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Proof step 1 from proof coef-product-le (conclusion)

∀ i. i ∈ ints → prime(i) ∧ j + 2 ≤ i ∧ i ≤ j * 2 + 1, ¬ dups(ints), 0 < j ⊦ Π ints ≤ binom_coef(2 * j + 1, j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
binom_coef(2 * j + 1, j) < Π ints, 0 < j, ∀ i. i ∈ ints → prime(i) ∧ j + 2 ≤ i ∧ i ≤ j * 2 + 1 ⊦ dups(ints)

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs