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Proof step 4 from proof prime-prime (previous step)

n % m = 0, prime(n), 2 ≤ m, prime(m), m * m ≤ n ⊦ n = 1, n = 0, m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-div inst: name: modex seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [m, n] flags: rewrite

Additional information

Used simplifier rules: mult-02: ⊦ prime(m) → (prime(m * n) ↔ n = 1);%zero-06: ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); 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%one-01: ⊦ m0 * m = 1 ↔ m0 = 1 ∧ m = 1; from specification nat-mult%le: ⊦ m0 ≠ 0 → (m0 * m ≤ m0 * n ↔ m ≤ n); from specification nat-mult%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat Used terms: m, n