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Proof step 211 from proof inv-evict (previous step)

# links(m, dirs) = 0, files[key.ino] = mkfile(m1, md0, m2, content0), files[m] = mkfile(m0, md, 0, content), evict(m, pcache)[key] = mkpentry(boolvar, buf), pcache[key] = mkpentry(boolvar0, buf0), key.data?, afs-cons(dirs, files), afs-cons(dirs, files -- m), synced(dirs, icache, pcache), m ∈ files, key ∈ evict(m, pcache), asynced1 → synced(files, icache, pcache), key ∈ pcache → # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar0 → key.part ∈ content0 ∧ buf0 = content0[key.part]), ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files ∧ (¬ pcache[key0].dirty → key0.part ∈ files[key0.ino].content ∧ pcache[key0].page = files[key0.ino].content[key0.part]), ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data? ⊦ key.ino = m, m = ROOT_INO, m ∈ dirs, # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf = content0[key.part])

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: key name: elim-02 seq: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)) subst: [key, m, m0] → [key, m3, m4]

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → ( datakey(ino, pageno) ∈ evict(ino0, pcache) ↔ datakey(ino, pageno) ∈ pcache); (s)%⊦ ino ≠ ino0 ∧ datakey(ino, pageno) ∈ pcache → evict(ino0, pcache)[datakey(ino, pageno)] = pcache[datakey(ino, pageno)]; (s)% ⊦ datakey(m, m0).data?; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws)% ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key, m3, m4