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Proof step 7 from proof gcd-div-gcd (previous step)

gcd(abs(i) / gcd(i, j), abs(j) / gcd(i, j)) = 1, gcd(i, j) = gcd(abs(i), abs(j)) ⊦ gcd(i / gcd(i, j), j / gcd(i, j)) = 1, i = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
⊦ gcd(i, j) = gcd(abs(i), abs(j))

Rule argument

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

Additional information

Used simplifier rules: gcd-zero-zero: ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;%gcd-abs: ⊦ abs(gcd(i, j)) = gcd(i, j);%abs: j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j); from specification int-div Used terms: i / gcd(i, j), j / gcd(i, j)