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Proof step 8 from proof div-pos-def (previous step)

0 < i, 0 < i0, 0 < j, 0 < j0 ⊦ j0 = 0, i0 = 0, rational(i / gcd(i, j) * j0 / gcd(i0, j0), i0 / gcd(i0, j0) * rational(i, j).denom) = rational(i * j0, j * i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)
Proof step 10:
i ≠ 0 ∧ j ≠ 0, 0 < i, 0 < i0, 0 < j, 0 < j0 ⊦ j0 = 0, i0 = 0, rational(i / gcd(i, j) * j0 / gcd(i0, j0), i0 / gcd(i0, j0) * abs(j) / gcd(i, j)) = rational(i * j0, j * i0)

Rule argument

name: denominator-pos rotate: F subst: [j, i] → [j, i]

Additional information

Used simplifier rules: denominator-zero: ⊦ rational(0, j).denom = 1;% ⊦ gcd(i, 0) = abs(i);% ⊦ 0 < j → abs(j) = j;% ⊦ gcd(i, j) = gcd(j, i);% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i * 0 = 0; Used terms: j, i