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Proof step 13 from proof div-pos-def (previous step)

¬(0 < j / gcd(i, j) * i0 / gcd(i0, j0) ∧ 0 < j * i0), 0 < i, 0 < i0, 0 < j, 0 < j0 ⊦ j = 0, i = 0, j0 = 0, i0 = 0, rational(i / gcd(i, j) * j0 / gcd(i0, j0), j / gcd(i, j) * i0 / gcd(i0, j0)) = rational(i * j0, j * i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i < j → ¬ j < i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ ¬ i < j ↔ j ≤ i;