[Imprint][Data Privacy Statement][E-Mail]



View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 12 from proof content-write (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ m < n → m % n = m; (s)%n ≠ 0 ⊦ (m + n0 * n) % n = m % n; (s)% ⊦ 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⌝ ↔ n + m < n0; (s)% ⊦ # ⌜nf0 to n⌝ = ⌜n⌝ ; (s)% ⊦ ⌜m + 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% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ n0 < m0 → (m0 * m + n0 < m0 * n ↔ m < n); (s)% ⊦ ⌜dx⌝ [n] = dx[n]; (s)% ⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m]; (s)