159 qed |
159 qed |
160 hence "sectxts_of_fds s' p fds = sectxts_of_fds s p fds" |
160 hence "sectxts_of_fds s' p fds = sectxts_of_fds s p fds" |
161 by (simp add:sectxts_of_fds_def) |
161 by (simp add:sectxts_of_fds_def) |
162 thus ?thesis using grant |
162 thus ?thesis using grant |
163 by (simp add:inherit_fds_check_def) |
163 by (simp add:inherit_fds_check_def) |
|
164 qed |
|
165 |
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166 |
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167 lemma enrich_inherit_fds_check_dup: |
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168 assumes grant: "inherit_fds_check s (up, nr, nt) p fds" and vd: "valid s" |
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169 and cfd2sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd s' p' fd = cfd2sfd s p fd" |
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170 and fd_in: "fds' \<subseteq> fds \<inter> proc_file_fds s p" |
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171 shows "inherit_fds_check s' (up, nr, nt) p' fds'" |
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172 proof- |
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173 have "sectxts_of_fds s' p' fds' \<subseteq> sectxts_of_fds s p fds" |
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174 proof- |
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175 have "\<And> fd sfd. \<lbrakk>fd \<in> fds'; sectxt_of_obj s' (O_fd p' fd) = Some sfd\<rbrakk> |
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176 \<Longrightarrow> \<exists> fd \<in> fds. sectxt_of_obj s (O_fd p fd) = Some sfd" |
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177 proof- |
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178 fix fd sfd |
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179 assume fd_in_fds': "fd \<in> fds'" |
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180 and sec: "sectxt_of_obj s' (O_fd p' fd) = Some sfd" |
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181 from fd_in_fds' fd_in |
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182 have fd_in_fds: "fd \<in> fds" and fd_in_cfds: "fd \<in> proc_file_fds s p" |
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183 by auto |
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184 from fd_in_cfds obtain f where ffd: "file_of_proc_fd s p fd = Some f" |
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185 by (auto simp:proc_file_fds_def) |
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186 moreover have "flags_of_proc_fd s p fd \<noteq> None" |
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187 using ffd vd by (auto dest:current_filefd_has_flags) |
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188 moreover have "cf2sfile s f \<noteq> None" |
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189 apply (rule notI) |
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190 apply (drule current_file_has_sfile') |
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191 using ffd |
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192 by (auto simp:vd is_file_in_current dest:file_of_pfd_is_file) |
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193 moreover have "sectxt_of_obj s (O_fd p fd) \<noteq> None" |
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194 using fd_in_cfds vd |
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195 apply (rule_tac notI) |
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196 by (auto dest!:current_has_sec' file_fds_subset_pfds[where p = p] intro:vd) |
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197 ultimately |
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198 have "sectxt_of_obj s (O_fd p fd) = Some sfd" |
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199 using fd_in_cfds cfd2sfd sec |
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200 apply (erule_tac x = fd in allE) |
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201 apply (auto simp:cfd2sfd_def split:option.splits) |
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202 done |
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203 thus "\<exists> fd \<in> fds. sectxt_of_obj s (O_fd p fd) = Some sfd" |
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204 using fd_in_fds |
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205 by (rule_tac x = fd in bexI, auto) |
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206 qed |
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207 thus ?thesis by (auto simp:sectxts_of_fds_def) |
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208 qed |
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209 thus ?thesis using grant |
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210 by (auto simp:inherit_fds_check_def inherit_fds_check_ctxt_def) |
164 qed |
211 qed |
165 |
212 |
166 lemma not_all_procs_cons: |
213 lemma not_all_procs_cons: |
167 "p \<notin> all_procs (e # s) \<Longrightarrow> p \<notin> all_procs s" |
214 "p \<notin> all_procs (e # s) \<Longrightarrow> p \<notin> all_procs s" |
168 by (case_tac e, auto) |
215 by (case_tac e, auto) |
1103 apply (frule vt_grant_os, frule vd_cons) |
1150 apply (frule vt_grant_os, frule vd_cons) |
1104 apply (case_tac a, auto simp:is_created_proc_def proc_file_fds_def |
1151 apply (case_tac a, auto simp:is_created_proc_def proc_file_fds_def |
1105 dest:not_all_procs_prop3 split:if_splits option.splits) |
1152 dest:not_all_procs_prop3 split:if_splits option.splits) |
1106 done |
1153 done |
1107 |
1154 |
|
1155 lemma enrich_proc_dup_ffd': |
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1156 "\<lbrakk>file_of_proc_fd (enrich_proc s p p') p' fd = Some f; is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk> |
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1157 \<Longrightarrow> file_of_proc_fd s p fd = Some f" |
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1158 apply (induct s, simp add:is_created_proc_def) |
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1159 apply (frule vt_grant_os, frule vd_cons) |
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1160 apply (case_tac a, auto simp:is_created_proc_def proc_file_fds_def |
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1161 dest:not_all_procs_prop3 split:if_splits option.splits) |
|
1162 done |
|
1163 |
1108 lemma current_fflag_in_fds: |
1164 lemma current_fflag_in_fds: |
1109 "\<lbrakk>flags_of_proc_fd s p fd = Some flag; valid s\<rbrakk> \<Longrightarrow> fd \<in> current_proc_fds s p" |
1165 "\<lbrakk>flags_of_proc_fd s p fd = Some flag; valid s\<rbrakk> \<Longrightarrow> fd \<in> current_proc_fds s p" |
1110 apply (induct s arbitrary:p) |
1166 apply (induct s arbitrary:p) |
1111 apply (simp add:flags_of_proc_fd.simps file_of_proc_fd.simps init_oflags_prop2) |
1167 apply (simp add:flags_of_proc_fd.simps file_of_proc_fd.simps init_oflags_prop2) |
1112 apply (frule vd_cons, frule vt_grant_os, case_tac a) |
1168 apply (frule vd_cons, frule vt_grant_os, case_tac a) |
1113 apply (auto split:if_splits option.splits dest:proc_fd_in_fds) |
1169 apply (auto split:if_splits option.splits dest:proc_fd_in_fds) |
1114 apply (auto simp:proc_file_fds_def) |
1170 done |
1115 sorry |
|
1116 |
|
1117 |
1171 |
1118 lemma current_fflag_has_ffd: |
1172 lemma current_fflag_has_ffd: |
1119 "\<lbrakk>flags_of_proc_fd s p fd = Some flag; valid s\<rbrakk> \<Longrightarrow> \<exists> f. file_of_proc_fd s p fd = Some f" |
1173 "\<lbrakk>flags_of_proc_fd s p fd = Some flag; valid s\<rbrakk> \<Longrightarrow> \<exists> f. file_of_proc_fd s p fd = Some f" |
1120 apply (induct s arbitrary:p) |
1174 apply (induct s arbitrary:p) |
1121 apply (simp add: file_of_proc_fd.simps init_fileflag_valid) |
1175 apply (simp add: file_of_proc_fd.simps init_fileflag_valid) |
1122 apply (frule vd_cons, frule vt_grant_os, case_tac a) |
1176 apply (frule vd_cons, frule vt_grant_os, case_tac a) |
1123 apply (auto split:if_splits option.splits dest:proc_fd_in_fds) |
1177 apply (auto split:if_splits option.splits dest:proc_fd_in_fds) |
|
1178 done |
|
1179 |
|
1180 lemma enrich_proc_dup_fflags: |
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1181 "\<lbrakk>flags_of_proc_fd s p fd = Some flag; is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk> |
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1182 \<Longrightarrow> flags_of_proc_fd (enrich_proc s p p') p' fd = Some (remove_create_flag flag) \<or> |
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1183 flags_of_proc_fd (enrich_proc s p p') p' fd = Some flag" |
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1184 apply (induct s arbitrary:p, simp add:is_created_proc_def) |
|
1185 apply (frule vt_grant_os, frule vd_cons) |
|
1186 apply (case_tac a, auto simp:is_created_proc_def proc_file_fds_def is_creat_flag_def |
|
1187 dest:not_all_procs_prop3 split:if_splits option.splits) |
|
1188 done |
|
1189 |
|
1190 lemma enrich_proc_dup_ffds: |
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1191 "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk> |
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1192 \<Longrightarrow> proc_file_fds (enrich_proc s p p') p' = proc_file_fds s p" |
1124 apply (auto simp:proc_file_fds_def) |
1193 apply (auto simp:proc_file_fds_def) |
1125 sorry |
1194 apply (rule_tac x = f in exI) |
1126 |
1195 apply (erule enrich_proc_dup_ffd', simp+) |
1127 lemma enrich_proc_dup_fflags: |
1196 apply (rule_tac x = f in exI) |
1128 "\<lbrakk>flags_of_proc_fd s p fd = Some f; is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk> |
1197 apply (erule enrich_proc_dup_ffd, simp+) |
1129 \<Longrightarrow> flags_of_proc_fd (enrich_proc s p p') p' fd = Some f" |
1198 done |
1130 apply (induct s, simp add:is_created_proc_def) |
|
1131 apply (frule vt_grant_os, frule vd_cons) |
|
1132 apply (case_tac a, auto simp:is_created_proc_def proc_file_fds_def |
|
1133 dest:not_all_procs_prop3 split:if_splits option.splits) |
|
1134 sorry |
|
1135 |
1199 |
1136 lemma enrich_proc_prop: |
1200 lemma enrich_proc_prop: |
1137 "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> |
1201 "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> |
1138 \<Longrightarrow> valid (enrich_proc s p p') \<and> |
1202 \<Longrightarrow> valid (enrich_proc s p p') \<and> |
1139 (\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and> |
1203 (\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and> |
1168 (\<forall>q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and> |
1232 (\<forall>q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and> |
1169 (\<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> |
1233 (\<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> |
1170 (\<forall>tp fd flags. |
1234 (\<forall>tp fd flags. |
1171 flags_of_proc_fd s tp fd = Some flags \<longrightarrow> flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and> |
1235 flags_of_proc_fd s tp fd = Some flags \<longrightarrow> flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and> |
1172 (\<forall>q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q) \<and> |
1236 (\<forall>q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q) \<and> |
1173 (\<forall>tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd)" |
1237 (\<forall>tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and> |
|
1238 (cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and> |
|
1239 (\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)" |
1174 using vd all_procs by auto |
1240 using vd all_procs by auto |
|
1241 have alive_pre: "is_created_proc s p \<Longrightarrow> (\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj)" |
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1242 using pre by simp |
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1243 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'))" |
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1244 using vd apply auto |
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1245 apply (drule is_file_or_dir, simp) |
|
1246 apply (erule disjE) |
|
1247 apply (erule_tac x = "O_file f" in allE, simp add:is_file_in_current) |
|
1248 apply (erule_tac x = "O_dir f" in allE, simp add:is_dir_in_current) |
|
1249 done |
1175 have "valid (enrich_proc (e # s) p p')" |
1250 have "valid (enrich_proc (e # s) p p')" |
1176 proof- |
1251 proof- |
1177 from pre have pre': "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p')" by simp |
1252 from pre have pre': "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p')" by simp |
1178 have "is_created_proc s p \<Longrightarrow> valid (e # enrich_proc s p p')" |
1253 have "is_created_proc s p \<Longrightarrow> valid (e # enrich_proc s p p')" |
1179 apply (frule pre') |
1254 apply (frule pre') |
1180 apply (erule_tac s = s in enrich_valid_intro_cons) |
1255 apply (erule_tac s = s in enrich_valid_intro_cons) |
1181 apply (simp_all add:os grant vd pre) |
1256 apply (simp_all add:os grant vd pre) |
1182 done |
1257 done |
1183 moreover have "\<And>f fds. \<lbrakk>valid (Execve p f fds # enrich_proc s p p'); is_created_proc s p\<rbrakk> |
1258 moreover have "\<And>f fds. \<lbrakk>valid (Execve p f fds # enrich_proc s p p'); is_created_proc s p; |
|
1259 valid (Execve p f fds # s); p' \<notin> all_procs s\<rbrakk> |
1184 \<Longrightarrow> valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')" |
1260 \<Longrightarrow> valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')" |
1185 apply (frule vt_grant_os, frule vt_grant) |
1261 proof- |
1186 apply (rule valid.intros(2)) |
1262 fix f fds |
1187 apply (simp_all split:option.splits add:sectxt_of_obj_simps is_file_simps) |
1263 assume a1: "valid (Execve p f fds # enrich_proc s p p')" and a2: "is_created_proc s p" |
1188 apply (auto simp add:proc_file_fds_def)[1] |
1264 and a3: "valid (Execve p f fds # s)" and a0: "p' \<notin> all_procs s" |
1189 |
1265 have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp" |
1190 sorry |
1266 and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf" |
|
1267 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" |
|
1268 and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> |
|
1269 file_of_proc_fd (enrich_proc s p p') tp fd = Some f" |
|
1270 and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p" |
|
1271 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" |
|
1272 using pre a2 by auto |
|
1273 show "valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')" |
|
1274 proof- |
|
1275 from a0 a3 have a0': "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3) |
|
1276 from a3 have grant: "grant s (Execve p f fds)" and os: "os_grant s (Execve p f fds)" |
|
1277 by (auto dest:vt_grant_os vt_grant simp del:os_grant.simps) |
|
1278 have f_in: "is_file (enrich_proc s p p') f" |
|
1279 proof- |
|
1280 from pre a2 |
|
1281 have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj" |
|
1282 by (auto) |
|
1283 show ?thesis using a3 a4 |
|
1284 apply (erule_tac x = "O_file f" in allE) |
|
1285 by (auto dest:vt_grant_os) |
|
1286 qed |
|
1287 moreover have a5: "proc_file_fds s p \<subseteq> proc_file_fds (Execve p f fds # enrich_proc s p p') p'" |
|
1288 using a3 a0' |
|
1289 apply (frule_tac vt_grant_os) |
|
1290 apply (auto simp:proc_file_fds_def) |
|
1291 apply (rule_tac x = fa in exI) |
|
1292 apply (erule enrich_proc_dup_ffd) |
|
1293 apply (simp_all add:vd all_procs a2) |
|
1294 done |
|
1295 ultimately have "os_grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))" |
|
1296 apply (auto simp:is_file_simps enrich_proc_dup_in a2 vd all_procs a1 enrich_proc_dup_ffds) |
|
1297 done |
|
1298 moreover have "grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))" |
|
1299 proof- |
|
1300 from grant obtain up rp tp uf rf tf |
|
1301 where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)" |
|
1302 and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)" |
|
1303 by (simp split:option.splits, blast) |
|
1304 with grant obtain pu nr nt where p3: "npctxt_execve (up, rp, tp) (uf, rf, tf) = Some (pu, nr, nt)" |
|
1305 by (simp split:option.splits del:npctxt_execve.simps, blast) |
|
1306 have p1': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)" |
|
1307 using p1 dup_sp a1 a0' |
|
1308 apply (simp add:sectxt_of_obj_simps) |
|
1309 by (simp add:cp2sproc_def split:option.splits) |
|
1310 from os have f_in': "is_file s f" by simp |
|
1311 from vd os have "\<exists> sf. cf2sfile s f = Some sf" |
|
1312 by (auto dest!:is_file_in_current current_file_has_sfile) |
|
1313 hence p2': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)" |
|
1314 using f_in p2 cf2sf os a1 |
|
1315 apply (erule_tac x = f in allE) |
|
1316 apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits) |
|
1317 apply (case_tac f, simp) |
|
1318 apply (drule_tac s = s in root_is_dir', simp add:vd, simp+) |
|
1319 done |
|
1320 from dup_sfd a5 have "\<forall>fd. fd \<in> proc_file_fds s p \<longrightarrow> |
|
1321 cfd2sfd (Execve p f fds # enrich_proc s p p') p' fd = cfd2sfd s p fd" |
|
1322 apply (rule_tac allI) |
|
1323 apply (erule_tac x = fd in allE, clarsimp) |
|
1324 apply (drule set_mp, simp) |
|
1325 apply (auto simp:cfd2sfd_execve proc_file_fds_def a1) |
|
1326 done |
|
1327 hence "inherit_fds_check (Execve p f fds # enrich_proc s p p') (up, nr, nt) p' (fds \<inter> proc_file_fds s p)" |
|
1328 using grant os p1 p2 p3 vd |
|
1329 apply (clarsimp) |
|
1330 apply (rule_tac s = s and p = p and fds = fds in enrich_inherit_fds_check_dup) |
|
1331 apply simp_all |
|
1332 done |
|
1333 moreover have "search_check (Execve p f fds # enrich_proc s p p') (up, rp, tp) f" |
|
1334 using p1 p2 p2' vd cf2sf f_in f_in' grant p3 f_in a1 |
|
1335 apply (rule_tac s = s in enrich_search_check) |
|
1336 apply (simp_all add:is_file_simps) |
|
1337 apply (rule allI, rule impI, erule_tac x = fa in allE, simp) |
|
1338 apply (drule_tac ff = fa in cf2sfile_other') |
|
1339 by (auto simp:a2 curf_pre) |
|
1340 ultimately show ?thesis |
|
1341 using p1' p2' p3 |
|
1342 apply (simp split:option.splits) |
|
1343 using grant p1 p2 |
|
1344 apply simp |
|
1345 done |
|
1346 qed |
|
1347 ultimately show ?thesis using a1 |
|
1348 by (erule_tac valid.intros(2), auto) |
|
1349 qed |
|
1350 qed |
1191 moreover have "\<And>tp fds. \<lbrakk>valid (Clone tp p fds # s); p' \<noteq> p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> |
1351 moreover have "\<And>tp fds. \<lbrakk>valid (Clone tp p fds # s); p' \<noteq> p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> |
1192 valid (Clone tp p' (fds \<inter> proc_file_fds s tp) # Clone tp p fds # s)" |
1352 valid (Clone tp p' (fds \<inter> proc_file_fds s tp) # Clone tp p fds # s)" |
1193 apply (frule vt_grant_os, frule vt_grant, drule not_all_procs_prop3) |
1353 apply (frule vt_grant_os, frule vt_grant, drule not_all_procs_prop3) |
1194 apply (rule valid.intros(2)) |
1354 apply (rule valid.intros(2)) |
1195 apply (simp_all split:option.splits add:sectxt_of_obj_simps) |
1355 apply (simp_all split:option.splits add:sectxt_of_obj_simps) |
1198 done |
1358 done |
1199 moreover have "\<And>f flags fd inum. |
1359 moreover have "\<And>f flags fd inum. |
1200 \<lbrakk>valid (Open p f flags fd inum # enrich_proc s p p'); is_created_proc s p\<rbrakk> |
1360 \<lbrakk>valid (Open p f flags fd inum # enrich_proc s p p'); is_created_proc s p\<rbrakk> |
1201 \<Longrightarrow> valid (Open p' f (remove_create_flag flags) fd inum # Open p f flags fd inum # enrich_proc s p p')" |
1361 \<Longrightarrow> valid (Open p' f (remove_create_flag flags) fd inum # Open p f flags fd inum # enrich_proc s p p')" |
1202 sorry |
1362 sorry |
1203 moreover have "\<And>fd. \<lbrakk>valid (CloseFd p fd # enrich_proc s p p'); is_created_proc s p\<rbrakk> |
1363 moreover have "\<And>fd. \<lbrakk>valid (CloseFd p fd # enrich_proc s p p'); is_created_proc s p; |
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1364 valid (CloseFd p fd # s); p' \<notin> all_procs s\<rbrakk> |
1204 \<Longrightarrow> valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')" |
1365 \<Longrightarrow> valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')" |
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1366 proof- |
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1367 fix fd |
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1368 assume a1: "valid (CloseFd p fd # enrich_proc s p p')" and a2: "is_created_proc s p" |
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1369 and a3: "p' \<notin> all_procs s" and a4: "valid (CloseFd p fd # s)" |
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1370 from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3) |
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1371 have "p' \<in> current_procs (enrich_proc s p p')" |
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1372 using a2 a3 vd |
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1373 by (auto intro:enrich_proc_dup_in) |
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1374 moreover have "fd \<in> current_proc_fds (enrich_proc s p p') p'" |
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1375 ultimately show "valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')" |
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1376 apply (rule valid.intros(2)) |
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1377 apply (simp_all add:a1 a0 a2 pre') |
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1378 |
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1379 |
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1380 |
1205 sorry |
1381 sorry |
1206 thus ?thesis using created_cons vd_cons all_procs_cons |
1382 (* |
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1383 thus ?thesis using created_cons vd_cons all_procs_cons |
1207 apply (case_tac e) |
1384 apply (case_tac e) |
1208 apply (auto simp:is_created_proc_simps split:if_splits) |
1385 apply (auto simp:is_created_proc_simps split:if_splits) |
1209 |
1386 *) |
1210 ultimately show ?thesis using created_cons vd_cons all_procs_cons |
1387 ultimately show ?thesis using created_cons vd_cons all_procs_cons |
1211 apply (case_tac e) |
1388 apply (case_tac e) |
1212 apply (auto simp:is_created_proc_simps split:if_splits) |
1389 apply (auto simp:is_created_proc_simps split:if_splits) |
1213 done |
1390 done |
1214 qed |
1391 qed |