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Proof step 6 from proof emptystream-cancel (previous step)

# σ = ⌜n⌝ , σ + σ⊥ = σ⊥ ⊦ σ = σ⊥ to n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ σ = σ2 ↔ # σ = # σ2 ∧ (∀ n. ⌜n⌝ < # σ → σ[n] = σ2[n])
Proof step 8:
#(σ + σ⊥) = # σ⊥, # σ = ⌜n⌝ , ∀ n. ⌜n⌝ < #(σ + σ⊥) → (σ + σ⊥)[n] = (σ⊥)[n] ⊦ σ = σ⊥ to 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 + σ⊥] flags: <all paths>

Additional information

Used terms: σ⊥, σ + σ⊥