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Proof step 24 from proof write-inv-rec (previous step)

# getpage(m0, content0) = VFS_PAGE_SIZE, n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, content0.stream = (content.stream to n0) + (⌜buf⌝ to n) + (content.stream from n0 + n), VFS_PAGE_SIZE = n3 + n2 + m, files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), files0[ino] = mkfile(m2, md0, m4, content), n2 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n + m ≤ # buf, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1, m + n2 ≤ VFS_PAGE_SIZE, n2 + m ≤ VFS_PAGE_SIZE ⊦ n3 + m = 0, (content0.stream to m0 * VFS_PAGE_SIZE) + ((content0.stream from m0 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE to n2) + ((⌜buf⌝ from n) to m) + ((((content0.stream from m0 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE) from n2 + m) to n3) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
n0 + n = m0 * VFS_PAGE_SIZE + n2, files1 -- ino = files0 -- ino, content0.stream = (content.stream to n0) + (⌜buf⌝ to n) + (content.stream from n0 + n), VFS_PAGE_SIZE = n3 + n2 + m, files0[ino] = mkfile(m2, md0, m4, content), files1[ino] = mkfile(m2, md0, # links(ino, dirs), content0), n2 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, n2 + m ≤ VFS_PAGE_SIZE, m + n2 ≤ VFS_PAGE_SIZE, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n + m ≤ # buf ⊦ n3 + m = 0, (content0.stream to m0 * VFS_PAGE_SIZE) + ((content0.stream from m0 * VFS_PAGE_SIZE) to n2) + ((⌜buf⌝ from n) to m) + ((((content0.stream from m0 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE) from n2 + m) to n3) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m)

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%¬ # σ0 < ⌜n⌝ ⊦ m < n → σ0 to n to m = σ0 to m; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ #(content.stream from n) = ∞; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, m0, content) → # getpage(n, content) = VFS_PAGE_SIZE; (s)