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Proof step 427 from proof refine-rename-file-negdentry (previous step)

cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), 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), cache_icache[entries0[str]] = mkientry(boolvar, inode), inode = mkinode(m4, md2, false, m5, m6, m7), 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), entries0[str] ∈ cache_icache, 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 ⊦ m5 = # links(entries0[str], cache_dirs), str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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