| dent = negdentry((q + str ').last), 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)), of-cons(of, dirs, files), psynced → asynced, ⌊err1⌋ ∨ err1 = ESUCCESS ∧ ispath(q, ROOT_INO, ino1, dirs, files) ∧ px-parent(user, q, ROOT_INO, dirs, files) ∨ err1 = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs, files) ∨ err1 = EACCESS ∧ p' ⊑ q ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ⊦ [skip] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(q + str ', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)), q + str ' = ε, err1 = ESUCCESS |
dent = negdentry((q + str ').last), 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)), of-cons(of, dirs, files), psynced → asynced, ⌊err1⌋ ∨ err1 = ESUCCESS ∧ ispath(q, ROOT_INO, ino1, dirs, files) ∧ px-parent(user, q, ROOT_INO, dirs, files) ∨ err1 = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs, files) ∨ err1 = EACCESS ∧ p' ⊑ q ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ⊦ ⟨posix_rmdir#(q + str ', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0), q + str ' = ε, err1 = ESUCCESS