Space/Time Hierarchy Theorem - proving the language of the machine is in the larger space class
A rich man walks into a bar and says, "I can buy this beer because I am a millionaire." Eloo says, "The beer costs \$5. I don't understand why this millionaire can buy it, but this guy with five dollars can't."

Remember that $\mathrm{DTIME}[f(n)]$ is the class of languages that can be decided by a deterministic Turing machine that uses at most $f(n)$ steps on any input of length&nbsp;$n$. So, since $t_1\log t_1\leq t_2$, anything in $\mathrm{DTIME}[t_1\log t_1]$ is in $\mathrm{DTIME}[t_2]$.