| isdir ↔ isdir0, root[path].dir? ↔ ino1 ∈ dirs, fs = abs-files(files), ofh = abs-of(of), 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), ⌊err0⌋ , psynced → asynced, ino1 ∈ dirs ∨ ino1 ∈ files ⊦ ⟨choose err0 with pre-fsync(path, isdir, err0, user, root, fs, ofh) in err := err0; psynced := ?⟩ ((psynced → asynced) ∧ err0 = err) |
root[path].dir? ↔ ino1 ∈ dirs, isdir ↔ isdir0, fs = abs-files(files), ofh = abs-of(of), 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), ⌊err1⌋ , psynced → asynced, ino1 ∈ dirs ∨ ino1 ∈ files ⊦ ∃ err0. pre-fsync(path, isdir, err0, user, root, fs, ofh) ∧ ⟨err := err0; psynced := ?⟩ ((psynced → asynced) ∧ err1 = err)