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Proof step 19 from proof gcdnex-prime (previous step)

n0 * m1 | m, n0 * m1 | m0, 2 ≤ m1, prime(m1), m1 ≤ n0, 2 ≤ n0 ⊦ m = 1, m0 = 1, m1 = 0, n0 * m1 = 1, n0 = 0, m1 = 1, m1 | m0 ∧ m1 | m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ m | n ↔ (∃ n0. m * n0 = n)
Proof step 21:
n0 * m1 | m, ∃ n1. (n0 * m1) * n1 = m0, 2 ≤ m1, prime(m1), m1 ≤ n0, 2 ≤ n0 ⊦ m = 1, m0 = 1, m1 = 0, n0 * m1 = 1, n0 = 0, m1 = 1, m1 | m0 ∧ m1 | m

Rule argument

spec: nat-prime inst: name: Divides seq: ⊦ m | n ↔ (∃ n0. m * n0 = n) subst: [n, m] → [m0, n0 * m1] flags: rewrite, current

Additional information

Used terms: m0, n0 * m1