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Proof step 4 from proof div-def-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 < j, 0 < j0, i ≠ 0 → rational(abs(i), j) / rational(abs(i0), j0) = rational(abs(i) * j0, j * abs(i0)) ⊦ rational(i, j) / rational(i0, j0) = rational(i * j0, j * i0), i0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < abs(i) ↔ i ≠ 0;