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Proof step 9 from proof canon-any (previous step)

0 < j, i < 0 ⊦ j = 0, i = 0, i / gcd(i, j) = rational(i / gcd(i, j), j / gcd(i, j)).num ∧ j / gcd(i, j) = rational(i / gcd(i, j), j / gcd(i, j)).denom

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)
Proof step 11:
i / gcd(i, j) ≠ 0 ∧ j / gcd(i, j) ≠ 0, 0 < j, i < 0 ⊦ j = 0, i = 0, i / gcd(i, j) = rational(i / gcd(i, j), j / gcd(i, j)).num ∧ j / gcd(i, j) = abs(j / gcd(i, j)) / gcd(i / gcd(i, j), j / gcd(i, j))

Rule argument

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

Additional information

Used simplifier rules: ⊦ i ≠ 0 → i / gcd(i, i0) ≠ 0;% ⊦ gcd(i, j) = gcd(j, i); Used terms: j / gcd(i, j), i / gcd(i, j)