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Proof step 15 from proof square-neq-any-pos-01 (previous step)

(j / gcd(j, j0) * j) / gcd(j, j0) = (j0 / gcd(j0, j) * j0 * i) / gcd(j, j0), 0 < i, 0 < j, 0 < j0 ⊦ gcd(j, j0) = 1, j = 0, j0 = 0, ∃ i0. i = i0 * i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ i * j = j * i
Proof step 17:
(j * j / gcd(j, j0)) / gcd(j, j0) = (j0 / gcd(j0, j) * j0 * i) / gcd(j, j0), 0 < i, 0 < j, 0 < j0 ⊦ gcd(j, j0) = 1, j = 0, j0 = 0, ∃ i0. i = i0 * i0

Rule argument

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

Additional information

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