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Proof step 10 from proof extensionality (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
∞ = # σ1, ∀ n. nf(n) = σ1[n] ⊦ ⌜nf⌝ = σ1

Rule argument

Additional information

Used simplifier rules: size-inf: ⊦ # ⌜nf⌝ = ∞;%sel-inf: ⊦ ⌜nf⌝ [n] = nf(n);%less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf