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Proof step 8 from proof canon-any (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
0 < j, i < 0 ⊦ j = 0, i = 0, i / gcd(i, j) = rational(i / gcd(i, j), j / gcd(i, j)).num ∧ j / gcd(i, j) = rational(i / gcd(i, j), j / gcd(i, j)).denom

Rule argument

Additional information

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