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Proof step 57 from proof square-neq-any-pos-02 (previous step)

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

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-zero-zero: ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;%gcd-abs: ⊦ abs(gcd(i, j)) = gcd(i, j);%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-neq-01: ⊦ 0 < i → (i * j = 0 ↔ j = 0); from specification int-mult%abs-eqall: ⊦ abs(i * j) = abs(i) * abs(j); from specification int-mult%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%abs: j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j); from specification int-div%square-eq: ⊦ i * i = j * j ↔ abs(i) = abs(j); from specification int-mult