Differentiation of Polynomials induces Well-Founded Relation

Theorem
Let $P$ be the set of all polynomials over $\R$ in one variable with real coefficients.

Let $\DD$ be a relation on $P$ defined as:
 * $\forall p_0, p_1 \in P: \tuple {p_0, p_1} \in \DD$ $p_0$ is the derivative of $p_1$.

Then $\DD$ is a well-founded relation on $P$.