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Proof step 18 from proof middle-coef-largest-01 (previous step)

binom_coef(2 * (j + 1), j + 1) = fac(2 * (j + 1)) / (fac(j + 1) * fac(2 * (j + 1) - j)) + binom_coef(2 * (j + 1), j), fac(2 * (j + 1)) / (fac(j + 1) * fac(2 * (j + 1) - j)) < 0, 0 ≤ j, binom_coef(2 * (j + 1), j + 1) < binom_coef(2 * (j + 1), j), j < 2 * (j + 1), ∀ i0, j0. i→n(i0 - j0) < i→n(j + 1 - j) → binom_coef(2 * i0, i0) < binom_coef(2 * i0, j0) ∧ j0 < i0 ∧ 0 ≤ j0 ∧ 0 < i0 → false ⊦

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