The inclusion of ideal-limit points under $\mathcal{I}^{\mathcal{K}}$-convergence

Let $f$ be a function into a topological space $X$, and let $L_f(\mathcal{I} \cup \mathcal{K})$ and $L_f(\mathcal{I}^{\mathcal{K}})$ denote the collections of $(\mathcal{I} \cup \mathcal{K})$-limit points and $\mathcal{I}^{\mathcal{K}}$-limit points of $f$, respectively. Here $\mathcal{I}$ and $\mathcal{K}$ are ideals satisfying the ideality condition.

Expected inclusion.

$$L_f(\mathcal{I} \cup \mathcal{K}) \subseteq L_f(\mathcal{I}^{\mathcal{K}}).$$

This is suggested by the preceding implications relating $\mathcal{K}$-, $\mathcal{I}^{\mathcal{K}}$-, and $(\mathcal{I} \cup \mathcal{K})$-convergence. The supplied text does not state a proof or resolution of this expected conclusion.