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Proof step 19 from proof content-write (previous step)

# buf = VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE + n1 = n0 + n * 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⌝ )[n0 ], ⌜n0⌝ < # ⌜buf⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
# buf = VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE + n1 = n0 + n * VFS_PAGE_SIZE, n1 < VFS_PAGE_SIZE, n1 < n0, n ≤ m0, VFS_PAGE_SIZE ≤ n0 ⊦ (m0 = n ∨ m0 ∈ content ⊃ content[n, buf][m0];zeropage)[n1] = (((n0 - VFS_PAGE_SIZE) + VFS_PAGE_SIZE) / VFS_PAGE_SIZE + n ∈ content ⊃ content[((n0 - VFS_PAGE_SIZE) + VFS_PAGE_SIZE) / VFS_PAGE_SIZE + n] ;zeropage ) [(n0 - VFS_PAGE_SIZE) % VFS_PAGE_SIZE ]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%n ≠ 0 ⊦ (m + n) % n = m % n; (s)%n ≠ 0 ⊦ (m + n0 * n) % n = m % n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%n ≠ 0 ⊦ (n0 + m * n) / n = n0 / n + m; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ ((nf0 from n))(m) = nf0(m + n); (s)% ⊦ ⌜nf0⌝ [n] = nf0(n); (s)% ⊦ ⌜m⌝ .n = m; (s)% ⊦ # ⌜buf⌝ = ⌜# buf⌝ ; (s)% ⊦ ¬ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ2[m - (# σ0).n]; (s)