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Proof step 26 from proof isSquare-mult-aux (previous step)

∃ i0. max_prime_divisor(j0) * i0 = j0, j0 * j0 = j * i * i, 0 < j0, 0 < j, 0 < i, ∀ j1, j, i. i→n(j1) < i→n(j0) → j1 * j1 = j * i * i ∧ 0 < j1 ∧ 0 < j ∧ 0 < i → i = 0 ∨ isSquare(j) ⊦ prime(j0), i = 0, isSquare(j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
j0 * j0 = j * i * i, max_prime_divisor(j0) * i0 = j0, 0 < i, 0 < j, 0 < j0, ∀ j1, j, i. i→n(j1) < i→n(j0) → j1 * j1 = j * i * i ∧ 0 < j1 ∧ 0 < j ∧ 0 < i → i = 0 ∨ isSquare(j) ⊦ i = 0, isSquare(j), prime(j0)

Rule argument

Additional information

Used simplifier rules: lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1