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Proof step 1 from proof toinf-empty2 (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

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