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Proof step 310 from proof inv-rename-dir-negdentry (previous step)

# links(entries0[str], dirs) = dirs[entries0[str]].nlink, dirs[m] = mkdir(m1, md, # links(m, dirs), m3, entries0), dirs[m0] = mkdir(m2, md2, # links(m0, dirs), m5, entries), dirs[entries0[str]] = mkdir(dirs[entries0[str]].size, md5, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, entries2), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ entries0, entries0[str] ∈ dirs, m ∈ dirs, m0 ∈ dirs, ¬ str0 ∈ entries, asynced0 → synced(files, icache, pcache), m0 = m → md1 = md0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(m, md0, true, # links(m, dirs), m3, m1), asynced; err, icache); icache_set#(mkinode(m0, md1, true, # links(m0, dirs), m5, m2), asynced; err, icache); skip; dcache_delete#(m, mkdentry(str, entries0[str]).name; err, dcache); dcache_set#(m0, str0, negdentry(str0); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced0 → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 311:
# links(entries0[str], dirs) = m6, dirs[entries0[str]] = mkdir(m4, md5, m6, m7, entries2), dirs[m0] = mkdir(m2, md2, # links(m0, dirs), m5, entries), dirs[m] = mkdir(m1, md, # links(m, dirs), m3, entries0), dirs[entries0[str]] = mkdir(m4, md3, m6, m7, entries1), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m0 ∈ dirs, m ∈ dirs, entries0[str] ∈ dirs, str ∈ entries0, m0 = m → md1 = md0, asynced0 → synced(files, icache, pcache), links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(m, md0, true, # links(m, dirs), m3, m1), asynced; err, icache); icache_set#(mkinode(m0, md1, true, # links(m0, dirs), m5, m2), asynced; err, icache); skip; dcache_delete#(m, mkdentry(str, entries0[str]).name; err, dcache); dcache_set#(m0, str0, negdentry(str0); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced0 → synced(files, icache, pcache))), str0 ∈ entries

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] → [dirs[entries0[str]], m4, md3, m6, m7, 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: dirs[entries0[str]], m4, md3, m6, m7, entries1