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Proof step 60 from proof make (previous step)

0 < i0, 0 < i0 / gcd(i, i0) ⊦ i0 = 0, i = 0, i / gcd(i, i0) = 0, rational(i / gcd(i, i0), i0 / gcd(i, i0)).denom = i0 / gcd(i, i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 61:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)

Rule argument

name: denominator-pos rotate: F subst: [j, i] → [i0 / gcd(i, i0), i / gcd(i, i0)]

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;%j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j);% ⊦ 0 < j → abs(j) = j;% ⊦ abs(gcd(i, j)) = gcd(i, j);% ⊦ i ≠ 0 → gcd(i / gcd(i, j), j / gcd(i, j)) = 1;% ⊦ i / 1 = i; Used terms: i0 / gcd(i, i0), i / gcd(i, i0)