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Proof step 53 from proof square-neq-any-pos-02 (previous step)

j * j / gcd(j0 * j1, j) = (j0 * j1) * (j0 * j1) / gcd(j0 * j1, j) * i, j / gcd(j, j0 * j1) * j / gcd(j0 * j1, j) = (j0 * j1) / gcd(j0 * j1, j) * (j0 * j1) / gcd(j0 * j1, j) * i, gcd(j, j0) = 1, 0 < j, 1 < j1 * j1 * i, 0 < j1, 0 < i, 0 < j0, prime(j1), j1 * j1 ≤ j1 * j1 * i, ∀ i1, j, j0. i→n(i1) < i→n(j1 * j1 * i) → j * j = i1 * j0 * j0 ∧ gcd(j, j0) = 1 ∧ 0 < j0 ∧ 0 < j ∧ 0 < i1 → (∃ i2. i1 = i2 * i2) ⊦ gcd(j0 * j1, j) = 1, j = 0, j0 = 0, j1 = 0, ∃ i1. j1 * j1 * i = i1 * i1, j / gcd(j, j0 * j1) * j / gcd(j, j0 * j1) = i * (j0 * j1) / gcd(j0 * j1, j) * (j0 * j1) / gcd(j0 * j1, j) ∧ gcd(j / gcd(j, j0 * j1), (j0 * j1) / gcd(j0 * j1, j)) = 1 ∧ 0 < (j0 * j1) / gcd(j0 * j1, j) ∧ 0 < j / gcd(j, j0 * j1) ∧ 0 < i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: gcd-com: ⊦ gcd(i, j) = gcd(j, i);%gcd-div-gcd: ⊦ i ≠ 0 → gcd(i / gcd(i, j), j / gcd(i, j)) = 1;%div-gcd-not-neg: ⊦ 0 < i → ¬ i / gcd(i, i0) ≤ 0;%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult