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Proof step 230 from proof inv-evict (previous step)

# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files -- m), afs-cons(dirs, files), icache-cons(icache, dirs, files), synced(dirs, icache, pcache), m ∈ files, ino ∈ icache, asynced1 → synced(files, icache, pcache), ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m ⊦ ino = m, m = ROOT_INO, m ∈ dirs, icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ icache[ino].inode.ino ∈ files ∧ icache[ino].inode.nlink = (files -- m)[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 -- m)[icache[ino].inode.ino].meta, false, (files -- m)[icache[ino].inode.ino].nlink, 0, (files -- m)[icache[ino].inode.ino].size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 231:
# 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) ) )

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [icache[ino].inode, m1, md0, boolvar, m2, m3, m4]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache[ino].inode, m1, md0, boolvar, m2, m3, m4