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Proof step 8 from proof equal-same (previous step)

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

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:
i0 ≠ 0 ∧ j ≠ 0, j / gcd(i, j) = abs(j) / gcd(i0, j), i / gcd(i, j) = rational(i0, j).num, 0 < j ⊦ i = i0, j = 0, i = 0

Rule argument

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

Additional information

Used simplifier rules: numerator-zero: ⊦ rational(0, j).num = 0;% ⊦ i ≠ 0 → i / gcd(i, i0) ≠ 0; Used terms: j, i0