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Proof step 3 from proof coef-sub (previous step)

⊦ 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)

Lemma coef-sub-mult