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Proof step 807 from proof refine-rename-file-dentry (previous step)

# links(m3, cache_dirs) = cache_dirs[m3].nlink, # links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m3].size = 0, cache_files[entries[str]] = mkfile(m1, md5, # links(entries[str], cache_dirs), content2), cache_dirs[m3] = mkdir(0, md8, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, # links(entries[str], cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, # links(entries0[str0], cache_dirs), content0), cache_dirs[m] = mkdir(cache_dirs[m].size, md7, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), cache_files[entries0[str0]] = mkfile(m0, md6, # links(entries0[str0], cache_dirs), content3), entries[str] = cache_dirs[m].entries[str], entries0[str0] = cache_dirs[m3].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 ∈ entries0, str ∈ entries, entries0[str0] ∈ cache_files, entries[str] ∈ cache_files, m3 ∈ cache_dirs, m ∈ cache_dirs, str ∈ cache_dirs[m].entries, str0 ∈ cache_dirs[m3].entries, ⌊err0⌋ , ¬ entries[str] ∈ cache_dirs, 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, entries[str]) = mkdentry(str0, entries0[str0])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 808:
# links(m, cache_dirs) = cache_dirs[m].nlink, # links(m3, cache_dirs) = m4, entries0[str0] = entries1[str0], entries[str] = cache_dirs[m].entries[str], cache_files[entries0[str0]] = mkfile(m0, md6, # links(entries0[str0], cache_dirs), content3), cache_dirs[m] = mkdir(cache_dirs[m].size, md7, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, # links(entries0[str0], cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, # links(entries[str], cache_dirs), content), cache_dirs[m3] = mkdir(0, md8, m4, m5, entries0), cache_files[entries[str]] = mkfile(m1, md5, # links(entries[str], cache_dirs), content2), cache_dirs[m3] = mkdir(m2, md1, m4, m5, entries1), m2 = 0, 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, str ∈ cache_dirs[m].entries, m ∈ cache_dirs, m3 ∈ cache_dirs, entries[str] ∈ cache_files, entries0[str0] ∈ cache_files, str ∈ entries, str0 ∈ entries0, ⌊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 ⊦ ⟨fail#(; ; err); asynced := ?⟩ (err0 = err ∧ (asynced ↔ asynced2)), entries[str] ∈ cache_dirs, m3 = m ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries0[str0])

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[m3], m2, md1, m4, m5, 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[m3], m2, md1, m4, m5, entries1