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Proof step 5 from proof mod-zero (previous step)

2 < n0 * n, prime(n0 * n), 2 ≤ n ⊦ n0 = 1, n0 = 0, n0 * n = 2, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-prime inst: name: mult seq: ⊦ m ≠ 1 ∧ n ≠ 1 → ¬ prime(m * n) subst: [n, m] → [n, n0] flags: rewrite, current

Additional information

Used simplifier rules: two-03: ⊦ m ≠ 1 → (m * m0 = 2 ↔ m = 2 ∧ m0 = 1); from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: n, n0