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Proof step 31 from proof abs-pos (previous step)

0 < j, 0 < j / gcd(i, j) ⊦ i = 0, j = 0, (abs(i) / gcd(i, j)) / gcd(abs(i) / gcd(i, j), j / gcd(i, j)) = abs(i) / gcd(abs(i), j), abs(i) / gcd(i, j) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ gcd(i, j) = gcd(abs(i), abs(j))
Proof step 33:
0 < j, 0 < j / gcd(i, j) ⊦ i = 0, j = 0, (abs(i) / gcd(i, j)) / gcd(abs(abs(i) / gcd(i, j)), abs(j / gcd(i, j))) = abs(i) / gcd(abs(i), j), abs(i) / gcd(i, j) = 0

Rule argument

seq: ⊦ gcd(i, j) = gcd(abs(i), abs(j)) subst: [j, i] → [j / gcd(i, j), abs(i) / gcd(i, j)] rotate: F spec: int-gcd inst: name: gcd-abs-rew-02

Additional information

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