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Proof step 371 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, pcache0[datakey(m, m3)] = mkpentry(boolvar0, buf), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), m = m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) = mkfile(m4, md, m6, content), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(dirs, icache, pcache0), datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, datakey(m, m3) ∈ pcache0, ¬ boolvar → m2 / VFS_PAGE_SIZE ∈ content0 ∧ buf0 = content0[m2 / VFS_PAGE_SIZE], asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, ∀ key. key ∈ pcache0 → key.data? ∧ # pcache0[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ pcache0[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache0[key].page = files0[key.ino].content[key.part]), m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, # buf = VFS_PAGE_SIZE ∧ m ∈ files0 ∧ (¬ boolvar0 → m3 ∈ content ∧ buf = content[m3])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 372:
# buf0 = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), pcache0[datakey(m0, m3)] = mkpentry(boolvar0, buf), m3 * VFS_PAGE_SIZE < min(m4, m2), afs-cons(dirs, files0[m0, mkfile(m4, md0, # links(m0, dirs), content0 upto min(m4, m2))]), afs-cons(dirs, files0), synced(dirs, icache, pcache0), datakey(m0, m3) ∈ pcache0, m0 ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ¬ boolvar → m2 / VFS_PAGE_SIZE ∈ content0 ∧ buf0 = content0[m2 / VFS_PAGE_SIZE], ∀ key. key ∈ pcache0 → key.data? ∧ # pcache0[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ pcache0[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache0[key].page = files0[key.ino].content[key.part]), ∀ key. key ∈ pcache0 → key.data? ⊦ # buf = VFS_PAGE_SIZE ∧ (¬ boolvar0 → m3 ∈ content0 ∧ buf = content0[m3]), m2 ≤ m4 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

Additional information

Used simplifier rules: ⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m]; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)