Why does equation (10) hold in the paper?

[superzhangmch]

Why does the second equality $\mathbb{E}[\nabla h(X_t)^T X_t’] = \mathbb{E}[\nabla h(X_t)^T v^X(X_t, t)]$ hold in equation (10)?
It’s not obvious to me why $v^X(X_t, t) = \mathbb{E}[X_t’ \mid X_t]$ leads to that equality, as pointed out in the paper.

为什么10式第2等号 $\mathbb{E}[\nabla h(X_t)^T X_t’] = \mathbb{E}[\nabla h(X_t)^T v^X(X_t, t)]$ 成立?
按原文，是因为 $v^X(X_t, t) = \mathbb{E}[X_t’ \mid X_t] $,为啥就导致成立？