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Proof step 37 from proof div-pos-def (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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