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Theorem walk-prepost-h

p_ino ∈ dirs, p_ino = ino, afs-cons(dirs, files), ispath(q, ROOT_INO, p_ino, dirs, files), q ≠ ε → px(user, parent(q), ROOT_INO, dirs, files) ⊦ [vfs_walk#(p, user, dirs, files, asynced; ino, err)] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p, p_ino, ino, dirs, files) ∧ px-parent(user, q + p, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p, p_ino, dirs, files) ∨ err = EACCESS ∧ p ≠ ε ∧ (∃ p'. p' ⊑ parent(p) ∧ ispath(p', p_ino, dirs, files) ∧ ¬ px(user, q + p', ROOT_INO, dirs, files)))

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