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Proof step 1 from proof mod-zero (conclusion)

⊦ m % n = 0 ∧ n < m ∧ 2 ≤ n → (prime(m) ↔ m = 2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
m % n = 0, n < m, 2 ≤ n, prime(m), 2 < m ⊦ m = 2, m = 0, n = 0

Rule argument

Additional information

Used simplifier rules: two: ⊦ prime(2);%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat