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Proof step 190 from proof inv-evict (previous step)

# links(m, dirs) = 0, icache[ino] = mkientry(boolvar, inode), evict(m, pcache)[datakey(ino, n)] = mkpentry(true, buf), files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files -- m), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ dirs, m ∈ files, datakey(ino, n) ∈ pcache, asynced1 → synced(files, icache, pcache), ino ∈ icache → ¬ boolvar, ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ ino = m, m = ROOT_INO, m ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 191:
# links(m, dirs) = 0, icache[ino] = mkientry(boolvar, inode), files[m] = mkfile(m0, md, 0, content), pcache[datakey(ino, n)] = mkpentry(true, buf), afs-cons(dirs, files), afs-cons(dirs, files -- m), synced(dirs, icache, pcache), datakey(ino, n) ∈ pcache, m ∈ files, ino ∈ dirs, ino ∈ icache → ¬ boolvar, asynced1 → synced(files, icache, pcache), ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data? ⊦ m = ROOT_INO, m ∈ dirs

Rule argument

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 ∧ datakey(ino, pageno) ∈ pcache → evict(ino0, pcache)[datakey(ino, pageno)] = pcache[datakey(ino, pageno)]; (s)