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Proof step 4 from proof gcd-div-gcd (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
0 < i, 0 < j ⊦ gcd(i / gcd(i, j), j / gcd(i, j)) = 1
Proof step 6:
gcd(abs(i) / gcd(abs(i), abs(j)), abs(j) / gcd(abs(i), abs(j))) = 1, gcd(i, j) = gcd(abs(i), abs(j)) ⊦ i ≠ 0 → gcd(i / gcd(abs(i), abs(j)), j / gcd(abs(i), abs(j))) = 1

Rule argument

spec: int-gcd inst: name: gcd-div-gcd-pos seq: 0 < i, 0 < j ⊦ gcd(i / gcd(i, j), j / gcd(i, j)) = 1 subst: [i, j] → [abs(i), abs(j)] flags: current, []

Additional information

Used simplifier rules: gcd-zero-03: ⊦ i ≠ 0 → gcd(i, 0) = abs(i);%gcd-zero-04: ⊦ gcd(i, 0) = abs(i);%abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs%abs-01: ⊦ abs(abs(i)) = abs(i); from specification int-abs%abs-07: ⊦ abs(i) = 0 ↔ i = 0; from specification int-abs%zero: j ≠ 0 ⊦ 0 / j = 0; from specification int-div%abs-01: j ≠ 0 ⊦ abs(i / abs(j)) = abs(i / j); from specification int-div%div-same: i ≠ 0 ⊦ i / i = 1; from specification int-div Used terms: abs(i), abs(j)