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Proof step 445 from proof refine-rename-dir-negdentry (previous step)

# links(entries1[str], cache_dirs) = cache_dirs[entries1[str]].nlink, # links(m, cache_dirs) = m1, # links(m3, cache_dirs) = cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs = 0, entries1[str] = cache_dirs[m3].entries[str], cache_dirs[m3] = mkdir(cache_dirs[m3].size, md4, cache_dirs[m3].nlink, 0, entries1), cache_dirs[m] = mkdir(m0, md3, m1, m2, entries0), cache_dirs[entries1[str]] = mkdir(cache_dirs[entries1[str]].size, md5, cache_dirs[entries1[str]].nlink, cache_dirs[entries1[str]].nsubdirs, entries2), cache_dirs[m] = mkdir(m0, md1, m1, m2, entries), 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), entries1[str] ∈ cache_dirs, str ∈ cache_dirs[m3].entries, m ∈ cache_dirs, m3 ∈ cache_dirs, str ∈ entries1, 1 ≤ cache_dirs[m3].size, ⌊err0⌋ , 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 ⊦ ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2)), cache_dirs[m3].size = 0, str0 ∈ entries, str0 ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 446:
# links(m3, cache_dirs) = cache_dirs[m3].nlink, # links(entries1[str], cache_dirs) = cache_dirs[entries1[str]].nlink, cache_dirs[m3].nsubdirs = 0, cache_dirs[entries1[str]] = mkdir(cache_dirs[entries1[str]].size, md5, cache_dirs[entries1[str]].nlink, cache_dirs[entries1[str]].nsubdirs, entries2), cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries), cache_dirs[m3] = mkdir(cache_dirs[m3].size, md4, cache_dirs[m3].nlink, 0, entries1), entries1[str] = cache_dirs[m3].entries[str], cache_dirs[m3].size ≠ 0, 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), str ∈ entries1, m3 ∈ cache_dirs, m ∈ cache_dirs, str ∈ cache_dirs[m3].entries, entries1[str] ∈ cache_dirs, 1 ≤ cache_dirs[m3].size, ⌊err0⌋ , ¬ str0 ∈ entries, 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 ⊦ ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)