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Proof step 21 from proof equality-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ i * j = j * i
Proof step 23:
i = i0 / gcd(i0, j0) * gcd(i, j), j = j0 / gcd(i0, j0) * gcd(i, j), 0 < j, 0 < j0 ⊦ j = 0, i0 / gcd(i0, j0) * j0 * gcd(i, j) = i0 * j0 / gcd(i0, j0) * gcd(i, j), j0 = 0, i0 = 0, i = 0

Rule argument

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

Additional information

Used terms: j0, gcd(i, j)