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Proof step 9 from proof stream-split-lastpage (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
n < VFS_PAGE_SIZE + m * VFS_PAGE_SIZE, n / VFS_PAGE_SIZE ∈ content, m * VFS_PAGE_SIZE ≤ n ⊦ content[n / VFS_PAGE_SIZE][n % VFS_PAGE_SIZE] = zero, m ∈ content

Rule argument

Additional information

Used simplifier rules: zerostream-size: ⊦ # σ⊥ = ∞;%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ n < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m * n < m1 * n + n ↔ m < m1 + 1 ∧ n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ (σ⊥)[n] = zero; (s)%m < n, ¬ # σ0 < ⌜n⌝ ⊦ (σ0 to n)[m] = σ0[m]; (s)%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ⌜m⌝ .n = m; (s)% ⊦ # ⌜nf0 to n⌝ = ⌜n⌝ ; (s)% ⊦ ¬ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ2[m - (# σ0).n]; (s)