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Proof step 11 from proof canon-any (previous step)

i / gcd(i, j) ≠ 0 ∧ j / gcd(i, j) ≠ 0, 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) = abs(j / gcd(i, j)) / gcd(i / gcd(i, j), j / gcd(i, j))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
0 < j, i < 0 ⊦ j = 0, i = 0, i / gcd(i, j) = rational(i / gcd(i, j), j / gcd(i, j)).num

Rule argument

Additional information

Used simplifier rules: ⊦ i / 1 = i;% ⊦ i ≠ 0 → gcd(i / gcd(i, j), j / gcd(i, j)) = 1;% ⊦ abs(gcd(i, j)) = gcd(i, j);% ⊦ 0 < j → abs(j) = j;%j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j);% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;% ⊦ gcd(i, j) = gcd(j, i);% ⊦ i ≠ 0 → i / gcd(i, i0) ≠ 0;