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Proof step 43 from proof isSquare-mult-aux (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: prime-divides seq: ⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0) subst: [j0, j, i] → [i, i, max_prime_divisor(j0)] flags: rewrite, current

Additional information

Used terms: i, i, max_prime_divisor(j0)