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Proof step 11 from proof content-trunc (previous step)

n1 < VFS_PAGE_SIZE, n2 < 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⌝ + σ⊥ )[m0 * VFS_PAGE_SIZE + n2 ], n1 = 0, ⌜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⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
n2 < VFS_PAGE_SIZE, n1 < VFS_PAGE_SIZE, VFS_PAGE_SIZE + VFS_PAGE_SIZE * n0 ≤ n2 + m0 * VFS_PAGE_SIZE ⊦ (m0 * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE + n1 ∧ m0 ∈ content ⊃ content[m0];zeropage)[n2] = zero, n1 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ + ⌜n1⌝ ↔ n + m < n0 + n1; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ (σ⊥)[n] = zero; (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 = m; (s)%n∞ ≠ ∞ ⊦ (⌜m⌝ + n∞).n = m + n∞.n; (s)% ⊦ ⌜m⌝ ≠ ∞; (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)% ⊦ # ⌜nf0 to n⌝ = ⌜n⌝ ; (s)% ⊦ ¬ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ2[m - (# σ0).n]; (s)