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Proof step 307 from proof inv-rename-dir-negdentry (previous step)

# links(m, dirs) = m2, # links(m0, dirs) = dirs[m0].nlink, # links(entries[str], dirs) = dirs[entries[str]].nlink, dirs[entries[str]] = mkdir(dirs[entries[str]].size, md5, dirs[entries[str]].nlink, dirs[entries[str]].nsubdirs, entries2), dirs[m0] = mkdir(dirs[m0].size, md4, dirs[m0].nlink, dirs[m0].nsubdirs, entries1), dirs[m] = mkdir(m1, md2, m2, m3, entries), entries[str] = entries0[str], dirs[m] = mkdir(m1, md, m2, m3, entries0), 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, entries[str] ∈ dirs, str ∈ entries, 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, m2, m3, m1), asynced; err, icache); icache_set#(mkinode(m0, md1, true, # links(m0, dirs), dirs[m0].nsubdirs, dirs[m0].size), asynced; err, icache); skip; dcache_delete#(m, mkdentry(str, entries[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 ∈ dirs[m0].entries, str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 308:
# links(entries0[str], dirs) = dirs[entries0[str]].nlink, # links(m0, dirs) = dirs[m0].nlink, dirs[m] = mkdir(m1, md, # links(m, dirs), m3, entries0), dirs[m0] = mkdir(dirs[m0].size, md4, dirs[m0].nlink, dirs[m0].nsubdirs, entries1), 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 ∈ entries1, ¬ str0 ∈ dirs[m0].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), dirs[m0].nsubdirs, dirs[m0].size), 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)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base