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Proof step 19 from proof square-neq-pos (previous step)

(j * j / gcd(j, j0)) / gcd(j, j0) = (j0 / gcd(j0, j) * j0 * i) / gcd(j, j0), prime(i), 0 < j, 0 < j0 ⊦ gcd(j, j0) = 1, j = 0, j0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ i0 ≠ 0 → (i0 * j) / gcd(i0, j0) = i0 / gcd(i0, j0) * j
Proof step 21:
j ≠ 0, j / gcd(j, j0) * j / gcd(j, j0) = (j0 / gcd(j0, j) * j0 * i) / gcd(j, j0), prime(i), 0 < j, 0 < j0 ⊦ gcd(j, j0) = 1, j = 0, j0 = 0

Rule argument

spec: int-gcd inst: name: gcd-div-shift seq: ⊦ i0 ≠ 0 → (i0 * j) / gcd(i0, j0) = i0 / gcd(i0, j0) * j subst: [j0, j, i0] → [j0, j / gcd(j, j0), j] flags: rewrite, current

Additional information

Used terms: j0, j / gcd(j, j0), j