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Proof step 229 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, (m5 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);mkfile(m7, md2, # links(m5, dirs), content2)) = mkfile(m0, md1, m4, content0), 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(m5, m6)] = mkpentry(false, content2[m6]), files1[m5] = mkfile(m7, md2, # links(m5, dirs), content2), 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, pcache), synced(dirs, icache, pcache0), m5 ∈ files1, datakey(m, n0) ∈ pcache, m ∈ files1, m ∈ files0, datakey(m5, m6) ∈ pcache, m6 ∈ content2, ⌊err0⌋ , ∀ key0. key0 ∈ pcache0 → key0.data? ∧ # pcache0[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files0 ∧ (¬ pcache0[key0].dirty → key0.part ∈ files0[key0.ino].content ∧ pcache0[key0].page = files0[key0.ino].content[key0.part]), ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ (¬ pcache[key0].dirty → key0.part ∈ files1[key0.ino].content ∧ pcache[key0].page = files1[key0.ino].content[key0.part]) ⊦ m6 ∈ content0 ∧ content2[m6] = content0[m6]

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 230:
# buf = VFS_PAGE_SIZE, (m5 = m ⊃ mkfile(m3, md, # links(m, dirs), content1[n0, buf]);mkfile(m7, md2, # links(m5, dirs), content2)) = mkfile(m0, md1, m4, content0), files1[m5] = mkfile(m7, md2, # links(m5, dirs), content2), pcache[datakey(m5, m6)] = mkpentry(false, content2[m6]), 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), m5 = m, 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, pcache0), synced(dirs, icache, pcache), m6 ∈ content2, datakey(m5, m6) ∈ pcache, m ∈ files0, m ∈ files1, datakey(m, n0) ∈ pcache, m5 ∈ files1, ⌊err0⌋ , ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ (¬ pcache[key0].dirty → key0.part ∈ files1[key0.ino].content ∧ pcache[key0].page = files1[key0.ino].content[key0.part]), ∀ key0. key0 ∈ pcache0 → key0.data? ∧ # pcache0[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files0 ∧ (¬ pcache0[key0].dirty → key0.part ∈ files0[key0.ino].content ∧ pcache0[key0].page = files0[key0.ino].content[key0.part]) ⊦ m6 ∈ content0 ∧ content2[m6] = content0[m6]

Rule argument

fma: m5 = m

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws) Used formulas: m5 = m