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

2 * i - j < i ∧ 0 ≤ 2 * i - j → ¬ binom_coef(2 * i, i) < binom_coef(2 * i, 2 * i - j), 0 ≤ j, j ≤ 2 * i, binom_coef(2 * i, i) < binom_coef(2 * i, 2 * i - j), 0 ≤ i, i ≤ j ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: numle-09: ⊦ j ≤ (* i1) * j ↔ 0 ≤ (i1 - 1) * j; from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%ler: ⊦ i ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%ax-04: ⊦ i + 0 = i; from specification int-basic2%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; 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%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%numls-05: ⊦ (* i2) * i < i + j0 ↔ (i2 - 1) * i < j0; from specification int-mult%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs