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Proof step 332 from proof refine-rmdir (previous step)

cache_dirs[entries[str]] = mkdir(m0, md, # links(entries[str], cache_dirs), m2, ∅), cache_dirs[m] = mkdir(m1, md0, # links(m, cache_dirs), 0, entries), 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 ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_dirs, 1 ≤ m1, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨choose err0 with ⌊err0⌋ in err := err0; asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), entries[str] = ROOT_INO, m1 = 0

Heuristic symbolic execution applied rule choose right

And obtained the following new goals

Rule argument

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