| 0 < j0, 0 < j, prime(i), ∀ i0, j1, j0. i→n(max_exp(i0, j1)) < i→n(max_exp(i, j)) → prime(i0) ∧ 0 < j1 ∧ 0 < j0 → max_exp(i0, j1 * j0) = max_exp(i0, j1) + max_exp(i0, j0) ⊦ i | j, max_exp(i, j * j0) = max_exp(i, j) + max_exp(i, j0) |
⊦ ¬ i | j ∧ prime(i) ∧ 0 < j → max_exp(i, j) = 0
¬ i | j ∧ prime(i) ∧ 0 < j, 0 < j0, 0 < j, prime(i), ∀ i0, j1, j0. i→n(max_exp(i0, j1)) < i→n(0) → prime(i0) ∧ 0 < j1 ∧ 0 < j0 → max_exp(i0, j1 * j0) = max_exp(i0, j1) + max_exp(i0, j0) ⊦ i | j, max_exp(i, j * j0) = 0 + max_exp(i, j0)
Used terms: j, i