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Proof step 11 from proof extensionality (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 12:
∞ = # ⌜nf0⌝ , ∀ n. nf(n) = ⌜nf0⌝ [n] ⊦ ⌜nf⌝ = ⌜nf0⌝

Rule argument

indvar: σ1

Additional information

Used simplifier rules: size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic