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Proof step 4 from proof extensionality (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 5:
⌜# x⌝ = # ⌜x0⌝ , ∀ n. n < # x → x[n] = ⌜x0⌝ [n] ⊦ ⌜x⌝ = ⌜x0⌝

Rule argument

indvar: σ1

Additional information

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