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Proof step 96 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) ⊦ i0 * i0 = i2 * i * i ∧ 0 < i0 ∧ 0 < i2 ∧ 0 < i, 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

Rule argument

Additional information

Used simplifier rules: lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%square-lez: ⊦ ¬ i * i < 0; from specification int-mult%zero-gr-03: ⊦ i ≤ 0 → (0 < i * j ↔ ¬ ¬(j < 0 ∧ i ≠ 0)); from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult