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Proof step 4 from proof equality-def (previous step)

0 < j, 0 < j0 ⊦ rational(i, j) = rational(i0, j0) ↔ rational(i * j0, 1) = rational(i0 * j, 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 < j, 0 < j0 ⊦ rational(i, j) = rational(i0, j0) ↔ i * j0 = i0 * j

Rule argument

Additional information

Used simplifier rules: equal-same: ⊦ 0 < j → (rational(i, j) = rational(i0, j) ↔ i = i0);