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Proof step 6 from proof refine-rmdir (previous step)

err = err0, fs = abs-files(files), root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ [vfs_rmdir#(path, user, of; err, dirs, files, asynced)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(path, user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0))

User applied rule call right

And obtained the following new goals

Proof step 7:
err = err0, fs = abs-files(files), root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ [if path = ε then err := EACCESS else let ino = ROOT_INO, dent = negdentry(path.last), path = parent(path), isdir = true, inode = ?, p_inode = ? in {vfs_walk#(path, user, dirs, files, asynced; ino, err); if err = ESUCCESS then vfs_may_delete_check#(ino, user, dirs, files, asynced; inode, isdir, dent, p_inode, err); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {afs_rmdir#(; inode, p_inode, dent, err, dirs, files; asynced); vfs_put_inode#(p_inode, of, asynced; err, dirs, files)}}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(path, user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0))

Rule argument

pos: right 1

Additional information

Used simplifier rules: vfs_rmdir#(PATH, USER, OF; ERR, DIRS, FILES, ASYNCED) {if PATH = ε then ERR := EACCESS else let INO = ROOT_INO, DENT = negdentry(PATH.last), PATH = parent(PATH), ISDIR = true, INODE = ?, DEL_INODE = ? in {vfs_walk#(PATH, USER, DIRS, FILES, ASYNCED; INO, ERR); if ERR = ESUCCESS then vfs_may_delete_check# (INO, USER, DIRS, FILES, ASYNCED ; INODE, ISDIR, DENT, DEL_INODE, ERR); if ERR = ESUCCESS then afs_check_commit#(DIRS, FILES; ERR; ASYNCED); if ERR = ESUCCESS then {afs_rmdir# (; INODE, DEL_INODE, DENT, ERR, DIRS, FILES; ASYNCED); vfs_put_inode# (DEL_INODE, OF, ASYNCED; ERR, DIRS, FILES)}} };