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Proof step 168 from proof inv-evict (previous step)

# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files -- m), afs-cons(dirs, files), synced(files, icache, pcache), m ∈ files, ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m ⊦ m = ROOT_INO, m ∈ dirs, ∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files -- m → synced(ino, icache -- m, evict(m, pcache))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 169:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), pcache[datakey(ino, n)].dirty, afs-cons(dirs, files), afs-cons(dirs, files -- m), synced(files, icache, pcache), m ∈ files, ino ∈ files, datakey(ino, n) ∈ pcache, ino ∈ icache → ¬ icache[ino].dirty, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data?, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ ino = m, 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)%⊦ ino ≠ ino0 → ( datakey(ino, pageno) ∈ evict(ino0, pcache) ↔ datakey(ino, pageno) ∈ pcache); (s)% ⊦ ino ≠ ino0 → (icache -- ino0)[ino] = icache[ino]; (s)% ⊦ ino ∈ icache -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ icache; (s)%⊦ synced(ino, icache, pcache) ↔ (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty); (s)% ⊦ ino ∈ files -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ files; (s)