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Proof step 184 from proof inv-truncate-buff-none-uncached (previous step)

(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, files1[m6] = mkfile(m5, md2, # links(m6, dirs), content1), pcache0[datakey(m6, m7)] = mkpentry(false, content1[m7]), files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), m6 = m3, 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), datakey(m6, m7) ∈ pcache0, m6 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ files1, m7 ∈ content1, m2 ≤ m, 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, m7 ∈ content ∧ content1[m7] = content[m7]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 185:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, pcache0[datakey(m3, m7)] = mkpentry(false, content0[m7]), files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), m7 * VFS_PAGE_SIZE < m2, m7 * VFS_PAGE_SIZE < m, 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), m7 ∈ content0, m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ files1, datakey(m3, m7) ∈ pcache0, m7 ∈ content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)], 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, content0[m7] = content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)][m7], datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ content[n0, buf] ↔ n = n0 ∨ n ∈ content; (ws)%⊦ 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)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%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)