  In a recent paper, Lin, Ruberman and Saveliev proved a splitting formula
expressing the Seiberg-Witten invariant $\lambda_{SW}(X)$ of a smooth
$4$-manifold with rational homology of $S^1\times S^3$ in terms of the
Fr{\o}yshov invariant $h(X)$ and a Lefschetz number in reduced monopole Floer
homology. In this note we observe that a similar splitting formula holds in
reduced instanton Floer homology.
