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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 ⊦ n = 1, n = 0, m = 0, 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);%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%twols-02: ⊦ m ≠ 0 → (m < 2 ↔ m = 1); from specification nat-basic1%mod-one: ⊦ m % 1 = 0; from specification nat-div%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: m