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Proof step 50 from proof isSquare-mult-aux (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
max_prime_divisor(j0) * i0 = j0, i0 * j0 = 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)

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%eq-nonzero: ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0); from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-eq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; from specification int-mult