:if_splits)
 apply (erule conjE, erule disjE)
-apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps)
 apply (erule exE, erule conjE)
-apply (case_tac "obj = O_file a", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "obj = O_file a", simp add:co2sobj.simps)
 apply (case_tac "obj = O_proc p")
 apply (rule_tac x = obj' in exI, frule_tac obj = obj' in co2sobj_sproc_imp, erule exE)
 apply (frule_tac obj = obj' in alive_co2sobj_closefd3, simp+)
 apply (simp add:co2sobj_closefd)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (frule_tac obj = obj in alive_co2sobj_closefd3, simp+)
 apply (rule_tac x = obj in exI, simp add:co2sobj_closefd)
-apply (auto simp add:co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:co2sobj.simps split:t_object.splits if_splits)[1]
 apply (erule conjE|erule exE|erule disjE)+
-apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps)
 apply (erule conjE, erule exE, erule conjE)
-apply (case_tac "obj = O_file a", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "obj = O_file a", simp add:co2sobj.simps)
 apply (case_tac "obj = O_proc p")
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (frule_tac obj = obj in alive_co2sobj_closefd3, simp+)
 apply (rule_tac x = obj in exI, simp add:co2sobj_closefd)
-apply (auto simp add:co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)[1]
+apply (auto simp add:co2sobj.simps split:t_object.splits if_splits)[1]
 apply (erule conjE|erule exE|erule disjE)+
 apply (drule same_inode_files_prop10, simp add:file_of_pfd_is_file, erule exE, erule conjE)
 apply (rule_tac x = "O_file f'" in exI)
@@ -1402,26 +1362,26 @@
 apply (frule_tac obj = "O_file f'" in co2sobj_closefd)
 apply (simp add:alive_simps)+
 apply (frule_tac f = "f'" in is_file_has_sfile', simp, erule exE)
-apply (simp add:co2sobj.simps cf2sfiles_prop tainted_eq_Tainted same_inodes_Tainted split:if_splits)
+apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted split:if_splits)
 apply (rule impI, erule bexE, erule conjE, erule_tac x = f'' in ballE, simp, simp)
 apply (erule bexE, erule conjE, erule_tac x = f'' in ballE, simp, simp)
 apply (erule conjE, erule disjE)
 apply (rule_tac x = "O_proc p" in exI)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (erule exE, erule conjE)
 apply (case_tac "obj = O_proc p")
 apply (rule_tac x = "obj'" in exI, simp, frule_tac obj = obj' in co2sobj_sproc_imp, erule exE)
 apply (frule_tac obj = obj' in alive_co2sobj_closefd3, simp+)
-apply (simp add:co2sobj_closefd tainted_eq_Tainted)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
-apply (case_tac "obj = O_file a", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj_closefd)
+apply (simp add:co2sobj.simps)
+apply (case_tac "obj = O_file a", simp add:co2sobj.simps)
 apply (frule_tac obj = obj in alive_co2sobj_closefd3, simp+)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_closefd)
 apply (case_tac "f = a", simp add:alive_simps)
 apply (case_tac "f \<in> same_inode_files s a")
-apply (simp add:co2sobj.simps cf2sfiles_prop tainted_eq_Tainted same_inodes_Tainted)
+apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (rule_tac x = obj in exI, simp add:co2sobj_closefd)
 apply (rule_tac x = obj in exI, simp add:co2sobj_closefd)
 apply (rule_tac x = obj in exI, simp add:co2sobj_closefd)
@@ -1433,20 +1393,20 @@
 apply (frule_tac obj = "O_file f'" in co2sobj_closefd)
 apply (simp add:alive_simps)+
 apply (frule_tac f = "f'" in is_file_has_sfile', simp, erule exE)
-apply (simp add:co2sobj.simps cf2sfiles_prop tainted_eq_Tainted same_inodes_Tainted split:if_splits)
+apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted split:if_splits)
 apply (rule impI, erule bexE, erule conjE, erule_tac x = f'' in ballE, simp, simp)
 apply (erule bexE, erule conjE, erule_tac x = f'' in ballE, simp, simp)
 apply (erule conjE, erule disjE)
 apply (rule_tac x = "O_proc p" in exI)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (erule conjE, erule exE, erule conjE)
-apply (case_tac "obj = O_proc p", simp add:co2sobj.simps tainted_eq_Tainted)
-apply (case_tac "obj = O_file a", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "obj = O_proc p", simp add:co2sobj.simps)
+apply (case_tac "obj = O_file a", simp add:co2sobj.simps)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_closefd)
 apply (case_tac "f \<in> same_inode_files s a")
-apply (simp add:co2sobj.simps cf2sfiles_prop tainted_eq_Tainted same_inodes_Tainted)
+apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (rule_tac x = obj in exI, simp add:co2sobj_closefd is_file_simps)
 apply (rule_tac x = obj in exI, simp add:co2sobj_closefd)
 apply (rule_tac x = obj in exI, simp add:co2sobj_closefd is_dir_simps)
@@ -1459,40 +1419,40 @@
 apply (rule set_eqI, rule iffI, erule CollectE, erule exE, erule conjE)
 apply (simp)
 apply (case_tac "obj = O_proc p")
-apply (simp add:co2sobj.simps tainted_eq_Tainted split:if_splits)
+apply (simp add:co2sobj.simps split:if_splits)
 apply (rule disjI2, rule_tac x = obj in exI, erule conjE)
 apply (simp add:alive_co2sobj_closefd')
 apply (frule_tac obj = obj in co2sobj_closefd, simp, simp split:t_object.splits if_splits)
 apply (simp, erule disjE)
-apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps)
 apply (erule exE, erule conjE)
 apply (case_tac "obj = O_proc p")
 apply (rule_tac x = obj' in exI, simp add:alive_co2sobj_closefd1)
 apply (frule_tac obj = obj' in co2sobj_closefd, simp add:alive_co2sobj_closefd1)
-apply (clarsimp split:t_object.splits if_splits option.splits simp:tainted_eq_Tainted co2sobj.simps)
+apply (clarsimp split:t_object.splits if_splits option.splits simp:tainted_eq_tainted co2sobj.simps)
 apply (rule_tac x = obj in exI, simp add:alive_co2sobj_closefd1)
 apply (frule_tac obj = obj in co2sobj_closefd, simp add:alive_co2sobj_closefd1)
-apply (clarsimp split:t_object.splits if_splits option.splits simp:tainted_eq_Tainted co2sobj.simps)
+apply (clarsimp split:t_object.splits if_splits option.splits simp:tainted_eq_tainted co2sobj.simps)
 apply (rule impI)
 apply (simp add:s2ss_def)
 apply (rule set_eqI, rule iffI, erule CollectE, erule exE, erule conjE)
 apply (simp)
 apply (case_tac "obj = O_proc p")
-apply (rule disjI1, simp add:co2sobj.simps tainted_eq_Tainted split:if_splits)
+apply (rule disjI1, simp add:co2sobj.simps split:if_splits)
 apply (rule disjI2, rule conjI, rule_tac x = obj in exI, simp add:alive_co2sobj_closefd')
 apply (frule_tac obj = obj in co2sobj_closefd, simp add:alive_co2sobj_closefd1)
-apply (clarsimp split:t_object.splits if_splits option.splits simp:tainted_eq_Tainted co2sobj.simps)
+apply (clarsimp split:t_object.splits if_splits option.splits simp:tainted_eq_tainted co2sobj.simps)
 apply (rule notI, erule_tac x = obj in allE, simp add:alive_co2sobj_closefd')
 apply (frule_tac obj = obj in co2sobj_closefd, simp add:alive_co2sobj_closefd1)
 apply (clarsimp split:t_object.splits if_splits option.splits)
 apply (simp)
 apply (erule disjE)
-apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (rule_tac x = "O_proc p" in exI, simp add:co2sobj.simps)
 apply (erule exE|erule conjE)+
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_closefd, simp add:alive_co2sobj_closefd1)
 apply (clarsimp split:t_object.splits if_splits option.splits 
-                simp:tainted_eq_Tainted co2sobj.simps alive_co2sobj_closefd1)
+                simp:tainted_eq_tainted co2sobj.simps alive_co2sobj_closefd1)
 done
 
 lemma alive_co2sobj_unlink:
@@ -1525,13 +1485,13 @@
 apply (rule notI, simp, frule_tac obj = obj in co2sobj_sfile_imp, erule exE, simp)
 apply (frule_tac obj = obj in co2sobj_unlink, simp)
 apply (erule_tac x = fa in allE, simp add:is_file_simps)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (tactic {*my_setiff_tac 1*})
-apply (case_tac "obj = O_file f", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "obj = O_file f", simp add:co2sobj.simps)
 apply (frule_tac alive_co2sobj_unlink, simp, simp)
 apply (frule_tac obj = obj in co2sobj_unlink, simp)
 apply (rule_tac x = obj in exI)
-apply (simp add:co2sobj.simps tainted_eq_Tainted split:t_object.splits if_splits)
+apply (simp add:co2sobj.simps split:t_object.splits if_splits)
 
 apply (rule impI|erule conjE|erule exE|rule conjI|erule bexE)+  defer
 
@@ -1545,7 +1505,7 @@
 apply (case_tac "fa \<in> same_inode_files s f")
 apply (rule disjI1)
 apply (simp add:co2sobj_unlink)
-apply (simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted cf2sfiles_prop split:if_splits)
+apply (simp add:co2sobj.simps same_inodes_tainted cf2sfiles_prop split:if_splits)
 apply (erule bexE, erule_tac x = f'' in ballE, simp, simp)
 apply (rule disjI2, simp, rule_tac x = obj in exI)
 apply (simp add:co2sobj_unlink is_file_simps)
@@ -1556,7 +1516,7 @@
 apply (drule same_inode_files_prop10, simp, erule exE, erule conjE)
 apply (rule_tac x = "O_file f'a" in exI, simp add:is_file_simps)
 apply (frule_tac obj = "O_file f'a" in co2sobj_unlink, simp add:same_inode_files_prop11 is_file_simps)
-apply (simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted cf2sfiles_prop 
+apply (simp add:co2sobj.simps same_inodes_tainted cf2sfiles_prop 
   is_file_simps same_inode_files_prop11 split:if_splits)
 apply (rule impI, erule bexE, erule_tac x = f'' in ballE, simp, simp)
 apply (erule bexE, erule_tac x = f'' in ballE, simp, simp)
@@ -1566,13 +1526,13 @@
 apply (case_tac "obj= O_file f")
 apply (rule_tac x = "O_file f'" in exI, simp add:is_file_simps)
 apply (frule_tac f' = f' in cf2sfiles_unlink, simp add:current_files_simps is_file_in_current)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink)
 apply (case_tac "fa \<in> same_inode_files s f")
 apply (rule_tac x = "O_file f'" in exI)
 apply (frule_tac f' = f' in cf2sfiles_unlink, simp add:current_files_simps is_file_in_current)
-apply (simp add:co2sobj.simps tainted_eq_Tainted is_file_simps cf2sfiles_prop same_inodes_Tainted)
+apply (simp add:co2sobj.simps is_file_simps cf2sfiles_prop same_inodes_tainted)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink is_file_simps)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink is_dir_simps)
@@ -1591,12 +1551,12 @@
 apply (case_tac "fa \<in> same_inode_files s f")
 apply (rule disjI1)
 apply (simp add:co2sobj_unlink)
-apply (simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted cf2sfiles_prop split:if_splits)
+apply (simp add:co2sobj.simps same_inodes_tainted cf2sfiles_prop split:if_splits)
 apply (erule bexE, erule_tac x = f'' in ballE, simp, simp)
 apply (rule disjI2, rule conjI, simp, rule_tac x = obj in exI)
 apply (simp add:co2sobj_unlink is_file_simps)
-apply (rule notI, simp add:co2sobj_unlink tainted_eq_Tainted)
-apply (erule_tac x = fa in allE, simp add:co2sobj.simps is_file_simps tainted_eq_Tainted)
+apply (rule notI, simp add:co2sobj_unlink)
+apply (erule_tac x = fa in allE, simp add:co2sobj.simps is_file_simps)
 apply (rule disjI2, rule conjI, simp, rule_tac x = obj in exI, simp add:co2sobj_unlink)
 apply (rule notI, simp add:co2sobj.simps split:option.splits)
 apply (rule disjI2, rule conjI, simp, rule_tac x = obj in exI, simp add:co2sobj_unlink is_dir_simps)
@@ -1607,16 +1567,16 @@
 apply (drule same_inode_files_prop10, simp, erule exE, erule conjE)
 apply (rule_tac x = "O_file f'" in exI, simp add:is_file_simps)
 apply (frule_tac obj = "O_file f'" in co2sobj_unlink, simp add:same_inode_files_prop11 is_file_simps)
-apply (simp add:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted cf2sfiles_prop 
+apply (simp add:co2sobj.simps same_inodes_tainted cf2sfiles_prop 
   is_file_simps same_inode_files_prop11 split:if_splits)
 apply (rule impI, erule bexE, erule_tac x = f'' in ballE, simp, simp)
 apply (erule bexE, erule_tac x = f'' in ballE, simp, simp)
 apply (tactic {*my_setiff_tac 1*}, simp)
-apply (case_tac "obj = O_file f", simp add:co2sobj.simps tainted_eq_Tainted)
+apply (case_tac "obj = O_file f", simp add:co2sobj.simps)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink)
 apply (case_tac "fa \<in> same_inode_files s f")
-apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_Tainted tainted_eq_Tainted)
+apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink is_file_simps)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink is_dir_simps)
@@ -1668,7 +1628,7 @@
 apply (rule conjI, rule notI, simp add:same_inode_files_prop9)
 apply (rule impI, frule_tac f' = f' in cf2sfiles_unlink)
 apply (simp add:current_files_simps is_file_simps is_file_in_current)
-apply (simp add:tainted_eq_Tainted same_inodes_Tainted cf2sfiles_prop)
+apply (simp: same_inodes_tainted cf2sfiles_prop)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink is_file_simps)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink is_dir_simps)
@@ -1687,7 +1647,7 @@
 apply (frule same_inode_files_prop11, frule_tac f = f' in is_file_has_sfile', simp add:vd_cons, erule exE)
 apply (frule_tac obj = "O_file f'" in co2sobj_unlink, simp)
 apply (simp split:if_splits option.splits add:is_file_simps)
-apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_Tainted tainted_eq_Tainted)
+apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (auto split:t_sobject.splits)[1]
 apply (simp add:is_file_simps same_inode_files_prop11)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
@@ -1698,7 +1658,7 @@
 apply (frule same_inode_files_prop11, frule_tac f = f' in is_file_has_sfile', simp add:vd_cons, erule exE)
 apply (frule_tac obj = "O_file f'" in co2sobj_unlink, simp)
 apply (simp split:if_splits option.splits add:is_file_simps)
-apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_Tainted tainted_eq_Tainted)
+apply (simp add:co2sobj.simps cf2sfiles_prop same_inodes_tainted)
 apply (auto split:t_sobject.splits)[1]
 apply (simp add:is_file_simps same_inode_files_prop11)
 apply (rule_tac x = obj in exI, simp add:co2sobj_unlink is_file_simps)
@@ -1783,97 +1743,9 @@
 where
  "update_s2ss_sfile s ss f sf \<equiv>
     if (\<exists> f'. is_file s f' \<and> f' \<notin> same_inode_files s f \<and> co2sobj s (O_file f') = co2sobj s (O_file f))
-       then ss \<union> {S_file (cf2sfiles s f \<union> {sf}) (O_file f \<in> Tainted s)}
-       else ss - {S_file (cf2sfiles s f) (O_file f \<in> Tainted s)} 
-               \<union> {S_file (cf2sfiles s f \<union> {sf}) (O_file f \<in> Tainted s)}"
-
-lemma s2ss_linkhard: "valid (LinkHard p f f' # s) \<Longrightarrow> s2ss (LinkHard p f f' # s) = (
-  case (cf2sfile (LinkHard p f f' # s) f') of
-    Some sf \<Rightarrow> update_s2ss_sfile s (s2ss s) f sf
-  | _       \<Rightarrow> {})"
-apply (frule vt_grant_os, frule vd_cons, clarsimp)
-apply (split option.splits)
-apply (rule conjI, rule impI, drule current_file_has_sfile', simp, simp add:current_files_simps)
-apply (rule allI, rule impI)
-
-apply (simp add:update_s2ss_sfile_def)
-apply (rule conjI, rule impI, erule exE, erule conjE, erule conjE)
-apply (simp add:s2ss_def)
-apply (tactic {*my_seteq_tac 1*})
-apply (case_tac "obj = O_file f'")
-apply (rule disjI1, simp add:co2sobj.simps cf2sfiles_linkhard tainted_eq_Tainted
-  same_inode_files_linkhard split:if_splits)
-apply (case_tac "O_file f' \<in> Tainted s")
-apply (drule Tainted_in_current, simp, simp add:is_file_in_current alive.simps, simp)
-apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (rule disjI2, simp, rule_tac x = obj in exI)
-apply (simp add:co2sobj_linkhard alive_linkhard)
-apply (case_tac "fa \<in> same_inode_files s f")
-apply (rule disjI1, simp add:co2sobj.simps cf2sfiles_linkhard tainted_eq_Tainted 
-  same_inodes_Tainted split:if_splits)
-apply (rule disjI2, simp, rule_tac x = obj in exI, simp add:co2sobj_linkhard is_file_simps)
-apply (rule disjI2, simp, rule_tac x = obj in exI, simp add:co2sobj_linkhard)
-apply (rule disjI2, simp, rule_tac x = obj in exI, simp add:co2sobj_linkhard is_dir_simps)
-apply (rule disjI2, simp, rule_tac x = obj in exI, simp add:co2sobj_linkhard)
-apply (tactic {*my_setiff_tac 1*})
-apply (rule_tac x = "O_file f" in exI)
-apply (frule_tac obj = "O_file f" in co2sobj_linkhard)
-apply (simp add:alive_linkhard)
-apply (simp add:alive_linkhard same_inode_files_prop9 split:t_object.splits)
-apply (tactic {*my_setiff_tac 1*})
-apply (case_tac "obj = O_file f'", simp add:alive_linkhard is_file_in_current)
-apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (rule_tac x = obj in exI, simp add:co2sobj_linkhard alive_linkhard)
-apply (case_tac "fa \<in> same_inode_files s f")
-apply (rule_tac x = "O_file f'a" in exI, simp add:co2sobj_linkhard alive_linkhard)
-apply (rule conjI, rule impI, simp add:is_file_in_current)
-apply (rule impI, simp add:co2sobj.simps cf2sfiles_prop tainted_eq_Tainted same_inodes_Tainted)
-apply (rule_tac x = obj in exI, simp add:co2sobj_linkhard alive_linkhard)
-apply (rule_tac x = obj in exI, simp add:co2sobj_linkhard alive_linkhard)
-apply (rule_tac x = obj in exI, simp add:co2sobj_linkhard alive_linkhard)
-apply (rule_tac x = obj in exI, simp add:co2sobj_linkhard alive_linkhard)
-
-apply (rule impI)
-apply (simp add:s2ss_def)
-apply (tactic {*my_seteq_tac 1*})
-apply (case_tac "obj = O_file f'", simp)
-apply (rule disjI1, simp add:co2sobj.simps cf2sfiles_linkhard tainted_eq_Tainted
-  same_inode_files_linkhard split:if_splits)
-apply (case_tac "O_file f' \<in> Tainted s")
-apply (drule Tainted_in_current, simp, simp add:is_file_in_current alive.simps, simp)
-apply (erule_tac obj = obj in co2sobj_some_caseD, simp)
-apply (rule disjI2, rule conjI, rule_tac x = obj in exI)
-apply (simp add:co2sobj_linkhard alive_linkhard)
-apply (rule notI, simp add:co2sobj.simps split:option.splits)
-apply (case_tac "fa \<in> same_inode_files s f")
-apply (rule disjI1, simp add:co2sobj.simps cf2sfiles_linkhard tainted_eq_Tainted 
-  same_inodes_Tainted split:if_splits)
-apply (simp, rule disjI2, rule conjI, rule_tac x = obj in exI, simp add:co2sobj_linkhard is_file_simps)
-apply (erule_tac x = fa in allE, rule notI)
-apply (simp add:co2sobj_linkhard is_file_simps)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
-apply (rule disjI2, simp, rule conjI, rule_tac x = obj in exI, simp add:co2sobj_linkhard)
-apply (rule notI, simp add:co2sobj.simps split:option.splits)
-apply (rule disjI2, simp, rule conjI, rule_tac x = obj in exI, simp add:co2sobj_linkhard is_dir_simps)
-apply (rule notI, simp add:co2sobj.simps split:option.splits)
-apply (rule disjI2, simp, rule conjI, rule_tac x = obj in exI, simp add:co2sobj_linkhard)
-apply (rule notI, simp add:co2sobj.simps split:option.splits)
-apply (tactic {*my_setiff_tac 1*})
-apply (rule_tac x = "O_file f" in exI)
-apply (frule_tac obj = "O_file f" in co2sobj_linkhard)
-apply (simp add:alive_linkhard)
-apply (simp add:alive_linkhard same_inode_files_prop9 split:t_object.splits)
-apply (tactic {*my_setiff_tac 1*})
-apply (case_tac "obj = O_file f'", simp add:alive_linkhard is_file_in_current)
-apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (rule_tac x = obj in exI, simp add:co2sobj_linkhard alive_linkhard)
-apply (case_tac "fa \<in> same_inode_files s f")
-apply (simp add:co2sobj.simps cf2sfiles_prop tainted_eq_Tainted same_inodes_Tainted)
-apply (rule_tac x = obj in exI, simp add:co2sobj_linkhard alive_linkhard)
-apply (rule_tac x = obj in exI, simp add:co2sobj_linkhard alive_linkhard)
-apply (rule_tac x = obj in exI, simp add:co2sobj_linkhard alive_linkhard)
-apply (rule_tac x = obj in exI, simp add:co2sobj_linkhard alive_linkhard)
-done
+       then ss \<union> {S_file (cf2sfiles s f \<union> {sf}) (O_file f \<in> tainted s)}
+       else ss - {S_file (cf2sfiles s f) (O_file f \<in> tainted s)} 
+               \<union> {S_file (cf2sfiles s f \<union> {sf}) (O_file f \<in> tainted s)}"
 
 lemma same_inode_files_prop12:
   "is_file s f \<Longrightarrow> f \<in> same_inode_files s f "
@@ -1889,7 +1761,7 @@
                \<union> {S_file (cf2sfiles s f) True}"
 
 lemma s2ss_truncate: "valid (Truncate p f len # s) \<Longrightarrow> s2ss (Truncate p f len # s) = (
-  if (O_file f \<notin> Tainted s \<and> O_proc p \<in> Tainted s \<and> len > 0)
+  if (O_file f \<notin> tainted s \<and> O_proc p \<in> tainted s \<and> len > 0)
   then update_s2ss_sfile_tainted s (s2ss s) f True
   else s2ss s)"
 apply (frule vt_grant_os, frule vd_cons, simp split:if_splits)
@@ -1900,11 +1772,11 @@
 apply (simp add:s2ss_def)
 apply (tactic {*my_seteq_tac 1*})
 apply (case_tac "obj = O_file f")
-apply (rule disjI1, simp add:co2sobj.simps tainted_eq_Tainted same_inode_files_prop12 cf2sfiles_other)
+apply (rule disjI1, simp add:co2sobj.simps same_inode_files_prop12 cf2sfiles_other)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (rule disjI2, simp, rule_tac x = obj in exI, simp add:co2sobj_truncate alive_simps)
 apply (case_tac "fa \<in> same_inode_files s f")
-apply (rule disjI1, simp add:co2sobj.simps tainted_eq_Tainted cf2sfiles_prop cf2sfiles_other)
+apply (rule disjI1, simp add:co2sobj.simps cf2sfiles_prop cf2sfiles_other)
 apply (rule disjI2, simp, rule_tac x = obj in exI)
 apply (simp add:co2sobj_truncate is_file_simps)
 apply (rule disjI2, simp, rule_tac x = obj in exI)
@@ -1915,14 +1787,14 @@
 apply (simp add:co2sobj_truncate)
 apply (tactic {*my_setiff_tac 1*})
 apply (rule_tac x = "O_file f" in exI)
-apply (simp add:co2sobj.simps is_file_simps tainted_eq_Tainted cf2sfiles_other same_inode_files_prop12)
+apply (simp add:co2sobj.simps is_file_simps cf2sfiles_other same_inode_files_prop12)
 apply (tactic {*my_setiff_tac 1*})
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (rule_tac x = obj in exI, simp add:co2sobj_truncate)
 apply (case_tac "fa \<in> same_inode_files s f")
 apply (rule_tac x = "O_file f'" in exI)
 apply (auto simp:co2sobj_truncate is_file_simps is_dir_simps split:t_object.splits)[1]
-apply (simp add:co2sobj.simps same_inodes_Tainted tainted_eq_Tainted cf2sfiles_prop)
+apply (simp add:co2sobj.simps same_inodes_tainted cf2sfiles_prop)
 apply (rule_tac x = obj in exI, simp add:co2sobj_truncate is_file_simps)
 apply (rule_tac x = obj in exI, simp add:co2sobj_truncate)
 apply (rule_tac x = obj in exI, simp add:co2sobj_truncate is_dir_simps)
@@ -1932,12 +1804,12 @@
 apply (simp add:s2ss_def)
 apply (tactic {*my_seteq_tac 1*})
 apply (case_tac "obj = O_file f")
-apply (rule disjI1, simp add:co2sobj.simps tainted_eq_Tainted same_inode_files_prop12 cf2sfiles_other)
+apply (rule disjI1, simp add:co2sobj.simps same_inode_files_prop12 cf2sfiles_other)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (rule disjI2, simp, rule conjI, rule_tac x = obj in exI, simp add:co2sobj_truncate alive_simps)
 apply (rule notI, simp add:co2sobj.simps split:option.splits)
 apply (case_tac "fa \<in> same_inode_files s f")
-apply (rule disjI1, simp add:co2sobj.simps tainted_eq_Tainted cf2sfiles_prop cf2sfiles_other)
+apply (rule disjI1, simp add:co2sobj.simps cf2sfiles_prop cf2sfiles_other)
 apply (rule disjI2, simp, rule conjI, rule_tac x = obj in exI)
 apply (simp add:co2sobj_truncate is_file_simps)
 apply (rule notI, simp add:co2sobj_truncate is_file_simps)
@@ -1954,12 +1826,12 @@
 apply (rule notI, simp add:co2sobj.simps split:option.splits)
 apply (tactic {*my_setiff_tac 1*})
 apply (rule_tac x = "O_file f" in exI)
-apply (simp add:co2sobj.simps is_file_simps tainted_eq_Tainted cf2sfiles_other same_inode_files_prop12)
+apply (simp add:co2sobj.simps is_file_simps cf2sfiles_other same_inode_files_prop12)
 apply (tactic {*my_setiff_tac 1*})
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (rule_tac x = obj in exI, simp add:co2sobj_truncate)
 apply (case_tac "fa \<in> same_inode_files s f")
-apply (simp add:co2sobj.simps same_inodes_Tainted tainted_eq_Tainted cf2sfiles_prop)
+apply (simp add:co2sobj.simps same_inodes_tainted cf2sfiles_prop)
 apply (rule_tac x = obj in exI, simp add:co2sobj_truncate is_file_simps)
 apply (rule_tac x = obj in exI, simp add:co2sobj_truncate)
 apply (rule_tac x = obj in exI, simp add:co2sobj_truncate is_dir_simps)
@@ -1969,13 +1841,13 @@
 apply (tactic {*my_seteq_tac 1*})
 apply (rule_tac x = obj in exI)
 apply (simp add:alive_simps co2sobj_truncate)
-apply (simp split:t_object.splits if_splits add:co2sobj.simps tainted_eq_Tainted)
-apply (case_tac "O_proc p \<in> Tainted s", simp add:same_inodes_Tainted)
+apply (simp split:t_object.splits if_splits add:co2sobj.simps)
+apply (case_tac "O_proc p \<in> tainted s", simp add:same_inodes_tainted)
 apply simp
 apply (tactic {*my_setiff_tac 1*})
 apply (rule_tac x = obj in exI)
 apply (simp add:alive_simps co2sobj_truncate)
-apply (auto split:t_object.splits if_splits simp:co2sobj.simps tainted_eq_Tainted same_inodes_Tainted)
+apply (auto split:t_object.splits if_splits simp:co2sobj.simps same_inodes_tainted)
 done
 
 lemma s2ss_createmsgq: "valid (CreateMsgq p q # s) \<Longrightarrow> s2ss (CreateMsgq p q # s) = 
@@ -2116,17 +1988,17 @@
 declare Product_Type.split_paired_Ex Product_Type.split_paired_All [simp del]
 
 lemma s2ss_shm_no_bk_elim':
-  "\<lbrakk>x \<notin> s2ss_shm_no_backup s pfrom; co2sobj s (O_proc p) = Some x; O_proc p \<notin> Tainted s;
+  "\<lbrakk>x \<notin> s2ss_shm_no_backup s pfrom; co2sobj s (O_proc p) = Some x; O_proc p \<notin> tainted s;
     valid s; info_flow_shm s pfrom p\<rbrakk>
    \<Longrightarrow> \<exists> p'. \<not> info_flow_shm s pfrom p' \<and> p' \<in> current_procs s \<and> co2sobj s (O_proc p') = Some x"
-apply (auto simp:s2ss_shm_no_backup_def co2sobj.simps tainted_eq_Tainted split:option.splits)
+apply (auto simp:s2ss_shm_no_backup_def co2sobj.simps split:option.splits)
 apply (erule_tac x = p in allE, auto)
 apply (rule_tac x = p' in exI, auto)
 done
 
 lemma s2ss_recvmsg: "valid (RecvMsg p q m # s) \<Longrightarrow> s2ss (RecvMsg p q m # s) = (
   case (cq2smsgq s q, cq2smsgq (RecvMsg p q m # s) q) of
-    (Some sq, Some sq') \<Rightarrow> if (O_msg q m \<in> Tainted s \<and> O_proc p \<notin> Tainted s)
+    (Some sq, Some sq') \<Rightarrow> if (O_msg q m \<in> tainted s \<and> O_proc p \<notin> tainted s)
                           then update_s2ss_obj s (update_s2ss_shm s p) (O_msgq q) (S_msgq sq) (S_msgq sq')
                           else update_s2ss_obj s (s2ss s) (O_msgq q) (S_msgq sq) (S_msgq sq')
   | _ \<Rightarrow> {})"
@@ -2175,7 +2047,7 @@
   split:t_object.splits if_splits option.splits)
 apply (auto simp:co2sobj.simps is_file_simps is_dir_simps)[1]
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "info_flow_shm s p pa \<and> O_proc pa \<notin> Tainted s")
+apply (case_tac "info_flow_shm s p pa \<and> O_proc pa \<notin> tainted s")
 apply (drule_tac p = pa in s2ss_shm_no_bk_elim', simp+)
 apply (erule exE|erule conjE)+
 apply (rule_tac x = "O_proc p'" in exI)
@@ -2184,7 +2056,7 @@
 apply (case_tac "info_flow_shm s p pa", simp)
 apply (frule_tac obj = obj in co2sobj_recvmsg, simp+)
 apply (case_tac "cp2sproc s pa", simp add:co2sobj.simps)
-apply (simp, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp, simp add:co2sobj.simps)
 apply (simp, frule_tac obj = obj in co2sobj_recvmsg, simp+)
 apply (rule_tac x = obj in exI, simp add:co2sobj_recvmsg alive_simps)
 apply (rule_tac x = obj in exI)
@@ -2203,7 +2075,7 @@
 apply (rule disjI1, simp add:co2sobj.simps)
 apply (rule disjI2, simp, rule_tac x = obj in exI)
 apply (simp add:co2sobj_recvmsg is_file_simps is_dir_simps split:t_object.splits if_splits option.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted info_flow_shm_Tainted)
+apply (simp add:co2sobj.simps info_flow_shm_tainted)
 apply (simp add:co2sobj.simps)
 apply (simp add:co2sobj.simps)
 apply (case_tac "msgs_of_queue s q", simp, simp)
@@ -2219,7 +2091,7 @@
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_recvmsg is_file_simps is_dir_simps alive_recvmsg 
   split:t_object.splits if_splits option.splits)
-apply (auto simp:co2sobj.simps is_file_simps is_dir_simps tainted_eq_Tainted info_flow_shm_Tainted)[1]
+apply (auto simp:co2sobj.simps is_file_simps is_dir_simps info_flow_shm_tainted)[1]
 
 apply (tactic {*my_clarify_tac 1*})
 apply (tactic {*my_seteq_tac 1*})
@@ -2228,14 +2100,14 @@
 apply (rule disjI2)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (case_tac "info_flow_shm s p pa")
-apply (case_tac "O_proc pa \<in> Tainted s")
+apply (case_tac "O_proc pa \<in> tainted s")
 apply (rule DiffI, rule UnI1, simp)
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_recvmsg, simp, simp split:option.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (erule s2ss_shm_no_bk_intro2, simp, simp)
 apply (rule DiffI, rule UnI2, rule CollectI)
-apply (simp only:co2sobj.simps tainted_eq_Tainted split:option.splits, simp)
+apply (simp only:co2sobj.simps split:option.splits, simp)
 apply (rule_tac x = ab in exI, simp)
 apply (rule_tac x = pa in exI, simp add:cp2sproc_other)
 apply (rule s2ss_shm_no_bk_intro2, simp, simp, simp)
@@ -2272,7 +2144,7 @@
   split:t_object.splits if_splits option.splits)
 apply (auto simp:co2sobj.simps is_file_simps is_dir_simps)[1]
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "info_flow_shm s p pa \<and> O_proc pa \<notin> Tainted s")
+apply (case_tac "info_flow_shm s p pa \<and> O_proc pa \<notin> tainted s")
 apply (drule_tac p = pa in s2ss_shm_no_bk_elim', simp+)
 apply (erule exE|erule conjE)+
 apply (rule_tac x = "O_proc p'" in exI)
@@ -2281,7 +2153,7 @@
 apply (case_tac "info_flow_shm s p pa", simp)
 apply (frule_tac obj = obj in co2sobj_recvmsg, simp+)
 apply (case_tac "cp2sproc s pa", simp add:co2sobj.simps)
-apply (simp, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp, simp add:co2sobj.simps)
 apply (simp, frule_tac obj = obj in co2sobj_recvmsg, simp+)
 apply (rule_tac x = obj in exI, simp add:co2sobj_recvmsg alive_simps)
 apply (rule_tac x = obj in exI)
@@ -2301,7 +2173,7 @@
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_recvmsg is_file_simps is_dir_simps alive_recvmsg 
   split:t_object.splits if_splits option.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted info_flow_shm_Tainted)
+apply (simp add:co2sobj.simps info_flow_shm_tainted)
 apply (simp add:co2sobj_recvmsg)
 apply (simp add:alive_recvmsg split:if_splits)
 apply (erule_tac x = obj in allE, simp split:t_object.splits if_splits option.splits)
@@ -2322,7 +2194,7 @@
 apply (simp add:alive_recvmsg, rule notI, simp add:co2sobj.simps)
 apply (rule conjI)
 apply (simp add:alive_recvmsg, rule notI, simp add:co2sobj.simps)
-apply (auto simp:co2sobj.simps tainted_eq_Tainted split:t_object.splits option.splits if_splits)[1]
+apply (auto simp:co2sobj.simps split:t_object.splits option.splits if_splits)[1]
 
 apply (tactic {*my_clarify_tac 1*})
 apply (tactic {*my_seteq_tac 1*})
@@ -2331,14 +2203,14 @@
 apply (rule disjI2)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (case_tac "info_flow_shm s p pa")
-apply (case_tac "O_proc pa \<in> Tainted s")
+apply (case_tac "O_proc pa \<in> tainted s")
 apply (rule DiffI, rule UnI1, simp)
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_recvmsg, simp, simp split:option.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (erule s2ss_shm_no_bk_intro2, simp, simp)
 apply (rule DiffI, rule UnI2, rule CollectI)
-apply (simp only:co2sobj.simps tainted_eq_Tainted split:option.splits, simp)
+apply (simp only:co2sobj.simps split:option.splits, simp)
 apply (rule_tac x = ab in exI, simp)
 apply (rule_tac x = pa in exI, simp add:cp2sproc_other)
 apply (rule s2ss_shm_no_bk_intro2, simp, simp, simp)
@@ -2374,7 +2246,7 @@
   split:t_object.splits if_splits option.splits)
 apply (auto simp:co2sobj.simps is_file_simps is_dir_simps)[1]
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "info_flow_shm s p pa \<and> O_proc pa \<notin> Tainted s")
+apply (case_tac "info_flow_shm s p pa \<and> O_proc pa \<notin> tainted s")
 apply (drule_tac p = pa in s2ss_shm_no_bk_elim', simp+)
 apply (erule exE|erule conjE)+
 apply (rule_tac x = "O_proc p'" in exI)
@@ -2383,7 +2255,7 @@
 apply (case_tac "info_flow_shm s p pa", simp)
 apply (frule_tac obj = obj in co2sobj_recvmsg, simp+)
 apply (case_tac "cp2sproc s pa", simp add:co2sobj.simps)
-apply (simp, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp, simp add:co2sobj.simps)
 apply (simp, frule_tac obj = obj in co2sobj_recvmsg, simp+)
 apply (rule_tac x = obj in exI, simp add:co2sobj_recvmsg alive_simps)
 apply (rule_tac x = obj in exI)
@@ -2403,7 +2275,7 @@
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_recvmsg is_file_simps is_dir_simps alive_recvmsg 
   split:t_object.splits if_splits option.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted info_flow_shm_Tainted)
+apply (simp add:co2sobj.simps info_flow_shm_tainted)
 apply (tactic {*my_setiff_tac 1*})
 apply (rule_tac x = "O_msgq q" in exI)
 apply (simp add:co2sobj.simps)
@@ -2418,7 +2290,7 @@
 apply (simp add:alive_recvmsg, rule notI, simp add:co2sobj.simps)
 apply (rule conjI)
 apply (simp add:alive_recvmsg, rule notI, simp add:co2sobj.simps)
-apply (auto simp:co2sobj.simps tainted_eq_Tainted split:t_object.splits option.splits if_splits)[1]
+apply (auto simp:co2sobj.simps split:t_object.splits option.splits if_splits)[1]
 
 apply (tactic {*my_clarify_tac 1*})
 apply (tactic {*my_seteq_tac 1*})
@@ -2427,15 +2299,15 @@
 apply (rule disjI2)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
 apply (case_tac "info_flow_shm s p pa")
-apply (case_tac "O_proc pa \<in> Tainted s")
+apply (case_tac "O_proc pa \<in> tainted s")
 apply (rule DiffI, rule DiffI, rule UnI1, simp)
 apply (rule_tac x = obj in exI)
 apply (frule_tac obj = obj in co2sobj_recvmsg, simp, simp split:option.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp add:co2sobj.simps)
 apply (erule s2ss_shm_no_bk_intro2, simp, simp)
 apply (simp, rule notI, simp add:co2sobj.simps split:option.splits)
 apply (rule DiffI, rule DiffI, rule UnI2, rule CollectI)
-apply (simp only:co2sobj.simps tainted_eq_Tainted split:option.splits, simp)
+apply (simp only:co2sobj.simps split:option.splits, simp)
 apply (rule_tac x = ab in exI, simp)
 apply (rule_tac x = pa in exI, simp add:cp2sproc_other)
 apply (rule s2ss_shm_no_bk_intro2, simp, simp, simp)
@@ -2475,7 +2347,7 @@
 apply (case_tac "obj = O_msgq q")
 apply (simp add:co2sobj.simps)
 apply (erule_tac obj = obj in co2sobj_some_caseD)
-apply (case_tac "info_flow_shm s p pa \<and> O_proc pa \<notin> Tainted s")
+apply (case_tac "info_flow_shm s p pa \<and> O_proc pa \<notin> tainted s")
 apply (drule_tac p = pa in s2ss_shm_no_bk_elim', simp+)
 apply (erule exE|erule conjE)+
 apply (rule_tac x = "O_proc p'" in exI)
@@ -2484,7 +2356,7 @@
 apply (case_tac "info_flow_shm s p pa", simp)
 apply (frule_tac obj = obj in co2sobj_recvmsg, simp+)
 apply (case_tac "cp2sproc s pa", simp add:co2sobj.simps)
-apply (simp, simp add:co2sobj.simps tainted_eq_Tainted)
+apply (simp, simp add:co2sobj.simps)
 apply (simp, frule_tac obj = obj in co2sobj_recvmsg, simp+)
 apply (rule_tac x = obj in exI, simp add:co2sobj_recvmsg alive_simps)
 apply (rule_tac x = obj in exI)
@@ -2504,7 +2376,7 @@
 apply (rule_tac x = obj in exI)
 apply (simp add:co2sobj_recvmsg is_file_simps is_dir_simps alive_recvmsg 
   split:t_object.splits if_splits option.splits)
-apply (simp add:co2sobj.simps tainted_eq_Tainted info_flow_shm_Tainted)
+apply (simp add:co2sobj.simps info_flow_shm_tainted)
 apply (rule notI, simp)
 apply (frule co2sobj_smsgq_imp, erule exE, simp)
 apply (simp add:co2sobj_recvmsg)
@@ -2521,7 +2393,7 @@
 apply (simp add:alive_recvmsg, rule notI, simp add:co2sobj.simps)
 apply (rule conjI)
 apply (simp add:alive_recvmsg, rule notI, simp add:co2sobj.simps)
-apply (auto simp:co2sobj.simps tainted_eq_Tainted intro: info_flow_shm_Tainted 
+apply (auto simp:co2sobj.simps intro: info_flow_shm_tainted 
 split:t_object.splits option.splits if_splits)[1]
 done
 
--- a/simple_selinux/Sectxt_prop.thy	Mon Dec 02 10:52:40 2013 +0800
+++ b/simple_selinux/Sectxt_prop.thy	Tue Dec 03 22:42:48 2013 +0800
@@ -31,14 +31,13 @@
   have p6: "\<And> p fd. fd \<in> current_proc_fds s p \<Longrightarrow> \<exists> t. type_of_obj s (O_fd p fd) = Some t"
     by (auto intro:a1)
   have p7: "\<And> n. n \<in> init_nodes \<Longrightarrow> \<exists> t. type_of_obj s (O_node n) = Some t" by (auto intro:a1)
-  have p8: "\<And> h. h \<in> current_shms s \<Longrightarrow> \<exists> t. type_of_obj s (O_shm h) = Some t" by (auto intro:a1)
   have p9: "\<And> q. q \<in> current_msgqs s \<Longrightarrow> \<exists> t. type_of_obj s (O_msgq q) = Some t" by (auto intro:a1)
   have p10: "\<And> q m. \<lbrakk>m \<in> set (msgs_of_queue s q); q \<in> current_msgqs s\<rbrakk>
     \<Longrightarrow> \<exists> t. type_of_obj s (O_msg q m) = Some t" by (auto intro:a1)
   show ?case using a5 a2 a4 a3
     apply (case_tac e)
     apply (auto split:option.splits t_object.splits if_splits t_socket_type.splits
-                dest!:a1' intro:a1 intro:p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 simp:alive_simps)
+                dest!:a1' intro:a1 p1 p2 p3 p4 p5 p6 p7 p9 p10 simp:alive_simps)
     apply (frule_tac p = nat1 in file_fds_subset_pfds)
     apply (rule a1, auto)
     done
@@ -71,14 +70,13 @@
   have p6: "\<And> p fd. fd \<in> current_proc_fds s p \<Longrightarrow> \<exists> t. user_of_obj s (O_fd p fd) = Some t"
     by (auto intro:a1)
   have p7: "\<And> n. n \<in> init_nodes \<Longrightarrow> \<exists> t. user_of_obj s (O_node n) = Some t" by (auto intro:a1)
-  have p8: "\<And> h. h \<in> current_shms s \<Longrightarrow> \<exists> t. user_of_obj s (O_shm h) = Some t" by (auto intro:a1)
   have p9: "\<And> q. q \<in> current_msgqs s \<Longrightarrow> \<exists> t. user_of_obj s (O_msgq q) = Some t" by (auto intro:a1)
   have p10: "\<And> q m. \<lbrakk>m \<in> set (msgs_of_queue s q); q \<in> current_msgqs s\<rbrakk>
     \<Longrightarrow> \<exists> t. user_of_obj s (O_msg q m) = Some t" by (auto intro:a1)
   show ?case using a5 a2 a4 a3
     apply (case_tac e)
     apply (auto split:option.splits t_object.splits if_splits t_socket_type.splits
-                dest!:a1' intro:a1 intro:p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 simp:alive_simps)
+                dest!:a1' intro:a1 intro:p1 p2 p3 p4 p5 p6 p7 p9 p10 simp:alive_simps)
     apply (frule_tac p = nat1 in file_fds_subset_pfds)
     apply (rule a1, auto)
     done
@@ -131,12 +129,6 @@
 lemma init_node_has_type': "\<lbrakk>type_of_obj s (O_node n) = None; valid s\<rbrakk> \<Longrightarrow> n \<notin> init_nodes" 
 by (auto intro:notI dest:init_node_has_type)
 
-lemma current_shm_has_type: "\<lbrakk>h \<in> current_shms s; valid s\<rbrakk> \<Longrightarrow> \<exists> t. type_of_obj s (O_shm h) = Some t" 
-by (auto intro:alive_obj_has_type)
-
-lemma current_shm_has_type': "\<lbrakk>type_of_obj s (O_shm h) = None; valid s\<rbrakk> \<Longrightarrow> h \<notin> current_shms s" 
-by (auto intro:notI dest:current_shm_has_type)
-
 lemma current_msgq_has_type: "\<lbrakk>q \<in> current_msgqs s; valid s\<rbrakk> \<Longrightarrow> \<exists> t. type_of_obj s (O_msgq q) = Some t" 
 by (auto intro:alive_obj_has_type)
 
@@ -152,11 +144,11 @@
 by (auto dest!:current_msg_has_type)
 
 lemmas current_has_type = alive_obj_has_type current_proc_has_type is_file_has_type is_dir_has_type 
-  is_tcp_has_type is_udp_has_type current_fd_has_type init_node_has_type current_shm_has_type
+  is_tcp_has_type is_udp_has_type current_fd_has_type init_node_has_type
   current_msgq_has_type current_msg_has_type
 
 lemmas current_has_type' = alive_obj_has_type' current_proc_has_type' is_file_has_type' is_dir_has_type'
-  is_tcp_has_type' is_udp_has_type' current_fd_has_type' init_node_has_type' current_shm_has_type'
+  is_tcp_has_type' is_udp_has_type' current_fd_has_type' init_node_has_type' 
   current_msgq_has_type' current_msg_has_type' 
 
 lemma alive_obj_has_user': "\<lbrakk>user_of_obj s obj = None; valid s\<rbrakk> \<Longrightarrow> \<not> alive s obj" 
@@ -206,12 +198,6 @@
 lemma init_node_has_user': "\<lbrakk>user_of_obj s (O_node n) = None; valid s\<rbrakk> \<Longrightarrow> n \<notin> init_nodes" 
 by (auto intro:notI dest:init_node_has_user)
 
-lemma current_shm_has_user: "\<lbrakk>h \<in> current_shms s; valid s\<rbrakk> \<Longrightarrow> \<exists> t. user_of_obj s (O_shm h) = Some t" 
-by (auto intro:alive_obj_has_user)
-
-lemma current_shm_has_user': "\<lbrakk>user_of_obj s (O_shm h) = None; valid s\<rbrakk> \<Longrightarrow> h \<notin> current_shms s" 
-by (auto intro:notI dest:current_shm_has_user)
-
 lemma current_msgq_has_user: "\<lbrakk>q \<in> current_msgqs s; valid s\<rbrakk> \<Longrightarrow> \<exists> t. user_of_obj s (O_msgq q) = Some t" 
 by (auto intro:alive_obj_has_user)
 
@@ -227,11 +213,11 @@
 by (auto dest!:current_msg_has_user)
 
 lemmas current_has_user = alive_obj_has_user current_proc_has_user is_file_has_user is_dir_has_user 
-  is_tcp_has_user is_udp_has_user current_fd_has_user init_node_has_user current_shm_has_user
+  is_tcp_has_user is_udp_has_user current_fd_has_user init_node_has_user
   current_msgq_has_user current_msg_has_user
 
 lemmas current_has_user' = alive_obj_has_user' current_proc_has_user' is_file_has_user' is_dir_has_user'
-  is_tcp_has_user' is_udp_has_user' current_fd_has_user' init_node_has_user' current_shm_has_user'
+  is_tcp_has_user' is_udp_has_user' current_fd_has_user' init_node_has_user'
   current_msgq_has_user' current_msg_has_user' 
 
 lemma current_proc_has_role:
@@ -334,15 +320,6 @@
 lemma init_node_has_sec'': "\<lbrakk>n \<in> init_nodes; valid s\<rbrakk> \<Longrightarrow> \<exists> u r t. sectxt_of_obj s (O_node n) = Some (u,r,t)" 
 by (drule init_node_has_sec, simp+)
 
-lemma current_shm_has_sec: "\<lbrakk>h \<in> current_shms s; valid s\<rbrakk> \<Longrightarrow> \<exists> sec. sectxt_of_obj s (O_shm h) = Some sec" 
-by (rule alive_obj_has_sec, simp+)
-
-lemma current_shm_has_sec': "\<lbrakk>sectxt_of_obj s (O_shm h) = None; valid s\<rbrakk> \<Longrightarrow> h \<notin> current_shms s" 
-by (auto intro:notI dest:current_shm_has_sec)
-
-lemma current_shm_has_sec'': "\<lbrakk>h \<in> current_shms s; valid s\<rbrakk> \<Longrightarrow> \<exists> u r t. sectxt_of_obj s (O_shm h) = Some (u,r,t)" 
-by (drule current_shm_has_sec, simp+)
-
 lemma current_msgq_has_sec: "\<lbrakk>q \<in> current_msgqs s; valid s\<rbrakk> \<Longrightarrow> \<exists> sec. sectxt_of_obj s (O_msgq q) = Some sec" 
 by (rule alive_obj_has_sec, simp+)
 
@@ -366,15 +343,15 @@
 by (drule current_msg_has_sec, simp+)
 
 lemmas current_has_sec = alive_obj_has_sec current_proc_has_sec is_file_has_sec is_dir_has_sec 
-  is_tcp_has_sec is_udp_has_sec current_fd_has_sec init_node_has_sec current_shm_has_sec
+  is_tcp_has_sec is_udp_has_sec current_fd_has_sec init_node_has_sec 
   current_msgq_has_sec current_msg_has_sec
 
 lemmas current_has_sec' = alive_obj_has_sec' current_proc_has_sec' is_file_has_sec' is_dir_has_sec'
-  is_tcp_has_sec' is_udp_has_sec' current_fd_has_sec' init_node_has_sec' current_shm_has_sec'
+  is_tcp_has_sec' is_udp_has_sec' current_fd_has_sec' init_node_has_sec' 
   current_msgq_has_sec' current_msg_has_sec' 
 
 lemmas current_has_sec'' = alive_obj_has_sec'' current_proc_has_sec'' is_file_has_sec'' is_dir_has_sec''
-  is_tcp_has_sec'' is_udp_has_sec'' current_fd_has_sec'' init_node_has_sec'' current_shm_has_sec''
+  is_tcp_has_sec'' is_udp_has_sec'' current_fd_has_sec'' init_node_has_sec'' 
   current_msgq_has_sec'' current_msg_has_sec'' 
 
 (************ root sec remains ************)
@@ -443,7 +420,7 @@
 done
 
 lemma sec_clone:
-  "valid (Clone p p' fds shms # s) \<Longrightarrow> sectxt_of_obj (Clone p p' fds shms # s) = (\<lambda> obj. 
+  "valid (Clone p p' fds # s) \<Longrightarrow> sectxt_of_obj (Clone p p' fds # s) = (\<lambda> obj. 
      case obj of 
        O_proc p'' \<Rightarrow> if (p'' = p') then sectxt_of_obj s (O_proc p) 
                      else sectxt_of_obj s obj
@@ -498,20 +475,6 @@
            dest!:current_has_type' current_proc_has_role' current_has_user')
 done
 
-lemma sec_linkhard:
-  "valid (LinkHard p f f' # s) \<Longrightarrow> sectxt_of_obj (LinkHard p f f' # s) = 
-     (sectxt_of_obj s) (O_file f' := 
-        (case parent f' of 
-           None \<Rightarrow> None
-         | Some pf \<Rightarrow> (case (sectxt_of_obj s (O_proc p), sectxt_of_obj s (O_dir pf)) of
-                         (Some psec, Some pfsec) \<Rightarrow> Some (fst psec, R_object, 
-                            type_transition ((snd o snd) psec) ((snd o snd) pfsec) C_file True)
-                      | _ \<Rightarrow> None)))"
-apply (rule ext, frule vd_cons, frule vt_grant_os, case_tac x)
-apply (auto simp:sectxt_of_obj_def split:option.splits if_splits
-           dest!:current_has_type' current_proc_has_role' current_has_user')
-done
-
 lemma sec_createmsgq:
   "valid (CreateMsgq p q # s) \<Longrightarrow> sectxt_of_obj (CreateMsgq p q # s) = (sectxt_of_obj s) (O_msgq q := 
      (case (sectxt_of_obj s (O_proc p)) of
@@ -533,16 +496,6 @@
            dest!:current_has_type' current_proc_has_role' current_has_user')
 done
 
-lemma sec_createshm:
-  "valid (CreateShM p h # s) \<Longrightarrow> sectxt_of_obj (CreateShM p h # s) = (sectxt_of_obj s) (O_shm h := 
-     case (sectxt_of_obj s (O_proc p)) of
-        Some psec \<Rightarrow> Some (fst psec, R_object, (snd o snd) psec)
-      | _ \<Rightarrow> None)"
-apply (rule ext, frule vd_cons, frule vt_grant_os, case_tac x)
-apply (auto simp:sectxt_of_obj_def split:option.splits if_splits
-           dest!:current_has_type' current_proc_has_role' current_has_user')
-done
-
 lemma sec_createsock:
   "valid (CreateSock p af st fd inum # s) \<Longrightarrow> sectxt_of_obj (CreateSock p af st fd inum # s) = (\<lambda> obj. 
      case obj of       
@@ -588,11 +541,10 @@
 
 lemma sec_others :
   "\<lbrakk>valid (e # s); 
-    \<forall> p p' fds shms. e \<noteq> Clone p p' fds shms;
+    \<forall> p p' fds. e \<noteq> Clone p p' fds;
     \<forall> p f fds. e \<noteq> Execve p f fds;
     \<forall> p f flags fd opt. e \<noteq> Open p f flags fd opt;
     \<forall> p f inum. e \<noteq> Mkdir p f inum;
-    \<forall> p f f'. e \<noteq> LinkHard p f f';
     \<forall> p q. e \<noteq> CreateMsgq p q;
     \<forall> p q m. e \<noteq> SendMsg p q m;
     \<forall> p h. e \<noteq> CreateShM p h;
@@ -648,18 +600,6 @@
   "valid (RemoveMsgq p q # s) \<Longrightarrow> sectxt_of_obj (RemoveMsgq p q # s) = sectxt_of_obj s"
 by (auto dest!:sec_others)
 
-lemma sec_attach:
-  "valid (Attach p h flag # s) \<Longrightarrow> sectxt_of_obj (Attach p h flag # s) = sectxt_of_obj s"
-by (auto dest!:sec_others)
-
-lemma sec_detach:
-  "valid (Detach p h # s) \<Longrightarrow> sectxt_of_obj (Detach p h # s) = sectxt_of_obj s"
-by (auto dest!:sec_others)
-
-lemma sec_deleteshm:
-  "valid (DeleteShM p h # s) \<Longrightarrow> sectxt_of_obj (DeleteShM p h # s) = sectxt_of_obj s"
-by (auto dest!:sec_others)
-
 lemma sec_bind:
   "valid (Bind p fd addr # s) \<Longrightarrow> sectxt_of_obj (Bind p fd addr # s) = sectxt_of_obj s"
 by (auto dest!:sec_others)
@@ -684,11 +624,10 @@
   "valid (Shutdown p fd how # s) \<Longrightarrow> sectxt_of_obj (Shutdown p fd how # s) = sectxt_of_obj s"
 by (auto dest!:sec_others)
 
-lemmas sectxt_of_obj_simps = sec_execve sec_open sec_mkdir sec_linkhard sec_createmsgq sec_sendmsg
-  sec_createshm sec_createsock sec_accept sec_clone sec_kill sec_ptrace sec_exit sec_readfile
+lemmas sectxt_of_obj_simps = sec_execve sec_open sec_mkdir sec_createmsgq sec_sendmsg
+  sec_createsock sec_accept sec_clone sec_kill sec_ptrace sec_exit sec_readfile
   sec_writefile sec_closefd sec_unlink sec_Rmdir sec_truncate sec_recvmsg sec_removemsgq
-  sec_attach sec_detach sec_deleteshm sec_bind sec_connect sec_listen sec_sendsock
-  sec_recvsock sec_shutdown
+  sec_bind sec_connect sec_listen sec_sendsock sec_recvsock sec_shutdown
 (* init_sectxt_prop *)
 
 (**************** get_parentfs_ctxts simpset **************)
--- a/simple_selinux/Tainted_prop.thy	Mon Dec 02 10:52:40 2013 +0800
+++ b/simple_selinux/Tainted_prop.thy	Tue Dec 03 22:42:48 2013 +0800
@@ -6,217 +6,50 @@
 
 context tainting begin
 
-lemma valid_Tainted_obj:
-  "\<lbrakk>obj \<in> Tainted s; valid s\<rbrakk> \<Longrightarrow> (\<forall> f. obj \<noteq> O_dir f) \<and> (\<forall> q. obj \<noteq> O_msgq q) \<and> (\<forall> h. obj \<noteq> O_shm h) \<and> (\<forall> p fd. obj \<noteq> O_fd p fd) \<and> (\<forall> s. obj \<noteq> O_tcp_sock s) \<and> (\<forall> s. obj \<noteq> O_udp_sock s)"
-apply (induct s, simp, drule seeds_in_init, case_tac obj, simp+)
+lemma valid_tainted_obj:
+  "\<lbrakk>obj \<in> tainted s; valid s\<rbrakk> \<Longrightarrow> (\<forall> f. obj \<noteq> O_dir f) \<and> (\<forall> q. obj \<noteq> O_msgq q) \<and>  (\<forall> p fd. obj \<noteq> O_fd p fd) \<and> (\<forall> s. obj \<noteq> O_tcp_sock s) \<and> (\<forall> s. obj \<noteq> O_udp_sock s)"
+apply (induct s, simp)
+apply (drule seeds_in_init, case_tac obj, simp+)
 apply (frule vd_cons, frule vt_grant_os, case_tac a)
 apply (auto split:if_splits option.splits)
 done
 
-lemma Tainted_in_current:
-  "\<lbrakk>obj \<in> Tainted s; valid s\<rbrakk> \<Longrightarrow> alive s obj"
+lemma dir_not_tainted: "\<lbrakk>O_dir f \<in> tainted s; valid s\<rbrakk> \<Longrightarrow> False"
+by (auto dest!:valid_tainted_obj)
+
+lemma msgq_not_tainted: "\<lbrakk>O_msgq q \<in> tainted s; valid s\<rbrakk> \<Longrightarrow> False"
+by (auto dest:valid_tainted_obj)
+
+lemma tainted_in_current:
+  "\<lbrakk>obj \<in> tainted s; valid s\<rbrakk> \<Longrightarrow> alive s obj"
 apply (induct s, simp)
 apply (drule seeds_in_init, case_tac obj, simp_all add:is_file_nil)
-apply (frule vd_cons, frule valid_Tainted_obj, simp, frule vt_grant_os, case_tac a)
-apply (auto simp:alive_simps split:if_splits option.splits t_object.splits
-           intro:same_inode_files_prop1 procs_of_shm_prop2 
-            dest:info_shm_flow_in_procs)
-apply (auto simp:same_inode_files_def is_file_def split:if_splits)
-done 
-
-lemma Tainted_proc_in_current:
-  "\<lbrakk>O_proc p \<in> Tainted s; valid s\<rbrakk> \<Longrightarrow> p \<in> current_procs s"
-by (drule Tainted_in_current, simp+)
-
-
-lemma info_flow_shm_Tainted:
-  "\<lbrakk>O_proc p \<in> Tainted s; info_flow_shm s p p'; valid s\<rbrakk> \<Longrightarrow> O_proc p' \<in> Tainted s"
-proof (induct s arbitrary:p p')
-  case Nil
-  thus ?case by (simp add:flow_shm_in_seeds)
-next
-  case (Cons e s)
-  hence p1: "O_proc p \<in> Tainted (e # s)" and p2: "info_flow_shm (e # s) p p'" and p3: "valid (e # s)"  
-    and p4: "\<And> p p'. \<lbrakk>O_proc p \<in> Tainted s; info_flow_shm s p p'\<rbrakk> \<Longrightarrow> O_proc p' \<in> Tainted s" 
-    and p5: "valid s" and p6: "os_grant s e"
-    by (auto dest:vd_cons intro:vd_cons vt_grant_os)
-  have p4': 
-    "\<And> p p' h flag. \<lbrakk>O_proc p \<in> Tainted s; (p, SHM_RDWR) \<in> procs_of_shm s h; (p', flag) \<in> procs_of_shm s h\<rbrakk> 
-                \<Longrightarrow> O_proc p' \<in> Tainted s"
-    by (rule p4, auto simp:info_flow_shm_def one_flow_shm_def procs_of_shm_prop2 p5)    
-  from p2 p3 have p7: "p \<in> current_procs (e # s)" and p8: "p' \<in> current_procs (e # s)" 
-    by (auto dest:info_shm_flow_in_procs) 
-  show ?case
-  proof (cases "self_shm s p p'")
-    case True with p1 show ?thesis by simp
-  next
-    case False
-    with p1 p2 p5 p6 p7 p8 p3 show ?thesis
-    apply (case_tac e)(*
-    prefer 7
-    apply (simp add:info_flow_shm_simps split:if_splits option.splits)
-    apply (rule allI|rule impI|rule conjI)+
-    apply simp
-    apply (case_tac "O_proc p \<in> Tainted s", drule_tac p'=p' in p4, simp+)
-    apply simp
-
-
-
-
-    apply (auto simp:info_flow_shm_simps one_flow_shm_def dest:Tainted_in_current 
-  intro:p4 p4' split:if_splits option.splits)
-    apply (auto simp:info_flow_shm_def one_flow_shm_def)
-
-
-
-    apply (auto simp:one_flow_shm_def intro:p4 p4' split:if_splits option.splits)
-
-
-
-    prefer 7
-    apply (simp split:if_splits option.splits)
-    apply (rule allI|rule impI|rule conjI)+
-
-
-    apply (auto dest:p4'   procs_of_shm_prop2 Tainted_in_current split:if_splits option.splits)[1]
-
-    apply (erule disjE, drule_tac p = p and p' = p' in p4', simp+)
-    apply (erule disjE, rule disjI2, rule disjI2, rule_tac x = h in exI, simp, rule_tac x= toflag in exI, simp)
-    apply ((erule exE|erule conjE)+)
-    
-
-    apply (auto simp:info_flow_shm_def dest:p4'
-           procs_of_shm_prop2 Tainted_in_current split:if_splits option.splits)[1]
-    apply (drule_tac p = p and p' = p' in p4')
-    apply (erule_tac x = ha in allE, simp)
-    apply (drule_tac p = "nat1" and p' = p' in p4')
-    apply (auto dest:p4'[where p = nat1 and p' = p'])
-    
-apply (induct s) 
-apply simp defer
-apply (frule vd_cons, frule vt_grant_os, case_tac a)
-apply (auto simp:info_flow_shm_def elim!:disjE)
-sorry *)
-  sorry
-qed
-qed
-
-lemma has_same_inode_comm:
-  "has_same_inode s f f' = has_same_inode s f' f"
-by (auto simp add:has_same_inode_def same_inode_files_def is_file_def)
-
-lemma tainted_imp_Tainted:
-  "obj \<in> tainted s \<Longrightarrow> obj \<in> Tainted s"
-apply (induct rule:tainted.induct)  (*
-apply (simp_all add:vd_cons) 
-apply (rule impI)
-
-apply (rule disjI2, rule_tac x = flag' in exI, simp)
-apply ((rule impI)+, erule_tac x = p' in allE, simp)
-*)
-apply (auto intro:info_flow_shm_Tainted simp:has_same_inode_def dest:vd_cons)
-apply (case_tac e, auto split:option.splits if_splits simp:alive_simps)
+apply (frule vd_cons, frule valid_tainted_obj, simp, frule vt_grant_os, case_tac a)
+apply (auto simp:alive_simps split:if_splits option.splits t_object.splits intro:file_of_pfd_is_file)
 done
 
-lemma Tainted_imp_tainted_aux_remain:
-  "\<lbrakk>obj \<in> Tainted s; valid (e # s); alive (e # s) obj; \<And> obj. obj \<in> Tainted s \<Longrightarrow> obj \<in> tainted s\<rbrakk>
-   \<Longrightarrow> obj \<in> tainted (e # s)"
-by (rule t_remain, auto)
-
-lemma Tainted_imp_tainted:
-  "\<lbrakk>obj \<in> Tainted s; valid s\<rbrakk> \<Longrightarrow> obj \<in> tainted s"
-apply (induct s arbitrary:obj, simp add:t_init)
-apply (frule Tainted_in_current, simp+)
-apply (frule vt_grant_os, frule vd_cons, case_tac a)
-apply (auto split:if_splits option.splits elim:Tainted_imp_tainted_aux_remain intro:tainted.intros
-  simp:has_same_inode_def)
-done
-
-lemma tainted_eq_Tainted:
-  "valid s \<Longrightarrow> (obj \<in> tainted s) = (obj \<in> Tainted s)"
-by (rule iffI, auto intro:Tainted_imp_tainted tainted_imp_Tainted)
-
-lemma info_flow_shm_tainted:
-  "\<lbrakk>O_proc p \<in> tainted s; info_flow_shm s p p'; valid s\<rbrakk> \<Longrightarrow> O_proc p' \<in> tainted s"
-by (simp only:tainted_eq_Tainted info_flow_shm_Tainted)
-
+lemma tainted_proc_in_current:
+  "\<lbrakk>O_proc p \<in> tainted s; valid s\<rbrakk> \<Longrightarrow> p \<in> current_procs s"
+by (drule tainted_in_current, simp+)
 
-lemma same_inode_files_Tainted:
-  "\<lbrakk>O_file f \<in> Tainted s; f' \<in> same_inode_files s f; valid s\<rbrakk> \<Longrightarrow> O_file f' \<in> Tainted s"
-apply (induct s arbitrary:f f', simp add:same_inode_in_seeds has_same_inode_def)
-apply (frule vt_grant_os, frule vd_cons, case_tac a)
-prefer 6
-apply (simp split:if_splits option.splits add:same_inode_files_open current_files_simps)
-prefer 8
-apply (frule Tainted_in_current, simp, simp add:alive.simps, drule is_file_in_current)
-apply (auto simp add:same_inode_files_closefd split:option.splits if_splits)[1]
-prefer 8
-apply (frule Tainted_in_current, simp, simp add:alive.simps, drule is_file_in_current)
-apply (auto simp add:same_inode_files_unlink split:option.splits if_splits)[1]
-prefer 10
-apply (auto split:if_splits option.splits simp:same_inode_files_linkhard current_files_simps)[1]
-apply (drule Tainted_in_current, simp, simp add:alive.simps is_file_in_current)
-apply (drule same_inode_files_prop5, simp)
-apply (drule same_inode_files_prop5, drule_tac f' = list1 and f'' = f' in same_inode_files_prop4, simp, simp)
-
-apply (auto simp:same_inode_files_other split:if_splits)
-apply (drule_tac f'' = f' and f' = f and f = fa in same_inode_files_prop4, simp+)
-apply (drule_tac f'' = f' and f' = f and f = list in same_inode_files_prop4, simp+)
+lemma t_remain: "\<lbrakk>obj \<in> tainted s; valid (e # s); alive (e # s) obj\<rbrakk> 
+             \<Longrightarrow> obj \<in> tainted (e # s)"
+apply (frule vd_cons, frule vt_grant_os, case_tac e)
+apply (auto simp:alive_simps split:option.splits if_splits)
 done
 
-lemma has_same_inode_Tainted:
-  "\<lbrakk>O_file f \<in> Tainted s; has_same_inode s f f'; valid s\<rbrakk> \<Longrightarrow> O_file f' \<in> Tainted s"
-by (simp add:has_same_inode_def same_inode_files_Tainted)
-
-lemma has_same_inode_tainted:
-  "\<lbrakk>O_file f \<in> tainted s; has_same_inode s f f'; valid s\<rbrakk> \<Longrightarrow> O_file f' \<in> tainted s"
-by (simp add:has_same_inode_Tainted tainted_eq_Tainted)
-
-lemma same_inodes_Tainted:
-  "\<lbrakk>f \<in> same_inode_files s f'; valid s\<rbrakk> \<Longrightarrow> (O_file f \<in> Tainted s) = (O_file f' \<in> Tainted s)"
-apply (frule same_inode_files_prop8, frule same_inode_files_prop7)
-apply (auto intro:has_same_inode_Tainted)
-done
-
-
-
-lemma tainted_in_current:
-  "obj \<in> tainted s \<Longrightarrow> alive s obj"
-apply (erule tainted.induct)
-apply (auto dest:vt_grant_os vd_cons info_shm_flow_in_procs procs_of_shm_prop2 simp:is_file_simps)
-apply (drule seeds_in_init, simp add:tobj_in_alive)
-apply (erule has_same_inode_prop2, simp, simp add:vd_cons)
-apply (frule vt_grant_os, simp)
-apply (erule has_same_inode_prop1, simp, simp add:vd_cons)
-done
-
-lemma tainted_is_valid:
-  "obj \<in> tainted s \<Longrightarrow> valid s"
-by (erule tainted.induct, auto intro:valid.intros)
-
 lemma t_remain_app:
   "\<lbrakk>obj \<in> tainted s; \<not> deleted obj (s' @ s); valid (s' @ s)\<rbrakk> 
   \<Longrightarrow> obj \<in> tainted (s' @ s)"
 apply (induct s', simp)
 apply (simp (no_asm) only:cons_app_simp_aux, rule t_remain)
 apply (simp_all add:not_deleted_cons_D vd_cons)
-apply (drule tainted_in_current, simp add:not_deleted_imp_alive_cons)
+apply (drule tainted_in_current)
+apply (simp add:vd_cons)
+apply (simp add:not_deleted_imp_alive_cons)
 done
 
-lemma valid_tainted_obj:
-  "obj \<in> tainted s \<Longrightarrow> (\<forall> f. obj \<noteq> O_dir f) \<and> (\<forall> q. obj \<noteq> O_msgq q) \<and> (\<forall> h. obj \<noteq> O_shm h) \<and> (\<forall> p fd. obj \<noteq> O_fd p fd) \<and> (\<forall> s. obj \<noteq> O_tcp_sock s) \<and> (\<forall> s. obj \<noteq> O_udp_sock s)"
-apply (erule tainted.induct)
-apply (drule seeds_in_init)
-by auto
 
-lemma dir_not_tainted: "O_dir f \<in> tainted s \<Longrightarrow> False"
-by (auto dest:valid_tainted_obj)
-
-lemma msgq_not_tainted: "O_msgq q \<in> tainted s \<Longrightarrow> False"
-by (auto dest:valid_tainted_obj)
-
-lemma shm_not_tainted: "O_shm h \<in> tainted s \<Longrightarrow> False"
-by (auto dest:valid_tainted_obj)
 
 end