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Proof step 274 from proof refine-rmdir (previous step)

cache_dirs[entries0[str]] = mkdir(m1, md3, # links(entries0[str], cache_dirs), m4, ∅), cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m1), dent = mkdentry(str, entries0[str]), err = err0, p_inode = mkinode(m, md, true, # links(m, cache_dirs), m2, m0), 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), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries0, m ∈ cache_dirs, entries0[str] ∈ cache_dirs, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨dent0 := mkdentry(str, entries0[str]); p_inode0 := mkinode(m, md, true, # links(m, cache_dirs), m2, m0); p_inode1 := mkinode(entries0[str], md0, true, # links(entries0[str], cache_dirs), m4, m1); cache_dirs0 := cache_dirs; afs_rmdir#(; p_inode0, p_inode1, dent0, err1, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = dent0 ∧ err = err1), entries0[str] = ROOT_INO

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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