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Proof step 3 from proof factor-rat-03 (previous step)

⊦ 0 < j ∧ 0 < i1 → rational(i1 * i, i1 * j).num = rational(i, j).num ∧ rational(i1 * i, i1 * j).denom = rational(i, j).denom

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
0 < j, 0 < i1 ⊦ rational(i1 * i, i1 * j).num = rational(i, j).num ∧ rational(i1 * i, i1 * j).denom = rational(i, j).denom

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)