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Proof step 179 from proof inv-truncate-buff-none-uncached (previous step)

# buf0 = VFS_PAGE_SIZE, (m6 = m3 ⊃ mkfile(m, md, # links(m6, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m5, md2, # links(m6, dirs), content1) ) = mkfile(m0, md0, m4, content), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[key] = mkpentry(boolvar0, buf0), files1[m6] = mkfile(m5, md2, # links(m6, dirs), content1), truncate(m3, m2, pcache0)[key] = mkpentry(boolvar, buf), key = datakey(m6, m7), key.data?, afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files1), synced(dirs, icache, pcache0), m3 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, key ∈ pcache0, m6 ∈ files1, m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ¬ boolvar0 → m7 ∈ content1 ∧ buf0 = content1[m7], ∀ key. key ∈ pcache0 → key.data?, ∀ key0. key0 ∈ pcache0 → key0.data? ∧ # pcache0[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ (¬ pcache0[key0].dirty → key0.part ∈ files1[key0.ino].content ∧ pcache0[key0].page = files1[key0.ino].content[key0.part]), m7 * VFS_PAGE_SIZE < m2 ∨ m3 ≠ m6 ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, # buf = VFS_PAGE_SIZE ∧ (¬ boolvar → m7 ∈ content ∧ buf = content[m7])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 180:
# buf0 = VFS_PAGE_SIZE, (m6 = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m5, md2, # links(m6, dirs), content1) ) = mkfile(m0, md0, m4, content), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, truncate(m3, m2, pcache0)[datakey(m6, m7)] = mkpentry(boolvar, buf), files1[m6] = mkfile(m5, md2, # links(m6, dirs), content1), pcache0[datakey(m6, m7)] = mkpentry(boolvar0, buf0), files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), afs-cons(dirs, files1), afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), synced(dirs, icache, pcache0), m6 ∈ files1, datakey(m6, m7) ∈ pcache0, m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ files1, m2 ≤ m, ¬ boolvar0 → m7 ∈ content1 ∧ buf0 = content1[m7], asynced2 → synced(files1, icache, pcache0), ∀ key0. key0 ∈ pcache0 → key0.data? ∧ # pcache0[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ (¬ pcache0[key0].dirty → key0.part ∈ files1[key0.ino].content ∧ pcache0[key0].page = files1[key0.ino].content[key0.part]), ∀ key. key ∈ pcache0 → key.data?, m7 * VFS_PAGE_SIZE < m2 ∨ m3 ≠ m6 ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, # buf = VFS_PAGE_SIZE ∧ (¬ boolvar → m7 ∈ content ∧ buf = content[m7])

Rule argument

Additional information

Used simplifier rules: ⊦ datakey(m, m0).data?; (s)