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Proof step 12 from proof write-inv-rec (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
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), 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 ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1, m + n2 ≤ VFS_PAGE_SIZE, n + m ≤ # buf ⊦ content0[m0, copy(buf, n, getpage(m0, content0), n2, m)].stream = (content.stream to n0) + (⌜buf⌝ to n + m) + (content.stream from n0 + n + m), VFS_PAGE_SIZE = 0

Rule argument

spec: nat-div name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [n0 + n, VFS_PAGE_SIZE, m0, n2]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: n0 + n, VFS_PAGE_SIZE, m0, n2