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Proof step 385 from proof refine-rename-file-negdentry (previous step)

# links(m3, cache_dirs) = m5, entries0[str] = entries[str], cache_dirs[m3] = mkdir(m2, md5, m5, m6, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, # links(entries0[str], cache_dirs), content), cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m4, entries1), cache_files[entries0[str]] = mkfile(m1, md3, # links(entries0[str], cache_dirs), content0), cache_dirs[m3] = mkdir(m2, md4, m5, m6, 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), str ∈ entries, m3 ∈ cache_dirs, entries0[str] ∈ cache_files, m ∈ cache_dirs, str ∈ entries0, 1 ≤ m2, ⌊err0⌋ , 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)), m2 = 0, entries0[str] ∈ cache_dirs, str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 386:
cache_files[entries[str]] = mkfile(m1, md3, # links(entries[str], cache_dirs), content0), cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m4, entries1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m9, md2, # links(entries[str], cache_dirs), content), cache_dirs[m3] = mkdir(m2, md4, # links(m3, cache_dirs), m6, entries), m2 ≠ 0, 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), m ∈ cache_dirs, entries[str] ∈ cache_files, m3 ∈ cache_dirs, str ∈ entries, 1 ≤ m2, ⌊err0⌋ , ¬ str0 ∈ entries1, ¬ entries[str] ∈ cache_dirs, 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))

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)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat