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Proof step 10 from proof div-pos-def (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 < i, 0 < i0, 0 < j, 0 < j0 ⊦ j = 0, i = 0, j0 = 0, i0 = 0, rational(i / gcd(i, j) * j0 / gcd(i0, j0), j / gcd(i, j) * i0 / gcd(i0, j0)) = rational(i * j0, j * i0)

Rule argument

Additional information

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