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Proof step 9 from proof content-trunc (previous step)

n2 < VFS_PAGE_SIZE, n1 < VFS_PAGE_SIZE ⊦ (m0 * VFS_PAGE_SIZE < n0 * VFS_PAGE_SIZE + n1 ∧ m0 ∈ content ⊃ content[m0];zeropage)[n2] = (⌜(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⊥ )[m0 * VFS_PAGE_SIZE + n2 ], n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: stream, inst: buffer-inf name: get-append-ls seq: ⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m] subst: [m, σ2, σ0] → [m0 * VFS_PAGE_SIZE + n2, σ⊥, ⌜ (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 ⌝ ] flags: <all paths>

Additional information

Used terms: m0 * VFS_PAGE_SIZE + n2, σ⊥, ⌜ (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 ⌝