Let $k$ be a finete field, $\bar{k}$ is an algebraic clousre of $k$, $\sigma \in Gal(\bar{k}/k)$ is the geometric Frobenius. Let $f:Y \to Spec(k)$ be a smooth, separated $k$-scheme of finite type, $c_i: Z \to Y, i=1,2$ be two morphisms such that $f\circ c_1=f\circ c_2=c$, and assume that $c_1$ is proper, $c_2$ is finite and etale. Let $r > 0$ be an integer. Let $S(Z,c)=\{ z \in Z(\bar{k}) : \sigma^r (c_1(z))=c_2\}$. Prove that $S(Z,c)$ is a finite set, and each point in $S$ has multiplicity one.