| # links(entries1[str0], cache_dirs) = cache_dirs[entries1[str0]].nlink, # links(m, cache_dirs) = cache_dirs[m].nlink, # links(m3, cache_dirs) = cache_dirs[m3].nlink, # links(entries0[str], cache_dirs) = cache_dirs[entries0[str]].nlink, cache_dirs[entries0[str]].entries = ∅, asynced1 ↔ true, entries1[str0] = cache_dirs[m3].entries[str0], entries0[str] = cache_dirs[m].entries[str], cache_dirs[entries1[str0]] = mkdir(cache_dirs[entries1[str0]].size, md3, cache_dirs[entries1[str0]].nlink, cache_dirs[entries1[str0]].nsubdirs, entries2), cache_dirs[entries0[str]] = mkdir(cache_dirs[entries0[str]].size, md4, cache_dirs[entries0[str]].nlink, cache_dirs[entries0[str]].nsubdirs, ∅), cache_dirs[m] = mkdir(cache_dirs[m].size, md5, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries0), cache_dirs[m3] = mkdir(cache_dirs[m3].size, md7, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries1), new_ino = m, old_ino = new_ino, old_ino = m3, 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), str0 ∈ cache_dirs[m3].entries, str ∈ cache_dirs[m].entries, str0 ∈ entries1, entries0[str] ∈ cache_dirs, entries1[str0] ∈ cache_dirs, m ∈ cache_dirs, m3 ∈ cache_dirs, str ∈ entries0, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced0)), entries0[str] = ROOT_INO, str ∈ entries0 ∧ str0 ∈ entries1 |