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Proof step 70 from proof refine-evict (previous step)

asynced ↔ cache_asynced, cache_dirs[m] = mkdir(m0, md0, # links(m, cache_dirs), m2, entries), 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, true, # links(m, cache_dirs), m2, m0), 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), pre-evict(inode, dirs, files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨if ino ∈ dirs then if dirs[ino].nlink = 0 then dirs := dirs -- ino else 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

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

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