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Proof step 41 from proof div-pos-def (previous step)

0 < gcd(j0, i0), 0 < gcd(i, j), 0 < (j * i0 / gcd(i0, j0)) / gcd(j, i), 0 < i0, 0 < j0, 0 < j, 0 < gcd(i0, j0), 0 < gcd(j, i), 0 < 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, gcd(j0, i0) * gcd(i, j) | j0 * i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i | j ∧ i0 | j0 → i * i0 | j * j0 subst: [j0, j, i0, i] → [i, j0, gcd(i, j), gcd(j0, i0)] rotate: F spec: int-gcd inst: name: divides-mult-02

Additional information

Used simplifier rules: ⊦ gcd(i, j) | i; Used terms: i, j0, gcd(i, j), gcd(j0, i0)