Savitch's theorem and time relation
I believe you left out big-Os around those bounds.

In any case, $\; \{0\} \subseteq \{\hspace{-0.02 in}0,\hspace{-0.05 in}1\hspace{-0.03 in}\} \;$ and $\; \{0\} \subseteq \{\hspace{-0.02 in}0,\hspace{-0.05 in}1,\hspace{-0.04 in}2\hspace{-0.02 in}\}$ , $\;$ even though $\: \{\hspace{-0.02 in}0,\hspace{-0.05 in}1\hspace{-0.03 in}\} \neq \{\hspace{-0.02 in}0,\hspace{-0.05 in}1,\hspace{-0.04 in}2\hspace{-0.02 in}\}$ .