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Proof step 131 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), icache[m1] = mkientry(boolvar0, mkinode(m1, md0, boolvar, m5, m3, m4)), files[m1] = mkfile(m2, md1, m5, content0), afs-cons(dirs, files), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), synced(dirs, icache, pcache), synced(files, icache, pcache), m1 ∈ files, m ∈ files, m1 ∈ icache, (boolvar0 ⊃ m3 = 0 ∧ ¬ boolvar;mkinode(m1, md0, boolvar, m5, m3, m4) = mkinode(m1, md1, false, m5, 0, m2)), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ 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, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ (boolvar0 ⊃ m5 = (m1 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[m1]).nlink ∧ m3 = 0 ∧ ¬ boolvar ; mkinode(m1, md0, boolvar, m5, m3, m4) = mkinode (m1, (m1 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[m1]).meta, false, (m1 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[m1]).nlink, 0, (m1 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[m1]).size) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 132:
# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), icache[m1] = mkientry(boolvar0, mkinode(m1, md0, boolvar, # links(m1, dirs), m3, m4)), files[m1] = mkfile(m2, md1, # links(m1, dirs), content0), afs-cons(dirs, files), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), synced(dirs, icache, pcache), synced(files, icache, pcache), m1 ∈ files, m ∈ files, m1 ∈ icache, (boolvar0 ⊃ m3 = 0 ∧ ¬ boolvar;mkinode(m1, md0, boolvar, # links(m1, dirs), m3, m4) = mkinode(m1, md1, false, # links(m1, dirs), 0, m2)), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ 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, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ (boolvar0 ⊃ # links(m1, dirs) = (m1 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);mkfile(m2, md1, # links(m1, dirs), content0)).nlink ∧ m3 = 0 ∧ ¬ boolvar ; mkinode(m1, md0, boolvar, # links(m1, dirs), m3, m4) = mkinode (m1, (m1 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);mkfile(m2, md1, # links(m1, dirs), content0)).meta, false, (m1 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);mkfile(m2, md1, # links(m1, dirs), content0)).nlink, 0, (m1 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);mkfile(m2, md1, # links(m1, dirs), content0)).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