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Proof step 3 from proof equality-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
i * j0 = i0 * j, 0 < j, 0 < j0, 0 < i, 0 < i0 ⊦ i / gcd(i, j) = i0 / gcd(i0, j0) ∧ rational(i, j).denom = rational(i0, j0).denom

Rule argument

Additional information

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