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Proof step 354 from proof inv-truncate-buff-none-uncached (previous step)

(m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));mkfile(m7, md2, # links(m, dirs), content1)) = mkfile(m4, md, m6, content), files0[m] = mkfile(m7, md2, # links(m, dirs), content1), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), pcache0[datakey(m, m3)] = mkpentry(false, content1[m3]), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), synced(dirs, icache, pcache0), m3 ∈ content1, m ∈ files0, m0 ∈ files0, datakey(m, m3) ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ∀ 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?, m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m3 ∈ content ∧ content1[m3] = content[m3], m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: m = m0

Additional information

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