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Proof step 28 from proof content-write (previous step)

# buf = VFS_PAGE_SIZE, (n + m) * VFS_PAGE_SIZE + n1 = (n2 + VFS_PAGE_SIZE) + n * VFS_PAGE_SIZE, n1 < VFS_PAGE_SIZE, n1 < n2 + 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 rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 30:
# buf = VFS_PAGE_SIZE, (VFS_PAGE_SIZE * n + VFS_PAGE_SIZE * m) + n1 = (n2 + VFS_PAGE_SIZE) + n * 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

Rule argument

spec: nat-mult name: dist seq: ⊦ m0 * (m + n) = m0 * m + m0 * n subst: [m0, n, m] → [VFS_PAGE_SIZE, m, n] flags: <all paths>

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: VFS_PAGE_SIZE, m, n