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Proof step 2 from proof extensionality (previous step)

# σ0 = # σ1, ∀ n. ⌜n⌝ < # σ1 → σ0[n] = σ1[n] ⊦ σ0 = σ1

User applied rule structural induction

And obtained the following new goals

Proof step 3:
# ⌜x⌝ = # σ1, ∀ n. ⌜n⌝ < # σ1 → ⌜x⌝ [n] = σ1[n] ⊦ ⌜x⌝ = σ1
Proof step 10:
# ⌜nf⌝ = # σ1, ∀ n. ⌜n⌝ < # σ1 → ⌜nf⌝ [n] = σ1[n] ⊦ ⌜nf⌝ = σ1

Rule argument

indvar: σ0

Additional information

Used simplifier rules: stream freely generated by ⌜ ⌝, ⌜ ⌝;;