| root[q].dir? ↔ ino1 ∈ dirs, err0 = err2, fs = abs-files(files), ofh = abs-of(of), path = q + str ', 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), px-parent(user, q, ROOT_INO, dirs, files), ⌊err1⌋ , psynced → asynced, ino1 ∈ dirs ∨ ino1 ∈ files ⊦ ∃ err. pre-mkdir(path, md, err, user, root, fs, ofh) ∧ ⟨err0 := err; if err0 = ESUCCESS then root[path] := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0) |
root[q].dir? ↔ ino1 ∈ dirs, 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), px-parent(user, q, ROOT_INO, dirs, files), ⌊err1⌋ , psynced → asynced, ino1 ∈ dirs ∨ ino1 ∈ files ⊦ ∃ err. pre-mkdir(q + str ', md, err, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := err; if err0 = ESUCCESS then root[q + str '] := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)