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Proof step 171 from proof inv-truncate-buff-none-uncached (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 172:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m3] = mkfile(m5, md2, # links(m3, dirs), content1), (∅)[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar0, buf0), afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content1[m2 / VFS_PAGE_SIZE, fill(content1[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 ∈ content1, m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ∀ 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]) ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, # (content1[m2 / VFS_PAGE_SIZE, fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)[m2 / VFS_PAGE_SIZE] = VFS_PAGE_SIZE ∧ m2 / VFS_PAGE_SIZE * VFS_PAGE_SIZE < m2 ∧ fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0) = (content1[m2 / VFS_PAGE_SIZE, fill(content1[m2 / VFS_PAGE_SIZE], 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)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ 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)% ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws)% ⊦ pcache[key, pe][key] = pe; (s)% ⊦ datakey(m, m0).ino = m; (s)