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Proof step 13 from proof not-prime (previous step)

2 < m * m, n < m * m, m | n, 2 ≤ n, ∀ n0. n0 < n → ¬ prime(n0) ∧ 2 ≤ n0 → (∃ m. m | n0 ∧ prime(m) ∧ m * m ≤ n0) ⊦ n = 1, m = n, m = 1, n = 0, m = 0, ∃ m. m | n ∧ prime(m) ∧ m * m ≤ n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ m | n ↔ (∃ n0. m * n0 = n)
Proof step 15:
2 < m * m, n < m * m, ∃ n0. m * n0 = n, 2 ≤ n, ∀ n0. n0 < n → ¬ prime(n0) ∧ 2 ≤ n0 → (∃ m. m | n0 ∧ prime(m) ∧ m * m ≤ n0) ⊦ n = 1, m = n, m = 1, n = 0, m = 0, ∃ m. m | n ∧ prime(m) ∧ m * m ≤ n

Rule argument

spec: nat-prime inst: name: Divides seq: ⊦ m | n ↔ (∃ n0. m * n0 = n) subst: [n, m] → [n, m] flags: rewrite, current

Additional information

Used terms: n, m