
diff -r 271e9818b6f6 -r 99af1986e1e0 simple_selinux/Co2sobj_prop.thy
--- 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
 




