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Proof step 69 from proof square-neq-any-pos-02 (previous step)

j1 | j0 * j0 * i0, i * j1 * i = j0 * j0 * i0, gcd(j1 * i, j0) = 1, prime(j1), j1 * j1 ≤ j1 * i0, 0 < j0, 0 ≤ j0, 1 < j1 * i0, 0 < j1 * i0, 0 < j1 * i, ∀ i1, j, j0. i→n(i1) < i→n(j1 * i0) → 0 < i1 ∧ 0 < j ∧ 0 < j0 ∧ gcd(j, j0) = 1 ∧ j * j = i1 * j0 * j0 → (∃ i2. i1 = i2 * i2) ⊦ j1 = 0, j1 | i0, ∃ i1. j1 * i0 = i1 * i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
i * j1 * i = j0 * j0 * i0, gcd(j1 * i, j0) = 1, prime(j1), j1 * j1 ≤ j1 * i0, 0 < j0, 0 ≤ j0, 1 < j1 * i0, 0 < j1 * i0, 0 < j1 * i, j1 | j0 * j0, ∀ i1, j, j0. i→n(i1) < i→n(j1 * i0) → 0 < i1 ∧ 0 < j ∧ 0 < j0 ∧ gcd(j, j0) = 1 ∧ j * j = i1 * j0 * j0 → (∃ i2. i1 = i2 * i2) ⊦ j1 = 0, j1 | i0, ∃ i1. j1 * i0 = i1 * i1

Rule argument

Additional information

Used simplifier rules: prime-divides: ⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0);%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult