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Proof step 330 from proof refine-link (previous step)

cache_dirs[m] = mkdir(m4, md2, # links(m, cache_dirs), m9, entries), cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), cache_files[entries0[str]] = mkfile(m1, md, # links(entries0[str], cache_dirs), content0), mkfile (cache_icache[entries0[str]].inode.size, cache_icache[entries0[str]].inode.meta, cache_icache[entries0[str]].inode.nlink, (cache_files ⊕ cache_pcache)[entries0[str]].content) = mkfile(m5, md1, m7, content), 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), ino ∈ cache_dirs, str ∈ entries0, m ∈ cache_dirs, entries0[str] ∈ cache_files, entries0[str] ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m7 = # links(entries0[str], cache_dirs), cache_icache[entries0[str]].inode.directory, str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 331:
cache_dirs[m] = mkdir(m4, md2, # links(m, cache_dirs), m9, entries), cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), cache_files[entries0[str]] = mkfile(m1, md, # 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), ino ∈ cache_dirs, str ∈ entries0, m ∈ cache_dirs, entries0[str] ∈ cache_files, entries0[str] ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ cache_icache[entries0[str]].inode.nlink = # links(entries0[str], cache_dirs), cache_icache[entries0[str]].inode.directory, str0 ∈ entries

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)