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Proof step 4 from proof prime-divides-coef (previous step)

j ≤ j * 2 + 1 ∧ 0 ≤ j → fac(j * 2 + 1 - j) * fac(j) | fac(j * 2 + 1), prime(j0), j0 ≤ j * 2 + 1, j + 2 ≤ j0, 0 < j ⊦ j0 | binom_coef(2 * j + 1, j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
prime(j0), j0 ≤ j * 2 + 1, j + 2 ≤ j0, 0 < j, fac(j + 1) * fac(j) | fac(j * 2 + 1), 0 ≤ j ⊦ j0 | binom_coef(2 * j + 1, j)

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%numsub: ⊦ i * (* j) + j0 - i = i * (j - 1) + j0; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; 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-12: ⊦ j ≤ (* i1) * j + i ↔ 0 ≤ (i1 - 1) * j + i; from specification int-mult