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Proof step 129 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), files0[key.ino] = mkfile(m5, md2, m6, content2), pcache0[key] = mkpentry(boolvar0, buf1), 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), pcache[key] = mkpentry(false, files1[key.ino].content[key.part]), 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, m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache, key ∈ pcache, key.ino ∈ files1, key ∈ pcache0 → # buf1 = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ boolvar0 → key.part ∈ content2 ∧ buf1 = content2[key.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]), ∀ 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 = datakey(m, n0), 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 130:
# buf = VFS_PAGE_SIZE, # files1[m7].content[m8] = VFS_PAGE_SIZE, (m7 = m ⊃ mkfile(m3, md, # links(m7, dirs), content1[n0, buf]);files1[m7]) = mkfile(m0, md1, m4, content0), pcache[key] = mkpentry(false, files1[m7].content[m8]), 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), pcache0[key] = mkpentry(boolvar0, buf1), files0[m7] = mkfile(m5, md2, m6, content2), key = datakey(m7, m8), 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), m7 ∈ files1, key ∈ pcache, datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, m8 ∈ files1[m7].content, key ∈ pcache0 → # buf1 = VFS_PAGE_SIZE ∧ m7 ∈ files0 ∧ (¬ boolvar0 → m8 ∈ content2 ∧ buf1 = content2[m8]), ∀ 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]) ⊦ key = datakey(m, n0), m8 ∈ content0 ∧ files1[m7].content[m8] = content0[m8]

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, m7, m8]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key, m7, m8