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Proof step 4 from proof middle-coef-largest (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i ≤ j, 0 ≤ i, binom_coef(2 * i, i) < binom_coef(2 * i, j), j ≤ 2 * i, 0 ≤ j ⊦

Rule argument

Additional information

Used simplifier rules: 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%numle-09: ⊦ j ≤ (* i1) * j ↔ 0 ≤ (i1 - 1) * j; from specification int-mult%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs