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Proof step 10 from proof middle-coef-largest-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lst-03: ⊦ i + j < i0 ∧ ¬ j < j0 → i + j0 < i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2