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Proof step 781 from proof refine-rename-dir-dentry (previous step)

cache_dirs[m] = mkdir(m0, md, # links(m, cache_dirs), m2, entries), cache_dirs[entries[str0]] = mkdir(m1, md0, # links(entries[str0], cache_dirs), m4, ∅), entries[str0] ≠ ROOT_INO, 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), str0 ∈ entries, m ∈ cache_dirs, entries[str0] ∈ cache_dirs, ⌊err1⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2))

Heuristic use patterns applied rule exists right

And obtained the following new goals

Proof step 782:
cache_dirs[entries[str0]] = mkdir(m1, md0, # links(entries[str0], cache_dirs), m4, ∅), cache_dirs[m] = mkdir(m0, md, # links(m, cache_dirs), m2, 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), entries[str0] ∈ cache_dirs, m ∈ cache_dirs, str0 ∈ entries, ⌊err1⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⌊err1⌋ ∧ ⟨err := err1; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ (err1 = err ∧ (asynced ↔ asynced2)), entries[str0] = ROOT_INO

Rule argument

pos: right 1 terms: err1 abort: T discard: F computed: F

Additional information

Used terms: err1