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Proof step 2 from proof coef-gcd (previous step)

gcd(i, j) = 1, j ≤ i, 0 ≤ j, 0 ≤ i ⊦ i | binom_coef(i, j)

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j ∧ j ≤ i → i * binom_coef(i - 1, j - 1) = j * binom_coef(i, j)
Proof step 4:
0 < j ∧ j ≤ i → i * binom_coef(i - 1, j - 1) = j * binom_coef(i, j), gcd(i, j) = 1, j ≤ i, 0 ≤ j, 0 ≤ i ⊦ i | binom_coef(i, j)

Rule argument

spec: int-fac inst: name: coef-mult-rec seq: ⊦ 0 < j ∧ j ≤ i → i * binom_coef(i - 1, j - 1) = j * binom_coef(i, j) subst: [j, i] → [j, i] flags: current, []

Additional information

Used terms: j, i