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Proof step 12 from proof prime-divides-coef (previous step)

(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)) * i) / (fac(j + 1) * fac(j))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
j ≠ 0 ⊦ (j * i) / j = i
Proof step 14:
fac(j) * fac(j + 1) ≠ 0, (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

Rule argument

spec: int-div inst: name: div-mult seq: j ≠ 0 ⊦ (j * i) / j = i subst: [i, j] → [i, fac(j) * fac(j + 1)] flags: rewrite

Additional information

Used simplifier rules: fac-not-zero: ⊦ fac(i) * fac(j) ≠ 0;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i, fac(j) * fac(j + 1)