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Proof step 113 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, 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), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache, dirs, files1), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache ⊦ ∀ key. key ∈ pcache[datakey(m, n0), mkpentry(false, buf)] → key.data? ∧ # pcache[datakey(m, n0), mkpentry(false, buf)][key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])]) ∧ ( ¬ pcache[datakey(m, n0), mkpentry(false, buf)][key].dirty → key.part ∈ files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])][key.ino].content ∧ pcache[datakey(m, n0), mkpentry(false, buf)][key].page = files1[m, mkfile(m3, md, # links(m, dirs), content1[n0, buf])][key.ino].content[key.part])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 114:
# buf = VFS_PAGE_SIZE, 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), 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])]), pcache-cons(pcache, dirs, files1), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), key ∈ pcache[datakey(m, n0), mkpentry(false, buf)], datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0 ⊦ key.data? ∧ # pcache[datakey(m, n0), mkpentry(false, buf)][key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files1 ∧ ( ¬ pcache[datakey(m, n0), mkpentry(false, buf)][key].dirty → key.part ∈ (key.ino = m ⊃ mkfile(m3, md, # links(key.ino, dirs), content1[n0, buf]);files1[key.ino]).content ∧ pcache[datakey(m, n0), mkpentry(false, buf)][key].page = (key.ino = m ⊃ mkfile(m3, md, # links(key.ino, dirs), content1[n0, buf]);files1[key.ino]).content[key.part])

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)