I have been studying stopping times, however i am stuck on how to prove that a random variable is actually a stopping time even if it is intuitivly obvious. For example, How do i show that \alpha=inf\{t>0 : B_t=-1 or B_t=2\} is a stopping time w.r.t the natural filtartion F_t^B generated by B_t....

I know that i must show \{\alpha<t\}\in F_t^B but dont actually know how to do this....