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Proof step 13 from proof prime-prime (previous step)

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

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 4 terms: m

Additional information

Used simplifier rules: one: ⊦ ¬ prime(1);% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≠ 0 → (m < 2 ↔ m = 1); (s)% ⊦ m % 1 = 0; (s) Used terms: m