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Proof step 14 from proof equal-same (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ i ≠ 0 → (i / gcd(i, j) = i0 ↔ i = i0 * gcd(i, j))
Proof step 16:
i ≠ 0, i = i0 / gcd(i0, j) * gcd(i, j), j = j / gcd(i0, j) * gcd(j, i), 0 < j ⊦ j = 0, i0 = 0, i = 0, i = i0

Rule argument

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

Additional information

Used terms: i0 / gcd(i0, j), j, i