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Proof step 215 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), key ∈ pcache, m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache, ⌊err0⌋ ⊦ key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files1 ∧ ( ¬ pcache[key].dirty → key.part ∈ (key.ino = m ⊃ mkfile(m3, md, # links(key.ino, dirs), content1[n0, buf]);files1[key.ino]).content ∧ pcache[key].page = (key.ino = m ⊃ mkfile(m3, md, # links(key.ino, dirs), content1[n0, buf]);files1[key.ino]).content[key.part])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 216:
# 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), pcache[key] = mkpentry(boolvar, 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])]), pcache-cons(pcache, dirs, files1), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, key ∈ pcache, ⌊err0⌋ ⊦ key.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files1 ∧ ( ¬ boolvar → key.part ∈ (key.ino = m ⊃ mkfile(m3, md, # links(key.ino, dirs), content1[n0, buf]);files1[key.ino]).content ∧ buf0 = (key.ino = m ⊃ mkfile(m3, md, # links(key.ino, dirs), content1[n0, buf]);files1[key.ino]).content[key.part])

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[key], boolvar, buf0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[key], boolvar, buf0