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Proof step 61 from proof inv-evict (previous step)

# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs -- m, files), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ m = ROOT_INO, ∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs -- m → synced(ino, icache -- m, pcache)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), pcache[datakey(ino, n)].dirty, afs-cons(dirs, files), afs-cons(dirs -- m, files), synced(dirs, icache, pcache), m ∈ dirs, ino ∈ dirs, datakey(ino, n) ∈ pcache, asynced1 → synced(files, icache, pcache), ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ ino = m, m = ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ 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 ∈ dirs -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ dirs; (s)