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Proof step 5 from proof equal-same (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)
Proof step 7:
i ≠ 0 ∧ j ≠ 0, abs(j) / gcd(i, j) = rational(i0, j).denom, rational(i, j).num = rational(i0, j).num, 0 < j ⊦ i = i0

Rule argument

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

Additional information

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