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Proof step 5 from proof content-trunc-exact (previous step)

⊦ # ⌜λ n. (n / VFS_PAGE_SIZE * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE ∧ n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage) [n % VFS_PAGE_SIZE ] ⌝ = #(⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to n0 * VFS_PAGE_SIZE⌝ + σ⊥) ∧ (∀ n. ⌜n⌝ < # ⌜λ n. (n / VFS_PAGE_SIZE * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE ∧ n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage) [n % VFS_PAGE_SIZE ] ⌝ → ⌜λ n. (n / VFS_PAGE_SIZE * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE ∧ n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage) [n % VFS_PAGE_SIZE ] ⌝ [n ] = (⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to n0 * VFS_PAGE_SIZE⌝ + σ⊥)[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ (n / VFS_PAGE_SIZE * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE ∧ n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE] = (⌜(λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE];zeropage)[n % VFS_PAGE_SIZE]) to n0 * VFS_PAGE_SIZE⌝ + σ⊥)[n]

Rule argument

Additional information

Used simplifier rules: zerostream-size: ⊦ # σ⊥ = ∞;% ⊦ ⌜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)% ⊦ # ⌜nf0 to n⌝ = ⌜n⌝ ; (s)% ⊦ #(σ0 + σ2) = # σ0 + # σ2; (s)% ⊦ # ⌜nf0⌝ = ∞; (s)