Question on time hierarchy How can I prove that $\mathsf{DTIME}^{\mathrm{Htm}}(n^2)$ is contained in $\mathsf{DTIME}^{\mathrm{Htm}}(n^3)$?

(sorry about how it is written. I mean the set of languages decided by a deterministic TM with an oracle to $\mathrm{Htm}$ in $n^2$ time and $n^3$ time).

If someone can please write the proof, it will be great.
A language is in $\mathsf{DTIME}(f(n))$ if there is a Turing machine accepting the language and running in time at most $f(n)$ (or, in some definitions, $O(f(n))$). Therefore $f(n) \leq g(n)$ implies that $\mathsf{DTIME}(f(n)) \subseteq \mathsf{DTIME}(g(n))$. The same holds for relativized classes.