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Proof step 225 from proof fsync-pages-inv (previous step)

# files1[key.ino].content[key.part] = VFS_PAGE_SIZE, # buf = VFS_PAGE_SIZE, (key.ino = m ⊃ mkfile(m3, md, # links(key.ino, dirs), content1[n0, buf]);files1[key.ino]) = mkfile(m0, md1, m4, content0), pcache[key] = mkpentry(false, files1[key.ino].content[key.part]), files1[m] = mkfile(m3, md, # links(m, dirs), content1), files0[m] = mkfile(m1, md0, # links(m, dirs), content), pcache[datakey(m, n0)] = mkpentry(true, buf), key.data?, n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]), afs-cons(dirs, files1), afs-cons(dirs, files0), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), key.part ∈ files1[key.ino].content, key ∈ pcache, m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache, key.ino ∈ files1, ⌊err0⌋ , ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ (¬ pcache[key0].dirty → key0.part ∈ files1[key0.ino].content ∧ pcache[key0].page = files1[key0.ino].content[key0.part]), ∀ key0. key0 ∈ pcache0 → key0.data? ∧ # pcache0[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files0 ∧ (¬ pcache0[key0].dirty → key0.part ∈ files0[key0.ino].content ∧ pcache0[key0].page = files0[key0.ino].content[key0.part]) ⊦ key.part ∈ content0 ∧ files1[key.ino].content[key.part] = content0[key.part]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 226:
# buf = VFS_PAGE_SIZE, # files1[m5].content[m6] = VFS_PAGE_SIZE, (m5 = m ⊃ mkfile(m3, md, # links(m5, dirs), content1[n0, buf]);files1[m5]) = mkfile(m0, md1, m4, content0), pcache[datakey(m, n0)] = mkpentry(true, buf), files0[m] = mkfile(m1, md0, # links(m, dirs), content), files1[m] = mkfile(m3, md, # links(m, dirs), content1), pcache[key] = mkpentry(false, files1[m5].content[m6]), key = datakey(m5, m6), key.data?, n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files1), afs-cons(dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), m5 ∈ files1, datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, key ∈ pcache, m6 ∈ files1[m5].content, ⌊err0⌋ , ∀ key0. key0 ∈ pcache0 → key0.data? ∧ # pcache0[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files0 ∧ (¬ pcache0[key0].dirty → key0.part ∈ files0[key0.ino].content ∧ pcache0[key0].page = files0[key0.ino].content[key0.part]), ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ (¬ pcache[key0].dirty → key0.part ∈ files1[key0.ino].content ∧ pcache[key0].page = files1[key0.ino].content[key0.part]) ⊦ m6 ∈ content0 ∧ files1[m5].content[m6] = content0[m6]

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, m5, m6]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key, m5, m6