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Proof step 48 from proof isSquare-mult-aux (previous step)

max_prime_divisor(j0) * i0 * j0 = j * i * i, max_prime_divisor(j0) * i0 = j0, max_prime_divisor(j0) | i, prime(max_prime_divisor(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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 50:
max_prime_divisor(j0) * i0 * j0 = j * i * i, max_prime_divisor(j0) * i0 = j0, ∃ i0. max_prime_divisor(j0) * i0 = i, prime(max_prime_divisor(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

spec: inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i, max_prime_divisor(j0)] flags: rewrite, current

Additional information

Used terms: i, max_prime_divisor(j0)