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Proof step 170 from proof fsync-pages-inv (previous step)

# 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[ino] = mkientry(boolvar0, mkinode(m0, md1, boolvar, m4, m5, m6)), 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, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), ino ∈ icache, datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files1) ;valid-ino(ino, dirs, files1) ∧ valid-inode(icache[ino].inode, dirs, files1) ) ⊦ m0 = ino ∧ (boolvar0 ⊃ ino ∈ files1 ∧ m4 = (ino = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[ino]).nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files1) ∧ mkinode(ino, md1, boolvar, m4, m5, m6) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[ino]).meta, false, (ino = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[ino]).nlink, 0, (ino = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[ino]).size) ) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 171:
# buf = VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar0, mkinode(m0, md1, boolvar, m4, m5, 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), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache, ino ∈ icache, ∀ 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) ) ) ⊦ m0 = ino ∧ (boolvar0 ⊃ ino ∈ files1 ∧ m4 = (ino = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[ino]).nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files1) ∧ mkinode(ino, md1, boolvar, m4, m5, m6) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[ino]).meta, false, (ino = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[ino]).nlink, 0, (ino = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[ino]).size) ) )

Rule argument

Additional information

Used simplifier rules: ⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)