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Proof step 22 from proof refine-readdir (previous step)

root[path].dir? ↔ ino1 ∈ dirs, err1 = ESUCCESS, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced ⊦ [vfs_may_open#(ino1, true, MODE_R, user, dirs, files, asynced; inode, err1); strings := strings0; if err1 = ESUCCESS then afs_readdir#(inode, dirs, files, asynced; strings, err1)] ⟨posix_readdir#(path, user, root, abs-files(files), abs-of(of); strings0, err0)⟩ ((psynced → asynced) ∧ strings = strings0 ∧ err1 = err0)

User applied rule call right

And obtained the following new goals

Proof step 23:
isdir ↔ true, root[path].dir? ↔ ino1 ∈ dirs, err = err1, err1 = ESUCCESS, ino = ino1, mode = MODE_R, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced ⊦ [afs_iget#(ino, dirs, files, asynced; inode, err); if err = ESUCCESS then if ¬(inode.directory ↔ isdir) then err := (inode.directory ⊃ EISDIR;ENOTDIR) else if (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, inode.meta) ∨ (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, inode.meta) then err := EACCESS; strings := strings0; err1 := err; if err1 = ESUCCESS then afs_readdir#(inode, dirs, files, asynced; strings, err1)] ⟨posix_readdir#(path, user, root, abs-files(files), abs-of(of); strings0, err0)⟩ ((psynced → asynced) ∧ strings = strings0 ∧ err1 = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: vfs_may_open# (INO, ISDIR, MODE, USER, DIRS, FILES, ASYNCED; INODE, ERR) {afs_iget#(INO, DIRS, FILES, ASYNCED; INODE, ERR); if ERR = ESUCCESS then if ¬(INODE.directory ↔ ISDIR) then ERR := (INODE.directory ⊃ EISDIR;ENOTDIR) else if (MODE = MODE_R ∨ MODE = MODE_RW) ∧ ¬ pr(USER, INODE.meta) ∨ (MODE = MODE_W ∨ MODE = MODE_RW) ∧ ¬ pw(USER, INODE.meta) then ERR := EACCESS };