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Proof step 21 from proof isSquare-mult-aux (previous step)

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)

User applied rule insert lemma

And obtained the following new goals

Proof step 22:
⊦ ¬ prime(i) ∧ 2 ≤ i → max_prime_divisor(i) | i
Proof step 23:
¬ prime(j0) ∧ 2 ≤ j0 → max_prime_divisor(j0) | 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)

Rule argument

spec: inst: name: max_prime_divisor-divides seq: ⊦ ¬ prime(i) ∧ 2 ≤ i → max_prime_divisor(i) | i subst: [i] → [j0] flags: current, []

Additional information

Used terms: j0