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Proof step 163 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, pcache[datakey(m, pageno), mkpentry(true, buf)][datakey(ino, n)] = mkpentry(true, buf0), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ dirs, m ∈ files, datakey(ino, n) ∈ pcache[datakey(m, pageno), mkpentry(true, buf)], ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 164:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, pageno), mkpentry(true, buf)][datakey(ino, n)] = mkpentry(true, buf0), icache[ino] = mkientry(boolvar, inode), afs-cons(dirs, files), synced(dirs, icache, pcache), datakey(ino, n) ∈ pcache[datakey(m, pageno), mkpentry(true, buf)], m ∈ files, ino ∈ dirs, ino ∈ icache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦

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