| dirs[ino1] = mkdir(# entries, md0, # links(ino1, dirs), m1, entries), dent = negdentry(str), err = ESUCCESS, err1 = EEXISTS, err2 = ESUCCESS, fs = abs-files(files), p_ino = ino1, 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), pre-lookup(p_ino, dent, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, dent.name ∈ dirs[p_ino].entries, psynced → asynced ⊦ [skip] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_mkdir#(q + str ', md, user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)) |
dirs[ino1] = mkdir(# entries, md0, # links(ino1, dirs), m1, entries), dent = negdentry(str), err = ESUCCESS, err1 = EEXISTS, err2 = ESUCCESS, fs = abs-files(files), p_ino = ino1, 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), pre-lookup(p_ino, dent, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), dent.name ∈ dirs[p_ino].entries, ino1 ∈ dirs, psynced → asynced ⊦ ⟨posix_mkdir#(q + str ', md, user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)