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Proof step 590 from proof inv-rename-dir-dentry (previous step)

# links(entries1[str], dirs) = dirs[entries1[str]].nlink, # links(m0, dirs) = dirs[m0].nlink, # links(m, dirs) = dirs[m].nlink, # links(entries[str0], dirs) = m2, dirs[entries1[str]].entries = ∅, dirs[m0] = mkdir(dirs[m0].size, md4, dirs[m0].nlink, dirs[m0].nsubdirs, entries), dirs[m] = mkdir(dirs[m].size, md7, dirs[m].nlink, dirs[m].nsubdirs, entries1), dirs[entries1[str]] = mkdir(dirs[entries1[str]].size, md6, dirs[entries1[str]].nlink, dirs[entries1[str]].nsubdirs, ∅), dirs[entries[str0]] = mkdir(m1, md3, m2, m3, entries2), entries1[str] = dirs[m].entries[str], entries[str0] = dirs[m0].entries[str0], dirs[entries[str0]] = mkdir(m1, md0, 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), str ∈ entries1, m0 ∈ dirs, m ∈ dirs, entries[str0] ∈ dirs, entries1[str] ∈ dirs, str0 ∈ entries, str ∈ dirs[m].entries, str0 ∈ dirs[m0].entries, m = m0 → md1 = md2, 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(m0, md2, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), asynced; err, icache); icache_set#(mkinode(m, md1, true, # links(m, dirs), dirs[m].nsubdirs, dirs[m].size), asynced; err, icache); if true then icache_set# (mkinode(entries1[str], md, true, # links(entries1[str], dirs), dirs[entries1[str]].nsubdirs, dirs[entries1[str]].size), asynced ; err, icache); dcache_delete#(m0, mkdentry(str0, entries[str0]).name; err, dcache); dcache_set#(m, mkdentry(str, entries1[str]).name, mkdentry(str, entries1[str]); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced0 → synced(files, icache, pcache))), entries1[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 591:
# links(m, dirs) = dirs[m].nlink, # links(m0, dirs) = dirs[m0].nlink, # links(entries1[str], dirs) = dirs[entries1[str]].nlink, dirs[entries1[str]].entries = ∅, entries[str0] = dirs[m0].entries[str0], entries1[str] = dirs[m].entries[str], dirs[entries[str0]] = mkdir(m1, md0, # links(entries[str0], dirs), m3, entries0), dirs[entries1[str]] = mkdir(dirs[entries1[str]].size, md6, dirs[entries1[str]].nlink, dirs[entries1[str]].nsubdirs, ∅), dirs[m] = mkdir(dirs[m].size, md7, dirs[m].nlink, dirs[m].nsubdirs, entries1), dirs[m0] = mkdir(dirs[m0].size, md4, dirs[m0].nlink, dirs[m0].nsubdirs, entries), entries1[str] ≠ ROOT_INO, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str0 ∈ dirs[m0].entries, str ∈ dirs[m].entries, str0 ∈ entries, entries1[str] ∈ dirs, entries[str0] ∈ dirs, m ∈ dirs, m0 ∈ dirs, str ∈ entries1, asynced0 → synced(files, icache, pcache), m = m0 → md1 = md2, 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(m0, md2, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), asynced; err, icache); icache_set#(mkinode(m, md1, true, # links(m, dirs), dirs[m].nsubdirs, dirs[m].size), asynced; err, icache); if true then icache_set# (mkinode(entries1[str], md, true, # links(entries1[str], dirs), dirs[entries1[str]].nsubdirs, dirs[entries1[str]].size), asynced ; err, icache); dcache_delete#(m0, mkdentry(str0, entries[str0]).name; err, dcache); dcache_set#(m, mkdentry(str, entries1[str]).name, mkdentry(str, entries1[str]); 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)