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Proof step 10 from proof prime-prime (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
m ≠ 0 ⊦ m | n ↔ n % m = 0
Proof step 12:
m ≠ 0, n % m = 0, prime(m), m * m ≤ n, ∀ m. 2 ≤ m ∧ prime(m) ∧ m * m ≤ n → n % m ≠ 0 ⊦ n = 1, n = 0, prime(n)

Rule argument

spec: nat-prime inst: name: divi-mod seq: m ≠ 0 ⊦ m | n ↔ n % m = 0 subst: [n, m] → [n, m] flags: rewrite, current

Additional information

Used simplifier rules: divi-zero-01: ⊦ 0 | m ↔ m = 0; Used terms: n, m