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Proof step 125 from proof fsync-pages-inv (previous step)

# 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), 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[datakey(m, n0), mkpentry(false, buf)][key] = mkpentry(boolvar, buf0), files0[key.ino] = mkfile(m5, md2, m6, content2), 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), m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache, key ∈ pcache[datakey(m, n0), mkpentry(false, buf)], key ∈ pcache0 → key.data? ∧ # 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.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files1 ∧ (¬ boolvar → key.part ∈ content0 ∧ buf0 = content0[key.part])

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 126:
# 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), pcache[datakey(m, n0), mkpentry(false, buf)][key] = mkpentry(boolvar, buf0), 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), 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), key ∈ pcache[datakey(m, n0), mkpentry(false, buf)], datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, key ∈ pcache0 → key.data? ∧ # buf1 = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ boolvar0 → key.part ∈ content2 ∧ buf1 = content2[key.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]), ∀ 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), key.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files1 ∧ (¬ boolvar → key.part ∈ content0 ∧ buf0 = content0[key.part])

Rule argument

fma: key = datakey(m, n0)

Additional information

Used simplifier rules: ⊦ pcache[key, pe][key] = pe; (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws)% ⊦ datakey(m, m0).ino = m; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ key ∈ pcache[key, pe]; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).part = m0; (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% ⊦ content[n, buf][n] = buf; (s)% ⊦ n ∈ content[n, buf]; (s) Used formulas: key = datakey(m, n0)