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Proof step 4 from proof isSquare-mult-aux (previous step)

prime(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) ⊦ i = 0, isSquare(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ prime(i) ∧ ¬ i | j → i * i0 ≠ j
Proof step 6:
¬(prime(j0) ∧ ¬ j0 | j * i * i), prime(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) ⊦ i = 0, isSquare(j)

Rule argument

spec: inst: name: prime-mult-eq seq: ⊦ prime(i) ∧ ¬ i | j → i * i0 ≠ j subst: [j, i0, i] → [j * i * i, j0, j0] flags: rewrite, current

Additional information

Used terms: j * i * i, j0, j0