
diff -r 1ac0c3031ed2 -r 0a68c605ae79 no_shm_selinux/Enrich2.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/no_shm_selinux/Enrich2.thy	Mon Dec 23 19:47:17 2013 +0800
@@ -0,0 +1,624 @@
+theory Enrich
+imports Main Flask Static Init_prop Valid_prop Tainted_prop Delete_prop Co2sobj_prop S2ss_prop S2ss_prop2
+ Temp Enrich
+begin
+
+context tainting_s begin
+
+lemma get_parentfs_ctxts_prop:
+  "\<lbrakk>get_parentfs_ctxts s (a # f) = Some ctxts; sectxt_of_obj s (O_dir f) = Some ctxt; valid s\<rbrakk>
+   \<Longrightarrow> ctxt \<in> set (ctxts)"
+apply (induct f)
+apply (auto split:option.splits)
+done
+
+lemma search_check_allp_intro:
+  "\<lbrakk>search_check s sp pf; get_parentfs_ctxts s pf = Some ctxts; valid s; is_dir s pf\<rbrakk>
+   \<Longrightarrow> search_check_allp sp (set ctxts)"
+apply (case_tac pf)
+apply (simp split:option.splits if_splits add:search_check_allp_def)
+apply (rule ballI)
+apply (auto simp:search_check_ctxt_def search_check_dir_def split:if_splits option.splits)
+apply (auto simp:search_check_allp_def search_check_file_def)
+apply (frule is_dir_not_file, simp)
+done
+
+lemma search_check_leveling_f:
+  "\<lbrakk>search_check s sp pf; parent f = Some pf; is_file s f; valid s;
+    sectxt_of_obj s (O_file f) = Some fctxt; search_check_file sp fctxt\<rbrakk>
+   \<Longrightarrow> search_check s sp f"
+apply (case_tac f, simp+)
+apply (auto split:option.splits simp:search_check_ctxt_def)
+apply (frule parentf_is_dir_prop2, simp)
+apply (erule get_pfs_secs_prop, simp)
+apply (erule_tac search_check_allp_intro, simp_all)
+apply (simp add:parentf_is_dir_prop2)
+done
+
+lemma enrich_proc_prop:
+  "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk>
+   \<Longrightarrow> valid (enrich_proc s p p') \<and> 
+       (\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and> 
+       (\<forall> obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive (enrich_proc s p p') obj) \<and>
+       (files_hung_by_del (enrich_proc s p p') = files_hung_by_del s) \<and> 
+       (\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp) \<and>
+       (\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and> 
+       (\<forall> q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and> 
+       (\<forall> tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f) \<and>
+       (\<forall> tp fd flags. flags_of_proc_fd s tp fd = Some flags \<longrightarrow> 
+                      flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and>
+       (\<forall> q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q) \<and>
+       (\<forall> tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and>
+       (cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and>
+       (\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)"
+proof (induct s)
+  case Nil
+  thus ?case by (auto simp:is_created_proc_def)
+next
+  case (Cons e s)
+  hence vd_cons: "valid (e # s)" and created_cons: "is_created_proc (e # s) p"
+    and all_procs_cons: "p' \<notin> all_procs (e # s)" and vd: "valid s" 
+    and os: "os_grant s e" and grant: "grant s e"
+    by (auto dest:vd_cons vt_grant_os vt_grant)
+  from all_procs_cons have all_procs: "p' \<notin> all_procs s" by (case_tac e, auto)
+  from Cons have pre: "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p') \<and>
+     (\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and>
+     (\<forall>obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive (enrich_proc s p p') obj) \<and>
+     files_hung_by_del (enrich_proc s p p') = files_hung_by_del s \<and>
+     (\<forall>tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp) \<and>
+     (\<forall>f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and>
+     (\<forall>q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and>
+     (\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f) \<and>
+     (\<forall>tp fd flags.
+         flags_of_proc_fd s tp fd = Some flags \<longrightarrow> flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and>
+     (\<forall>q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q) \<and>
+     (\<forall>tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and>     
+     (cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and>
+     (\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)"
+    using vd all_procs by auto
+  have alive_pre: "is_created_proc s p \<Longrightarrow> (\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj)"
+    using pre by simp
+  hence curf_pre: "is_created_proc s p \<Longrightarrow> (\<forall>f. f \<in> current_files s \<longrightarrow> f \<in> current_files (enrich_proc s p p'))"
+    using vd apply auto
+    apply (drule is_file_or_dir, simp)
+    apply (erule disjE)
+    apply (erule_tac x = "O_file f" in allE, simp add:is_file_in_current)
+    apply (erule_tac x = "O_dir f" in allE, simp add:is_dir_in_current)
+    done
+  have vd_enrich_cons: "valid (enrich_proc (e # s) p p')"
+  proof-
+    from pre have pre': "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p')" by simp
+    have "is_created_proc s p \<Longrightarrow> valid (e # enrich_proc s p p')" 
+      apply (frule pre')
+      apply (erule_tac s = s in enrich_valid_intro_cons)
+      apply (simp_all add:os grant vd pre)
+      done  
+    moreover have "\<And>f fds. \<lbrakk>valid (Execve p f fds # enrich_proc s p p'); is_created_proc s p; 
+      valid (Execve p f fds # s); p' \<notin> all_procs s\<rbrakk>
+      \<Longrightarrow> valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')"
+    proof-
+      fix f fds
+      assume a1: "valid (Execve p f fds # enrich_proc s p p')" and a2: "is_created_proc s p"
+        and a3: "valid (Execve p f fds # s)" and a0: "p' \<notin> all_procs s"
+      have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
+        and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
+        and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
+        and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> 
+                                   file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
+        and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
+        and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
+        using pre a2 by auto
+      show "valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')"
+      proof-
+        from a0 a3 have a0': "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3)
+        from a3 have grant: "grant s (Execve p f fds)" and os: "os_grant s (Execve p f fds)"
+          by (auto dest:vt_grant_os vt_grant simp del:os_grant.simps)
+        have f_in: "is_file (enrich_proc s p p') f" 
+        proof-
+          from pre a2
+          have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj"
+            by (auto)
+          show ?thesis using a3 a4
+            apply (erule_tac x = "O_file f" in allE)
+            by (auto dest:vt_grant_os)
+        qed
+        moreover have a5: "proc_file_fds s p \<subseteq> proc_file_fds (Execve p f fds # enrich_proc s p p') p'" 
+          using a3 a0'
+          apply (frule_tac vt_grant_os)
+          apply (auto simp:proc_file_fds_def)
+          apply (rule_tac x = fa in exI)
+          apply (erule enrich_proc_dup_ffd)
+          apply (simp_all add:vd all_procs a2)
+          done
+        ultimately have "os_grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))"
+          apply (auto simp:is_file_simps enrich_proc_dup_in a2 vd all_procs a1 enrich_proc_dup_ffds)
+          done
+        moreover have "grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))"
+        proof-
+          from grant obtain up rp tp uf rf tf 
+            where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+            and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)" 
+            by (simp split:option.splits, blast)
+          with grant obtain pu nr nt where p3: "npctxt_execve (up, rp, tp) (uf, rf, tf) = Some (pu, nr, nt)"
+            by (simp split:option.splits del:npctxt_execve.simps, blast)
+          have p1': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)"
+            using p1 dup_sp a1 a0'
+            apply (simp add:sectxt_of_obj_simps)
+            by (simp add:cp2sproc_def split:option.splits)
+          from os have f_in': "is_file s f"  by simp 
+          from vd os have "\<exists> sf. cf2sfile s f = Some sf"
+            by (auto dest!:is_file_in_current current_file_has_sfile)
+          hence p2': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)" 
+            using f_in p2 cf2sf os a1
+            apply (erule_tac x = f in allE)
+            apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits)
+            apply (case_tac f, simp)
+            apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
+            done 
+          from dup_sfd a5 have "\<forall>fd. fd \<in> proc_file_fds s p \<longrightarrow> 
+            cfd2sfd (Execve p f fds # enrich_proc s p p') p' fd = cfd2sfd s p fd"
+            apply (rule_tac allI)
+            apply (erule_tac x = fd in allE, clarsimp)
+            apply (drule set_mp, simp)
+            apply (auto simp:cfd2sfd_execve proc_file_fds_def a1)
+            done
+          hence "inherit_fds_check (Execve p f fds # enrich_proc s p p') (up, nr, nt) p' (fds \<inter> proc_file_fds s p)"
+            using grant os p1 p2 p3 vd
+            apply (clarsimp)
+            apply (rule_tac s = s and p = p and fds = fds in enrich_inherit_fds_check_dup)
+            apply simp_all
+            done
+          moreover have "search_check (Execve p f fds # enrich_proc s p p') (up, rp, tp) f"
+            using p1 p2 p2' vd cf2sf f_in f_in' grant p3 f_in a1
+            apply (rule_tac s = s in enrich_search_check)
+            apply (simp_all add:is_file_simps)
+            apply (rule allI, rule impI, erule_tac x = fa in allE, simp)
+            apply (drule_tac ff = fa in cf2sfile_other')
+            by (auto simp:a2 curf_pre)
+          ultimately show ?thesis 
+            using p1' p2' p3
+            apply (simp split:option.splits)
+            using grant p1 p2
+            apply simp
+            done
+        qed
+        ultimately show ?thesis using a1
+          by (erule_tac valid.intros(2), auto)
+      qed
+    qed
+    moreover have "\<And>tp fds. \<lbrakk>valid (Clone tp p fds # s); p' \<noteq> p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> 
+      valid (Clone tp p' (fds \<inter> proc_file_fds s tp) # Clone tp p fds # s)"
+      apply (frule vt_grant_os, frule vt_grant, drule not_all_procs_prop3)
+      apply (rule valid.intros(2))
+      apply (simp_all split:option.splits add:sectxt_of_obj_simps)
+      apply (auto simp add:proc_file_fds_def)[1]
+      apply (auto simp:inherit_fds_check_def sectxt_of_obj_simps sectxts_of_fds_def inherit_fds_check_ctxt_def)
+      done
+    moreover have "\<And>f flags fd opt. \<lbrakk>valid (Open p f flags fd opt # enrich_proc s p p'); 
+      is_created_proc s p; valid (Open p f flags fd opt # s); p' \<notin> all_procs s\<rbrakk>
+       \<Longrightarrow> valid (Open p' f (remove_create_flag flags) fd None # Open p f flags fd opt # enrich_proc s p p')"
+    proof-
+      fix f flags fd opt
+      assume a1: "valid (Open p f flags fd opt # enrich_proc s p p')" and a2: "is_created_proc s p"
+        and a3: "valid (Open p f flags fd opt # s)" and a4: "p' \<notin> all_procs s"
+      have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
+        and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
+        and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
+        and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> 
+                                   file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
+        and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
+        and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
+        using pre a2 by auto
+      from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3 split:option.splits)
+      have a5: "p' \<in> current_procs (enrich_proc s p p')" 
+        using a2 a3 vd
+        apply (erule_tac enrich_proc_dup_in)
+        by (simp_all add:vd a4)
+      have a6: "is_file (Open p f flags fd opt # enrich_proc s p p') f"
+        using a1 a3
+        by (auto simp:is_file_open dest:vt_grant_os)
+      have a7: "fd \<notin> current_proc_fds (enrich_proc s p p') p'"
+        using a2 a4 vd
+        apply (simp add:enrich_proc_dup_ffds_eq_fds)
+        apply (rule notI)
+        apply (drule_tac p = p in file_fds_subset_pfds)
+        apply (drule set_mp, simp)
+        using a3
+        apply (drule_tac vt_grant_os)
+        apply (auto split:option.splits)
+        done
+      from a1 have a8: "valid (enrich_proc s p p')" by (erule_tac valid.cases, auto)
+      from a3 have grant: "grant s (Open p f flags fd opt)" and os: "os_grant s (Open p f flags fd opt)"
+        by (auto dest:vt_grant_os vt_grant)
+      show "valid (Open p' f (remove_create_flag flags) fd None # Open p f flags fd opt # enrich_proc s p p')"
+      proof (cases opt)
+        case None
+        have f_in: "is_file (enrich_proc s p p') f" 
+        proof-
+          from pre a2
+          have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj"
+            by (auto)
+          show ?thesis using a3 a4 None
+            apply (erule_tac x = "O_file f" in allE)
+            by (auto dest:vt_grant_os)
+        qed
+        from grant None obtain up rp tp uf rf tf 
+          where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+          and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)" 
+          apply (simp split:option.splits)
+          by (case_tac a, case_tac aa, blast)
+        have p1': "sectxt_of_obj (Open p f flags fd opt # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)"
+          using p1 dup_sp a1
+          apply (simp add:sectxt_of_obj_simps)
+          by (simp add:cp2sproc_def split:option.splits)
+        from os None have f_in': "is_file s f" by simp 
+        from vd os None have "\<exists> sf. cf2sfile s f = Some sf"
+          by (auto dest!:is_file_in_current current_file_has_sfile)
+        hence p2': "sectxt_of_obj (Open p f flags fd opt # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)" 
+          using p2 cf2sf os a1 None f_in' vd f_in
+          apply (erule_tac x = f in allE)
+          apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits)
+          apply (case_tac f, simp)
+          apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
+          done 
+        have "search_check (Open p f flags fd opt # enrich_proc s p p') (up, rp, tp) f"
+          using p1 p2 p2' vd cf2sf f_in f_in' grant f_in a1 None
+          apply (rule_tac s = s in enrich_search_check)
+          apply (simp_all add:is_file_simps)
+          apply (rule allI, rule impI, erule_tac x = fa in allE, simp)
+          apply (simp add:cf2sfile_open_none)
+          done
+        thus ?thesis using a0 a5 a6 a7 None a1
+          apply (rule_tac valid.intros(2))
+          apply (simp_all add:a1)
+          apply (case_tac flags, simp add:is_creat_excl_flag_def)
+          using p1' p2'
+          apply simp
+          using grant p1 p2
+          apply (simp add:oflags_check_remove_create)
+          done
+      next
+        case (Some inum)
+        with os obtain pf where parent: "parent f = Some pf" by auto
+        with grant Some obtain pu rp pt pfu pfr pft where
+          p1: "sectxt_of_obj s (O_proc p) = Some (pu, rp, pt)" 
+          and p2: "sectxt_of_obj s (O_dir pf) = Some (pfu, pfr, pft)"
+          apply (simp split:option.splits)
+          apply (case_tac a, case_tac aa, blast)
+          done
+        from p1 have p1': "sectxt_of_obj (enrich_proc s p p') (O_proc p) = Some (pu, rp, pt)"
+          using cp2sp os
+          apply (erule_tac x = p in allE)
+          apply (auto split:option.splits simp:cp2sproc_def)
+          done
+        from os parent Some
+        have pf_in: "is_dir s pf" by auto
+        hence "\<exists> sf. cf2sfile s pf = Some sf" using vd
+          by (auto dest!:is_dir_in_current current_file_has_sfile)
+        from a1 parent Some have pf_in': "is_dir (enrich_proc s p p') pf" 
+          apply (frule_tac vt_grant_os)
+          by (clarsimp)
+        have p2': "sectxt_of_obj (enrich_proc s p p') (O_dir pf) = Some (pfu, pfr, pft)"
+        proof-
+          have "cf2sfile (enrich_proc s p p') pf = cf2sfile s pf"
+            using cf2sf pf_in
+            apply (drule_tac is_dir_in_current)
+            apply (erule_tac x = pf in allE)
+            by simp
+          with pf_in pf_in' p2 vd Some a8
+          show ?thesis            
+            apply (frule_tac is_dir_not_file)
+            apply (frule_tac s = "enrich_proc s p p'" in is_dir_not_file)
+            apply (simp add:cf2sfile_def)
+            apply (case_tac pf, simp) 
+            apply (simp add:sroot_def root_sec_remains)            
+            by (auto split:option.splits dest!:current_has_sec' get_pfs_secs_prop' dest:parentf_is_dir_prop1)        
+        qed
+        from p1 have dup: "sectxt_of_obj (Open p f flags fd (Some inum) # enrich_proc s p p') (O_proc p') 
+          = Some (pu, rp, pt)"
+          using a1 Some
+          apply (simp add:sec_open)
+          using dup_sp
+          apply (auto split:option.splits if_splits simp:cp2sproc_def)
+          done        
+        have nsf: "sectxt_of_obj (Open p f flags fd (Some inum) # enrich_proc s p p') (O_file f) 
+          = Some (pu, R_object, type_transition pt pft C_file True)"
+          using a1 Some p1 p2 parent p2' p1'
+          by (simp add:sec_open)
+        have "search_check (Open p f flags fd (Some inum) # enrich_proc s p p') (pu, rp, pt) f"
+        proof-
+          have "search_check (Open p f flags fd (Some inum) # enrich_proc s p p') (pu, rp, pt) pf"
+            using grant Some parent p1 p2 vd a1 pf_in pf_in' p2'
+            apply simp 
+            apply (rule_tac s = s in enrich_search_check') 
+            apply (simp_all add:is_dir_simps sectxt_of_obj_simps)
+            apply (rule allI, rule impI)
+            apply (case_tac "fa = f")
+            using os Some
+            apply simp
+            apply (drule_tac f' = fa in cf2sfile_open)
+            apply (simp add:current_files_simps)
+            using curf_pre a2
+            apply simp
+            apply simp
+            using cf2sf
+            apply simp
+            done
+          moreover have "is_file (Open p f flags fd (Some inum) # enrich_proc s p p') f"
+            using a1 Some
+            by (simp add:is_file_open)
+          ultimately 
+          show ?thesis
+            using parent a1 Some nsf
+            apply (erule_tac search_check_leveling_f)
+            apply (simp_all)
+            apply (simp add:search_check_file_def)
+            apply (simp add:permission_check.simps)
+            sorry
+        qed
+        thus ?thesis using a0 a5 a6 a7 a1 Some
+          apply (rule_tac valid.intros(2))
+          apply (simp add:a1)
+          apply simp
+          apply (case_tac flags, simp add:is_creat_excl_flag_def)
+          using grant p1 p2 parent dup nsf
+          apply (simp add:oflags_check_remove_create)
+          done
+      qed
+    qed
+    moreover have "\<And>fd. \<lbrakk>valid (CloseFd p fd # enrich_proc s p p'); is_created_proc s p; 
+      valid (CloseFd p fd # s); p' \<notin> all_procs s; fd \<in> proc_file_fds s p\<rbrakk>
+      \<Longrightarrow> valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')"
+    proof-
+      fix fd
+      assume a1: "valid (CloseFd p fd # enrich_proc s p p')" and a2: "is_created_proc s p" 
+        and a3: "p' \<notin> all_procs s" and a4: "valid (CloseFd p fd # s)"
+        and a5: "fd \<in> proc_file_fds s p"
+      from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3)
+      have "p' \<in> current_procs (enrich_proc s p p')" 
+        using a2 a3 vd
+        by (auto intro:enrich_proc_dup_in)
+      moreover have "fd \<in> current_proc_fds (enrich_proc s p p') p'"      
+        using a5 a2 a3 vd pre'
+        apply (simp)
+        apply (drule_tac s = "enrich_proc s p p'" and p = p' in file_fds_subset_pfds)
+        apply (erule set_mp)
+        apply (simp add:enrich_proc_dup_ffds)
+        done
+      ultimately show "valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')"
+        apply (rule_tac valid.intros(2))
+        apply (simp_all add:a1 a0 a2 pre')
+        done
+    qed
+    moreover have "\<And> fd. \<lbrakk>valid (ReadFile p fd # enrich_proc s p p');
+            is_created_proc s p; valid (ReadFile p fd # s); p' \<notin> all_procs s\<rbrakk>
+           \<Longrightarrow> valid (ReadFile p' fd # ReadFile p fd # enrich_proc s p p')"
+    proof-
+      fix fd
+      assume a1: "valid (ReadFile p fd # enrich_proc s p p')" and a2: "is_created_proc s p"
+        and a3: "valid (ReadFile p fd # s)" and a4: "p' \<notin> all_procs s"
+      from a3 have os: "os_grant s (ReadFile p fd)" and grant: "grant s (ReadFile p fd)"
+        by (auto dest:vt_grant_os vt_grant)
+      have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
+        and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
+        and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
+        and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> 
+                                   file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
+        and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
+        and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
+        using pre a2 by auto
+      have vd_enrich: "valid (enrich_proc s p p')" using a1 by (auto dest:valid.cases)
+      show "valid (ReadFile p' fd # ReadFile p fd # enrich_proc s p p')"
+      proof-
+        have "os_grant (ReadFile p fd # enrich_proc s p p') (ReadFile p' fd)"
+          using a1 a2 a4 vd os
+          apply (clarsimp simp:current_files_simps enrich_proc_dup_in enrich_proc_dup_ffds_eq_fds)
+          apply (simp add:proc_file_fds_def)
+          apply (rule conjI)
+          apply (rule_tac x = f in exI, simp add:enrich_proc_dup_ffd)
+          using curf_pre
+          apply (simp)
+          apply (drule enrich_proc_dup_fflags)
+          apply simp_all
+          apply (erule disjE)
+          apply auto
+          apply (simp add:is_read_flag_def)
+          done
+        moreover have "grant (ReadFile p fd # enrich_proc s p p') (ReadFile p' fd)"
+        proof-
+          from grant obtain f sp sfd sf where p1: "file_of_proc_fd s p fd = Some f"
+            and p2: "sectxt_of_obj s (O_proc p) = Some sp" 
+            and p3: "sectxt_of_obj s (O_fd p fd) = Some sfd"
+            and p4: "sectxt_of_obj s (O_file f) = Some sf"
+            by (auto split:option.splits) 
+          from os obtain flag where p0: "flags_of_proc_fd s p fd = Some flag"
+            by auto
+          from os have f_in_s: "f \<in> current_files s" using p1 by simp
+          from p1 vd have isfile_s: "is_file s f" by (erule_tac file_of_pfd_is_file, simp)
+          with alive_pre a2 have isfile_s': "is_file (enrich_proc s p p') f"
+            apply simp
+            apply (erule_tac x = "O_file f" in allE, simp)
+            done          
+          from p0 obtain flag' where p0': "flags_of_proc_fd (enrich_proc s p p') p' fd = Some flag'"
+            and p0'': "(flag' = flag) \<or> (flag' = remove_create_flag flag)"
+            using a2 a4 vd
+            apply (drule_tac enrich_proc_dup_fflags)
+            apply auto
+            apply (case_tac flag, auto)
+            apply (case_tac flag, auto)
+            done            
+          from p1 have p1': "file_of_proc_fd (enrich_proc s p p') p' fd = Some f"
+            using a2 a4 vd
+            by (simp add:enrich_proc_dup_ffd)
+          from p2 have p2': "sectxt_of_obj (enrich_proc s p p') (O_proc p') = Some sp"
+            using dup_sp
+            by (auto simp:cp2sproc_def split:option.splits)
+          from p3 p1 p1' p0 p0' os have p3': "sectxt_of_obj (enrich_proc s p p') (O_fd p' fd) = Some sfd"
+            using dup_sfd
+            apply (erule_tac x = fd in allE)
+            apply (auto simp:proc_file_fds_def cfd2sfd_def split:option.splits)
+            apply (drule current_file_has_sfile')
+            apply (simp add:vd, simp)
+            apply (drule current_file_has_sfile')
+            apply (simp add:vd, simp)
+            done
+          from p4 have p4': "sectxt_of_obj (enrich_proc s p p') (O_file f) = Some sf" 
+            using f_in_s cf2sf isfile_s isfile_s' a1 vd_enrich vd
+            apply (erule_tac x = f in allE)
+            apply (simp)
+            apply (auto simp:cf2sfile_def split:option.splits 
+              dest!:current_has_sec' get_pfs_secs_prop' dest:parentf_is_dir is_file_in_current)
+            apply (case_tac f, simp, drule root_is_dir', simp, simp, simp)
+            done
+          show ?thesis using p1' p2' p3' p4' a1
+            apply (simp add:sectxt_of_obj_simps)
+            using grant p1 p2 p3 p4 
+            apply simp
+            done
+        qed
+        ultimately show ?thesis
+          using a1
+          by (erule_tac valid.intros(2), simp+)
+      qed
+    qed
+    ultimately show ?thesis 
+      using created_cons vd_cons all_procs_cons
+      apply (case_tac e)
+      apply (auto simp:is_created_proc_simps split:if_splits)
+      done
+  qed
+  moreover have "\<forall>obj. alive (e # s) obj \<longrightarrow> alive (enrich_proc (e # s) p p') obj"
+    sorry
+  moreover have "\<forall>obj. enrich_not_alive (e # s) obj \<longrightarrow> enrich_not_alive (enrich_proc (e # s) p p') obj"
+    sorry
+  moreover have "files_hung_by_del (enrich_proc (e # s) p p') = files_hung_by_del (e # s)"
+    sorry
+  moreover have "\<forall>tp. tp \<in> current_procs (e # s) \<longrightarrow> cp2sproc (enrich_proc (e # s) p p') tp = cp2sproc (e # s) tp"
+    sorry
+  moreover have "\<forall>f. f \<in> current_files (e # s) \<longrightarrow> cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
+    sorry
+  moreover have "\<forall>q. q \<in> current_msgqs (e # s) \<longrightarrow> cq2smsgq (enrich_proc (e # s) p p') q = cq2smsgq (e # s) q"
+    sorry
+  moreover have "\<forall>tp fd f. file_of_proc_fd (e # s) tp fd = Some f \<longrightarrow> 
+    file_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some f"
+    sorry
+  moreover have "\<forall>tp fd flags. flags_of_proc_fd (e # s) tp fd = Some flags \<longrightarrow>
+        flags_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some flags"
+    sorry
+  moreover have "\<forall>q. msgs_of_queue (enrich_proc (e # s) p p') q = msgs_of_queue (e # s) q"
+    sorry 
+  moreover have "\<forall>tp fd. fd \<in> proc_file_fds (e # s) tp \<longrightarrow> 
+    cfd2sfd (enrich_proc (e # s) p p') tp fd = cfd2sfd (e # s) tp fd"
+    sorry 
+  moreover have "cp2sproc (enrich_proc (e # s) p p') p' = cp2sproc (e # s) p"
+  proof-
+    from pre have b0: "is_created_proc s p \<Longrightarrow> cp2sproc (enrich_proc s p p') p' = cp2sproc s p" by simp
+    have b1: "\<And> tp f fds. \<lbrakk>valid (enrich_proc (Execve tp f fds # s) p p'); valid (Execve tp f fds # s);
+      is_created_proc (Execve tp f fds # s) p; p' \<notin> all_procs (Execve tp f fds # s)\<rbrakk>
+      \<Longrightarrow> cp2sproc (enrich_proc (Execve tp f fds # s) p p') p' = cp2sproc (Execve tp f fds # s) p"
+    proof-
+      fix tp f fds
+      assume a1: "valid (enrich_proc (Execve tp f fds # s) p p')"
+      and a2: "valid (Execve tp f fds # s)" and a3: "is_created_proc (Execve tp f fds # s) p"
+      and a4: "p' \<notin> all_procs (Execve tp f fds # s)"
+      show "cp2sproc (enrich_proc (Execve tp f fds # s) p p') p' = cp2sproc (Execve tp f fds # s) p"
+      proof (cases "tp = p")
+        case True
+        show ?thesis using True a1 a2 a3 a4
+          thm not_all_procs_prop3
+          apply (auto simp add:cp2sproc_execve is_created_proc_def split:option.splits dest!:current_has_sec' 
+            dest:vt_grant_os not_all_procs_prop2 not_all_procs_prop3)
+          
+          sorry
+      next
+        case False
+        show ?thesis sorry
+      qed
+    qed
+    have b2: "\<And> tp fd. cp2sproc (enrich_proc (ReadFile tp fd # s) p p') p' = cp2sproc (ReadFile tp fd # s) p"
+      sorry
+    have b3: "\<And> tp. cp2sproc (enrich_proc (Exit tp # s) p p') p' = cp2sproc (Exit tp # s) p"
+      sorry
+    have b4: "\<And> tp tp'. cp2sproc (enrich_proc (Kill tp tp' # s) p p') p' = cp2sproc (Kill tp tp' # s) p"
+      sorry
+    have b5: "\<And> tp tp' fds. cp2sproc (enrich_proc (Clone tp tp' fds # s) p p') p' = 
+      cp2sproc (Clone tp tp' fds # s) p"
+      sorry
+    have b6: "\<And> tp f flags fd opt. cp2sproc (enrich_proc (Open tp f flags fd opt # s) p p') p' =
+      cp2sproc (Open tp f flags fd opt # s) p"
+      sorry
+    have b7: "\<And> tp fd. cp2sproc (enrich_proc (CloseFd tp fd # s) p p') p' = cp2sproc (CloseFd tp fd # s) p"
+      sorry
+    show ?thesis using vd_enrich_cons
+      apply (case_tac e)
+      apply (simp_all only:b1 b2 b3 b4 b5 b6 b7)
+      using created_cons vd_enrich_cons vd_cons b0
+      apply (auto simp:cp2sproc_other is_created_proc_def)
+      done
+  qed
+  moreover have "\<forall> fd. fd \<in> proc_file_fds (e # s) p \<longrightarrow> 
+    cfd2sfd (enrich_proc (e # s) p p') p' fd = cfd2sfd (e # s) p fd"
+    sorry
+  ultimately show ?case
+    by simp
+qed
+  
+
+lemma enrich_proc_valid:
+  "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (enrich_proc s p p')"
+by (auto dest:enrich_proc_prop)
+
+lemma enrich_proc_valid:
+  "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> " 
+
+ 
+
+lemma enrich_proc_tainted: 
+  "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
+   \<Longrightarrow> tainted (enrich_proc s p p') = (if (O_proc p \<in> tainted s) 
+         then tainted s \<union> {O_proc p'} else tainted s)"
+apply (induct s)
+apply (simp add:is_created_proc_def)
+apply (frule vt_grant_os, frule vd_cons, simp)
+apply (frule enrich_proc_dup_in, simp+)
+apply (frule not_all_procs_prop3)
+apply (case_tac a)
+prefer 3
+apply (simp split:if_splits)
+apply (rule impI|rule conjI)+
+apply (simp add:is_created_proc_def)
+apply (auto simp:is_created_proc_def split:if_splits dest:tainted_in_current)[1]
+apply (simp add:is_created_proc_def)
+
+prefer 4
+apply (simp split:if_splits)
+apply (rule impI|rule conjI)+
+apply (simp add:is_created_proc_def)
+apply (auto simp:is_created_proc_def split:if_splits dest:tainted_in_current)[1]
+apply (simp add:is_created_proc_def)
+
+prefer 4
+apply (auto simp:is_created_proc_def split:if_splits option.splits dest:tainted_in_current)[1]
+
+prefer 4
+apply (auto simp:is_created_proc_def split:if_splits option.splits dest:tainted_in_current enrich_proc_dup_ffd enrich_proc_dup_ffd')[1]
+
+
+
+lemma enrich_proc_dup_tainted:
+  "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
+   \<Longrightarrow> (O_proc p' \<in> tainted (enrich_proc s p p')) = (O_proc p \<in> tainted s)"
+apply (induct s)
+apply (simp add:is_created_proc_def)
+apply (frule vt_grant_os, frule vd_cons)
+apply (case_tac a)
+apply (auto simp:is_created_proc_def)[1]
+
+
+lemma enrich_proc_tainted:
+  ""
+
+
+end
+
+end
\ No newline at end of file




