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Proof step 756 from proof refine-rename-dir-dentry (previous step)

cache_dirs[m3] = mkdir(0, md1, # links(m3, cache_dirs), m2, entries), cache_dirs[m] = mkdir(m5, md4, # links(m, cache_dirs), m8, entries2), cache_dirs[entries2[str]] = mkdir(m1, md3, # links(entries2[str], cache_dirs), m6, ∅), cache_dirs[entries[str0]] = mkdir(m0, md2, # links(entries[str0], cache_dirs), m4, entries1), entries2[str] ≠ 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), m3 ∈ cache_dirs, m ∈ cache_dirs, entries[str0] ∈ cache_dirs, entries2[str] ∈ cache_dirs, str ∈ entries2, str0 ∈ entries, ⌊err0⌋ , m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2)), m3 = m ∧ mkdentry(str, entries2[str]) = mkdentry(str0, entries[str0])

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 757:
cache_dirs[entries[str0]] = mkdir(m0, md2, # links(entries[str0], cache_dirs), m4, entries1), cache_dirs[entries2[str]] = mkdir(m1, md3, # links(entries2[str], cache_dirs), m6, ∅), cache_dirs[m] = mkdir(m5, md4, # links(m, cache_dirs), m8, entries2), cache_dirs[m3] = mkdir(0, md1, # links(m3, 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), str0 ∈ entries, str ∈ entries2, entries2[str] ∈ cache_dirs, entries[str0] ∈ cache_dirs, m ∈ cache_dirs, m3 ∈ cache_dirs, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟨choose err0 with ⌊err0⌋ in err := err0; asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2)), entries2[str] = ROOT_INO, m3 = m ∧ mkdentry(str, entries2[str]) = mkdentry(str0, entries[str0])

Rule argument

pos: right 1

Additional information

Used simplifier rules: fail#(; ; ERR){choose ERR0 with ⌊ERR0⌋ in ERR := ERR0};