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Proof step 1 from proof to-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: to-zero: ⊦ σ to 0 = [];