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Proof step 7 from proof coef-product-le (previous step)

0 < j, binom_coef(2 * j + 1, j) < Π ints, j0 ∈ ints, ∀ i. i ∈ ints → prime(i) ∧ j + 2 ≤ i ∧ i ≤ j * 2 + 1 ⊦ dups(ints), prime(j0) ∧ j0 | binom_coef(2 * j + 1, j)

User applied rule all left

And obtained the following new goals

Proof step 8:
0 < j, binom_coef(2 * j + 1, j) < Π ints, j0 ∈ ints, j0 ∈ ints → prime(j0) ∧ j + 2 ≤ j0 ∧ j0 ≤ j * 2 + 1 ⊦ dups(ints), prime(j0) ∧ j0 | binom_coef(2 * j + 1, j)

Rule argument

pos: left 4 terms: j0 abort: F discard: T computed: T

Additional information

Used terms: j0