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Proof step 102 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar, inode), pcache[datakey(m, n0), mkpentry(false, buf)][datakey(ino, n)] = mkpentry(true, buf0), files1[m] = mkfile(m3, md, # links(m, dirs), content1), files0[m] = mkfile(m1, md0, # links(m, dirs), content), pcache[datakey(m, n0)] = mkpentry(true, buf), n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]), afs-cons(dirs, files1), afs-cons(dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), ino ∈ dirs, m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache, datakey(ino, n) ∈ pcache[datakey(m, n0), mkpentry(false, buf)], ino ∈ icache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ datakey(ino, n) = datakey(m, n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 103:
# buf = VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar, inode), pcache[datakey(m, n0)] = mkpentry(true, buf), files0[m] = mkfile(m1, md0, # links(m, dirs), content), files1[m] = mkfile(m3, md, # links(m, dirs), content1), pcache[datakey(ino, n)] = mkpentry(true, buf0), n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files1), afs-cons(dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, ino ∈ dirs, datakey(ino, n) ∈ pcache, ino ∈ icache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ datakey(ino, n) = datakey(m, n0)

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)