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Proof step 6 from proof equality-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)
Proof step 8:
i0 ≠ 0 ∧ j0 ≠ 0, i / gcd(i, j) = rational(i0, j0).num, j / gcd(i, j) = abs(j0) / gcd(i0, j0), 0 < j, 0 < j0 ⊦ i * j0 = i0 * j, j = 0, i = 0

Rule argument

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

Additional information

Used simplifier rules: denominator-zero: ⊦ rational(0, j).denom = 1;%numerator-zero: ⊦ rational(0, j).num = 0;%denominator-zero-den: ⊦ i ≠ 0 → rational(i, 0).denom = 1;%numerator-zero-den: ⊦ i ≠ 0 → rational(i, 0).num = i;% ⊦ i ≠ 0 → i / gcd(i, i0) ≠ 0;% ⊦ i * 0 = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 < i → (i * j = 0 ↔ j = 0); Used terms: j0, i0