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Proof step 4 from proof div-pos-def (previous step)

0 < i, 0 < i0, 0 < j, 0 < j0 ⊦ rational(rational(i, j).num * rational(i0, j0).denom, rational(i, j).denom * rational(i0, j0).num) = rational(i * j0, j * i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 < i, 0 < i0, 0 < j, 0 < j0 ⊦ rational(rational(i0, j0).denom * i / gcd(i, j), i0 / gcd(i0, j0) * rational(i, j).denom) = rational(i * j0, j * i0)

Rule argument

Additional information

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