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Proof step 11 from proof div-pos-def (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ 0 < j ∧ 0 < j0 → (rational(i, j) = rational(i0, j0) ↔ i * j0 = i0 * j)
Proof step 13:
¬(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)
Proof step 16:
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, (i / gcd(i, j) * j0 / gcd(i0, j0)) * j * i0 = (i * j0) * j / gcd(i, j) * i0 / gcd(i0, j0)

Rule argument

name: equality-def rotate: F subst: [j0, i0, j, i] → [j * i0, i * j0, j / gcd(i, j) * i0 / gcd(i0, j0), i / gcd(i, j) * j0 / gcd(i0, j0)]

Additional information

Used terms: j * i0, i * j0, j / gcd(i, j) * i0 / gcd(i0, j0), i / gcd(i, j) * j0 / gcd(i0, j0)