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Proof step 5 from proof content-write (previous step)

# buf = VFS_PAGE_SIZE ⊦ # ⌜λ n0. (n0 / VFS_PAGE_SIZE ∈ content[n, buf] ⊃ content[n, buf][n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE]⌝ = # ( ⌜(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⌝ ) ∧ (∀ n0. ⌜n0⌝ < # ⌜λ n0. (n0 / VFS_PAGE_SIZE ∈ content[n, buf] ⊃ content[n, buf][n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE]⌝ → ⌜λ n0. (n0 / VFS_PAGE_SIZE ∈ content[n, buf] ⊃ content[n, buf][n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE]⌝ [n0] = ( ⌜(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⌝ )[n0 ])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜nf0⌝ [n] = nf0(n); (s)% ⊦ ⌜m⌝ < ∞; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%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⌝ + ∞ = ∞; (s)% ⊦ # ⌜buf⌝ = ⌜# buf⌝ ; (s)% ⊦ # ⌜nf0 to n⌝ = ⌜n⌝ ; (s)% ⊦ #(σ0 + σ2) = # σ0 + # σ2; (s)% ⊦ # ⌜nf0⌝ = ∞; (s)