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Proof step 39 from proof abs-pos (previous step)

gcd(i, j) ≠ 0, gcd(i, j) ≠ 0, 0 < j, 0 < j / gcd(i, j) ⊦ i = 0, j = 0, (abs(i) / gcd(i, j)) / gcd(abs(i) / abs(gcd(i, j)), abs(j) / abs(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 40:
⊦ abs(gcd(i, j)) = gcd(i, j)
Proof step 41:
gcd(i, j) ≠ 0, gcd(i, j) ≠ 0, 0 < j, 0 < j / gcd(i, j) ⊦ i = 0, j = 0, (abs(i) / gcd(i, j)) / gcd(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: ⊦ abs(gcd(i, j)) = gcd(i, j) subst: [j, i] → [j, i] rotate: F spec: int-gcd inst: name: gcd-abs

Additional information

Used terms: j, i