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Proof step 171 from proof inv-evict (previous step)

# links(m, dirs) = 0, pcache[datakey(ino, n)] = mkpentry(true, buf), files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), afs-cons(dirs, files -- m), synced(files, icache, pcache), m ∈ files, ino ∈ files, datakey(ino, n) ∈ pcache, ino ∈ icache → ¬ icache[ino].dirty, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m, ∀ key. key ∈ pcache → key.data?, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ ino = m, m = ROOT_INO, m ∈ dirs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 172:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), pcache[datakey(ino, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar, inode), afs-cons(dirs, files -- m), afs-cons(dirs, files), synced(files, icache, pcache), datakey(ino, n) ∈ pcache, ino ∈ files, m ∈ files, ino ∈ icache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ evict(m, pcache) → key.data? ∧ key.ino ≠ m ⊦ ino = m, m = ROOT_INO, m ∈ dirs

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[ino], boolvar, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[ino], boolvar, inode