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Proof step 5 from proof coef-mult-rec-lower (previous step)

j ≤ i, 0 < j, 0 < i, fac(i - j) * fac(j) | fac(i), 0 ≤ j, 0 ≤ i ⊦ binom_coef(i, j) * j = binom_coef(i, j - 1) * (i + 1 - j)

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:
j - 1 ≤ i ∧ 0 ≤ j - 1 → fac(i - (j - 1)) * fac(j - 1) | fac(i), j ≤ i, 0 < j, 0 < i, fac(i - j) * fac(j) | fac(i), 0 ≤ j, 0 ≤ i ⊦ binom_coef(i, j) * j = binom_coef(i, j - 1) * (i + 1 - j)

Rule argument

spec: inst: name: fac-divides seq: ⊦ i ≤ j ∧ 0 ≤ i → fac(j - i) * fac(i) | fac(j) subst: [i, j] → [j - 1, i] flags: current, []

Additional information

Used terms: j - 1, i