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Proof step 482 from proof refine-rename-dir-negdentry (previous step)

cache_dirs[m3] = mkdir(0, md1, # links(m3, cache_dirs), m2, entries), cache_dirs[m] = mkdir(m0, md2, # links(m, cache_dirs), m4, entries1), cache_dirs[entries[str]] = mkdir(m1, md3, # links(entries[str], cache_dirs), m6, entries0), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), 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), str ∈ entries, m ∈ cache_dirs, m3 ∈ cache_dirs, entries[str] ∈ cache_dirs, ⌊err1⌋ , ¬ str0 ∈ entries1, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2))

Heuristic use patterns applied rule exists right

And obtained the following new goals

Proof step 483:
cache_dirs[entries[str]] = mkdir(m1, md3, # links(entries[str], cache_dirs), m6, entries0), cache_dirs[m] = mkdir(m0, md2, # links(m, cache_dirs), m4, entries1), cache_dirs[m3] = mkdir(0, md1, # links(m3, cache_dirs), m2, entries), 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), entries[str] ∈ cache_dirs, m3 ∈ cache_dirs, m ∈ cache_dirs, str ∈ entries, ⌊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 ⊦ ⌊err1⌋ ∧ ⟨err := err1; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), str0 ∈ entries1

Rule argument

pos: right 1 terms: err1 abort: T discard: F computed: F

Additional information

Used terms: err1