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Proof step 197 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), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced1 → synced(files, icache, pcache), ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m ⊦ m = ROOT_INO, pcache-cons(evict(m, pcache), dirs, files -- m), m ∈ dirs

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 198:
⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]))
Proof step 199:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), afs-cons(dirs, files -- m), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced1 → synced(files, icache, pcache), ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data? ⊦ m = ROOT_INO, m ∈ dirs, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ # evict(m, pcache)[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files -- m) ∧ ( ¬ evict(m, pcache)[key].dirty → key.part ∈ (files -- m)[key.ino].content ∧ evict(m, pcache)[key].page = (files -- m)[key.ino].content[key.part])

Rule argument

spec: cache-base name: pcache-cons seq: ⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])) subst: [pcache, dirs, files] → [evict(m, pcache), dirs, files -- m] flags: <all paths>

Additional information

Used terms: evict(m, pcache), dirs, files -- m