  For arbitrary Coxeter systems, we prove that inverse Kazhdan-Lusztig
polynomials satisfy a monotonicity property. This follows from the validity of
Soergel's conjecture and the existence of injective morphisms between Rouquier
complexes in the mixed perverse Hecke category. The monotonicity property is
generalised to parabolic Kazhdan-Lusztig polynomials.
