Heegaard Floer homology, degree-one maps and splicing knot complements

Let $K$ denote a knot inside the homology sphere $Y$ and $K^{\mathrm{\prime }}$ denote a knot inside a homology sphere $L$-space. Let $X=Y(K,K^{\mathrm{\prime }})$ denote the 3-manifold obtained by splicing the complements of $K$ and $K^{\mathrm{\prime }}$. We show that $\text{rank}(\widehat{HF}(X))\ge \text{rank}(\widehat{HF}(Y))$.