--- a/Delete_prop.thy	Wed May 08 10:00:38 2013 +0800
+++ b/Delete_prop.thy	Thu May 09 11:19:44 2013 +0800
@@ -1,5 +1,5 @@
 theory Deleted_prop
-imports Main Flask Flask_type Init_prop Alive_prop
+imports Main Flask Flask_type Init_prop Alive_prop Current_files_prop
 begin
 
 context flask begin
@@ -10,21 +10,132 @@
 lemma not_deleted_cons_D: "\<not> deleted obj (e # s) \<Longrightarrow> \<not> deleted obj s" 
 by (auto dest:deleted_cons_I)
 
-lemma not_deleted_imp_exists:
+lemma not_deleted_init_file:
+  "\<lbrakk>\<not> deleted (O_file f) s; valid s; is_init_file f\<rbrakk> \<Longrightarrow> is_file s f"
+apply (induct s, simp add:is_init_file_prop1)
+apply (frule vd_cons, frule vt_grant_os)
+apply (case_tac a) prefer 6 apply (case_tac option)
+apply (auto simp:is_file_simps split:option.splits)
+done
+
+lemma not_deleted_init_dir:
+  "\<lbrakk>\<not> deleted (O_dir f) s; valid s; is_init_dir f\<rbrakk> \<Longrightarrow> is_dir s f"
+apply (induct s, simp add:is_init_dir_prop1)
+apply (frule vd_cons, frule vt_grant_os)
+apply (case_tac a) prefer 6 apply (case_tac option)
+apply (auto simp:is_dir_simps split:option.splits)
+done
+
+lemma not_deleted_init_proc:
+  "\<lbrakk>\<not> deleted (O_proc p) s; p \<in> init_procs\<rbrakk> \<Longrightarrow> p \<in> current_procs s"
+apply (induct s, simp)
+by (case_tac a, auto)
+
+(**** ???*)
+lemma current_fd_imp_current_proc:
+  "\<lbrakk>fd \<in> current_proc_fds s p; valid s\<rbrakk> \<Longrightarrow> p \<in> current_procs s"
+apply (induct s)
+apply (simp add:init_fds_of_proc_prop1)
+apply (frule vd_cons, drule vt_grant_os, case_tac a)
+by (auto split:if_splits option.splits)
+
+lemma not_deleted_init_fd_aux:
+  "\<lbrakk>\<not> deleted (O_fd p fd) s; valid s; fd \<in> init_fds_of_proc p\<rbrakk> 
+   \<Longrightarrow> fd \<in> current_proc_fds s p \<and> \<not> deleted (O_proc p) s"
+apply (induct s arbitrary: p, simp)
+apply (frule vd_cons, drule vt_grant_os)
+apply (case_tac a, auto dest:current_fd_imp_current_proc)
+done
+
+lemma not_deleted_init_fd2:
+  "\<lbrakk>\<not> deleted (O_fd p fd) s; fd \<in> init_fds_of_proc p; valid s\<rbrakk> \<Longrightarrow> \<not> deleted (O_proc p) s"
+by (auto dest:not_deleted_init_fd_aux)
+
+lemma not_deleted_init_fd1:
+  "\<lbrakk>\<not> deleted (O_fd p fd) s; valid s; fd \<in> init_fds_of_proc p\<rbrakk> \<Longrightarrow> fd \<in> current_proc_fds s p"
+by (auto dest:not_deleted_init_fd_aux)
+
+lemma not_deleted_init_tcp_aux:
+  "\<lbrakk>\<not> deleted (O_tcp_sock (p,fd)) s; valid s; is_init_tcp_sock (p,fd)\<rbrakk> 
+   \<Longrightarrow> is_tcp_sock s (p,fd) \<and> \<not> deleted (O_proc p) s"
+apply (induct s arbitrary:p, simp add:is_init_tcp_sock_prop1)
+apply (frule vd_cons, frule vt_grant_os)
+apply (case_tac a) prefer 6 apply (case_tac option)
+by (auto simp:is_tcp_sock_simps split:option.splits t_socket_type.splits 
+         dest:is_tcp_sock_imp_curernt_proc)
+
+lemma not_deleted_init_tcp1:
+  "\<lbrakk>\<not> deleted (O_tcp_sock (p,fd)) s; valid s; is_init_tcp_sock (p,fd)\<rbrakk> 
+   \<Longrightarrow> is_tcp_sock s (p,fd)"
+by (auto dest:not_deleted_init_tcp_aux)
+
+lemma not_deleted_init_tcp2:
+  "\<lbrakk>\<not> deleted (O_tcp_sock (p,fd)) s; valid s; is_init_tcp_sock (p,fd)\<rbrakk> 
+   \<Longrightarrow> \<not> deleted (O_proc p) s"
+by (auto dest:not_deleted_init_tcp_aux)
+
+lemma not_deleted_init_udp_aux:
+  "\<lbrakk>\<not> deleted (O_udp_sock (p,fd)) s; valid s; is_init_udp_sock (p,fd)\<rbrakk> 
+   \<Longrightarrow> is_udp_sock s (p,fd) \<and> \<not> deleted (O_proc p) s"
+apply (induct s arbitrary:p, simp add:is_init_udp_sock_prop1)
+apply (frule vd_cons, frule vt_grant_os)
+apply (case_tac a) prefer 6 apply (case_tac option)
+by (auto simp:is_udp_sock_simps split:option.splits t_socket_type.splits 
+         dest:is_udp_sock_imp_curernt_proc)
+
+lemma not_deleted_init_udp1:
+  "\<lbrakk>\<not> deleted (O_udp_sock (p,fd)) s; valid s; is_init_udp_sock (p,fd)\<rbrakk> 
+   \<Longrightarrow> is_udp_sock s (p,fd)"
+by (auto dest:not_deleted_init_udp_aux)
+
+lemma not_deleted_init_udp2:
+  "\<lbrakk>\<not> deleted (O_udp_sock (p,fd)) s; valid s; is_init_udp_sock (p,fd)\<rbrakk> 
+   \<Longrightarrow> \<not> deleted (O_proc p) s"
+by (auto dest:not_deleted_init_udp_aux)
+
+lemma not_deleted_init_shm:
+  "\<lbrakk>\<not> deleted (O_shm h) s; h \<in> init_shms\<rbrakk> \<Longrightarrow> h \<in> current_shms s"
+apply (induct s, simp)
+by (case_tac a, auto)
+
+lemma not_deleted_init_msgq:
+  "\<lbrakk>\<not> deleted (O_msgq q) s; q \<in> init_msgqs\<rbrakk> \<Longrightarrow> q \<in> current_msgqs s"
+apply (induct s, simp)
+by (case_tac a, auto)
+
+lemma current_msg_imp_current_msgq:
+  "\<lbrakk>m \<in> set (msgs_of_queue s q); valid s\<rbrakk> \<Longrightarrow> q \<in> current_msgqs s"
+apply (induct s)
+apply (simp add:init_msgs_valid)
+apply (frule vd_cons, drule vt_grant_os)
+apply (case_tac a, auto split:if_splits)
+done
+
+lemma not_deleted_init_msg:
+  "\<lbrakk>\<not> deleted (O_msg q m) s; valid s; m \<in> set (init_msgs_of_queue q)\<rbrakk> \<Longrightarrow> m \<in> set (msgs_of_queue s q)"
+apply (induct s, simp)
+apply (frule vd_cons, frule vt_grant_os)
+apply (case_tac a, auto dest:current_msg_imp_current_msgq)
+apply (case_tac "msgs_of_queue s q", simp+)
+done
+
+lemma not_deleted_imp_alive:
   "\<lbrakk>\<not> deleted obj s; valid s; init_alive obj\<rbrakk> \<Longrightarrow> alive s obj"
-apply (induct s, simp add:init_alive_prop)
-apply (frule vd_cons)
-apply (case_tac a, auto simp:alive_simps split:t_object.splits)
-pr 19
+apply (case_tac obj)
+apply (auto dest!:not_deleted_init_msg not_deleted_init_file not_deleted_init_dir not_deleted_init_proc
+  not_deleted_init_fd1 not_deleted_init_tcp1 not_deleted_init_udp1 not_deleted_init_shm 
+  not_deleted_init_msgq 
+           intro:is_file_in_current is_dir_in_current is_tcp_in_current is_udp_in_current 
+  current_msg_imp_current_msgq)
 done
 
 lemma cons_app_simp_aux:
   "(a # b) @ c = a # (b @ c)" by auto
 
-lemma not_deleted_imp_exists':
-  "\<lbrakk>\<not> deleted obj (s'@s); exists s obj\<rbrakk> \<Longrightarrow> exists (s'@s) obj"
+lemma not_deleted_imp_alive_app:
+  "\<lbrakk>\<not> deleted obj (s'@s); alive s obj\<rbrakk> \<Longrightarrow> alive (s'@s) obj"
 apply (induct s', simp, simp only:cons_app_simp_aux)
-apply (frule not_deleted_cons_D)
+apply (frule not_deleted_cons_D, simp)
 apply (case_tac a, case_tac [!] obj, auto)
 done