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Proof step 193 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, # links(m0, dirs) = files1[m0].nlink, files0[m0] = mkfile(m4, md2, # links(m0, dirs), content0), icache[m0] = mkientry(boolvar0, mkinode(m0, md1, false, # links(m0, dirs), 0, m6)), 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), 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), m0 ∈ icache, m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache, m0 ∈ files0, m0 ∈ files1, ¬ boolvar0 → mkinode(m0, md1, false, # links(m0, dirs), 0, m6) = mkinode(m0, md2, false, # links(m0, dirs), 0, m4), (boolvar0 ⊃ # links(m0, dirs) = files1[m0].nlink ;mkinode(m0, md1, false, # links(m0, dirs), 0, m6) = mkinode(m0, files1[m0].meta, false, files1[m0].nlink, 0, files1[m0].size) ), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files1 ∧ icache[ino0].inode.nlink = files1[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files1) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files1[icache[ino0].inode.ino].meta, false, files1[icache[ino0].inode.ino].nlink, 0, files1[icache[ino0].inode.ino].size) ) ), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files0 ∧ icache[ino0].inode.nlink = files0[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files0) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files0[icache[ino0].inode.ino].meta, false, files0[icache[ino0].inode.ino].nlink, 0, files0[icache[ino0].inode.ino].size) ) ) ⊦ (boolvar0 ⊃ # links(m0, dirs) = (m0 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[m0]).nlink ; mkinode(m0, md1, false, # links(m0, dirs), 0, m6) = mkinode (m0, (m0 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[m0]).meta, false, (m0 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[m0]).nlink, 0, (m0 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[m0]).size) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 194:
# links(m0, dirs) = files1[m0].nlink, # buf = VFS_PAGE_SIZE, 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), icache[m0] = mkientry(boolvar0, mkinode(m0, md1, false, files1[m0].nlink, 0, m6)), files0[m0] = mkfile(m4, md2, files1[m0].nlink, content0), 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), m0 ∈ files1, m0 ∈ files0, datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, m0 ∈ icache, ¬ boolvar0 → mkinode(m0, md1, false, files1[m0].nlink, 0, m6) = mkinode(m0, md2, false, files1[m0].nlink, 0, m4), ¬ boolvar0 → mkinode(m0, md1, false, files1[m0].nlink, 0, m6) = mkinode(m0, files1[m0].meta, false, files1[m0].nlink, 0, files1[m0].size), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files0 ∧ icache[ino0].inode.nlink = files0[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files0) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files0[icache[ino0].inode.ino].meta, false, files0[icache[ino0].inode.ino].nlink, 0, files0[icache[ino0].inode.ino].size) ) ), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files1 ∧ icache[ino0].inode.nlink = files1[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files1) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files1[icache[ino0].inode.ino].meta, false, files1[icache[ino0].inode.ino].nlink, 0, files1[icache[ino0].inode.ino].size) ) ) ⊦ (boolvar0 ⊃ files1[m0].nlink = (m0 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[m0]).nlink ; mkinode(m0, md1, false, files1[m0].nlink, 0, m6) = mkinode (m0, (m0 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[m0]).meta, false, (m0 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[m0]).nlink, 0, (m0 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[m0]).size) )

Rule argument

Additional information

Used simplifier rules: 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