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Proof step 257 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, 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), icache-cons(icache, dirs, files0), icache-cons(icache, dirs, files1), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), ino ∈ icache, m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache, ⌊err0⌋ ⊦ icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ icache[ino].inode.ino ∈ files1 ∧ icache[ino].inode.nlink = (icache[ino].inode.ino = m ⊃ mkfile(m3, md, # links(icache[ino].inode.ino, dirs), content1[n0, buf]);files1[icache[ino].inode.ino]) .nlink ∧ icache[ino].inode.nsubdirs = 0 ∧ ¬ icache[ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files1) ∧ icache[ino].inode = (icache[ino].inode.ino ∈ dirs ⊃ mkinode (icache[ino].inode.ino, dirs[icache[ino].inode.ino].meta, true, dirs[icache[ino].inode.ino].nlink, dirs[icache[ino].inode.ino].nsubdirs, dirs[icache[ino].inode.ino].size) ;mkinode (icache[ino].inode.ino, (icache[ino].inode.ino = m ⊃ mkfile(m3, md, # links(icache[ino].inode.ino, dirs), content1[n0, buf]);files1[icache[ino].inode.ino]) .meta, false, (icache[ino].inode.ino = m ⊃ mkfile(m3, md, # links(icache[ino].inode.ino, dirs), content1[n0, buf]);files1[icache[ino].inode.ino]) .nlink, 0, (icache[ino].inode.ino = m ⊃ mkfile(m3, md, # links(icache[ino].inode.ino, dirs), content1[n0, buf]);files1[icache[ino].inode.ino]) .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 258:
# buf = VFS_PAGE_SIZE, icache[ino].inode = mkinode(m0, md1, boolvar, m4, m5, m6), 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), 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])]), icache-cons(icache, dirs, files1), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, ino ∈ icache, ⌊err0⌋ ⊦ m0 = ino ∧ (icache[ino].dirty ⊃ m0 ∈ files1 ∧ m4 = (m0 = m ⊃ mkfile(m3, md, # links(m0, dirs), content1[n0, buf]);files1[m0]).nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files1) ∧ icache[ino].inode = (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode (m0, (m0 = m ⊃ mkfile(m3, md, # links(m0, dirs), content1[n0, buf]);files1[m0]).meta, false, (m0 = m ⊃ mkfile(m3, md, # links(m0, dirs), content1[n0, buf]);files1[m0]).nlink, 0, (m0 = m ⊃ mkfile(m3, md, # links(m0, dirs), content1[n0, buf]);files1[m0]).size) ) )

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [icache[ino].inode, m0, md1, boolvar, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache[ino].inode, m0, md1, boolvar, m4, m5, m6