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Proof step 3 from proof tobuf-rev (previous step)

⊦ # σ = ∞, ⌜σ.buf⌝ = σ

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n])
Proof step 5:
⊦ # σ = ∞, # ⌜σ.buf⌝ = # σ ∧ (∀ n. ⌜n⌝ < # ⌜σ.buf⌝ → ⌜σ.buf⌝ [n] = σ[n])

Rule argument

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

Additional information

Used terms: σ, ⌜σ.buf⌝