| root[path].dir? ↔ ino1 ∈ dirs, fs = abs-files(files), 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 ⊦ [skip] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_truncate#(path, n, user, root, abs-of(of); err2, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err0 = err2)) |
root[path].dir? ↔ ino1 ∈ dirs, fs = abs-files(files), 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 ⊦ ⟨posix_truncate#(path, n, user, root, abs-of(of); err2, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err0 = err2)