  In this paper, it is shown that for $d\in\mathbb{N}$, a minimal system
$(X,T)$ is a $d$-step pro-nilsystem if its enveloping semigroup is a $d$-step
top-nilpotent group, answering an open question by Donoso. Thus, combining the
previous result of Donoso, it turns out that a minimal system $(X,T)$ is a
$d$-step pro-nilsystem if and only if its enveloping semigroup is a $d$-step
top-nilpotent group.
