[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 19 from proof refine-readdir (previous step)

isdir ↔ true, err1 = ESUCCESS, mode = MODE_R, strings = strings0, root.dir?, dom of < ino0, 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, ⌊err1⌋ ∨ err1 = ESUCCESS ∧ ispath(path, ROOT_INO, ino1, dirs, files) ∧ px-parent(user, path, ROOT_INO, dirs, files) ∨ err1 = ENOENT ∧ ¬ ispath(path, ROOT_INO, dirs, files) ∨ err1 = EACCESS ∧ path ≠ ε ∧ p' ⊑ parent(path) ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ⊦ [vfs_may_open#(ino1, isdir, mode, user, dirs, files, asynced; inode, err1); 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs)
Proof step 21:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 22:
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)

Rule argument

Additional information

Used simplifier rules: path-in: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs);%path-in-eq: ⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files));% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)% ⊦ ESUCCESS ≠ EACCESS; (s)% ⊦ ESUCCESS ≠ ENOENT; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)