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Proof step 6 from proof content-trunc-exact (previous step)

⊦ (n / VFS_PAGE_SIZE * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE ∧ n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE] = (⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to n0 * VFS_PAGE_SIZE⌝ + σ⊥)[n]

User applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
n = m0 * VFS_PAGE_SIZE + n1, n1 < VFS_PAGE_SIZE ⊦ VFS_PAGE_SIZE = 0, (m0 * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE ∧ m0 ∈ content ⊃ content[m0];zeropage)[n1] = (⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to n0 * VFS_PAGE_SIZE⌝ + σ⊥)[n]

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, m, n1]

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, m, n1