The comparison properties and large subalgebra are inheritance

Abstract

Let $A$ be a an infinite dimensional stably finite unital simple separable exact ${\rm C^*}$-algebra. Let $B\subset A$ be a stably large subalgebra in $A$ such that $B$ has $m$-comparison of positive elements property (strong tracial $m$-comparison of positive elements property). Then $A$ has $m$-comparison of positive elements property (strong tracial $m$-comparison of positive elements property).