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Proof step 4 from proof factor-rat-03 (previous step)

0 < j, 0 < i1 ⊦ rational(i1 * i, i1 * j).num = rational(i, j).num ∧ rational(i1 * i, i1 * j).denom = rational(i, j).denom

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)
Proof step 6:
i1 * i ≠ 0 ∧ i1 * j ≠ 0, 0 < j, 0 < i1 ⊦ rational(i1 * i, i1 * j).num = rational(i, j).num ∧ abs(i1 * j) / gcd(i1 * i, i1 * j) = rational(i, j).denom

Rule argument

name: denominator-pos rotate: F subst: [j, i] → [i1 * j, i1 * i]

Additional information

Used simplifier rules: numerator-zero: ⊦ rational(0, j).num = 0;%denominator-zero: ⊦ rational(0, j).denom = 1;% ⊦ 0 < i → (i * j = 0 ↔ j = 0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i * 0 = 0; Used terms: i1 * j, i1 * i