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Proof step 7 from proof equality-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)
Proof step 9:
i0 ≠ 0 ∧ j0 ≠ 0, i * j0 = i0 * j, 0 < j, 0 < j0, 0 < i, 0 < i0 ⊦ j = 0, i = 0, i / gcd(i, j) = i0 / gcd(i0, j0) ∧ j / gcd(i, j) = abs(j0) / gcd(i0, j0)

Rule argument

name: denominator-pos rotate: F subst: [j, i] → [j0, i0]

Additional information

Used simplifier rules: ⊦ i * 0 = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; Used terms: j0, i0