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Proof step 4 from proof denom-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)
Proof step 6:
i ≠ 0 ∧ j ≠ 0, j < 0 ⊦ rational(i, j).num = rational(~ i, ~ j).num ∧ abs(j) / gcd(i, j) = rational(~ i, ~ j).denom

Rule argument

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

Additional information

Used simplifier rules: numerator-zero: ⊦ rational(0, j).num = 0;%denominator-zero: ⊦ rational(0, j).denom = 1; Used terms: j, i