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Proof step 22 from proof square-neq-pos (previous step)

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, j0 = 0, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ i * j = j * i
Proof step 24:
j / gcd(j, j0) * j / gcd(j, j0) = ((j0 * i) * j0 / gcd(j0, j)) / gcd(j, j0), prime(i), 0 < j, 0 < j0 ⊦ gcd(j, j0) = 1, j0 = 0, j = 0

Rule argument

spec: int-mult inst: name: commutativity seq: ⊦ i * j = j * i subst: [j, i] → [j0 * i, j0 / gcd(j0, j)] flags: rewrite

Additional information

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