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Proof step 1 from proof prod-eq-one (conclusion)

⊦ Π nats = 1 ∧ m < # nats → nats[m] = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
Π nats = 1, m < # nats ⊦ nats[m] = 1, nats = []

Rule argument

Additional information

Used simplifier rules: ⊦ # nats = 0 ↔ nats = [];% ⊦ m < n → n ≠ 0; (forward)