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Proof step 29 from proof square-neq-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ prime(i) ∧ gcd(j, j0) = 1 ∧ 0 < j ∧ 0 ≤ j0 → j * j ≠ i * j0 * j0

Rule argument

spec: int-gcd inst: name: square-neq-pos-h seq: ⊦ prime(i) ∧ gcd(j, j0) = 1 ∧ 0 < j ∧ 0 ≤ j0 → j * j ≠ i * j0 * j0 subst: [j0, i, j] → [j0 / gcd(j0, j), i, j / gcd(j, j0)] flags: rewrite, current

Additional information

Used simplifier rules: gcd-div-gcd: ⊦ i ≠ 0 → gcd(i / gcd(i, j), j / gcd(i, j)) = 1;%gcd-com: ⊦ gcd(i, j) = gcd(j, i);%div-gcd-not-neg: ⊦ 0 < i → ¬ i / gcd(i, i0) ≤ 0;%gcd-nls-zero: ⊦ 0 < i → ¬ i / gcd(i, j) < 0;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j0 / gcd(j0, j), i, j / gcd(j, j0)