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Proof step 8 from proof coef-product-le (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
j0 ≤ j * 2 + 1, j + 2 ≤ j0, prime(j0), j0 ∈ ints, binom_coef(2 * j + 1, j) < Π ints, 0 < j ⊦ j0 | binom_coef(2 * j + 1, j), dups(ints)

Rule argument

Additional information

Used simplifier rules: leone: ⊦ 1 ≤ i ↔ 0 < 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%one: ⊦ 1 * i = i; from specification int-mult%numle-08: ⊦ i + j ≤ (* i1) * i ↔ j ≤ (i1 - 1) * i; from specification int-mult%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%minus-add: i < 0 ⊦ (* i) + j = j - ~ i; from specification int-abs%numle-01: ⊦ i + (* j) ≤ i0 + (* j0) ↔ i ≤ i0 + (j0 - j); from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs