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Proof step 23 from proof div-pos-def (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ i ≠ 0 → i / gcd(i, j) * j0 = (i * j0) / gcd(i, j)
Proof step 25:
i0 ≠ 0, 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 = ((i0 * i * j0 * j) / gcd(i0, j0)) / gcd(j, i), j = 0, gcd(j, i) = 0

Rule argument

seq: ⊦ i ≠ 0 → i / gcd(i, j) * j0 = (i * j0) / gcd(i, j) subst: [j0, j, i] → [i * j0 * j, j0, i0] rotate: F spec: int-gcd inst: name: gcd-div-mult-shift

Additional information

Used simplifier rules: ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i * j0 * j, j0, i0