| root[q0].dir? ↔ ino2 ∈ dirs, files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), err0 = err1, 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(q0, ROOT_INO, ino2, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, ⌊err1⌋ , psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, ino2 ∈ dirs ∨ ino2 ∈ files ⊦ ⟨psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0), root[q + str '].dir?, entries0[str] ∈ dirs |