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Proof step 31 from proof equality-01 (previous step)

i0 ≠ 0, 0 < gcd(i, j), i = i0 / gcd(i0, j0) * gcd(i, j), j = j0 / gcd(i0, j0) * gcd(i, j), 0 < j, 0 < j0 ⊦ j = 0, (i0 * j0) / gcd(i0, j0) = i0 * j0 / gcd(i0, j0), j0 = 0, i0 = 0, i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ i ≠ 0 → i / gcd(i, j) * j0 = (i * j0) / gcd(i, j)

Rule argument

seq: ⊦ i ≠ 0 → i / gcd(i, j) * j0 = (i * j0) / gcd(i, j) subst: [j0, j, i] → [i0, i0, j0] rotate: F spec: int-gcd inst: name: gcd-div-mult-shift

Additional information

Used simplifier rules: ⊦ gcd(i, j) = gcd(j, i);% ⊦ i * j = j * i; Used terms: i0, i0, j0