The inheritance tracial topological rank zero for centrally large subalgebra

Let $A$ be an infinite-dimensional unital simple C*-algebra such that A has $\mu$-$oz\mathrm{L}\mathrm{L}\mathrm{P}$ property for any $\mu \in (0,1)$. Let $B\subseteq A$ be a centrally large subalgebra of $A$ such that $B$ has tracial topological rank zero. Then $A$ has tracial topological rank zero.