I'm doing this little homework assignment on Ramsey numbers, the question is: Show that $$s_1 \leq s_2 \Rightarrow R(s_1,t)\leq R(s_2,t).$$

I've tried classifying it into these four cases:

The graph on $R(s_1,t)$ vertices has a clique of size $s_1$, and the graph on $R(s_2,t)$ vertices has a clique of size $s_2$,

Both graphs have an independent set of size $t$,

The graph on $R(s_1,t)$ vertices has a clique of size $s_1$, and the graph on $R(s_2,t)$ vertices has an independent set of size $t$,

The graph on $R(s_1,t)$ vertices has an independent set size $t$, and the graph on $R(s_2,t)$ vertices has a clique of size $s_2$.

Cases 1 and 2 seem trivial but since we can't compare $t$ to $s_1$ and $s_2$, I have absolutely no idea how to handle cases 3 and 4. Or was considering four cases a brilliant idea?