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Proof step 21 from proof content-trunc (previous step)

n1 < VFS_PAGE_SIZE, n2 < VFS_PAGE_SIZE, ⌜m0 * VFS_PAGE_SIZE + n2⌝ < # ⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to VFS_PAGE_SIZE * n0 + VFS_PAGE_SIZE⌝ ⊦ (m0 * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE + n1 ∧ m0 ∈ content ⊃ content[m0];zeropage)[n2] = ⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to VFS_PAGE_SIZE * n0 + VFS_PAGE_SIZE⌝ [m0 * VFS_PAGE_SIZE + n2 ], n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
n2 + m0 * VFS_PAGE_SIZE < VFS_PAGE_SIZE + VFS_PAGE_SIZE * n0, n1 < VFS_PAGE_SIZE, n2 < VFS_PAGE_SIZE ⊦ (m0 * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE + n1 ∧ m0 ∈ content ⊃ content[m0];zeropage)[n2] = (m0 ∈ content ⊃ content[m0];zeropage)[n2], n1 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → m % n = m; (s)%n ≠ 0 ⊦ (m + n0 * n) % n = m % n; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ n + 0 = n; (s)% ⊦ m < n → m / n = 0; (s)%n ≠ 0 ⊦ (n0 + m * n) / n = n0 / n + m; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%m < n ⊦ (nf0 to n)[m] = nf0(m); (s)%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ + ⌜n1⌝ ↔ n + m < n0 + n1; (s)% ⊦ # ⌜nf0 to n⌝ = ⌜n⌝ ; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜dx⌝ [n] = dx[n]; (s)