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Proof step 3 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⊥

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: stream, inst: buffer-inf name: extensionality seq: ⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n]) subst: [σ2, σ] → [ ⌜ (λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE] ;zeropage ) [n % VFS_PAGE_SIZE ]) to n0 * VFS_PAGE_SIZE ⌝ + σ⊥, ⌜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 ] ⌝ ] flags: <all paths>

Additional information

Used terms: ⌜ (λ n. (n / VFS_PAGE_SIZE ∈ content ⊃ content[n / VFS_PAGE_SIZE] ;zeropage ) [n % VFS_PAGE_SIZE ]) to n0 * VFS_PAGE_SIZE ⌝ + σ⊥, ⌜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 ] ⌝