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Proof step 274 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, icache[m0] = mkientry(boolvar0, 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])]), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), m0 ∈ icache, datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, m0 ∈ files1, ⌊err0⌋ , (boolvar0 ⊃ m0 ∈ files0 ∧ m4 = files0[m0].nlink ∧ m5 = 0 ∧ ¬ boolvar ; (m0 ∈ dirs ∨ m0 ∈ files0) ∧ mkinode(m0, md1, boolvar, m4, m5, m6) = (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files0[m0].meta, false, files0[m0].nlink, 0, files0[m0].size) ) ), (boolvar0 ⊃ m0 ∈ files1 ∧ m4 = files1[m0].nlink ∧ m5 = 0 ∧ ¬ boolvar ; (m0 ∈ dirs ∨ m0 ∈ files1) ∧ mkinode(m0, md1, boolvar, m4, m5, m6) = (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;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 ⊃ m0 ∈ files1 ∧ m4 = (m0 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[m0]).nlink ∧ m5 = 0 ∧ ¬ boolvar ; (m0 ∈ dirs ∨ m0 ∈ files1) ∧ mkinode(m0, md1, boolvar, m4, m5, m6) = (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(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 275:
# buf = VFS_PAGE_SIZE, icache[m0] = mkientry(boolvar0, 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])]), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), m0 ∈ icache, datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, m0 ∈ files1, ⌊err0⌋ , (boolvar0 ⊃ m4 = files1[m0].nlink ∧ m5 = 0 ∧ ¬ boolvar ;mkinode(m0, md1, boolvar, m4, m5, m6) = mkinode(m0, files1[m0].meta, false, files1[m0].nlink, 0, files1[m0].size) ), (boolvar0 ⊃ m0 ∈ files0 ∧ m4 = files0[m0].nlink ∧ m5 = 0 ∧ ¬ boolvar ;(m0 ∈ dirs ∨ m0 ∈ files0) ∧ mkinode(m0, md1, boolvar, m4, m5, m6) = mkinode(m0, files0[m0].meta, false, files0[m0].nlink, 0, files0[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 ⊃ m4 = (m0 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);files1[m0]).nlink ∧ m5 = 0 ∧ ¬ boolvar ; mkinode(m0, md1, boolvar, m4, m5, 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(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)