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Proof step 6 from proof denom-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
j < 0 ⊦ j = 0, i = 0, rational(i, j).num = rational(~ i, ~ j).num ∧ j / gcd(i, j) + rational(~ i, ~ j).denom = 0

Rule argument

Additional information

Used simplifier rules: ⊦ ~ i = j ↔ i + j = 0;%j ≠ 0 ⊦ ~ i / j = ~(i / j);% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;% ⊦ i < 0 → abs(i) = ~ i;