| cache_dirs[entries2[str]] = mkdir(m1, md2, # links(entries2[str], cache_dirs), m5, entries0), cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries), cache_dirs[m3] = mkdir(m4, md3, # links(m3, cache_dirs), m7, entries2), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m3 ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries2, entries2[str] ∈ cache_dirs, 1 ≤ m4, 1 ≤ m7, ⌊err1⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨asynced := ?⟩ (err1 = err1 ∧ (asynced ↔ asynced2)), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), m4 = 0, m7 = 0, str0 ∈ entries |