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Proof step 231 from proof inv-evict (previous step)

# links(m, dirs) = 0, icache[ino].inode = mkinode(m1, md0, boolvar, m2, m3, m4), files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), afs-cons(dirs, files -- m), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino ∈ icache, m ∈ files, asynced1 → synced(files, icache, pcache), ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data? ⊦ ino = m, m = ROOT_INO, m ∈ dirs, m1 = ino ∧ (icache[ino].dirty ⊃ m1 ∈ files ∧ m2 = (files -- m)[m1].nlink ∧ m3 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[ino].inode = (m1 ∈ dirs ⊃ mkinode(m1, dirs[m1].meta, true, dirs[m1].nlink, dirs[m1].nsubdirs, dirs[m1].size) ;mkinode(m1, (files -- m)[m1].meta, false, (files -- m)[m1].nlink, 0, (files -- m)[m1].size) ) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 232:
# links(m, dirs) = 0, icache[ino].inode = mkinode(m1, md0, boolvar, m2, m3, m4), files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), afs-cons(dirs, files -- m), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), ino ∈ icache, m ∈ files, asynced1 → synced(files, icache, pcache), ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data? ⊦ ino = m, m = ROOT_INO, m ∈ dirs, m1 = ino ∧ (icache[ino].dirty ⊃ ino ∈ files ∧ m2 = 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, (files -- m)[ino].meta, false, (files -- m)[ino].nlink, 0, (files -- m)[ino].size) ) )

Rule argument

Additional information

Used simplifier rules: ino ∈ files ⊦ ino ≠ ino0 → (files -- ino0)[ino] = files[ino]; (s)