If S and T are stopping times, with $S \leq T$, X is a continuous stochastic process, if T reduces X, does S reduce X?

Question

For T a stopping time and X a continuous stochastic process, we say T reduces X if $(X_{t∧T})_{t\geq0}$ is a martingale. If S is also a stopping time and $S \leq T$, how do we show that S also reduces X? It makes sense I'm just not sure how to show it, it's page 123 of Revuz and Yor's book if I've not explained well?