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Proof step 3 from proof getbyte-drop-lower (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
n = m0 * VFS_PAGE_SIZE + n0, n < m * VFS_PAGE_SIZE, n0 < VFS_PAGE_SIZE ⊦ VFS_PAGE_SIZE = 0, (m0 ∈ content[m, buf] ⊃ content[m, buf][m0];zeropage)[n0] = (m0 ∈ content ⊃ content[m0];zeropage)[n0], 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: [m, n, m0, n0] → [n, 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: n, VFS_PAGE_SIZE, m0, n0