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Proof step 12 from proof square-neq-pos (previous step)

j / gcd(j, j0) * j = ((j0 * j0) * i) / gcd(j, j0), prime(i), 0 < j, 0 ≤ j0 ⊦ gcd(j, j0) = 1, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: gcd-com: ⊦ gcd(i, j) = gcd(j, i);%gcd-zero-03: ⊦ i ≠ 0 → gcd(i, 0) = abs(i);%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%div-same: i ≠ 0 ⊦ i / i = 1; from specification int-div%one: ⊦ 1 * i = i; from specification int-mult%zero-left: ⊦ 0 * i = 0; from specification int-mult%zero: j ≠ 0 ⊦ 0 / j = 0; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, j0 * i, j0