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Proof step 9 from proof denom-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: num-neg: ⊦ j ≠ 0 → rational(~ i, ~ j).num = rational(i, j).num;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ~ i + i = 0;%j ≠ 0 ⊦ ~ i / j = ~(i / j);% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;% ⊦ gcd(~ i, j) = gcd(i, j);% ⊦ i < 0 → abs(i) = ~ i;% ⊦ abs(~ i) = abs(i);% ⊦ ~ i = 0 ↔ i = 0;% ⊦ gcd(i, j) = gcd(j, i);