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Proof step 8 from proof middle-coef-divides-not (previous step)

j | fac(2 * i) / (fac(2 * i - i) * fac(i)), 2 * i < j, prime(j), 0 < i, 0 ≤ i, fac(2 * i - i) * fac(i) | fac(2 * i) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 10:
j | fac(2 * i) / (fac(2 * i - i) * fac(i)), 2 * i < j, prime(j), 0 < i, 0 ≤ i, ∃ i0. (fac(2 * i - i) * fac(i)) * i0 = fac(2 * i) ⊦

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [fac(2 * i), fac(2 * i - i) * fac(i)] flags: rewrite

Additional information

Used terms: fac(2 * i), fac(2 * i - i) * fac(i)