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Proof step 19 from proof div-pos-def (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
0 < i, 0 < j, 0 < j0, 0 < i0, 0 < (j * i0 / gcd(i0, j0)) / gcd(j, i) ⊦ i = 0, j0 = 0, i0 = 0, (i / gcd(i, j) * j0 / gcd(i0, j0)) * j * i0 = (i * j0) * (j * i0 / gcd(i0, j0)) / gcd(j, i), j = 0

Rule argument

Additional information

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