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Proof step 21 from proof write-inv-rec (previous step)

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 ⊦ (content0.stream to m0 * VFS_PAGE_SIZE) + (⌜getpage(m0, content0)⌝ to n2) + ((⌜buf⌝ from n) to m) + ((⌜getpage(m0, content0)⌝ 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 22:
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 ⊦ (content0.stream to m0 * VFS_PAGE_SIZE) + (⌜getpage(m0, content0)⌝ to n2) + ((⌜buf⌝ from n) to m) + ((⌜getpage(m0, content0)⌝ 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), n3 + m = 0

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult