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Proof step 168 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, pcache0[datakey(m3, m6)] = mkpentry(boolvar, buf), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), buf-opt.some?, m6 * VFS_PAGE_SIZE < m, m6 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), synced(dirs, icache, pcache0), m3 ∈ files0, datakey(m3, m6) ∈ pcache0, m2 ≤ m, asynced1 → synced(files0, icache, pcache0), datakey(m3, m6) ∈ pcache0 → datakey(m3, m6).data? ∧ # pcache0[datakey(m3, m6)].page = VFS_PAGE_SIZE ∧ datakey(m3, m6).ino ∈ files0 ∧ ( ¬ pcache0[datakey(m3, m6)].dirty → datakey(m3, m6).part ∈ files0[datakey(m3, m6).ino].content ∧ pcache0[datakey(m3, m6)].page = files0[datakey(m3, m6).ino].content[datakey(m3, m6).part]), ∀ key. key ∈ pcache0 → key.data?, ∀ 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]) ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m3, m6) = datakey(m3, m2 / VFS_PAGE_SIZE), # buf = VFS_PAGE_SIZE ∧ ( ¬ boolvar → m6 ∈ content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] ∧ buf = content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)][m6])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 169:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[datakey(m3, m6)] = mkpentry(false, content0[m6]), buf-opt.some?, m6 * VFS_PAGE_SIZE < m2, m6 * VFS_PAGE_SIZE < m, afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), synced(dirs, icache, pcache0), m6 ∈ content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)], m6 ∈ content0, datakey(m3, m6) ∈ pcache0, m3 ∈ files0, m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ 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]), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, content0[m6] = content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)][m6], datakey(m3, m6) = datakey(m3, m2 / VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ n ∈ content[n0, buf] ↔ n = n0 ∨ n ∈ content; (ws)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkpentry(boolvar, buf).dirty ↔ boolvar; (s)% ⊦ mkpentry(boolvar, buf).page = buf; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).data?; (s)