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Proof step 1 from proof toinf-empty (conclusion)

⊦ n∞ < # σ → (σ to∞ n∞ = [] ↔ n∞ = ⌜0⌝ )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
σ to∞ n∞ = [], n∞ < # σ ⊦ n∞ = ⌜0⌝

Rule argument

Additional information

Used simplifier rules: toinf-fin: ⊦ σ to∞ ⌜n⌝ = σ to n;%to-zero: ⊦ σ to 0 = [];