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Proof step 776 from proof refine-rename-dir-dentry (previous step)

# links(entries[str0], cache_dirs) = cache_dirs[entries[str0]].nlink, cache_dirs[entries[str0]].entries = ∅, cache_dirs[entries[str0]] = mkdir(cache_dirs[entries[str0]].size, md3, cache_dirs[entries[str0]].nlink, cache_dirs[entries[str0]].nsubdirs, entries2), cache_dirs[entries[str0]] = mkdir(cache_dirs[entries[str0]].size, md4, cache_dirs[entries[str0]].nlink, cache_dirs[entries[str0]].nsubdirs, ∅), cache_dirs[m] = mkdir(m0, md, # links(m, cache_dirs), m2, entries), entries[str0] ≠ ROOT_INO, 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, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 777:
# links(entries[str0], cache_dirs) = m3, cache_dirs[m] = mkdir(m0, md, # links(m, cache_dirs), m2, entries), cache_dirs[entries[str0]] = mkdir(m1, md4, m3, m4, ∅), cache_dirs[entries[str0]] = mkdir(m1, md3, m3, m4, entries2), cache_dirs[entries[str0]] = mkdir(m1, md0, m3, m4, entries0), entries0 = ∅, 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, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2)), entries[str0] = ROOT_INO

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [cache_dirs[entries[str0]], m1, md0, m3, m4, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: cache_dirs[entries[str0]], m1, md0, m3, m4, entries0