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Proof step 319 from proof refine-link (previous step)

cache_dirs[m] = mkdir(m4, md2, # links(m, cache_dirs), m9, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m5, md1, m7, content), 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, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ entries, (∃ ino0. ino0 ∈ cache_dirs ∧ (links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO) ∧ str ∈ cache_dirs[ino0].entries ∧ entries0[str] = cache_dirs[ino0].entries[str]) ∧ m7 = # links(entries0[str], cache_dirs)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 2

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