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Proof step 227 from proof inv-rmdir (previous step)

# links(m, dirs) = dirs[m].nlink, # links(entries[str], dirs) = m1, dirs[m] = mkdir(dirs[m].size, md3, dirs[m].nlink, dirs[m].nsubdirs, entries), dirs[entries[str]] = mkdir(m0, md2, m1, m2, ∅), entries[str] = dirs[m].entries[str], dirs[entries[str]] = mkdir(m0, md1, m1, m2, entries0), entries0 = ∅, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, str ∈ entries, entries[str] ∈ dirs, str ∈ dirs[m].entries, asynced1 → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(entries[str], md0, true, m1, m2, m0), asynced; err, icache); icache_set#(mkinode(m, md, true, # links(m, dirs), dirs[m].nsubdirs, dirs[m].size), asynced; err, icache); dcache_delete#(m, mkdentry(str, entries[str]).name; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))), entries[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 228:
# links(m, dirs) = dirs[m].nlink, entries[str] = dirs[m].entries[str], dirs[entries[str]] = mkdir(m0, md1, # links(entries[str], dirs), m2, ∅), dirs[m] = mkdir(dirs[m].size, md3, dirs[m].nlink, dirs[m].nsubdirs, entries), entries[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), str ∈ dirs[m].entries, entries[str] ∈ dirs, str ∈ entries, m ∈ dirs, asynced1 → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(entries[str], md0, true, # links(entries[str], dirs), m2, m0), asynced; err, icache); icache_set#(mkinode(m, md, true, # links(m, dirs), dirs[m].nsubdirs, dirs[m].size), asynced; err, icache); dcache_delete#(m, mkdentry(str, entries[str]).name; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → 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)