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Proof step 151 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, (key.ino = m3 ⊃ mkfile(m, md, # links(key.ino, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[key.ino] ) = mkfile(m0, md0, m4, content), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))][key] = mkpentry(boolvar, buf), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), key = datakey(m3, m2 / VFS_PAGE_SIZE), buf-opt.some?, 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), key ∈ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))], m3 ∈ files0, m2 ≤ m, key ∈ pcache0 → key.data?, asynced1 → synced(files0, icache, pcache0), ∀ 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, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ boolvar → key.part ∈ content ∧ buf = content[key.part])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 152:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), buf-opt.some?, 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, m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ 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, # (content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)[m2 / VFS_PAGE_SIZE] = VFS_PAGE_SIZE ∧ m2 / VFS_PAGE_SIZE * VFS_PAGE_SIZE < m2 ∧ fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0) = (content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)[m2 / VFS_PAGE_SIZE]

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ content[n, buf]; (s)% ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ key ∈ pcache[key, pe]; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ datakey(m, m0).ino = m; (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws)% ⊦ pcache[key, pe][key] = pe; (s)