Kazhdan–Lusztig monotonicity property B

Let $(W,S)$ be a Coxeter system, and let $P_{y,w}$ denote its Kazhdan–Lusztig polynomials for $y,w\in W$, with $\leq$ the Bruhat order. Property B. The polynomials $P_{y,w}$ are decreasing for fixed $w$, in the sense that

$$P_{y,w}-P_{z,w}$$

has nonnegative coefficients whenever $y,z,w\in W$ and $y\leq z$. The source notes that this property is known for all finite Coxeter systems, while its validity for arbitrary Coxeter systems is part of the conjectural package.