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Proof step 125 from proof inv-writepage (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 126:
# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), icache[m1] = mkientry(boolvar0, mkinode(m1, md0, boolvar, m2, m3, m4)), 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), m ∈ files, m1 ∈ icache, (boolvar0 ⊃ m1 ∈ files ∧ m2 = files[m1].nlink ∧ m3 = 0 ∧ ¬ boolvar ; (m1 ∈ dirs ∨ m1 ∈ files) ∧ mkinode(m1, md0, boolvar, m2, m3, m4) = (m1 ∈ dirs ⊃ mkinode(m1, dirs[m1].meta, true, dirs[m1].nlink, dirs[m1].nsubdirs, dirs[m1].size) ;mkinode(m1, files[m1].meta, false, files[m1].nlink, 0, files[m1].size) ) ), ∀ 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 ⊃ m1 ∈ files ∧ m2 = (m1 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[m1]).nlink ∧ m3 = 0 ∧ ¬ boolvar ; (m1 ∈ dirs ∨ m1 ∈ files) ∧ mkinode(m1, md0, boolvar, m2, m3, m4) = (m1 ∈ dirs ⊃ mkinode(m1, dirs[m1].meta, true, dirs[m1].nlink, dirs[m1].nsubdirs, dirs[m1].size) ;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) ) )

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkientry(boolvar, inode).dirty ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)