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Proof step 3 from proof prime-smallest (previous step)

prime(n) ⊦ n ≠ 0 ∧ n ≠ 1 ∧ (∀ m. 2 ≤ m ∧ m * m ≤ n → n % m ≠ 0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
n % m = 0, prime(n), 2 ≤ m, m * m ≤ n ⊦ n = 1, n = 0, m = 0

Rule argument

Additional information

Used simplifier rules: zero: ⊦ ¬ prime(0);%one: ⊦ ¬ prime(1);%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat