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Proof step 454 from proof refine-evict (previous step)

asynced ↔ cache_asynced, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_files[m] = mkfile(m1, md1, # links(m, cache_dirs), content0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = afs_dirs, err = err0, files = afs_files, ino = inode.ino, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, m2), 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), pre-evict(inode, dirs, files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨if files[ino].nlink = 0 then files := files -- ino⟩ (dirs = cache_dirs ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ ESUCCESS = ESUCCESS), # links(m, cache_dirs) = 0, links(m, cache_dirs) = ∅, m = ROOT_INO, m ∈ cache_dirs, ino ∈ dirs

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

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