Weak induction for natural numbers: P(0) -> ∀x (P(x) -> P(x+1)) -> ∀x P(x).

Strong induction for natural numbers: ∀x ((∀y < x Q(y)) -> Q(x)) -> ∀x Q(x).

To prove strong induction for a given property Q, apply weak induction where P(x) is ∀y < x Q(y).