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Proof step 62 from proof refine-lookup (previous step)

cache_dirs[p_ino] = mkdir(m, md, # links(p_ino, cache_dirs), m1, entries), dcache = cache_dcache, dent = mkdentry(dent0.name, entries[dent0.name]), err = ESUCCESS, key = dentrykey(p_ino, name), name = dent0.name, 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), dent0.name ∈ entries, p_ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨dent1 := dent0; afs_lookup#(p_ino, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; dent0, err0)⟩ (mkdentry(dent1.name, entries[dent1.name]) = dent0 ∧ err = err0), dentrykey(p_ino, dent0.name) ∈ cache_dcache

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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