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Proof step 6 from proof content-trunc (previous step)

n1 < VFS_PAGE_SIZE ⊦ n1 = 0, ∀ n. ⌜n⌝ < # ⌜λ n. (n / VFS_PAGE_SIZE * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE + n1 ∧ 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 + n1 ∧ 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 VFS_PAGE_SIZE * n0 + VFS_PAGE_SIZE⌝ + σ⊥ )[n ]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
n1 < VFS_PAGE_SIZE ⊦ (n / VFS_PAGE_SIZE * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE + n1 ∧ 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 VFS_PAGE_SIZE * n0 + VFS_PAGE_SIZE⌝ + σ⊥)[n], n1 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜m⌝ < ∞; (s)% ⊦ # ⌜nf0⌝ = ∞; (s)% ⊦ ⌜nf0⌝ [n] = nf0(n); (s)