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Proof step 27 from proof equality-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < j → (i * j = i0 * j ↔ i = i0) subst: [i0, j, i] → [i0 * j0 / gcd(i0, j0), gcd(i, j), i0 / gcd(i0, j0) * j0] rotate: F spec: int-mult inst: name: eq-pos-01

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ gcd(i, j) ≤ 0 ↔ gcd(i, j) = 0;% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0; Used terms: i0 * j0 / gcd(i0, j0), gcd(i, j), i0 / gcd(i0, j0) * j0