  Every discrete definable subset of a closed asymptotic couple with ordered
scalar field $\boldsymbol k$ is shown to be contained in a finite-dimensional
$\boldsymbol k$-linear subspace of that couple. It follows that the
differential-valued field $\mathbb T$ of transseries induces more structure on
its value group than what is definable in its asymptotic couple equipped with
its scalar multiplication by real numbers, where this asymptotic couple is
construed as a two-sorted structure with $\mathbb R$ as the underlying set for
the second sort.
