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Proof step 829 from proof refine-rename-file-dentry (previous step)

# links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m] = mkdir(cache_dirs[m].size, md8, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m12, md3, # links(entries0[str0], cache_dirs), content), cache_dirs[m] = mkdir(cache_dirs[m].size, md7, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), cache_files[entries0[str0]] = mkfile(m1, md5, # links(entries0[str0], cache_dirs), content2), entries[str0] = entries0[str0], entries0[str0] = cache_dirs[m].entries[str0], 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, str0 ∈ entries0, entries0[str0] ∈ cache_files, m ∈ cache_dirs, str0 ∈ cache_dirs[m].entries, ⌊err0⌋ , ¬ entries0[str0] ∈ cache_dirs, 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 830:
# links(m, cache_dirs) = m2, entries0[str0] = entries1[str0], entries[str0] = entries0[str0], cache_files[entries0[str0]] = mkfile(m1, md5, # links(entries0[str0], cache_dirs), content2), cache_dirs[m] = mkdir(m0, md7, m2, m3, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m12, md3, # links(entries0[str0], cache_dirs), content), cache_dirs[m] = mkdir(m0, md8, m2, m3, entries0), cache_dirs[m] = mkdir(m0, md, m2, m3, entries1), 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 ∈ entries1, m ∈ cache_dirs, entries0[str0] ∈ cache_files, str0 ∈ entries0, 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)), entries0[str0] ∈ cache_dirs

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[m], m1, md, m2, m3, entries1]

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[m], m1, md, m2, m3, entries1