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Proof step 5 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 ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 6:
⊦ i ≤ j ∧ 0 ≤ i → fac(j - i) * fac(i) | fac(j)
Proof step 7:
i ≤ 2 * i ∧ 0 ≤ i → fac(2 * i - i) * fac(i) | fac(2 * i), j | fac(2 * i) / (fac(2 * i - i) * fac(i)), 2 * i < j, prime(j), 0 < i, 0 ≤ i ⊦

Rule argument

spec: inst: name: fac-divides seq: ⊦ i ≤ j ∧ 0 ≤ i → fac(j - i) * fac(i) | fac(j) subst: [i, j] → [i, 2 * i] flags: current, []

Additional information

Used terms: i, 2 * i