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Proof step 53 from proof isSquare-mult-aux (previous step)

max_prime_divisor(j0) * i0 = j0, max_prime_divisor(j0) * i0 * i0 = j * i1 * max_prime_divisor(j0) * i1, prime(max_prime_divisor(j0)), 0 < j, 0 < j0, 0 < max_prime_divisor(j0) * i1, ∀ j1, j, i. i→n(j1) < i→n(j0) → j1 * j1 = j * i * i ∧ 0 < j1 ∧ 0 < j ∧ 0 < i → i = 0 ∨ isSquare(j) ⊦ max_prime_divisor(j0) = 0, i1 = 0, isSquare(j), prime(j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 54:
⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0)
Proof step 55:
max_prime_divisor(j0) ≠ 0, max_prime_divisor(j0) * i0 = j0, i0 * i0 = i1 * i1 * j, prime(max_prime_divisor(j0)), 0 < j, 0 < j0, 0 < max_prime_divisor(j0) * i1, ∀ j1, j, i. i→n(j1) < i→n(j0) → j1 * j1 = j * i * i ∧ 0 < j1 ∧ 0 < j ∧ 0 < i → i = 0 ∨ isSquare(j) ⊦ max_prime_divisor(j0) = 0, i1 = 0, isSquare(j), prime(j0)

Rule argument

spec: int-mult inst: name: eq-nonzero seq: ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0) subst: [j0, j, i] → [i1 * i1 * j, i0 * i0, max_prime_divisor(j0)] flags: rewrite

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i1 * i1 * j, i0 * i0, max_prime_divisor(j0)