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Proof step 1 from proof stream-upto (conclusion)

⊦ (content upto n).stream to n = content.stream to n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n])
Proof step 3:
⊦ #((content upto n).stream to n) = #(content.stream to n) ∧ (∀ n0. ⌜n0⌝ < #((content upto n).stream to n) → ((content upto n).stream to n)[n0] = (content.stream to n)[n0])

Rule argument

spec: stream, inst: buffer-inf name: extensionality seq: ⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n]) subst: [σ2, σ] → [content.stream to n, (content upto n).stream to n] flags: <all paths>

Additional information

Used terms: content.stream to n, (content upto n).stream to n