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Proof step 6 from proof equality-pos (previous step)

i ≠ 0 ∧ j ≠ 0, i * j0 = i0 * j, 0 < j, 0 < j0, 0 < i, 0 < i0 ⊦ i / gcd(i, j) = i0 / gcd(i0, j0) ∧ abs(j) / gcd(i, j) = rational(i0, j0).denom

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
i * j0 = i0 * j, 0 < j, 0 < j0, 0 < i, 0 < i0 ⊦ j = 0, i = 0, i / gcd(i, j) = i0 / gcd(i0, j0) ∧ j / gcd(i, j) = rational(i0, j0).denom

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < j → abs(j) = j;