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Proof step 31 from proof content-write (previous step)

# buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE * m + n1 = n2 + VFS_PAGE_SIZE, n1 < n2 + VFS_PAGE_SIZE, n1 < VFS_PAGE_SIZE ⊦ (n + m ∈ content ⊃ content[n + m];zeropage)[n1] = ((n2 + VFS_PAGE_SIZE) / VFS_PAGE_SIZE + n ∈ content ⊃ content[(n2 + VFS_PAGE_SIZE) / VFS_PAGE_SIZE + n];zeropage)[n2 % VFS_PAGE_SIZE], m = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
# buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE * m + n1 = n2 + VFS_PAGE_SIZE, n2 + VFS_PAGE_SIZE = m0 * VFS_PAGE_SIZE + n0, n1 < VFS_PAGE_SIZE, n1 < n2 + VFS_PAGE_SIZE, n0 < VFS_PAGE_SIZE ⊦ VFS_PAGE_SIZE = 0, (n + m ∈ content ⊃ content[n + m];zeropage)[n1] = (m0 + n ∈ content ⊃ content[m0 + n];zeropage)[n2 % VFS_PAGE_SIZE], m = 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: [n, m, m0, n0] → [VFS_PAGE_SIZE, n2 + VFS_PAGE_SIZE, m0, n0]

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: VFS_PAGE_SIZE, n2 + VFS_PAGE_SIZE, m0, n0