The proposition is given as follows:
Let $f:X\to Y$ be a morphism of schemes of finite type over an algebraically closed field $k$ of characteristic $0$. For any r, let $X_r=\{\text{closed points $x\in X$|rank $T_{f,x}\leq r$}\}$. Then $dim\overline{f(X_r)}\leq r$.
I just can't understand the first step:
Let $Y'$ be any irreducible component of $\overline{f(X_r)}$, and let $X'$ be an irreducible component of $\overline{X_r}$ which dominates $Y'$.
I wonder why can we find such a irreducible component $X'$? I have tried to find the inverse image of the generic point of $Y'$, but the generic point may not be in $f(\overline{X_r})$... So I don't know what can I do to repaire it.