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Proof step 1 from proof prime-prime (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: one: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); from specification nat-basic1