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Proof step 138 from proof inv-write_inode (previous step)

icache[ino] = mkientry(boolvar2, mkinode(m6, md2, boolvar1, m7, m8, m9)), icache[m1] = mkientry(false, mkinode(m1, md0, true, # links(m1, dirs), m2, m0)), dirs[m1] = mkdir(m0, md0, # links(m1, dirs), m2, entries), afs-cons(dirs[m1, mkdir(m0, md, # links(m1, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ icache, m1 ∈ icache, m1 ∈ dirs, asynced2 → synced(files, icache, pcache), m1 ∈ icache → icache[m1].inode.ino = m1 ∧ (icache[m1].dirty ⊃ icache[m1].inode.ino ∈ files ∧ icache[m1].inode.nlink = files[icache[m1].inode.ino].nlink ∧ icache[m1].inode.nsubdirs = 0 ∧ ¬ icache[m1].inode.directory ; (m1 ∈ dirs ∨ m1 ∈ files) ∧ icache[m1].inode = (icache[m1].inode.ino ∈ dirs ⊃ mkinode (icache[m1].inode.ino, dirs[icache[m1].inode.ino].meta, true, dirs[icache[m1].inode.ino].nlink, dirs[icache[m1].inode.ino].nsubdirs, dirs[icache[m1].inode.ino].size) ;mkinode (icache[m1].inode.ino, files[icache[m1].inode.ino].meta, false, files[icache[m1].inode.ino].nlink, 0, files[icache[m1].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) ) ) ⊦ ino = m1, m6 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m7 = files[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md2, boolvar1, m7, m8, m9) = (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) ) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 139:
icache[ino] = mkientry(boolvar2, mkinode(m6, md2, boolvar1, m7, m8, m9)), icache[m1] = mkientry(false, mkinode(m1, md0, true, # links(m1, dirs), m2, m0)), dirs[m1] = mkdir(m0, md0, # links(m1, dirs), m2, entries), afs-cons(dirs[m1, mkdir(m0, md, # links(m1, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ icache, m1 ∈ icache, m1 ∈ dirs, asynced2 → synced(files, icache, pcache), ∀ 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) ) ) ⊦ ino = m1, m6 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m7 = files[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md2, boolvar1, m7, m8, m9) = (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) ) )

Rule argument

Additional information

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