Submartingale and expectation

Question

Assume $(X_n)_{n \geq 0}$ is a submartingale and $T_1$, $T_2$ are stopping times such that $P(T_2\leq k)=1$ and $P(T_1\leq k)=1$. Is it true that $E[X_{T_1}]$ and $E[X_{T_2}]$ are less than or equal to $E[X_k]$? My idea is that it is true.