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Proof step 199 from proof inv-evict (previous step)

# 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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 200:
# 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), key ∈ evict(m, 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, m ∈ dirs, key.data? ∧ # evict(m, pcache)[key].page = VFS_PAGE_SIZE ∧ key.ino ≠ m ∧ key.ino ∈ files ∧ (¬ evict(m, pcache)[key].dirty → key.part ∈ files[key.ino].content ∧ evict(m, pcache)[key].page = files[key.ino].content[key.part])

Rule argument

Additional information

Used simplifier rules: ino ∈ files ⊦ ino ≠ ino0 → (files -- ino0)[ino] = files[ino]; (s)% ⊦ ino ∈ files -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)