diff -r 1a1df29d3507 -r d9dc04c3ea90 no_shm_selinux/Co2sobj_prop.thy
--- a/no_shm_selinux/Co2sobj_prop.thy	Wed Jan 08 18:40:38 2014 +0800
+++ b/no_shm_selinux/Co2sobj_prop.thy	Thu Jan 09 14:39:00 2014 +0800
@@ -1842,8 +1842,8 @@
 (* 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)
+  "\<lbrakk>valid (Execve p f fds # s); dalive (Execve p f fds # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Execve p f fds # s) obj = (
+      if (obj = D_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))
             | _       \<Rightarrow> None) 
@@ -1859,8 +1859,8 @@
 done
 
 lemma co2sobj_execve':
-  "\<lbrakk>valid (Execve p f fds # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Execve p f fds # s) obj = (
-      if (obj = O_proc p)
+  "\<lbrakk>valid (Execve p f fds # s); dalive s obj\<rbrakk> \<Longrightarrow> co2sobj (Execve p f fds # s) obj = (
+      if (obj = D_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))
             | _       \<Rightarrow> None) 
@@ -1876,8 +1876,8 @@
 done
 
 lemma co2sobj_clone':
-  "\<lbrakk>valid (Clone p p' fds # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Clone p p' fds # s) obj = (
-      if (obj = O_proc p')
+  "\<lbrakk>valid (Clone p p' fds # s); dalive s obj\<rbrakk> \<Longrightarrow> co2sobj (Clone p p' fds # s) obj = (
+      if (obj = D_proc p')
       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)
@@ -1895,9 +1895,9 @@
 done
 
 lemma co2sobj_clone:
-  "\<lbrakk>valid (Clone p p' fds # s); alive (Clone p p' fds # s) obj\<rbrakk> 
+  "\<lbrakk>valid (Clone p p' fds # s); dalive (Clone p p' fds # s) obj\<rbrakk> 
    \<Longrightarrow> co2sobj (Clone p p' fds # s) obj = (
-      if (obj = O_proc p')
+      if (obj = D_proc p')
       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)
@@ -1920,7 +1920,7 @@
 
 (*
 lemma co2sobj_ptrace:
-  "\<lbrakk>valid (Ptrace p p' # s); alive s obj\<rbrakk>\<Longrightarrow> co2sobj (Ptrace p p' # s) obj = (
+  "\<lbrakk>valid (Ptrace p p' # s); dalive s obj\<rbrakk>\<Longrightarrow> co2sobj (Ptrace p p' # s) obj = (
      case obj of
        O_proc p'' \<Rightarrow> if (info_flow_shm s p' p'') 
                      then (case (cp2sproc s p'') of 
@@ -1945,9 +1945,9 @@
 *)
 
 lemma co2sobj_ptrace:
-  "\<lbrakk>valid (Ptrace p p' # s); alive s obj\<rbrakk>\<Longrightarrow> co2sobj (Ptrace p p' # s) obj = (
+  "\<lbrakk>valid (Ptrace p p' # s); dalive s obj\<rbrakk>\<Longrightarrow> co2sobj (Ptrace p p' # s) obj = (
      case obj of
-       O_proc p'' \<Rightarrow> if (p'' = p') 
+       D_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))
                            | _       \<Rightarrow> None)
@@ -1955,7 +1955,7 @@
                           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))
                                 | _       \<Rightarrow> None)
-                          else co2sobj s (O_proc p'')
+                          else co2sobj s (D_proc p'')
     | _          \<Rightarrow> co2sobj s obj)"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
 apply (simp_all add:current_files_simps cq2smsgq_other cf2sfiles_other)
@@ -1970,18 +1970,18 @@
 
 
 lemma co2sobj_open:
-  "\<lbrakk>valid (Open p f flag fd opt # s); alive (Open p f flag fd opt # s) obj\<rbrakk> 
+  "\<lbrakk>valid (Open p f flag fd opt # s); dalive (Open p f flag fd opt # s) obj\<rbrakk> 
    \<Longrightarrow> co2sobj (Open p f flag fd opt # s) obj = (case obj of 
-     O_file f' \<Rightarrow> if (f' = f \<and> opt \<noteq> None)
+     D_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))
                         | _       \<Rightarrow> None)
-                  else co2sobj s (O_file f')
-   | O_proc p' \<Rightarrow> if (p' = p) 
+                  else co2sobj s (D_file f')
+   | D_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))
                         | _       \<Rightarrow> None)
-                  else co2sobj s (O_proc p')
+                  else co2sobj s (D_proc p')
    | _         \<Rightarrow> co2sobj s obj )"
 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
 apply (auto simp:cp2sproc_simps split:option.splits
@@ -2015,7 +2015,7 @@
 
 (*
 lemma co2sobj_readfile:
-  "\<lbrakk>valid (ReadFile p fd # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (ReadFile p fd # s) obj = (
+  "\<lbrakk>valid (ReadFile p fd # s); dalive 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)
@@ -2036,9 +2036,9 @@
 done
 *)
 lemma co2sobj_readfile:
-  "\<lbrakk>valid (ReadFile p fd # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (ReadFile p fd # s) obj = (
+  "\<lbrakk>valid (ReadFile p fd # s); dalive 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
+       D_proc p' \<Rightarrow> (case (file_of_proc_fd s p fd) of
                        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)
@@ -2056,9 +2056,9 @@
 done
 
 lemma co2sobj_writefile:
-  "\<lbrakk>valid (WriteFile p fd # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (WriteFile p fd # s) obj = (
+  "\<lbrakk>valid (WriteFile p fd # s); dalive 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
+       D_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))
@@ -2077,18 +2077,18 @@
 by (auto simp:same_inode_files_def is_file_def has_same_inode_def split:if_splits option.splits)
 
 lemma co2sobj_closefd:
-  "\<lbrakk>valid (CloseFd p fd # s); alive (CloseFd p fd # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CloseFd p fd # s) obj = (
+  "\<lbrakk>valid (CloseFd p fd # s); dalive (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 
+        D_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
+                                   then (case (cf2sfile s f, co2sobj s (D_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') 
+      | D_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))
                             | _       \<Rightarrow> None)
@@ -2115,11 +2115,11 @@
 done
 
 lemma co2sobj_unlink:
-  "\<lbrakk>valid (UnLink p f # s); alive (UnLink p f # s) obj\<rbrakk> \<Longrightarrow> co2sobj (UnLink p f # s) obj = (
+  "\<lbrakk>valid (UnLink p f # s); dalive (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> 
+        D_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
+                     then (case (cf2sfile s f, co2sobj s (D_file f')) of
                              (Some sf, Some (S_file sfs b)) \<Rightarrow> Some (S_file (sfs - {sf}) b)
                            | _                              \<Rightarrow> None)
                      else co2sobj s obj
@@ -2142,7 +2142,7 @@
 done
 
 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"
+  "\<lbrakk>valid (Rmdir p f # s); dalive (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 cq2smsgq_other) (* ch2sshm_other*)
 apply (auto simp:cp2sproc_simps split:option.splits if_splits
@@ -2154,8 +2154,8 @@
 done
 
 lemma co2sobj_mkdir:
-  "\<lbrakk>valid (Mkdir p f i # s); alive (Mkdir p f i # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Mkdir p f i # s) obj = (
-      if (obj = O_dir f) 
+  "\<lbrakk>valid (Mkdir p f i # s); dalive (Mkdir p f i # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Mkdir p f i # s) obj = (
+      if (obj = D_dir f) 
       then (case (cf2sfile (Mkdir p f i # s) f) of 
               Some sf \<Rightarrow> Some (S_dir sf)
             | _       \<Rightarrow> None)
@@ -2171,10 +2171,10 @@
 done
 
 lemma co2sobj_linkhard:
-  "\<lbrakk>valid (LinkHard p oldf f # s); alive (LinkHard p oldf f # s) obj\<rbrakk> 
+  "\<lbrakk>valid (LinkHard p oldf f # s); dalive (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)
+      D_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)
@@ -2197,9 +2197,9 @@
 done
 
 lemma co2sobj_truncate:
-  "\<lbrakk>valid (Truncate p f len # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Truncate p f len # s) obj = (
+  "\<lbrakk>valid (Truncate p f len # s); dalive 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)
+        D_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))
                      else co2sobj s obj
       | _         \<Rightarrow> co2sobj s obj)"
@@ -2213,7 +2213,7 @@
 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"
+  "\<lbrakk>valid (Kill p p' # s); dalive (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 cq2smsgq_other) (* ch2sshm_other *)
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
@@ -2223,7 +2223,7 @@
 done
 
 lemma co2sobj_exit:
-  "\<lbrakk>valid (Exit p # s); alive (Exit p # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Exit p # s) obj = co2sobj s obj"
+  "\<lbrakk>valid (Exit p # s); dalive (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 cq2smsgq_other)
 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
@@ -2233,9 +2233,9 @@
 done
 
 lemma co2sobj_createmsgq:
-  "\<lbrakk>valid (CreateMsgq p q # s); alive (CreateMsgq p q # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CreateMsgq p q # s) obj = (
+  "\<lbrakk>valid (CreateMsgq p q # s); dalive (CreateMsgq p q # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CreateMsgq p q # s) obj = (
       case obj of
-        O_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (CreateMsgq p q # s) q) of
+        D_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (CreateMsgq p q # s) q) of
                                          Some sq \<Rightarrow> Some (S_msgq sq)
                                        | _       \<Rightarrow> None)
                      else co2sobj s obj
@@ -2250,9 +2250,9 @@
 done
 
 lemma co2sobj_sendmsg:
-  "\<lbrakk>valid (SendMsg p q m # s); alive (SendMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (SendMsg p q m # s) obj = (
+  "\<lbrakk>valid (SendMsg p q m # s); dalive (SendMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (SendMsg p q m # s) obj = (
       case obj of
-        O_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (SendMsg p q m # s) q) of
+        D_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (SendMsg p q m # s) q) of
                                          Some sq \<Rightarrow> Some (S_msgq sq)
                                        | _       \<Rightarrow> None)
                      else co2sobj s obj
@@ -2267,13 +2267,13 @@
 done
 
 lemma co2sobj_recvmsg:
-  "\<lbrakk>valid (RecvMsg p q m # s); alive (RecvMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (RecvMsg p q m # s) obj = (
+  "\<lbrakk>valid (RecvMsg p q m # s); dalive (RecvMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (RecvMsg p q m # s) obj = (
       case obj of
-        O_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (RecvMsg p q m # s) q) of
+        D_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (RecvMsg p q m # s) q) of
                                          Some sq \<Rightarrow> Some (S_msgq sq)
                                        | _       \<Rightarrow> None)
                      else co2sobj s obj
-      | O_proc p' \<Rightarrow> if (p' = p \<and> O_msg q m \<in> tainted s)
+      | D_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)
@@ -2289,7 +2289,7 @@
 done
 (*
 lemma co2sobj_recvmsg:
-  "\<lbrakk>valid (RecvMsg p q m # s); alive (RecvMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (RecvMsg p q m # s) obj = (
+  "\<lbrakk>valid (RecvMsg p q m # s); dalive (RecvMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (RecvMsg p q m # s) obj = (
       case obj of
         O_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (RecvMsg p q m # s) q) of
                                          Some sq \<Rightarrow> Some (S_msgq sq)
@@ -2312,7 +2312,7 @@
 *)
 
 lemma co2sobj_removemsgq:
-  "\<lbrakk>valid (RemoveMsgq p q # s); alive (RemoveMsgq p q # s) obj\<rbrakk> 
+  "\<lbrakk>valid (RemoveMsgq p q # s); dalive (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 cq2smsgq_other)
@@ -2325,7 +2325,7 @@
 
 (*
 lemma co2sobj_createshm:
-  "\<lbrakk>valid (CreateShM p h # s); alive (CreateShM p h # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CreateShM p h # s) obj = (
+  "\<lbrakk>valid (CreateShM p h # s); dalive (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)
@@ -2342,7 +2342,7 @@
 done
 
 lemma co2sobj_detach:
-  "\<lbrakk>valid (Detach p h # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Detach p h # s) obj = (
+  "\<lbrakk>valid (Detach p h # s); dalive 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))
@@ -2360,7 +2360,7 @@
 done
 
 lemma co2sobj_deleteshm:
-  "\<lbrakk>valid (DeleteShM p h # s); alive (DeleteShM p h # s) obj\<rbrakk> \<Longrightarrow> co2sobj (DeleteShM p h # s) obj = (
+  "\<lbrakk>valid (DeleteShM p h # s); dalive (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))
@@ -2385,7 +2385,7 @@
 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 = (
+  "\<lbrakk>valid (Attach p h flag # s); dalive 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
@@ -2426,8 +2426,45 @@
 done
 *)
 
+lemma co2sobj_bind:
+  "valid (Bind p fd addr # s) \<Longrightarrow> co2sobj (Bind p fd addr # s) = co2sobj s"
+apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
+by auto
+
+lemma co2sobj_connect:
+  "valid (Connect p fd addr # s) \<Longrightarrow> co2sobj (Connect p fd addr # s) = co2sobj s"
+apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
+by auto
+
+lemma co2sobj_createsock:
+  "valid (CreateSock p af st fd inum # s) \<Longrightarrow> co2sobj (CreateSock p af st fd inum # s) = co2sobj s"
+apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
+by auto
+
+lemma co2sobj_accept:
+  "valid (Accept p fd addr port fd' inum # s) \<Longrightarrow> co2sobj (Accept p fd addr port fd' inum # s) = co2sobj s"
+apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
+by auto
+
+lemma co2sobj_listen:
+  "valid (Listen p fd # s) \<Longrightarrow> co2sobj (Listen p fd # s) = co2sobj s"
+apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
+by auto
+lemma co2sobj_sendsock:
+  "valid (SendSock p fd # s) \<Longrightarrow> co2sobj (SendSock p fd # s) = co2sobj s"
+apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
+by auto
+lemma co2sobj_recvsock:
+  "valid (RecvSock p fd # s) \<Longrightarrow> co2sobj (RecvSock p fd # s) = co2sobj s"
+apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
+by auto
+lemma co2sobj_shutdown:
+  "valid (Shutdown p fd addr # s) \<Longrightarrow> co2sobj (Shutdown p fd addr # s) = co2sobj s"
+apply (frule vd_cons, frule vt_grant, rule ext, case_tac x)
+by auto
+
 lemma co2sobj_other:
-  "\<lbrakk>valid (e # s); alive (e # s) obj; 
+  "\<lbrakk>valid (e # s); dalive (e # s) obj; 
     \<forall> p f fds. e \<noteq> Execve p f fds;
     \<forall> p p' fds. e \<noteq> Clone p p' fds;
     \<forall> p p'. e \<noteq> Ptrace p p';
@@ -2456,8 +2493,8 @@
   co2sobj_writefile co2sobj_closefd co2sobj_unlink co2sobj_rmdir co2sobj_mkdir co2sobj_linkhard
   co2sobj_truncate co2sobj_kill co2sobj_exit co2sobj_createmsgq co2sobj_sendmsg co2sobj_recvmsg
   co2sobj_removemsgq (* co2sobj_attach co2sobj_detach co2sobj_createshm co2sobj_deleteshm *)
-
-
+  co2sobj_createsock co2sobj_accept co2sobj_listen co2sobj_sendsock co2sobj_recvsock 
+  co2sobj_shutdown co2sobj_bind co2sobj_connect
 
 end