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Proof step 16 from proof prime-divides-coef (previous step)

j0 | (fac(j) * fac(j + 1)) * i, (fac(j) * fac(j + 1)) * i = fac(j * 2 + 1), 0 ≤ j, 0 < j, j + 2 ≤ j0, j0 ≤ j * 2 + 1, prime(j0) ⊦ j0 | i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
(fac(j) * fac(j + 1)) * i = fac(j * 2 + 1), 0 ≤ j, 0 < j, j + 2 ≤ j0, j0 ≤ j * 2 + 1, prime(j0), j0 | fac(j) * fac(j + 1) ⊦ j0 | i

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%prime-divides: ⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0); from specification int-gcd