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Proof step 14 from proof content-write (previous step)

# buf = VFS_PAGE_SIZE, n1 < VFS_PAGE_SIZE ⊦ (m0 = n ∨ m0 ∈ content ⊃ content[n, buf][m0];zeropage)[n1] = (⌜buf⌝ + ⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) from VFS_PAGE_SIZE * n + VFS_PAGE_SIZE⌝ )[ m0 * VFS_PAGE_SIZE + n1 - (# ⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to n * VFS_PAGE_SIZE⌝ ).n ], ⌜m0 * VFS_PAGE_SIZE + n1⌝ < # ⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to n * VFS_PAGE_SIZE⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# buf = VFS_PAGE_SIZE, n1 < VFS_PAGE_SIZE, n ≤ m0 ⊦ (m0 = n ∨ m0 ∈ content ⊃ content[n, buf][m0];zeropage)[n1] = (⌜buf⌝ + ⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) from VFS_PAGE_SIZE * n + VFS_PAGE_SIZE⌝ )[m0 * VFS_PAGE_SIZE + n1 - n * VFS_PAGE_SIZE ]

Rule argument

Additional information

Used simplifier rules: 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%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ n0 < m0 → (m0 * m + n0 < m0 * n ↔ m < n); (s)% ⊦ ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ ↔ n + m < n0; (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 = m; (s)% ⊦ # ⌜nf0 to n⌝ = ⌜n⌝ ; (s)