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Proof step 89 from proof isSquare-mult-aux (previous step)

max_prime_divisor(j0) * i0 = j0, i0 * i0 = i * i * i2, prime(max_prime_divisor(j0)), 0 < i, 0 < j0, 0 < max_prime_divisor(j0) * max_prime_divisor(j0) * i2, ∀ 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→n(i0) < i→n(j0), i = 0, max_prime_divisor(j0) = 0, max_prime_divisor(j0) | i, isSquare(max_prime_divisor(j0) * max_prime_divisor(j0) * i2), prime(j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 90:
i0 * i0 = i * i * i2, max_prime_divisor(j0) * i0 = j0, j0 ≤ abs(i0), 0 < max_prime_divisor(j0) * max_prime_divisor(j0) * i2, 0 < j0, 0 < i, prime(max_prime_divisor(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) ⊦ max_prime_divisor(j0) = 0, i = 0, i0 = 0, prime(j0), isSquare(max_prime_divisor(j0) * max_prime_divisor(j0) * i2), max_prime_divisor(j0) | i

Rule argument

Additional information

Used simplifier rules: abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%labs: ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j); from specification intnat