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Proof step 165 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar, inode), 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 → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ datakey(ino, n) = datakey(m, pageno)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 166:
# buf = VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar, inode), pcache[datakey(ino, n)] = mkpentry(true, buf0), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ files, ino ∈ dirs, datakey(ino, n) ∈ pcache, ino ∈ icache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ datakey(ino, n) = datakey(m, pageno)

Rule argument

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (key ∈ pcache[key0, pe] ↔ key ∈ pcache); (s)% ⊦ key ≠ key0 → pcache[key0, pe][key] = pcache[key]; (s)