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

j ≤ i, 0 < j, 0 < i ⊦ binom_coef(i, j) = (fac(i) * (i + 1 - 2 * j)) / (fac(j) * fac(i + 1 - j)) + binom_coef(i, j - 1)

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 1 ≤ j ∧ j ≤ i → (binom_coef(i, j) - binom_coef(i, j - 1)) * fac(j) * fac(i + 1 - j) = fac(i) * (i + 1 - 2 * j)
Proof step 4:
1 ≤ j ∧ j ≤ i → (binom_coef(i, j) - binom_coef(i, j - 1)) * fac(j) * fac(i + 1 - j) = fac(i) * (i + 1 - 2 * j), j ≤ i, 0 < j, 0 < i ⊦ binom_coef(i, j) = (fac(i) * (i + 1 - 2 * j)) / (fac(j) * fac(i + 1 - j)) + binom_coef(i, j - 1)

Rule argument

spec: inst: name: coef-sub-mult seq: ⊦ 1 ≤ j ∧ j ≤ i → (binom_coef(i, j) - binom_coef(i, j - 1)) * fac(j) * fac(i + 1 - j) = fac(i) * (i + 1 - 2 * j) subst: [j, i] → [j, i] flags: current, []

Additional information

Used terms: j, i