| isdir ↔ false, entries[str] ∈ dirs ↔ root[q + str '].dir?, isdir1 ↔ false, isdir0 ↔ isdir1, dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), err = err0, err1 = err, fs = abs-files(files), p_inode = inode, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, str ∈ entries, ⌊err0⌋ , psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, entries[str] ∈ dirs ∨ entries[str] ∈ files ⊦ [skip] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_unlink#(q + str ', user, abs-of(of); err2, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err2)) |
isdir0 ↔ isdir1, isdir1 ↔ false, entries[str] ∈ dirs ↔ root[q + str '].dir?, isdir ↔ false, dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), err = err0, err1 = err, fs = abs-files(files), p_inode = inode, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries, ino1 ∈ dirs, ⌊err0⌋ , psynced → asynced, entries[str] ∈ dirs ∨ entries[str] ∈ files, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_unlink#(q + str ', user, abs-of(of); err2, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err2)