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Proof step 9 from proof middle-coef-largest-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 10:
j + 1 < i, binom_coef(2 * i, j + 1) = (fac(2 * i) * (2 * i + 1 - 2 * (j + 1))) / (fac(j + 1) * fac(2 * i - j)) + binom_coef(2 * i, j), j < 2 * i, binom_coef(2 * i, i) < binom_coef(2 * i, j), j < i, 0 ≤ j, 0 < i, ∀ i0, j0. i→n(i0 - j0) < i→n(i - j) → binom_coef(2 * i0, i0) < binom_coef(2 * i0, j0) ∧ j0 < i0 ∧ 0 ≤ j0 ∧ 0 < i0 → false ⊦ binom_coef(2 * i, i) < binom_coef(2 * i, j + 1) ∧ j + 1 < i
Proof step 17:
binom_coef(2 * i, j + 1) = (fac(2 * i) * (2 * i + 1 - 2 * (j + 1))) / (fac(j + 1) * fac(2 * i - j)) + binom_coef(2 * i, j), j < 2 * i, binom_coef(2 * i, i) < binom_coef(2 * i, j), j < i, 0 ≤ j, 0 < i, ∀ i0, j0. i→n(i0 - j0) < i→n(i - j) → binom_coef(2 * i0, i0) < binom_coef(2 * i0, j0) ∧ j0 < i0 ∧ 0 ≤ j0 ∧ 0 < i0 → false ⊦ j + 1 < i, binom_coef(2 * i, i) < binom_coef(2 * i, j + 1) ∧ j + 1 < i

Rule argument

fma: j + 1 < i

Additional information

Used formulas: j + 1 < i