The monotonicity conjecture for Lascar equivalence of countable tuples

Let $\overline a$ and $\overline b$ be countable tuples from a monster model, with $\overline b$ containing $\overline a$. Let $E_L^{\overline a}$ and $E_L^{\overline b}$ be the corresponding Lascar-equivalence relations, and let $F_L^{\overline a}$ and $F_L^{\overline b}$ be their restrictions to the respective Kim--Pillay classes. Tuple monotonicity conjecture. One has

$$E_L^{\overline a}\leq_B E_L^{\overline b}\qquad\text{and}\qquad F_L^{\overline a}\leq_B F_L^{\overline b}.$$

This is proposed as a generalization of the preceding upper-bound conjecture; no resolution is supplied in the paper.