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Proof step 419 from proof refine-rename-file-negdentry (previous step)

cache_icache[entries0[str]] = mkientry(boolvar0, mkinode(m4, md5, boolvar, m5, m6, m7)), cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, m11, content), cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), cache_files[entries0[str]] = mkfile(m1, md1, # links(entries0[str], cache_dirs), content0), 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 ∈ entries0, m3 ∈ cache_dirs, entries0[str] ∈ cache_files, m ∈ cache_dirs, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m11 = # links(entries0[str], cache_dirs), str0 ∈ entries, entries0[str] ∈ cache_icache ∧ ¬ boolvar

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 420:
cache_files[entries0[str]] = mkfile(m1, md1, # links(entries0[str], cache_dirs), content0), cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, m11, content), cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), cache_icache[entries0[str]] = mkientry(boolvar0, mkinode(m4, md5, boolvar, m5, m6, m7)), 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), m ∈ cache_dirs, entries0[str] ∈ cache_files, m3 ∈ cache_dirs, str ∈ entries0, entries0[str] ∈ cache_icache, 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 ⊦ m11 = # links(entries0[str], cache_dirs), str0 ∈ entries, entries0[str] ∈ cache_icache ∧ ¬ boolvar

Rule argument

fma: entries0[str] ∈ cache_icache

Additional information

Used simplifier rules: ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s) Used formulas: entries0[str] ∈ cache_icache