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Proof step 13 from proof middle-coef-largest-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: fac-le-zero: ⊦ i * fac(j) ≤ 0 ↔ i ≤ 0;%fac-pos-01: ⊦ ¬ fac(i) ≤ 0;%fac-ls-zero: ⊦ i * fac(j) < 0 ↔ i < 0;%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%ax-04: ⊦ i + 0 = i; from specification int-basic2%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs